A Review of Recent Developments in Turbulence

Modeling of Flows around Road Vehicles Kartheek Chandra

UNC Charlotte

Charlotte, NC, USA

In the partial completion of MEGR 7090:006 Vehicular Aerodynamics

Under Guidance of Dr. Mesbah Uddin

Abstract:

Even though Detached-eddy simulation (DES) was first developed in 1997 and first time used in 1999 our

aim in this paper is to portray the recent developments and proposals in DES models suggest after 2005 like

cubic explicit algebraic stress models by Greschner et al. in 2008 and zonal DES in which in which the use of

a single but versatile equation set is very important and has worked for Simon et al. in 2007 for base flow.

DES is more capable presently than either unsteady Reynolds-averaged Navier-Stokes (RANS) or large-eddy

simulation (LES) for High Reynolds Number but it is weak against grids with wall spacing same as boundary

layer thickness.

Key words:

Turbulence, Separation, Modelling

I. INTRODUCTION

The above picture is an Acoustic isosurface

around a symmetrical Ford Ka automobile (es turbo

3.1) (Mendonca et al. 2002). Figure courtesy of F.

Mendonca and Ford Motor Co.

Boundary layers and LES content around the

wheels and mirror are important. The separation

line near the end of the roof is the major cause of

drag and also responsible for the accuracy of RANS

models.

II. BACKGROUND:

The challenge of highReynolds number, and

massively separated flows for RANS and LES

models and hence DES model is created.

For a pure LES model to run for a ground

vehicle we need 1011 grid points and 107 time steps

for which we dont have the computational costs to

bear as of now. Infact an estimation by Spalart is

told that the problem cannot be addressed till 2045

A.D (Spalart 2000). No breakthrough in LES had

ooccured from 1997. RANS is pretty accurate to

predict boundary layers but not large separation

regions.

In the original proposed DES model in 1997, we

used LES at fine grid regions and RANS in non-fine

grid regions. But between these two a grey matter is

present which does not belong to either LES or

RANS category. A grid spacing parameter, is

introduced with RANS origin and which works

flexible in the grey region.

The simulations were incorrect through

Unsteady RANS (URANS) which was the leading

models for prediction through CFD simulations till

2005. In 2005 DES is found to be more accurate

than URANS for 3D geometry lift and drag

fluct

uations. The reason is the mesh, which doesnt

become coarser in URANS and DES makes the

mesh fine enough.

In the below mentioned figure Vorticity iso-

surfaces by a small circular cylinder are shown

with: ReD = 5 104, laminar separation. Cd between

1.151.25. (1) Shear-stress transport (SST)

turbulence model steady Reynolds-averaged

Navier-Stokes (RANS), Cd = 0.78; (2) SST 2D

unsteady RANS, Cd = 1.73; (3) SST 3D unsteady

RANS, with Cd = 1.24; (4) Spalart-Allmaras (SA)

detached-eddy simulation (DES), coarse grid, Cd =

1.16; (5) SA DES, fine grid, Cd = 1.26; (6) SST

DES, fine grid, Cd = 1.28. Figure courtesy of A.

Travin.

III. DES ON SIMPLE SPHERE

Figure IIIa

Figure IIIb

The figures shown above are flow visualizations

and pressure distributions on a simple sphere as a

bluff body.

Firufi

Figure shown above is phase averaged vorticity

contours for the same sphere as the cylinder. And

the final picture is a simulation conducted on DES

model and mockered lines are simulations done on

different models.

LES generates well at the Kolmogorov viscous

scale limitation, and wall modeling predicts the

similar viscous-sublayer scale. In its RANS mode,

DES in addition to the LES generated advantages

depicts the boundary-layer eddies of all sizes. But if

these eddies become dependent on the geomotry,

then we need to solve the eddies through LES

simulation which increase the points to more than

108 points which we are using right now. But this is

increased at computational cost.

IV. DISADVANTAGES

1. Modeled-Stress Depletion and Grid-Induced Separation

2. Logarithmic-Layer Mismatch

3. Slow Large-Eddy Simulation Development in Mixing Layers

V. APPLICATIONS

Noise is one important direction we can go to

through DES models developed by Mockett et al.

(2008) and Greschner et al. (2008): aerodynamic

noise.

The above mentioned figure depicts the

experimental noise and DES models noise depicted

by Greschner et al. in 2008. In the belo mentioned

figures in Chauvet et al. 2007 shows the

epxperimetal and computational schlieren of a

supersonic jet.

