The purpose of this paper is to develop a second-moment closure with a near-wall turbulent pressure diffusion model for three-dimensional complex flows, and to evaluate the influence of the turbulent diffusion term on the prediction of detached and secondary flows. A complete turbulent diffusion model including a near-wall turbulent pressure diffusion closure for the slow part was developed based on the tensorial form of Lumley and included in a re-calibrated wall-normal-free Reynolds-stress model developed by Gerolymos and Vallet. The proposed model was validated against several one-, two, and three-dimensional complex flows.
Issue Section:
Technical Papers
1.
Kim
, J.
, Moin
, P.
, and Moser
, R.
, 1987, “Turbulence Statistics in Fully Developed Channel Flow at Low-Reynolds-Number
,” J. Fluid Mech.
0022-1120, 177
, pp. 133
–166
.2.
Le
, H.
, Moin
, P.
, and Kim
, J.
, 1997, “Direct Numerical Simulation of Turbulent Flow Over a Backward-Facing Step
,” J. Fluid Mech.
0022-1120, 330
, pp. 349
–374
.3.
Daly
, B. J.
, and Harlow
, F. H.
, 1970, “Transport Equations in Turbulence
,” Phys. Fluids
0031-9171, 13
, pp. 2634
–2649
.4.
Hanjalić
, K.
, and Launder
, B. E.
, 1972, “A Reynolds Stress Model of Turbulence and Its Application to Thin Shear Flows
,” J. Fluid Mech.
0022-1120, 52
, pp. 609
–638
.5.
Hirt
, C. W.
, 1969, “Generalized Turbulence Transport Equations
,” Int Sem. of Int. Center for Heat and Mass Transfer
, Herceg Novi, Yugoslavia.6.
Lumley
, J. L.
, 1979, “Second Order Modeling of Turbulent Flows
,” Prediction Methods for Turbulent Flows
, VKI Lecture Series
, von Kármán Institute for Fluid Dynamics
, Rhode-sur-Génèse, Jan.7.
Launder
, B. E.
, Reynolds
, W. C.
, Rodi
, W.
, Mathieu
, J.
, and Jeandel
, D.
, 1984, Turbulence Models and Their Applications II
, No. 56 in Collection de la Direction des Etudes et Recherches d’Electricite de France, Eyrolles, Paris.8.
Gerolymos
, G. A.
, Sauret
, E.
, and Vallet
, I.
, 2004, “Contribution to the Single-Point-Closure Reynolds-Stress Modelling of Inhomogeneous Flow
,” Theor. Comput. Fluid Dyn.
0935-4964, 17
(5–6
), pp. 407
–431
.9.
Gessner
, F. B.
, and Emery
, A. F.
, 1981, “The Numerical Prediction of Developing Turbulent Flow in Rectangular Ducts
,” ASME J. Fluids Eng.
0098-2202, 103
, pp. 445
–455
.10.
Gerolymos
, G. A.
, Sauret
, E.
, and Vallet
, I.
, 2004, “Oblique-Shock-Wave∕Boundary-Layer Interaction Using Near-Wall Reynolds-Stress Models
,” AIAA J.
0001-1452, 42
(6
), pp. 1089
–1100
.11.
Settles
, G. S.
, Vas
, I. E.
, and Bogdonoff
, S. M.
, 1976, “Details of a Shock-Separated Turbulent Boundary-Layer at a Compression Corner
,” AIAA J.
0001-1452, 14
(12
), pp. 1709
–1715
.12.
Cormack
, D. E.
, Leal
, L. G.
, and Seinfeld
, J. H.
, 1978, “An Evaluation of Mean Reynolds Stress Turbulence Models: The Triple Velocity Correlation
,” ASME J. Fluids Eng.
0098-2202, 100
, pp. 47
–54
.13.
Amano
, R. S.
, and Goel
, P.
, 1986, “Triple-Velocity Products in a Channel With Backward-Facing Step
,” AIAA J.
0001-1452, 24
(6
), pp. 1040
–1043
.14.
Schwarz
, W. R.
, and Bradshaw
, P.
, 1994, “Term-by-Term Tests of Stress-Transport Turbulence Models in a 3-D Boundary-Layer
,” Phys. Fluids
1070-6631, 6
(2
), pp. 986
–998
.15.
Hanjalić
, K.
, 1994, “Advanced Turbulence Closure Models: A View of Current Status and Future Prospects
,” Int. J. Heat Fluid Flow
0142-727X, 15
, pp. 178
–203
.16.
Gatski
, T. B.
, 2004, “Constitutive Equations for Turbulent Flows
,” Theor. Comput. Fluid Dyn.
0935-4964, 18
(5
), pp. 345
–369
.17.
Lumley
, J. L.
, 1978, “Computational Modeling of Turbulent Flows
,” Adv. Appl. Mech.
0065-2156, 18
, pp. 123
–176
.18.
