stochastic aerodynamics

8/9/2019 Stochastic Aerodynamics

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Stochastic Aerodynamics:

An Application to Bluff

Body with Variable Gust

Inlets

Dr. Imran Afgan

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Breakdown of Work

Modelling and Numerics LES (Standard Smagorinsky) model with Code_Saturne

Conforming/Non-Conforming Mesh Refinement Investigation

Bluff Body 1 (Flat Plate)

Bluff Body 2 (Cylinder arrays)

Code_Saturne Development

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Bluff Body 1 (Flat Plate)

Establish a test case with for flow over a Bluff body (Normal & oblique

Flat Plate) using literature review Code_Saturne user programming tweaking to obtain desired output

variables

Testing of Code_Saturne on the user subroutines for a simple channelflow

Benchmark the test case with available data Use Generalized Chaos polynomial (gCP) as a Black box to obtain

desired input parameters

Perform a number of LES runs to obtain the output variables.

Postprocess the output variables by gCP to obtain a set of data for thedesired range

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Bluff Body 2 (Cylinder Arrays) Establish test cases with flow over a wide range of

tube bundle configurations Benchmark the test case with available data

Testing a number of non-conforming meshes for a

complete parametric study

Perform a refined LES/DNS of the tube bundles with

various inlet

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Over & Above Bluff Body 2 (Cylinder arrays)

Perform a refined LES/DNS of the tube bundles with

various inlet conditions

Perform a gCP analysis much like Case 1 to generate

a test database

Code_Saturne Development

Implementation of Wall adapting Local Eddy Viscosity

Model in Code_Saturne via user subroutines

Benchmark the case with a channel flow simulation

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Case 1: Flat Plate Establishment of test case and Flow parameters

Re (2.5 x 104 2.5 x 105)

Uniform Inlet

2 Configurations to be tested

Flat Plate normal (900) to the inflow

Flat Plate oblique (450) to the inflow

Lift, drag, Pressure, Admittance Parameter, U,V,W,

some higher order statistics uiuj

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Geometry

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6H

24H

15HH

Height (y): H

Thickness (x): 0.1H

Length (z): 14H (Spanwise direction Periodic BC


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Numerical Grid

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2 D Mesh contains 250,000 cells


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Flat Plate Data

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Application of Gust Inlet

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( )( )

[ ]

2 2

0 4( )( ) sin 3

/ 2

is Gust Life, is Amplitude and 0,

t t Tu t U A t T TT

T A t T

= + +

T

A

( , , , ) velocity signal with gust inlet

( , , ), ( , , ) decoupling life and amplitude of gust

( , , ) for different cases, where is number of cases choseni i

u f x t T A

u f x t A u f x t T

u f x t A i

=

= =

=


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gPC Pre-processor

( , , )u x t

( , , ) where 1,inlet ju x t z j Nq=

CFD Solver

Code_Saturne

PDF of Stochastic Input is chosen a priori andassigned

Nq number of Quadrature points are also chosen apriori

var( , , ) where 1,

iable jO x t z j Nq=

Stochastic Collection Method

2

( , , ), ( )( , ) where k=0,K

( )

k

k

k

O x tO x t

=

where

( , , ), ( ) ( , , ). ( ). ( )k kO x t O x t d

=

Can be approximated by Monte Carlo method or quasi Monte Carlo method

We on the other hand use Deterministic Numerical Quadrature Method

var

0

( , , ), ( ) . ( , , ). ( ) where 0,Z

k j j k j

j

O x t w O x t z z k K =

= =

Wherejw is the weight function, ( )k is the orthogonal polynomial which depends up

the PDF selection criteria

gPC Method

Some Selected Classical orthogonal PolynomialsRandom field data is now represented using

gPC expansion of the form

0

( ; , ) ( , ). ( )K

k k k

k

O x t w O x t =

=


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Case 2: Tube Bundles Cross flow over square in-line tube bundles with 4 different gap ratios was tested. P/D=1.2, 1.5, 1.6

and 1.75

Comparison was made with experimental data and with LES of Code Saturne

P/D=1.5 case was also simulated with conventional URANS models

Average Cp comparison

for P/D=1.5 case

Cross sectional View of

the grid

Pseudo-average mean velocity streamlines. From left to right: P/D=1.2, P/D=1.5, P/D=1.6 and P/D=1.75

