Instability and turbulence Instability and turbulence in flows of automotive and in flows of automotive and

aeronautical interestaeronautical interest

D. Tordella, M. Onorato, M. Iovieno, S. Scarsoglio, P. D. Tordella, M. Onorato, M. Iovieno, S. Scarsoglio, P. Bailey, Bailey,

C. Tribuzi, C. Haigermoser, L. Vesely, M. NovaraC. Tribuzi, C. Haigermoser, L. Vesely, M. Novara

Unione Industriale TorinoUnione Industriale Torino

4 Settembre 20074 Settembre 2007

Dipartimento di Ingegneria Aeronautica e SpazialeDipartimento di Ingegneria Aeronautica e Spaziale

Politecnico di TorinoPolitecnico di Torino

Unione Industriale TorinoUnione Industriale Torino

Hydrodynamic stability Hydrodynamic stability in bluff-body wakesin bluff-body wakes

Daniela Tordella, Stefania ScarsoglioDaniela Tordella, Stefania ScarsoglioDipartimento di Ingegneria Aeronautica e SpazialeDipartimento di Ingegneria Aeronautica e Spaziale

Politecnico di TorinoPolitecnico di Torino

MotivationMotivation

Stability analysisStability analysis To understand the reasons for the To understand the reasons for the

breakdown of laminar flow;breakdown of laminar flow; To predict the transition to turbulenceTo predict the transition to turbulence

Two-dimensional wake past a Two-dimensional wake past a circular cylindercircular cylinder Circular cylinder is the quintessential bluff-Circular cylinder is the quintessential bluff-

body;body; Important prototype of free shear flow for Important prototype of free shear flow for

applications in fluid mechanicsapplications in fluid mechanics

ApplicationApplication

Bluff-body wakes;Bluff-body wakes;

Sequence of bodies moving one Sequence of bodies moving one respect to each other (unsteady respect to each other (unsteady motion):motion): automotive (highways);automotive (highways); aeronautical (runways)aeronautical (runways)

Theory (initial-value problem) Theory (initial-value problem) unsteady motion configurations where unsteady motion configurations where perturbations (bodies moving) can perturbations (bodies moving) can arbitrarily occurarbitrarily occur

Key points:Key points: Linear analysis in free flows:Linear analysis in free flows:

Non linear aspects do not substantially affect the Non linear aspects do not substantially affect the most unstable waves (true also for high most unstable waves (true also for high ReRe););

Linear theory results (frequency and Linear theory results (frequency and wavenumber) represent the large scale wavenumber) represent the large scale structures of the fully developed turbulent flowstructures of the fully developed turbulent flow

For high For high ReRe, the most unstable waves are , the most unstable waves are long (long ( 10 spatial scales D); 10 spatial scales D);

Long waves slowly dissipate in time;Long waves slowly dissipate in time;

Time scales order: ~ hoursTime scales order: ~ hours

Physical problemPhysical problem

R = 60

Normal mode theoryNormal mode theory

(a)-(b): R=100, y(a)-(b): R=100, y00=0, x=0, x00=9, k=1.7, α=9, k=1.7, αii =-0.05, β =-0.05, β00=1, =1, symmetric initial condition, (a) Φ=π/8, r=0.0826, (b) symmetric initial condition, (a) Φ=π/8, r=0.0826, (b) Φ=(3/8)π, r=-0.0168. (c): R=100, yΦ=(3/8)π, r=-0.0168. (c): R=100, y00=0, x=0, x00=11, k=0.6, =11, k=0.6, ααii=0.02, β=0.02, β00=1, asymmetric initial condition, Φ=π/4, =1, asymmetric initial condition, Φ=π/4, r=0.0038.r=0.0038.

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Initial-value problemInitial-value problem

PublicationsPublications

A synthetic perturbative hypothesis for the multiscale analysis of A synthetic perturbative hypothesis for the multiscale analysis of the convective wake instabilitythe convective wake instability - D. Tordella, S. Scarsoglio and M. - D. Tordella, S. Scarsoglio and M. Belan - Phys. Fluids, Vol. 18, No. 5 - (2006)Belan - Phys. Fluids, Vol. 18, No. 5 - (2006)

22nd IFIP TC 7 Conference on System Modeling and Optimization - 22nd IFIP TC 7 Conference on System Modeling and Optimization - AnalysisAnalysisof the convective instability of the two-dimensional wake of the convective instability of the two-dimensional wake (S. (S. Scarsoglio, D. Tordella, M. Belan) - 18/22 luglio 2005 – TorinoScarsoglio, D. Tordella, M. Belan) - 18/22 luglio 2005 – Torino 6th Euromech Fluid Mechanics Conference (EFMC6) - 6th Euromech Fluid Mechanics Conference (EFMC6) - A synthetic A synthetic perturbative hypothesis for multiscale analysis of bluff-body wake perturbative hypothesis for multiscale analysis of bluff-body wake instabilityinstability (D.Tordella, S. Scarsoglio, M. Belan) - June 26-30, 2006 - (D.Tordella, S. Scarsoglio, M. Belan) - June 26-30, 2006 - Stockholm, SwedenStockholm, Sweden

