book of abstracts - technion...book of abstracts department of physics sam houston state university...

The 7th International Symposium"Bifurcations and Instabilities in Fluid Dynamics"

( BIFD-2017 )

July 11 - 14, 2017 The Woodlands, TX, USA

BOOK OF ABSTRACTS

Department of Physics

Sam Houston State University

Huntsville, TX

2017

Welcome to BIFD 2017!

BIFD 2017 is the seventh edition of an international conference founded more than a decade ago to treat the topicsof Bifurcations and Instabilities in Fluid Dynamics.

The scope of BIFD includes the classical hydrodynamic instabilities in shear, rotating and convective ows (Taylor-Couette, Rayleigh-Bénard, Kelvin-Helmholtz, Bénard-Marangoni, Rayleigh-Taylor, Farady) and related topics such asow in thin lms, transition to turbulence, magnetohydrodynamics, geophysical and astrophysical uids, ow control,bio-locomotion and propulsion. Industrial, environmental and biomedical applications are welcome; experimental,theoretical and computational studies are all encouraged.

The Local Organizing Committee of BIFD 2017 is:Alex Mikishev, Sam Houston State University (chair)Barry Friedman, Sam Houston State UniversityVladimir Ajaev, Southern Methodist UniversityVemuri Balakotaiah, University of Houston

Previous BIFD conferences include:BIFD 2004 Madeira, PortugalBIFD 2006 Technical University of Denmark (DTU), Lyngby, DenmarkBIFD 2009 University of Nottingham, United KingdomBIFD 2011 Universitat Politecnica de Catalunya, Barcelona, SpainBIFD 2013 Technion Israel Institute of Technology, Haifa, IsraelBIFD 2015 Ecole Superieure de Physique et de Chimie Industrielle (ESPCI), Paris FrancePast organizers have been P. Bar-Yoseph, A. Oron, A. Gelfgat, M. Brons, A. Clie, A. Meseguer, F. Marques, I.Mercader, L. Tuckerman, and J. E. Wesfreid.

Despite the dicult traveling conditions, participants from over 23 countries, (5 continents) are attending the confer-ence. We thank the participants for making the eort to come to Texas! This is the rst time BIFD has been held inNorth America, in particular in The Woodlands, Texas. The Woodlands is a master planned community developedby George P. Mitchell, a rst generation Texan and the son of Greek immigrants. As well as his interests in TheWoodlands, George Mitchell revolutionized the oil and gas industry by developing techniques to extract gas and oilfrom shale.

We thank Sam Houston State University for its support and wish all of you a very productive and enjoyable conference!

The BIFD international advisory committee is:Pinhas Bar-Yoseph TechnionMorten Brøns Technical University DenmarkAlexander Gelfgat Tel Aviv UniversityAlexander Oron Technion

The Bifurcations and Instabilities in Fluid Dynamics Association is a non-prot organization devoted to promotion ofresearch in instabilities and bifurcations in uid mechanics, whose main objective is the realization of this bi-annualinternational scientic conference.

Web-site: https://www.shsu.edu/bifd2017Email: [email protected]

Contents

STABILITY OF ELECTROLYTE FILMS ON SUBSTRATES WITH SPATIALLY PERIODICCHARGE DENSITY M.S. Jutley and V.S. Ajaev 1

PATTERN FORMATION IN TAYLOR-COUETTE FLOW VIA MD SIMULATIONS MeheboobAlam and Nandu Gopan 2

EVOLUTION OF THE ELECTROHYDRODYNAMIC INSTABILITY IN AMICROCHANNEL:EXPERIMENT Sercan Altundemir, Pinar Eribol and A. Kerem Uguz 3

EXPANSION AND INSTABILITY OF CONCENTRATED BACTERIAL DROPLETS Igor S.Aranson, Andrey Sokolov, Leandro D. Rubio & John F. Brady 4

CHOOSING BASIS FUNCTIONS OF WEIGHTED RESIDUAL METHOD FOR MODELINGTHE JOINT FLOW OF LIQUID FILM AND TURBULENT GAS Dmitriy Arkhipov and OlegTsvelodub 5

ANALYSIS OF THERMO-DIFFUSIVE CELLULAR INSTABILITIES IN CONTINUUM COM-BUSTION FRONTS Hossein Azizi, Sebastian Gurevich and Nikolas Provatas 6

FLOW IN BIFURCATIONS, RECONNECTIONS AND LARGER NETWORKS Samire Baltaand Frank T. Smith 7

NON-MODAL STABILITY ANALYSIS OF STRATIFIED TWO-PHASE CHANNEL FLOWS I.Barmak, A. Gelfgat, A. Ulmann, and N. Brauner 8

APPEARANCE FLUID ROTATION IN THIN THERMO-GRAVITY BOUNDARY LAYER ATLOCAL COOLING FREE BOUNDARY Vladimir Batishchev 9

OSCILLATORY THERMOCAPILLARY DYNAMICS OF FILMS COUPLED TO SUBSTRATEHEAT CONDUCTION William Batson, Linda Cummings and Lou Kondic 10

THERMOCAPILLARYMODULATION OF SELF-REWETTING FILMSWilliam Batson, YehudaAgnon and Alex Oron 11

PHYSICS OF SWARMING BACTERIA Avraham Be'er and Gil Ariel 12

INFLUENCE OF CHANNEL INCLINATION ONMHD-HEATTRANSFER OF LIQUIDMETALFLOW Ivan Belyaev, Denis Chernysh, Nikita Luchinkin, Natalia Pyatnitskaya and Nikita Ra-suvanov 13

EXPERIMENTAL INVESTIGATION OF TEMPERATURE INSTABILITIES ACCOMPANY-ING MHD-HEATTRANSFER IN LIQUID METAL FLOW Ivan Belyaev, Ivan Melnikov, IvanPoddubny, Nikita Rasuvanov and Valentin Sveridov 14

STABILITY OF THIN LIQUID CURTAINS Eugene Benilov 15

CAN VIBRATION STABILIZE AN OTHERWISE UNSTABLE LIQUID BRIDGE? Eugene Be-nilov 16

THE ROLE OF THE SURFACE TENSION IN PLANAR SHEAR FLOWS L. Biancoore, E.Heifetz, J. Hoepner and F. Gallaire 17

4

FREE SURFACE FLOW OF TWO SUPERPOSED FLUIDS: STABILITY ANALYSIS ANDMODELLING Lamia Bourdache and Amar Djema 18

MOMENTUM BASED APPROXIMATION OF INCOMPRESSIBLE MULTIPHASE FLOWSAND APPLICATION TO METAL PAD ROLL INSTABILITY Loïc Cappanera, Jean-LucGuermond, Wietze Herreman and Caroline Nore 19

THERMAL FALLING FILMS, A TALE OFWAVE ANDHEATNicolas Cellier, Christian Ruyer-Quil, Nadia Caney, Philippe Bandelier and Benoit Stutz 20

FINITE-TIME BLOW-UP OF SOLUTIONS IN THIN-FILM EQUATIONS Marina Chugunovaand Roman Taranets 21

GLOBAL STABILITY ANALYSIS OF THREE-DIMENSIONAL ROUND JET DIFFUSIONFLAMES C. Mancini, M. Farano, J.-C. Robinet, P. De Palma and S. Cherubini 22

DROPLETS ARISING FROM A LIQUID FILAMENT: WETTING AND DEWETTING PRO-CESSES Javier A. Diez, Alejandro G. González, Pablo Ravazzoli and Ingrith Cuellar 23

MAGNETIC FIELD EFFECT ON THE LINEAR STABILITY OF PERFECT MAGNETICFLUID SLOSHING IN A RECTANGULAR TANK Rabah Djeghiour, Bachir Meziani andOuerdia Ourrad 24

NUMERICAL BIFURCATION ANALYSIS IN LAMINAR-TURBULENT TRANSITION FOR3D KOLMOGOROV-TYPE FLOW Nick Evstigneev 26

THE EMERGENCE OF HAIRPIN VORTICES FROMEXACT COHERENT STATES IN PLANEPOISEUILLE FLOWM. Farano, P. De Palma, J.-C. Robinet, S. Cherubini and T. M. Schneider 27

"SMART" PASSIVE THERMAL INSULATION OF CONFINED NATURAL CONVECTIONHEAT TRANSFER: AN APPLICATION TO HOLLOW CONSTRUCTION BLOCKS ShaharIdan and Yuri Feldman 28

BIFURCATIONS OF CONVECTION DRIVEN DYNAMOS IN SPHERICAL SHELLS FredFeudel and Laurette Tuckerman 29

ELECTROOSMOSIS FLOW OF TWO LAYERS DIELECTRIC-ELECTROLYTE SYSTEM INDCANDAC EXTERNAL ELECTRIC FIELDSG.S. Ganchenko, E.V. Gorbacheva, S. Amirou-dine and E.A. Demekhin 30

LINEAR STABILITY OF THE LID-DRIVEN FLOW IN A CUBE Alexander Gelfgat 31

UNSTABLE GRID OF FILAMENTS ON A SUBSTRATE AND DROP PATTERNS AlejandroG. González, Javier A. Diez, Ingrith Cuellar and Pablo Ravazzoli 32

INFLUENCE OF MAGNETIC FIELDS ON SIMULTANEOUS STATIONARY SOLUTIONS OFTWO-DIMENSIONAL FLOWS AT LOW MAGNETIC REYNOLDS NUMBERS Julián M.Granados, Carlos A. Bustamante, Henry Power and Whady F. Flórez 33

KOOPMAN MODE ANALYSES OF FLUID FLOWS Gemunu Gunaratne 34

ASYMPTOTICS OF A HORIZONTAL LIQUID BRIDGE M. Haynes, S.B.G. O'Brien and E.S.Benilov 35

HYDRODYNAMIC STABILITY OF FLOW IN A SWIRL FLOWCHANNEL Benjamín Herrmann-Priesnitz, Williams R. Calderón Muñoz, Gerardo Diaz and Rodrigo Soto 36

A STUDY OF TRANSIENT GROWTH BEHAVIOR IN A CONSTRICTED CHANNEL JoãoAnderson Isler, Rafael dos Santos Gioria and Bruno Souza Carmo 37

THE SUSTAINING MECHANISM OF TURBULENT BANDS IN PLANE CHANNEL FLOWTakahiro Kanazawa, Masaki Shimizu and Genta Kawahara 38

MARANGONI EFFECTS ON A THIN LIQUID FILM COATING A SPHERE Di Kang, MarinaChugunova and Ali Nadim 39

PRESSURE IN ACTIVE FLUIDS: A GROWINGMONOLAYER Evgeniy Khain and Lev Tsimring 40

ELECTROTHERMALLY DRIVENNONLINEARVORTEX PATTERNS ON ELECTRODE AR-RAY AT PHYSIOLOGICAL CONDUCTIVITIES Anil Koklu and Ahmet C. Sabuncu 41

DOUBLE DIFFUSION CONVECTION IN A HELE-SHAW CELL WITH VIBRATIONS NikolaiKozlov, Alexey Mizev, Andrey Shmyrov, Mariya Denisova and Konstantin Kostarev 42

STEADY FLOW IN AN ANNULUS WITH A VARYING NUMBER OF DEFLECTORS ATROTATIONAL VIBRATION Nikolai Kozlov 43

STABILITY OF FLUID THROUGH SOFT-WALLED TUBES AND CHANNELS V. Kumaran 44

SMART ACTIVE BIOLOGICAL MATTER Herbert Levine 45

GROUND EXPERIMENT ON BUOYANT-THERMOCAPILLARY CONVECTION IN LARGESCALE LIQUID BRIDGE Duan Li, Wang Jia and Kang Qi 46

EFFECT OF POOL ROTATION ON THERMOCAPILLARY CONVECTION INSTABILITIESIN ANNULAR POOL OF MEDIUM PRANDTL LIQUID Han-Ming Li and Wan-Yuan Shi 47

CONVECTION INSTABILITIES IN A LIQUIDMETAL PIPE FLOWWITH STRONG TRANS-VERSEMAGNETIC FIELDYaroslav Listratov, Nikita Rasuvanov, Valentin Sviridov and OlegZikanov 48

DNS OF MIXED CONVECTION IN A LIQUID METAL HORIZONTAL PIPE FLOW WITHTRANSVERSEMAGNETIC FIELD Dmitry Ognerubov, Yaroslav Listratov, Valentin Sviridovand Oleg Zikanov 49

INSTABILITIES OF COUETTE-POISEUILLE FLOW FOR SHEAR-THINNING FLUIDS UN-DER CROSSFLOW Yu-Quan Liu 50

CHARACTERISTICS AND MECHANISM OF THE TRANSITION TO UNSTEADY FLOWIN RANDOM PACKED BED USING FAST MAGNETIC RESONANCE IMAGINGMeichenLu, Andrew J. Sederman and Lynn F. Gladden 51

GRAVITY MODULATION EFFECT ON THE ONSET OF THE SORET-INDUCED CONVEC-TION IN POROUS MEDIUM Tatyana P. Lyubimova and Irina S. Faizrakhmanova 52

THERMAL CONVECTION IN AN INCLINED POROUS LAYER HEATED FROM BELOWTatyana P. Lyubimova and Igor D. Muratov 53

KELVIN - HELMHOLTZ INSTABILITY AT THE INTERFACE OF NEWTONIAN VISCOUSFLUID ANDVISCO-PLASTIC FLUIDMOVING PARALLEL TO EACHOTHER IN POROUSMEDIUM T.P. Lyubimova and E.V. Kolesov 54

GENERATION OF AVERAGE FLOWS NEAR FLUID INTERFACE UNDER TANGENTIALVIBRATIONS D.V. Lyubimov, T.P. Lyubimova, A.A. Cherepanov, A.O. Ivantsov and A.V.Perminov 55

ON THE ORIGIN OF THE ASYMMETRIC VORTEX SHEDDING MODE IN THE WAKE OF2 SIDE-BY-SIDE SQUARE CYLINDERS Shengwei Ma, Chang-Wei Kang, Teck-Bin ArthurLim and Chih-Hua Wu 56

NUMERICAL ANALYSIS OF THE CONVECTIVE HEAT TRANSFER COUPLED WITHPHASE CHANGE IN THE EVAPORATIVE COOLING PROCESS Junkun Ma 57

NONMODAL AND NONLINEAR DYNAMICS OF HELICAL MAGNETOROTATIONAL IN-STABILITY George Mamatsashvili and Frank Stefani 58

ACOUSTIC DRAINAGE Amihai Horesh, Matvery Morozov and Ofer Manor 59

NONLINEAR CONSEQUENCES OF THE DARRIEUS-LANDAU INSTABILITY IN COMBUS-TION Moshe Matalon 60

DISTURBANCE GROWTH DURING HAIRPIN VORTEX GENERATION IN A LAMINAR-BOUNDARY-LAYER FLOW Kazuo Matsuura 62

PARAMETRICALLY EXCITED LONG-SCALE MARANGONI CONVECTION IN A LIQUIDLAYER COVERED BY INSOLUBLE SURFACTANT Alexander B. Mikishev and AlexanderA. Nepomnyashchy 63

IMMERSED BOUNDARYMETHODANDASYMPTOTIC NUMERICALMETHOD FOR STEADYSIMULATION OF INCOMPRESSIBLE VISCOUS FLOW AROUND MOVING OBSTACLEA. Monnier, J.M. Cadou, G. Girault and Y. Guevel 64

MULTIPLE SOLUTIONS IN SWIRLING JET FLOWS Davide Montagnani and Franco Auteri 65

PROPAGATING SURFACE ACOUSTIC WAVES CAN DRIVE COATING FLOWSMatvey Mo-rozov, Amihai Horesh and Ofer Manor 66

MAXIMAL HEAT TRANSFER BETWEEN TWO PARALLEL PLATES Shingo Motoki, GentaKawahara and Masaki Shimizu 67

PREDICTION OF THIN PLATE FLUTTER INSTABILITY IN TURBULENT FLOWS BASEDON LINEAR STABILITY ANALYSIS Johann Moulin and Olivier Marquet 68

A STUDY ABOUT THE STEADY-STATE REGIME ON ROTATING COMPRESSIBLE FLU-IDS AND ITS APPLICATION ON A DIFFRACTION PROBLEM Erick Muiño-García andJosé Marín-Antuña 69

INTERFACIAL INSTABILITY OF PHASE CHANGE Ranga Narayanan 70

THE HYDRODYNAMIC BROOM: SWEEPING OF A POLYMER FILM BYMEANS OF CON-VECTION CELLS IN A LIQUID LAYER Iman Nejati, Mathias Dietzel and Steen Hardt 71

EFFECT OF LOW REYNOLDS NUMBER INSTABILITIES ON THE DRAG AND MIXINGCAPABILITY Nikesh, S. W. Gepner and J. Szumbarski 72

VISCOELASTIC EFFECT ON ROLL CELLS IN ROTATING PLANE COUETTE FLOW To-mohiro Nimura and Takahiro Tsukahara 73

CHAOS ANALYSIS OF TRANSITION FLOW IN A NATURAL CONVECTION LOOPHiroyukiNishikawa and Takashi Watanabe 74

DYNAMICS OF HIDDEN ATTRACTORS IN SIMPLIFIED NOVEL 5-D HYPERCHAOTICLORENZ-LIKE SYSTEMS Olurotimi S. Ojoniyi and Abdulahi N. Njah 75

RAYLEIGH-TAYLOR INSTABILITY IN THIN LIQUID FILMS SUBJECTED TO HARMONICVIBRATION Elad Sterman-Cohen, Michael Bestehorn and Alex Oron 76

EFFECT OF ELECTRICAL MARANGONI NUMBER ON ELECTROHYDRODYNAMIC IN-STABILITY S. Canberk Ozan and A. Kerem Uguz 77

ANALYSIS OF SPATIO-TEMPORAL STRUCTURES IN THE THREE-DIMENSIONAL CYLIN-DER WAKE José Miguel Pérez, Soledad Le Clainche and José M. Vega 78

FLUID/ELASTIC MODES OF A FLEXIBLE PLATE CLAMPED ON A CYLINDER Jean-LouPster, Marco Carini and Olivier Marquet 79

PATTERN SELECTION IN DEFIANCE OF LINEAR THEORY Jason R. Picardo and RangaNarayanan 80

EVAPORATIVE SUPPRESION OF RAYLEIGH-TAYLOR INSTABILITY IN PURE AND BI-NARY MIXTURES Dipin S. Pillai and Ranga Narayanan 81

DSMC SIMULATIONS OF HIGH MACH NUMBER TAYLOR-COUETTE FLOW S. Pradhan 82

THERMOCAPILLARY CONVECTION EXPERIMENT FACILITY AND RESULTS OF LIQ-UID BRIDGE ABOARD THE TG-2 SPACELAB Kang Qi, Duan Li, Hu Liang, Wu Di, WangJia and Hu Wenrui 83

DESIGN OF AN EXPERIMENTAL DEVICE THE EVALUATION OF HYDRODINAMIC PRO-FILES Luis Fernando Arredondo Rodríguez and Esperanza Rodriguez Morales 84

INSTABILITY OF THE FLOW IN SUSPENDED THERMOCAPILLARY THIN FILMS FrancescoRomanó and Hendrik C. Kuhlmann 85

NUMERICAL STUDY OF THE TRANSITION TO TURBULENCE IN PARTICULATE PIPEFLOWS Anthony Rouquier, Chris Pringle and Alban Potherat 86

EFFECT OF INHOMOGENEOUS FLOW ON KELVIN-HELMHOLZ INSTABILITY D. Lin, S.Sen, W. Scale, N. Petulante & M.L. Goldstein 87

INSTABILITY OF A MISCIBLE INTERFACE UNDER PERIODIC EXCITATIONS ValentinaShevtsova, Viktar Yasnou, Aliaksandr Mialdun, Yuri Gaponenko and Alexander Nepomnyashchy 88

CONTROL OF HYDROTHERMAL INSTABILITY IN LIQUID BRIDGE BY PARALLEL GASFLOW Viktar Yasnou, Aliaksandr Mialdun, Yuri Gaponenko and Valentina Shevtsova 89

MECHANISMS OF JET INSTABILITY Vladimir Shtern 90

EFFECT OF ROTATION ON THE MONOTONIC INSTABILITY MODE OF ADVECTIVEFLOW IN A HORIZONTAL INCOMPRESSIBLE FLUID LAYER WITH RIGID BOUND-ARIES IN THE CASE OF NORMAL SPIRAL PERTURBATIONS Konstantin Shvarts andDmitriy Chikulaev 91

EXPERIMENTAL STUDY OF TRANSITION TO TURBULENCE IN PARTICULATE PIPEFLOW Sanjay Singh, Alban Pothérat and Chris Pringle 92

KINEMATIC DYNAMO IN A FOURIER TETRAHEDRON Rodion Stepanov and Franck Plunian 93

STEADY FLOWS IN OSCILLATING ELASTIC SPHEROIDAL CAVITY. DEPENDENCY ONTHE DIMENSIONLESS FREQUENCY Stanislav Subbotin, Victor Kozlov and Rustam Sabirov 94

EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE INSTABILITY OF THEELECTROVORTEX FLOW IN HEMISPHERICAL CONTAINER Igor Teplyakov, DmitriyVinogradov, Irina Klementyeva and Yury Ivochkin 95

STABILIZING UNSTABLE FLOWS BY COARSE MESH OBSERVABLES AND ACTUATORS- A PAVEMENT TO DATA ASSIMILATION Edriss S. Titi 96

RUNOUT AND POWER DISSIPATED IN MONODISPERSE GRANULAR DENSE FLOWSLuis Armando Torres-Cisneros, Gabriel Perez-Ángeli, Roberto Bartali, Gustavo Manuel Rodríguez-Liñán and Yuri Nahmad-Molinari 97

OBSERVATIONS OF NEWDOUBLE SPLASHING FORDROP IMPACT ONTO LIQUID FILMPei-Hsun Tsai and An-Bang Wang 98

QUASI-GEOSTROPHIC EFFECTS ON THE STABILITY OF THE RAYLEIGH MODEL SUB-JECT TO A UNIFORM SHEAR Orkan M. Umurhan and Luca Biancoore 99

PARAMETRIC EXCITATION OF SURFACE WAVES IN HORIZONTAL CONTAINERS UN-DER MIXED HORIZONTAL/VERTICAL VIBRATION Jose M. Perez-Gracia, FernandoVaras and José M. Vega 100

ELECTROSTATIC CONTROL OF THE EVAPORATION OF NANOPARTICLE-LADENDROPSAlexander Wray, Demetrios T. Papageorgiou, Richard V. Craster, Khellil Seane, Omar K.Matar 101

WEAK SYNCHRONIZATION AND LARGE-SCALE COLLECTIVE OSCILLATION IN DENSEBACTERIAL SUSPENSIONS Chong Chen, Song Liu, Xia-qing Shi, Hugues Chaté and YilinWu 102

STABILITY ENHANCEMENT OF A NATURAL CIRCULATION LOOP USING MAGNETICNANOFLUID: AN EXPERIMENTAL STUDY Tabish Wahidi and Ajay Kumar Yadav 103

NUMERICAL STUDY ON THE STABILITY OF MAGNETIC NANOFLUID BASED NATU-RAL CIRCULATION LOOP Allen Chacko, Aashish Kumari and Ajay Kumar Yadav 104

ON THE SECONDARY INSTABILITY IN PLANAR SHEAR FLOW PAST A CIRCULARCYLINDER Doohyun Park and Kyung-Soo Yang 105

MIXED CONVECTION IN A DOWNWARD FLOW IN A VERTICAL DUCT IN THE PRES-ENCE OF STRONG MAGNETIC FIELD Xuan Zhang and Oleg Zikanov 106

EFFECT OF THE SYMMETRY OF A ROTATING MAGNETIC FIELD ON THE FLOWINSTABILITY OF THE CONDUCTING LIQUID (TAYLOR'S AND WAVY VORTICES)Alexander Zibold 107

INSTABILITIES IN EXTREME MAGNETOCONVECTION Oleg Zikanov, Xuan Zhang andYaroslav Listratov 108

BIFD 2017, July 11-14, Sam Houston State University, The Woodlands, TX, USA

STABILITY OF ELECTROLYTE FILMS ON SUBSTRATES WITH SPATIALLY PERIODICCHARGE DENSITY

Mahnprit S. Jutley & Vladimir S. Ajaev

Department of Mathematics, Southern Methodist University, Dallas, Texas, 75275, USA

The rupture of thin liquid lms on solid surfaces is important to numerous current and emerging engineering ap-plications. Our work was motivated by experimental observations of electrostatically-driven rupture and follows thegeneral framework developed recently [1, 2]. We consider a thin lm of liquid electrolyte on an electrically chargedsubstrate. Using the Debye-Hückel equation to model the electrostatic potential and the Navier-Stokes equationsfor uid ow, instability resulting from small base state perturbations of arbitrary wavelength are considered. Thegeometric conguration is shown in Fig. 1. The top deforming surface is characterized by the charge density q∗ whilethe solid substrate has a prescribed periodic charge density q∗. Cases of simple sinusoidal variation and of square-wave type patterns are considered. Calculations are carried out by two dierent approaches: an evolution equation isobtained within the framework of a lubrication-type model, and, secondly, Fourier expansion of all terms is used andthe corresponding coecients of the rst order correction to the interface shape are found. Stability analysis of thelinear and nonlinear problem is conducted.

y*

x*

q *

q~ *

^

Figure 0.1: A sketch of the geometric conguration used in the stability analysis.

References

[1] C.Y. Kao, A.A. Golovin, S.H. Davis, Rupture of thin lms with resonant substrate patterning, J Colloid Interface Sci, 303, 532545(2006)

[2] V.S.Ajaev, E.Y.Gatapova, and O.A.Kabov,Stability and break-up of thin liquid lms on patterned and structured surfaces, Adv. Coll.Interface Sci. 228, 92104 (2016).

1


PATTERN FORMATION IN TAYLOR-COUETTE FLOW VIA MD SIMULATIONS

Meheboob Alam & Nandu Gopan

Engineering Mechanics Unit, Jawaharlal Nehru Center for Advanced Scientic Research, Jakkur P.O., Bangalore560064, India

The Taylor-Couette (TC) ow conguration describes the ow between two coaxial cylinders which can be indepen-dently counter-rotating or co-rotating as shown schematically in the left panel in Fig. 1. This ow is known to bealways stable for outer cylinder rotating at any speed with an stationary inner cylinder, but is centrifugally unstablewhen the inner cylinder rotates beyond a minimum speed [1, 2] with the outer cylinder being stationary, or, rotatingwith a minimum speed (including both co-rotation and counter-rotation cases). Later experimental works [2, 3] un-covered the full phase diagram of patterns admitted by the Taylor-Couette ow. In this work, we present results frommolecular dynamics (MD) simulations of Taylor-Couette ow using the LAMMPS simulation code with appropriateboundary conditions. The inner and outer cylinders are allowed to rotate at dierent angular velocities (ωi and ω0)and the critical value of angular velocity of inner cylinder rotation (ωcr

i ), at which the ow behaviour deviates fromthe laminar Couette ow (see the middle panel in Fig. 1), is noted for dierent angular velocities of the outer cylinder(ω0) this helped us to construct the phase-diagram of patterns in the (ωi, ω0)-plane. For the special case of stationaryouter cylinder (ω0 = 0), our result on the critical value of the inner cylinder rotation ωcr

i (ω0 = 0) ≈ 0.055 agree wellwith previous MD simulation [4]. The primary bifurcation is found to be the onset of stationary Taylor vortices, anexample of which is shown in the right panel in Fig. 1. The onset of other vortical patterns (wavy vortex, spirals, etc.[3]) and the eects of compressibility on them will be discussed.

Figure 0.1: Left: Taylor-Coutte setup. Middle: Velocity eld in (r, z)-plane at ωi = 0.05. Right: Taylor vortices at ωi = 0.06. For bothcases the outer cylinder is stationary (ω0 = 0).

References

[1] G.I. Taylor, Stability of a viscous liquid contained between two rotating cylinders, Phil. Trans. Royal Soc. Lond. A, 233, 289343(1923)

[2] D. Cole, Transition in circular Couette ow J. Fluid Mech. 21, 385425 (1965)

[3] C.D. Andrereck, S.S. Liu, and H.L. Swinney, Flow regimes in a circular Couette system with independently rotated cylinders J. FluidMech.164, 155183 (1986)

[4] D. Hirschfeld and D.C. Rapaport, Molecular dynamics simulation of Taylor-Couette vortex formation Phys. Rev. Lett. 80, 5337(1998)

2


EVOLUTION OF THE ELECTROHYDRODYNAMIC INSTABILITY IN A MICROCHANNEL:EXPERIMENT

Sercan Altundemir, Pinar Eribol & A. Kerem Uguz

Department of Chemical Engineering, Bogazici University, Istanbul, 34342, Turkey

The interface between two immiscible, incompressible Newtonian uids can be destabilized in the presence of anapplied electric eld. The instability originating from the electric eld may result in droplet formation as the deformedinterface aps one of the walls and the captured liquid slug becomes spherical due to interfacial tension. The electricalproperties of the uids, i.e. conductivities and permittivities are the determinant factors of the eect of the electriceld. Furthermore, the direction of the electric eld which can be normal or parallel to the ow direction, can havedierent eect on the stability of the interface. In this work, the stability of the interface between two Newtonian,immiscible liquids which are assumed incompressible and leaky dielectric will be investigated experimentally undereither normal or parallel electric eld. The liquids are injected into the microchannel using a syringe pump. Thevoltage at which the interface becomes unstable, i.e. the critical voltage will be determined. Then, the evolution ofthe interface from the rst measured deection of the interface to the droplet formation will be analyzed. Moreover,the wavelength of the deected interface and the shape and the size of the droplet will be investigated for parameterslike the height to width ratio of the channel, the ow rate ratios of the liquids, and the viscosity ratios of the liquids.

3


EXPANSION AND INSTABILITY OF CONCENTRATED BACTERIAL DROPLETS

Igor S. Aranson1, Andrey Sokolov2, Leonardo Dominguez Rubio1, & John F. Brady3

1Dept. Biomed. Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA2Materials Science Division, Argonne National Laboratory, Argonne, Illinois, 60439, USA

3Dept. Chem. Engineering, California Institute of Technology, Pasadena, California, 91115, USA

Suspensions of motile bacteria or synthetic microswimmers, termed active matter, manifest a remarkable propensityfor self-organization and formation of large-scale coherent structures. Most active matter research deals with almosthomogeneous in space systems and little is known about the dynamics of active matter under strong connement.Here we report on experimental and theoretical studies on the expansion of highly concentrated bacterial droplets intoan ambient bacteria-free uid. The droplet is formed beneath a rapidly rotating solid macroscopic particle inserted inthe suspension ([1]). We observed vigorous inability of the droplet reminiscent of a supernova explosion, see Figure 1.The phenomenon is explained in terms of continuum rst-principle theory based on the swim pressure concept ([2]).Our ndings provide insights into the dynamics of active matter under extreme conditions and signicantly expandthe scope of experimental and analytic tools for control and manipulation of active systems.

Figure 0.1: (left) Stable bacterial concentration distribution. Scale bar is 50 µm. (right) Supernova-like explosion of the concentratedbacterial droplet 1 sec after cessation of rotation.

References

[1] A. Sokolov and I. Aranson, Rapid expulsion of microswimmers by a vortical ow, Nature Commun. 7, 11114 (2016)

[2] S.C. Takatori, W. Yan, and J.F. Brady, Swim pressure: stress generation in active matter, Phys. Rev. Lett. 113, 028103 (2014)

4


CHOOSING BASIS FUNCTIONS OF WEIGHTED RESIDUAL METHOD FOR MODELING THEJOINT FLOW OF LIQUID FILM AND TURBULENT GAS

Dmitriy Arkhipov & Oleg Tsvelodub

Institute of Thermophysics SB RAS & Novosibirsk State University, Novosibirsk, Russian Federation

One of the approaches to solving the moving boundary problem comes from rewriting of the hydrodynamic equations innew variables, transforming the ow area into the strip of constant thickness: x = x, η = y/h(x, t), t = t. For thecase of a free falling lm on a vertical plane the following system was obtained in the long wavelength approximation[1]:

∂(hu)

∂t+

∂(hu2)

∂x+

∂(huv)

∂η=

σ

ρh∂3h

∂x3+

ν

h

∂2u

∂η2+ gh, (1)

∂h

∂t+

∂(hu)

∂x+

∂(hv)

∂η= 0 (2)

u(x, 0, t) = 0, v(x, 0, t) = 0,∂u

∂η(x, 1, t) = 0, v(x, 1, t) = 0 (3)

Here σ is the surface tension, ρ is the density, ν is the kinematic viscosity, g is the free fall acceleration, h is the localthickness, u and v are the contravariant velocity components corresponding to coordinates x and η, respectively.

The work [2] shows that the conservative system of equations has a specic symmetry of parity in the ow region,extended over the transverse coordinate. The use of this symmetry in the choice of basis functions in the method ofweighted residuals allows signicantly simplifying the form of resulting equations. In particular, it appears that thebasis of the popular model of Ruyer-Quil and Manneville [3] consists only of symmetric functions. The calculationspresented in [2] show that a wide class of steady-state traveling wave solutions of the system satises the propertiesof the discovered symmetry. However, the existence and evolution of "asymmetric" solutions have remained unclearup to now. In addition, the work notes that the complication of the boundary conditions on the free surface is likelyto lead to symmetry breaking and the need to use the full set of basis functions, including "asymmetric".

The present study proves that in the class of functions with bounded second derivative, all solutions of the conservativesystem of equations are presented by a full set of symmetric basis functions. Choosing such a set it may be decided oneven-numbered Chebyshev polynomials, modied so that each element of the basis satises the boundary conditionsof the problem. Consideration of the gas ow impact at the joint ow interface is shown to entail no fundamen-tal diculties in constructing the basis. The inhomogeneity of boundary conditions can be taken into account byintroducing only one "odd" function in the system of basis functions and by building the orthogonal subspace of sym-metric functions, satisfying boundary conditions of the problem with homogeneous boundary conditions. Technically,this subspace is determined using the orthogonal Housholder transform, playing an important role in modern com-putational mathematics due to its high eciency and accuracy, compared to classical methods (e.g., Gram-Schmidtorthogonalization).

The evolution of waves in the co-current ow of turbulent gas and liquid lm in a vertical channel has been calculated.The results are compared with calculations by integral models. The computational eciency of the proposed methodcomparable to classical integrated approaches is demonstrated. The accounting of non-self-similar velocity proleleads to additional short-wave dissipation, which allows reducing the spatial resolution and therefore increasing thecalculation time step.

References

[1] S.V. Alekseenko, D.G. Arkhipov, O. Y. Tsvelodub, Divergent system of equations for a uid lm..., Doklady physics 56, 2225(2011).

[2] D. Arkhipov, I. Vozhakov, D. Markovich, O. Tsvelodub, Symmetry in the problem of wave modes Europ. Journ. Mech.-B 59, 5256(2016).

[3] C. Ruyer-Quil, P. Manneville Improved modeling of ows down inclined planes, Europ. Phys. Journ. B 15, 357369 (2000).

5


ANALYSIS OF THERMO-DIFFUSIVE CELLULAR INSTABILITIES IN CONTINUUMCOMBUSTION FRONTS

Hossein Azizi, Sebastian Gurevich & Nikolas Provatas

Department of Physics, Centre for the Physics of Materials, McGill University, Montreal, QC, Canada

We explore numerically the morphological patterns of thermo-diusive instabilities in combustion fronts with a con-tinuum fuel source, within a range of Lewis numbers and ignition temperatures, focusing on the cellular regime. Forthis purpose, we generalize the recent model of Brailovsky et al. [1] to include distinct process kinetics and reactantheterogeneity. The generalized model is derived analytically and validated with other established models in the limitof innite Lewis number for zero-order and rst-order kinetics. Cellular and dendritic instabilities are found at lowLewis numbers. These are studied using a dynamic adaptive mesh renement technique that allows very large com-putational domains, thus allowing us to reduce nite size eects that can aect or even preclude the emergence ofthese patterns. Our numerical linear stability analysis is consistent with the analytical results of Brailovsky et al. [1]The distinct types of dynamics found in the vicinity of the critical Lewis number, ranging from steady-state cells tocontinued tip-splitting and cellmerging, are well described within the framework of thermo-diusive instabilities andare consistent with previous numerical studies. These types of dynamics are classied as quasi-linear and characterizedby low amplitude cells that may be strongly aected by the mode selection mechanism and growth prescribed by thelinear theory. Below this range of Lewis number, highly non-linear eects become prominent and large amplitude,complex cellular and seaweed dendritic morphologies emerge. The cellular patterns simulated in this work are similarto those observed in experiments of ame propagation over a bed of nano-aluminum powder burning with a counterowing oxidizer [2]. These resemble the dendritic ngers in the limit of low-Lewis number (Fig. 1 ). It is noteworthythat the physical dimension of our computational domain is roughly close to their experimental setup.

Figure 0.1: (Colour online) Temporal history of evolution of 1D front corresponds to isotherm θ(x; y) = θig for model parameters MM(n = 1; Le = 0.05; θig = 0.75). The initial interface is a sinusoidal wave mode k = 0.025π/δc and system size is Lx = 600δc;Ly = 160δc.Colours represents dierent length scales emerging in the tip-splitting process, with dotted green line representing a cell from a primary tip-split event and dash-dotted red line and blue (dark gray) line representing cells formed during secondary and tertiary splitting, respectively.The direction of front propagation is shown by the arrow.

References

[1] I. Brailovsky, P.V. Gordon, L. Kagan, and G. Sivashinsky, Diusive-thermal instabilities in premixed ames: Stepwise ignition-temperature kinetics, Combustion and Flame, 162, 20772086 (2015)

[2] J.Y. Malchi, R.A. Yetter, S.F. Son, G.A. Risha, Nano-aluminum ame spread with ngering combustion instabilities Proceedings ofthe Combustion Institute 31, 26172624 (2007)

6


FLOW IN BIFURCATIONS, RECONNECTIONS AND LARGER NETWORKS

Samire Balta & Frank T. Smith

Department of Mathematics, University College London, London, WC1E6BT, United Kingdom

We investigate ow in bifurcations, multi-branching vessels, reconnections and larger networks. Control of the internalow networks by means of the end pressures is investigated together with eects from the individual vessel shapes,for relatively high ow rates. Favourable conditions tend to lead to limit cycles. It is found that adverse conditionshowever may provoke high internal transient pressures and ow surges even when the end conditions remain mild. Asingle nonlinear evolution equation is derived rationally, for a small and large network, which within a certain rangeadmits the impact of all the end pressures and the overall properties of vessel shape and assigns the ow through theentire network.

We propose a generalization of the work of Balta, Smith [1].

L2=0.53

0.53

0.5

T

P2

P1

P0

p2

p0

p1

L2=3

3L2=0.5

u2

u1

u0

FIG 5

−2

−1

0

1

2

3

0 2.5 5 7.5 10 12.5 15

Figure 0.1: Velocities and internal pressures, versus time T , as length eect takes values 0.5 or 3. Imposed end pressures are shown as Pn.

References

[1] S. Balta, F. T. Smith, Inviscid and low-viscosity ows in multi-branching and reconnecting networks, Journal of Eng. Math., 118(2016).

[2] T. J. Pedley, Mathematical modelling of arterial uid dynamics, Journal of Eng. Math., 47(3), 419444 (2003).

[3] F. T. Smith, On internal uid dynamics, Bulletin of Mathematical Sciences, 2(1), 125180 (2012).

7


NON-MODAL STABILITY ANALYSIS OF STRATIFIED TWO-PHASE CHANNEL FLOWS

I. Barmak, A. Gelfgat, A. Ulmann, & N. Brauner

School of Mechanical Engineering, Tel Aviv University, Tel Aviv 69978, Israel

We study non-modal disturbances growth in various linearly stable gas-liquid and liquid-liquid ow congurationsin horizontal and inclined channels. The non-modal (transient) growth is characterized by the growth function andoptimal disturbances [1] that exhibits a maximum gain for transfer of energy from the mean ow to disturbances.These disturbances can lead to the onset of instability in stratied two-phase ows, not predicted by the modalstability analysis [2], and thereby can result in reduction of the parameter regions where smooth stratied ow can beconsidered as a stable conguration. The eect of dierent ow parameters on the transient growth is also studied.

Instead of dealing with the eigenvalue problem, the non-modal approach addresses the linearized equations (Orr-Sommerfeld and Squire) in the form of the initial value problem [3]. The non-orthogonality of eigenvectors leadsto appearance of their inner products in the denition of the energy norm, which is a natural disturbance measureand consists of the kinetic, interfacial capillary and gravitational potential components of energy. The validity ofthe numerical solution has been conrmed through the comparison with the numerical solution of Yecko [4] for azero-gravity system. Contours of the maximal energy growth in the plane of streamwise and spanwise wavenumbersfor a linearly stable horizontal air-water ow are presented in Fig. 1. Denitions of ow parameters can be found in[2].

Figure 0.1: Maximal possible energy growth of 3D disturbances in a linearly stable horizontal air-water ow.