Moser
, R. D.
, Kim
, J.
, and Mansour
, N. N.
, 1999, “Direct Numerical Simulation of Turbulent Channel Flow up to Reτ=590
,” Phys. Fluids
1070-6631, 11
(4
), pp. 943
–945
.19.
Schwarz
, W. R.
, and Bradshaw
, P.
, 1993, “Measurements in a Pressure-Driven 3-D Turbulent Boundary-Layer During Development and Decay
,” AIAA J.
0001-1452, 31
(7
), pp. 1207
–1214
.20.
Demuren
, A. O.
, and Sarkar
, S.
, 1993, “Perspective: Systematic Study of Reynolds Closure Models in the Computations of Plane Channel Flows
,” ASME J. Fluids Eng.
0098-2202, 115
, pp. 5
–12
.21.
Laufer
, J.
, 1950, Investigation of Turbulent Flow in a 2-D Channel
, NACA Report No. 1053: (supersedes NACA Tech. Note 2123 (1950)).22.
Mellor
, G. L.
, and Herring
, H. J.
, 1973, “A Survey of the Mean Turbulent Field Closure Models
,” AIAA J.
0001-1452, 11
(5
), pp. 590
–599
.23.
Speziale
, C. G.
, Sarkar
, S.
, and Gatski
, T. B.
, 1991, “Modelling the Pressure-Strain Correlation of Turbulence: An Invariant Dynamical Systems Approach
,” J. Fluid Mech.
0022-1120, 227
, pp. 245
–272
.24.
Fu
, S.
, 1993, “Modelling of the Pressure-Velocity Correlation in Turbulence Diffusion
,” Comput. Fluids
0045-7930, 22
, pp. 199
–205
.25.
Straatman
, A. G.
, 1999, “A Modified Model for Diffusion in Second-Moment Turbulence Closures
,” ASME J. Fluids Eng.
0098-2202, 121
, pp. 747
–756
.26.
Ramaprian
, B. R.
, and Chandrasckhara
, M. S.
, 1985, “LDA Measurements in Plane Turbulent Jets
,” ASME J. Fluids Eng.
0098-2202, 107
, pp. 264
–271
.27.
Taulbee
, D. B.
, Hussein
, H.
, and Capp
, S.
, 1987, The Round Jet: Experiment and Inferences on Turbulence Modelling
, 6th Symposium on Turbulence Shear Flows
, Toulouse, Sept.28.
Kim
, J.
, Kline
, S. J.
, and Johnson
, J. P.
, 1980, “Investigation of a Reattaching Turbulent Shear Layer: Flow Over a Backward-Facing Step
,” ASME J. Fluids Eng.
0098-2202, 102
, pp. 302
–308
.29.
Suga
, K.
, 2004, “Modeling the Rapid Part of the Pressure-Diffusion Process in the Reynolds Stress Transport Equation
,” ASME J. Fluids Eng.
0098-2202, 126
, pp. 634
–641
.30.
Craft
, T. J.
, and Launder
, B.
, 1996, “A Reynolds-Stress Model Designed for Complex Geometries
,” Int. J. Heat Fluid Flow
0142-727X, 17
, pp. 245
–254
.31.
Yao
, Y. F.
, Thomas
, T. G.
, and Sandham
, N. D.
, 2001, “Direct Numerical Simulation of Turbulent Flow Over a Rectangular Trailing Edge
,” Theor. Comput. Fluid Dyn.
0935-4964, 14
(5–6
), pp. 337
–358
.32.
Launder
, B. E.
, and Tselepidakis
, D. P.
, 1994, “Application of a New Second-Moment Closure to Turbulent Channel Flow Rotating in Orthogonal Mode
,” Int. J. Heat Fluid Flow
0142-727X, 15
, pp. 2
–10
.33.
So
, R. M. C.
, and Yuan
, S. P.
, 1999, “A Geometry Independent Near-Wall Reynolds-Stress Closure
,” Int. J. Eng. Sci.
0020-7225, 37
, pp. 33
–57
.34.
Gerolymos
, G. A.
, and Vallet
, I.
, 2001, “Wall-Normal-Free Near-Wall Reynolds-Stress Closure for 3-D Compressible Separated Flows
,” AIAA J.
0001-1452, 39
(10
), pp. 1833
–1842
.35.
Chou
, P. Y.
, 1945, “On Velocity Correlations and the Solutions of the Equations of Turbulent Fluctuations
,” Q. Appl. Math.
0033-569X, 3
, pp. 38
–54
.36.
Launder
, B. E.
, and Shima
, N.
, 1989, “2-Moment Closure for the Near-Wall Sublayer: Development and Application
,” AIAA J.
0001-1452, 27
(10
), pp. 1319
–1325
.37.
Rotta
, J.
, 1951, “Statistische Theorie nichthomogener Turbulenz—1. Mitteilung
,” Z. Phys.