59th Annual Meeting Division of Fluid Dynamics (APS-DFD) - 59th Annual Meeting Division of Fluid Dynamics (APS-DFD) - Initial-value problem for the two-dimensional growing wakeInitial-value problem for the two-dimensional growing wake (S. (S. Scarsoglio, D.Tordella and W. O. Criminale) – November 19-21, 2006 - Scarsoglio, D.Tordella and W. O. Criminale) – November 19-21, 2006 - Tampa, FloridaTampa, Florida

11th Advanced European Turbulence Conference - 11th Advanced European Turbulence Conference - Temporal Temporal dynamics of small perturbations for a two-dimensional growing wake dynamics of small perturbations for a two-dimensional growing wake (S. Scarsoglio, D.Tordella and W. O. Criminale) - June 25-28, 2007 - (S. Scarsoglio, D.Tordella and W. O. Criminale) - June 25-28, 2007 - Porto, PortugalPorto, Portugal

Transient and asymptotic behaviour of small three-dimensional Transient and asymptotic behaviour of small three-dimensional perturbations applied to a growing wakeperturbations applied to a growing wake – S. Scarsoglio, D. Tordella – S. Scarsoglio, D. Tordella and W. O. Criminale – submitted to J. Fluid Mech. 2007and W. O. Criminale – submitted to J. Fluid Mech. 2007

Streamwise evolution of the entrainment in a steady two-Streamwise evolution of the entrainment in a steady two-dimensional bluff-body wakedimensional bluff-body wake – D. Tordella, S. Scarsoglio – submitted – D. Tordella, S. Scarsoglio – submitted to J. Eng. Math. 2007to J. Eng. Math. 2007

Convective instability in wake intermediate asymptotics - M. Belan, Convective instability in wake intermediate asymptotics - M. Belan, D. Tordella - D. Tordella - J. Fluid Mech., 552 : 127-136, 2006. J. Fluid Mech., 552 : 127-136, 2006.

On the domain of validity of the near-parallel combined stability On the domain of validity of the near-parallel combined stability analysis for the 2D intermediate and far bluff body wakeanalysis for the 2D intermediate and far bluff body wake - D. Tordella, - D. Tordella, M. Belan - ZAMM, 85 (1): 51-65 2005M. Belan - ZAMM, 85 (1): 51-65 2005

A new matched asymptotic expansion for the intermediate and far A new matched asymptotic expansion for the intermediate and far flow behind a finite bodyflow behind a finite body – D. Tordella, M. Belan - Phys. Fluids, 15 (7): – D. Tordella, M. Belan - Phys. Fluids, 15 (7): 1897-1906 2003 1897-1906 2003 Asymptotic expansions for two dimensional symmetrical laminar Asymptotic expansions for two dimensional symmetrical laminar wakeswakes - M. Belan, D. Tordella - ZAMM, 82 (4): 219-234 2002 - M. Belan, D. Tordella - ZAMM, 82 (4): 219-234 2002

Turbulent transportTurbulent transport--

Trasporto turbolentoTrasporto turbolento

Prof. D TordellaProf. D TordellaMichele IovienoMichele IovienoPeter BaileyPeter Bailey

MotivationMotivation TurbulenceTurbulence

Scales: large (geometry); small (molecular)Scales: large (geometry); small (molecular) Most energy at large scalesMost energy at large scales

MotivationMotivation TurbulenceTurbulence

Scales: large (geometry); small (molecular)Scales: large (geometry); small (molecular) Most energy at large scalesMost energy at large scales – let us ignore – let us ignore

the small scale ?the small scale ?

MotivationMotivation TurbulenceTurbulence

Scales: large (geometry); small (molecular)Scales: large (geometry); small (molecular) Most energy at large scalesMost energy at large scales – let us ignore – let us ignore

the small scale ?the small scale ?

Practical reasons (Applications)Practical reasons (Applications) Effect on light and sound wave propagationEffect on light and sound wave propagation Combustion/chemical reactors – small scale Combustion/chemical reactors – small scale

level dynamics determine reaction ratelevel dynamics determine reaction rate Parametrization of subgrid scale terms in LES, Parametrization of subgrid scale terms in LES,

k-eps and other turbulence modelsk-eps and other turbulence models

MotivationMotivation TurbulenceTurbulence

Scales: large (geometry); small (molecular)Scales: large (geometry); small (molecular) Most energy at large scalesMost energy at large scales – let us ignore the small – let us ignore the small

scale ?scale ?