References

[1] B. F. Farrell, Optimal excitation of perturbations in viscous shear ow, Phys. Fluids, 31, 20932102 (1988)

[2] I. Barmak, A.Yu. Gelfgat, A. Ullmann, and N. Brauner, Stability of stratied two-phase ows in inclined channels Phys. Fluids28,084101(2016)

[3] S.C. Reddy and D.S. Henningson, Energy growth in viscous channel ows J. Fluid Mech.252, 209238 (1993)

[4] P. Yecko, Disturbance growth in two-uid channel ow: The role of capillarity Int. J. Multiphase Flow 34, 272282 (2008)

8


APPEARANCE FLUID ROTATION IN THIN THERMO-GRAVITY BOUNDARY LAYER ATLOCAL COOLING FREE BOUNDARY

Vladimir Batishchev

Institute of Mathematics, Mechanics and Computer Science, Southern Federal University,Rostov-on-Don, RUSSIA

Thermo-capillary boundary layers near the free surface of the liquid have been studied extensively in the second halfof the last century in connection with experiments in space. However, in a eld of gravity in layers of nite thicknessMarangoni eect can be neglected. In this case, near the free surface of the liquid may appears thermo-gravitationalboundary layer in the absence of surface shear stresses. When cooling to the free surface of the uid rotation occurin the boundary layer as a result of the bifurcation. This eect may explain one of the reasons of occurrence of atornado.

In this report, we performed a numerical calculation of axisymmetric stationary ow in a thermo-gravitational bound-ary layer near the free surface, which is given the uneven distribution of temperature. The solution is based on theequations of motion of the uid in Oberbeck-Boussinesq approximation in the absence of the Marangoni eect. It isassumed that in the region outside the boundary layer there is an external untwisted liquid stream, which is describedby the equations of motion of an inviscid uid. The temperature and pressure of the uid depends on the radialcoordinate on the square law. We constructed the asymptotic expansion of the solution at low coecients of viscosityand thermal conductivity.

Fluid ow regimes are divided into two types basic and secondary. Basic regimes describe uid ow without rotation.Secondary or rotational regimes are the result of the bifurcation of the basic regimes only when the free surface iscooled . The solution depends on two parameters U and τ . U parameter is proportional to the velocity of the externalow on the free boundary. Parameter τ is proportional to the temperature of the boundary. We have calculated thedependence of solutions on these parameters. Only one basic regime was found by heating (τ < 0) the free boundary.Upon cooling the free boundary, we calculated two basic regimes for each pair of xed values U and τ . These regimesexist only if U ≥ Um > 0 and τ > 0 . The bifurcation value of the velocity of the external ow of a power dependson a parameter τ . The asymptotic behavior of the rotational regimes obtained in the neighborhood of a bifurcationpoint. We got the branching equation whose coecients are found by numerical method. Only two rotational regimesare branched from the basic regime in the bifurcation point. Figure 1 shows the amplitude of the heat ux Q in theboundary layer, depending on the velocity of the external uid ow U on the free surface. The rotational regimes arerepresented by the dashed curve. B - bifurcation point. Basic regimes are shown by the solid line.

Conclusion. We have shown, uid rotation appears in the thermo-gravitational boundary layer when the free surfaceis locally cooled. The rotation of the uid outside the boundary layer is absent. The rotational eect is the result ofthe bifurcation of the basic stationary regime. The rotational regimes exist when the velocity of the external ow doesnot exceed its bifurcation value, including the case of no external uid ow. The rotational eect is not observed inthe presence of local heating of the free boundary.

Figure 0.1: The dependence of the heat ux Q from the outer ow velocity U .

9


OSCILLATORY THERMOCAPILLARY DYNAMICS OF FILMS COUPLED TO SUBSTRATEHEAT CONDUCTION

William Batson, Linda Cummings & Lou Kondic

Department of Mathematical Sciences, New Jersey Institute of TechnologyUniversity Heights, Newark, New Jersey, 07102, USA

By invoking the long-wave approximation to study thin liquid lms, one typically derives a single nonlinear PDE forthe spatiotemporal evolution of that is rst order in time to describe the evolution of the local lm thickness. As aresult, linear analysis predicts monotonic monotonic growth/decay of spatially periodic perturbations. In some works,oscillatory modes of thin lm instability have been uncovered in models that couple the lm thickness to a seconddierential equation that is also rst order in time. Coupled variables that have been considered include interfacialsurfactant concentration or a second lm thickness that arises in bilayer systems.

Practically, this work is motivated by laser irradiation-driven thermocapillary breakup of nanoscopic metal lmsthat sit atop substrates. Viewed as a promising mechanism of nano scale patterning, experimental metal lms[1]oftentimes lie on substrates with large thermal conductivity relative to that of the lm. Theoretically, this assumptionleads to a coupling between the evolution equation for the lm thickness and the full, time-dependent heat conductionproblem in the substrate. Most recently, Dong & Kondic[2] have demonstrated with nonlinear numerical calculationsthat such systems can exhibit oscillatory temporal dynamics.

Towards being able to predict the regimes one should expect oscillatory modes in the laser irradiated problem, we rstconsider the simpler thermocapillary problem of a lm heated from below. The lm is in contact with a substrate oflarge thickness and relatively large thermal conductivity, and a coupled nonlinear model for the lm thickness and thesystem temperature has been derived. In this talk we will present the linear analysis of this model. Preliminary resultssuggest that unstable oscillatory modes arise for specic parameter ranges when a heat ux is xed at the bottom ofthe substrate; however, when the temperature at the bottom of the substrate is xed, only stable oscillatory modesappear to be present.

References

[1] J. Trice, D. Thomas, C. Favazza, R. Sureshkumar and R. Kalyanaraman,Pulsed-laser-induced dewetting in nanoscopic metal lms:Theory and experiments, Phys. Rev. B 75, 235439 (2007).

[2] N. Dong and L. Kondic,Instability of nanometric uid lms on a thermally conductive substrate, Phys. Rev. Fluids 1, 063901 (2016).

10


THERMOCAPILLARY MODULATION OF SELF-REWETTING FILMS

William Batson1,2, Yehuda Agnon1 & Alex Oron2

1Faculty of Civil Engineering, Technion-Israel Institute of Technology, Haifa 32000 Israel2Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000 Israel

Here we consider the self-rewetting uids (SRWFs, [1]) that exhibit a well-dened minimum surface tension withrespect to temperature, in contrast to those where surface tension decreases linearly. Utilization of SRWFs has grownsignicantly in the past decade, due to observations that heat transfer is enhanced in applications such as lm boilingand pulsating heat pipes[2]. With similar applications in mind, we investigate the dynamics of a thin SRWF lmwhich is subjected to a temperature modulation in the bounding gas. A model is developed within the framework ofthe long-wave approximation, and a time-averaged thermocapillary driving force for destabilization is uncovered forSRWFs that results from the nonlinear surface tension. Linear analysis of the nonlinear PDE for the lm thickness isused to determine the critical conditions at which this driving force destabilizes the lm, and, numerical investigationof this evolution equation reveals that linearly unstable perturbations saturate to regular periodic solutions (when themodulational frequency is set properly). Properties of these ows such as bifurcation from the at quiescent state andlong-domain ows, where multiple unstable linear modes interact, are also discussed.

References

[1] Y. Abe,Self-Rewetting Fluids, Ann. N. Y. Acad. Sci, 1077, 650-667 (2006).

[2] N. Zhang, Innovative heat pipe systems using a new working uid, Int. Comm. Heat Mass Trans. 28, 1025-1033 (2001).

11


PHYSICS OF SWARMING BACTERIA

Avraham Be'er1 & Gil Ariel2

1Zuckerberg Institute for Water Research, The Jacob Blaustein Institutes for Desert Research, Ben-GurionUniversity of the Negev, Sede Boqer Campus 84990, Midreshet Ben-Gurion, Israel

2Department of Mathematics, Bar-Ilan University, Ramat Gan 52000, Israel

Bacterial swarming is a complex phenomenon in which thousands of agellated cells migrate collectively on surfaces.During the motion the bacteria form whirls and jets, and move in coherent clusters. The cells are often considered asself-propelled rods, or motorized elongated particles that move at small Reynolds numbers. This intricate motion isintensively studied by physicists, mathematicians and biologists to expose its evolutionary advantage and the ways inwhich the cells communicate.Here we present recent results from three studies: [1] The discovery of Levy walk in swarming bacteria cell trajectoriesthat have straight stretches for extended lengths whose variance is innite, which is dierent from random walk observedin most other bacterial systems, [2] Self-aggregation into clusters and anomalous statistics with a non-Gaussian velocitydistribution, all stemming from antibiotic stress, and [3] Puzzled cell trajectories that move at their own will against,or perpendicular to the main collective ow.

References

[1] G. Ariel, A. Rabani, S. Benisty, J. D. Partridge, R. M. Harshey and Avraham Be'er,Swarming Bacteria Migrate by Lévy Walk, NatureCommunications 6, 8496 (2015).

[2] S. Benisty, E. Ben-Jacob, G. Ariel and A. Be'er,Antibiotic-induced anomalous statistics of collective bacterial swarming, Phys. Rev.Lett. 114, 018105 (2015).

[3] S. D. Ryan, G. Ariel, and A. Be'er,Anomalous uctuations in the orientation and velocity of swarming bacteria, Biophysical Journal111, 247-255 (2016).

12


INFLUENCE OF CHANNEL INCLINATION ON MHD-HEATTRANSFER OF LIQUID METALFLOW

Ivan Belyaev1, Denis Chernysh2, Nikita Luchinkin2,Natalia Pyatnitskaya1 and Nikita Rasuvanov1

1Joint Institute for High Temperatures of Russian Academy of Science , Moscow, Russia2Moscow Power Engineering Institute, Moscow, Russia

Liquid metal usage is usually connected to high thermal loads. In this case, natural convection can create signicantinuence on the ow hydrodynamics. For a long time, not enough attention was given to this fact because of relativelyhigh liquid metal heat transfer coecients, and therefore lack of interest in studying of the detailed ow structure,for example, to enhance heat transfer. However, in the last decade specic convective structures were observedexperimentally in channels [1], that naturally evolve under the inuence of strong magnetic eld. Large orderedvortices can develop and stably exist in the liquid metal ow not only in conditions close to the cooling system of atokamak, but in the absence of a strong external magnetic eld (such as projects of fast nuclear reactors, liquid-metalbatteries, metal oxide chemical reactors, electrolytic baths, molds) with some relations Reynolds and Grashof criteria.A clear understanding of liquid metal mixed convection laws can give new approaches to monitoring and diagnosing ofsuch systems, to increase their reliability and eciency. Experimental [2] and Numerical [3] investigations have shownthat in containers natural convection without magnetic eld can change its regularities signicantly due to inclination.

At earlier stages of the study we examined eects of a longitudinal magnetic eld on hydrodynamics and heat transferin the downow of liquid metal in inclined tubes [4]. It was found that for inclinations up to 45 to the horizonheat transfer characteristics are much closer to the horizontal case than to the vertical. Stable large scale circulationdeveloping without interruption of a forced convection was found experimentally in a strong longitudinal magneticeld. Such a ow conguration provided extremely low average heat transfer.

In this study, we perform experimental and numerical [5] investigation of a liquid metal ow in an inclined rectangularchannel under the inuence of cross-coplanar magnetic eld. It is known that the secondary ow in the form of rolls [6]can be formed in horizontal tubes due to transverse magnetic eld. Periodic disruptions [7,8] are observed in verticaltubes and channels. How the transition between these forms of mixed convection will occur in inclined channels is atopic of a present study.

Work is supported by RF president grant MK-1133.2017.8.

References

[1] I.A. Belyaev et al.,Specic features of liquid metal heat transfer in a tokamak reactor, Magnetohydrodynamics 49, (2013).

[2] A. Mamykin et al.,Turbulent convective heat transfer in an inclined tube with liquid sodium, Magnetohydrodynamics 1, 063901 (2016).

[3] O. Shishkina & S. Horn ,Thermal convection in inclined cylindrical containers,J. Fluid Mech. 790, (2016).

[4] I.A. Belyaev et al.,Liquid metal downow in an inclined heated tube aected by a longitudinal magnetic eld , Magnetohydrodynamics51, 673-684 (2016).

[5] I.A. Belyaev et al.,Engineering approach to numerical simulation of MHD heat transfer, Magnetohydrodynamics 52, 379-389 (2016).

[6] I.A. Belyaev et al,Temperature uctuations in a liquid metal MHD-ow in a horizontal inhomogeneously heated tube,High Tempera-ture 53, 734-741 (2015).

[7] I. A. Melnikov et al.,Experimental investigation of MHD heat transfer in a vertical round tube aected by transverse magnetic eld, Fusion Eng. & Design 112, 505-512 (2016).

[8] O. Zikanov & Y. Listratov,Numerical investigation of MHD heat transfer in a vertical round tube aected by transverse magneticeld, Fusion Eng. & Design 113, 151-161 (2016).

13


EXPERIMENTAL INVESTIGATION OF TEMPERATURE INSTABILITIES ACCOMPANYINGMHD-HEATTRANSFER IN LIQUID METAL FLOW

Ivan Belyaev1, Ivan Melnikov1, Ivan Poddubny2,Nikita Rasuvanov1 and Valentin Sveridov2

1Joint Institute for High Temperatures of Russian Academy of Science , Moscow, Russia2Moscow Power Engineering Institute, Moscow, Russia

The experimental investigations of hydrodynamics and heat transfer aected by magnetic eld have been performedfor many years by the MPEI-JIHT research group [1]. Expected MHD-congurations close to TOKAMAK reactorconditions were considered using mercury as a model liquid. Such a kind of coolant allows to minimize the resultsuncertainty - experimental data have been obtained with high precision. Measured data include averaged over timetemperature elds, local wall temperature distributions and statistical characteristics of temperature uctuationsin a ow. Measuring such data has become possible due to unique microthermocouple invasive probe technique.Measurements have been performed in mercury ow aected by transverse or coplanar magnetic eld. Deep analysisof experimental data showed that combined exposure of a strong magnetic eld and buoyancy manifests itself inpreviously unknown forms. It was found that unexpected modes of liquid metal ow [2] accompanied by abnormallyhigh temperature uctuations occur in a ow [3, 4]. Figure 1 illustrates researched area considering available modeparameters (Ha,Re,Gr). Area of unexpected instability was localized due to the summarization of a signicantamount of experimental points. It is still unclear, how explored issues will perform in conditions of real devices withHartman numbers up to 104. Further experimental program has been developed taking into account mode parametersextension (especially Ha number) due to constructing of the new mercury facility HELMEF.

Figure 0.1: Areas of intense temperature uctuation, downow in a round tube with one side heating [3], Grq = 0.65x108. I-Area of stableow; Transition region (abnormal uctuations are not periodic); II-Area of fully developed abnormal temperature uctuations.

References

[1] V.M. Batenin et al, Modernization of the experimental base for studies of MHD heat exchange at advanced nuclear power facilitie,High Temperature 53, 904-907 (2015)

[2] I.A. Belyaev, Specic features of liquid metal heat transfer in a tokamak reactor , Magnetohydrodynamics 49 (2013)

[3] I.A. Melnikov et al., Experimental investigation of MHD heat transfer in a vertical round tube aected by transverse magnetic eld, Fusion Eng. & Design 112,505512 (2016)

[4] I.R. Kirilov et al., Buoyancy eects in vertical rectangular duct with coplanar magnetic eld and single sided heat load, Fusion Eng.& Design 104, 18 (2016)

14


STABILITY OF THIN LIQUID CURTAINS

Eugene Benilov

Department of Mathematics and Statistics, University of Limerick, Limerick, V94 T9PX, Ireland

The process of curtain coating is traditionally used for manufacturing photographic materials and, more recently,paper. Typically, a liquid curtain is formed using a reservoir with a slot (outlet) in its bottom; having emerged fromthe outlet, the curtain falls under gravity until it hits the substrate to be coated. Clearly, for this to work as anindustrial process, the falling curtain should be hydrodynamically stable.

The stability of liquid curtains with respect to small perturbations was rst considered by Lin [1] using a somewhatintuitive approach, not based on a formal asymptotic expansion. A stability criterion was obtained, predicting thatall curtains with a suciently small Weber number, We < 1, are unstable. It was also argued that the instability iscaused by sinuous perturbations, travelling upstream. The conclusions obtained appeared to agree with the availableexperimental results [2, 3]. The eect of the surrounding air on the curtains stability was examined in [4, 5], using thesame intuitive approach as that of [1].

Note, however, that, in experiments of [2, 3], the curtain was perturbed by a solid object inserted in the ow, sothat the resulting perturbations could hardly be assumed small. Subtler experiments were carried out in [6, 7], withperturbations created by either uctuations of air pressure or a thin needle, respectively. On the basis of theseexperiments the authors of [6] concluded that despite the fact that previous work... shows that curtains... [with]We < 1 are unstable to small disturbances, our experiments show that these curtains can exist over a wide range ofow conditions. A similar conclusion was drawn in [7], where it was also claimed that a curtain can disintegrate onlydue to a hole (i.e. a large perturbation).

In the present work, we examine the stability of liquid curtains using formal asymptotic expansions, and thus showthat all curtains are linearly stable with respect to sinuous perturbations. We also calculate an expression for theperturbations speed (which is similar to the corresponding result of [1, 4, 5], but with an extra term). Then, adoptingthe hypothesis of [8] that suciently strong, upstream travelling perturbations can destabilize the curtain we obtaina stability criterion for large perturbations.

References

[1] S.P. Lin, Stability of a viscous liquid curtain, J. Fluid Mech. 104, 111118 (1981).

[2] D.R. Brown, A study of the behaviour of a thin sheet of a moving liquid, J. Fluid Mech. 10, 297-305 (1961).

[3] S. P. Lin and G. Roberts, Waves in a viscous liquid curtain, J. Fluid Mech. 112, 443-458 (1981).

[4] X. Li, Temporal instability of plane gas sheets in a viscous liquid medium, Chem. Eng. Sci. 48, 2973-2981 (1993).

[5] X. Li,On the instability of plane liquid sheets in two gas streams of unequal velocities, Acta Mech. 106, 137-156 (1994).

[6] D. S. Finnicum, S. J. Weinstein, and K. J. Ruschak,The eect of applied pressure on the shape of a two-dimensional liquid curtainfalling under the inuence of gravity, J. Fluid Mech. 255, 647-665 (1993).

[7] J. S. Roche, N. Le Grand, P. Brunet, L. Lebon, and L. Limat,Pertubations on a liquid curtain near break-up: Wakes and free edges,Phys. Fluids 18, 082101 (2006).

[8] R. J. Dyson, J. Brander, C. J. W. Breward, and P. D. Howell,Long-wavelength stability of an unsupported multilayer liquid lm fallingunder gravity, J. Eng. Math. 64, 237-250 (2009).

15


CAN VIBRATION STABILIZE AN OTHERWISE UNSTABLE LIQUID BRIDGE?

Eugene Benilov

Department of Mathematics and Statistics, University of Limerick, Limerick, V94 T9PX, Ireland

It is well known (e.g. [1] and references therein) that suciently slender liquid bridges between coaxial disks areunstable due to PlateauRayleigh instability. It has also been shown [2][4] that, for a bridge with a vertical axis,gravity strengthens the instability.

This paper examines vertical bridges between coaxial disks, experiencing high-frequency small-amplitude verticalvibration. Given the generally destabilizing nature of vibration, one would expect it to reduce the parameter range ofstable bridges. It turns out, however, that this is not necessarily the case.

Mathematically, we shall demonstrate that the (fast) vibration and (slow) natural motions of the bridge can beseparated asymptotically: the former is described by a mixed DirichletNeumann problem for the Laplace equation inthe domain occupied by the bridge, and the latter is governed by the NavierStokes equations with a vibration-inducedforce and pressure elds (the latter is applied at the free surface). It turns out that, if the vibration amplitude of theupper disk is greater than that of the lower disk, the vibration-induced pressure gradient is opposite to the hydrostaticone. As a result, the destabilizing eect of gravity can be weakened or even cancelled altogether.

To illustrate this eect, we examine almost cylindrical bridges (which implies that surface tension is stronger thangravity and vibration, and the disks radii do not dier much from the bridges mean radius). This simple particularcase has been extensively studied for static bridges (e.g. [2][4]), so it should be a reasonable departure point whenstudying vibrating ones.

References

[1] J. Meseguer, L. A. Slobozhanin, and J.M. Perales, in Microgravity Sciences: Results and Analysis of Recent Spaceights, edited by H.J. Rath, Advances in Space Research, Vol. 16 (Pergamon Press, Inc., Oxford, 1995), p. 5.

[2] S. R. Coriell, S. C. Hardy, and M. R. Cordes, Stability of liquid zone, Colloid Interface Sci. 60, 126-136 (1977).

[3] S. R. Coriell and M. R. Cordes, Theory of molten zone shape and stability, J. Cryst. Growth 42, 466-472 (1977).

[4] E. A. Boucher and M. J. B. Evans, Capillary phenomena. XII. Properties of uid bridges between solids in a gravitational eld, Chem.Eng. Sci. 48, 2973-2981 (1993).

16


THE ROLE OF THE SURFACE TENSION IN PLANAR SHEAR FLOWS

L. Biancoore1, E. Heifetz2, J. Hoepner3, F. Gallaire4

1 Department of Mechanical Engineering, Bilkent University, 06800 Bilkent, Ankara, Turkey2 Department of Geophysics and Planetary Sciences, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel

3 CNRS (UMR 7190), Université Pierre et Marie Curie, Institut Jean le Rond d'Alembert, 75005, Paris, France4 EPFL/LFMI, Route Cantonale, Lausanne, Switzerland.

Both surface tension and buoyancy force in stable stratication act to restore perturbed interfaces back to their initialpositions. Hence, both are intuitively considered as stabilizing agents. Nevertheless, the Taylor-Cauleld instability[1] is a counter example in which the presence of buoyancy forces in stable stratication destabilize shear ows. Anexplanation for this instability lies in the fact that stable stratication supports the existence of gravity waves [2].When two vertically separated gravity waves propagating horizontally against the shear they may become phaselocked and amplify each other to form a resonance instability. Surface tension is similar to buoyancy but its restoringmechanism is more ecient at small wavelengths.

Here we show how a modication of the Taylor-Cauleld conguration, including two interfaces between three stablystratied immiscible uids, supports interfacial capillary-gravity whose interaction yields resonance instability. Fur-thermore, when the three uids have the same density, an instability arises solely due to a pure counter-propagatingcapillary wave resonance. The linear stability analysis predicts a maximum growth-rate of the pure capillary waveinstability for an intermediate value of surface tension corresponding to We−1 = 5, where We denotes the Webernumber (see g. 1 a). We perform direct numerical simulation (DNS) for this setup (see g. 1 a) and nd nonlineardestabilization when 2 ≤ We−1 ≤ 10, in good agreement with the linear stability analysis. The instability is presentalso when viscosity is introduced, although it is gradually damped and eventually quenched.

Figure 0.1: Pure capillary setup. (a) Linear stability analysis: contours of the growth rate in the plane k-We−1. (b) DNS: eld of theconcentration of the inner uid (α2) in the plane x-y for Re = 107 and We−1 = 5 at dierent time. The instability is growing. The colorof the arrows in grayscale depict the velocity magnitude |u|.

References

[1] C.-C. P. Cauleld, Multiple linear instability of layered stratied shear ow, J. Fluid Mech. 258, 255285 (1994).

[2] A. Rabinovich, O. M. Umurhan, and N. Harnik, F. Lott, & E. Heifetz, E., Vorticity inversion and action-at-a-distance instability instably stratied shear ow, J. Fluid Mech. 670, 301325 (2011).

17


FREE SURFACE FLOW OF TWO SUPERPOSED FLUIDS: STABILITY ANALYSIS ANDMODELLING

Lamia Bourdache & Amar Djema

Laboratoire de Physique théorique, Université de Bejaia, route de Targa Ouzemmour, Bejaia 06000, Algeria

A linear stability analysis of a stratied free surface ow of two immiscible superposed uids is performed. The owis over a at inclined plane without temperature gradient. For convenience the uids are assumed to be Newtonianand incompressible. In contrast of the previous works in the eld , such as the work of K.P.Chen [1] and Hu et al [2].where the neutral curves were obtained using a Tchebychev collocation method, we use a Riccati method . As known,this displays the existence of two dierent branches that contribute to convective instability: long and short waveswhich coexist for some range of the control parameters.When focusing on long wave instabilities, for a specic range of th control parameters, the ow is modeled with acoherent weighted residual approach already used in the case of the ow in a channel in the work of Amaouche et al[3].

References

[1] C.P.Chen, Wave formation in the gravity-driven low-Reynolds number ow of two liquid lms down an inclined plane, Phys. FluidsA, 5,30383048 (1993).

[2] Hu et al, Linear temporal and spatiotemporal stability analysis of two-layer falling lms with density statication, Phys. Rev. E77,026302 (2008).

[3] M.Amaouche ,N.Mehidi , N.Amatousse,Linear stability of a two-layer ow down an inclined channel: a second order weighted residualapproach , Phys. Fluids,19, 1-14 (2007).

18


MOMENTUM BASED APPROXIMATION OF INCOMPRESSIBLE MULTIPHASE FLOWS ANDAPPLICATION TO METAL PAD ROLL INSTABILITY

Loïc Cappanera1, Jean-Luc Guermond2, Wietze Herreman3 & Caroline Nore3

1 Department of Computational and Applied Mathematics, Rice University, Houston, TX, USA2 Department of Mathematics, Texas A&M University, College Station, TX, USA

3 Laboratoire d'Informatique pour la Mecanique et les Sciences de l'Ingenieur, Universite Paris-Sud, France

Variable density ows and multi-uid models occur in many applications ranging from magnetohydrodynamics togeophysical ows. We present here a new method to approximate the Navier-Stokes equations using the momentumm := ρu with the density, ρ, and the velocity, u, while the uid interface is tracked via a level set representation.This method has been implemented and tested in the hybrid spectral-nite element code SFEMaNS developed byGuermond and Nore for the past decade [1].

In the frame of variable density problems, the mass matrix associated with the term ρ∂tu needs to be recomputed ateach time step. The product of ρ and ∂t can be expensive when using high-order nite elements, or cannot be madeimplicit when using spectral methods. We propose an alternative formulation which uses the momentum, m := ρuas dependent variable for the Navier-Stokes equations. The diculty now lies in the viscous dissipation that dependson the velocity and thereby must be treated explicitly to avoid recomputing the associated matrix at every time step.In that order the dissipation operator −∇·(η∇su) is rewritten as follows: −∇·(νmax∇sm) + ∇·(νmax∇sm − η∇su)where η is the dynamical viscosity. The rst term is then made implicit so the correction ∇·(νmax∇sm− η∇su) canbe made explicit. In addition, the level set and momentum equations are stabilized with an articial viscosity, calledviscosity entropy [2]. This viscosity is locally made proportional to the residual of the momentum equation denedby: ResNS = ∂tm + ∇·(m ⊗ u) − ∇·(η∇su) + ∇p − f with f the forcing term that includes the gravity and surfacetension force. This technique does not perturb the approximation in the regions where the solution is smooth, but itinduces diusion in the regions where the solution experiences large gradients.

After implementing this method in the code SFEMaNS, we study the inuence of the modeling of the viscous term,with the gradient ∇u or with the strain rate tensor ∇su, with a Newton-Bucket set up and a bottom rotatingdisk experiment [3]. These tests underline the importance of the strain rate tensor when the dynamical viscosityis variable. SFEMaNS can also consider problems with surface tension eects. A non axisymmetric test case, thatconsists of perturbing a bubble interface and computing the oscillation period, is performed. Eventually, we study themetal pad roll instability that can occur in aluminum production cell. The set up consists of a cylinder lled with twoimmiscible uids of large ratio of electrical conductivity in the presence of a vertical electrical current and a verticalmagnetic eld. We show that if the magnitude of the ambient magnetic eld is large enough, the interface undergoesa rotating-tilting motion, as shown in gure 0.1, that is is called metal pad roll instability.

Figure 0.1: Metal Pad Roll instability. Snapshots of the interface evolution between two uids. Ratio of electrical conductivities is 100.

References

[1] J.-L. Guermond, R. Laguerre, J. Léorat, and C. Nore. Nonlinear magnetohydrodynamics in axisymmetric heterogeneous domains usinga Fourier/nite element technique and an interior penalty method, J. Comput. Phys.,228,(2009).

[2] J.-.L. Guermond, R. Pasquetti, B. Popov,From suitable weak solutions to entropy viscosity, Quality and Reliability of Large-EddySimulations II, ERCOFTAC Series, 1, 16, Part 3, 73-390, (2011).

[3] L. Kahouadji and L. Martin Witkowski, Free surface due to a ow driven by a rotating disk inside a vertical cylindrical tank:axisymmetric conguration, Phys. Fluids, 26, 072105, (2014).

19


THERMAL FALLING FILMS, A TALE OF WAVE AND HEAT

Nicolas Cellier1, Christian Ruyer-Quil1,4, Nadia Caney2,Philippe Bandelier3 & Benoit Stutz1

1LOCIE (UMR CNRS 5271), 2LEGI (UMR CNRS 5519), 3CEA-LETI4 Institut Universitaire de France

Heat transfer across a wavy lm falling on a hot plate depends not only on uid thermal characteristics, but also onthe hydrodynamic state of the ow: experimental works ([1, 2]) show a non negligible impact of the hydrodynamicinstabilities on transfer intensication compared to at lms.

An asymptotic model based on weighted residual integrated boundary layer (WRIBL) method ([4]) has been written forthe uid dynamic (based on Navier and Stokes equation) and the heat transfer (based on the Fourier law). Comparedto previous attempts [3], this new formulation compares satisfactorily to the solutions to the Fourier equation even atlarge values of the Prandtl number. Less expensive than direct numerical simulations (DNS), solving this asymptoticmodel allows for fast exploration of the physical parameters and their impacts on the heat ux and the interactionbetween hydrodynamics and heat transfer. One of the main goals is to use that tool and the comprehension of theseinteractions in order to improve the industrial equipments employing heated falling lms. One way could be to forcebenecial instabilities with the plate shape design. To this aim, we have included the eect of a corrugated plate shapein the models within a soft slope hypothesis.

The rst part of this work is devoted to the applicability range of the model and a validation between DNS and theasymptotic model by error computation and results comparison between both methods. Next, the reproducibility ofthe experimental results on the heat transfer intensication occurring on heated falling lm will be discussed. Finally,the interaction between the hydrodynamic regime locked by frequency forcing and heat transfer across the lm willbe considered.

hN

uP

r = 7

.00

width

Nu

Pr =

35.

00

width

Figure 0.1: Snapshots of temporal simulations for dierent hydrodynamic regimes and dierent thermal characteristics along a verticalheated plate. (Re = 15, Pr = 7 and Pr = 35, Ka = 3300, Bi = 0.1). The columns are two dierent forcing frequencies. The lm thicknessis displayed in black, the Nusselt number is displayed in blue for two dierent Prandtl numbers. The dashed blue line represents the atlm reference.

Acknowledgement : Funding for this project was provided by a grant from la Région Rhône-Alpes

References

[1] David P. Frisk and E. James Davis, The enhancement of heat transfer by waves in stratied gas-liquid ow, Int. J. Heat and MassTransf. 15(8), 1537-1552 (1972)

[2] Armel Gonda, Philippe Lancereau, Philippe Bandelier, Lingai Luo, Yilin Fan, and Sylvain Benezech, Water falling lm evaporationon a corrugated plate, Int. J. Therm. Sci. 81, 29-37 (2014).

[3] Seram Kalliadasis, Christian Ruyer-Quil, Benoit Scheid, and Manuel García Velarde, Falling liquid lms, vol. 176, Springer-Verlag(2012).

[4] Christian Ruyer-Quil and Paul Manneville, Improved modeling of ows down inclined planes, Eur. Phys. J. B 15(2), 357-369 (2000).

20


FINITE-TIME BLOW-UP OF SOLUTIONS IN THIN-FILM EQUATIONS

Marina Chugunova1 & Roman Taranets2

1Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA 91711, USA2 Institute of Applied Mathematics and Mechanics of the NASU, Sloviansk, 84100, Ukraine

We propose a generalization of the work of A.Bertozzi and M.Pugh [1]. Namely, for a wide family of long-wave unstablethin-lm equations we prove existence of non-negative weak solutions blowing-up in a nite time. Specically, buildingthese solutions from initial data with negative energy, we show that their L∞-norms go to innity as t → T ∗> 0,T ∗ < 1. In addition, using the Bourgains type approach, we obtain qualitative information about the blow-up andprove mass concentration phenomenon.

Figure 0.1: Numerical blow-up simulations for initial data with negative energy.

References

[1] A. L. Bertozzi and M. C. Pugh Finite-time blow-up of solutions of some long-wave unstable thin lm equations, Indiana Univ. Math.J. 49(4), 13231366 (2000)

21


GLOBAL STABILITY ANALYSIS OF THREE-DIMENSIONAL ROUND JET DIFFUSIONFLAMES

C. Mancini1,2, M. Farano1,2, J.-C. Robinet2, P. De Palma1 & S. Cherubini1

11DMMM, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy2DynFluid Laboratory, Arts et Metiers ParisTech, 151 Boulevard de l'Hopital, 75013 Paris, France

This work provides a global stability analysis of three-dimensional round jet diusion ames. The low-Mach-number(LMN) NavierStokes (NS) equation for reacting ows are solved together with a transport equation for the mixturefraction describing the local composition of the uid. A source term is added to the energy conservation equation tomodel the chemical heat release as a function of the Damköhler (Da) number and of the reaction rate. The latter iscomputed according to an Arrhenius law [1, 2]. The equations are solved by the spectral-element code NEK5000 [3]with Legendre polynomial reconstruction of degree 7 and second-order accurate Runge-Kutta time integration scheme.In order to compute the base ow for the stability analysis, a selective frequency damping (SFD) approach has beenemployed. The global stability analysis has been performed by a matrix-free time-stepper approach applied to theLMN-NS equations, using an Arnoldi method to compute the most unstable modes. The numerical model has beenrstly validated by comparison with the results for the axysimmetric diusion ame provided in reference [2]. Then, athree-dimensional global stability analysis has been performed for a round jet diusion ame inspired by that studiedin reference [4], with Reynolds number Re = 500 and seven values of Da = 1, 1.5, 2, 3, 4, 5, 6 × 105. The analysis hasunveiled several instability mechanisms for dierent values of Da. For the two smallest values of Da, the base owobtained by the SFD approach recalls a "cold ame" structure, with low values of the temperature. These ameshave a strongly unsteady behavior due to the presence of four unstable modes. For higher values of Da, two familiesof modes (called A and B) can be identied. Mode A is unstable for Da = 2× 105 and Da = 3× 105 and it becomesstable for Da ≥ 3× 105; whereas mode B is always stable in the considered range of Da. Direct numerical simulationconrms that for Da > 3 × 105 a steady solution is obtained. The typical structure of modes A and B is shown ingure 0.1 a) and b), respectively, for the case with Da = 2 × 105. The unstable mode A is located mainly in thefront part of the reacting jet, where a pocket of instability at low frequency is found. Whereas, the stable mode Bextends in the rear part of the ame and is characterized by higher frequency. Finally, it is noteworthy that for allthe considered cases, the ames are characterized by a cellular structure with four cells.

Figure 0.1: Mixture-fraction contours for the eigenvectors of modes A (a) and B (b) obtained with Da = 2× 105.

References

[1] J. W. Nichols, P. J. Schmid, The eect of a lifted ame on the stability of round fuel jet, J. Fluid. Mech. 609, 275 (2008)

[2] U. A. Qadri, G. J. Chandler, M. P. Juniper, Self sustained hydrodynamic oscillations in lifted jet diusion ames: origin and control,J. Fluid. Mech. 775, 201222 (2015).

[3] P. F. Fischer, J. W. Lottes, S. G. Kerkemeir, nek5000 Web pages, http://nek5000.mcs.anl.gov (2008).

[4] C. E. Frouzakis, A. G. Tomboulides, P. Papas, P. F. Fischer, R. M. Rais, P. A. Monkewitz, K. Boulouchos, Three-dimensional numericalsimulations of cellular jet diusion ames, Proc. Combust. Inst. 30, 185192 (2005).

22


DROPLETS ARISING FROM A LIQUID FILAMENT: WETTING AND DEWETTINGPROCESSES

Javier A. Diez, Alejandro G. González, Pablo Ravazzoli & Ingrith Cuellar Instituto de Física Arroyo Seco(CIFICEN-CONICET-CICPBA), Universidad Nacional del Centro de la Provincia de Buenos Aires, Pinto 399,

7000, Tandil, Argentina.

We study the hydrodynamic mechanisms involved in the motion of the contact line formed at the end region of aliquid lament laying on a planar and horizontal substrate. Since the ow develops under partially wetting conditions,the tip of the lament recedes and forms a bulged region (head), that subsequently develops a neck region behind it.Later on, the neck breaks up leading to a separated drop, while the rest of the lament restarts the sequence (seeFig. 0.1). One main feature of this ow is that the whole dynamics and nal drop shapes are strongly inuenced bythe hysteresis of the contact angle typical in most of the liquid/substrate systems. The time evolution till breakupis studied experimentally and pictured in terms of a wettability theory which involves the CoxVoinov hydrodynamicapproach [1, 2] combined with the molecular kinetic theory developed by Blake [3]. The parameters of this theoryare determined for our liquid/substrate system (silicon oil / coated glass). The experimental results of the retractinglament are described in terms of a simple heuristic model, and also compared with numerical simulations of the fullNavierStokes equations. This study is of special interest in the context of pulsed laser induce dewetting (PLiD).

Figure 0.1: (a) Side and (b) top views of laments with dierent width, w, at several times.

References

[1] O.V. Voinov, Hydrodynamics of wetting, Fluid Dyn. 11, 714 (1976).

[2] R.G. Cox, The dynamics of the spreading of liquids on a solid surface. Part 1: Viscous ow, J. Fluid Mech. 168, 169 (1986).

[3] T. D. Blake and J. M. Haynes, Kinetics of liquid/liquid displacement, J. Colloid. Interface Sci. 30, 421 (1969).

23


MAGNETIC FIELD EFFECT ON THE LINEAR STABILITY OF PERFECT MAGNETIC FLUIDSLOSHING IN A RECTANGULAR TANK

Rabah Djeghiour, Bachir Meziani & Ouerdia Ourrad

Department of Physics Theorique, A. Mira University, Bejaia, Campus Targa Ouzemour, 06000 Bejaia, ALGERIA

Magnetic uid is used to control the position of the liquid fuel in space. In particular, when a magnetic eld isapplied to magnetic uid, several interesting characteristics have been observed because of the combination of strongmagnetism and liquidity. In this paper, we examine sloshing in a magnetic uid in a rectangular tank in the presenceof horizontal or vertical magnetic eld applied to the free interface. Sloshing is liquid vibration phenomenon causedby tank movement. When the liquid cargo is in transit, the sloshing would aect severely the system stability andleading to damage or fatigue of the structure. So it is necessary to decrease impact of the sloshing and avoid largeamplitude resonance. Sloshing has been studied for many years by analytical, numerical, and experimental methods.In many early studies, the analytical method was dominant.

Zelazo and Melcher [1] studied the linear stability of an ideal magnetic uid on a rigid horizontal plane under atangential magnetic eld theoretically, as well as experimentally. They found that the magnetic eld has a stabilizinginuence on the stability of the uid surface. Elhefnawy [2] studied the nonlinear evolution of horizontal interfaceseparating two magnetic uids of dierent densities including surface tension eects, the inuence of gravity force, thevertical magnetic eld, and constant acceleration in a direction normal to interface. He used multiple scales methodand obtain two nonlinear Schrodinger equations describing the behavior of a perturbed system. He got the linearbreaking wavenumber, which separates stability region from that of instability. Recently, Sirwah [3] has examinedthe linear and nonlinear behaviors of interfacial waves propagating at interface separating two semi-innite layers ofsubsonic gas and streaming viscous magnetic liquid in presence of uniform normal magnetic eld nding dierent casesof instabilities.

In this paper, we propose linear theory of sloshing of magnetic uid in a rectangular tank in the presence of horizontalor/and vertical magnetic eld applied to the free interface. Linear theory depends on neglecting the nonlinear termsfrom the motion equation as well as the boundary conditions. Separation of variables method is used to determinethe dispersion relation. The latter relation is studied analytically and numerically in the case of horizontal magneticeld with respect to uid depth and vertical magnetic eld as a function of waves number.

Figure 0.1: Variation of dimensionless frequency in a rectangular tank in the presence of the horizontal magnetic eld applied to the free

interface with respect to the depth of the uid h/l, for n = 3, H(1)01 = 1 and µ = 0.1.

We show in Figure 1 variations of natural frequency of the magnetic uid in a rectangular tank in presence of horizontalmagnetic eld applied to free interface with and without surface tension as a function of dimensioless uid depth h/l. We have noticed, whatever the frequency, increase is faster for low loads and they are stabilized with increase of thelatter. This gure also shows that the capillary eect is shifted up to values of these frequencies. It is noted that thepresence of surface tension induces eigenfrequencies increase

In the stability diagram given in Figure 2, where H(1)02 is vertical magnetic eld and k is wave number, we obtain the

so-called neutral curve separates the stable fron unstable regions. The unstable region width decreases with surfacetension increase.

24


Figure 0.2: Inuence of capillarity on frequencies in a rectangular tank with presence of vertical magnetic eld applied to free interfaceversus wave number k, for µ = 0.1, h = 0.5 and l = 1.

References

[1] R.E. Zelazo and J.R. Melcher, Dynamics and stability of ferrouids: Surface interaction, J. Fluid Mech. 39, 124 (1969)

[2] A.R.F. Elhefnawy, The Rayleigh-Taylor instability in magnetic uids and nonlinear interfacial waves, Can. J. Physics 70, 603609(1992).

[3] M.A. Sirwan, Nonlinear Kelvin-instability of magnetized surface waves on a subsonic gas-viscous potential liquid interface, J. PhysicsA, 70, 603 (2007).