0044-3328, 129
, pp. 547
–572
.38.
Naot
, D.
, Shavit
, A.
, and Wolfshtein
, M.
, 1970, “Interactions Between Components of the Turbulent Velocity Correlation Tensor Due to Pressure Fluctuations
,” Isr. J. Technol.
0021-2202, 8
(3
), pp. 259
–269
.39.
Pot
, T.
, Délery
, J. M.
, and Quelin
, C.
, 1991, Interactions Onde-de-choc∕Couche-limite dans un Canal Transsonique 3-d
. Rap. Tech. 92-7078-AY-116-A, ONERA.40.
Sauret
, E.
, 2004, “Analyse et Développement de Modèles de Turbulence au Second-Ordre Procheparoi
,” Doctorat, Université Pierre-et-Marie-Curie, Paris, Sept.41.
Magnaudet
, J.
, 1993, “Modelling of Inhomogeneous Turbulence in the Absence of Mean Velocity Gradients
,” Appl. Sci. Res.
0003-6994, 51
, pp. 525
–531
.42.
Younis
, B. A.
, Gatski
, T. B.
, and Speziale
, C. G.
, 2000, “Towards a Rational Model for the Triple Velocity Correlations of Turbulence
,” Proc. R. Soc. London, Ser. A
1364-5021, 456
, pp. 909
–920
.43.
Gerolymos
, G. A.
, and Vallet
, I.
, 1999, “Effect des Modèles de Diffusion Turbulente et de Redistribution du Tenseur de Reymolds en Ecoulement Transsonique Décollé
,” In Actes (CD-Rom) du 14, Congrès Français de Mécanique, 30 aug–3 sep 1999, Toulouse, ENSAE (Paper No. 5049).44.
Klebanoff
, P. S.
, 1955, “Characteristics of Turbulence in a Boundary-Layer With Zero Pressure Gradient
,” NACA, Report No. 1247.45.
Reda
, D. C.
, and Murphy
, J. D.
, 1973, “Shock-Wave∕Turbulent-Boundary-Layer Interactions in Rectangular Channels
,” AIAA J.
0001-1452, 11
(2
), pp. 139
–140
(also AIAA Paper No. 72-715, 1972).46.
Ott
, P.
, Bölcs
, A.
, and Fransson
, T. H.
, 1995, “Experimental and Numerical Study of the Time-Dependent Pressure Response of a Shock-Wave Oscillating in a Nozzle
,” ASME J. Turbomach.
0889-504X, 117
(1
), pp. 106
–114
.47.
Doukelis
, A.
, Mathioudakis
, K.
, and Papailiou
, K. D.
, 1998, “The Effect of Tip Clearance Gap Size and Wall Rotation on the Performance of a High-Speed Annular Compressor Cascade
,” ASME Paper No. 98-GT-38.48.
Gerolymos
, G. A.
, Sauret
, E.
, and Vallet
, I.
, 2004, “Influence of Inflow-Turbulence in Shock-Wave∕Turbulent-Boundary-Layer Interaction Computations
,” AIAA J.
0001-1452, 42
(6
), pp. 1101
–1106
.49.
Chassaing
, J. C.
, Gerolymos
, G. A.
, and Vallet
, I.
, 2003, “Efficient and Robust Reynolds-Stress Model Computation of 3-D Compressible Flows
,” AIAA J.
0001-1452, 41
(5
), pp. 763
–773
.50.
Gerolymos
, G. A.
, and Vallet
, I.
, 2005, “Mean-Flow-Multigrid for Implicit Reynolds-Stress-Model Computations
,” AIAA J.
0001-1452, 43
(9
), pp. 1887
–1898
.51.
Gerolymos
, G. A.
, Vallet
, I.
, Bölcs
, A.
, and Ott
, P.
, 1996, “Computation of Unsteady 3-D Transonic Nozzle Flows Using k‐ε Turbulence Closure
,” AIAA J.
0001-1452, 34
(7
), pp. 1331
–1340
.52.
Gerolymos
, G. A.
, Neubauer
, J.
, Sharma
, V. C.
, and Vallet
, I.
, 2002, “Improved Prediction of Turbomachinery Flows Using Near-Wall Reynolds-Stress Model
,” ASME J. Turbomach.
0889-504X, 124
(1
), pp. 86
–99
.53.
Launder
, B. E.
, and Sharma
, B. I.
, 1974, “Application of the Energy Dissipation Model of Turbulence to the Calculation of Flows Near a Spinning Disk
,” Lett. Heat Mass Transfer
0094-4548, 1
, pp. 131
–138
.54.
Schülein
, E.
, 2006, “Skin-Friction and Heat Flux Measurements in Shock∕Boundary-Layer Interaction Flows
,” AIAA J.
0001-1452, 44
(8
), pp. 1732
–1741
.Copyright © 2007
by American Society of Mechanical Engineers
You do not currently have access to this content.