Average Velocity contours at

mid section for P/D=1.5 case

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WALE Model*

Based on the traceless part of the

square of the velocity gradient tensor

Where the Wale constant is

estimated as

Model is based purely on wall

behaviour and dimensional analysis

so no additional and/or special walltreatments are required

( )

( ) ( )

3/ 2

12 2

5/ 45/ 22

& &

( ) ( ) & &

d d

ij ij

T W W d d

ij ij ij ij

OP

v C COP S S= =

+

( )3/ 2

1/ 2

2 2

1

2

2 ij ijW S

ij ij

S S

C C

OPS SOP

=

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* Nicoud, F., Ducros, F. 1999. Subgrid scale stress modelling based on the square of the

velocity gradient tensor. Flow, Turbulence and Combustion. Vol 62, 183-200


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Bibliography Flat Plate Breuer, M., Jovicic, N. 2001. Separated Flow Around a Flat Plate at High Incidence: An LES

Investigation. Journal of Turbulence, 1468-5248, Vol. 2, N 18.

Chen, J. M., Fang, Y. -C. 1996. Strouhal Numbers of Inclined Flat Plates. Journal of WindEngineering and Industrial Aerodynamics, 61, pp 99-112.

Drabble, M. J., Grant, I., Armstrong, B. J., Barnes, F. H. 1990. The Aerodynamic Admittance of aSquare Plate in a Flow with a Fully Coherent Fluctuation. Physics of Fluids A 2(6), pp 1005-1013.

Dennis, S. C. R., Wang Qiang, Coutanceau, M., Launay, J. L. 1993. Viscous Flow Normal to aFlat Plate at Moderate Reynolds Numbers. Journal of Fluid Mechanics. Vol. 248, pp 605-635.

Fage, A., Johansen, F. C. 1927. On the Flow of Air behind an Inclined Flat Plate of Infinite Span.

Proceedings of the Royal Society of London, Series A. Vol. 116, No. 773, pp 170-197. Julien, S., Lasheras, J., Chomaz, J,-M. 2003. Three-Dimensional Instability and Vorticity Patters in

the Wake of a Flat Plate. Journal of Fluid Mechanics. Vol. 479, pp 155-189.

Julien, S., Ortiz, S., Chomaz, J.-M. 2004. Secondary Instability Mechanisms in the Wake of a FlatPlate. European Journal of Mechanics B/Fluids. Vol. 23, pp 157-165.

Kiya, M., Matsumura, M. 1988. Incoherent Turbulence Structure in the Near Wake of a Normal

Plate. Journal of Fluid Mechanics. Vol 190, pp 343-356. Leder, A. 1991. Dynamics of Fluid Mixing in Separated Flows. Physics of Fluids A 3, pp 1741-

1748.

Mazharoglu, C., Hacisenvki, H. 1999. Coherent and Incoherent Flow Structures Behind a NormalFlat Plate. Experimental Thermal and Fluid Science 19, pp 160-167.

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http://www.informaworld.com/smpp/title~db=all~content=t713665472~tab=issueslist~branches=2#v2http://www.informaworld.com/smpp/title~db=all~content=t713665472~tab=issueslist~branches=2#v2http://www.informaworld.com/smpp/title~db=all~content=t713665472~tab=issueslist~branches=2#v2


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Najjar, F. M., Vanka, S. P. 1995a. Simulations of the Unsteady Separated Flow Past a NormalFlat Plate. International Journal of Numerical Methods in Fluids. Vol. 21, pp 525-547.

Najjar, F. M., Vanka, S. P. 1995b. Effects of Intrinsic Three-Dimensionality on the DragCharacteristics of a Normal Flat Plate. Physics of Fluids 7(10), pp 2516-2518.

Najjar, F. M., Balachandar, S. 1998. Low Frequency Unsteadyness in the Wake of a Normal FlatPlate. Journal of Fluid Mechanics. Vol. 370, pp 101-147.

Narasimhamurthy, V. D., Andersson, H. I. 2009. Numerical Simulation of the Turbulent WakeBehind a Normal Flat Plate. International Journal of Heat and Fluid Flow. 30, pp 1037-1043.