25


NUMERICAL BIFURCATION ANALYSIS IN LAMINAR-TURBULENT TRANSITION FOR 3DKOLMOGOROV-TYPE FLOW

Nick Evstigneev

Lab. 11-3 (Chaotic Dynamical Systems), Federal Research Center Informatics and Control, Institute for SystemAnalysis, 117312, Moscow, pr. 60-letiya Oktyabrya, 9, Russia

We are considering the following generalized 3D Kolmogorov-type problem for incompressible Navier-Stokes equations on aperiodic domain Ω = 4π × 2π × 2π:

∇ · u = 0,∂u

∂t+ (u · ∇)u = −∇p+

1

R∆u+ (sin(y) cos(z); 0; 0)T , (4)

where R is the Reynolds number, u is a velocity vector and p is a pressure. We analyze bifurcation scenarios with R being abifurcation parameter. The analogue of the problem for 2D domain was studied in for example [1], [2], [3] and for 3D domain in[4], [5], but with a dierent forcing term. It was found that in 2D case the solutions are undergoing systems of pitchfork, Hopf,doubling period and Sharkovskiy cascade bifurcations, see [6]. The main solution of the system (4) is:

u(x, t) = R(1/2− e−2t/R/2)(sin(y) cos(z); 0; 0)T , t ≥ 0. (5)

The system (4) is subject to discrete rotation symmetry around a point (2π, π, π), discrete shift and reect symmetries andcontinuous translation in x direction. The symmetry groups become generators for Hopf bifurcations as it is stated in [7]. Weperform the stability analysis of the main solution (5) arriving to the system of simplied equations that can be solved usingGalerkin method. In order to analyze bifurcations of solutions for the full system with dierent R number we use spectralmethod with 512× 256× 256 harmonics (with projector for pressure and exact diusion part) and Implicitly Restarted Arnoldimethod to analyze eigenvalues of the system. All methods are implemented on multiple GPUs using the matrix-free approach.

We consider two problem setups where the rst exploits symmetry groups and the other does not. We nd that the rst

bifurcation at R = 5.129 coincides for linear stability analysis using simplied problem and full set of discrete equations.

We further analyze all secondary bifurcations by constructing phase spaces, Poincare sections and eigenvalue edstimation of

monodromy and Jacobi matrices. We outline the following bifurcation scenarios for laminar-turbulent transition process:

Symmetry exploiting setup:

PF ∗ → C →1.[C → C2 → C4 → ... → Cn → ... → C18 → C14 → ... → C7 → C5 → C3]N → Chaos2.PF (point) → C → 2DT → 3DT → 3DTResonance → ChaosFull setup:

PF ∗ → C → [C → C2 → C4 → ... → Cn → ... → C2 · 9 → C2 · 7 → ... → C7 → C5 → C3]‡N → Chaos‡→ 2DT → 2DT2 → 2DT4 → 2DT5 → 2DT3 → Chaos... → 2DT → 2DTResonance → Chaos.Here PF ∗ is a subcritical pitchfork bifurcation, Cn is a limited cycle of period n, 1....N is a brunch number 1 that can

be repeated N times on dierent attractors, PF (point) is a supercritical pitchfork bifurcation, nDTm is an n- dimensional

invariant torus of period m with TResonance being a resonance torus, Chaos is a solution on the chaotic attractor. We depict a

possible Hopf bifurcation inside every cycle with ‡. The complication of solutions in physical space can be observed in [8].

References

[1] L.D.Meshalkin and Ya.G.Sinai., Investigation of the Stability of a Stationary Solution of a System of Equations for the Plane Movementof an Incompressible Viscous Liquid, Prikl. Mat. Mekh., 25 (6), 11401143, (1961).

[2] N. F. Bondarenko, M. Z. Gak, and F. V. Dolzhanskiy, Laboratory and theoretical models of plane periodic ows, Izv. Akad. NaukSSSR, Fiz. Atmos. Okeana 15, 711, (1979)

[3] D.Lucas and R.Kerswell, Spatiotemporal dynamics in two-dimensional Kolmogorov ow over large domains, J. Fluid Mech., 750,518-554, (2014).

[4] V.Borue and S.A.Orszag, Numerical study of three-dimensional Kolmogorov ow at high Reynolds numbers, J. Fluid Mech., 306, 293,(2006).

[5] S.Musacchio, and G.Boetta, Turbulent channel without boundaries: The periodic Kolmogorov ow, Phys. Rev. E 89, 023004, (2014).

[6] N.M.Evstigneev, N.A.Magnitskii, and D.A.Silaev., Qualitative Analysis of Dynamics in Kolmogorov Problem on a Flow of a ViscousIncompressible Fluid, Di. Equations, 51(10), 114, (2015).

[7] P.Ashwin, O.Podvigina., Hopf bifurcation with cubic symmetry and instability of ABC ow, Proc. R. Soc. Lond. A, 459, 18011827,(2003).

[8] 3D Generalized Kolmogorov ow in physical space for dierent Reynolds numbers: https://goo.gl/NEVwth

26


THE EMERGENCE OF HAIRPIN VORTICES FROM EXACT COHERENT STATES IN PLANEPOISEUILLE FLOW

M. Farano1,2,3, P. De Palma1, J.-C. Robinet2, S. Cherubini1,2 & T. M. Schneider3

1DMMM, Politecnico di Bari, Via Re david 200, 70125 Bari, Italy2Dynuid Laboratory, Arts et Metiers ParisThech, 151 Boulevard de l'Hopital, 75013 Paris, France

3ECPS, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

Coherent structures such as streaks and hairpin vortices are recurrently observed in transitional and turbulent shearows. Of those streak structures have been captured by fully nonlinear non-trivial exact coherent states (ECS)composed of streamwise vortices and streaks, such as that rst found by Nagata [1]. Hairpin-like ow structureshowever have not yet been directly related to exact coherent states in the form of nonlinear xed points or periodicorbits. Many numerical and experimental studies report the presence of strong energetic events, i.e. bursts [2],associated with the onset of hairpin vortices. This observation has led to the idea that hairpin structures might belinked to a state space trajectory leaving an ECS in a direction of strong energetic growth. In this work we showthat hairpin-like structures are observed following the most energetic trajectories lying not on the unstable but on thestable manifold of an ECS. Their strong energetic growth is a consequence of the non-orthogonality of its eigenmodes.We consider plane Poiseuille ow at Re = 2300, focusing on the travelling wave named TW2 in [3]. We determine theinitial condition u(0), constrained to an energy shell E0 = ||u(0)−uECS ||22 around TW2, which shows maximal energygrowth at a given target time T while leaving TW2. Technically, we use an adjoint-based nonlinear optimizationalgorithm to maximize the distance E(T ) = ||u(T )− uECS ||22 from TW2 for dierent values of T [4].

Figure 0.1: Optimal ow state for Topt = 10 and E0 = 1 × 10−6. Isosurfaces of Q-criterion of the istantaneous velocity (green) andisosurface of streamwise velocity deviation from TW2 (blue negative, red positive).

Figure 1 shows the evolution of the optimal ow state from t = 0 to T = 10. Instantaneous vortical structures areshown by the green surfaces whereas the red and blue ones represent the streamwise velocity deviations from TW2. Att = 0 (left frame) the instantaneous ow state closely resembles TW2, characterized by inclined streamwise vortices.At t = 5 the vortices start to be modulated by the alternating streamwise velocity patches anking them (middle).The structure eventually evolves into a train of hairpin vortices at target time t = 10 (right). Projecting the initialdisturbance on the unstable modes of TW2, we nd that the component of the optimal perturbation in the unstablemanifold is very small. Consequently, the formation of hairpin vortices appears to follow an optimal path on thestable manifold of TW2, with energetic growth driven by the non-orthogonality of the (stable and unstable) modesof the eigenspectrum. To verify this result we remove the contribution of the unstable modes from u(t = 0) and usethis modied initial condition to initialize the direct numerical simulation. The resulting ow evolution follows thesame dynamics previously observed, featuring the formation of hairpin vortices at the selected target time. Theseresults suggest that the recurrence of hairpin vortices in shear ows might be due to the existence of a preferred highlyenergetic path leaving the ECS along its stable manifold bypassing the ow dynamics along the unstable manifold.

References

[1] M. Nagata, Three-dimensional nite-amplitude solution in plane Couette ow : bifurcation from innity, J. Fluid Mech. 217, 519527(1990).

[2] R. J. Adrian, Hairpin vortex organization in wall turbulence, Phys. Fluids 19, 041301 (2007).

[3] J. Gibson, E. Brand, Spanwise-localized solutions of planar shear ows, J. Fluid Mech. 745, 2561 (2009).

[4] S. Cherubini, P. De Palma, J.-Ch. Robinet, A. Bottaro, Rapid path to transition via nonlinear localized optimal perturbations in aboundary-layer ow, Phys. Rev. E 82, 066302 (2010).

27


"SMART" PASSIVE THERMAL INSULATION OF CONFINED NATURAL CONVECTIONHEAT TRANSFER: AN APPLICATION TO HOLLOW CONSTRUCTION BLOCKS

Shahar Idan & Yuri Feldman

Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

A method for the design of smart passive thermo-insulating materials based on the statistical evaluation of the connednatural convection ow in the presence of heterogeneous porous media is presented. The method is a direct extension ofthe concept of smart thermally insulating materials intelligently adapted to specic engineering congurations recentlyestablished in [1]. An application of the concept for the enhancement of the insulating eciency of hollow constructionblocks is discussed (see Figure 1). Conned natural convection ow developing inside a dierentially heated cavity(comprising a convenient model for the air lled cavity in the mid-core of a hollow construction block) is chosen asa computational testbed. The heterogeneous porous media are modelled by unconnected packed beds of equi- andnon-equi-sized cylinders. Each cylinder is intelligently placed in the bulk of the natural convection ow to ecientlysuppress the momentum in the most energetic regions of the ow. The spatial location of each cylinder is obtainedby applying linear stability analysis to the 2D natural convection ow in the presence of the modelled porous media.The ow is treated by using the mesoscale approach, implicitly resolving the ow elds in the vicinity of the immersedcylinders by the immersed boundary method. The linear stability analysis is performed by utilizing the methodologydetailed in our recent work [2]. The results obtained for 2D congurations are validated for realistic 3D ows. Basicstatistical evaluation of the generated porous media patterns is performed in order to generalize the developed methodof design of smart thermo-insulating materials. It is shown that the eciency of the thermal insulation of the porousmedia is closely related to the diameter of the cylinders modelling it. This study comprises an important milestone inthe design and manufacture of smart thermo-insulating materials from available o-the-shelf porous materials.

Figure 0.1: Physical model of the hollow block with insulator implants of smart porous media : (a) general exploded view ; (b) cross sectionview determining 2D model of dierentially heated cavity

References

[1] Y. Gulberg and Y. Feldman, Flow control through the use of heterogeneous porous media : "Smart" passive thermo-insulating materials,Int. J. Therm. Sci. 110, 369382 (2016).

[2] Y. Feldman and Y. Gulberg, An extension of the immersed boundary method based on the distributed Lagrange multiplier approach,J. Comp. Phys. 322, 248266 (2016).

28


BIFURCATIONS OF CONVECTION DRIVEN DYNAMOS IN SPHERICAL SHELLS

Fred Feudel1 & Laurette Tuckerman2

1Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam, Germany2Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), CNRS, ESPCI Paris, PSL Research

University, Sorbonne Université, Univ. Paris Diderot, 10 rue Vauquelin, 75005 Paris, France

Convection of buoyancy driven electrically conducting uids in rotating spherical shells represents an idealized modelfor the generation of magnetic elds in a number of astrophysical applications. We study the magnetohydrodynamic(MHD) equations in a rotating spherical shell by heating the uid from the inner shell surface under the action of aradially directed gravity force for dierent rotation rates. For a critical Rayleigh number, the ow can enhance andmaintain a magnetic eld via the induction equation, generating a self-sustained dynamo.

In order to study the bifurcations we applied path-following techniques by incorporating a Newton solver into aspectral code developed by Hollerbach [1]. We study the bifurcations for a xed magnetic and viscous Prandtl numberwhile the Ekman and the Rayleigh numbers are varied. Starting from the conductive state we compute the primarybifurcations and trace the convective solutions which appear in the form of rotating waves (RWs). In particular, wedemonstrate a typical scenario for dynamo generation in which the magnetic branches bifurcate subcritically from thepure convective states which are unstable at this Rayleigh number (due to previous nonmagnetic bifurcations). Thebifurcating magnetic solutions are created with several positive eigenvalues, but are stabilized by a sequence of furthersaddle-node bifurcations.

Figure 0.1 demonstrates an example where at the Ekman number, Ek = 0.00164, two stable nonmagnetic rotatingwave (RWs) with cyclic symmetries, Z3 and Z4, bifurcate from the conductive state. Corresponding magnetic brancheswith the same cyclic symmetry are generated in secondary subcritical bifurcations (thick dashed lines). These branchesare stabilized via a sequence of subsequent turning points. The resulting stable portions of the dynamo branches aredepicted by thick solid lines in the gure. The axial cyclic symmetry of the original ows is retained and the Lorentzforce in the momentum equation does not deform the ow structure substantially. Therefore, the stable magneticsolutions can be classied as weak-eld dynamos [2].

A typical feature of convection-driven dynamo generation is multistability, which is established by the coexistenceof nonmagnetic and magnetic RWs with dierent cyclic symmetries. For a couple of Ekman numbers we computesystematically their bifurcation diagrams by tracing both stable and unstable branches.

Figure 0.1: Primary branches of nonmagnetic RWs (thin lines) and secondary magnetic branches (thick lines) at Ek=0.00164. The globalfunction, E = Ekin + 0.25Emag on the vertical axis, as a function of a modied Rayleigh number Ra. Stable (unstable) branches aremarked by solid (dashed) lines

References

[1] R. Hollerbach, A spectral solution of the magneto-convection equations in spherical geometry, Int. J. Num. Meth. Fluids 32, 773797(2000).

[2] E. Dormy, Strong-eld spherical dynamos, J. Fluid Mech. 500, 500513 (2016).

29


ELECTROOSMOSIS FLOW OF TWO LAYERS DIELECTRIC-ELECTROLYTE SYSTEM IN DCAND AC EXTERNAL ELECTRIC FIELDS

G.S. Ganchenko1, E.V. Gorbacheva2, S. Amiroudine3 & E.A. Demekhin1

1Laboratory of Micro-and Nanoscale Electro-and Hydrodynamics, Financial University, Krasnodar, Russia2Kuban State University, Krasnodar, Russia

3ECPS, Université de Bordeaux, I2M, UMR CNRS 5295, France

The two-phase microow of two immiscible viscous liquids bounded by two charged solid walls is scrutinised. One ofthe liquids is an electrolyte, while the other is a dielectric, an interface between these two liquids is assumed to bea free surface. An external electric eld,E∞ (see Fig. 1) is directed along the channel and gives the electroosmoticmotion of the electrolyte, which implies the motion of the dielectric through the interface. Such a process is used inthe set-up with a necessity of transportation of dielectric liquids in microscales. In the experiments and for practicalissues [1] the classical method of pumping liquids through the channels (by the creation of pressure dierence) is stillused along with the electroosmotic eect. In this conguration, an external pressure gradient is included into themodel of the phenomenon. The problem is closely related to the problem of the investigation of a thin lm ow on acharged surface [2, 3].

The use of an AC electric eld is of particular practical interest, because it allows to avoid the undesirable chemicalreactions and the destruction of the materials. In this work a linear stability of 1D solution with respect to smallperturbations is investigated for dierent sets of parameters (the ratio of viscosities of the two liquids, the charge on thechannel walls, the amplitude and frequency of the external electric eld) [4]. This study based on the Floquet theory.Both long-wave and short-wave types of instability are found in the system. The rst arises at smaller amplitudesof an external electric eld intensity, while the second manifests itself by more rapid development of perturbations.The external pressure gradient stabilises the system, if the direction of generated ow concides with the direction ofelectroosmotic electrolyte motion, otherwise the destabilisation of the ow is observed.

The work is supported by the Russian Foundation for Basic Research project No. 15-08-02483-a.

Figure 0.1: Electro-osmotic two-phase electrolyte-dielectric ow under an external tangential DC-AC electric eld and pressure gradient.

References

[1] H. Li, T.N. Wong, and N.-T. Nguyen,Electrohydrodynamic and shear-stress interfacial instability of two streaming viscous liquid insidea microchannel for tangential electric elds, Micro and Nanosystems 4,1424 (2012)

[2] C. Ketelaar and V.S. Ajaev, Eect of charge regulation on the stability of electrolyte lms,Phys. Rev. E 89, 0324011 (2014).

[3] G.S. Ganchenko, E.A. Demekhin, M. Mayur, and S. Amiroudine, Electrokinetic instability of liquid micro-and nano lms with a mobilecharge, Phys. Fluids 27, 062002 (2015).

[4] E.A. Demekhin, G.S. Ganchenko, A. Navarkar, and S. Amiroudine, The stability of two layer dielectric-electrolyte micro-ow subjectedto an external electric eld, Phys. Fluids 28, 092003 (2016).

30


LINEAR STABILITY OF THE LID-DRIVEN FLOW IN A CUBE

Alexander Gelfgat

School of Mechanical Engineering, Faculty of Engineering, Tel-Aviv University, Tel-Aviv, 69978, Israel

In the present study we consider two dierent formulations of the lid-driven ow in a cube. In the rst, the classicalone, the lid moves parallel to one of the side walls, so that it becomes a straight-forward 3D extension of the famousbenchmark of the lid-driven ow in a square cavity. In the second formulation the lid moves parallel to the verticaldiagonal cube plane, so that all the three velocity components have comparable minimal and maximal values. Thebenchmark results for steady states of these ows can be found in [1, 2].

Until now, all the instability studies for the lid-driven cavity in a cube [3][10] were carried out using the straight-forward time integration, rather than the eigenvalue analysis. The leading eigenvalues were computed in several studies[9, 11] to determine whether the ow is stable or unstable, however no attempt to arrive to an accurate value of thecritical Reynolds number was done. It is well known that computation of primary steady oscillatory transition is amore challenging problem, compared to the calculation of a steady ow only, since it requires an accurate computationof the most unstable perturbation mode along with the steady base ow. The most unstable perturbation is representedby the leading eigenvector of the momentum and continuity equations linearized around the steady state. Thus, anapplication of the eigenvalue analysis would be the most natural choice for such kind of problems. However, at nespatial resolutions, the size of the algebraic eigenvalue problem becomes so large that the task seems to be unaordable.

In the present study we propose a novel method for calculating of Krylov vectors, which are divergence free and satisfyall the boundary conditions. Basing on this we apply the Krylov-subspace-based Newton iteration for calculation ofsteady ows, and the Arnoldi iteration for computation of the leading eigenvalue and eigenvector. We report solvedlinear stability problems for both formulations, varying the grid from 1003 to 2563 nite volumes. Followed by theRichardson extrapolation, this allows us to obtain the benchmark quality values of the critical Reynolds number andthe critical oscillation frequency. Additionally, we discuss visualization of three-dimensional ows proposed in [12] andpatterns of the most unstable perturbations.

References

[1] S. Albensoeder and H.C. Kuhlmann,Accurate three-dimensional lid-driven cavity ow, J. Comput. Phys., 206, 536-558 (2006)

[2] Y. Feldman and A. Gelfgat, From multi- to single-grid CFD on massively parallel computers: numerical experiments on lid-drivenow in a cube using pressurevelocity coupled formulation, Computers &Fluids 46, 218223 (2011).

[3] Y. Feldman and A. Gelfgat, Oscillatory instability of a 3D lid-driven ow in a cube, Phys. Fluids 22, 093602 (2010)

[4] F. Hammami , N. Ben-Cheikh, A. Campo, B. Ben-Beya, T. Lili Prediction of unsteady states in Lid-driven cavities lled with anincompressible viscous uid, Int. J. Modern Phys. C. 23, 1250030 (2012)

[5] M. Mynam and A.D. Pathak, Lattice Boltzmann simulation of steady and oscillatory ows in lid-driven cubic cavity, Int. J. ModernPhys. C 24,1350005 (2013)

[6] H.W. Chang, P.Y. Hong, L.S. Lin and C.A. Lin, Simulations of ow instability in three dimensional deep cavities with multi relaxationtime lattice Boltzmann method on graphic processing units,Computers & Fluids 88, 866-871 (1977)

[7] H.C. Kuhlmann and S. Albensoeder, Stability of the steady three-dimensional lid-driven ow in a cube and the supercritical owdynamics, Phys. Fluids 26, 024104 (2014)

[8] K. Anupindi, W. Lai and, S. Frankel, Characterization of oscillatory instability in lid driven cavity ows using lattice Boltzmannmethod, Computers & Fluids 92, 7-21 (2014)

[9] J.C. Loiseau, J.C. Robinet and E. Leriche, Intermittency and transition to chaos in the cubical lid-driven cavity ow, Fluid Dyn. Res.48,061421 (2016)

[10] Y. Feldman, Theoretical analysis of three-dimensional bifurcated ow inside a diagonally lid-driven cavity, Theor. Comput. FluidDyn. 29, 245261 (2015)

[11] F. Gómez, R. Gómez and V. Theolis, On three-dimensional global linear instability analysis of ows with standard aerodynamicscodes, Aerospace Sci. and Technol. 32, 223234 (2014)

[12] A. Gelfgat, Visualization of three-dimensional incompressible ows by quasi-two-dimensional divergence-free projections in arbitraryow regions, Theor Comput. Fluid Dyn., 30, 339-348 (2016)

31


UNSTABLE GRID OF FILAMENTS ON A SUBSTRATE AND DROP PATTERNS

Alejandro G. González & Javier A. Diez & Ingrith Cuellar & Pablo Ravazzoli

Instituto de Física Arroyo Seco (CIFICEN-CONICET-CICPBA), Universidad Nacional del Centro de la Provinciade Buenos Aires, Pinto 399, 7000, Tandil, Argentina.

We arrange grids of silicon oil laments on a glass substrate, and consider rectangles of dierent size as well as lamentsof varying widths (see e.g. Fig. 0.1(a)). This conguration evolves by forming drops at the corners of each rectanglewhile the remaining shorter laments develop a succession of breakups that lead to a series of drops whose shapesare quite dierent from those at the corners. While the latter can be related to previous studies [1, 2], the formercorrespond to a new morphology.

After the formation of the corner drops, the resulting system is suitable to study the evolution of short lamentswith controlled length. We focus on the analysis of the relation between the initial lament length and the numberof emerging drops. We develop a single model that accounts for the unstable evolution by taking into account botha quasi equilibrium at the heads of the laments and the Stokes ow balance at the necks. The model determinesthree characteristic lengths, namely, the length of the head, Lh, and two typical lengths of the distance between necksand heads, Ls and Ll (see Fig. 0.1(b)). The dierent sums of these parameters determine when a system evolvesinto a single drop or into two drops. We compare the experimental results to the model predictions and nd a goodagreement. The model is extended to predict when a system ends up with n similar drops. The regions of existence ofthe dierent patterns are contrasted with experiments and the possibility of the system evolving to either n or n− 1drops is considered.

(a)

(b)

Figure 0.1: (a) Time evolution of a square conguration obtained by two pairs of parallel laments that are superimposed perpendicularto each other. The insets show the two dierent types of drops that are obtained at the intersections and at the laments. (b) Top viewof a lament whose ends are stopped and a neck is evolving towards breakup. In this case, both solutions for the distance to the neck areshown: Ls and Ll.

References

[1] A. G. González, J. A. Diez, R. Gratton, and J. Gomba, Rupture of a uid strip under partial wetting conditions, Europhysics Letters77, 44001 (2007).

[2] P. D. Ravazzoli, A. G. González, and J. A. Diez, Drops with non-circular footprints, Phys. Fluids 28, 042104 (2016).

32


INFLUENCE OF MAGNETIC FIELDS ON SIMULTANEOUS STATIONARY SOLUTIONS OFTWO-DIMENSIONAL FLOWS AT LOW MAGNETIC REYNOLDS NUMBERS

Julián M. Granados1, Carlos A. Bustamante2, Henry Power3 & Whady F. Flórez2

1Facultad de Ingenierías, Institución Universitaria de Envigado, Envigado, Colombia2Instituto de Energía, Materiales y Medio Ambiente, Universidad Ponticia Bolivariana, Medellín, Colombia3School of Mechanical, Materials and Manufacturing Engineering, University of Nottingham, University Park,

Nottingham, UK

The presence of magnetic elds can aect the behaviour of an electrically conductive uid ow modifying its structureand, consequently, the bifurcation map. In the interaction between a magnetic eld and a two-dimensional incompress-ible Newtonian uid ow (Magnetohydrodynamics), the electrically charged particles are substituted by an electricallyconducting uid ow. Therefore, forces on the individual charges are replaced by the bulk force acting on the medium.According to results reported in the literature on Magnetohydrodynamics (MHD) problems, mostly obtained usingmesh based methods, the ow pattern and its properties depend on the ow regime [1]; the intensity and orientationof the magnetic eld [2] and the geometric characteristics [3].Simultaneous steady-state solutions with and without the eect of the magnetic eld are obtained by the meshlessMethod of Approximated Stokes Particular Solutions (MASPS) [4] in cases where the magnetic Reynolds number isvery low (Rem << 1) that correspond to one way interaction situations, i.e., magnetic eld aects the uid ow butnot vice versa. Symmetric solutions, obtained at low values of the Reynolds number (Re) in both 4SLDC and suddenexpansion channel ows, bifurcate in an unstable symmetric solution and two stable asymmetric solutions at criticalvalues of Re (Rec) of 130 and 217, respectively. In both cases, several stationary bifurcations occur in greater valuesof Re while a Hopf bifurcation is detected with the MASPS in the interval [720, 730] for the 4SLDC ow. Bifurcationmaps, constructed for dierent values of the Hartmannn number (Ha), show the rearrangement of the bifurcationpoints as Ha increases (see Figure 0.1). A classical perturbation analysis is implemented to assess the stability ofbranches in the bifurcation maps. The obtained ow patterns are the result of the damping eect of the magnetic eldon the velocity component perpendicular to the eld. The inuence of magnetic elds on the simultaneous solutionshave not been reported before for these problems in the literature.

Figure 0.1: Bifurcation maps of the steady-state solutions in the 4SLDC ow in the presence of a vertical magnetic eld with a) Ha = 0,b) Ha = 5 and c) Ha = 10.

References

[1] O. Zikanov, D. Krasnov, T. Boeck, A. Thess, M. Rossi Laminar-Turbulent Transition in Magnetohydrodynamic Duct, Pipe, andChannel Flows, Appl. Mech. Rev. 66, 030802 (2014).

[2] G. Mutschke, V. Shatrov, G. Gerbeth Cylinder wake control by magnetic elds in liquid metal ows, Experimental Thermal and FluidScience 16, 9299 (1998).

[3] P. Yu, J. Qiu, Q. Qin, Z. F. Tian Numerical investigation of natural convection in a rectangular cavity under dierent directions ofuniform magnetic eld, Int. J. Heat Mass Tran. 67, 11311144 (2013).

[4] J. M. Granados, C. A. Bustamante, H. Power, W. F. Flórez A global Stokes method of approximated particular solutions for unsteadytwo-dimensional Navier- Stokes system of equations, Int. J. Comput. Math. In Press (2016).

33


KOOPMAN MODE ANALYSES OF FLUID FLOWS

Gemunu Gunaratne

Department of Physics, University of Houston, Houston, TX 77204,USA

Analytical and computational studies of uid and reacting ows are extremely challenging, due in part to nonlinearitiesof the underlying system of equations and long-range coupling. Recent developments in high-resolution high-frequencyexperimental data capture provide an alternative approach that relies on modal decomposition of experimental data.We use Koopman mode analysis, a nonlinear generalization of normal mode analysis, to decompose a ow into itsconstituents. Koopman modes are global structures, each of which evolve with a single complex growth rate. Flowanalysis also requires a method to dierentiate constituents that are robust (i.e., common between nominally identicalexperiments) from noise and non-robust features. We introduce a technique for this task based on Koopman modeanalysis. The methodology is used to identify critical ow constituents in (1) cellular patterns on ame fronts, (2)instabilities in reacting ows behind a barrier, (3) injector ows, and (4) swirling combustion.

34


ASYMPTOTICS OF A HORIZONTAL LIQUID BRIDGE

M. Haynes, S.B.G. O'Brien & E.S. Benilov

MACSI, Department of Mathematics and Statistics, University of Limerick, Ireland

Based on the paper [1], we model a horizontal liquid bridge using the Laplace Young equation written as a system ofrst order ordinary dierential equations. We use the Bond number as a small parameter to deduce an asymptoticsolution which is then compared with numerical solutions. The perturbation approach demonstrates that equilibriumis only possible if the contact angle lies within a hysteresis interval and the analysis relates the width of this intervalto the Bond number. This result is veried by comparison with a global force balance. In addition, we examine thequasi-static evolution of such a two dimensional bridge.

Figure 0.1: Schematic of the problem

References

[1] M Haynes, S.B.G. O'Brien and E.S. Benilov, Asymptotics of a horizontal liquid bridge, Phys. Fluids 28, 042107 (2016).

35


HYDRODYNAMIC STABILITY OF FLOW IN A SWIRL FLOW CHANNEL

Benjamín Herrmann-Priesnitz1, Williams R. Calderón Muñoz1, Gerardo Diaz2 & Rodrigo Soto3

1Department of Mechanical Engineering, Universidad de Chile, Beauchef 851, Santiago, Chile2School of Engineering, University of California-Merced, 5200 North Lake Rd., Merced, CA 95343, USA

3Physics Department, Universidad de Chile, Av. Blanco Encalada 2008, Santiago, Chile

A local and temporal linear stability analysis of ow in a swirl ow channel is presented. A schematic representationof the channel is shown in Fig. 0.1. The device consists of a cylindrical cavity where uid is admitted through theperiphery, ow is conned between the top and bottom walls, it spirals radially inward and exits through an outletport at the center. The structure of hydrodynamic boundary layers that develop on the top and bottom walls wasinvestigated numerically by Herrmann-Priesnitz et al. [1, 2]. The inuence of a Reynolds number and the ow inletangle over the ow patterns was analyzed, it was found that rotation of the uid induces a crossow and entrainmentof uid towards the cavity walls. In some cases, the uid dynamics in the swirl ow channel is similar to that observedin other elementary rotating boundary layer ows, such as Ekman and Bödewadt layers. Hydrodynamic stability ofthese elementary ows has been studied by several authors [3, 4]. In this work, order of magnitude arguments are usedto reduce the perturbation equations to the well known Orr-Sommerfeld and Squire equations. A Chebyshev spectralcollocation method is used to solve the resulting generalized eigenvalue problem. The base ow is found to be unstableto radial waves when boundary layers do not merge and have an important crossow component. A ow visualizationexperiment is proposed, where dye diusion will be observed for a qualitative comparison with the present results.

(a)(b)

Figure 0.1: Schematic representation of a swirl ow channel. (a) Top view. (b) Cross-sectional view.

References

[1] B. Herrmann-Priesnitz, W. R. Calderón-Muñoz, E. A. Salas, A. Vargas-Uscategui, M. A. Duarte-Mermoud, and D. A. Tor-res,Hydrodynamic structure of the boundary layers in a rotating cylindrical cavity with radial inow, Phys. Fluids, 28, 033601 (2016)

[2] B. Herrmann-Priesnitz, W. R. Calderón-Muñoz, A. Valencia, and R. Soto,Thermal design exploration of a swirl ow microchannelheat sink for high heat ux applications based on numerical simulations, Appl. Thermal Eng. 109 2234 (2016)

[3] E. Serre, S. Hugues, E. Crespo del Arco, A. Randriamampianina, and P. Bontoux, Axisymmetric and three-dimensional instabilitiesin an Ekman boundary layer ow, Int. J. Heat and Fluid Flow 22, 82 (2001)

[4] J. M. Lopez, F. Marques, A. M. Rubio, and M. Avila, Crossow instability of nite Bödewadt ows: Transients and spiral waves,Phys. Fluids 21, 114107 (2009)

36


A STUDY OF TRANSIENT GROWTH BEHAVIOR IN A CONSTRICTED CHANNEL

João Anderson Isler1, Rafael dos Santos Gioria2 & Bruno Souza Carmo1

1Department of Mechanical Engineering, Poli, University of São Paulo, São Paulo, Brazil2Department of Mining and Petroleum Engineering, Poli, University of São Paulo, São Paulo, Brazil

The aim of the present work is to explore the dependence on Reynolds number and spanwise wavenumber of themaximum energy growth in two distinct ow regimes in a constricted channel. Symmetric and asymmetric steadyows were chosen as base ows for the stability analysis, in order to highlight the main features in each systemand compare their stability behavior before and after primary ow instability using non-normal theory. Beside this,convective mechanisms which take the optimal initial disturbances to their maximum growth are investigated, in thesense of classifying the dierent initial disturbances that appear in each ow regime.

Transient energy growth is argued to play an important role in steady ows in complex conned geometries due tolocalized regions of convective instability as observed by Blackburn et al. [1] in a backward-facing step and Cantwellet al. [2] in an axisymmetric pipe with a sudden expansion. Grith et al. [4] compared optimal transient growth withexperimental observation for steady ow through an abrupt axisymmetric stenosis. In addition, non-normal stabilityhas been extensively investigated with respect the dependence on Reynolds number in the last years in conned[1, 2, 3, 5, 6] and unconned ow [7].

In this scenario, non-normal stability analysis was applied to study energy growth behavior in a constricted channel.Dependence on Reynolds number (Re) and spanwise wavenumber (β) of optimal initial disturbances was investigated insymmetric and asymmetric stable two-dimensional ows and comparisons were made between these two ow regimes.Empirical functions were extracted in order to study how the initial disturbances exchange energy with the baseows. Exponential maximum growth rates were observed to be proportional to Re5/4 and Re for the symmetric andasymmetric ows, respectively. The asymmetric ow has similar growth rate as that found by Blackburn et al. [1] inthe ow past a backward-facing step. Exponential maximum growth rates were related with time of maximum growth,using Re or β as parameters in both ow regimes. It is shown that there are notable constant ratios of maximumgrowth and time of maximum growth, thus the initial disturbances grow to their energy peaks with constant rates.Furthermore, direct numerical simulations of the perturbed base ows were performed with random noise as initialconditions for Reynolds number close to the critical to validate the transition mechanism.

References

[1] J. H. M. Blackburn, D. Barkley, and S. J. Sherwin, Convective instability and transient growth in ow over a backward-facing step,J.Fluid Mech. 603, 271-304 (2008)

[2] C. D. Cantwell, D. Barkley, and H. M. Blackburn, Transient growth analysis of ow through a sudden expansion in a circular pipe,Phys.Fluids 22, 034101 (2010).

[3] H. M. Blackburn, S. J. Sherwin, and D. Barkley Convective instability and transient growth in steady and pulsatile stenotic ows, J.Fluid Mech. 607, 267-277 (2008).

[4] M. D. Grith, M. C. Thompson, T. Leweke, and K. Hourigan, Convective instability in steady stenotic ow: optimal transient growthand experimental observation, J. Fluid Mech. 655, 504-514 (2010).

[5] D. M. Smith and H. M. Blackburn, Transient growth analysis for axisymmetric pulsatile pipe ows in a rigid straight circular pipe,17th Australasian Fluid Mech. Conference, Auckland, New Zealand (2010).

[6] G. J. Sheard and H. M. Blackburn, Steady Inow Through a Model Aneurysm: Global and Transient Stability, 17th Australasian FluidMech. Conference, Auckland, New Zealand (2010).

[7] C.D. Cantwell and D. Barkley, Camputational study of subcritical response in ow past a circular cylinder, Phys.Rev. E 82, 026315(2010).

37


THE SUSTAINING MECHANISM OF TURBULENT BANDS IN PLANE CHANNEL FLOW

Takahiro Kanazawa, Masaki Shimizu & Genta Kawahara

Graduate School of Engineering Science, Osaka University, Osaka, Japan

In wall-bounded shear ow between parallel plates such as Couette ow and Poiseuille ow, spatiotemporal intermittentturbulence called turbulent spots [1] or turbulent bands [2] is observed in the transition from laminar ow to turbulence.The onset of these disturbances has an important clue to understand in the subcritical transition to turbulence. Inthis study, we approach the origin of localized turbulence, especially the turbulent band.

We consider incompressible ow with the constant bulk velocity U driven by spatially constant body force betweentwo parallel plates separated by a distance 2h. This system is governed by the incompressible Navier-Stokes equationsin non-dimensional form using the channel half distance h and the center-line velocity of laminar ow Uc = 3U/2. TheReynolds number is dened by Re = hUc

ν = 3hU2ν = 3

2Rem, where ν is the kinematic viscosity. For spatial discretizationwe use a spectral Galerkin method, Fourier series in the streamwise and spanwise directions and Chebyshev polynomialsin the wall-normal direction, and the aliasing error is removed for all the directions. These equations are integrated byusing a Crank-Nicolson method for the viscous term and a 2nd-order Adams-Bashforth method for the others. Thenumerical domain is set to be 100h, 2h, 100h in the streamwise, wall-normal and spanwise direction, respectively.

By setting a very large numerical domain, a turbulent band localized in the longitudinal direction is observed [3]. Thehigh-speed region exists in the downstream edge periodically generating the counter-rotating tubular vortices. Thevortices are left behind and form the band structure. Then we attempt to extract the downstream edge region bythe spatially localized dumping force in expectation of a simple dynamics [4]. The Navier-Stokes equation with thedumping term is given by

∂u

∂t+ u · ∇u = −∇p+

1

Re∆u− αf (x, z, t) (u− ULFex) (6)

where α is the dumping coecient, f is the spatially distributed function like a windowing function [5] and ULF is thelaminar prole. At each time step, we dump the upstream region of the band following procedure. First, we identifythe local maximum point of streamwise velocity in the downstream edge region which propagates in the streamwiseand spanwise directions, and then the centre of dumping force is dened at a certain distance away from this pointalong the upstream side of the band.

As the initial condition, the localized disturbance is used in the early stage of forming the turbulent band to preventsplitting by dumping the part of the turbulent band. Then, we found the turbulent band sustains only around thedownstream edge region. Adjusting the dumping parameter, the sustaining turbulence represents periodic motionwhich arises from a saddle-node bifurcation at a nite value of the Reynolds number. The solution shows cyclicdynamics of generation and decay of vortices. Correspondingly, if the damping force is reduced, the upper-branchsolution loses its stability and eventually a chaotic solution appears to exhibit a longer array of complex vortices.

References

[1] D. R. Carlson, S. E. Widnall, M. F. Peeters, A ow-visualization study of transition in plane Poiseuille ow, Journal of Fluid Mechanics121, 487505 (1982).

[2] T. Tsukahara, Y. Seki, H. Kawahara, D. Tochio, DNS of turbulent channel ow at very low Reynolds numbers, in Proceedings of the4th International Symposium on Turbulence and Shear Flow Phenomena, Williamsburg, VA, USA, June 2729, 935940 (2005).

[3] X. Xiong, J. Tao, S. Chen, L. Brandt, Turbulent bands in plane-Poiseuille ow at moderate Reynolds numbers, Phys. Fluids 27.4,041702 (2015).

[4] J Jimenez, Mark P. Simens, Low-dimensional dynamics of a turbulent wall ow, J. Fluid Mech. 435, 8191 (2001).

[5] J. F. Gibson, E. Brand, Spanwise-localized solutions of planar shear ows, J. Fluid Mech. 745, 2561 (2014).

38


MARANGONI EFFECTS ON A THIN LIQUID FILM COATING A SPHERE

Di Kang, Marina Chugunova & Ali Nadim

Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA 91711, USA

We study the time evolution of a thin liquid lm coating the outer surface of a sphere in the presence of gravity,surface tension and thermal gradients. We derive the fourth-order nonlinear partial dierential equation that modelsthe thin lm dynamics, including Marangoni terms arising from the dependence of surface tension on temperature.We consider two dierent heating regimes with axial or radial thermal gradients. We analyze the stability of a uniformcoating under small perturbations and carry out numerical simulations in COMSOL for a range of parameter values.In the case of an axial temperature gradient, we nd steady states with either uniform lm thickness, or with dropsforming at the top or bottom of the sphere, depending on the total volume of liquid in the lm, dictating whethergravity or Marangoni eects dominate. In the case of a radial temperature gradient, a stability analysis reveals themost unstable non-axisymmetric modes on an initially uniform coating lm.

Figure 0.1: Comparison between results from linear stability analysis (left) and full evolution equation (right) with a radial thermal gradient.

39


PRESSURE IN ACTIVE FLUIDS: A GROWING MONOLAYER

Evgeniy Khain1 & Lev Tsimring2,3

1Department of Physics, Oakland University, Rochester, MI 48309, USA2BioCircuits Institute, UCSD, 9500 Gilman Drive, La Jolla, California 92093-0328, USA

3San Diego Center for Systems Biology, University of California San Diego, La Jolla, CA 92093, USA

The key feature of an active system is that it is adaptive and is able to adjust itself to changing environment. Thisadaptive behavior on a microscopic level (scale of a single cell) leads to emergent macroscopic collective phenomena.Understanding this connection between microscopic adaptivity and emergent collective phenomena is central to inves-tigation of active systems. A system of dividing and growing cells provides a basic example of active matter far fromequilibrium. Living cells in a dense system are all in contact with each other. The common assumption is that suchcells stop dividing due to a lack of space. Recent experimental observations [1, 2] have shown, however, that cellscontinue dividing for a while, forcing other cells in the system shrink, to allow the newborn cells to grow to a normalsize. Due to these pressure eects, the average cell size dramatically decreases with time, and the dispersion in cellsizes decreases, too. The collective cell behavior becomes even more complex when the system is expanding: cells nearthe edges are larger and migrate faster, while cells deep inside the colony are smaller and move slower [3].

