Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
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On Constructing an Explicit Algebraic Stress Model Without Wall-Damping Function

  • Park, Noma (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Yoo, Jung-Yul (School of Mechanical and Aerospace Engineering, Seoul National University)
  • Published : 2002.11.01
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Abstract

In the present study, an explicit algebraic stress model is shown to be the exact tensor representation of algebraic stress model by directly solving a set of algebraic equations without resort to tensor representation theory. This repeals the constraints on the Reynolds stress, which are based on the principle of material frame indifference and positive semi-definiteness. An a priori test of the explicit algebraic stress model is carried out by using the DNS database for a fully developed channel flow at Rer = 135. It is confirmed that two-point correlation function between the velocity fluctuation and the Laplacians of the pressure-gradient i s anisotropic and asymmetric in the wall-normal direction. Thus, a novel composite algebraic Reynolds stress model is proposed and applied to the channel flow calculation, which incorporates non-local effect in the algebraic framework to predict near-wall behavior correctly.

Keywords

References

  1. Adumitroaie, V., Ristorcelli, J.R. and Taulbee, D.B., 1999, 'Progress in Favre-Reynolds Stress Closures for Compressible Flows,' Phys. Fluids, Vol.11, No.9, pp. 2696-2719 https://doi.org/10.1063/1.870130
  2. Apsley, D.D. and Leschziner, M.A., 1998, 'A New Low-Reynolds-Number Nonlinear Two-Equation Turbulence Model for Complex Flows,' Int. J. Heat and Fluid Flow, Vol. 19, pp. 209-222 https://doi.org/10.1016/S0142-727X(97)10007-8
  3. Choi, H., Moin, P. and Kim, J., 1993, 'Direct Numerical Simulation of Turbulent Flow over Riblets,' J. Fluid Mech., Vol. 255, pp. 503-539 https://doi.org/10.1017/S0022112093002575
  4. Choi, H. and Moin, P., 1994, 'Effects of the Computational Time Step on Numerical Solutions of Turbulent Flow,' J. Comput. Phys., Vol. 113, pp. 1-4 https://doi.org/10.1006/jcph.1994.1112
  5. Choi, H., Moin, P. and Kim, J., 1994, 'Active Turbulence Control for Drag Reduction in Wall-Bounded Flows,' J. Fluid Mech., Vol. 262, pp. 75-110 https://doi.org/10.1017/S0022112094000431
  6. Durbin, P.A., 1991, 'Near-Wall Turbulence Closure Modeling without Damping Functions,' Theoret. Comput. Fluid Dynamics, Vol. 3, pp. 1-13 https://doi.org/10.1007/BF00271513
  7. Durbin, P.A., 1993, 'A Reynolds Stress Model for Near-Wall Turbulence,' J. Fluid Mech., Vol. 249, pp. 465-498 https://doi.org/10.1017/S0022112093001259
  8. Gatski, T.B. and Speziale, C.G., 1993, 'On Explicit Algebraic Stress Models for Complex Turbulent Flows,' J. Fluid Mech., Vol. 254, pp. 59-78 https://doi.org/10.1017/S0022112093002034
  9. Girimaji, S.S., 1997, 'A Galilean Invariant Explicit Algebraic Reynolds Stress Model for Turbulent Curved Flows,' Phys. Fluids, Vol. 9, No. 4, pp. 1067-1077 https://doi.org/10.1063/1.869200
  10. Hallback, M., Groth, J. and Johansson, A.V., 1990, 'An Algebraic Model for Nonisotropic Turbulent Dissipation Rate in Reynolds Stress Closures,' Phys. Fluids A, Vol. 2, No. 10, pp. 1859-1866 https://doi.org/10.1063/1.857660
  11. Hanjalic, K., 1994, 'Advanced Turbulence Closure Models: A View of Current Status and Future Prospects,' Int. J. Heat and Fluid Flow, Vol. 15, pp. 178-203 https://doi.org/10.1016/0142-727X(94)90038-8
  12. Hanjalic, K. and Jakirlic, S., 1993, 'A Model of Stress Dissipation in Second-Moment Closures,' Appl. Scientific Research, Vol. 51, pp. 513-518 https://doi.org/10.1007/BF01082584
  13. Kasagi, N., Horiuti, K., Miyake, T., Miyauchi, T. and Nagano, Y., 1992, Establishment of the Direct Numerical Simulation Databases of Turbulent Transport Phenomena, Grant-in-Aid for Cooperative Research No. 02302043, the Ministry of Education, Science and Culture, Japan
  14. Kuroda, A., 1990, Direct Numerical Simulation of Couette-Poiseuille Flows, Dr. Eng. Thesis, the University of Tokyo