Perry, A. E., Steiner, T. R. 1987. Large-scale Vortex Structures in Turbulent Wakes behind Bluff

Bodies. Part 1: Vortex Formation Processes. Journal of Fluid Mechanics. Vol. 174, pp 233-270. Steiner, T. R., Perry, A. E., 1987. Large-scale Vortex Structures in Turbulent Wakes behind Bluff

Bodies. Part 2: Far-Wake Structures. Journal of Fluid Mechanics. Vol. 174, pp 271-298.

Saha, A. K. 2007. Far-Wake Characteristics of Two-Dimensional Flow past a normal flat plate.Physics of Fluids. Vol. 19, Article 128110.

Tamaddon-Jahromi, H. R., Townsend, P, Wbster, M. F. 1994. Unsteady Viscous Flow Past a Flat

Plate Orthogonal to the Flow. Computers and Fluids. Vol. 23, No. 2, pp 433-446. Wu, S. J., Miau, J. J., Hu, C. C., Chou, J. H. 2005. On Low-Frequency modulations and three-

dimensionality in Vortex Shedding Behind a Normal Plate. Journal of Fluid Mechanics. Vol. 526,pp 117-146.

Yeung, W. W. H., Pakinson, G. V. 1997. On the Steady Separated Flow Around and Inclined FlatPlate. Journal of Fluid Mechanics. Vol. 333, pp 403-413.

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Bibliography Flat Plate (cont.)


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Bibliography Tube Bundles Aiba, S., Tsuchida, H., Ota, T. 1982. Heat Transfer around Tubes in In-line Tube Banks. Bull. JSME, 25, 919-926.

Benhamadouche, S., Laurence, D., 2003. LES, coarse LES, and transient RANS comparisons on the flow acrosstube bundle. Int. J. Heat and Fluid Flow 4, 470-479.

Benhamadouche, S., Laurence, D., Jarrin, N., Afgan, I., Moulinec, C. 2005. Large Eddy Simulation of Flow AcrossIn-line Tube Bundles, 11th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11),Popes Palace Conference Center, Avignon, France. Paper: 405.

Boris, J.P., Grinstein, F.F., Oran, E.S., Kolbe, R.L. 1992. New Insights into LES. Fluid Dynamics Res. 10, 199-228.

Bouris, D., Bergeles, G. 1999. Two dimensional Time Dependent Simulation of the Subcritical Flow in a StaggeredTube Bundle using a Subgrid-scale Model. J. Heat and Fluid Flow 20:2, 105-114.

Bouris, D., Papadakis, G., Bergeles, G. 2001. Numerical Evaluation of Alternate Tube Configurations for ParticleDeposition Rate in Heat Exchanger Tube Bundles. J. Heat and Fluid Flow 22:5, 525-536.

Breuer, M., Rodi, W. 1994. LES of Turbulent Flow through a Straight Square Duct and 1800 End. Voke, P. et al.(Eds), Direct and LES I. Kluwer Academic Publishers, Dordrecht. 273-285.

Celik, I. B., Cehreli, Z. N., Yavuz, I. 2005. Index of resolution quality for Large Eddy Simulations. J. of Fluids Engg,127, 949-958.

Chen, S. S. 1987. Flow-Induced Vibration of Circular Cylindrical Structures. Hemisphere publishing corporation.

Chen, S.S., Jendrzejczyk, J.A. 1987. Fluid Excitation Forces Acting on a Square Tube Array. JSME TransactionsVol 109, 415-423.

Ferziger, J.H., Peric, M. 2002. Computational Methods for Fluid Dynamics. Springer, third edition. Fitz-Hugh, J.S. 1973. Flow Induced Vibration in Heat Exchangers. Proc. Int. Sym. on Vibration Problems in

Industry, Keswick, UK, Paper No. 427; in Flow induced vibration of circular cylinder structures by Chen, S. S.

Frohlich, J. Rodi, W. 2002. Introduction to Large Eddy Simulation of Turbulent Flows. Closure strategies forturbulent and transitional flows by B. Launder and N. Sandham, Cambridge University press. 267-298.

Hassan, Y., Ibrahim, W. 1997. Turbulence Prediction in Two-Dimensional Tube Bundle Flows using Large EddySimulation, Nuclear Technology 119, 11-28.

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