This exciting experimental data raises fundamental questions about mechanical interactions between cells in a densesystem. The system seems to be able to release pressure just by adjusting cell sizes. What mechanisms govern thispressure release? What macroscopic description is appropriate for this type of phenomena in an expanding system,when the cells move collectively? In this work, we present a mathematical model that predicts the temporal evolutionof cell size distribution in a closed system; the theoretical predictions are in a good agreement with recent experimentalobservations.

References

[1] A. Puliato, L. Hufnagel, P. Neveu, S. Streichan, A. Sigal, D. K. Fygenson and B. I. Shraiman, Collective and single cell behavior inepithelial contact inhibition, Proc. Nat. Ac. Sci. USA 109, 739744 (2012).

[2] S.M. Zehnder, M. Suaris, M.M. Bellaire and T.E. Angelini, Cell Volume Fluctuations in MDCK Monolayers, Biophys. J. 108, 247-250(2015)

[3] M. Reay, L. Petitjean, S. Coscoy, E. Grasland-Mongrain, F. Amblard, A. Buguin, and P. Silberzan, Orientation and polarity incollectively migrating cell structures: statics and dynamics, Biophys. J. 100, 2566-2575 (2011)

40


ELECTROTHERMALLY DRIVEN NONLINEAR VORTEX PATTERNS ON ELECTRODEARRAY AT PHYSIOLOGICAL CONDUCTIVITIES

Anil Koklu & Ahmet C. Sabuncu

Department of Mechanical Engineering, Southern Methodist University, Dallas, TX 75205, USA

Electrothermal ow is due to gradients in liquid conductivity and permittivity induced by Joule heating. It basicallycauses to form vorticies at the edge of electrode where the electric eld is maximum. Electrothermal ow is present invarious micro scale biomedical devices provided that an electrical energy is applied to liquids at sucient magnitudes.Electrothermal ow has been utilized to enhance bio-assays. In this work, electrothermal ow is experimentally andnumerically examined at physiological conductivity using dierent channel heights and various excitation frequencies.PIV (Particle Image Velocimetry) measurements of the ow eld is taken. The micro-chamber includes 3 electrodepairs, where electrode width is 500 µm and electrode gap distance is 50 µm. Experiments indicate a global owconsisting of two counter rotating vortices in the chamber after critical conductivity and channel height. Liquidconductivity is varied while keeping the other operational parameters constant. The experimental results indicatethat the conductivity plays a signicant role on the number of vortices. Fig. 1 illustrates the map of dierent vortexpatterns with lines showing transitions between patterns. For our experimental conguration, the critical liquidconductivity is found as 2 µS/cm for changing number of vortices and their intensity when channel depth is greaterthan certain height (200 µm). For liquid conductivities higher than this height, a pattern of two global counter vorticesare observed in the chamber. If the liquid conductivity is lower than the critical conductivity, vortices start to form ateach electrode edge. Below a certain channel height (20 µm), no uid motion is observed even though the electrodesare energized at the highest limit (20 Vpp) for whole conductivities of medium. Electrothermal ow is numericallysimulated using COMSOL. Numerical simulations does not match with the experimental ndings at high conductivitymediums. Several possible factors were put forward to explain the discrepancy between numerical and experimentalresults which are electric double layer, singularities in the simulated electric eld at the edges of electrodes, the eectof convective eects, the violation of quasi-electrostatic limit, inuence of illumination light and time derivative oftemporal temperature uctuations.

Figure 0.1: Summary of the ow observations made in the microuidic chamber using dierent channel heights and liquid conductivities.

References

[1] Anil Koklu et al., Electrothermal ow on electrodes arrays at physiological conductivities,IET Nanobiotechnology 10(2), 54-61 (2016).

41


DOUBLE DIFFUSION CONVECTION IN A HELE-SHAW CELL WITH VIBRATIONS

Nikolai Kozlov, Alexey Mizev, Andrey Shmyrov, Mariya Denisova & Konstantin Kostarev

Laboratory of Hydrodynamic Stability, Institute of Continuous Media Mechanics, Perm, 614013, Russia

An experimental investigation is carried out on the dynamics of a double layered system, consisting of miscible liquids aqueous solutions of matters with dierent diusion coecients. The studied system is put in a Hele-Shaw cell andplaced in the eld of vertical translational vibrations. It is known that the nger convection develops in the contactzone of miscible liquids in the case when the solutes have dierent diusion coecients, for instance, double diusionconvection between sodium chloride and sucrose solutions [1]. Investigation of vibrational impact on such systems isan interesting problem.

The cuvette is xed vertically on the platform of an electrodynamic vibrator. In experiments, interferometric techniqueis applied to study the density (concentration) eld. The interferometer is placed on an independed basis with respectto the vibrator, and additionally the vibrator is installed on pneumatic absorbing supports. The same system isstudied in the absense of vibrations and a comparison is done of the two cases. It is found that vibrations slow downthe convection induced by the diusion. The role of vibrational parameters is analyzed.

Figure 0.1: A Hele-Shaw cell in the vibration eld.

References

[1] Scott E. Pringle, Robert J. Glass, Clay A. Cooper, Double-Diusive Finger Convection in a HeleShaw Cell: An Experiment Exploringthe Evolution of Concentration Fields, Length Scales and Mass Transfer, Transport in Porous Media 47, 195214 (2002).

42


STEADY FLOW IN AN ANNULUS WITH A VARYING NUMBER OF DEFLECTORS ATROTATIONAL VIBRATION

Nikolai Kozlov

Laboratory of Hydrodynamic Stability, Institute of Continuous Media Mechanics, Perm, 614013, Russia

A numerical study is carried on of the dynamics of an isothermal liquid in an annulus whose boundaries make rotationalvibrations. On the outer boundary, one or several deectors are placed regularly. The problem is considered in a two-dimensional formulation. As it was earlier shown by comparing numerical and experimental results [1], this approachis valid for the considered problem in the case of relativley small vibration amplitudes. The case of high frequencyoscillations is considered.

As a result of oscillations, a single deector generates a steady ow in the form of a symmetric vortex pair in theStokes boundary layer and a coherent vortex pair in the non-viscous domain. The size of the seondary vortices growswith vibration amplitude. Upon reaching a threshold amplitude value, one of the vortices extends transforming into alarge-scale vortex, which encircles annulus inner boundary. Comparison of the cases with dierent number of activatorsshows that their number aects the ow intensity, but does not inuence the threshold of large-scale vortex emergence.

1.14e-021.09e-021.03e-029.71e-039.14e-038.57e-038.00e-037.43e-036.85e-036.28e-035.71e-035.14e-034.57e-034.00e-033.43e-032.86e-032.28e-031.71e-031.14e-035.71e-045.14e-09

Figure 0.1: Vector plot of the average velocity. The colormap is scaled in m/s. The ow is slighly asymmetric with respect to the activatorat vibration of 10 Hz with the amplitude 0.03 rad.

References

[1] Nikolai V. Kozlov, Dominique Pareau, Andrey Ivantsov, Moncef Stambouli, Steady ow instability in annulus with deectors atrotational vibration, Fluid Dynamics Res. 48, 061416 (2016).

43


STABILITY OF FLUID THROUGH SOFT-WALLED TUBES AND CHANNELS

V. Kumaran

Department of Chemical Engineering, Indian Institute of Science, Bangalore 560 012, India

The nature of the ow in a channel or a tube (laminar or turbulent ow) is of importance in chemical engineeringapplications, because the drag force and transport coecients in turbulent ows are orders of magnitude higher thanthose in laminar ows. It is well known that the transition from a laminar to a turbulent ow in a rigid tube takesplace at a Reynolds number of about 2100. This lecture will examine the nature of the transition in channels andtubes with exible walls, such as those encountered in biological and biotechnological applications.

Our theoretical studies ([1, 2]) show that the ow past a exible surface is qualitatively dierent from the ow past arigid surface, and there are mechanisms of destabilisation for the ow past a exible surface that are not present inthe ow past a rigid surface. This is primarily because there is an additional parameter in the problem, which is theelasticity of the tube wall, which is not present in the ow past rigid surfaces. Our classication of these instabilities isbased on the Reynolds number regime, the ow structure, the scaling of the critical Reynolds number Re = (ρV R/µ)with the dimensionless parameter Σ = (ρGR2/µ2), and the mechanism that destabilises the ow. Here, ρ and µ arethe uid density and viscosity, G is the elastic modulus of the wall material, R is the cross-stream length scale andV is the maximum velocity. Both linear and non-linear stability analysis have been used to identify the parameterregimes where the ow becomes unstable, and the scaling laws for the variation of the critical Reynolds number withthe dimensionless elasticity have been identied. Weakly non-linear studies have also been carried out to determinethe nature of the bifurcation after destabilisation. Our theoretical studies show that in a exible tube or channel,there are three important types of instabilities which could result in a transition from a laminar to a more complicatedow prole.

At low Reynolds number, even when inertia is neglected, there could be an instability when the parameter (V µ/GR)exceeds a critcial value. The mechanism of destabilisation is the transfer of energy from the mean ow to theuctuations due to the shear work done at the surface. At high Reynolds number, there are two dierent modes ofinstability. For the high Reynolds number `inviscid' modes, the transition Reynolds number is proportional to Σ1/2.The mechanism of instability, which is the eect of viscous stresses in an internal critical layer of thickness Re−1/3

within the ow, is identical to that for the ow in rigid tubes and channels. For the high Reynolds number wall modeinstability, the transition Reynolds number increases proportional to Σ3/4. Here, there is a viscous layer of thicknessRe−1/3 at the wall, the the mechanism of instability is the transfer of energy from the mean ow to uctuations dueto the work done at the uid-solid interface.

The existence of an instability in the absence of uid inertia in the low Reynolds number regime has also beenexperimentally conrmed, and the experimental results are in quantitative agreement with theoretical predictions([3]). In addition, it is experimentally shown that the ow in a soft tube could become unstable at a Reynolds numberas low as 500 ([4]), much below the transition Reynolds number of 2100 for a rigid tube. In a rigid microchannel ofsmallest dimension about 100µm, the ow could become unstable at a Reynolds number as low as 200, in contrastto the transition Reynolds number of 1200 in a rigid channel ([5]). In both these cases, the mechanism of transitionis consistent with the wall mode destabilisation. However, it is necessary to incorporate the change in the shape ofthe channel or tube due to the imposed pressure gradient, and the consequent change in the pressure and the velocityproles, in order to accurately predict the transition Reynolds number ([4, 6]).

References

[1] V. Kumaran, Hydrodynamic stability of ow through exible channels and tubes, in Flow through collapsible tubes and past other highlycompliant surfaces, P. W. Carpenter and T. J. Pedley eds., Kluwer Academic, (2003).

[2] V. Shankar, Stability of uid ow through deformable tubes and channels: An overview, Sadhana, 40, 925-943 (2015).

[3] V. Kumaran,Experimental studies on the ow through soft tubes and channels, Sadhana, 40, 911-923, 2015.

[4] M. K. S. Verma and V. Kumaran, A dynamical instability due to uid-wall coupling lowers the transition Reynolds number in the owthrough a exible tube,J. Fluid Mech. 705, 322-347, 2012.

[5] M. K. S. Verma and V. Kumaran, A multi-fold decrease in the transition Reynolds number, and ultra-fast mixing, in a micro-channeldue to a dynamical instability induced by a soft wall, J. Fluid Mech. 727, 407-455, 2013.

[6] . K. S. Verma and V. Kumaran, Stability of the ow in a soft tube deformed due to an applied pressure gradient, Phys. Rev. E 91,043001, 2015.

44


SMART ACTIVE BIOLOGICAL MATTER(plenary lecture)

Herbert Levine

Center for Theoretical Biological Physics, MS-142, Rice University, Houston, TX 77005, USA

The concept of active matter is by now well-established both in its original context of the ocking of biologicalorganisms and in its extension to systems such as granular materials or colloids that are actively driven. Here weargue that in general we need to go one step further to understand many biological processes, progressing from activematter to smart matter. Smart matter consists of entities that contain sophisticated sensory capabilities that enablethem to determine their local conditions and adjust their equations of motion accordingly. This notion introduces anew class of models in which hydrodynamic processes are coupled to signaling systems; this talk will examples of thesemodels from the eld of cell motility and its application to cancer metastasis.

45


GROUND EXPERIMENT ON BUOYANT-THERMOCAPILLARY CONVECTION IN LARGESCALE LIQUID BRIDGE

Duan Li1,2, Wang Jia2 & Kang Qi1,2

1National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China2School of Engineering Science, University of Chinese Academy of Sciences, Beijing, China

Marangoni convection is the uid motion driven by surface tension dierences caused by thermal gradients along aliquid-gas liquid interface, which becomes of particular importance in the ow systems such as droplets, bubbles, liquidcontainers and liquid bridges. The half oating zone liquid bridge (LB, hereafter) which is referred to some liquidlimited into two coaxial rods by surface tension has been proposed to produce high-quality single crystal of high purity.Because the surface tension gradient was decided negatively by the temperature, the driving force is directed from thecooler end to the hotter end of the gas-liquid interface. By the joint eects of gravity and surface tension, Marangoniconvection will be generated in the zone. The ow driven by the temperature dierence between the disks, ∆T , isdirected from the upper heated disk toward the lower cooled disk along the free surface and returns back inside theliquid. It is well known that when T exceeds the critical value, ∆Tc, Marangoni convection in the bridge will transformfrom steady, axisymmetric state to the oscillatory, non-axisymmetric one. The appearance of such an unsteady owcan seriously lead to the deterioration of the quality in the grown crystals. The mechanisms of instability have auniversal character in many elds. Consequently, a large number of studies have been conducted for the instabilitymechanisms in LBs [1]-[3].

To cooperate with Chinese TG-2 space experiment project, this paper studies the critical conditions at the onset oftransition and nonlinear regimes of bouyant-thermocapillary convection in large scale liquid bridge with large Prandtlnumber under normal gravity. Surface temperature distribution is obtained by thermal infrared camera to studytemperature oscillation, temporal-spatial analysis and modal structures of the temperature eld. It is found that thecritical value of buoyant-thermocapillary convection in half-zone liquid bridge can be aected by geometric parameters.In large Prandtl number conditions, the critical temperature dierence will change with the volume ratio nonlinearly,in addition the convection will change from steady ow to a sequence of instabilities. Various wave patterns will appearwith increasing Marangoni number, and a chaotic state will emerge with further increased temperature dierence.

Figure 0.1: Flow regimes of (a) Rg1: steady axisymmetric ow, (b) Rg2: steady nonaxisymmetric ow, (c) Rg3: stangding ow, (d) Rg4:travelling wave ow, (e) Rg5: local two waves separation, (f) Rg6: chaotic ow.

References[1] M. Levenstam and G. Amberg, Hydrodynamic instabilities of thermocapillary ow in half zone, J. Fluid Mech. 297, 357372 (1995).

[2] Z.M. Tang, W.R. Hu and N. Imaishi , Two bifurcation transitions of the oating half zone convection., Int. J. Heat and Mass Transf.44, 12991307 (2001)

[3] K. Li, Satoshi Matsumoto, Nobuyuki Imaishi and Wen-Rui Hu, Marangoni ow in oating half zone of molten tin, Int. J. Heat andMass Transf. 83, 575585 (2015)

46


EFFECT OF POOL ROTATION ON THERMOCAPILLARY CONVECTION INSTABILITIES INANNULAR POOL OF MEDIUM PRANDTL LIQUID

Han-Ming Li1 & Wan-Yuan Shi2

1College of Power Engineering, Chongqing University, Chongqing 400044, China2Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Ministry of Education, Chongqing

400044, China

Linear stability of thermocapillary convection in a rotating annular pool (aspect ratio Γ = d/(r0 − ri) = 0.25,ri/r0 = 0.5) of a medium Prandtl number liquid (Pr = 6.7) is investigated. The neutral Reynolds numbers for theincipience of instabilities are determined by linear stability analysis assuming a counterclockwise rotation directionand the underlying mechanisms are analyzed by energy budgets. The results reveal four types of instabilities over awide range of Taylor number (0 ≤ Ta ≤ 1000). A typical hydrothermal wave (Type I) is the primary instability ofaxisymmetric steady thermocapillary convection for Ta < 59. The slow rotation destabilizes the basic ow whereas fastrotation stabilizes it when the Ta > 24. With increasing Taylor number, three new types of instabilities (Type II, IIIand IV) arise as critical mode in sequence for 59 < Ta < 137, 137 < Ta < 222, and 222 < Ta < 1000, respectively (seeFig. 1). The critical Reynolds numbers for the onset of these three oscillatory bifurcations all increase with increasingTaylor number. The energy budgets reveal that all the ow instabilities are basically driven by the hydrothermalwave instability mechanism of medium Prandtl number liquid [1]. But the pool rotation aects the energy transfersbetween the basic state and the perturbation eld signicantly and leads to dierent oscillatory bifurcations.

Figure 0.1: Stability diagram as a function of Taylor number for liquid of Γ = 0.25.

References

[1] M.K. Smith, Instability mechanisms in dynamic thermocapillary liquid layers, Phys. Fluids 29, 3182-3186 (1986).

47


CONVECTION INSTABILITIES IN A LIQUID METAL PIPE FLOW WITH STRONGTRANSVERSE MAGNETIC FIELD

Yaroslav Listratov1, Nikita Rasuvanov2, Valentin Sviridov2 & Oleg Zikanov3

1National Research University MPEI, Moscow 111250, Russian Federation2JIHT RAS, Moscow 125412, Russian Federation

3University of Michigan - Dearborn, MI 48128-1491, USA

Results of the experiments and numerical simulations of liquid metal ows in a long pipe are presented. The eect ofimposed magnetic elds on heat transfer in liquid metal ows in case of low magnetic Reynolds and Prandtl numbersand high Hartmann number is considered. These situations are relevant to the liquid metal blankets currently designedto be used for cooling, power conversion and tritium breeding in future nuclear fusion reactors [1].The experimental investigations are provided by a joint team of MPEI-JIHT RAS at the MHD-facility. It combinestwo mercury loops, where investigations in a longitudinal and in a transverse magnetic eld are available [2]. Thenumerical model approximates the entire setup of the experiment. The objective of the simulations is to reveal themechanisms leading to the high-amplitude uctuations of temperature observed in the experiments. The ow in ahorizontal or vertical pipes is considered. The examined ow cogurations are shown in Fig. 0.1a, where the vectors:V is the ow velocity, g is the gravity acceleration, B is the imposed magnetic eld. The pipe wall is electricallyinsulated. Heating is uniform in length, and, in a general case, non-uniform over the perimeter of the tube crosssection (Fig. 0.1b). But in the limiting cases the pipe wall subject to constant ux heating in the lower half of thehorizontal pipe or on the side of the vertical pipe.

Figure 0.2: Flow domain: (a) ow conguration, (b) heating congurations.

The simulations produce results in good agreement with the experiment and lead us to an explanation of the observedphenomenon of anomalous high-amplitude temperature uctuations. In a horizontal pipe in a ows at high Grashofand Hartmann numbers, the conventional turbulence is suppressed by the strong magnetic eld. At the same time, thethermal convection structures with zero or weak gradients along the magnetic eld are allowed to grow in amplitudeand develop the complex unsteady dynamics resulting in the uctuations [1]. In case of the downward ow in avertical pipe when half of the pipe's wall is heated, and strong imposed horizontal magnetic eld perpendicular to thetemperature gradient the uctuations are caused by growth and quasi-periodic breakdown of the pairs of ascendingand descending jets related to the elevator-mode thermal convection [4].

References[1] S. Smolentsev, R. Moreau, L. Buhler, C. Mistrangelo, MHD thermuid issues of liquid-metal blankets: phenomena and advances,

Fusion Eng. Des. 85, (7-9), 1196-1205 (2010).

[2] I.A. Belyaev, L.G. Genin, Ya.I. Listratov, I.A. Melnikov, V.G. Sviridov, E.V. Sviridov, Yu.P. Ivochkin, N.G. Razuvanov, and Yu.S.Shpansky, Specic features of liquid metal heat transfer in a TOKAMAK reactor, Magnetohydrodynamics 49, 177-190 (2013).

[3] O. Zikanov, Y. Listratov, and V. G. Sviridov, Natural convection in horizontal pipe ow with strong transverse magnetic eld, J. FluidMech. 720, 486-516 (2013).

[4] O. Zikanov and Y. Listratov, Numerical investigation of MHD heat transfer in a vertical round tube aected by transverse magneticeld., Fusion Eng. Des. 113, 151-161 (2016).

48


DNS OF MIXED CONVECTION IN A LIQUID METAL HORIZONTAL PIPE FLOW WITHTRANSVERSE MAGNETIC FIELD

Dmitry Ognerubov1, Yaroslav Listratov1, Valentin Sviridov2 & Oleg Zikanov3

1National Research University MPEI, Moscow 111250, Russian Federation2JIHT RAS, Moscow 125412, Russian Federation

3University of Michigan - Dearborn, MI 48128-1491, USA

Numerical simulations of the ow of a liquid metal in a horizontal pipe are performed. The conguration reproducesthe experiments for the case of a ow in a horizontal pipe with the lower part of the wall heated and transversehorizontal magnetic eld. A specic manifestation of the convection eect, which also has signicant implications forthe blanket design is anomalous temperature uctuations detected in experiments. It is found that, at the magneticeld strength far exceeding the laminarization threshold, the natural convection develops in the form of coherentquasi-two-dimensional rolls aligned with the magnetic eld. Transport of the rolls by the mean ow causes high-amplitude, low-frequency uctuations of temperature. This result was previously conrmed via stability analysis anddirect numerical simulations [1].This work is an extension of a detailed parametric study based on a large number of simulations within the parameterrange where the anomalous temperature uctuations are found in the experiment. For example, we see in Fig. 0.1 thatthe ow visibly changes at the input the magnet zone. A pattern of upward and downward motions and associatedvariations of temperature appear even at low Gr. But if Gr is not higher they are weak as we move downstream.With the higher Gr, velocity perturbations associated with this motion increases in amplitude and the temperatureuctuations are generated in the ow.

Figure 0.1: DNS results for Re=9000, Ha=300, Pr=0.025 at various values of Gr : (a) distributions of the transverse magnetic eld B andwall heating qw along the computational domain; (b-i) fully developed ow shown using snapshots of vertical velocity Vy in the vertical(b-d-f-h) and horizontal (c-e-g-i) cross-section through the pipe axis. The scales of transverse and streamwise coordinates in (b-i) arerelated as 1:5.

References[1] O. Zikanov, Y. Listratov, and V. G. Sviridov, Natural convection in horizontal pipe ow with strong transverse magnetic eld, J. Fluid

Mech. 720, 486-516 (2013).

49


INSTABILITIES OF COUETTE-POISEUILLE FLOW FOR SHEAR-THINNING FLUIDS UNDERCROSSFLOW

Yu-Quan Liu

Department of Oshore Oil & Gas Engineering, School of Petroleum Engineering, China University of Petroleum,Qingdao 266580, Shandong Province, China

Channel ows of shear-thinning uids exist extensively within nature world and industry. Eects of shear-thinningproperty on ow stability have drawn lots of research focus during the last decades. In this study, the linear stabilityanalysis is performed to discuss the instabilities of plane Couette-Poiseuille ow of shear-thinning uids (includingpower-law and Carreau uids) with uniform crossow. Results indicate that the basic ow of power-law uid canmaintain Couette velocity prole as long as a relation between crossow and pressure gradient is satised. Therefore,the basic ow is not inuenced by shear-thinning property, which aects ow stability only by an additional viscousterm in the stability equation. The long-wave instability mechanism dominates around the critical crossow Reynoldsnumber that makes the stable ow unstable. This critical crossow Reynolds number tends towards a constant asthe streamwise Reynolds number increases, which decreases as shear-thinning property is enhanced. A linear relationbetween the constant for a power-law uid and that for a Newtonian uid is discovered, implying the destabilizationeect of shear-thinning property. When the restriction between crossow and pressure gradient is removed, the criticalcrossow Reynolds number decreases rst and then increases as shear-thinning property is enhanced, which embodiesthe dual eects of shear-thinning property on ow stability - stabilization of altering the basic ow and destabilizationof an additional viscous term in the stability equation.

Figure 0.1: Variations of critical crossow Reynolds number Rcf,crit with Couette number Co under dierent parameters of Carreau uid.

References[1] F. Nicoud and J. R. Angilella, Eects of uniform injection at the wall on the stability of Couette-like ows, Phys. Rev. 56(3),

30003009 (1997)

[2] J. H. M. Fransson and P. H. Alfredsson, On the hydrodynamic stability of channel ow with cross ow, Phys. Fluids 15, 436441(2003)

[3] A. Guha and I. A. Frigaard, On the stability of plane Couette-Poiseuille ow with uniform crossow, J. Fluid Mech. 656, 417447(2010)

[4] S. Cowley and F. Smith, On the stability of Poiseuille-Couette ow: a bifurcation from innity, J. Fluid Mech. 156, 83-100 (1985)

[5] R. Liu and Q. S. Liu, Non-modal instability in plane Couette ow of a power-law uid, J. Fluid Mech. 676,145171 (2011).

50


CHARACTERISTICS AND MECHANISM OF THE TRANSITION TO UNSTEADY FLOW INRANDOM PACKED BED USING FAST MAGNETIC RESONANCE IMAGING

Meichen Lu, Andrew J. Sederman & Lynn F. Gladden

Department of Chem. Engineering and Biotechnology, University of Cambridge, Cambridge CB2 3RA, UK

The understanding of uid ow through porous media is of importance in many elds including chemical engineering,geohydrology and mechanical engineering and the transition between dierent ow regimes has been widely studied.The onset of unsteadiness in a randomly packed bed of spheres has been shown using micro-electrode techniques tobe between Reynolds number Recrit of 100 and 150, where Re = Usfdp/ν is based on the supercial velocity Usf

and particle diameter dp, but Recrit and the amplitude of uctuations are sensitive to the location of measurements.A numerical study using lattice-Boltzmann methods suggested that the onset of unsteadiness in a closed packingstructure occurs via Hopf bifurcation and the periodic behaviour arises from the interactions of vortices [1]. There isa lack of experimental evidence on the ow topology in sphere packings which could help reveal the mechanism of thetransitional behaviour and validate these simulation results.

MRI can be used to measure quantitative velocity elds non-invasively in an optically opaque system, such as a packedbed of spheres. In this work we used MRI spiral imaging which is particularly suited to systems with high shear whencompared to other fast MRI imaging techniques [2]. 2D velocity images at dierent axial positions in a 16.4mmdiameter packed bed with 4.76mm beads were measured at Re from 113 to 221 at a spatial resolution of 0.281µm.Combined with sparse acquisition data sampling and compressed sensing reconstruction, three-component velocitymeasurements were recorded at 33Hz and a single velocity component was measured at 131Hz. By segmenting theaxial slices into pores, the variance of velocity uctuation in each pore has been used to quantify the transition tounsteady ow and shown that it is a highly inhomogeneous process, with dierent pores becoming unstready at Recritranging from 120 to 180. One important mechanism of the onset of unsteadiness is the interaction between the vorticesand the pore structure. The size of steady vortices are observed to grow with and at a critical their strength andlocations begin to uctuate, as shown in Fig. 1(a). The quantitative analysis in Fig. 1(b) shows that the level oflocal unsteadiness, measured by the variance in velocity, follows the same trend as the change in the location andstrength of pore vortices. The localised oscillation of stable vortices is the dominant feature of instability and they arefurther observed to undergo break-down and reforming, similar to eddies in turbulent ow. Overall, this study hasdemonstrated the potential of MRI in characterising and probing the mechanism of ow instability in porous mediaand revealed that the pore-scale vortices play an important role in the process.

Figure 0.1: (a) Time series of images of vorticity (colour scale) and velocity vector (arrows) plot for the normalised transverse velocitiesat Re = 157 for a wall-bounded pore (measured at 21Hz). (b) The standard deviation in the location of the vortex, the area-averagedvorticity (the error bar is the standard deviation) and the variance in the velocity at dierent Re for the structure in (a).

References[1] R. J. Hill and D. L. Koch, The transition from steady to weakly turbulent ow in a close-packed ordered array of spheres, J. Fluid

Mech. 465, 5977 (2002)

[2] A. B. Tayler, D. J. Holland, A. J. Sederman, and L. F. Gladden, Time resolved velocity measurements of unsteady systems using spiralimaging, J. Magn. Reson. 211, 110 (2011)

51


GRAVITY MODULATION EFFECT ON THE ONSET OF THE SORET-INDUCEDCONVECTION IN POROUS MEDIUM

Tatyana P. Lyubimova1 & Irina S. Faizrakhmanova2

1Laboratory of CFD, Institute of Continuous Media Mechanics UB RAS, Perm, 614990, Russia2General Physics Department, Perm National Research Polytechnic University, Perm, 614990, Russia

It is known that periodic external elds may strongly inuence hydrodynamic stability and heat and mass transfer.The gravity modulation is found to be one of the most simple and low-energetic periodic external factors. In thepresent work we consider gravity modulation eect on the onset of instabilities in square cavity lled with the porousmedium saturated by a binary uid and subjected to the uniform vertical temperature gradient and modulated gravityeld. The concentration gradient is induced by the temperature gradient due to the presence of the Soret eect. It isassumed that the cavity boundaries are rigid and impermeable for the uid. We restrict ourselves to the consideration oftwo-dimensional problem. The governing equations for the Soret-induced convection of binary uid in porous mediumare written in the Darcy-Boussinesq approximation. The base state of the system corresponds to the quiescent uidand uniform vertical gradients of temperature and concentration. To study the linear stability of this base state werepresent stream function, temperature and concentration in the form of sums of the base state and small perturbations,substitute these expressions in the equations and boundary conditions and perform linearization. Then we obtainthe linear stability problem which describes the behavior of small perturbations of the convectionless state in themodulated gravity eld. This problem allows separation of variables. Two methods were applied for the determinationof linear stability boundaries: Fourier amplitude method and Galerkin method. The calculations were performed forthe most dangerous instability mode which corresponds to single vortex structure of perturbations. Both Galerkinand Fourier amplitude method allow to obtain the system of dierential equations for the perturbations amplitudes,this system could be integrated numerically by any method, in our work we use the Runge-Kutta-Fehlberg method of5th order of precision and the shooting method. Since we consider periodic forcing, according to the Floquet theorywe represented the solution as 2π-periodic function, by integration of the obtained system of dierential equations wefound monodromy matrix, its eigenvalues, the Floquet multiplicator and then the growth rate of the perturbations.The real part of the growth rate is equal to zero at the stability boundary, where the perturbations neither grownor decay. Imaginary part of the growth rate allows to classify the perturbations. Without gravity modulation theappearance of the both monotonic and oscillatory instabilities was found in the work of A. Bahloul et al [1]. In ourwork we studied the inuence of gravity modulation on the both monotonic and oscillatory instabilities. The neutralstability curves have been obtained for a wide range of the system parameters. It was found that in the system underconsideration synchronous, subharmonic and quasiperiodic instabilities are possible. We plotted the stability maps onthe parameter plane of Soret number and Rayleigh number for the dierent modulation amplitude. Also the stabilitymaps in the parameter plane of the inverse modulation frequency and modulation amplitude was obtained for dierentRayleigh number values. In the parameter area where without modulation only monotonic instability is possible, withthe growth of the modulation amplitude the critical Rayleigh number becomes smaller, thus the gravity modulationmakes stabilizing eect; in the parameter area where both monotonic and oscillatory instability are possible, thereis the quasiperiodic instability and additional subharmonic and synchronous instability regions appear. Thus, fordierent parameter values the gravity modulation may either stabilize or destabilize the Soret-induced convection inporous media.

The study was supported by Russian Science Foundation.

References

[1] A. Bahloul , N. Boutana , P. Vasseur, Double-diusive and Soret-induced convection in shallow horizontal porous layer, J. Fluid Mech.491, 325-352 (2003).

52


THERMAL CONVECTION IN AN INCLINED POROUS LAYER HEATED FROM BELOW

Tatyana P. Lyubimova1,2 & Igor D. Muratov1

1Laboratory of CFD, Institute of Continuous Media Mechanics UB RAS, Perm, 614013, Russia2Theoretical Physics Department, Perm State University, Perm, 614990, Russia

Thermal convection in an inclined porous layer saturated by the uid is considered in the framework of the Darcy-Boussinesq approximation. It is assumed that the temperature distribution maintained at the rigid boundaries of thelayer is consistent with the conductive state existence conditions (strictly vertical temperature gradient).

Exact solution of the linear stability problem for this conguration was obtained in [1]. Critical values of the Rayleighnumber and structure of critical perturbations are found. It is shown that the nite-wavelength perturbations aremost dangerous. For any layer orientations except for horizontal one there is also longwave instability howeverthe threshold for its excitation is higher than that for the nite-wavelength instability. When the layer orientationapproaches vertical, the wave number of critical perturbations tends to zero. As known [2], in the case of tilted layer ofhomogeneous uid, the transition to the longwave instability takes place at some critical angle of the layer inclination.

In the present paper onset and supercritical regimes of thermal convection in an inclined porous layer saturated bythe uid is studied numerically by nite dierence method. The length of computational domain is xed, it equals tothe wavelength of critical perturbations.

The calculations show that at the Rayleigh number values slightly higher that critical value according to the lineartheory [1] (small supercriticalities) the stationary regimes are established after the transient process. For the parameterrange covered in the calculation the stationary ow intensity follows the square root law, i.e. the bifurcation issupercritical.

As shown in [1], for any layer orientations, the critical perturbation structure is such that the boundaries betweenconvection cells are strictly vertical, besides the distance between the cells in horizontal direction does not depend on thelayer inclination and equals to the layer thickness and convective vortices of dierent directions of uid circulation areequivalent. Non-linear calculations, performed in the present work, show that already at small enough supercriticalitiesthe equavalence of vortices of dierent directions is broken and the boundaries between the vortices cease to bestrictly vertical. With the increase of supercriticality the non-equivalence between the vortices of dierent direction isenhanced.

At certain value of the Rayleigh number (for layer inclination angle equal to π/4 this value of the Rayleigh numberis approximately equal to 68) the stationary ow becomes unstable and is replaced by stationary oscillations. At theRayleigh number slightly exceeding this value, the oscillation shape is close to sinusoidal, with further growth of theRayleigh number the oscillation shape become close to the typical shape of relaxation oscillations. In this case, duringthe part of oscillation period, the through ow is observed in the layer, the streamfunction has the same sign all overthe layer. The oscillation period grows with the increase of the Rayleigh number.

When the Rayleigh number approaches the value at which, according to the linear stability theory [1], conductivestate becomes unstable to the longwave perturbations (for the inclination angle equal to π/4 this value of the Rayleighnumber is equal to 8π2) the oscillation period tends to innity (the oscillation frequency tends to zero), the stationaryoscillations are replaced by unlimited monotonic growth of the ow intensity: the ow intensity grows exponentiallywith time and the ow structure becomes close to that observed in the case of plane-parallel ow.

The calculations carried out for the inclination angle equal to π/6 show that in this case the ow structure transfor-mation with the increase of the Rayleigh number is accompanied by the hysteresis : in some range of the Rayleighnumber values the solution is non-unique. At the Rayleigh number approximately equal to 134, the stationary owwhich corresponds to the upper branch of solutions becomes unstable and is replaced by the oscillations.

The study was supported from the grant of President of Russian Federation for the support of Leading ScienticSchools of Russian Federation (grant NSh-9176.2016.1).

References[1] A.K.Kolesnikov and D.V.Lyubimov, On the convective instability of a liquid in an inclined layer of a porous medium, J. Appl. Mech.

and Tech. Phys. 145, 400404 (1973)

[2] G.Z. Gershuni and E.M. Zhukhovitskii, Convective Stability of Incompressible Fluids, Keter Publications, Jerusalem, 1976

53


KELVIN - HELMHOLTZ INSTABILITY AT THE INTERFACE OF NEWTONIAN VISCOUSFLUID AND VISCO-PLASTIC FLUID MOVING PARALLEL TO EACH OTHER IN POROUS

MEDIUM

T.P. Lyubimova1,2 & E.V. Kolesov1

1Laboratory of CFD, Institute of Continuous Media Mechanics UB RAS, Perm, 614013, Russia2Theoretical Physics Department, Perm State University, Perm, 614990, Russia

It is known that the interface between two uids, moving parallel to each other with dierent velocities, at some relativevelocity of motion becomes unstable with respect to the tangential shear instability (Kelvin Helmholtz instability).For interface between two immiscible inviscid uids the stability criterion was obtained in [1, 2]. The interface betweenthe viscous gas and viscous liquid was studied in [3] in the framework of the quasi-potential approximation, whichignores the presence of tangential viscous stresses at the interface taking into account only normal viscous stresses, andassumes the existence of slip boundary conditions at the rigid walls. Works [4]-[7] are devoted to the investigation of thelinear Kelvin Helmholtz instability in the case of interface between stationary ows in a porous medium. This problemhas peculiarities compared to the case of homogeneous uids. In particular, for homogeneous uids the viscosity inmany cases is important only in a thin layer near the interface, which justies the formulation of the problem for anon-viscous uid with the tangential discontinuity of the velocity at the interface, moreover, in this case the tangentialjump can be arbitrary. In porous medium the friction on the skeleton is always large, while the viscous momentumdiusion is usually negligible. As the result, the velocity jump is possible, but cannot be arbitrary, such that forstationary ows the ratio of the velocities on both sides of the interface is a denite function of the uid viscosity.Another distinction from the case of homogeneous uids is very small contribution of nonlinear convective terms inthe momentum equation, which strongly modies the scenario of the onset of the Kelvin Helmholtz instability.

In [1] the occurrence of Kelvin-Helmholtz instability at the interface of plane-parallel ows in porous media is investi-gated within the Darcy and Forchheimer models. A system of two immiscible incompressible viscous uids of dierentdensities (less dense uids is above more dense one) in an inclined porous layer bounded by two parallel rigid plates inthe presence of uniform pressure gradient is considered. Within the Darcy model a criterion for stability is obtained,which implies that the instability may occur under certain ratios of densities and dynamic viscosities of uids. Thesolution of the same problem within the Forchheimer model allowed to obtain the criterion for the occurrence ofKelvin-Helmholtz instability without additional restrictions to the ratio of densities and viscosities of uids.

In the present paper the occurrence of Kelvin - Helmholtz instability at the interface of plane-parallel ows of theNewtonian viscous uid and visco-plastic uid in porous medium is investigated. The velocities of base ows in twouids and the relationship between them are obtained. The squared critical velocity dependences on the wave numberare obtained for dierent values of the other parameters: the porosity of the medium, the viscosities of the uids, theyield pressure gradient. The stability maps in dierent parameter planes are plotted. It is shown that the increase inthe yield pressure gradient and viscosity of the visco-plastic uid decreases the instability threshold and the increasein the porosity of the medium or the viscosity of the Newtonian uid make stabilizing eect.

The study was supported from the grant of President of Russian Federation for the support of Leading ScienticSchools of Russian Federation (grant NSh-9176.2016.1).

References[1] H.Helmholtz, Über discontinuierliche Flüssigkeits-Bewegungen,Monatsber. der König. Preus. Akademie der Wissensch. zu Berlin 145,

400404 (1973)

[2] Lord Kelvin (William Thomson), Hydrokinetic solutions and observations, Philos.Magazine 42, 362 (1871)

[3] T.Funada and D.D.Joseph, Viscous potential ow analysis of Kelvin-Helmholtz instability in a channel, J. Fluid Mech. 445, 263 (2001)

[4] R.Raghavan and S.S. Marsden, A theoretical study of the instability in the parallel ow of immiscible liquids in a porous medium,Quart. J. Mech. and Appl. Math. 26, 205 (1973)

[5] H.H. Bau, Kelvin-Helmholtz instability for parallel ow in porous media: A linear theory, Phys. Fluids 25, 17191722 (1973)

[6] R.Asthana, M.K. Awasthi, and G.S. Agrawal, Kelvin-Helmholtz instability of two viscous uids in porous medium, Int. J. of Appl.Math and Mech. 8 (14), 1 (2012)

[7] T.Ramstad and A.Hansen, Capillary-Driven Instability of Immiscible Fluid Interfaces Flowing in Parallel in Porous Media, Phys.Rev E, 78, 035302 (2008)

54


GENERATION OF AVERAGE FLOWS NEAR FLUID INTERFACE UNDER TANGENTIALVIBRATIONS

D.V. Lyubimov1, T.P. Lyubimova1,2, A.A. Cherepanov1, A.O. Ivantsov1,2 & A.V. Perminov 3

1Theoretical Physics Department, Perm State University, Perm 614990, Russia2Laboratory of CFD, Institute of Continuous Media Mechanics UB RAS, Perm 614013 , Russia

3Department of Physics, Perm National Polytechnic University, Perm 614990, Russia

We study viscosity eect on generation of average ow near uid interface under tangential vibrations. The generationof average ow near free surface was studied earlier by Longuet-Higgins [1] and the uid interface was consideredby Dore [2]. It follows from these studies that the mechanism of average ow generation in these situations diersconsiderably from the case of Schlichting generation near rigid surfaces [3]. In particular the generation near freesurface and uid interface is related to the eective disbalance of tangential stresses, while Schlichting generation isassociated with the eective disbalance of tangential velocities. However, in the present study it is demonstrated thatin the case of high viscosity contrast the Schlichting mechanism of generation should be taken into account and thecorresponding eective boundary conditions are derived.

The developed theoretical approach is implemented to the problem of average ow generation at the interface betweentwo immiscible uids under horizontal vibrations. In the experiments performed by Wolf [4] it was found that undersuciently intensive horizontal vibrations the interface between two layers of immiscible uids becomes unstable,which results in the formation of the frozen wave.