  15. Koroda, A., Kasagi, N. and Hirata, M., 1989, 'A Direct Numerical Simulation of the Fully Developed Turbulent Channel Flow,' International Symposium on Computational Fluid Dynamics, Nagoya, 1989, pp. 1174-1179
  16. Koroda, A., Kasagi, N. and Hirata, M., 1989, 'A Direct Numerical Simulation of the Fully Developed Turbulent Channel Flow,' Numer. Met. Fluid Dyn., 1990, Vol. 2, pp. 1012-1017
  17. Launder, B.E., Reece, G. and Rodi, W., 1975, 'Progress in the Development of a reynolds-Stress Turbulence Closure,' J. Fluid Mech., Vol. 68, pp. 537-566 https://doi.org/10.1017/S0022112075001814
  18. Lele, S.K., 1992, 'Compact Finite Difference Schemes with Spectral-like Resolution,' J. Comp. Phys., Vol. 103, pp. 16-42 https://doi.org/10.1016/0021-9991(92)90324-R
  19. Manceau, R. and HanJalic, K., 2000, 'A New Form of the Elliptic Relaxation Equation to Ac-count for Wall Effects in RANS Modelling,' Phys. Fluids, Vol. 12, No. 9, pp. 2345-2351 https://doi.org/10.1063/1.1287517
  20. Manceau, R., Wang, M. and Laurence, D., 2001, 'Inhomogeneity and Anisotropy Effects on the Redistribution Term in Reynolds-Averaged Navier-Strokes Modelling,' J. Fluid Mech., Vol. 438, pp. 307-338 https://doi.org/10.1017/S0022112001004451
  21. Manceau, R. and Hanjalic, K., 2002, 'Elliptic Blending Model: A New Near-Wall Reynolds-Stress Turbulence Closure,' Phys. Fluids, Vol. 14, No. 2, pp. 744-754 https://doi.org/10.1063/1.1432693
  22. Mansour, N.N., Kim, J. and Moin, P., 1988, 'Reynolds-Stress and Dissipation-Rate Budgets in a Turbulent Channel Flow,' J. Fluid Mech., Vol. 194, pp. 15-44 https://doi.org/10.1017/S0022112088002885
  23. Moser, R.D., Kim, J. and Mansour, M.M., 1998, 'DNS of Turbulent Channel Flow up to $Re_{\tau}$= 590,' Phys. Fluids, Vol. 11, No. 4, pp. 943-945 https://doi.org/10.1063/1.869966
  24. Parneix, S., Laurence, D. and Durbin, P.A., 1998, 'A Procedure for Using DNS Databases,' J. Fluids Engrg., Vol. 120, pp. 40-47 https://doi.org/10.1115/1.2819658
  25. Pope, S.B., 1975, 'A More General Effective-Viscosity Hypothesis,' J. Fluid Mech., Vol. 72, Part 2, pp. 331-340 https://doi.org/10.1017/S0022112075003382
  26. Rodi, W., 1976, 'A New Algebraic Relation for Calculating the Reynolds Stresses,' Z. Angew. Math. Mech., Vol. 56, pp. 219-221 https://doi.org/10.1002/zamm.19760560510
  27. Smith, G.F., 1971, 'On Isotropic Functions of Symmetric Tensors, Skew-Symmetric Tensors and Vectors,' Intl J. Engrg Sci., Vol. 9, pp. 899-916 https://doi.org/10.1016/0020-7225(71)90023-1
  28. Spalart, P.R. and Speziale, C.G., 1999, 'A Note on Constraints in Turbulence Modelling,' J. Fluid Mech., Vol. 391, pp. 373-376 https://doi.org/10.1017/S0022112099005388
  29. Speziale, C.G., 1979, 'Invariance of Turbulent Closure Models,' Phys. Fluids, Vol. 22, pp. 1033-1037 https://doi.org/10.1063/1.862708
  30. Speziale, C.G. and Gatski, T.B., 1997, 'Ananlysis and Modelling of Anisotropies in the Dissipation Rate of Turbulence,' J. Fluid Mech., Vol. 344, pp. 155-180 https://doi.org/10.1017/S002211209700596X
  31. 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., Vol. 227, pp. 245-272 https://doi.org/10.1017/S0022112091000101
  32. Taulbee, D.B., 1992, 'An Improved Algebraic Reynolds Stress Model and Corresponding Nonlinear Stress Model,' Phys. Fluid A, Vol. 4, No. 11, pp. 2555-2561 https://doi.org/10.1063/1.858442
  33. Vreman, B., Geurts, B. and Kurerten, H., 1996, 'Comparison of Numerical Schemes in Large-Eddy Simulation of the Temporal Mixing Layer,' Int. J. Numer. Meth. Fluids, 22, pp. 297-311 https://doi.org/10.1002/(SICI)1097-0363(19960229)22:4<297::AID-FLD361>3.0.CO;2-X
  34. Wang, L., 1997, 'Frame-Indifferent and Positive-Definite Reynolds Stress-Strain Relation,' J. Fluid Mech., Vol. 352, pp. 341-358 https://doi.org/10.1017/S0022112097007532
  35. Wallin, S. and Johansson, A.V., 2000, 'An Explicit Algebraic Reynolds Stress Model for Incompressible and Compressible Turbulent Flows,' J. Fluid Mech., Vol. 403, pp. 89-132 https://doi.org/10.1017/S0022112099007004
  36. Wolfram, S., 1988, Mathematica, Addison-wesley