Practical reasons (Applications)Practical reasons (Applications) Effect on light and sound wave propagationEffect on light and sound wave propagation Combustion/chemical reactors – small scale level dynamics Combustion/chemical reactors – small scale level dynamics

determine reaction ratedetermine reaction rate Parametrization of subgrid scale terms in LES, k-eps and Parametrization of subgrid scale terms in LES, k-eps and

other turbulence modelsother turbulence models

Our study of shearless turbulent mixing allowed us Our study of shearless turbulent mixing allowed us to discover a set of general propertiesto discover a set of general properties

Turbulent mixingTurbulent mixing

Homogeneous Isotropic Turbulence (HIT) is the Homogeneous Isotropic Turbulence (HIT) is the simplest turbulence possiblesimplest turbulence possible

A HIT mixing is the simplest turbulence mixingA HIT mixing is the simplest turbulence mixing We investigate this mixing without a mean shear We investigate this mixing without a mean shear

and without a length scale and without a length scale to date this configuration is shown to lack to date this configuration is shown to lack

intermittencyintermittency

Turbulent mixingTurbulent mixing

Homogeneous Isotropic Turbulence (HIT) is the Homogeneous Isotropic Turbulence (HIT) is the simplest turbulence possiblesimplest turbulence possible

A HIT mixing is the simplest turbulence mixingA HIT mixing is the simplest turbulence mixing We investigate this mixing without a mean shear We investigate this mixing without a mean shear

and without a length scale and without a length scale to date this configuration is shown to lack to date this configuration is shown to lack

intermittencyintermittency

State of the ArtState of the Art Empirically investigated by Gilbert (1980) and Veeravalli & Empirically investigated by Gilbert (1980) and Veeravalli &

Warhaft (1989)Warhaft (1989) by passive grid generated turbulence. Grids of equal solidity but differing by passive grid generated turbulence. Grids of equal solidity but differing

sizesize adjacent turbulence fields of differing kinetic energy and integral length adjacent turbulence fields of differing kinetic energy and integral length

scale, without mean shearscale, without mean shear

State of the ArtState of the Art Empirically investigated by Gilbert (1980) and Veeravalli & Empirically investigated by Gilbert (1980) and Veeravalli &

Warhaft (1989)Warhaft (1989) by passive grid generated turbulence. Grids of equal solidity but differing by passive grid generated turbulence. Grids of equal solidity but differing

sizesize adjacent turbulence fields of differing kinetic energy and integral length adjacent turbulence fields of differing kinetic energy and integral length

scale, without mean shearscale, without mean shear in planes downstream of grid, no mean shear, we have a HIT mixing with in planes downstream of grid, no mean shear, we have a HIT mixing with

different scalesdifferent scales

State of the ArtState of the Art Empirically investigated by Gilbert (1980) and Veeravalli & Empirically investigated by Gilbert (1980) and Veeravalli &

Warhaft (1989)Warhaft (1989) by passive grid generated turbulence. Grids of equal solidity but differing by passive grid generated turbulence. Grids of equal solidity but differing

sizesize adjacent turbulence fields of differing kinetic energy and integral length adjacent turbulence fields of differing kinetic energy and integral length

scale, without mean shearscale, without mean shear in planes downstream of grid, no mean shear, we have a HIT mixing with in planes downstream of grid, no mean shear, we have a HIT mixing with

different scalesdifferent scales Analyze and determine time and spatial properties of the turbulence Analyze and determine time and spatial properties of the turbulence

energy production as a function of these ratios energy production as a function of these ratios

State of the ArtState of the Art Empirically investigated by Gilbert (1980) and Veeravalli & Empirically investigated by Gilbert (1980) and Veeravalli &

Warhaft (1989)Warhaft (1989) by passive grid generated turbulence. Grids of equal solidity but differing by passive grid generated turbulence. Grids of equal solidity but differing

sizesize adjacent turbulence fields of differing kinetic energy and integral length adjacent turbulence fields of differing kinetic energy and integral length

scale, without mean shearscale, without mean shear in planes downstream of grid, no mean shear, we have a HIT mixing with in planes downstream of grid, no mean shear, we have a HIT mixing with

different scalesdifferent scales Analyze and determine time and spatial properties of the turbulence Analyze and determine time and spatial properties of the turbulence

energy production as a function of these ratios energy production as a function of these ratios in computation we can go one step better. Empirically length and in computation we can go one step better. Empirically length and

energy scales are intrinsically linked. However in the computation we are energy scales are intrinsically linked. However in the computation we are able to alter these independently and get a better insight into the able to alter these independently and get a better insight into the interrelationsinterrelations