A theoretical description of this phenomenon was suggested in [5]. Considering the case of small-amplitude high-frequency vibrations they showed that the frozen wave arises due to the development of the Kelvin-Helmholtz instabilityand derived the analytical expression for the critical vibration intensity. The instability was shown to be longwavein the case where the layer thickness is less than a certain critical value. For thicker layers the nite wavelengthinstability is more dangerous, which leads to the formation of the frozen wave. The assumption of high-frequencyvibrations was relaxed by [6] where vibrations of arbitrary amplitude were considered. The results of further studiesincluding consideration of uid layers of dierent thicknesses can be found in the book of [7].

We performed direct numerical simulations of the frozen wave development in a rectangular cavity with the horizontaldimension much larger that the vertical one (g. The numerical results on average ow structure and intensity agreewell with the derived 1) analytical formulas for the eective boundary condition. The inuence of viscosity andsuperciality on structure of average ows near the interface is studied.

This work was supported by RFBR (Russian Foundation for Basic Research), project N 15-01-09069.

Figure 0.1: Generation of average ow near the interface.

References

[1] M.S. Longuet-Higgins, Mass Transport in Water Waves, Phil. Trans. 245, 535-581 (1953)

[2] B.D. Dore, On mass transport induced by interfacial oscillations at a single frequency, Proc. Camb. Phil. Soc. 74, 33-347 (1973)

[3] H. Schlichting, Boundary layer theory , New York:McGraw-Hill (1968)

[4] G.H. Wolf, The dynamic stabilization of Rayleigh-Taylor instability and corresponding dynamic equilibrium, Z. Physik.B227, 291-300(1969)

[5] D.V. Lyubimov and A.A. Cherepanov, Development of a steady relief at the interface of uids in a oscillatory eld, Fluid Dynamics21, 849-854 (1987)

[6] M.V. Khenner, D.V. Lyubimova, T.S. Belozerova, B. Roux, Stability of plane-parallel oscillatory ow in a two-layer system, Eur. J.Mech. B/Fluids, 18, 1085-1101 (1999)

[7] D.V. Lyubimov, T.P. Lyubimova, A.A. Cherepanov, Dynamics of interfaces in vibrational elds, Moscow: FizMatLit (in Russian)(2003)

55


ON THE ORIGIN OF THE ASYMMETRIC VORTEX SHEDDING MODE IN THE WAKE OF 2SIDE-BY-SIDE SQUARE CYLINDERS

Shengwei Ma, Chang-Wei Kang, Teck-Bin Arthur Lim & Chih-Hua Wu

Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), Singapore

For ow across 2 side-by-side cylinders at low Reynolds numbers (Re = U0D/ν, where U0 is the freestream velocity,ν kinematic viscosity of the uid, and D the diameter of the cylinder), Hopf bifurcation will be observed at a criticalReynolds number depending on gap ratio (g∗ = g/D, where g is the spacing between 2 cylinders), and the wake thenbecomes unsteady. Above this critical Re, the periodic vortex shedding results in one or two von Kármán vortexstreets in the wake depending on g∗ and Re. The centerline of the vortex street(s) in most cases aligns with thegap center. But as observed in both experiments [1] and CFD simulations [2], in certain ranges of g∗ and Re, thecenterline of the vortex street(s) may shift towards one cylinder, instead of aligning with the centerline of the gap.The mean ow eld is also biased towards one cylinder. The origin of such asymmetric vortex shedding wake modewas investigated with global (BiGlobal) linear stability analysis using Nektar++ in this study.

Global linear stability analysis revealed that for g∗ up to 10 and Re up to 200, there are 4 fundamental unstablemodes as shown in Figure 1: single vortex street mode, in-phase two-vortex-street mode, anti-phase two-vortex-streetmode, and stationary (non-oscillatory) mode. The rst 3 modes are linked to the recirculation bubbles in the wake ofthe base ow; while the stationary mode is originated from the gap ow between the two recirculation bubbles in thebase ow. When peak ow velocity presents in the center of the gap, a pitchfork bifurcation may occur and resultingin this stationary mode. This mode is unstable only when g∗ ≥ 0.3. For g∗ ≤ 0.8, the onset Reynolds number ofthis mode decreases quickly with g∗, then increases for g∗ > 0.8. At most gap ratios, the growth rate rst increaseswith Reynolds number, then decreases. For g∗ = 0.7, this mode is the dominant unstable mode in Reynolds numberrange from 51.77 to 62.5. In other ranges of g∗ and Re, stationary mode was not the most unstable mode. It wasalso found that stationary mode is unstable only in certain Reynolds number range at a given gap ratio. IncreasingReynolds number may make this mode stable. This is opposite to other 3 modes. Global linear stability analysis wascomplemented with DNS simulations in the study. It was concluded that the origin of the deected (biased) meanow is the stationary mode identied in the linear stability analysis and the asymmetric vortex shedding wake modeis the result of the superposition of the stationary mode and the single vortex street mode.

Figure 0.1: Mode shape (Uy) of 4 fundamental modes. The white line marks the recirculation region (Ux = 0) in the base ow. (a) singlevortex street mode; (b) stationary mode; (c) in-phase two-vortex-street mode; (d) anti-phase two-vortex-street mode.

References

[1] C. H. K. Williamson, Evolution of a single wake behind a pair of blu bodies, J. Fluid Mech. 159, 1-18 (1985)

[2] S. Kang, Characteristics of ow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers, Phys. Fluids15, 2486-2498 (2003)

56


NUMERICAL ANALYSIS OF THE CONVECTIVE HEAT TRANSFER COUPLED WITH PHASECHANGE IN THE EVAPORATIVE COOLING PROCESS

Junkun Ma

Department of Agricul. Sci. & Eng. Technology, Sam Houston State University, Huntsville TX, 77341 USA

Absorption cooling technology involving evaporation of refrigerant has been widely used for cooling and refrigerationin both domestic and industrial applications with recent focus on developing systems powered by solar energy source[1]. Among many of the successfully developed systems, the LiBr-H2O based single-eect absorption system is oneof the simplest and requires relative low temperature heat source (∼ 90C) which makes it more suitable for solarpowered applications. The thermodynamic processes in an absorption-cooling device involve heat transfer in the formsof convection and diusion coupled with refrigerant (H2O in the LiBr−H2O system) phase changes due to evaporationand condensation. For the LiBr − H20 system, cooling is induced when condensed liquid water is introduced intoan evaporator via an expansion valve causing the liquid water to evaporate continuously into vapour. By circling aworking uid through a heat exchanger located in the evaporator, the working uid is cooled and then subsequentlyused for cooling applications.

Since the interaction between the vapour and heat exchanger in the evaporator is very complicated and the vapourdensity changes greatly in space due to evaporation and condensation, the vapour experiences compressible turbulentow. Using COMSOL numerical simulation software package, this complicated process can be modeled and numericallysimulated. Fig. 1 is an example demonstrating how liquid phase water with initial temperature of 80C cools as afunction of time when subjected to a constant airow at the speed of 2m/s [2]. The gure shows results with andwithout considering evaporative cooling, and the results show a signicant dierence at the end of 20 minutes. UsingCOMSOL software, this study presents the interaction between vapour and the heat exchanger as well as how systemparameters such as vapour ow rate in the evaporator and pressure aect the cooling of the working uid circlingthrough the heat exchanger in the evaporator, which determines the performance of the system.

Figure 0.1: Temperature change hot water as a function of time.

References

[1] Zhai, X. Q., Qu, M., Li, Y., and Wang, R. Z., A review for research and new design options of solar absorption cooling systems,Renewable and sustainable energy reviews 15(9), 4416-4423 (2011)

[2] COMSOL Inc. Evaporative Cooling of Water

57


NONMODAL AND NONLINEAR DYNAMICS OF HELICAL MAGNETOROTATIONALINSTABILITY

George Mamatsashvili & Frank Stefani

Helmholtz-Zentrum Dresden-Rossendorf, PO Box 510119, D-01314 Dresden, Germany

The helical magnetorotational instability (HMRI), a relative of standard MRI (SMRI), has become a subject of activeresearch in recent years in connection with the experiments on magnetized cylindrical Taylor-Couette (TC) ows. Itoccurs in the presence of helical magnetic eld, consisting of azimuthal and axial components and, like SMRI with onlyaxial magnetic eld, taps into the rotational energy of the ow [1]. However, a main advantage of HMRI is that, beinggoverned by the Reynolds (Re) and Hartmann (Ha) numbers, it persists even at very small magnetic Prandtl numberstypical to liquid metals, in contrast to SMRI. The linear development of HMRI has been widely studied theoreticallyusing both classical modal (see [2] and references therein) and more recently by nonmodal [3] stability analysis, wherea fundamental connection between nonmodal dynamics and dissipation-induced (double-diusive) modal instabilities,such as HMRI, has been demonstrated (Fig. 1a,b). A series of specially designed liquid metal TC experiments [4, 5]provided the rst experimental evidence of HMRI and reproduced the main results of the linear theory, such as thestability threshold and propagation speed (frequency) of HMRI-wave. More importantly, these experiments revealedmuch richer dynamics of HMRI as a function of system parameters (Re, Ha, etc.) than that obtained from the linearanalysis only. These results prompted further theoretical studies of the nonlinear development of HMRI [6, 7, 8], butdetailed physics of its saturation and sustenance still remains missing, especially when comparison with the experimentis concerned.

Figure 0.1: Nonmodal growth factor for HMRI and in the nonmagnetic case vs. Rossby number (a) and its connection (red lines) withthe modal growth rate of HMRI (b). Energy spectra versus vertical wavenumber k in the quasi-steady state at two dierent regimes ofnonlinear saturation, at Re = 1590 (c) and Re = 3000 (d) for the same Ha = 12.

Motivated by the experimental results of [5], we investigate the evolution of HMRI, from its linear growth to nonlinearsaturation using numerical simulations. We show that depending on the Reynolds number, two regimes of saturationcan be realized. At Re below a certain critical value (but higher than the instability threshold), the saturation energylinearly depends on Re and the corresponding energy spectrum is dominated by the most unstable mode and itsmultiple wavenumbers (Fig. 1c), while at larger Re, the energy increases with Re, but not linearly, and the relatedspectrum looks like turbulent spectrum, being much smoother over wavenumbers (Fig. 1d). The nonlinear stateremains markedly axisymmetric (m = 0) and at high Re can be viewed as a 2D turbulence [9], whose properties arefurther examined.

References

[1] R. Hollerbach, G. Rüdiger, Phys. Rev. Lett., 95, 124501 (2005).

[2] O. Kirillov, F. Stefani, Y. Fukumoto, J. Fluid. Mech., 760, 591 (2014).

[3] G. Mamatsashvili, F. Stefani , Phys. Rev. E., 94, 051203 (2016)

[4] F. Stefani, T. Gundrum, G. Gerbeth, G. Rüdiger, M. Schultz, J. Szklarski, R. Hollerbach, Phys. Rev. Lett., 97, 184502 (2006)

[5] F, Stefani, G. Gerbeth, T. Gundrum, R. Hollerbach, J. Priede, G. Rüdiger, J. Szklarski, Phys. Rev. E., 80, 066303 (2009)

[6] J. Szklarski, G. Rüdiger, Astron. Nachrichten, 327, 844 (2006)

[7] W. Liu, J. Goodman, H. Ji, Phys. Rev. E, 76, 016310 (2007)

[8] A. Child, R. Hollerbach, B. Marston, S. Tobias, J. Plasma. Phys., 82, 18 (2016)

[9] Y. Zhao, J. Tao, O. Zikanov, Phys. Rev. E, 89, 033002 (2014)

58


ACOUSTIC DRAINAGE

Amihai Horesh, Matvery Morozov & Ofer Manor

Department of Chemical Engineering, Technion, Haifa, Israel

The drainage of liquid lms determines the fate of an abundant number of natural phenomena and engineeringapplications, from the stability of suspensions and emulsions and the eciency of particulate separation and coatingprocedures to the stability of tear lms and the adhesion of bacteria to solids. Here we explore the physics of drainageof a micron thick liquid lm trapped between a solid and a micro-bubble while it is exposed to a propagating MHzRayleigh surface acoustic wave (SAW).

The most interesting observation we report is related to the rate of drainage. In the absence of the SAW, theintermediate liquid lm between the bubble and the solid drains due to capillary stresses for a period of one to twelvehours (according with the viscosity of the draining liquid in our experiments). However, the drainage of the lm inthe presence of the SAW is reduced to minutes. The viscous penetration of the acoustic wave into the liquid generatesan acoustic ow that breaks the symmetry of the liquid lm. The lm deforms in a manner akin to a kinematic waveuntil capillary stresses, resisting this motion, impose self-similar lm geometry, supporting fast drainage of liquid outof the lm.

We explore this intriguing phenomenon using both experiment and theory. We have designed a well-dened experimentwhere we utilized previous ndings on the geometry of long bubbles moving in rectangular tubes. By abruptly arrestingthe motion of a bubble in a microuidic channel we imposed a model system for the drainage of a micron-thick convexlm. In particular, this procedure allows for reducing the dimensionality of the drainage. The micron-thick lmbetween the bubble and the solid was then exposed to a front of a MHz SAW, propagating in the solid substrate ofthe channel and along (and opposite) the draining path.

A corresponding theory of acoustic ow in the intermediate liquid lm is in good agreement with experiment, high-lighting the struggle between acoustic and capillary mechanisms in the microenvironment explored. In particular,both theory and experiment predict the time of drainage support a power low with the ratio between the acoustic andcapillary stresses in the liquid lm, which may be explained by the self-similar behavior of the draining lm.

Figure 0.1: A bubble in a microuidic channel under the inuence of a surface acoustic wave (SAW); from left to right: the SAW microuidicplatform, a sketch of the view of the bubble from above, a sketch of the cross section view of the bubble and the intermediate liquid lm.

59


NONLINEAR CONSEQUENCES OF THE DARRIEUS-LANDAU INSTABILITY INCOMBUSTION

(plenary lecture)

Moshe Matalon

Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801,USA

The most prominent intrinsic combustion instability is the hydrodynamic instability, discovered independently byDarrieus [1] and Landau [2]. It results from the gas expansion caused by the heat released during combustion, whichinduces hydrodynamic disturbances that enhance perturbations of the ame front. The Darrieus-Landau instabilityhas many ramications in combustion of premixed gases: it is responsible for the formation of sharp fold creases andcrests pointing towards the burned gas region, for the convex (towards the fresh mixture) curving of ames propagatingin narrow tubes, and for the self-wrinkling of the surface of large expanding ames.

Darrieus and Landau carried out a linear stability analysis of a planar premixed ame, treating the ame as a surfaceof density discontinuity that propagates at a constant speed. They showed that planar ames are unconditionallyunstable with wrinkles of short wavelength growing faster than wrinkles of long wavelength. Their result, however,becomes inadequate for short wavelength disturbances that are comparable with the ame thickness. Recent studiesexploited the multi-scale nature of the problem and incorporated in the modeling eects due to the internal amestructure that are described on the diusion length scale, which is much smaller than the hydrodynamic length.Asymptotic matching led to an expression for the ame speed that deviates from the (constant) laminar ame speedand depends on the mixture properties and local ow conditions [3, 4]. This led to the recognition that thermo-diusiveeects occurring inside the ame zone often induce stabilizing inuences that were not accounted for in the Darrieus-Landau description. In particular, in mixtures that are decient in their heavier (less mobile) component, such aslean hydrocarbon-air or rich hydrogen-air mixtures, thermo-diusive eects tend to stabilize the short wavelengthdisturbances. Large scale ames where diusion eects have a minimal inuence remain linearly unstable, whichraises the question about their long time evolution.

In this presentation we focus on the nonlinear development of hydrodynamically unstable ames. We show that,as a result of the instability, large-scale ames acquire cusp-like conformations with elongated intrusions pointingtoward the burned gas region, as shown in Fig 1. These structures are stable and, because of their larger surfacearea, propagate at a speed that is substantially larger than the laminar ame speed . The solid black curve in thegure is the ame front, the solid curves are representative streamlines, and the various color shades (blue to orange)correspond to regions of increased velocity. The ow pattern demonstrates the deection of streamlines upon crossingthe ame front, which is a consequence of gas expansion, and the induced vortical motion in the unburned gas that isotherwise at rest, which is responsible for sustaining the cellular structure by pushing" the crests upward. The results,based on the hydrodynamic asymptotic model in two-and three-dimensions, are derived (i) from a weakly-nonlinearanalysis, which assumes that the density contrast across the ame is relatively small, and (ii) from a fully-nonlinearnumerical study that is valid for realistic density variations [5, 6]. Finally, the eect of the Darrieus-Landau instabilityon turbulent ames will be demonstrated by showing, for conditions near criticality, the transition from a planar"turbulent ame brush propagating at a speed that is increased solely by the turbulence, into a much thicker brush ofhighly-corrugated cusped-shape ames that propagates at a speed that is further augmented by the instability [7, 8].

References

[1] G. Darrieus, Propagation dun front de amme, Unpublished work, presented at La Technique Moderne, (1938)

[2] L. D. Landau, On the theory of slow combustion, Acta Physicochimica USSR 19, 77 (1944)

[3] M. Matalon, C. Cui and J. Bechtold, Flames as gasdynamic discontinuities, J. Fluid Mech. 124, 239 (1982)

[4] M. Matalon and B.J. Matkowsky, Hydrodynamic theory of premixed ames: eects of stoichiometry, variable transport coecientsand arbitrary reaction orders, J. Fluid Mech. 487, 179 (2003)

[5] Y. Rastigejev and M. Matalon, Nonlinear evolution of hydrodynamically unstable premixed ames, J. Fluid Mech. 554, 371 (2006)

[6] F. Creta and M. Matalon, Strain rate eects on the development of hydrodynamically unstable ames, Proc. Combust. Inst. 33, 1087(2011)

[7] F. Creta and M. Matalon, Propagation of wrinkled turbulent ames in the context of hydrodynamic theory, J. Fluid Mech. 680, 225(2011)

[8] N. Fogla, F. Creta and M. Matalon, Eect of folds/pockets on the propagation of premixed turbulent ames, Combust. Flame 162,2758 (2015)

60


Figure 0.1: Cusp-like ame steadily propagating in a quiescent combustible gas mixture.

61


DISTURBANCE GROWTH DURING HAIRPIN VORTEX GENERATION IN ALAMINAR-BOUNDARY-LAYER FLOW

Kazuo Matsuura

Graduate School of Science and Engineering, Ehime University, 3 Bunkyo-cho, Matsuyama, Ehime, 790-8577, Japan

Eects of circulation on the evolution of vortex tubes and associated response of near-wall ows in the shear of laminarboundary-layer ows are investigated using a model proposed by Hon andWalker [1]. Direct numerical simulations withair freestream Mach number of 0.5 are conducted. Firstly, dynamics of single hairpin vortex is investigated. Numeroussecondary hairpin vortices much more than previously reported, which are regularly aligned in the streamwise direction,are allowed to be newly generated according to the shear-layer instability of the legs of an initial hairpin vortex. Smallscale turbulence is then produced when the circulation is suciently large. Secondly, a straight vortex tube model isinvestigated. Sinuous deformation of a shear layer, which leads to the generation of discrete hairpin vortices, becomesobvious especially near the upper region of the vortex tube. In order to quantify the initial instability triggering thegeneration of the secondary hairpin vortices, quasi-linear stability analysis is conducted. While only one unstablemode appears when the circulation is small, two modes, i.e., o-wall mode and near-wall mode, appear when thecirculation is large [2]. The cases of circulation where the two modes appear correspond to those of circulation wherethe production of small-scale turbulence is observed in the simulations of the single hairpin vortex. Evolution of themodes associated with hairpin vortex generation is investigated.

Figure 0.1: Generation of small-hairpin vortices from a modeled hairpin vortex [2]

References

[1] T.L. Hon and J.D.A. Walker , Evolution of hairpin vortices in a shear ow, Computers and Fluids 20(3), 343-358 (1991)

[2] K. Matsuura, Direct numerical simulation of a straight vortex tube in a laminar boundary-layer ow, Int. J. Comp. Methods andExp. Measur. 4(4), 474-483 (2016)

62


PARAMETRICALLY EXCITED LONG-SCALE MARANGONI CONVECTION IN A LIQUIDLAYER COVERED BY INSOLUBLE SURFACTANT

Alexander B. Mikishev1,2 & Alexander A. Nepomnyashchy3

1Department of Physics, Sam Houston State University, Huntsville, TX 77341, USA2Embry-Riddle Aeronautical University-Worldwide, Daytona Beach, FL 32114, USA

3Department of Mathematics, Technion-Israel Institute of Technology, Haifa, 3200 Israel

We consider an innite horizontal liquid layer with a deformable upper surface heated from below so that appliedheated ux changes periodically with the zeroth average value. The liquid layer is covered by insoluble surfactant.In our previous reseach of the problem [1], in the absence of the surfactant, we found the existence of a monotonicmode of instability with respect to large-scale disturbances. The presence of an insoluble surfactant on the freesurface generates an additional mode of instability an oscillatory one. By means of a multi-scale method, weaklynonlinear amplitude equations which govern the spatio-temporal evolution of the surface distortion and disturbancesof temperature and surfactant concentration, are derived. The bifurcation analysis for stationary waves, which appeardue to the monotonic instability of the base solution, is performed. Also, other types of 2D convective patterns areconsidered.

The research was partially supported by ERAU Research Award #13373.

References

[1] A.B. Mikishev, A.A. Nepomnyashchy, and B.L. Smorodin, Long-scale nonlinear evolution of parametrically excited Marangoni con-vection, J. Physics: Conf. Series 216, 012004 (2010)

63


IMMERSED BOUNDARY METHOD AND ASYMPTOTIC NUMERICAL METHOD FORSTEADY SIMULATION OF INCOMPRESSIBLE VISCOUS FLOW AROUND MOVING

OBSTACLE

A. Monnier1, J.M. Cadou1, G. Girault1,2 & Y. Guevel1

1Univ. Bretagne-Sud, EA 4250, LIMATB, F-56100 Lorient, France2Centre de recherche, Ecoles Militaires de Saint-Cyr Coëtquidan, F-56381 Guer, France

Fluid-structure interaction (FSI) is a very important issue for marine structures (submarine cables or exible pipes),engineering structures (large bridges) or in the energy sector (wind turbines, fuel rod in nuclear plant).

Thus, it is known that elastic cylinders in uid ow experience structural oscillations caused by vortex shedding,known as vortex-induced vibrations (VIV). The academic example is the elastically mounted rigid cylinder in a steadyincoming ow, free to oscillate in the cross-ow direction ([5]). Such a problem belongs to the class of FSI problem.

In this study, it is proposed to perform a numerical bifurcation analysis of an incompressible viscous cross-ow arounda moving obstacle. For this purpose, an Eulerian Finite Element (FE) discretization is associated with immersedboundary methods to take account of FSI eects. Bifurcation analysis is performed using the Asymptotic NumericalMethod (ANM) which associates a perturbation method with a continuation technique.

For the model, the ow is described according to the Navier-Stokes (NS) equations. The obstacle is described usingthe Penalty Method, rstly. Thus, it is dened an additional term into the NS equations corresponding to forcescreated at the uid/solid interface. This technique is easy to implement but precision on the obstacle description isweak. To improve precision, the uid/solid interface is precisely tracked using the Ghost-Cell method ([1], [2]).

The bifurcation analysis is realized using the ANM. Perturbing the unknowns into power series expansions with highorder terms and adapting bifurcation indicators to the FSI context, both steady-state and Hopf bifurcations in theuid can be computed.

For the steady-state bifurcation, it is demonstrated that the criterion proposed by Cochelin and Médale [3] allows toprecisely determine the bifurcation. This criterion is based on detection of a geometric series into the power seriesexpansion and allows to compute the geometric factor which represents the critical parameter, namely the criticalReynolds number. Branch switching technique is also introduced and allows to compute the bifurcated solutionsemanating from the steady-state bifurcation.

For the Hopf bifurcation, the algorithm developed by Brezillon et al. [4] is adopted and a time periodic solution hasto be computed. A bifurcation indicator is introduced and main steps of the algorithm consist in searching minimumvalues of the indicator and using the latter as initial guesses in a Newton procedure.

Several academic problems are studied in order to evaluate the robustness of ANM based techniques in a FSI context.The bifurcation analysis of a ow in a rectangular channel with sudden contraction and expansion is proposed. Inthis example, FSI techniques are used to describe the boundaries. Finally, the academic problem of a ow arounda cylinder free to oscillate is analysed and Hopf bifurcation is obtained. All the numerical results demonstrate theeciency of the proposed algorithm.

References

[1] R. Mittal, H. Dong, M. Bozkurttas, FM Najjar, A. Vargas, and A. von Loebbecke, A versatile sharp interface immersed boundarymethod for incompressible ows with complex boundaries. Journal of computational physics, 227(10), 4825 4852 (2008).

[2] Y.H. Tseng & J.H. Ferziger, A ghost-cell immersed boundary method for ow in complex geometry. Journal of computational physics,192(2), 593 623 (2003).

[3] Cochelin, B. & Medale, M. Power series analysis as a major breakthrough to improve the eciency of Asymptotic Numerical Methodin the vicinity of bifurcations. Journal of Computational Physics 236, 594 607 (2013).

[4] Brezillon, A., Girault, G. & Cadou, J. M. A numerical algorithm coupling a bifurcating indicator and a direct method for the compu-tation of Hopf bifurcation points in uid mechanics. Computers & Fluids 39, 1226 1240 (2010).

[5] Placzek, A., Sigrist, J.-F. & Hamdouni, A. Numerical simulation of an oscillating cylinder in a cross-ow at low Reynolds number:Forced and free oscillations. Computers & Fluids 38, 80 100 (2009).

64


MULTIPLE SOLUTIONS IN SWIRLING JET FLOWS

Davide Montagnani & Franco Auteri

Politecnico di Milano, Milano, Italy

Vortex breakdown is a remarkable feature of several ows, such as tip vortices produced over delta wings, rotatingpipe ows and swirling jets. Vortex breakdown occurs as the rotational-to-axial velocity ratio exceeds a critical value:an abrupt change of the axial velocity near the axis occurs, a stagnation point appears in the ow as the vortexcore widens and a new coherent structure replaces the jet-like state. Experimental investigations carried out overdierent ows have identied three predominant breakdown congurations: the bubble, the spiral and the cone. Theexperimental investigations have led authors to ambiguous and conicting conclusions: for instance, it is not clearif the breakdown results from helical instabilities or it is an independent state, over which the helical instabilitiesmay grow. Experimental investigations are made dicult by the strong sensitivity of the ow to slight variations ofparameters, external disturbances, geometry of the domain and far-eld conditions. All these factors can alter thealready complex behavior of the ow in the space of parameters (Re, S): the observed hysteretic behavior and domainsof multiple solutions may be blurred by the high sensitivity of the ow to perturbations[6].

Numerical analysis of a swirling jet incompressible ow is performed in order to describe a region of the space ofparameters (Re, S) and unravel at least some of the phenomena located in this region. First, continuation of the steadyaxisymmetric baseow is performed for dierent values of swirl number S starting from the unique solution of the Stokesproblem, being the problem linear. Arc-length continuation method is used in order to cope with multiple solutionsoriginating from turning point bifurcations. Global stability analysis is performed to better describe the multiple steadysolutions and check the consistency of the results found. Once a bifurcation is found, its continuation in the (Re, S)space is performed in order to draw the corresponding neutral curve. Higher-codimensional bifurcations originateat the intersections of dierent neutral curves. Centre-manifold reduction of the bifurcating ow[1] is performed todescribe the local behavior of the ow in a neighbourhood of a bifurcation: even though the radius of convergence ofthe low-dimensional approximation is likely to be very small, the weakly non linear analysis is able to give some localinformation about the structural modications in the phase space in a neighbourhood of the bifurcations.

The present results reveal the existence of a multiple-solution domain: modal analysis shows that the intermediatesolutions are unstable and connected to the outer stable solutions by two turning point bifurcations. The descriptionof a limited region of the space of parameters (Re, S) will be presented in details at the conference.

Figure 0.2: Slice of a multiple-solutions domain: average axial velocity on the axis as a function of Re, for xed S.

References

[1] M. Carini, F. Auteri, F. Giannetti, Centre-manifold reduction of bifurcating ows, J. Fluid Mech 767, 109145 (2015).

[2] P. Billant, J.M. Chomaz, P. Huerre, Experimental study of vortex breakdown in swirling jets, J. Fluid Mech 376, 183219 (1998).

65


PROPAGATING SURFACE ACOUSTIC WAVES CAN DRIVE COATING FLOWS

Matvey Morozov, Amihai Horesh, & Ofer Manor

Department of Chemical Engineering, Technion Israel Institute of Technology, 32000 Haifa, Israel

Recent experimental observations revealed a rich variety of physical phenomena arising from the interaction of thinliquid lms with MHz-frequency surface acoustic waves (SAW) [1, 2]. In this work we theoretically investigate theinteraction of a Rayleigh SAW with a thin liquid lm lying atop a solid substrate. Specically, we revisit the Landauand Levich analysis [3] of a coating ow in the case where the ow in the lm is supported by a Rayleigh SAW,propagating in the solid substrate as shown in Fig. 0.1. By means of the lubrication approximation and multiscaleasymptotic expansion of the equations describing the uid ow due to SAW, we obtain an evolution equation governingthe large-scale dynamics of the lm. Further numerical analysis of the evolution equation reveals that the SAW-drivenow in the lm is similar to a dip coating ow. We show that in a steady state the thin-lm evolution equation reducesto a generalized Landau-Levich equation with the dragging velocity, imposed by the SAW, depending on the locallm thickness. We also demonstrate that the generalized Landau-Levich equation has a branch of stable steady statesolutions and a branch of unstable solutions. The branches meet at a saddle-node bifurcation point corresponding tothe threshold value of the SAW intensity. Below the threshold value no steady states were found and our numericalcomputations suggest a gradual thinning of the liquid lm from its initial geometry [4].

Figure 0.1: A at liquid lm of the constant thickness h∞ is dragged out of a static meniscus with curvature 1/R.

We further employ the thin-lm evolution equation to elucidate the eect of SAW excitation on a long bubble connedin a rectangular capillary. It has been shown that propagation of a long bubble through a polygonal capillary lledwith liquid results in a thin liquid lm sandwiched between the bubble and the walls of the channel [5]. We consideredthe latter lm in the presence of a SAW propagating along one of the channel walls. Our numerical analysis suggeststhat SAW excitation greatly accelerates the decay of the liquid lm clamped under the bubble.

References

[1] A. R. Rezk, O. Manor, J. R. Friend, and L. Y. Yeo, Unique ngering instabilities and soliton-like wave propagation in thinacoustowetting lms, Nat. Commun. 3, 1167 (2012).

[2] G. Altshuler and O. Manor, Spreading dynamics of a partially wetting water lm atop a MHz substrate vibration, Phys. Fluids 27,102103 (2015).

[3] L. Landau and B. Levich, Dragging of a liquid by a moving plate, Acta Physicochem. URSS 17, 141153 (1942).

[4] M. Morozov and O. Manor, An extended Landau-Levich model for the dragging of a thin liquid lm with a propagating surfaceacoustic wave, J. Fluid Mech. 810, 307322 (2017).

[5] H. Wong, C. J. Radke, and S. Morris, The motion of long bubbles in polygonal capillaries. Part 1. Thin lms, J. Fluid Mech. 292,71 (1995).

66


MAXIMAL HEAT TRANSFER BETWEEN TWO PARALLEL PLATES

Shingo Motoki, Genta Kawahara & Masaki Shimizu

Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 5608531, Japan

We explore a velocity eld maximizing heat transfer between two parallel plates of a constant temperature dierence.In this work, we found optimal states which give maximal transfer, i.e. wall-normal heat ux, under the xedtotal energy dissipation (or equivalently total enstrophy). The velocity eld is supposed to be incompressible, time-independent and periodic in the wall-parallel directions, and temperature is determined in terms of the velocity asa solution to an advection-diusion equation. By using a variational method, we derive non-linear EulerLagrangeequations, and numerically solve them to obtain the optimal states. The solutions have been obtained by using thesame numerical procedure as in Motoki et al. [1]. The present variational problem is similar to that formulated byHassanzadeh et al.[2]; however, we consider a no-slip boundary condition and extend a search range of optimal statesto a three-dimensional velocity eld.

The strength of velocity eld u is measured by Péclet number Pe = H2⟨|∇u|2

⟩1/2/κ (where H and κ respectively

indicate the distance between the bottom and top plates and the thermal diusivity, and ⟨·⟩ is a volume average).For small Pe, the optimal state exhibits a two-dimensional velocity eld which consists of large-scale circulation rollsshown in gure 0.1(a). For large Pe, however, a three-dimensional optimal state arises from the two-dimensionalsolution. As Pe increases, in the three-dimensional velocity eld, convection cells are formatted, and then small-scalevortex structures appear near the bottom and top plates so that they may bring about the higher heat ux (see gure0.1b).

In the three-dimensional optimal states, we found the scaling of the maximal Nusselt number Nu with Pe as Nu ∼Pe2/3 (gure0.1c). By estimating the Rayleigh number Ra from the total energy budget equation for the Boussinesqequations, Pe2 = Ra(Nu−1) (see [2]), the scaling can be related to Nu ∼ Ra1/2. The exponent 1/2 of Ra is consistentwith the scaling of the upper bound in the RayleighBénard convection with the no-slip boundary condition [3, 4].

In our presentation, we will show the bifurcation properties of solutions to the non-linear EulerLagrange system, anddiscuss the mechanisms of heat transfer enhancement and the scaling of Nu with Pe and Ra.

Figure 0.1: (a,b) Isosurfaces of the temperature uctuation θ about the conductive state in the optimal states. Red and blue objectivesrepresent isosurfaces of θ/∆T = +0.35 and −0.35, respectively, where ∆T is the temperature dierence between the bottom and top plates.The contours and vectors in (a) respectively show the distribution of θ and the velocity vectors (uy, uz) in the plane x = 0.5πH = 0. (c)Nusselt number Nu as a function of Péclet number Pe in the optimal states. Red circles indicate the optimal states and blue circles arevalues obtained in the two-dimensional velocity eld. The dashed line represents the power t Nu − 1 = 0.082Ra2/3 determined in therange 1800 < Pe < 8800. The inset shows the compensated Nu.

References

[1] S. Motoki, G. Kawahara and M. Shimizu, Optimal heat transfer enhancement in plane Couette ow, arXiv:1702.03412 [physics.u-dyn](2017)

[2] P. Hassanzadeh, G. P. Chini and C. R. Doering, Wall to wall optimal transport, J. Fluid Mech., 751, 627662 (2014)

[3] C. R. Doering and P. Constantin, Variational bounds on energy dissipation in incompressible ows. III. Convection, Phys. Rev. E, 53,59575981 (1996)

[4] S. C. Plasting and R. R. Kerswell, Improved upper bound on the energy dissipation rate in plane Couette ow: the full solution toBusse's problem and the ConstantinDoeringHopf problem with one-dimensional background eld, J. Fluid Mech., 477, 363379(2003)

67


PREDICTION OF THIN PLATE FLUTTER INSTABILITY IN TURBULENT FLOWS BASEDON LINEAR STABILITY ANALYSIS

Johann Moulin & Olivier Marquet

ONERA-DAFE, 8 rue des Vertugadins, 92190 Meudon, France

Among aeroelastic instabilities, utter has been widely investigated due to its destructive eects on structures. Thecritical velocity above which the instability arises is highly dependent on the shape of the particular body. The mostwidely used method to determine this velocity is based on the determination of utter-derivatives [1], for which ananalytical solution only exists in the case of a perfectly streamlined body [2]. Otherwise, experimental or numericalinvestigations are needed to determine those utter-derivatives.

A linear stability analysis is proposed here to predict the utter instability of a rectangular plate mounted on twosprings (pitching and heaving) in a turbulent ow. A similar approach has been recently used to predict the pathoscillations of buoyancy-driven bodies [3] in low-Reynolds number regime, and is here extended to high-Reynoldsnumber ows. The base ow around the xed plate is computed as a steady solution of the RANS equations, closedwith a Spalart-Allmaras model. The linear stability of this base ow is investigated by determining the spectrumof the uid/structure Jacobian operator, which is obtained by linearizing the uid RANS equations, the turbulencemodel and the structural equations.

Lift coecients of the steady ow have been computed at various angles of attack and Reynolds number Re = 27500(Figure a) showing that the Spalart-Allmaras model well reproduces the experimental results of [4]. For zero angleof attack, the laminar ow detaches at the sharp-corner leading-edge and reattaches around one sixth of the chord asresult of the creation of turbulent eddy viscosity. A turbulent boundary layer then develops and separates at the blutrailing-edge, forming a recirculation region.

To reproduce the experimental conditions of [4], the uid-structure stability analysis of the zero-angle of attacksolution is performed for the non-dimensionnal natural frequencies ω0,h = 0.16 (heaving) and ω0,p = 0.19 (pitching).The eigenvalue spectrum displayed in Figure b exhibits two unstable modes, illustrated by the blue and red dots. Thefrequency of the blue eigenvalue corresponds to a Strouhal number of 0.14 based on the plate width, characteristicof a uid wake mode (Figure c, top). The frequency of the red eigenvalue is much lower (0.15) and close to theheaving frequency ω0,h. In addition, the spatial structure of the mode highly diers from the wake mode one since it isconcentrated in the leading-edge recirculation regions (Figure c, bottom). This mode seems to be responsible for theutter instability. A mode associated to the pitching motion is also found in the spectrum but is stable for this set ofparameters. By tuning the natural pitching and heaving frequencies, we will show how the system stability is modiedby the uid-structure interaction. In particular, the prediction of the utter velocity threshold will be compared tothe experiments of [4].

Figure 0.1: (a) Some base ow features : lift versus incidence curve (top) and leading edge recirculation regions (bottom); (b) Spectrumof the uid-structure system.Two unstable modes are observed : a uid wake mode and a uid-structure utter mode; (c) Axial velocityof the unstable wake (top) and utter (bottom) modes of the uid-structure system (α = 0).

References

[1] R.H. Scanlan, J.J. Tomko, Airfoil and bridge deck utter derivatives, J. of Eng. Mech., 97, 1717-1737 (1971).

[2] T. Theodorsen, General Theory of Aerodynamic Instability and the Mechanism of Flutter, NACA Technical Report 496 (1935).

[3] J. Tchoufag , D. Fabre D., and J. Magnaudet, Global linear stability analysis of the wake and path of buoyancy-driven disks and thincylinders, J. Fluid Mech. , 740, 278-311 (2014).

[4] X. Amandolese, S. Michelin, M. Choquel, Low speed utter and limit cycle oscillations of a two-degree-of-freedom at plate in a windtunnel, Journal of Fluids and Structures 43, 244-255 (2013).

68


A STUDY ABOUT THE STEADY-STATE REGIME ON ROTATING COMPRESSIBLE FLUIDSAND ITS APPLICATION ON A DIFFRACTION PROBLEM

Erick Muiño-García1 & José Marín-Antuña2

1Department of Applied Physics, CINVESTAV-IPN, Merida, Yucatan 97310, Mexico2Department of Theoretical Physics, Faculty of Physics, University of Havana, Vedado, La Habana 10400, Cuba

We develop a general study about the steady-state regime on rotating compressible uids. We deduce an equation forthe amplitude of the stabilized oscillations, and we obtain its fundamental solution. We establish the non-stationaryproblem for the eld of velocities generated by the diraction of an acoustic wave in a nite barrier within a rotatingcompressible uid. Additionally, we analytically solve this problem and we study its behavior when the time tends toinnity. Then we apply the previously developed theory for the steady-state regime to obtain the mentioned eld ofvelocities for long times, and by doing so, we nd that the system reaches a steady-state regime. We verify that thesame expressions of the limit amplitude are obtained.

69


INTERFACIAL INSTABILITY OF PHASE CHANGE(plenary lecture)

Ranga Narayanan

Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA

The interfacial instability of phase change is manifested by morphological changes of the interface in the face of imposedgradients. For example in the case of evaporative instability or solidication instability an imposed temperaturegradient leads to positive reinforcement of phase change and interface deection. The interfacial energy as wellas thermal diusion decide the wavelength of the patterns. Likewise in the case of electrodeposition an imposedvoltage dierence leads to both electrochemical potential as well as ion concentration gradients which act to aggravatedisturbances at the electrode surfaces. The interfacial energy per unit area, which is the same as the interfacialtension in the case of uid/uid interfaces, acts to modify the pressure dierence in the case of uid/uid systems,the equilibrium melt temperature in the case of solid/ liquid interfaces, and the rate of electron transfer in the caseof electrode/electrolyte interfaces. While the role of interfacial energy is dierent in the three phase change problems,the eect is the same. It is one of stabilization.

In this talk we will contrast the above three phase change instabilities and explain why it is easy to see clear discernibleinterfacial patterns in the case where thermal gradients are imposed but not so easy to see clear features in the casewhere liquid concentration gradients are imposed. The common features of the models but the stark dierences in theresults will be discussed by way of computations and physical experiments.

Acknowledgment: Support from NASA-CASIS GA-2015-218 is gratefully acknowledged.

70


THE HYDRODYNAMIC BROOM: SWEEPING OF A POLYMER FILM BY MEANS OFCONVECTION CELLS IN A LIQUID LAYER

Iman Nejati1, Mathias Dietzel2 & Steen Hardt2

1Institute for Technical Thermodynamics, TU Darmstadt, Darmstadt, Germany2Institute for Nano- and Microuidics, TU Darmstadt, Darmstadt, Germany

Over the last decades, various methodologies to micro-pattern thin polymer lms have been developed with the aimof rectifying the shortcomings of more conventional fabrication methods based on photo-lithography. In this context,methods based on hydrodynamic instabilities in thin lms are of particular interest, since they achieve opticallysmooth structures while allowing for parallel patterning of large areas. On the one hand, lm deformations causedby long-wavelength (LW) instabilities are notorious for exhibiting irregularities in pattern wavelength. On the otherhand, while the pattern planform symmetry aliated with short-wavelength (SW) cellular instabilities is typicallyvery regular, the surface deformations remain shallow in comparison to the lm thickness. Here, a novel experimentalapproach to pattern thin polymer lms is presented, which combines the uniformity of the cellular SW-instabilitywith large LW-interfacial deformations. To this end, a conjugated system, which is composed of a thin polymer lm(less than 20 microns) curable by ultraviolet (UV) light and a thick layer of peruorinated hydrocarbon (FC-70, a fewhundred microns), is exposed to a transverse temperature gradient (gure 1(a)).