Experimental Schlieren

Comupational Schlieren through DES model.

The DES model is simple to let LES in and

robust to capture shocks. Hence by comparing the

two results one through experiment and another

through simulations we can say that we dont need

to separately use LES at all for high reynolds

numbered and high velocity flows.

VI. RECENT PROPOSALS

A. Alternative RANS Models

The original construction of DES rested on the

simple Spalart-Allmaras model and no CFD should

be restricted to only one model. Hence researches

are trying for SST models and Greschner et al.s in

2008 proposed cubic explicit algebraic stress

models.

B. Zonal Detached-Eddy Simulation

In zonal DES, we explicitly mark different

regions as RANS or as DES models proposed by

Deck in 2005. In wing buffet zonal DES worked

well for Brunet & Deck, Slimon for a Duck.

C. Delayed Detached-Eddy Simulation and

Improved Delayed

The motive behind this model is not to be

specific like zonal DES and hence Menter & Kuntz

in 2002 proposed this DDES which detects

boundary layers and prolongs full RANS mode.

DDES was proved that it resolved GIS, without

hindering LES function after separation. For

example, it handled a backward-facing-step flow

perfectly, even with grids that causes severe MSD

both upstream of the step and also along the

opposite wall. DDES, because of its robustness can

be called as new DES.

Improved delayed DES (IDDES) is more

motivated yet (Shur et al. in 2008). The approach is

also non-zonal and aims at resolving log-layer

mismatch in addition to MSD.

VII. CONCLUDING REMARKS

We can say that DES in more preferable

compared to RANS or LES models but we still have

a lot to achieve as we not yet predicted 10%

accurately each of Drag and Lift. And yet we take

conduct the simulations at a very high

computational cost.

VIII. FUTURE WORK

1. Resolution between geometries needs to be

improved and a better grid is to be generated.

2. Link between DES and DNS flow is to be

time-honored.

IX. COPYRIGHT FORMS

Some of the material used in this paper is

copyright information and hence cant be revealed

completely. But sufficient details are mentioned to

understand the intended material.

ACKNOWLEDGMENT

I would like to thank Philippe R. Spalart, Boeing

Commercial Airplanes, Seattle,Washington 98124;

email: philippe.r.spalart@boeing.com for his

insightful books and articles in these related issues.

His article is on DES is an astute understanding

material of the same.

REFERENCES

1. Forsythe JR, Hoffmann KA, Squires KD.

2002. Detached-eddy simulation with

compressibility corrections applied to a

supersonic axisymmetric base flow.

Presented at AIAA Aerosp. Sci. Meet.

Exhib., 40th, Reno, Pap. No. AIAA-2002-

0586

2. Forsythe JR, Strang WZ, Squires KD. 2006.

Six degree of freedom computation of the F-

15E entering a spin. Presented at AIAA

Aerosp. Sci. Meet. Exhib., 44th, Reno, Pap.

No. AIAA-2006-0858

3. Forsythe JR, Squires KD, Wurtzler E, Spalart

PR. 2004. Detached-eddy simulation of the

F-15E at high alpha. J. Aircraft 41:193200

4. Frolich J, von Terzi D. 2008. Hybrid

LES/RANS methods for the simulation of

turbulent flows. Prog. Aerosp. Sci. 44:34977

5. Fu S, Xiao Z, Chen H, Zhang Y, Huang J.

2007. Simulation of wing-body junction

flows with hybrid RANS/LES methods. Int.

J. Heat Fluid Flow 28:137990

6. Greschner B, Jacob MC, Casalino D, Thiele

F. 2008. Prediction of sound generated by a

rod-airfoil configuration using EASM DES

and the generalised Lighthill/FW-H analogy.

Comp. Fluids 37:40213

7. Hamed A, Basu D, Das K. 2003. Detached

eddy simulation of supersonic flow over

cavity. Presented at AIAA Aerosp. Sci. Meet.

Exhib., 41st, Reno, Pap. No. AIAA-2003-

0549

8. Hedges LS, Travin A, Spalart PR. 2002.

Detached-eddy simulations over a simplified

landing gear. J. Fluids Eng. 124:41323

9. Hou Y, Mahesh K. 2004. A robust, colocated,

implicit algorithm for direct numerical

simulation of compressible, turbulent flows.

J. Comp. Phys. 205:20521

10. Kapadia S, Roy S, Wurtzler K. 2003.

Detached-eddy simulation over a reference

Ahmed car model. Presented at Thermophys.