Analysis of MixingAnalysis of Mixing The principle means to identify turbulent The principle means to identify turbulent

intermittence here is through one point intermittence here is through one point velocity statisticsvelocity statistics

We look at:We look at: S (skewness) S (skewness) == the flow of kinetic energythe flow of kinetic energy K (kurtosis)K (kurtosis)== the flow of Sthe flow of S

S remains 0, K=3 in HITS remains 0, K=3 in HIT

S moves from 0 as the S moves from 0 as the mixing begins, remains mixing begins, remains close to 0 outside the close to 0 outside the mixingmixing

Penetration is from high Penetration is from high energy field into the low energy field into the low energy side, shown as energy side, shown as fraction of the mixing layer fraction of the mixing layer thicknessthickness

As energy ratio is As energy ratio is increased we note a linear increased we note a linear log relation before the log relation before the energy flow asymptotes to energy flow asymptotes to its maximumits maximum

Flow of kinetic energy Flow of kinetic energy and penetrationand penetration

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Flow visualisationFlow visualisation

Mixing enhancement (retardation) if the gradients of energy and Mixing enhancement (retardation) if the gradients of energy and length scale are concurrent (opposite) length scale are concurrent (opposite) {Journal of Fluid Mechanics, 2006} {Journal of Fluid Mechanics, 2006}Scaling law for the mixing penetration with respect to the Scaling law for the mixing penetration with respect to the turbulent kinetic energy ratioturbulent kinetic energy ratio {Journal of Fluid Mechanics, 2006} {Journal of Fluid Mechanics, 2006}Sufficiency of the presence of a gradient of kinetic energy for Sufficiency of the presence of a gradient of kinetic energy for Gaussian departure in turbulenceGaussian departure in turbulence {in review for American Physical {in review for American Physical Society Physical Review E, 2007}Society Physical Review E, 2007}

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Turbulent Cavity FlowsTurbulent Cavity Flows--

Flussi della cavità turbulentaFlussi della cavità turbulenta

AeroTraNet network: (supported by Marie Curie Actions)AeroTraNet network: (supported by Marie Curie Actions)

Prof. D TordellaProf. D TordellaProf. M Onorato*Prof. M Onorato*Michele IovienoMichele IovienoPeter BaileyPeter BaileyChristian Haigermoser*Christian Haigermoser*Lukas Vesely*Lukas Vesely*

MotivationMotivation

Statistical ResultsStatistical Results Statistical ResultsStatistical Results Time averaged flowTime averaged flow Shear layer impinges onto the forward facing stepShear layer impinges onto the forward facing step Primary and secondary recirculation zonesPrimary and secondary recirculation zones

Time averaged flowTime averaged flow Shear layer impinges onto the forward facing stepShear layer impinges onto the forward facing step Primary and secondary recirculation zonesPrimary and secondary recirculation zones

Time-resolved Time-resolved Results Results

Time-resolved Time-resolved Results Results

Vortex identification:Vortex identification: Vorticity Vorticity ωωzz

λλcici-vortex-identification criteria; -vortex-identification criteria; λλcici = swirling strength = swirling strength

Vortex identification:Vortex identification: Vorticity Vorticity ωωzz

λλcici-vortex-identification criteria; -vortex-identification criteria; λλcici = swirling strength = swirling strength

Vortices – > Vortices – > Click Click herehere

Vortices – > Vortices – > Click Click herehere

Time-Resolved Time-Resolved DragDrag

Time-Resolved Time-Resolved DragDrag

Drag coefficient time historyDrag coefficient time history CCDD reveals oscillation frequency of f≈2.8Hz (FFT), corresponding to St reveals oscillation frequency of f≈2.8Hz (FFT), corresponding to StHH=0.08 =0.08 Highest contribution to CHighest contribution to CDD from Reynolds stress term from Reynolds stress term Contributions to CContributions to CDD along x/H along x/H

Drag coefficient time historyDrag coefficient time history CCDD reveals oscillation frequency of f≈2.8Hz (FFT), corresponding to St reveals oscillation frequency of f≈2.8Hz (FFT), corresponding to StHH=0.08 =0.08 Highest contribution to CHighest contribution to CDD from Reynolds stress term from Reynolds stress term Contributions to CContributions to CDD along x/H along x/H

Low dragLow drag High dragHigh drag

DRAG FROM CONDITIONAL ANALYSISDRAG FROM CONDITIONAL ANALYSIS