Figure 0.1: (a) Schematic conguration of the coupled system (side view). (b) Typical three dimensional topography plot of the liquid-liquid interface. Here, the thickness of the upper layer is 550 µm, while the lower lm has the thickness of 13 µm. (c) Typical simulationresult for shear-driven LW deformation of the lower lm (side view, in blue). For illustrative purposes, the upper layer is rescaled. Thedimensionless horizontal and vertical coordinates of the lower lm are denoted by X and H, respectively.

By exceeding a critical temperature dierence, SW Bénard-Marangoni convection cells develop in the upper liquidlayer, which shear and deform the liquid-liquid interface into a periodic array of lenses. The pattern at the liquid-liquidinterface has the same horizontal planform symmetry as the convection cells emerging in the upper layer. Subsequently,the patterned polymer lm is cured and solidied by UV light (see gure 1(b)). Next to fabricating a periodic arrayof lenses, this method can also be used for producing other shapes of interest. This can be achieved with relative easeby engineering the temperature distribution at the liquid-gas interface using a relief mask along the cooled substrate.To analyze the pattern formation in more detail, the behavior of the coupled system is simulated by means of amathematical model (see gure 1 (c)). More specically, the velocity and temperature elds in the upper layer areobtained from the two-dimensional (2D) Navier-Stokes and energy equations, while the evolution of the lower thin lmis captured in the framework of the lubrication approximation. It is shown that the behavior of the coupled systemreveals some remarkable dierences when compared to the corresponding single-layer setup, especially with respect tothe marginal stability and bifurcation behavior [1]. The numerical results are found to be in good agreement with theexperimental ndings.

References

[1] I. Nejati, M. Dietzel, S. Hardt, Conjugated liquid layers driven by the short-wavelength Bénard-Marangoni instability: Experimentand numerical simulation, J. Fluid Mech. 783, 4671 (2015).

71


EFFECT OF LOW REYNOLDS NUMBER INSTABILITIES ON THE DRAG AND MIXINGCAPABILITY

Nikesh, S. W. Gepner & J. Szumbarski

Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Nowowiejska 24, 00-665,Warsaw, Poland

Flow in a channel with grooves parallel to the ow direction has been studied by means of spectrally accurate DirectNumerical Simulations, with the primary goal of establishing channel geometries that enhance achievable laminarmixing at possibly low drag increase. This investigation follows the lines of the previous research [1] where low-Reynolds-number ow destabilizing by transversely oriented wall waviness has been reported. The detailed mechanismof destabilization by grooves parallel to the ow direction have been further investigated in the recent work of Flo-ryan [2]. In the current study, symmetric grooves of dierent shapes of the industrial usefulness (trapezoidal, triangle,square) of moderate and large amplitudes (up to 80 % of the mean opening) are considered. Stability with respectto small disturbances is investigated using the direct numerical simulations (DNS) of the Linearized Navier-Stokes(LNS) equations, performed by means of the open-source ow solver Nektar++ [3]. In these simulations, the long-termasymptotic response to initial perturbation is determined and the least attenuated (or most amplied) form of theperturbation (the unstable mode) is identied and tracked over a range of geometric and ow parameters. Criticalconditions for the onset of instabilities at a range of parameters are also obtained. The groove shape having thelargest mixing capability is identied by analyzing the structure of the disturbance. Finally, nonlinear saturationof the unstable modes and the resulting secondary ows are examined by means of direct numerical solution of thefull nonlinear Navier-Stokes system. Our results indicate that secondary ows, at saturation, can maintain the dragreducing properties for a limited range of Reynolds numbers.

Figure 0.1: (a) Geometry of the channel with corrugation amplitude and wave number, α =1 and corrugation amplitude S, (b) isolinesof the non-dimensional ow rate w.r.t to the ow rate of the plane Poiseuille ow, QP indicating the drag reducing and drag increasingregion and isolines of the Critical Reynolds number, Recr of the unstable mode.

References

[1] Szumbarski, J., Instability of viscous incompressible ow in a channel with transversely corrugated walls, Journal of Theoretical AndApplied Mechanics 45(3), 659-683 (2007).

[2] A. Mohammadi, H. V. Moradi & J. M. Floryan, New instability mode in grooved channel, J. Fluid Mech. 778, pp. 691-720, (2015).

[3] Cantwell, C.D., Moxey, D., Comerford, A., Bolis, A., Rocco, G., Mengaldo, G., Grazia, D. De, Yakovlev, S., Lombard, J.-E., Ekelschot,D., Jordi, B., Xu, H., Mohamied, Y., Eskilsson, C., Nelson, B., Vos, P., Biotto, C., Kirby, R.M. & Sherwin, S.J., l Nektar++: Anopen-source spectral element framework, Computer Physics Communications 192, 205-219, (2015).

72


VISCOELASTIC EFFECT ON ROLL CELLS IN ROTATING PLANE COUETTE FLOW

Tomohiro Nimura & Takahiro Tsukahara

Department of Mechanical Engineering, Tokyo University of Science, Chiba, 278-8510, Japan

In the wall-bounded shear ow, longitudinal structures such as quasi-streamwise rolls (or vortex) and low-speed streaksnear the wall are not formed separately, but they interact with each other, giving rise to self-sustaining process ofthe turbulent motions [1]. This process would be disturbed by uid viscoelasticity, when polymer/surfactant additiveis mixed into a water ow: that is, the Toms eect. The eects of viscoelasticity on the streamwise structures areknown to cause suppressions of eddies, bursting, and frictional drag in the wall turbulence [2, 3]. However, thoseeects that contribute to the streamwise-structure variations and the ow stability are not yet simple to interpret.If one may focus on the self-sustaining process aected by viscoelasticity with fully-turbulent background ows, thewide range of energy spectra of vortices should make the analysis complicated. In other words, it would be dicultto discriminate the inuence only of viscoelasticity from the self-sustaining process, because the elasticity may induceinstability that is dierent from the inertial one. Here, we propose a simple way to reveal the viscoelastic eects onstreamwise rolls by choosing the rotating plane Couette ow (RPCF) as a wall-bounded shear ow. In RPCF, variousow regimes including laminar and turbulent states are provided by stable/unstable stratication due to the spanwisesystem rotation. The property of roll cells is determined deterministically, uniquely, and dependently on the twocontrol parameters: the Reynolds number Rew and the rotation number Ω (see their denitions in Ref. [4]). This factenables us to make up arbitrarily a ow accompanied by two-dimensional steady roll cells in laminar ow. It shouldbe noted that the roll cells can organize even in turbulent ow [4]. Simply put, one can investigate systematically theviscoelastic eects on the roll cells to reveal the interaction among modulated turbulence factors, in RPCF.With emphasis on steady roll cells in laminar ows as the initial target of parametric studies, we conducted directnumerical simulation. We set up small domains of 7.5h × h × 2.0h or 3.0h (h: the channel width), to capture, atleast, a pair of roll cells. Figure 1 (a) indicates the steady 2-dimensional roll cell at Rew = 25 and Ω = 10 in theNewtonian uid, which structure is homogeneous in the x direction. Figure 1 (b) shows also the steady roll cell, but ina viscoelastic uid at Rew = 100 and the same Ω as (a). Although the ow (b) exhibits the uniformity in x similarly to(a), the roll shape is deformed by the viscoelastic force, predicted by using the Giesekus model [5] for the constitutiveequation. The deformed roll cells in (b) has an intense vorticity compared to (a). It is conjectured that (b) arisesfrom the suppression of spanwise-momentum transport in the ow, where the 3-dimensional roll cells are formed inNewtonian counterpart. We would discuss its mechanism and show other variations at dierent parameter values.

Figure 0.1: Instantaneous velocity elds in the cross section. (a) Newtonian uid and (b) viscoelastic uid for the Weissenberg numberof Wiw = 1500 and the viscosity ratio between solvent and solution of β = 0.8. Contour of streamwise velocity uctuation u′. Velocityvectors in the cross-streamwise plane show the streamwise rolls. The length of reference vector is same in (a) and (b)

References

[1] F. Walee, Self-sustaining process in shear ows, Phys. Fluids, 9(4), 883900 (1997).

[2] R. Sureshkumar, A. N. Beris, and R. A. Handler, Direct numerical simulation of the turbulent channel ow of a polymer solution,Phys. Fluids 9(3), 743755 (1997).

[3] K. Kim et al., Dynamics of hairpin vortices and polymer-induced turbulent drag reduction, Phys. Rev. Lett., 100, 134504 (2008).

[4] T. Tsukahara, N. Tillmark, and P. H. Alfredsson, Flow regimes in a plane Couette ow with system rotation, J. Fluid Mech. 648, 533(2010).

[5] H. Giesekus, A simple constitutive equation for polymer uids based on the concept of deformation-dependent tensorial mobility, J.Non-Newt. Fluid Mech. 11, 69109 (1982).

73


CHAOS ANALYSIS OF TRANSITION FLOW IN A NATURAL CONVECTION LOOP

Hiroyuki Nishikawa & Takashi Watanabe

Graduate School of Information Science, Nagoya University, Nagoya, 464-8601, Japan

An experimental and a time series analysis have been made on the ow in a rectangular natural convection loop,and the nonlinear dynamics of chaotic ow and the bifurcation of ow modes are investigated. The loop made ofPyrex glass tube of inner radius 1.5cm is close to a square in shape. The lower and upper branches are heated atconstant heat ux and cooled at constant wall temperature, respectively, and the right and left branches are thermallyinsulated. Heat input Q ranges from 0 to 950W (1.40 to 25.1 kW/m2). In the present rectangular loop, an instabilitywith reversal ow occurred in the wide range from Q = 150 to 900W . When the ow reversal occurs, the oscillationabruptly amplies. We reveled the conditions under which the unstable ow occurs by changing the displacement angleθ in the vertical plane. Figure 1 shows the bifurcation diagram made by the relationship between average amplitudeand frequency in various measured data. In the case of θ = 0 (horizontal position), with the increase of Q, the owin the loop shows transitions from a laminar to an unstable ow, and the unstable to a turbulent ow. Even whenthe heat input is constant, a mutual transition between the unstable ow and the turbulent ow may occur. Thesetransitions are induced by the dynamic disturbance inside the uid [1]. On the other hand, when θ = 10, the reversalow does not occur, and the transition from the laminar ow to the turbulent ow occurs directly. In addition, ahysteresis for the temperature oscillation occurs remarkably in the case where the heating input is increased ("upcondition") and the case where it is decreased ("down condition"). In order to understand the characteristics of owtransitions, a geometrical structure and a scaling property for reconstructed attractor in a phase space were evaluatedby the recurrence plot analysis [2] and various information measures [3]. As a result, it was found that the attractor ofthe turbulence data have a periodical structure and a fractal property (scaling law) similar to the unstable ow. Whenfocusing on a recurrence time of the attractor, we can explain the ow transition as a second order phase transitionphenomenon. It also depicts the identication of the order parameter characterising the ow state transition.

Figure 0.1: Bifurcation of oscillations in a rectangular natural convection loop.

References

[1] H. Nishikawa, K. Matsumura, S. Okino, T. Watanabe, F. Suda, Detection of the chaotic ow instability in a natural convection loopusing the recurrence plot analysis and the nonlinear prediction, J. Thermal Sci and Technol. 10-2, 15-00236 (2015)

[2] N. Marwan, M. C. Romano, M. Thiel, J. Kurths, Recurrence plots for the analysis of complex systems, Physics Reports 438, 237329(2007)

[3] ] M. Ichimiya and I. Nakamura, Analysis of laminar-turbulent transition process in mixing layer with various information mea-sures,Trans. JSME, 83-845, 16-00497, 1-19 (2017)

74


DYNAMICS OF HIDDEN ATTRACTORS IN SIMPLIFIED NOVEL 5-D HYPERCHAOTICLORENZ-LIKE SYSTEMS

Olurotimi S. Ojoniyi1 & Abdulahi N. Njah2

1Department of Physics, Tai Solarin University of Education, Ijagun, Ijebu Ode, Ogun state, Nigeria2Department of Physics, University of Lagos, Lagos, Nigeria

Apart from the classical work of Poincare on the existence of chaos, Lorenz model [1] in uid mechanics has servedas a paradigm for unusual dynamics in weather and other disciplines. In reality, we have high dimensional dissipativedynamical systems which have complex time signals. These systems may be used in secure communications, highquality synchronization, neural networks and uid dynamics. [2] A number of high dimensional dissipative autonomous5-D Lorenz and Lorenz-like systems have been proposed with terms more than ten and with equilibrium points. [3],[4] A 5-D system with ten terms and without equilibrium (hidden attractors) has also been recently proposed. [5]In this paper, by extensive numerical search, we present simplied novel 5-D hyperchaotic Lorenz-like models withnine terms, one without equilibrium points, the other with line equilibrium. The dynamics of these systems wasextensively studied by Lyapunov exponents spectrum, dimensions, [6] bifurcations and Poincare sections.The unusualchaotic and hyperchaotic dynamical behavior of these hidden attractors with fewer terms when compared with Lorenzand Lorenz-like systems is a signature of complexity that can be studied through simple systems.

References

[1] E.N. Lorenzi, Deterministic non-periodic ow, J. Atmos. Sci., 130141 (1963)

[2] Z.E. Musielak, D.E. Musielak, High-dimensional chaos in dissipative and driven dynamical systems, In: IASTED International con-ference on modern nonlinear theoy: Bifurcation and chaos, Tutorial paper. Montreal, Canada 140 (2007)

[3] Y. Qigui, C.A. Chuntao, A 5D hyperchaotic system with three positive Lyapunov exponents coined, Int. J. Bifur. and Chaos 23, 1350109(2011).

[4] S. Vaidyanathan, C. Volos, and V. Pham, Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system withthree positive Lyapunov exponents and its SPICE implementation, J.Polish Acad. Sci. 24, 409-446 (2014).

[5] O.S. Ojoniyi, A.N. Njah, A 5D hyperchaotic Sprott B system with coexisting hidden attractors, Chaos, Solitons and Fractals 87,172-181 (2016).

[6] A. Wolf, J.B. Swift, E.I. Swinney, and J.A. Vastano, Determining Lyapunov exponents from a time series, Physica D 16, 285-317(1985).

75


RAYLEIGH-TAYLOR INSTABILITY IN THIN LIQUID FILMS SUBJECTED TO HARMONICVIBRATION

Elad Sterman-Cohen1,2, Michael Bestehorn3 & Alex Oron2

1Rafael-Advanced Defense Systems Ltd., P.O. Box 2250(19), Haifa 3102102, Israel2Department of Mechanical Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel3Department of Theoretical Physics, Brandenburg University of Technology, 03044 Cottbus, Germany

The dynamics of the Rayleigh-Taylor instability of a two-dimensional thin liquid lm placed on the underside of aplanar substrate subjected to either normal or tangential harmonic forcing is investigated here in the framework ofa set of long-wave evolution equations accounting for inertial eects derived earlier by Bestehorn, Han and Oron [1]and Bestehorn [2]. In the case of tangential vibration, linear stability analysis of the time-periodic base state witha at interface shows the existence of the domain of wavenumbers where the lm is unconditionally unstable. Inthe case of normal vibration, linear stability analysis of the base state reveals that the instability threshold of thesystem is depicted by a combination of distinct thresholds separate for the Rayleigh-Taylor and Faraday instabilities.The nonlinear dynamics of the lm interface in the case of the static substrate results in lm rupture, however, inthe presence of the substrate vibration in the lateral direction, the lm interface saturates in certain domains in theparameter space, so that the continuity of the lm interface is preserved even in the domains of unconditional linearinstability while undergoing time-periodic harmonic evolution. In the case of the normal vibration, the lm evolutionmay exhibit time-periodic, harmonic or subharmonic saturated waves apart of rupture. Enhancement of the frequencyor amplitude of the substrate forcing promotes destabilization of the system and a tendency to lm rupture at thenonlinear stage of its evolution. A possibility of saturation of Rayleigh- Taylor instability by either normal or unidi-rectional tangential forcing in three dimensions is also demonstrated.

The research was partially supported by Grant 1228-405.10 from the Germany-Israel Foundation (GIF) to M. B. andA. O., and by the David T. Siegel Chair in Fluid Mechanics to A. O.

References

[1] M. Bestehorn, Q. Han and A. Oron, Nonlinear pattern formation in thin liquid lms under external vibrations, Phys. Rev. E 88,023025 (2013)

[2] M. Bestehorn, Laterally extended thin liquid lms with inertia under external vibrations, Phys. Fluids 25, 114106 (2013)

76


EFFECT OF ELECTRICAL MARANGONI NUMBER ON ELECTROHYDRODYNAMICINSTABILITY

S. Canberk Ozan & A. Kerem Uguz

Department of Chemical Engineering, Bogazici University, Bebek, 34342, Istanbul, Turkey

It is possible to deect an interface between two immiscible uids owing in a micro channel by introducing externalforces, such as electric eld. If the electric eld has a destabilizing eect [1] and is strong enough, the interface deects[2]. The interface may continue to deect, reaching one of the walls of the channel and eventually it ruptures. Theruptured interface and the channel wall encapsulate one phase, which transforms into a micro droplet due to theinterfacial tension, once leaves the electrode area. The critical voltage, at which the interface becomes unstable isstudied in several works [1, 3], and the evolution of the interface is investigated [4]. However, in those numericalworks in the literature, the dependence of the interfacial tension on the magnitude of the electric eld is neglected.Consideration of such a dependence, creates the electrical Marangoni number, which may be on the order of a thousandin micro channels [5]. In this work, the eect of the electrical Marangoni number in the conguration of two immiscible,leaky dielectric, Newtonian uids that are subjected to a normal electric eld will be investigated. A parametricstudy including the applied voltage or dimensionless electric number, viscosity and depth ratios of the uids will beinvestigated. In addition, the focus will be on the eect of the electrical Marangoni number.

References

[1] A.K. Uguz, Electric eld eect on a two-uid interface instability in channel ow for fast electric times, Phys. Fluids 20, 031702(2008)

[2] P. Eribol and A.K. Uguz, , Experimental investigation of electrohydrodynamic instabilities in micro channels, Eur. Phys. J. - Spec.Topics 224, 425-434 (2015)

[3] O.Ozen et al., Electrohydrodynamic linear stability of two immiscible uids in channel ow, Electrochim. Acta, 51, 5316-5323 (2006)

[4] R.V. Craster and O.K. Matar, Electrically induced pattern formation in thin leaky dielectric lms, Phys. Fluids 17, 032104 (2005)

[5] R. Narayanan and D. Schwabe, Interfacial uid dynamics and transport processes,Vol. 628 Springer (2006)

77


ANALYSIS OF SPATIO-TEMPORAL STRUCTURES IN THE THREE-DIMENSIONALCYLINDER WAKE

José Miguel Pérez, Soledad Le Clainche & José M. Vega

School of Aerospace Engineering, Universidad Politécnica de Madrid, Madrid, 28040, Spain

The main goal of this work is to present a higher order dynamic mode decomposition (HODMD) to study spatio-temporal patterns of the three dimensional wake of a circular cylinder. This technique considers two main steps. Asrst step a singular value decoposition (SVD) is used with the aim of removing either the spatial redundancies or toclean the noise in data coming from both, numerical simulations and experiments. As second step, the spatio-temporalHODMD generalizes standad DMD [1] combining the classical method with time-lagged snapshots [2]. This method ishighly accurate and its good performance has been tested in a wide range of applications [3, 4]. The results obtainedwith HODMD will be compared with classical Floquet stability analysis results, showing that HODMD is suitable tostudy instabilities in cases in which the classical theory may nd some diculties (i.e.: when the data analyzed arelimited in space (experiments) or when the base ow is quasi-periodic.

References

[1] P.Schmid , Dynamic mode decomposition of numerical and experimental data, J. Fluid Mech. 656, 5-28 (2010)

[2] F. Takens, Detecting strange attractors in turbulence, Lecture Notes in Math., D.A. Rand and L.-S. Young. eds., Springer-Verlag (1981)

[3] S. Le Clainche, J.M. Vega Higher order dynamic mode decomposition, SIAM J. on Appl. Dyn. Sys. (in press) (2017)

[4] S. Le Clainche, J.M. Vega, J. Soria, Higher order dynamic mode decomposition of noisy experimental data: the ow structure of azero-net-massux, Exp. Therm and Fluid Sci. (submitted) (2017)

78


FLUID/ELASTIC MODES OF A FLEXIBLE PLATE CLAMPED ON A CYLINDER

Jean-Lou Pster, Marco Carini & Olivier Marquet

ONERA The French Aerospace Lab, F92190 Meudon, France

The interaction of an elastic plate clamped at the rear of a rigid circular cylinder with a surrounding low Reynolds-number ow is investigated numerically using time-marching nonlinear simulations and linear stability analysis. Thecoupling between the incompressible ow described by the Navier-Stokes equations and the thick elastic plate, modelledas a nonlinear hyperelastic material, is ensured by an Arbitrary Lagrangian Eulerian formulation [2].

Results of unsteady nonlinear simulations performed at Reynolds number Re = 80 and a uid/solid density ratioof 1 exhibit the following typical features, already reported for similar congurations [1, 4]. For high values of thebending stiness Kb, no appreciable deformation of the elastic plate is observed and the wake ow remains steady. Bydecreasing the bending stiness, a periodic vortex shedding appears in the ow associated with an oscillation of theplate at the same apping frequency. This regime is characterized by a zero time-averaged aerodynamic force. Furtherreducing the stiness causes the onset of a deviated periodic solution. The elastic plate aps around a time-averagedposition deviated from the streamwise direction corresponding with a non-zero mean lift force. [1, 3].

The onset of those apping states is studied based on a linear stability analysis of the nonlinear steady solutions. Theuid/elastic global modes associated to positive temporal growth rate are investigated for a large range of bendingstiness as seen in Figure 1. Starting from high values of the bending stiness, the so-called bending mode 1 (blue)gets unstable for Kb ≤ 0.26. Close to this threshold, its frequency matches the non-linear frequency determined fromunsteady nonlinear simulations. The spatial structure of this mode displays the typical pattern of a vortex-sheddinghydrodynamic mode and a one-node structural vibration mode. For Kb ≤ 0.030 a second mode gets unstable. Thissteady mode breaks the spatial symmetry of the steady state. The non-linear oscillation of the clamped elastic platearound a deviated time-averaged position, also observed in [1], can be understood as the coexistence of the linearbending mode 1 and the symmetry-breaking steady mode. Further reducing Kb rst stabilizes the bending mode 1but then destabilizes the so-called bending mode 2, for Kb ≤ 0.0035. In this case the vibration of the elastic plate ischaracterized by a bi-nodal structure. We will discuss about the interaction between these linear modes, which giverise either to symmetric or unsymmetric oscillations in the non-linear limit-cycle. Exploring further the parameterspace also allows the determination of the sensitivity of the dynamics with respect to control parameters, then pavingthe way for control strategies.

Figure 0.1: Leading eigenvalue growth-rate and circular frequency as a function of Kb for a case at Re = 80 and symmetric steady baseow;and plot (for representative cases of each branch) of the associated real part of pressure mode component, showing (a,c) unsteady modeswith one or two bending modes, and (c) a steady mode.

References

[1] Bagheri, S. , Mazzino, A. and Bottaro, A. , Spontaneous symmetry breaking of a hinged apping lament generates lift, Phys. Rev.Lett. 109, 154502 (2012)

[2] Donea, J., Huerta, A., Ponthot, J.-Ph. and Rodrigez-Ferran, A., Arbitrary Lagrangian-Eulerian Methods, Encyclopedia of Computa-tional Mechanics (2004)

[3] Lacis, U., Brosse, N., Ingremeau, F., Mazzino, A., Lundell, F., Kellay, H. and Bagheri, S., Passive appendages generate drift throughsymmetry breaking, Nature (2014)

[4] Jinmo Lee and Donghyun You, Study of vortex-shedding-induced vibration of a exible splitter plate behind a cylinder, Phys. Fluids25, 110811 (2013)

79


PATTERN SELECTION IN DEFIANCE OF LINEAR THEORY

Jason R. Picardo1 & Ranga Narayanan2

1Department of Chemical Engineering, IIT Madras, Chennai, TN 600036, India2Department of Chemical Engineering, University of Florida, Gainesville, Fl 32608, USA

One of oldest paradigms in interfacial pattern formation is that the wavelength with the largest linear growth ratedominates the emergent pattern. It was rst propounded by Lord Rayleigh in his study of the capillary instability ofjets [1], and has since been applied to a variety of problems, e.g. the Rayleigh-Taylor instability of liquid pending froma ceiling, and viscous ngering of a water-oil interface [2]. In the present study, we test the limits of this hypothesis,by examining nonlinear pattern selection in a subcritical system that has a linear growth curve (dispersion curve) withtwo peaks of equal height. Such a system is obtained in a physical situation consisting of two liquid layers pendingfrom a heated ceiling, and exposed to a passive gas. Both interfaces are then susceptible to thermocapillary andRayleigh-Taylor instabilities. The two peak-modes correspond to patterns that are qualitatively very dierent, butgrow with the same linear growth rate. Consequently, any selection between them must occur via nonlinear eects.The basic question we ask is whether both peak-modes will be manifest in the nal pattern, as linear theory suggests,or whether nonlinearity will lead to unexpected consequences.

Long wavelength evolution equations [3, 4] are derived, to provide a computationally ecient means for exploring thedynamics of the system. We use a combination of numerical simulations and low-dimensional amplitude equations totrace the nonlinear evolution of the interfacial pattern and understand the subtle interactions between the two peakmodes. Surprisingly, we nd that one of the peak-modes can completely dominate the other, to the extent that thenal interfacial pattern is devoid of any trace of the second peak-mode. Far from being governed by simple lineartheory, the nal pattern is sensitive even to the phase dierence between peak-mode perturbations.

Acknowledgment: Support from NASA-CASIS GA-2015-218 is gratefully acknowledged.

References

[1] Lord Rayleigh , On the capillary phenomena of jets, Proc. R. Soc. Lond. 29, 71-97 (1879)

[2] L.E. Johns and R. Narayanan., Interfacial instability, Springer-Verlag, New York (2002)

[3] A. Oron, S. H. Davis, S. G. Banko, Long-scale evolution of thin liquid lms, Rev.Mod.Phys. 69(3), 931-980 (1997)

[4] G. F. Dietze, C. Ruyer-Quil, Wavy liquid lms in interaction with a conned laminar gas ow, J. Fluid Mech. 722, 348-393 (2013)

80


EVAPORATIVE SUPPRESION OF RAYLEIGH-TAYLOR INSTABILITY IN PURE ANDBINARY MIXTURES

Dipin S. Pillai & Ranga Narayanan

Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA

The classic conguration of an interface between a liquid lying above its vapor is well-known to be unstable due tothe Rayleigh-Taylor instability. We study this heavy-over-light conguration in the presence of evaporation. For this,a model conguration of a liquid lying above its vapor conned between two at plates is chosen. The system isheated from the vapor side by maintaining the temperature of the plate in contact with the vapor higher than that incontact with the liquid. A weighted residual-integral boundary layer (WRIBL) model based on the long-wavelengthapproximation is developed for this system. Most earlier works used a one-sided model with passive vapor phase[1, 2, 3, 4]. Similar to the work of Kantani [5], we consider both liquid and vapor phases to be active, thereby ensuringthat the total mass of the system always remains conserved. However we also consider the eect of inertia by usingthe WRIBL method.

Figure 0.1: Interface prole for pure ethanol. (a) Steady interface conguration for ∆T = 50C (b) Pure Rayleigh-Taylor like behaviorfor ∆T = 1C

We show that strong evaporation (large ∆T ) can linearly stabilize Rayleigh-Taylor instability. Interestingly, whenevaporation is weak (lower ∆T ) and the system is linearly unstable, it can still evolve nonlinearly to a steady stableinterface conguration that sustains a stable layer of vapor (c.f. Figure 0.1a). Momentum inertia is shown to slowdown the rate at which the interface reaches its steady conguration. It also results in non-monotonic evolution of theinterface. The thermal inertia is shown to have a stabilizing role. On further weakening of evaporation (negligible∆T ),the interface approaches the bottom plate (c.f. Figure 0.1b). Under such conditions, the system exhibits features ofa pure Rayleigh-Taylor and exhibit hydrodynamic sliding as observed by Lister and co-workers [6] .The study is extended to the case of a binary mixture where solutal Marangoni eect is also taken into account. Westudy a specic choice of binary mixture (ethanol-sec butanol), wherein the less volatile component (ethanol) hashigher surface tension. It is shown that the solutal Marangoni eect associated with such a binary mixture rendersthe system more unstable compared to pure component system, but never unstable enough that a binary system cancause the interface to fall while a pure system might cause it to be stably suspended.Acknowledgements : NASA-CASIS GA-2015-218

References

[1] A. Oron, S.H. Davis and S.G. Banko, Long-scale evolution of thin liquid lms, Rev. Mod. Phys. 69, 931980 (1997).

[2] M. Bestehorn and D. Merkt, Regular surface patterns on Rayleigh-Taylor unstable evaporating lms heated from below, Phys. Rev.Lett.97, 127802 (2006).

[3] N. Murisic and L. Kondic, On modeling evaporation, Ann. Univ.Ferrara. 54, 277286 (2008).

[4] A.D. Narendranath, J.C. Hermanson, R.W. Kolkka, A.A. Struthers and J.S. Allen, The eect of gravity on the stability of an evaporatingliquid lm, Microgravity Sci. Technol. 26, 189199 (2014).

[5] K. Kanatani and A. Oron, Nonlinear dynamics of conned thin liquid-vapor bilayer systems with phase change, Phys. Fluids.23,032102 (2011).

[6] John R. Lister, John M. Rallison and Simon J. Rees, The nonlinear dynamics of pendent drops on a thin lm coating the undersideof a ceiling, Journal of Fluid Mechanics 647, 239264 (2010).

81


DSMC SIMULATIONS OF HIGH MACH NUMBER TAYLOR-COUETTE FLOW

S. Pradhan

Department of Chemical Engineering, Indian Institute of Science, Bangalore- 560 012, India

The main focus of this work is to characterize the Taylor-Couette ow of ideal gas between two coaxial cylinders at Machnumber Ma = (Uw/

√kbTw/m) in the range 0.01 < Ma < 10, and Knudsen number Kn = (1/(

√2πd2nd(r2 − r1)))

in the range 0.001 < Kn < 5, using two-dimensional (2D) direct simulation Monte Carlo (DSMC) simulations [1]-[7].Here,r1 and r2 are the radius of inner and outer cylinder respectively, Uw is the circumferential wall velocity of theinner cylinder, Tw is the isothermal wall temperature, nd is the number density of the gas molecules, m and d arethe molecular mass and diameter, and kb is the Boltzmann constant. The cylindrical surfaces are specied as beingdiusely reecting with the thermal accommodation coecient equal to one.

In the present analysis of high Mach number compressible Taylor-Couette ow using DSMC method, wall slip in thetemperature and the velocities are found to be signicant ([1, 2]). Slip occurs because the temperature/velocity of themolecules incident on the wall could be very dierent from that of the wall, even though the temperature/velocity ofthe reected molecules is equal to that of the wall. Due to the high surface speed of the inner cylinder, signicantheating of the gas is taking place. The gas temperature increases until the heat transfer to the surface equals the workdone in moving the surface. The highest temperature is obtained near the moving surface of the inner cylinder at aradius of about (1.26r1).

In a compressible Taylor-Couette ow we examine the result that the splitting of the Taylor vortices takes place pro-portional as (L/(r2− r1)). The resolution suggested by our simulation is that even though the Mach number based onthe wall velocity and temperature is large, the local Mach number based on the local dissipation velocity in regions ofhigh shear decreases due to an increase in temperature. Due to this, the ratio of the mean free path and characteristicsow scale (λ/(r2r1)) appears to taper o in the high Mach number limit.

A modication of the velocity prole in the viscous rotating boundary layer near the wall, which takes into accounttemperature and density variations, is derived. The variation of the velocity and temperature is predicted underthe assumption that the increase in temperature across the viscous rotating boundary layer is larger than the walltemperature. It is found that the scaling laws do depend on the molecular model, through the dependence of viscosityand thermal conductivity on the temperature. The predicted law, are found to be in good agreement with simulations,for two dierent molecular models, the hard-sphere and the variable hard-sphere.

References

[1] S. Pradhan and V. Kumaran, The generalized Onsager model for the secondary ow in a high-speed rotating cylinder, J. Fluid Mech.686, 109-159 (2011)

[2] V. Kumaran and S. Pradhan, The generalized Onsager model for a binary gas mixture,J.Fluid Mech. 753, 237329 (2014)

[3] G.A. Bird, Molecular gas dynamics and the direct simulation of gas ows,Clarendon Press, Oxford (1994)

[4] G.A. Bird, Recent advances and current challenges for DSMC, Comput. Math. Appl. 35, 1-14 (1998)

[5] C. Cercignani, Rareed Gas Dynamics,Cambridge University Press (2000)

[6] M. Usami, Direct simulation Monte Carlo on Taylor vortex ow,In Rareed Gas Dynamics (ed. J. Harvey & G. Lord), vol. 1, pp.389395. Oxford University Press (1995)

[7] S. Stefanov and C. Cercignani, Monte Carlo simulation of the TaylorCouette ow of a rareed gas, J. Fluid Mech. 256, 199-213 (1993)

82


THERMOCAPILLARY CONVECTION EXPERIMENT FACILITY AND RESULTS OF LIQUIDBRIDGE ABOARD THE TG-2 SPACELAB

Kang Qi1,2, Duan Li1,2, Hu Liang1, Wu Di1, Wang Jia1 & Hu Wenrui1,2

1National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China2School of Engineering Science, University of Chinese Academy of Sciences, Beijing, China

Thermocapillary convection has always been a hot topic of great importance in either crystal growth or thin lms sci-ence. The space microgravity environment provides a good research platform for study of thermocapillary convectionmechanism. The mutual coupling between the uid interface and convection shows a complex physical mechanism,and the convection pattern transformation and oscillation behavior are the main characteristics of the convectioninstability and transition. Japan [1, 2] has conducted the study of the instability of liquid bridge on the InternationalSpace Station (ISS) owing to the reduction of gravity in space.

In the present study, a space experiment about thermocapillary convection in a liquid bridge system has been performedaboard the TG-2 spacelab. A payload for space experiment has been established, which includes a liquid bridgethermocapillary convection system, a thermocouple temperature controlling system and measurement system, twoCCD camera, and experiment controlling system. The problem related to the volume eects has been studied, for thepurpose of profoundly understanding the instability and oscillation mechanism. The comparative analysis betweenthe ground experiments results and the space experiment results has been nished. It is helpful to deeply understandthe nonlinear characteristics, ow stability, bifurcated transition, and other basic laws of the thermocapillary owsystem, and it is also benecial to realize and improve the processing and chemical technology of the ground and spacematerials.

Figure 0.1: A payload for space experiment liquid bridge.

Figure 0.2: The temperature oscillation.

References

[1] Kawamura H, Nishino K, Mastumoto S. , Report on microgravity experiments of Maragoni convection aboard international spacestation, J. Heat Transfer134,031005-031018 (2012)

[2] Taishi Yano, Koichi Nishino, Hiroshi Kawamura, Ichiro Ueno, Satoshi Matsumoto, Mitsuru Ohnishi, Masato Sakural, 3-D PTVmeasurement of Marangoni convection in liquid bridge in space experiment, Exp. Fluids 53, 9-20 (2012)

83


DESIGN OF AN EXPERIMENTAL DEVICE THE EVALUATION OF HYDRODINAMICPROFILES

Luis Fernando Arredondo Rodríguez1 & Esperanza Rodriguez Morales2

1Irapuato Superior Technologic Institute,Road to Cerrito of Galomo No.50, P.C :37980,San JoséIturbide,Guanajuato, Mexico

2Queretaro Technologic Institute WN, Technologic Av. Downtown Queretaro: 76000. Queretaro, Mexico

This report describes the research work undertaken aimed to design an experimental device that allows for assessmenttests on hydrodynamic proles used in hydro turbines.

Device sketches were made taking into account the components that could be included, where one of the most impor-tant characteristics is related with the return of the uid from the testing channel to the storage tank, without owlosses during testing, because the system must not operate without water during testing.

One device was chosen between several proposed, following with the calculations for the desired ow rate, to nallydetermine the resistance of the materials that is needed to its construction. SolidWorks software was used to designthe selected device.

Figure 0.1: Experienced device already installed.

References

[1] A. Bahaj, W.M.J. Batten and G. McCann, Experimental verications of numerical predictions for the hydrodynamic performance ofhorizontal axis marine current turbines, Renew. Energy 32, 2479-2490 (2007)

[2] Luste.E, Luznik L., Flack K.A., Walker J. M. and Van Benthem M.C., The inuence of surface gravity waves on marine currentturbine performance, Int. J. Marine Energy 3-4, 27-40 (2013)

84


INSTABILITY OF THE FLOW IN SUSPENDED THERMOCAPILLARY THIN FILMS

Francesco Romanó & Hendrik C. Kuhlmann

Institute of Fluid Mechanics and Heat Transfer, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria

We consider two coplanar semi-innite plates of thickness 2H in z direction which are separated in x direction by agap of constant width L. If a liquid lm is clamped in the gap such that the four edges of the lm are pinned alongthe sharp edges of the two plates a liquid bridge is formed in the x, z plane (see g. 0.1). The lm is kept in place bysurface tension forces. It is assumed that the liquid lm is innitely extended in third (y) direction.

Figure 0.1: Sketch of equilibrium shapes of a plane liquid bridge under zero gravity. Shown are equilibrium shapes for quiescent isothermalconditions (dashed line) and for dynamic thermocapillary ow conditions (solid line). The limit of a small lm thickness ϵ = H/L ≪ 1 isconsidered.

A basic two-dimensional uid motion due to thermocapillary forces is generated in the liquid lm by keeping thesupporting plates at dierent temperatures. We consider the limit of a thin lm. By means of an order-of-magnitudeanalysis based on the small aspect ratio ϵ = H/L ≪ 1, we derive a simplied model to investigate the three-dimensionalglobal ow stability. A parametric study is carried out varying Prandtl, Reynolds and capillary numbers as well asthe non-dimensional lm thickness ϵ = H/L and the ratio of the volume of liquid per depth to the cross section of thegap 2HL).

Typically, the three-dimensional ow arises in form of large counter-rotating circulation cells with motion predomi-nantly in x, y plane. Various interpretations have been proposed to explain this large-scale motion [1, 2, 3]. Resultsof a linear stability analysis in the framework of the simplied model are presented and compared with experimentalresults and full numerical simulations [1]. We focus on an in-depth analysis of the mechanisms driving the instability.

References

[1] B. Messmer, T. Lemee, K. Ikebukuro, I. Ueno, R. Narayanan, Conned thermo-capillary ows in a double free-surface lm with smallMarangoni Numbers, International Journal of Heat and Mass Transfer, 78, 10601067 (2014)

[2] H. Kuhlmann, Large-Scale Liquid Motion in Free Thermocapillary Films, Microgravity Science and Technology, 26, 397400 (2014)

[3] L. Fei, K. Ikebukuro, T. Katsuta, T. Kaneko, I. Ueno, D. R. Pettit, Eect of Static Deformation on Basic Flow Patterns inThermocapillary-Driven Free Liquid Film, Microgravity Science and Technology, 18 (2016)

85


NUMERICAL STUDY OF THE TRANSITION TO TURBULENCE IN PARTICULATE PIPEFLOWS

Anthony Rouquier, Chris Pringle & Alban Potherat

Department of Applied Mathematics, University of Coventry, Coventry, United Kingdom

We present a stability analysis of a pipe ow with particle suspension. Particles are considered solid, spherical, heavywith an unique size and density. The particles are, in our physical model, modelled as a continuous phase and forthe uid-particles interactions only the Stokes drag is taken into account, the other forces being neglected. We usea linear stability analysis to study the inuence of the addition of particles to the global stability of the ow. Singlephase pipe ows have been proven to be globally stable for any Reynolds number, we nd that this is also the case forparticulate pipe ows. The eect of particles varies with the concentration and the size of the particles, but it remainsrelatively weak.

One of the major diculty in simulating a particulate laden ow is the modelling of particles. In order to circumventthe problem, instead of modelling particles as discrete entities, we parametrize them with continuous variables, muchlike the uid. A similar model is used in [1] for a study of channel ows. The system of equations for our model is:

∂tu = −ρ−1∇p− (u · ∇)u+ ν∇2u+ ρ−1KN(up − u),

∂tup = −mN(up · ∇)up +KN(u− up),

∂tN = −∇(Nup), ∇ · u = 0.

With u and up the velocity elds for the uid and particles, mN represents the mass of the particles per unit volume.K is the Stokes drag dened such as K = 6πrρ, ν with r the radius of a particle. We used in a rst time a linearstability analysis to study the inuence of the addition of particles to the global stability of the ow. The equationsfor the perturbation leads to a modied Orr-Sommerfeld problem. It is known that the pipe ow is linearly stable tovery high Reynolds numbers and it is theorised that pipe ows are always linearly stable. We nd the same result forparticle laden pipe ows, but the addition of particles does aect the temporal growthrate of the perturbation. Theimpact on the ow also depends on the particle size as seen in the gure below.