Conf., 36th, Orlando, Pap. No. AIAA-2003-

0857

11. Krishnan V, Squires KD, Forsythe JR. 2004.

Prediction of separated flow characteristics

over a hump using RANS and DES.

Presented at AIAA Flow Control Conf., 2nd,

Portland, Pap. No. AIAA-2004-2224

12. Langtry RB, Spalart PR. 2007. Detached-

eddy simulation of a nose landing-gear

cavity. Presented at. IUTAM Symp.

Unsteady Separated Flows and Their

Control, Corfu, Greece

13. Maddox S, Squires KD, Wurtzler KE,

Forsythe JR. 2004. Detached-eddy simulation

of the ground transportation system.

McCallen et al. 2004, pp. 89104

14. Allen R, Mendonca F, Kirkham D. 2005.

RANS and DES turbulence model

predictions of noise on the M219 cavity at M

= 0.85. Int. J. Aeroacoust. 4:13551

15. Breuer M, Jovicic N, Mazaev K. 2003.

Comparison of DES, RANS and LES for the

separated flow around a flat plate at high

incidence. Int. J. Numer. Methods Fluids

41:35788

16. Brunet V, Deck SF. 2008. Zonal-detached

eddy simulation of transonic buffet on a civil

aircraft type configuration. Peng & Haase

2008, pp. 18291

17. Bunge U, Mockett C, Thiele F. 2007.

Guidelines for implementing detached-eddy

simulation using different models. Aerosp.

Sci. Technol. 11:37685

18. Caruelle B, Ducros F. 2003. Detached-eddy

simulations of attached and detached

boundary layers. Int. J. CFD 17:43351

19. Chalot F, Levasseur V, Mallet M, Petit G,

Reau N. 2007. LES and DES simulations for

aircraft design. Presented at AIAA Aerosp.

Sci. Meet. Exhib., 45th, Reno, Pap. No.

AIAA-2007-0723

20. Chauvet N, Deck S, Jacquin L. 2007. Zonal

detached eddy simulation of a controlled

propulsive jet. AIAA J. 45:245873

21. Constantinescu GS, Pacheco R, Squires KD.

2002. Detached-eddy simulation of flow over

a sphere. Presented at AIAA Aerosp. Sci.

Meet. Exhib., 40th, Reno, Pap. No. AIAA-

2002-0425

22. Constantinides Y, Oakley OH. 2006.

Numerical prediction of bare and straked

cylinder VIV. Proc. 25th Int. Conf. Offshore

Mech. Artic Eng., Pap. No. OMAE2006-

92334. New York: ASME Int.

23. Cummings RM, Morton SA, Forsythe JR.

2004. Detached-eddy simulation of slat and

flap aerodynamics for a high-lift wing.

Presented at AIAA Aerosp. Sci. Meet.

Exhib., 42nd, Reno, Pap. No. AIAA-2004-

1233

24. Deck S. 2005. Zonal detached-eddy

simulation of the flow around a high-lift

configuration with deployed slat and flap.

AIAA J. 43:237284

25. Deck S, Thorigny P. 2007. Unsteadiness of

an axisymmetric separating-reattaching flow.

Phys. Fluids 19:065103

26. Egorov Y, Menter F. 2008. Development and

application of SST-SAS turbulence model in

the DESider project. Peng & Haase 2008, pp.

26170

27. McCallen R, Browand F, Ross J, eds. 2004.

The Aerodynamics of Heavy Vehicles:

Trucks, Buses, and Trains. New York:

Springer

28. Mellen CP, Fr olich J, Rodi W. 2003.

Lessons from LESFOIL project on large-

eddy simulation of flow around an airfoil.

AIAA J. 41:57381

29. Mendonca F, Allen R, de Charentenay J,

Kirkham D. 2003. CFD prediction of

narrowband and broadband cavity acoustics

atM = 0.85. Presented at AIAA/CEAS

Aeroacoust. Conf. Exhib., Hilton Head,

South Carolina, Pap. No. AIAA-2003-3303

30. Mendonca F, Allen R, de Charentenay

J, Lewis M. 2002. Towards

understanding LES and DES for

industrial aeroacoustic predictions.

Presented at Int.Workshop LES Acoust.,

Gottingen

31. Menter FR, Kuntz M. 2002. Adaptation

of eddy-viscosity turbulence models to

unsteady separated flow behind

vehicles. See McCallen et al. 2004, pp.