On the Figure is the normalised growthrate (particles have a stabilising eect on the ow if is superior to 1, destabilisingotherwise) against SR, a nondimensional Stokes number proportional to the square of the particle radius, for a particleconcentration of 1Reynolds number of 1000 and various wavenumbers. In the limit of very small particles, the particlesbehave as passive tracers only aect the linear stability by modifying the global density of the ow. For very high SR,the uid and particles velocities are decoupled (the Stokes drag is converging towards 0) so the particles do not aectthe growthrate of the perturbation. This last property is the opposite of what is physically expected and illustratesthe limit of our model.

At medium particle size the comportment is non-monotonic, with a decrease followed by an increase in the normalisedeigenvalue. After the second peak the values converges back to 1. The curves have a similar shape for all Reynoldsand wave numbers, with a shift towards higher Stokes numbers with a Reynolds number increases and one towardstowards lower Stokes numbers with a wavenumber number increases. Preliminar results for transient growth analysisshow similar results, the addition to small particles increase the energy growth while bigger particles decreases it.

References

[1] J. Klinkenberg, HC de Lange, L. Brandt, Modal and non-modal stability of particle-laden channel ow, Phys. Fluids 23, (2011)

86


EFFECT OF INHOMOGENEOUS FLOW ON KELVIN-HELMHOLZ INSTABILITY

D. Lin1, S. Sen2,3,4, W. Scale1, N. Petulante4, & M.L. Goldstein5,6,7

1Virginia Tech., VA, USA, 2College of William & Mary, Virginia, USA3 National Institute of Aerospace, Virginia, USA, 4 Bowie State University, Maryland, USA

5NASA - Goddard Space Flight Center, Maryland, USA, 6University of Maryland, Baltimore, MD, USA7 University of Colorado, Colorado, USA

We study the eect of inhomogeneous ow on the Kelvin-Helmholz instability and turbulence. The inhomogeneousow includes both ow shear and ow curvature. The eect of ow curvature (second radial derivative of ow) isshown to have signicant eect in controlling the turbulence level contrary to the usual prediction that ow shear(rst radial derivative of ow) alone controls the turbulence level. The detail result of this simulation will be reported.

In this study of ow curvature eects, a two-dimensional hybrid model is used to simulate the Kelvin-Helmholtzinstability (KHI). The hybrid model treats the ions as particles, and electrons as massless uid. Pressure and resistivityare assumed as isotropic. A classical conguration for the study of KHI is investigated, i.e. transverse shear ow touniform background magnetic eld. This is thought as the most unstable situation in magnetohydrodynamic (MHD)theory. There are 50 super particles per cell in the current simulations, which number could be increased to as muchas 200 in the future. The boundary is periodic along the ow direction and reective in the perpendicular direction.The code was originally developed by the Los Alamos National Laboratory and has been successfully applied to thestudy of Kelvin-Helmholtz instability on the Earth's magnetopause. In this study, the code has been running on theAdvanced Research Computing (ARC) platforms of Virginia Tech.

Four distinct shear proles are simulated to investigate the eects of ow curvature on the growth of the KH instability:uniform ow, linear shear without curvature, quadratic prole with positive curvature, and quadratic prole withnegative curvature.

By comparing plasma ows from the four simulations with the same amount of time of evolvement, it is visible thatthe KH vortex is most nonlinearly developed in the case of negative curvature. In the case of linear shear, the vortexis less developed, but coalesce of two adjacent vortices is about to occur. Two vortices can also be seen in the case ofpositive curvature. The uniform ow basically keeps stable.

This work is supported by the DOE grant DE-SC0016397

87


INSTABILITY OF A MISCIBLE INTERFACE UNDER PERIODIC EXCITATIONS

Valentina Shevtsova1, Viktar Yasnou1, Aliaksandr Mialdun1, Yuri Gaponenko1 &Alexander Nepomnyashchy2

1Microgravity Research Centre, CP-EP-165/62, ULB, Brussels, Belgium2Department of Mathematics, Technion, Haifa 32000, Israel

The interfacial tension between immiscible uids is an equilibrium thermodynamic property that results from dierentcohesion forces between various types of molecules. The nature of the interface between two dierent miscible uidshas been the topic of an intense study for more than a hundred years in the elds of physics and chemistry. Kortewegproposed in 1901 that stress caused by a density gradient could act like interfacial tension. Zeldovich [1] consideringfree energy suggested that the transient surface tension could be evaluated as σ ∼ ∆c2/δ, where ∆c is the change incomposition expressed as a mole fraction, and δ is the width of the transition zone. Here we consider an even trickiermiscible interface. Two dierent binary mixtures of closely matching viscosities, which will be brought into contact ina closed cell, are composed of the same molecules (water and isopropanol, IPA) but at dierent concentrations.

Two superposed layers of incompressible and miscible liquids are placed in a rectangular container. The lower mixturecontains 90% of water and 10% of IPA while the upper liquid contains 50% of water and 50% of IPA. Our recentexperiments under normal and reduced gravity conditions have shown that application of shear stresses along themiscible interface, such as periodic excitations, leads to an interfacial instability instead of an active diusion process[2]-[5]. We present experimental evidence that the rich diversity of interfacial patterns occurs in miscible liquids underhorizontal vibrations.

Our experiments in terrestrial conditions demonstrate that an interfacial instability has a threshold which depends onthe frequency and amplitude. The observed regular structures above the threshold look static and are often referredto as frozen waves [2, 3]; an example of this wavy pattern is shown in Fig.1 (left). However, the most intriguingis the novel type of pattern generated by lateral walls. Generally these patterns can be seen as a wave spreadingfrom the wall along the interface with decaying amplitude and, literally, can be called a sh spine, see Fig.1 (right).We suggest that the sh-spine pattern has no threshold, and at the lowest tested forcing its horizontal extension iscontracted to the point. The existence of sh-spine pattern aects frozen wave instability. At large amplitudes, thereexists a strong competition between the two mechanisms: the sh spines generated by walls and the Kelvin-Helmholzmode of instability (here frozen waves). This dynamics coupling considerably enriches the phenomena. The observedphenomena are conrmed numerically and explained theoretically that the mean (streaming) ow is responsible forthe formation of the new pattern.

Figure 0.1: Interfacial pattern selection observed in the experiments: (left) frozen waves; (right) sh-spine pattern.

References

[1] Y.B. Zeldovich, Interfacial tension between miscible liquids (in Russian),Zhur. Fiz. Kim. 23, 931-935 (1949)

[2] Y.A. Gaponenko, M. Torregrosa, V. Yasnou, A. Mialdun, V. Shevtsova, Dynamics of the interface between miscible liquids subjectedto horizontal vibration,J.Fluid Mech. 784,342-372 (2015)

[3] Y.A. Gaponenko, M. Torregrosa, V. Yasnou, A. Mialdun, V. Shevtsova, Interfacial pattern selection in miscible liquids under vibration,Soft Matter 11, 8221-8224 (2015)

[4] V. Shevtsova, Y. Gaponenko, V.Yasnou, A. Mialdun, A. Nepomnyashchy, Wall-Generated Pattern on a Periodically Excited MiscibleLiquid/Liquid Interface, Langmuir 31, 5550-5553 (2015)

[5] Y. Gaponenko, V. Shevtsova, Shape of diusive interface under periodic excitations at dierent gravity levels,Microgravity Sci. Technol.28, 431 (2016)

88


CONTROL OF HYDROTHERMAL INSTABILITY IN LIQUID BRIDGE BY PARALLEL GASFLOW

Viktar Yasnou, Aliaksandr Mialdun, Yuri Gaponenko & Valentina Shevtsova

Microgravity Research Centre, CP-EP-165/62, ULB, Brussels, Belgium

Hydrothermal instabilities in a liquid bridge have been extensively studied since the 80s using dierent test liquidsand at various volume and aspect ratios [1]. Lately, the eect of ambient gas on the stability of a ow inside a liquidbridge has become an object of investigation. A typical liquid bridge is a nite volume of liquid conned between twosolid cylindrical rods, kept in its position by surface tension. A non-isothermal liquid bridge can be regarded as thesimplest idealization of the conguration appearing in the oating zone technique, which is used for crystal growthand purication of high melting-point materials. This study is connected to the microgravity experiment JEREMI(Japanese European Research Experiment on Marangoni Instabilities) where the use of a forced coaxial gas streamis proposed to control the hydrothermal instabilities in liquid bridges [2]. The results of a recent numerical study oninstability caused by a gas stream along the interface of an axisymmetric liquid bridge [3] have shown that the coolingof the interface may cause Pearson-like type of instability prior to the appearance of typical hydrothermal waves.

We present an experimental study on ow stability in a liquid bridge when ambient gas is moving along the interfacewith well-controlled velocity and temperature. The experiments are conducted in a ground laboratory where thestationary ow appears at arbitrary tiny values of imposed ∆T due to thermocapillary stresses and evolves underthe action of both Marangoni and buoyancy forces. For studies in the gravitational eld, the choice of the liquidbridge volume is a very delicate question. From the previous studies, it is well known, that when a dimensionlessvolume approaches unity, v = V ol/πR2d → 1, the critical wave number changes and frequency undergoes a sharpdrop/increase. On the numerical side, most calculations are done for a straight interface, i.e., when the dimensionlessvolume is equal to unity. Keeping in mind the comparison with the forthcoming numerical simulations, we decided toconduct experiments with v = 1 even though the test liquid is weakly evaporating. On the experimental side, it is achallenging task to maintain a constant volume with high precision. The volume of the liquid was calculated in realtime from its shape as measured by an optical system. The amount of the evaporated liquid was compensated withthe help of a syringe pump controlled by a computer.

The experimental study reports on non-isothermal experiments in liquid bridges while the counter-current gas moveswith constant velocity: (a)V = 0; 0.1m/s and 0.5m/s. The experiments are carried out for a wide range of gastemperature. The discussion concerning the experimental observations is based on the records of the thermocouplesimbedded into the liquid near the upper rod. The experiments are able to capture not only the critical parametersbut also all the non-linear transitions in the system. One of the most intriguing Fourier maps is shown in Fig.1.

Figure 0.1: Fourier map for the experiment with gas velocity V = 0.5m/s at temperature T = 28C.

References

[1] D. Schwabe , Thermocapillary Liquid Bridges and Marangoni Convection under MicrogravityResults and Lessons Learned, MicrogravitySci Technol. 26, 1-10 (2014)

[2] V. Shevtsova, Y. Gaponenko, H.C. Kuhlmann, M. Lappa, M. Lukasser, S. Matsumoto, A. Mialdun, J.M. Montanero, K. Nishino and I.Ueno. , The JEREMI-Project on Thermocapillary Convection in Liquid Bridges. Part B: Overview on Impact of Co-axial Gas Flow,FDMP 10, 197-240 (2014)

[3] V. Shevtsova, Y. A. Gaponenko and A. Nepomnyashchy, Thermocapillary ow regimes and instability caused by a gas stream alongthe interface, J. Fluid Mech. 714, 644-670 (2013)

89


MECHANISMS OF JET INSTABILITY(plenary lecture)

Vladimir Shtern

Laboratory for Chemical Technology, Ghent University, B-9052 Gent, Belgium

The shear-layer (Kelvin-Helmholtz) instability discovered one and half century ago is strong typically developing atrather small values of the Reynolds number Re. Jet-like ows suer from this instability because they involve shearlayers. In addition, a jet entrains an ambient uid that causes the jet deceleration. It was revealed [1] that thedeceleration decreases the critical Re by one order of magnitude. This feature had not been recognized earlier becausethe stability theory focused on parallel and nearly parallel ows while the deceleration eect is strongly non-parallel.The situation changed when a new approach had been developed for the stability of conical similarity ows. Thisapproach reduces the stability problem to ordinary dierential equations while exactly conserves the acceleration terms[1]. This allows for studying of the deceleration eect in a wide family of swirl-free, swirling, thermal-convection, andmagneto-hydrodynamic ows [2].

The development of numeric technique for stability studies of two-dimensional ows allowed for better understandingof the instability nature of the Vogel-Escudier ow [3]. It was found for an elongated cylinder with one rotating enddisk and the other walls being stationary that a kind of swirling jet develops in the bulk ow which suers from theshear layer instability. If the other end disk co-rotates, the centrifugal instability becomes more dangerous than theshear-layer instability [3].

A striking stability feature was observed for the thermal convection in a rotating cylindrical container whose end diskshave dierent temperatures while the sidewall is adiabatic [4]. As the rotation speeds up, a jet-like motion emergesnear the sidewall. The radial prole of axial velocity has a sharp peak near the wall and two inection points. Theshear-layer instability, occurring at the Prandtl number Pr = 0, becomes suppressed by the stabilized eect of angularmomentum stratication. It was found that this eect is strengthened by the cold end disk. For Pr > 0, the thermalconvection develops the stable stratication of uid density as well. This makes stable the convection of mercury(Pr = 0.015), air (Pr = 0.7) and water (Pr = 5.8) in the entire range of rotation speed available in the numericalsimulations [4].

The stability technique had been further developed for two-uid ows [5]. A technical diculty had been overcomerelated to the linearization of a complicated equation describing the normal stress balance at a bent interface. Thistechnique was applied for the stability study of water-spout ow [6]. A vertical cylindrical container is lled with airand water. The ow is driven by the rotating top disk while other walls are stationary. The rotation deforms theinterface upward near the axis and downward near the sidewall. The air (water) meridional circulation is clockwise(anticlockwise). As the rotation speeds up, the clockwise water circulation emerges near the bottom center, expands,and occupies the most of water domain, except a thin layer of anticlockwise circulation adjacent to the interface. Thejet-like motion develops near the interface both in air and water. The instability focuses in the air jet-like motionafter the thin layer is well formed. The instability is of shear-layer type except for a small air volume fraction (around0.1) where the instability is centrifugal. As the air ows from the sidewall to the axis near the interface, streamlinerst converge and then diverge. The shear-layer instability focuses where the streamline start to diverge, hence thedeceleration eect also works here.

References

[1] V. Shtern, F. Hussain, Eect of deceleration on jet instability, J. Fluid Mech. 480, 283-309 (2003)

[2] V. Shtern, Counterows,Cambridge University Press (2012)

[3] M. Herrada, V. Shtern, M. Torregrosa, The instability nature of the Vogel-Escudier ow,J. Fluid Mech. 766,590-610 (2015)

[4] M. Herrada, V. Shtern, Stability of thermal convection in a rotating cylindrical container, Phys. Fluids 28, 083601 (2016)

[5] M. Herrada and J. Montaneroi, A numerical method to study the dynamics of capillary uid systems, J. Comput. Phys. 306, 137-147(2016)

[6] L. Carrion, M. Herrada, V. Shtern, Instability of a water-spout ow, Phys. Fluids 28, 034107 (2016)

90


EFFECT OF ROTATION ON THE MONOTONIC INSTABILITY MODE OF ADVECTIVE FLOWIN A HORIZONTAL INCOMPRESSIBLE FLUID LAYER WITH RIGID BOUNDARIES IN THE

CASE OF NORMAL SPIRAL PERTURBATIONS

Konstantin Shvarts & Dmitriy Chikulaev

Department of Applied Mathematics, Perm State University, Perm, Russia

New most dangerous regimes instability of advective ow in rotating horizontal liquid layer in a wide range of thePrandtl number (Pr) and the Taylor number (Ta) are studied. We study the monotonic instability mode of anadvective ow [1] in a rotating horizontal layer of incompressible uid with rigid boundaries, which depend on Pr andTa in the case of spiral perturbations using a small perturbation method. In calculations, we apply the grid methodto the one-dimensional problem. The system of equations and necessary parameters of the nu merical solution arepresented. The neutral curves describing the dependence of the Grashof number on the wave number for dierentvalues of Ta and Pr are presented. Two hydrodynamic modes of instability are revealed. The eect of rotation onthese modes is investigated in the range of 0 ≤ Ta ≤ 105 at Prandtl numbers in the range of 0 < Pr ≤ 20. The regionof the rst monotonic mode is expanded with respect to Pr in the range of 0 to 0.3 with increasing Taylor numberfrom 4 to 370. The second monotonic mode arises in the range 0.3 < Pr ≤ 1 at Ta = 370, and the region of thismode is expanded with respect to Pr in the range from 0.3 to 0 and from 1 to 20 with increasing Ta. The curvesdescribing the dependence of the Grashof number on the Taylor and Prandtl numbers are given. The rst mode ismore dangerous than the second mode for a xed value of the Prandtl number at Pr ≤ 0, 1. However, the secondmode is more dangerous than the rst monotonic mode in the range of 0.1 < Pr ≤ 0.3. The second mode is moredangerous than the rst mode for a xed value of Ta in the range of the simultaneous existence of both monotonicmodes.

References

[1] K.G. Schwarz , Eect of Rotation on the Stability of Advective Flow in a Horizontal Fluid Layer at a Small Prandtl Number,FluidDyn. 40(2),193-201 (2005)

91


EXPERIMENTAL STUDY OF TRANSITION TO TURBULENCE IN PARTICULATE PIPEFLOW

Sanjay Singh, Alban Pothérat & Chris Pringle

Applied Mathematics Research Centre, Faculty of Engineering and Computing, Coventry University, CV1 5FB,United Kingdom

Transition in particulate pipe ow is much more complicated compared to that of single phase ow in that not only theow rates but also the particle size and concentration inuence transition. Despite its wide applications in industriessuch as oil and gas, chemical and food process, transition to turbulence in particulate pipe ow has not been studiedextensively. To date, Matas [1] is the only experimental study where indication of transition was quantied by pressuredrop measurements. In this study, we propose to employ a constant mass ux system based on Darbyshire [2], andconduct velocity measurements using two-phase particle image velocimetry (PIV) to map and characterise the owstructures in the transitional regime in particulate pipe ow.

Figure 0.1: A schematic diagram (front view) of the rig. Inlet (1) is connected by a ange (2) to the pipes (3) which are held by pipeunions on supports (4). Piston-cylinder arrangement (5) sucks in uid, driven by actuation system (6). The rig rests on wooden blocks (7).Recirculation system consists of gravity driven uid passing through the meshes (8) into the reservoir (9) as overow from a suspensiontank (10), through the control valve (11) when the pump is operational. All dimensions are in cm. Drawing not to scale.

To this end an experimental rig consisting of a 12 m long horizontal glass pipe with 20 mm in diameter is being set upas shown in Figure 1. A heavy uid (liquid) serves to match the density of spherical, monodisperse glass beads (solidparticles) to achieve neutral buoyancy under controlled volume fraction ranging between 0.01-0.20. For two-phase, 2DPIV, the liquid is seeded with silver-coated glass beads (tracers) of relatively smaller size to follow the ow passivelyand represents the uid phase, whereas the bigger sized particles act as the solid phase. Laser sheet is used to lightthe plane in the longitudinal and transversal with the camera oriented respectively to take successive images in thesetwo planes. Due to the varying sizes and optical properties of the particles and the tracers, a simultaneous two phasedetection method as described in Khalitov [3] is applied. The image processing involves two steps. In the rst step,the image consisting of both particles and tracers are pre-treated, followed by detection and seperation of the solidparticles using various algorithm. Finally, the images from the two seperated phases : particles (solid) and tracers(uid) are processed respectively using standard PIV data analysis software to obtain the velocity measurements.Results from this research oer unique insight into the transitional regimes encountered in particulate pipe ow, theeects of addition of particles on the ow structures and how they dier in comparison to single phase ow.

References

[1] J.-P. Matas, J. F. Morris, E. Guazzelli , Transition to turbulence in constant-mass-ux pipe ow, Phys. Rev. Lett 90,014501 (2003)

[2] A. G. Darbyshire, T. Mullin, Transition to turbulence in constant-mass-ux pipe ow, J. Fluid Mech. 289, 83-114 (1995)

[3] D. A. Khalitov, E. K. Longmire, Simultaneous two-phase PIV by two-parameter phase discrimination, Exp. Fluids 32, 252-268 (2002)

92


KINEMATIC DYNAMO IN A FOURIER TETRAHEDRON

Rodion Stepanov1 & Franck Plunian2

1Institute of continuous media mechanics, Perm 614013, Russia2Université Grenoble Alpes, Institut des Sciences de la Terre, 38058 Grenoble Cedex 9, France

It is generally believed that helicity can play a signicant role in turbulent systems, e.g. supporting the generationof large-scale magnetic elds, but its exact contribution is not clearly understood. For example they are well-knownexamples of large scale dynamos produced by a ow which is pointwise non-helical. In any case a break of mirrorsymmetry seems to be always at the heart of the dynamo mechanism. Most of the dynamo studies are based onsolutions of the mean eld equations, direct numerical simulations or shell model of turbulence. Another framework toanalyze such processes is the use of helical mode decomposition. In pure hydrodynamics such framework has proveduseful to study the processes responsible for helicity cascades [1]-[3]. It has also been used in the analysis of MHDmode interactions [4].

The present work deals with the kinematic dynamo problem, solving the induction equation within the framework ofhelical Fourier modes decomposition. We show that the simplest modes conguration leading to an unstable solutionis in the form of a tetrahedron (gure 1). Here the dynamo is produced by only two ow scales corresponding to thewave number vectors k and p. The magnetic eld is generated within the four triads of the tetrahedron. We ndnecessary conditions for the dynamo action, not necessarily related to ow helicity. The results help to understandgeneric dynamo ows like the one studied by G.O. Roberts (1972).

Figure 0.1: Conguration of interacting triads: (k, p, q), (k, p, q), (k, p, q), (k, p, q).

This work was supported by the Russian Science Foundation RSF-DST-16-41-02012.

References

[1] L. Biferale, S. Musacchio, and F. Toschi, Inverse Energy Cascade in Three-Dimensional Isotropic Turbulence, Phys. Rev Lett. 108,164501 (2012)

[2] R. Stepanov, E. Golbraikh, P. Frick, and A. Shestakov, Hindered Energy Cascade in Highly Helical Isotropic Turbulence, Phys. Rev.Lett. 115, 234501 (2015)

[3] Kessar M., Plunian F., Stepanov R., Balarac G., Non-Kolmogorov cascade of helicity-driven turbulence, Phys. Rev. E 92, 031004(2015)

[4] M. Linkmann, A. Berera, M. McKay, and J. Jäger, t, Helical mode interactions and spectral transfer processes in magnetohydrodynamicturbulence, J. Fluid Mech. 791, 61 (2011)

93


STEADY FLOWS IN OSCILLATING ELASTIC SPHEROIDAL CAVITY. DEPENDENCY ONTHE DIMENSIONLESS FREQUENCY

Stanislav Subbotin1, Victor Kozlov & Rustam Sabirov2

1Laboratory of Vibrational Hydromechanics, Perm State Humanitarian Pedagogical University, Perm, Russia2Department of Applied Physics, Perm National Research Polytechnic University, Perm, Russia

We study experimentally the steady ows of viscous liquid in the cavity, excited by oscillations of its elastic boundaries.The cavity has the shape of a spheroid located between two plates, one of which oscillates along the cavity symmetryaxis. The structure of steady ow is investigated by PIVmethod. It was found that the periodic deformation ofthe cavity leads to the appearance of a steady ow in the cavity. The ow structure signicantly depends on thedimensionless frequency ω = ΩR2/nu , where Ω is the frequency of deformations of the cavity, R is the cavity radius,ν is the kinematic viscosity of the uid. The transformation of a steady ows structure with dimensionless frequency isinvestigated in details. At low dimensionless frequency, when the viscous forces completely determine the oscillationsof the uid in the cavity, the steady ow has the form of large-scale toroidal vortices (Fig. 1a). On the cavity axis theliquid moves towards the cavity poles.

Figure 0.1: The structure of the steady ow at low and high valuies of the dimensionless frequency ( ω = 56 (a) and ω = 3490 (b)). Thedashed line shows the no deformed cavity shape..

With increase of the thickness of the dynamic boundary layers decreases and toroidal vortexes (which transverse size isproportional to the thickness of the dynamic boundary layers) shift towards the cavity walls. At high ω, the large-scalesecondary ows exist in the bulk of the cavity (Fig. 1b), the direction of uid motion is opposite to the case of lowω . In the high-frequency limit, the structure of steady ow does not depend on the dimensionless frequency and itsintensity is determined by one dimensionless parameter the pulsation Reynolds number; the experimental results areconsistent with the theoretical studies of a steady ow structure in the oscillating liquid droplet coated with adsorptionlayer [1].

Acknowlegements: The work was supported by the the RFBR (project No. 16-31-60099).

References

[1] V.A. Murtsovkin, V.M. Muller, Steady-state ows induced by oscillations of a drop with an adsorption layer,J. Colloid Interface Sci.151, 150-156 (1992)

94


EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE INSTABILITY OF THEELECTROVORTEX FLOW IN HEMISPHERICAL CONTAINER

Igor Teplyakov, Dmitriy Vinogradov, Irina Klementyeva & Yury Ivochkin

Joint institute for high temperatures, Russian Academy of Sciences, Moscow, 111395, Russia

Electrovortex ow (EVF) is formed as a result of interaction of the non-uniform electric current passing through theliquid metal with own magnetic eld of this current [1]. Such ows signicantly aect many processes in electromet-allurgy (electroslag remelting, various electric melting furnace).

Usually it is assumed that in the system with an axially symmetric central electrode without inuence of externalmagnetic elds EVT has the shape of a toroidal vortex. External axial magnetic eld in this geometry leads to theazimuthal swirl of the ow. Thus, the secondary vortex rotating in a vertical plane opposite main EVF ow and pushingit to the periphery of the bath occurs in the volume of the liquid metal. However, the results of our experiments haveshown that the structure of real EVF is more complicated and signicantly dierent from the expected hydrodynamicsystem, consisting of one or two stationary toroidal vortexes. It has been found, that for a signicant (∼ 40% andhigher) level of the low-frequency velocity uctuations connected most likely with the emergence of the self-oscillationmode electrovortex ow occurs in the amount of current-carrying uid [2, 3].

Figure 0.1: 1 - container; 2 - eutectic alloy In-Ga-Sn; 3 - small electrode; 4,5 - current leads; 6 - ber-optical transducer.

Experimental studies were carried out at the following setup. An eutectic indium gallium-tin alloy lled copperhemispherical container Small electrode - steel or copper cylinder was immersed into the alloy. Direct current (upto 1000A) passed through the metal. The coil of copper tube was used to create an external longitudinal magneticeld. Special unit with microprocessor was constructed to provide pulsed current through the liquid or pulsed externalmagnetic eld.

Measurements of velocity were carried out with the ber-optical transducers, Transducer of velocity is a glass conewith diameter from 50mcm to 1 mm with ber-optical system placed inside. Deecting of cone the stream of underliquid leads to changing of the electric signal. Numerical calculation was based on solving of the following motionequation using electrodynamic approximation:

∂tU+ (U·)U = −∇p+ (1/√S)∆U+ (cos θ − 1)eθ/4π2r3 sin θ −N sin θeϕ/2πr2. (7)

We used the following parameters: S = Re2 = µ0I2/ρν2, N = BextIR2/ρν

2, where I - current, Bext-external axialmagnetic eld, R2 - radius of the container.

It was shown that the stationary external magnetic eld, which causes an azimuthal swirl of the axisymmetric electricow, leads to the generation of the intensive hydrodynamic self-oscillating processes in the currentcarrying liquidmetal.

This work was supported by Russian Scientic Fund (grant 17-19-01745).

References

[1] V. Bojarevics, J. Frejbergs, E.I. Shilova, E.V. Shcherbinin, Electrically Induced Vortical Flows,Kluwer Academic Publishers, Dordrecht,Boston, London, (1989)

[2] A. Kharicha, I. Teplyakov, Yu. Ivochkin, M. Wu, A. Ludwig, A. Guseva, Experimental and numerical analysis of free surface defor-mation in an electrically driven ow, Exp. Therm. and Fluid Sci. 62, 192-201 (2015)

[3] Yu. P. Ivochkin, I. O. Teplyakov and D. A. Vinogradov, Yu. P. Ivochkin, I. O. Teplyakov and D. A. Vinogradov, Magnetohydrody-namics 52 (1/2), 277-286 (2016)

95


STABILIZING UNSTABLE FLOWS BY COARSE MESH OBSERVABLES AND ACTUATORS - APAVEMENT TO DATA ASSIMILATION

(plenary lecture)

Edriss S. Titi1,2

1 Texas A&M University, College Station, TX, USA2 The Weizmann Institute of Science, Rehovot, Israel

One of the main characteristics of innite-dimensional dissipative evolution equations, such as the Navier-Stokesequations and reaction-diusion systems, is that their long-time dynamics is determined by nitely many parameters nite number of determining modes, nodes, volume elements and other determining interpolants. In this talk Iwill show how to explore this nite-dimensional feature of the long-time behavior of innite-dimensional dissipativesystems to design nite-dimensional feedback control for stabilizing their solutions. Notably, it is observed that thisvery same approach can be implemented for designing data assimilation algorithms of weather and climate predictionsbased on discrete measurements.

96


RUNOUT AND POWER DISSIPATED IN MONODISPERSE GRANULAR DENSE FLOWS

Luis Armando Torres-Cisneros1, Gabriel Perez-Ángeli1,2, Roberto Bartali2,Gustavo Manuel Rodríguez-Liñán3, & Yuri Nahmad-Molinari3

1Departamento de Física Aplicada, CINVESTAV del IPN Unidad Mérida, Mérida, Yucatán, México2Facultad de Ciencias, Universidad Autónoma de San Luis Potos, San Luis Potosí, México

3Instituto de Física Manuel Sandoval Vallarta, Universidad Autónoma de San Luis Potosí, San Luis Potosí, México

Nowaday an interesting and very important problem to solve in natural hazards is to determine the runout (themaximum distance achieved by the front) of landslides and rock avalanches to safe comunities that were build inzones closer to a hill. To study at lab-scale the runout we made experiments to measure the runout obtained bymonodisperse avalanches composed by 4 kg of andesite rocks with sizes ranging from phi = 4 (0.0625 mm) to phi =-4 (16 mm) in the Krumbein phi scale. The mass was let ow on a ramp inclined at 27, 32, 37, 42 degrees. Herewe found that as we increase the size of the particles keeping the total mass constant we obtain a bigger runout. Ourmain hypothesis is that as we decrease the size of the particles the power dissipated by the ow increases.

To get an insight on it there are in literature many references that tackle the trouble from two main perspectives: oneconsiders that the ow is a continuum uid with a certain viscosity using deep-averaged equations, the second takes inaccount that commonly this kind of ows are composed by fragmented solid matter that, while there is an avalanchingprocess are colliding. We take this second perspective and we develope a two-dimensional molecular dynamics codeto reproduce avalanches as is shown in Fig. 1. The particles are modelled as dumbell-like particles, Fig. 1. And wemeasure the power dissipated by ten dierent avalanches changing the particle size in each one from a radii r = 0.53cm(65 536 particles) to r = 12cm (128 particles), keeping the total mass constant. We found that, as we expect in anavalanching process a decrease in particle size means an increase in the power dissipated (Fig. 2).

Figure 0.1: This gure show a sequence of an avalanching process when: a) the material is initially congured, b) the mass is owing andc) the material is deposited. In d) we show a very simple draw of the shape of each particle.

Figure 0.2: This gure shows the power dissipated by monodisperse avalanches composed by sizes ranging from a radii r = 0.53cm (65 536particles) to r = 12cm (128 particles).

97


OBSERVATIONS OF NEW DOUBLE SPLASHING FOR DROP IMPACT ONTO LIQUID FILM

Pei-Hsun Tsai & An-Bang Wang

Institute of Applied Mechanics, National Taiwan University, Taiwan

The splashing morphologies induced by drop impact upon a wetted surface have been systematically investigated.As shown in Fig. 1(a), double splashing phenomena have been found with increasing drop impact velocity (Vi) ata certain thickness of liquid lm (H∗ = H/D, D is drop diameter), i.e., it follows the region of (I) non-splash, (II)splash and surprisingly (III) non-splash, and then splash (IV) again. From our analysis, such a double-splashingcharacter appears in the liquid system with low surface tension but high viscosity. Moreover, for high impact energyover the second splashing threshold, bubbles will be ejected from the crown tips, as shown in (V), instead of commonlyobserved droplet splashing, due to the folding of liquid sheet. On the other hand, the liquid sheet growing on the thinliquid lm could also break from the roots and retracted upwards to form a torus of liquid, turning into necklace-likesplashing as shown in (VI). Based on experimental results of dierent liquid viscosities, the lower and upper splashingthresholds with respect to the thickness of liquid lm could be correlated as We0.5Oh−0.4 = 143 − 17H∗−0.44 andWe0.5Oh−0.4 = 153− 11H∗−0.5, which are far from the previous threshold in the literature [1, 2]. These results haveshown not only the beauty of drop dynamics but also the fundamental complexity of single drop impact in nature.

Figure 0.1: (a) The dependence of splash regimes on the thickness of liquid lm. The silicone oil of 50 cSt was used as the lm anddrop liquid. The drop diameter was 3.84 mm. Dashed and dash-dot lines are the splashing thresholds from [1] and [2], respectively. Thesequential images show: I. Non-splash (H∗ = 0.44, Vi = 4.29m/s). II. Typical crown splash (H∗ = 0.44, Vi = 4.75m/s). III. Non-splash(H∗ = 0.44, Vi = 4.95m/s). IV. Revival crown splash (H∗ = 0.44, Vi = 5.21m/s) V. Ejected bubble splash (H∗ = 1.00, Vi = 5.45m/s).VI. Necklace splash (H∗ = 0.30, Vi = 6.35m/s). All black scale bars are 5 mm. (b) Double splashing thresholds for drop impact of siliconeoil in the viscosity range from 20 cSt to 50cSt.

References

[1] G.E. Cossali, A. Coghe, and M. Marengo, The impact of a single drop on a wetted solid surface, Exp. Fluids 22, 463-472 (1997)

[2] T. Okawa, T. Shiraishi and T. Mori, Production of secondary drops during the single water drop impact onto a plane water surface,Exp. Fluids 41, 965-974 (2006)

98


QUASI-GEOSTROPHIC EFFECTS ON THE STABILITY OF THE RAYLEIGH MODELSUBJECT TO A UNIFORM SHEAR

Orkan M. Umurhan1 & Luca Biancoore2

1NASA Ames Research Center, Space Science Division, Moett Field, CA 94035, USA2Department of Mechanical Engineering, Bilkent University 06800 Bilkent, Ankara, Turkey

Thin strips of anomalous vorticity are commonplace in the Earths atmosphere, in particular in very high Reynoldsnumber 2D vortical ows and analogous 3D stably stratied ows. The classical inviscid Rayleigh model subject to anadverse or favorable uniform shear is often used to model these strips [1, 2]. In this work we rst revisit the stabilityanalysis of this model with the kernel-wave perspective [3] introducing also the quasi-geostrophic (QG) approximation.With the kernel-wave perspective the instability of the Rayleigh model is viewed as the interaction of the two counter-propagating Rossby waves (CRWs) created at the vorticity edges. The important parameters of our study are thevorticity of the uniform shear m and the Rossby deformation radius Ld. In gure 1-(left panel) growth rate contoursin the k − m plane (where k is the wavenumber) are illustrated when QG eects are important (i.e.Ld = 10). Wend that an adverse shear (m < 0) stabilizes the system and a favorable shear (m > 0) strengthens the instabilitythese trends are consistent with predictions under conditions where QG eects are absent [2]. We discuss how thisstabilization is due to how the uniform shear asymmetrically aects the two uncoupled CRWs with hindering (helping)the interaction when m < 0 (m > 0). We further nd that as QG eects are introduced (to be shown in presentation)we notice a general damping of the instability ifm > 0. Interestingly QG eects do have a dual inuence for an adverseshear: (i) the maximum of the growth rate is damped, while (ii) a destabilization is noticed for small k. Finally wehave conducted direct numerical simulations (DNS) of the transition to turbulence of the inviscid Rayleigh modelsubject to an uniform shear under QG approximation. The DNS conrm the trends for both m and Ld observed inlinear stability analysis: an adverse (favorable) shear retards (accelerates) the transition. However the strength of theturbulent transition is enhanced under adverse shear, e.g., gure1-(right panel), wh ile it is relatively benign but noless destructive for favorable shear.

Figure 0.1: (Left panel) Contours of the growth rate in the plane k−m for dierent values of Ld = 10. (Right panel) Nonlinear developmentfor values of Ld = 10,m = −0.5. Q is the potential vorticity.

References

[1] Lord Rayleigh, The theory of sound, Dover (1945)

[2] D.G. Dritschel, On the stabilization of a two-dimensional vortex strip by adverse shear, J. Fluid Mech. 206, 193-221 (1989)

[3] E. Heifetz, C.H. Bishop, and P. Alpert, Counter-propagating Rossby waves in the barotropic Rayleigh model of shear instability, Quart.J. Royal Meteo. Society 125, 2835- 2853 (1999)

99


PARAMETRIC EXCITATION OF SURFACE WAVES IN HORIZONTAL CONTAINERS UNDERMIXED HORIZONTAL/VERTICAL VIBRATION

Jose M. Perez-Gracia, Fernando Varas & José M. Vega

E.T.S.I. Aeronáutica y del Espacio, Universidad Politécnica de Madrid, 28040 - Madrid, Spain

Vibrating containers are of paramount scientic and technological interest in a wide range of elds, including sloshingin vibrating tanks and g-jitter in space platforms, which aect on board experiments involving uids. The vibratingboundaries produce harmonic oscillations by direct excitation of arbitrarily small amplitude. These oscillations, inturn, generate subharmonic waves by parametric excitation [1] as the forcing acceleration exceeds a threshold value.The simplest case, which admits near thresholdafairly simple analysis [2], is vertical vibration of a perfectly athorizontal free surface. The resulting subharmonic waves, rst observed by Faraday [3],have received a tremendousattention in the literature as a paradigm of pattern-forming systems. Beyond threshold, Faraday waves exhibit a largevariety of intriguing spatio-temporal patterns [4] and, moreover, they promote mean ows, also observed by Faraday[3] himself and rst explained by Rayleigh [5], which have been shown [6] to aect the dynamics of the primary waves,producing new phenomena, such as drifts in otherwise standing waves [7].

More general vibrating devices, such as vibrating wavemakers and horizontally vibrating containers,produce non-uniform forcing, which is less accessible to the analysis,even restricting to the primary patterns, which are genericallycalled crosswaves[8] and were already observed by Faraday [3] as produced by a vibrating plate or cork. For thesecross-waves, the primary patterns at threshold are expected to be exactly subharmonic (namely, with a frequency equalto a half of the forcing frequency), standing, and with their crests either aligned perpendicularly to the wavemaker,which have been assumed/conrmed in a variety of theoretical/experimental papers, all in the gravity limit. However,oblique crosswaves, whose wave crests are not perpendicular to the wavemaker,have been encountered in the capillary-gravity limit by Shemer and Chamesse [9], who attributed obliqueness to side-band eects, and also experimentally[10, 11, 12]. In addition, Punzmann et al. [13] have observed some curious behavior of mean ows in which obliquecross-waves seem to play a major role.

With the above in mind, this talk will consider the subharmonic waves that are generated in vibrating containersunder mixed horizontal/vertical vibration in a low viscosity liquid. The analysis relies in a general two-dimensionalamplitude equation, with appropriate boundary conditions, which was recently derived from rst principles by us [14].This equation is used to calculate the subharmonic instability threshold and the associated primary patterns, whichcan be either strictly subharmonic (with a frequency equal to the forcing frequency) and thus periodic or quasi-periodic(exhibiting two incommensurable frequencies) and may show dierent orientations. Dependence of these properties onthe various non-dimensional parameters (measuring the container depth, width and length, viscous eects, capillary-gravity balance, and the horizontal/vertical relative intensities and phase shifts) are discussed,keeping in mind possibleexperiments and making specic predictions on these.

References

[1] S. Fauve , Parametric instabilities,in Dynamics of Nonlinear and Disordered Systems (ed. G. Matinez-Mekler & T.H. Seligman), 67-115,World Scientic, (1995)

[2] T. B. Benjamin and F. Ursell, The stability of the plane free surface of a liquid in vertical periodic motion, Proc. Roy. Soc. London A225, 505 (1954)

[3] M. Faraday, On the forms and states assumed by uids in contact with vibrating elastic surfaces, Phil. Trans. R. Soc. Lond. 121,319(1831)

[4] A. Kudrolli and J.P. Gollub,Patterns and spatio-temporal chaos in parametrically forced surface waves: A systematic survey at largeaspect ratio,Physica D 97, 133 (1996)

[5] J.W.S. Lord Rayleigh, The circulation of air observed in Kundts tubes, and on some allied acoustical problems, Phil. Trans. Roy. Soc.London 175, 1 (1883)

[6] M. Higuera, J.M. Vega, and E. Knobloch, Coupled amplitude-streaming ow equations for nearly inviscid Faraday waves in smallaspect ratio containers, J. Nonlinear Sci. 12, 505 (2002)

[7] E. Martin, C. Martel, and J. M. Vega, Drift instability of standing Faraday waves, J. Fluid Mech. 467,57 (2002)

[8] J.Miles and D. Hendersonl, Parametrically forced surface waves, Annu. Rev. Fluid Mech. 22,143 (1990)

[9] L. Shemer and M. Chamesse , Experiments on nonlinear gravity-capillary waves,J. Fluid Mech. 380,205 (1999)

[10] S. Taneda, Visual observations of the ow around a half-submerged oscillating circular cylinder, Fluid Dyn. Res. 13, 119 (1994)

[11] J. Porter, I. Tinao, A. Laveron-Simavilla, and C.A. Lopez, Pattern selection in a horizontally vibrated container, Fluid Dyn. Res. 44,065501 (2012)

[12] F. Moisy, G.J. Michon, M. Rabaud, and E. Sultan, Cross-waves induced by the vertical oscillation of a fully immersed vertical plate,Phys. Fluids 10, (2014)

[13] H. Punzmann, N. Francois, H. Xia, G. Falkovich and M. Shats, Generation and reversal of surface ows by propagating waves, NaturePhysics134,031005-031018 (2012)

[14] J.M. Perez-Gracia, J. Porter, F. Varas, and J.M. Vega, Subharmonic capillary-gravity waves in large containers subject to horizontalvibrations, J. Fluid Mech. 739, 196 (2014)

100


ELECTROSTATIC CONTROL OF THE EVAPORATION OF NANOPARTICLE-LADEN DROPS

Alexander Wray1, Demetrios T. Papageorgiou2, Richard V. Craster2, Khellil Seane3, Omar K.Matar4

1Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, UK2Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2BZ, UK

3Institute for Materials and Processes, School of Engineering, The University of Edinburgh, King's Buildings,Mayeld Road, Edinburgh EH9 3JL, UK

4Department of Chemical Engineering, Imperial College London, South Kensington Campus, SW7 2AZ, UK

The coee stain eect, as described by Deegan et al., 1997 has received a wide array of attention in recent years, dueto its simultaneous appeal to both familiarity for the casual observer, as well as the non-trivial underlying physics. Inparticular, the mechanism at work relies on the interplay of three separate eects: contact line pinning, inhomogeneousevaporative ux and capillarity-induced ow. What is more, the eect (and its suppression) has a diverse range ofindustrial applications such as MALDI Spectrometry, Biochemical sample recover and OLED printing.

We investigate the behaviour of an evaporating, nanoparticle laden droplet deposited on a precursor lm. The modelallows for the weakening of the previously common assumption that the interface shape was a spherical cap, andretains eects of viscosity, capillarity, concentration-dependent rheology and Marangoni eects. After demonstratingthat the model recovers the ring-like formation, we allow the substrate to be an electrode, and incorporate a secondelectrode above the drop. A potential dierence between the electrodes induces a Maxwell stress at the interface whichwe demonstrate can used to exert control over the particle distribution.

The model is derived via the use of lubrication theory. The low-order nature of it is demonstrated to allow rapidnumerical simulation; this is exploited to map out the behaviour across parameter space. Limits of particular industrialrelevance, such as suppression of the ring-eect via the use of electric elds, are examined in detail, as well as thebroader possibilities such as droplet surgery as shown in Figure 0.1.

Figure 0.1: A droplet being split into two separate segments via the use of an electric eld. The two droplets then proceed to evaporateindependently. Reprinted from [2].

References

[1] A. W. Wray, D. T. Papageorgiou, R. V. Craster, K. Seane, O. K. Matar, Electrostatic Suppression of the Coee-stain Eect",Langmuir, 30 58495858 (2014).

[2] A. W. Wray, D. T. Papageorgiou, R. V. Craster, K. Seane, O. K. Matar, Electrostatic Suppression of the Coee-stain Eect",Procedia IUTAM, 15 172177 (2015).

101


WEAK SYNCHRONIZATION AND LARGE-SCALE COLLECTIVE OSCILLATION IN DENSEBACTERIAL SUSPENSIONS

Chong Chen1, Song Liu1, Xia-qing Shi2, Hugues Chaté3,4 & Yilin Wu1

1Department of Physics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong, P.R. China2Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006,

China3Service de Physique de lEtat Condensé, CEA, CNRS, Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette,

France4Beijing Computational Science Research Center, Beijing 100094, China

Collective oscillatory behavior is ubiquitous in nature and it plays a vital role in many biological processes. Col-lective oscillations in biological multicellular systems often arise from coupling mediated by diusive chemicals, byelectrochemical mechanisms, or by biomechanical interaction between cells and their physical environment. In theseexamples, the phase of some oscillatory intracellular degree of freedom is synchronized. Here, in contrast, we dis-covered a unique 'weak synchronization' mechanism that does not require long-range coupling, nor even inherentoscillation of individual cells: We found that millions of motile cells in dense bacterial suspensions can self-organizeinto highly robust collective oscillatory motion, while individuals move in an erratic manner. Over large spatial scaleswe found that the phase of the oscillations is in fact organized into a centimeter scale traveling wave. We presenta model of noisy self-propelled particles with strictly local interactions that accounts faithfully for our observations.These ndings expand our knowledge of biological self-organization and reveal a new type of long-range order in activematter systems. The mechanism of collective oscillation uncovered here may inspire new strategies to control theself-organization of active matter and swarming robots.

Figure 0.1: Two uid tracers underwent synchronized oscillation in elliptical trajectories, revealing highly robust collective oscillatorymotion of bacteria. Scale bar, 20 µm

References

[1] Chong Chen, Song Liu, Xiaqing Shi, Hugues Chaté, Yilin Wu , Weak synchronization and large-scale collective oscillation in densebacterial suspensions, Nature, doi:10.1038/nature20817 (2017)

102


STABILITY ENHANCEMENT OF A NATURAL CIRCULATION LOOP USING MAGNETICNANOFLUID: AN EXPERIMENTAL STUDY

Tabish Wahidi & Ajay Kumar Yadav

Department of Mechanical Engineering, NIT Karnataka, Surathkal, Mangalore 575 025, India

The circulation ability of internal uid driven by buoyancy as a result of density dierences caused by heating andcooling of dierent sections of loop is termed as natural circulation loop (NCL). It is a simple and veracious heat transferdevice that does not require any moving components like pumps and compressors. The chaotic nonlinear dynamicalbehavior, a ow reversal and oscillation of uid in the loop is known as instability. The appealing aspect of this researchis to control instability in ow patterns of NCL which is a major disadvantage of this loop. Controlling instabilitywithout deteriorating the performance of the loop is a challenging task for researchers. The present experimentalinvestigation is carried out to nd the feasibility of magnetically pulled nanouid in a natural circulation loop toenhance the stability. For the stability analysis, parametric study is performed over a range of operational parametersof heat input in the nanouid with Iron oxide particles having concentration of 0-1% by volume that are convectedmaterially in the thermosyphon loop in a distance dependent magnetic eld. To study the type of motions, a squarecopper loop is heated from below by Nichrome electric heating wire and cooled from above keeping both the verticaltubes adiabatic as shown in Fig. 1. The novelty arises due to application of magnetic eld to attract the magneticnanouid (loop uid) in the direction of ow to suppress instability. The electrical conductivity of uid and presenceof magnetic eld interaction become deciding factor for the ow pattern which are often unexpected. The stabilityand transient behaviour of loop depend on various thermophysical parameters. The unexplored dependent variablesstudied on the basis of uid dynamic instability characteristics are the mass ow rate, axial velocity, uid temperatureand pressure gradient of the loop uid. Obtained results show better stabilization of system due to viscous nature ofnanouid and the action of magnetic eld for various heat input.

Figure 0.1: Schematic view of experimental test setup.

103


NUMERICAL STUDY ON THE STABILITY OF MAGNETIC NANOFLUID BASED NATURALCIRCULATION LOOP

Allen Chacko, Aashish Kumari & Ajay Kumar Yadav

Department of Mechanical Engineering, NIT Karnataka, Surathkal, Mangalore 575 025, India

Natural circulation loop (NCL) is a heat transfer device in which ow is driven by buoyancy caused by thermallygenerated density gradient without the requirement of any external pump/compressor. Usually heat source is locatedbelow the heat sink to promote natural circulation. When both the heat source and heat sink conditions are maintainedconstant, steady state circulation is expected to be achieved, which can continue indenitely, if the integrity of theloop is maintained. However, natural circulation systems are susceptible to several kinds of instability mainly due tothe nonlinear nature of the natural circulation process and its low driving force. Therefore, any disturbance in thedriving force will aect the ow which in turn will lead to an oscillatory behavior even in cases where eventually asteady state is expected.

An eective method to tackle this problem of instability is by using magnetic nanouids instead of the traditional loopuids like water, refrigerants, secondary uids. The application of a local magnetic eld (as shown in gure 1) createsan additional body force acting on the uid. This body force contributes to the direction of ow, thereby reducinginstabilities. In Addition to this, use of magnetic nanouids has other added advantages, enhanced heat transfercoecients in the presence of external magnetic eld and stable ow due to high friction factor. The main objectiveof this research work is to carry out numerical studies on magnetic nanouid based NCL for better understandingof instability behaviors and its control. The behavior of the loop is studied by varying, input power range 0-3kW,Magnetic eld between 0-0.5T and concentration of magnetic nanouid from 0-2%. The results indicate that therehas been a signicant reduction in the amplitude of oscillation of mass ow rate as time progresses. In other wordsthe oscillations of the mass ow rate decays faster and a steady mass ow rate is achieved in a shorter time interval.

Figure 0.1: Schematic of rectangular natural circulation loop.

104


ON THE SECONDARY INSTABILITY IN PLANAR SHEAR FLOW PAST A CIRCULARCYLINDER

Doohyun Park & Kyung-Soo Yang

Department of Mechanical Engineering, Inha University, Incheon, 22212, Republic of Korea

The eects of planar shear on the secondary instability in the ow past a circular cylinder have been studied by usingFloquet stability ananlysis. An immersed boundary method [1] was used in order to implement a circular cylinder in aCartesian grid system. The key parameters are the Reynolds number (Re) based on the inlet center velocity (Uc ) andthe cylinder diameter (D) and the shear parameter (K) dened as K = GD/Uc. Here, G is the velocity gradient in thevertical direction. The ranges of Re and K considered in the present investigation are and , respectively. Increasingshear renders the ow more unstable to the primary instability, known as Hopf bifurcation in which a steady owbifurcates into a time-periodic ow. The critical Reynolds number of the primary instability (Rec1) becomes lower withincreasing K. Above another higher critical Reynolds number (Rec2), a secondary instability of three-dimensional (3D)nature sets in. In the case of uniform ow (K = 0), the secondary instability manifests itself in the form of 3D modes,namely A, B, and QP in the ascending order of Rec2 [2]. We found, however, that presence of planar shear breaks thesymmetry of the time-periodic base ow, signicantly aecting the characteristics of the secondary instability. ModeQP is turned into mode C by the asymmetry induced by the planar shear. The planar shear stabilizes modes A andB, but destabilizes mode C. As a result, crossover of criticality between C and A, B occurs with increasing K. In thecase of K = 0.2, the maximum planar shear considered in the present study, mode C is even dominant over modesA and B, and Rec2 of mode C is even lower than that of mode A without shear. The eects of planar shear on thespatial and temporal characteristics of the 3D modes are discussed. Neutral stability curves of the 3D modes for eachK are also presented. Direct Numerical Simulation was performed in order to verify our Floquet stability analysis,yielding good agreement with our Floquet results.

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) (No. 2015R1A2A2A01002981).

Figure 0.1: Instantaneous streamwise vorticity contours of Floquet mode (mode C), Re=150, K=0.2, β=4.1. Solid and dashed linesrepresent positive and negative values of spanwise vorticity of the base ow, respectively (lines, ωz = ±0.2).

References

[1] J. Yang, E. Balaras, An embedded-boundary formulation for large-eddy simulation of turbulent ows interacting with moving bound-aries,J. Comput. Phys. 215, 12-40 (2006)

[2] C. H. K. Williamson, The existence of two stages in the transition to three-dimensionality of a circular cylinder wake, Phys. Fluids31, 3165-3168 (1988)

105


MIXED CONVECTION IN A DOWNWARD FLOW IN A VERTICAL DUCT IN THEPRESENCE OF STRONG MAGNETIC FIELD

Xuan Zhang & Oleg Zikanov

Department of Mechanical Engineering, University of Michigan-Dearborn, MI 48128 USA

Mixed convection in a downward ow in a vertical duct with one wall heated in the presence of strong magnetic eldis analyzed in this work. The work is motivated by the design of liquid metal blankets for a tokamak fusion reactorwhich experience strong magnetic eld and strong heat ux. The conguration considered in this work is a segmentof a DCLL (Dual Coolant Lead Lithium) blanket, a square duct, within which liquid metal ows downward and themagnetic eld is imposed perpendicularly to the ow direction. The duct walls are assumed to be thermally andelectrically insulated except that constant heating ux is imposed at one wall. As the magnetic eld is very strong andperpendicular to one set of the duct walls, the ow is studied as two-dimensional using the approximation of [1]) anddirect numerical simulations. The computations are conducted at Pr = 0.0321, 5000 ≤ Re ≤ 105, 106 ≤ Gr ≤ 1010

and 103 ≤ Ha ≤ 104.

In a insulated duct with non-zero downward ow and strong heating ux, the temperature of the uid grows downwardalong the duct. The uid becomes hotter in the lower part, i.e. unstably stratied. As observed in the simulations, apair of strong jets is formed due to the associated buoyancy force. The upward jet near the heated wall grows fast.SImilar jets also occur in a hydrodynamic ow but they can not be observed due to their breakdown into turbulence.In our conguration, the jets are stabilized by the strong magnetic eld, but periodically become unstable and breakdown at some parameters.

Three typical ow regimes: steady-state, intermittent, or unstable with developed instability are identied dependingon the parameters (see gure 0.1) [2]. When the mean ow is very fast, the growth of temperature along the ductis insignicant, and the jets are weak and stable. Flow reaches a steady state with a hot spot near the exit (seegure 0.1a). When the ow moves moderately fast (Re is not very large), the temperature grows faster and thejets become much stronger. When Gr and Ha are xed, there is a critical Reynolds number Recr below which jetsare unstable and break down into strong vortices leading to large temperature uctuations (see gure 0.1c). Anintermittent state (see gure 0.1b) also exists at the parameters close to the critical values, where the breakdown eventis followed by a steady state during which the jets are reformed. The results of a parametric study show that the owbehavior is dominated by the buoyancy eect and magnetic damping together. At the conditions of a fusion reactor,the ow is likely to be unstable with developed instability.

Figure 0.1: Instantaneous distribution of temperature T in the ows of three typical regimes: Gr = 109, Ha = 5000, Re = 4 × 104 (a)(steady-state), Re = 3 × 104 (b) (intermittent) and Re = 2 × 104 (c) (unstable with developed instability). The mean ow is directeddownwards, and the heating is applied to the wall at x = −1. The ow is approximated as two-dimensional due to the strong magneticeld oriented perpendicularly to the plane of the paper [1].

References

[1] J. Sommeria, R. Moreau,Why, how and when MHD-turbulence becomes two-dimensional, J. Fluid Mech. 118, 507518 (1982).

[2] X. Zhang, Thermal convection in liquid metal blankets for tokamak fusion reactors, Doctoral Thesis, University of Michigan-Dearborn(2017).

106


EFFECT OF THE SYMMETRY OF A ROTATING MAGNETIC FIELD ON THE FLOWINSTABILITY OF THE CONDUCTING LIQUID (TAYLOR'S AND WAVY VORTICES)

Alexander Zibold

Donetsk, 283001 Ukraine

Stationary instability of axisymmetric laminar ow of a viscous conducting liquid in the innitely long circular cylinder,arising under the inuence of coaxially rotating magnetic eld (RMF) of any rotary symmetry, has been investigated.Analyzing stability of similar type of ow, Lin [1] has noticed, that the rst approximation equations for smallperturbations of velocity and pressure allow for periodic solution with respect to ϕ and z :

f = f(r) exp(σt+ inϕ+ iaz),

where n is the integer number, and a is the real (dimensionless wave number).

Usually one deals with a special case of rotary symmetry n = 0. In this case a primary ow is independent of ϕ ,but the disturbances of velocity ur, uϕ, uz and pressure q are not zero. Stability of a primary azimuthal ow and 3Dhydrodynamic structures thus arising - Taylor's vortices - are investigated in sucient detail [2, 3].

Case n = 0 corresponds to the occurrence of the so-called wavy vortices when waves propagate along the axes ofTaylor's vortices. The problem of stability of a primary azimuthal ow concerning occurrence of Taylor's vortices, andwavy vortices of dierent orders for one pair of poles (p = 1) of the RMF is considered in [4]. Expanding the area of thisproblem parameters for any symmetry of the RMF is oered. The problem is solved for two cases: in low-frequencyapproach and for any value of relative frequency. With the use of Galerkin's method the curves of neutral stabilitycorresponding to occurrence of Taylor's and wavy vortices are calculated. It is shown, that Taylor's vortices at p = 1arise in wide enough, but limited range of ow parameters, but upon the increase in parameters, they lose stabilityand convert to wavy vortices. It is established, that under certain conditions the loss of stability of a primary owleads to the direct appearance of wavy vortices of some order, by-passing a stage of Taylor's vortices. On the curve ofneutral stability separating area of one-dimensional azimuthal ow from the region of a three-dimensional vortical ow,points of bifurcation, corresponding to transition from a secondary ow in the form of Taylor's vortices to a secondaryow in the form of wavy vortices with n = 1 and with consecutively higher orders of a sinuosity, are dened further.It is characteristic, that such transitions are accompanied by step-wise increase in wave number, i.e. transition tosmaller and smaller scale vortices. Such a cascade of bifurcations is observed as on the branch of the neutral stabilitycorresponding to low-frequency approach, and on the branch corresponding to the case of arbitrary values of relativefrequency. With increase in the order of rotary symmetry of the RMF (p = 2) the range of parameters at which lossof stability of a primary ow leads to occurrence of Taylor's vortices, is reduced. At p = 3 Taylor's vortices do notarise at all, and at once there are wavy vortices with n ≥ 1. At p = 4 a zone of occurrence of wavy vortices with n = 1is reduced, and at p = 5 wavy vortices appear already only at n ≥ 2. The increases in values of Hartmann number,relative frequency and an order of rotary symmetry of the RMF reduce the characteristic size both Taylor's and wavyvortices. The vortices centre is thus displaced towards the cylinder wall.

The executed research allows one to expand our views about the mechanisms of the rise of the instability of theconducting liquid ow generated by the RMF of any rotary symmetry in innitely long cylindrical vessel. The resultsobtained thus far allow us to predict the loss of stability of a primary ow occurrence of a secondary ow in Taylor'svortices or wavy vortices of this or that order depending on the level of the power aecting the liquid and on the orderof rotary symmetry of the RMF. Apparently, these conclusions would likely be fair and for long enough cylinders

References

[1] C.C. Lin , The Theory of Hydrodynamic Stability, Cambridge: Cambridge University Press (1955)

[2] A. B. Kapusta, A. F. Zibold, Stationary instability of axisymmetric ow of a liquid in a rotating magnetic eld, Magnetohydrodynamics13 (1977)

[3] A.F. Zibold, Stationary instability of axisymmetric ow of liquid in a weak rotating magnetic eld,, Magnetohydrodynamics, 20 (1984)

[4] A.F. Zibold, Instability of a ow of the conducting liquid generated by the rotating magnetic eld: Taylor's and wavy vortices, FluidDyn. Res. (in press)

107


INSTABILITIES IN EXTREME MAGNETOCONVECTION

Oleg Zikanov1, Xuan Zhang1 & Yaroslav Listratov2

1Department of Mechanical Engineering, University of Michigan - Dearborn, Dearborn, MI 48128, USA2Moscow Power Engineering Institute, Moscow, 111250, Russia

Extreme magnetoconvection is the thermal convection in an electrically conducting uid (for example, a liquid metal)that occurs in the presence of an imposed magnetic eld. We analyze this phenomenon computationally focusing onthe case of very strong static elds (the Hartmann number up to 104) and strong heating (the Grashof number up to1012). Our goals are to understand the nature of the ow and to explore the implications for the design of liquid metalblankets of tokamak fusion reactors and other liquid metal systems. It is found that, as the intense Joule dissipationof induced electric currents suppresses conventional turbulence, the ows begin to demonstrate extreme, unusual andcounter-intuitive behaviors dominated by magnetohydrodynamic instabilities. The specic examples, explained indetail in the references below, include:

• Flows in horizontal ducts and pipes with heating from below and transverse horizontal magnetic elds [1, 2].Here, the convection instability in the form of rolls aligned with the magnetic eld and transported by the meanow leads to slow, high-amplitude (so-called anomalous) uctuations of temperature.

• Downward ows in vertical ducts and pipes withe heating from the side and horizontal magnetic eld perpen-dicular to the temperature gradient [3, 4]. In these ows, anomalous temperature uctuations of even higheramplitude are caused by periodic breakdown of the elevator convection modes - exponentially growing structuresin the form of pairs of upward and downward jets.

• Flow in horizontal ducts with nonuniform internal heating and strong axial magnetic eld [5, 6, 7]. These owsare rendered either perfectly or nearly two-dimensional by the magnetic eld. In the simplest case of zero meanow, isothermal walls, and purely axial magnetic eld, classical two-dimensional turbulence is developed. Theow is modied substantially, in particular the turbulence is suppressed, when practical life complexities, suchas the mean ow along the duct or the additional vertical magnetic eld are introduced.

References

[1] O. Zikanov, Y. Listratov, V. G. Sviridov, Natural convection in horizontal pipe ow with strong transverse magnetic eld, J. FluidMech. 720, 486-516 (2013)

[2] X. Zhang, O. Zikanov, Mixed convection in a horizontal duct with bottom heating and strong transverse magnetic eld, J. Fluid Mech.757, 33-56 (2014)

[3] L. Liu, O. Zikanov, Elevator mode convection in ows with strong magnetic elds, Phys. Fluids 27(4) , 044103 (2015)

[4] O. Zikanov, Y. Listratov, Numerical investigation of MHD heat transfer in a vertical round tube aected by transverse magnetic eld,Fusion Eng. Des. 113, 151-161 (2016)

[5] X. Zhang, O. Zikanov, Two-dimensional turbulent convection in a toroidal duct of a liquid metal blanket of a fusion reactor, J. FluidMech. 779, 36-52 (2015)

[6] X. Zhang, O. Zikanov Thermal convection in toroidal ducts of a liquid metal blanket. Part I: Eect of poloidal magnetic eld, FusionEng. Des.(submitted) (2016)

[7] X. Zhang, O. Zikanov Thermal convection in toroidal ducts of a liquid metal blanket. Part II: Eect of mean ow,Fusion Eng. Des.(submitted) (2016)

108

List of participants

• Vladimir Ajaev Department of Mathematics, Southern Methodist University, Dallas, TX, USAEmail: [email protected]

• Meheboob Alam Engineering Mech. Unit, J. Nehru Center for Advanced Research, Jakkur P.O., Bangalore560064, IndiaEmail: [email protected]

• Igor Aranson Department of Biomed. Engineering, Pennsylvania State University, University Park, Pennsyl-vania 16802, USAEmail:[email protected]

• Dmitriy Arkhipov Institute of Thermophysics SB RAS and Novosibirsk State University, Novosibirsk, RussiaEmail: [email protected]

• Vemuri Balakotaiah Department of Chemical Engineering, University of Houston, Houston, TX, USAEmail: [email protected]

• Samire Balta Department of Mathematics, University College London, London, WC1 E6BT, United KingdomEmail: [email protected]

• Pinhas Z. Bar-Yoseph Department of Mech. Engineering, Technion, Haifa 3200, IsraelEmail: [email protected]

• Ilya Barmak School of Mech. Engineering, Tel-Aviv University, Tel-Aviv 69978, IsraelEmail: [email protected]

• Vladimir Batishchev Institute of Mathematics, Mechanics and Computer Sci., Southern Federal University,Rostov/Don, RussiaEmail: [email protected]

• William Batson Department of Math. Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USAEmail: [email protected]

• Avraham Beer Zuckerberg Institute for Water Research, Ben-Gurion University, Sde Boker Campus, 84990Midreshet Ben-Gurion, IsraelEmail: [email protected]

• Ivan Belyaev Joint Institute for High Temperatures RAS, Moscow, RussiaEmail: [email protected]

• Eugene Benilov Department of Mathematics, University of Limerick, Limerick, V94 T9PX, IrelandEmail: [email protected]

109


• Luca Biancoore Department of Mechanical Engineering, Bilkent University, 06800 Bilkent, Ankara, TurkeyEmail: [email protected]

• Lamia Bourdache Laboratoire de Physique theorique, Universite De Bejaia, Bejaia 06000, AlgeriaEmail: [email protected]

• Morten Brøns Technical University of Denmark, Kongens Lyngby, DenmarkEmail: [email protected]

• Loic Cappanera Department of Computational and Applied Math., Rice University, Houston, TX, USAEmail: [email protected]

• Bruno Souza Carmo Department of Mech. Engineering, Poli, University of Sao Paolo, Sao Paolo, BrazilEmail: [email protected]

• Nicolas Cellier LOCIE, Universite de Savoie Mont-Blanc, FranceEmail: [email protected]

• Marina Chugunova Institute Math. Sciences, Claremont Graduate University, Claremont, CA 91711, USAEmail: [email protected]

• Pietro De Palma DMMM, Politecnico di Bari, via Re David 200, 70125, Bari, ItalyEmail: [email protected]

• Javier A. Diez Instituto de Fisica Arroyo Seco, Universidad Nacional del Centro de la Provincia de BuenosAires, Pinto 399, 7000 Tandil, ArgentinaEmail: [email protected]

• Nick Evstigneev Lab. 11-3, Federal Research Center Informatics and Control, Institute System Analysis,117312 Moscow, RussiaEmail: [email protected]

• Mirko Farano DMMM, Politecnico di Bari, via Re David 200, 70125, Bari, ItalyEmail: [email protected]

• Yuri Feldman Department of Mech. Engineering, Ben-Gurion University, Beer-Sheva 84105, IsraelEmail: [email protected]

• Fred Feudel Institut fur Physik und Astronomie, Universitat Potsdam, 14476 Potsdam, GermanyEmail: [email protected]

• Barry Friedman Department of Physics, Sam Houston State University, Huntsville, TX 77341, USAEmail: [email protected]

• Alexander Gelfgat School of Mech. Engineering, Tel-Aviv University, Tel-Aviv 69978, IsraelEmail: [email protected]

• Julian M. Granados Facultad de Ingenierias, Institucion Universitaria de Envigado, Envigado, ColombiaEmail: [email protected]

110


• Gemunu Gunaratne Department of Physics, University of Houston, Houston, TX 77204, USAEmail: [email protected]

• Matthew Haynes Department of Mathematics, University of Limerick, Limerick, V94 T9PX, IrelandEmail: [email protected]

• Benjamin Herrman-Priesnitz Department of Mech. Engineering Universidad de Chile, Santiago, ChileEmail: [email protected]

• Di Kang Institute of Math. Sciences, Claremont Graduate University, Claremont, CA, USAEmail: [email protected]

• Genta Kawahara Graduate School of Engineering Sci., Osaka University, Osaka, JapanEmail: [email protected]

• Evgeniy Khain Department of Physics, Oakland University, Rochester, MI 48309, USAEmail: [email protected]

• Anil Koklu Department of Mech. Engineering, Southern Methodist University, Dallas, TX 75205, USAEmail: [email protected]

• Nikolai Kozlov Lab. Hydrodynamic Stability, Institute of Continuous Media Mechanics, Perm 614013, RussiaEmail: [email protected]

• V. Kumaran Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, IndiaEmail: [email protected]

• Herbert Levine Center for Theoretical Biological Physics, MS-142, Rice University, Houston, TX 77005, USAEmail: [email protected]

• Duan Li National Microgravity Lab., Institute of Mechanics CAS, Beijing, ChinaEmail: [email protected]

• Han-Ming Li College of Power Engineering, Chongqing University, Chongqing, 400044, ChinaEmail: [email protected]

• Yaroslav Listratov National Research University MPEI, Moscow 111250, RussiaEmail: [email protected]

• Yu-Quan Liu School of Petroleum Engineering, China University of Petroleum, Qingdao 266580 ShondongProvince, ChinaEmail: [email protected]

• Meichen Lu Department of Chem. Engineering, University of Cambridge, Cambridge CB2 3RA, United King-domEmail: [email protected]

• Tatyana P. Lyubimova Lab of CFD, Institute of Continuous Media Mechanics UB RAS, Perm 614990, RussiaEmail: [email protected]

111


• Junkun Ma Department of Agricul. Sci. and Eng. Technology, Sam Houston State University, Huntsville, TX77341, USAEmail: [email protected]

• George Mamatsashvili Helmholtz-Zentrum Dresden Rosendorf, P.O. Box 510119, D-01314 Dresden, GermanyEmail: [email protected]

• Moshe Matalon Dept. Mech. Science and Engineering, University of Illinois at Urbana-Champaign, Urbana,IL 61801, USAEmail: [email protected]

• Kazuo Matsuura Graduate School of Science and Eng., Ehime University, 3 Bunkyo-cho, Matsuyama, Ehime,790-8577, JapanEmail: [email protected]

• Bachir Meziani Dept. Physics Theoretique, A. Mira University, Bejaia, Campus Targe Ouzemour, 06000 Be-jaia, AlgeriaEmail: [email protected]

• Alexander Mikishev Department of Physics, Sam Houston State University, Huntsville, TX 77341, USAEmail: [email protected]

• Antoine Monnier Universite Bretagne Sud, EA 4250, LIMATB F-56100, Lorient, FranceEmail: [email protected]

• Davide Montagnani Politecnico di Milano, Milano, ItalyEmail: [email protected]

• Matvey Morozov Department of Chemical Engineerin, Technio, Haifa, 32000, IsraelEmail: [email protected]

• Shingo Motoki Graduate School of Eng. Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka,560-8531, JapanEmail: [email protected]

• Johann Moulin ONERA-DAFE, 8 rue des Vertugadins, 92190 Meudon, FranceEmail: [email protected]

• Eric Muiño-Garcia Department of Applied Physics, CINVESTAV-IPN, Merida, Yucatan 97310, MexicoEmail: [email protected]

• Ranga Narayanan Department of Chem. Engineering, University of Florida, Gainesville, FL 32611, USAEmail: [email protected]

• Alexander A. Nepomnyashchy Department of Mathematics, Technion, Haifa 32000, IsraelEmail: [email protected]

• Nikesh Institute Aeronautics and Appl. Mechanics, Warsaw University of Technology, Nowowiejska 24, 00-665Warsaw, PolandEmail: [email protected]

112


• Tomohiro Nimura Department of Mech. Engineering, Tokyo University of Science, Chiba 278-8510, JapanEmail: [email protected]

• Hiroyuki Nishikawa Graduate School of Information Science, Nagoya University, Nagoya, 464-8601, JapanEmail: [email protected]

• Olurotimi Ojoniyi Department of Physics, Tai Solaria University of Education, Ijagun, Ijeba Ode, NigeriaEmail: [email protected]

• Alex Oron Department of Mech. Engineering, Technion, Haifa 32000, IsraelEmail: [email protected]

• Jose Miguel Perez School of Aerospace Eng., Universidad Politecnica de Madrid, Madrid, SpainEmail: [email protected]

• Jean-Lou Pster ONERA F-92190 Meudon, FranceEmail: [email protected]

• Dipin S. Pillai Department of Chem. Engineering, University of Florida, Gainesville, FL 32611, USAEmail: [email protected]

• S. Pradhan Department of Chem. Engineering, IIS, Bangalore 560012, IndiaEmail: [email protected]

• Kang Qi National Microgravity Laboratory, Institute of Mechanics CAS, Bejing, ChinaEmail: [email protected]

• Luis Fernando Arredondo Rodriguez Irapuato Superior Technologic Institute, Road to Cerrito og Galomb#50, PC 37980 San Jose Itarbide, MexicoEmail: [email protected]

• Francesco Romano Institute of Fluid Mechanics and Heat Transfer, TU Wien, 1060 Wien, AustriaEmail: [email protected]

• Anthony Rouquier Department of Applied Mathematics, University of Coventry, Coventry, United KingdomEmail: [email protected]

• Sudip Sen National Institute of Aerospace and College William & Mary, VA, USAEmail:[email protected]

• Valentina Shevtsova Microgravity Research Center, CP-EP-165/62, ULB, Brussels, BelgiumEmail: [email protected]

• Vladimir N. Shtern Laboratory Chem. Technology, Ghent University, B-9052 Ghent, BelgiumEmail: [email protected]

• Sanjay Singh Applied Math. Research Center, Faculty of Engineering and Computing, Coventry University,CV1 5FB, United KingdomEmail: [email protected]

113


• Rodion Stepanov Institute of Continuous Media Mechanics, 614013, Perm, RussiaEmail: [email protected]

• Edward W. Swim Department of Mathematics ans Statistics, Sam Houston State University, Huntsville, TX77341, USAEmail: [email protected]

• Igor Teplyakov Joint Institute for High Temperatures RAS, Moscow 111395, RussiaEmail: [email protected]

• Edriss Titi Department of Mathematics, Texas A&M, College Station, TX, USAEmail: [email protected]

• Luis Armando Torres-Cisneros Dept. Fisica Aplicada, CINVESTAV del IPN, Merida, Yucatan, MexicoEmail: [email protected]

• Pei-Hsun Tsai Institute of Appl. Mechanics, National Taiwan University, TaiwanEmail: [email protected]

• Takahiro Tsukahara Dept. Mech. Engineering, Tokyo University of Science, Chiba 278-8510, JapanEmail: [email protected]

• Kerem Uguz Dept. Chemical Engineering, Bogazici University, Istanbul, 34342, TurkeyEmail: [email protected]

• Orkan Umurhan NASA Ames Research Center, Space Sci. Division, Moett Field, CA 94035, USAEmail: [email protected]

• Jose Manuel Vega E.T.S.I. Aeronautica y del Espacio, Universidad Politecnica de Madrid, 2804 Madrid, SpainEmail: [email protected]

• Tabish Wahidi Department of Mech. Engineering, NIT Karnataka, Mangalore 575025, IndiaEmail: [email protected]

• Takashi Watanabe Graduate School of Information Science, Nagoya University, Nagoya, 464-8601, JapanEmail: [email protected]

• Alexander Wray Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH,United KingdomEmail: [email protected]

• Yilin Wu Department of Physics, The Chinese University of Hong Kong, China/Hong KongEmail: [email protected]

• Ajay Kumar Yadav Department of Mech. Engineering, NIT Karnataka, Mangalore 575025, IndiaEmail: [email protected]

• Kyung-Soo Yang Department of Mech. Engineering, Inha University, Inchcon 22212, KoreaEmail: [email protected]

114


• Oleg Zikanov Department of Mech. Engineering, U Michigan-Dearborn, MI 48128, USAEmail: [email protected]

• Xuan Zhang Department of Mech. Engineering, U Michigan-Dearborn, MI 48128, USAEmail: [email protected]

115

Author's Index

AgnonYehuda, 11

AjaevVladimir, 1

AlamMeheboob, 2

AltundemirSercan, 3

AmiroudineS., 30

AransonIgor, 4

ArielGil, 12

ArkhipovDmitriy, 5

AuteriFranco, 65

AziziHossein, 6

BaltaSamire, 7

BandelierPhilippe, 20

BarmakI., 8

BataliRoberto, 97

BatishchevVladimir, 9

BatsonWilliam, 10, 11

Be'erAvraham, 12

BelyaevIvan, 13, 14

BenilovEugene, 15, 16, 35

BestehornMichael, 76

BiancooreLuca, 17, 99

BourdacheLamia, 18

BradyJohn F., 4

BraunerN., 8

Bustamante

Carlos A., 33

CadouJ.M., 64

CaneyNadia, 20

CappaneraLoïc, 19

CariniMarco, 79

CarmoBruno Souza, 37

CellierNicolas, 20

ChackoAllen, 104

ChatéHugues, 102

ChenChong, 102

ChernyshDenis, 13

CherubiniS., 22, 27

ChikulaevDmitriy, 91

ChugunovaMarina, 21, 39

ClaincheSoledad Le, 78

CrasterRichard V., 101

CuellarIngrith, 23, 32

CummingsLinda, 10

De PalmaP., 22, 27

DemekhinE.A., 30

DenisovaMariya, 42

DiWu, 83

DiazGerardo, 36

DietzelMathias, 71

Diez

117


Javier A., 23, 32Djeghiour

Rabah, 24Djema

Amar, 18

EribolPinar, 3

EvstigneevNick, 26

FaizrakhmanovaIrina S., 52

FaranoM., 22, 27

FeldmanYuri, 28

FeudelFred, 29

FlórezWhady F., 33

GallaireF., 17

GanchenkoG.S., 30

GaponenkoYuri, 88, 89

GelfgatA., 8, 31

GepnerS.W., 72

GioriaRafael dos Santos, 37

GiraultG., 64

GladdenLynn F., 51

GoldsteinM.L., 87

GonzálezAlejandro G., 23, 32

GopanNandu, 2

GorbachevaE.V., 30

GranadosJulián M., 33

GuermondJean-Luc, 19

GuevelY., 64

GunaratneGemunu, 34

GurevichSebastian, 6

HardtSteen, 71

HaynesMatthew, 35

HeifetzE., 17

HerremanWietze, 19

Herrmann-PriesnitzBenjamín, 36

HoepnerJ., 17

HoreshAmihai, 59, 66

IdanShahar, 28

IslerJoão Anderson, 37

IvochkinYury, 95

JiaWang, 46, 83

JutleyMahnprit, 1

KanazawaTakahiro, 38

KangChang-Wei, 56Di, 39

KawaharaGenta, 38, 67

KhainEvgeniy, 40

KlementyevaIrina, 95

KokluAnil, 41

KolesovE.V., 54

KondicLou, 10

KostarevKonstantin, 42

KozlovVictor, 94Nikolai, 42, 43

KuhlmannHedrik C., 85

KumaranV., 44

KumariAashish, 104

LevineHerbert, 45

LiDuan, 46, 83Han-Ming, 47

LiangHu, 83

LimTeck-Bin Arthur, 56

118


LinD., 87

ListratovYaroslav, 48, 49, 108

LiuSong, 102Yu-Quan, 50

LuMeichen, 51

LuchinkinNikita, 13

LyubimovaTatyana P., 5254

MaJunkun, 57Shengwei, 56

MamatsashviliGeorge, 58

ManciniC., 22

ManorOfer, 59, 66

MarquetOlivier, 68, 79

Marín-AntuñaJosé, 69

MatalonMoshe, 60

MatarOmar K., 101

MatsuuraKazuo, 62

MelnikovIvan, 14

MezianiBachir, 24

MialdunAliaksandr, 88, 89

MikishevAlexander B., 63

MizevAlexay, 42

MonnierA., 64

MontagnaniDavide, 65

MoralesEsperanza Rodriguez, 84

MorozovMatvey, 59, 66

MotokiShingo, 67

MoulinJohann, 68

MuñozWilliams R. Calderón, 36

Muiño-GarcíaErick, 69

Muratov

Igor D., 53

NadimAli, 39

Nahmad-MolinariYuri, 97

NaranayananRanga, 70

NarayananRanga, 80, 81

NejatiIman, 71

NepomnyashchyAlexander A., 63, 88

Nikesh, 72Nimura

Tomohiro, 73Nishikawa

Hiroyuki, 74Njah

Abdulahi N., 75Nore

Caroline, 19

O'BrienS.B.G, 35

OgnerubovDmitriy, 49

OjoniyiOlurotimi S., 75

OronAlex, 11, 76

OurradOuerdia, 24

OzanS. Canberk, 77

PapageorgiouDemetrios T., 101

ParkDoohyun, 105

Perez-GarciaJose M., 100

Perez-ÁngeliGabriel, 97

PetulanteN., 87

PsterJean-Lou, 79

PicardoJason R., 80

PillaiDipin S., 81

PlunianFranck, 93

PoddubnyIvan, 14

PotheratAlban, 86

PothératAlban, 92

119


PowerHenry, 33

PradhanS., 82

PringleChris, 92

ProvatasNikolas, 6

PyatnitskayaNatalia, 13

PérezJosé Miguel, 78

QiKang, 46, 83

RasuvanovNikita, 13, 14, 48

RavazzoliPablo, 23, 32

RobinetJ.-C., 22, 27

RodríguezLuis Fernando Arredondo, 84

Rodríguez-LiñánGustavo Manuel, 97

RomanóFrancesco, 85

RouquierAnthony, 86

RubioLeonardo, 4

Ruyer-QuilChristian, 20

SabirovRustam, 94

SabuncuAhmet C., 41

ScaleW., 87

SchneiderT.M., 27

SedermanAndrew J., 51

SeaneKhellil, 101

SenS., 87

ShevtsovaValentina, 88, 89

ShiWan-Yuan, 47Xia-qing, 102

ShimizuMasaki, 38, 67

ShmyrovAndrey, 42

ShternVladimir, 90

Shvarts

Konstantin, 91Singh

Sanjay, 92Smith

Frank T., 7Sokolov

Andrey, 4Soto

Rodrigo, 36Stefani

Frank, 58Stepanov

Rodion, 93Sterman-Cohen

Elad, 76Stutz

Benoit, 20Subbotin

Stanislav, 94Sveridov

Valentin, 14Sviridov

Valentin, 48, 49Szumbarski

J., 72

TaranetsRoman, 21

TeplyakovIgor, 95

TitiEdriss S., 96

Torres-CisnerosLuis Armando, 97

TsaiPei-Hsun, 98

TsimringLev, 40

TsukaharaTakahiro, 73

TsvelodubOleg, 5

TuckermanLaurette, 29

UguzA. Kerem, 3, 77

UlmannA., 8

UmurhanOrkan M., 99

VarasFernando, 100

VegaJosé M., 78, 100

VinogradovDmitriy, 95

WahidiTabish, 103

120


WangAn-Bang, 98

WatanabeTakashi, 74

WenruiHu, 83

WrayAlexander, 101

WuChih-Hua, 56Yilin, 102

Yadav

Ajay Kumar, 103, 104Yang

Kyung-Soo, 105Yasnou

Viktar, 88, 89

ZhangXuan, 106, 108

ZiboldAlexander, 107

ZikanovOleg, 48, 49, 106, 108

121

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