33952

32. Menter FR, Kuntz M, Bender R. 2003.

A scale-adaptive simulation model for

turbulent flow predictions. Presented at

AIAA Aerosp. Sci. Meet. Exhib., 41st,

Reno, Pap. No. AIAA-2003-0767

33. Mitchell AM, Molton P, Berberis D,

Delery J. 2000. Oscillation of vortex

breakdown location and control of the

time-averaged location by blowing.

AIAA J. 38:793803

34. Mockett C, Greschner B, Knacke T,

Perrin R, Yan J, Thiele F. 2008.

Demonstration of improved DES

methods for generic and industrial

applications. See Peng & Haase 2008,

pp. 22231

35. Mockett C, Thiele F. 2007. Overview of

detached-eddy simulation for external

and internal turbulent flow applications.

Presented at Int. Conf. Fluid Mech., 5th,

Shanghai, China

36. Morton SA. 2003. High Reynolds

numberDESsimulations of vortex

breakdown over a 70 degree delta wing.

Presented at Appl. Aerodyn. Conf., 21st,

Orlando, Pap. No. AIAA-2003-4217

37. Simon F, Deck S, Guillen P, Sagaut P,

Merlen A. 2007. Numerical simulation

of the compressible mixing layer past an

axisymmetric trailing edge. J. Fluid

Mech. 591:21553

38. Slimon S. 2003. Computation of internal

separated flows using a zonal detached

eddy simulation approach. Proc. ASME

Int. Mech. Eng. Congr., Pap. No.

IMECE2003-43881. New York: ASME

Int.

39. Spalart PR. 2000. Strategies for

turbulence modelling and simulations.

Int. J. Heat Fluid Flow 21:25263

Spalart PR. 2001. Young persons guide

to detached-eddy simulation grids. Tech.

Rep. NASA CR-2001-211032.

40. Langley Res. Center, Hampton,Va.

http://techreports.larc.nasa.gov/ltrs/PDF/

2001/cr/NASA-2001-cr211032.pdf

41. Sagaut P, Deck S, Terracol M. 2006.

Multiscale and Multiresolution

Approaches to Turbulence. London:

Imp. Coll.Press

42. Shieh CM, Morris PJ. 2001.

Comparison of two- and three-

dimensional cavity flows. Presented at

AIAA Aerosp. Sci. Meet. Exhib., 39th,

Reno, Pap. No. AIAA-2001-0511

43. Shur ML, Spalart PR, Squires KD,

Strelets M, Travin A. 2005a. Three-

dimensionality in unsteady Reynolds

averaged Navier-Stokes simulations of

two-dimensional geometries. AIAA J.

43:123042

44. Shur ML, Spalart PR, Strelets MKh.

2005b. Noise prediction for increasingly

complex jets. Part I: methods and tests.

Int J. Aeroacoust. 4:21346

45. ShurML,Spalart PR,

StreletsMKh.2005c. Noise prediction for

increasingly complex jets. Part II:

applications. Int J. Aeroacoust. 4:247

66

46. Travin AK, Shur ML, Spalart PR,

Strelets MKh. 2004. On URANS

solutions with LES-like behaviour.

Presented at Eur. Cong. Comput.

Methods Appl. Sci. Eng., Jyvaskyla,

Finland

47. Travin AK, Shur ML, Spalart PR,

Strelets MKh. 2006. Improvement of

Delayed Detached-Eddy Simulation for

LES with wall modelling. Presented at

Eur. Conf. CFD, ECCOMAS CDF

2006. Delft, Neth.

48. Wilcox DC. 1998. Turbulence Modeling

for CFD. La Ca nada, CA: DCW Ind.

49. Wilson RP, Haupt SE, Peltier LJ, Kunz

RF. 2006. Detached Eddy Simulation of

a surface mounted cube at high

Reynolds number. Proc. ASME Joint

U.S. Eur. Fluids Eng. Summer Meet.

New York: ASME Int.

50. Yan J, Tawackolian K, Michel U, Thiele

F. 2007. Computation of jet noise using

a hybrid approach. Presented at

AIAA/CEAS Aeroacoust. Conf., 13th,

Pap. No. AIAA-2007-3621

51. Ziefle J, Kleiser L. 2008.

Compressibility effects on turbulent

separated flow in streamwise-periodic

hill channel, part 2. See Peng & Haase

2008, pp. 31625