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On the Realizability of Nonlinear Stress–Strain Relationships for Reynolds Stress Closures

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Abstract

A class of recently developed explicit algebraic stress models based on tensorially quadratic stress--strain relations [7] is subjected to a systematical realizability analysis. It is found that these models, which are of particular interest for their rigorous derivation from linear second-moment closure models, tend to produce inappropriate unrealizable results like negative turbulence energy components, even in simple shear flows. The cause of the defect is identified in conjunction with a set of realizability-furnishing constraints on the model coefficients. With the exception of the silent normal stress component in accelerated flow, the nature and rationale of the explicit algebraic stress model suggested by Gatski and Speziale [7] can be extended to maintain the realizability principle. Results obtained from the corresponding quasi-realizable quadratic eddy-viscosity model are reported in comparison with other nonlinear modelling practices.

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References

  1. Abid, R., Rumsey, C. and Gatski, T., Prediction of nonequlibrium turbulent flows with explicit algebraic stress models. AIAA Journal 33 (1995) 2026–2031.

    Google Scholar 

  2. Almeida, G.P., Durão, D.F.G. and Heitor, M.V., Wake flows behind two-dimensional model hills. Experimental Thermal and Fluid Science 7 (1993) 87–101.

    Article  Google Scholar 

  3. Bardina, J., Ferziger, J. H. and Reynolds, W.C., Improved turbulence models based on largeeddy simulation of homogeneous, incompressible turbulent flows. Technical Report TF-19, Stanford University (1983).

  4. Bertoglio, J.P., Homogeneous turbulent field within a rotating frame. AIAA Journal 20 (1982) 1175–1181.

    Google Scholar 

  5. Craft, T., Launder, B.E. and Suga, K., A non-linear eddy-viscosity model including sensitivity to stress anisotropy. In: Durst, F., Launder, B.E., Schmidt, F. and Whitelaw, J.H. (eds.), Proceedings of the 10th Symposium on Turbulent Shear Flows. Pennsylvania State University (1995) pp. 23–19.

  6. Fu, S., Launder, B.E. and Tselepidakis, D., Accommodating the effects of high strain rates in modelling the pressure-strain correlations. Technical Report TFD/87/5, University of Manchester Institute of Science (1987).

  7. Gatski, T. and Speziale, C., On explicit algebraic stress models for complex turbulent flows. J. Fluid Mech. 254 (1993) 59–75.

    Google Scholar 

  8. Gibson, M.M. and Launder, B.E., Ground effects on the pressure fluctuations in the atmospheric boundary layer. J. Fluid Mech. 86 (1978) 491–511.

    Google Scholar 

  9. Girimaji, S.S., Fully-explicit and self-consistent Reynolds stress model. ICASE Report 95-82, NASA Langley Research Center (1995).

  10. Johnston, J.P., Halleen, R.M. and Lezius, D.K., Effects of a spanwise rotation on the structure of two-dimensional fully-developed channel flow. J. Fluid Mech. 56 (1972) 533–558.

    Google Scholar 

  11. Jones, W.P. and Launder, B.E., Prediction of laminarization with a two-equation turbulence model. Internat. J. Heat Mass Transfer. 15, (1972) 301–314.

    Article  Google Scholar 

  12. Laufer, J., Investigation of turbulent flow in a two dimensional channel. NACA Technical Report 1053 (1951).

  13. Launder, B.E., Reece, G. and Rodi, W., Progress in the development of a Reynolds stress turbulence closure. J. Fluid Mech. 68 (1975) 537–566.

    Google Scholar 

  14. Lezius, D.K. and Johnston, J.P., Roll-cell instabilities in rotating laminar and turbulent channel flow. J. Fluid Mech. 77 (1976) 153–175.

    Google Scholar 

  15. Lumley, J.L., Computational modelling of turbulent flows. Adv. Appl. Mech. 18 (1978) 123–176.

    Google Scholar 

  16. Pope, S.B., A more general effective viscosity hypothesis. J. Fluid Mech. 72 (1975) 331–340.

    Google Scholar 

  17. Reynolds, W.C., Fundamentals of turbulence for turbulence modeling and simulation. In: NATO (ed.), Lecture Notes for Von Kármán Institute, ARGARD Lecture Series No. 86. NATO, New York (1987).

    Google Scholar 

  18. Rodi, W., A new algebraic relation for calculating the Reynolds stresses. ZAMM 56 (1976) T219–T221.

    Google Scholar 

  19. Sarkar, S. and Speziale, C.G., A simple nonlinear model for the return to isotropy in turbulence. Phys. Fluids A 2 (1990) 84–93.

    Article  Google Scholar 

  20. Schumann, U., Realizability of Reynolds stress turbulence models. Phys. Fluids 20 (1977) 721–725.

    Article  Google Scholar 

  21. Shih, T.H. and Lumley, J.L., Modeling the pressure correlation terms in Reynolds stress and scalar flux equations. Sibley School of Mechanics & Aerospace Engineering Report FDA-85-3, Cornell University (1985).

  22. Shih, T.H., Zhu, J. and Lumley, J.L., A realizable Reynolds stress algebraic equation model. NASA TM-105993 (ICOMP Report 92-27), NASA Lewis Research Center (1993).

  23. Speziale, C.G., On nonlinear K-l and K-ε models of turbulence. J. Fluid Mech. 178 (1987) 459–475.

    Google Scholar 

  24. Speziale, C., Abid, R. and Blaisdell, G., On the consistency of Reynolds stress turbulence closure with hydrodynamic stability theory. ICASE Report 95-46, NASA Langley Research Center (1995).

  25. Speziale, C.G. and Mac Giolla Mhuiris, N., Scaling laws for homogeneous turbulent shear flows in a rotating frame. Phys. Fluids A 1 (1989) 294–301.

    Article  Google Scholar 

  26. Speziale, C.G. and Mac Giolla Mhuiris, N., On the prediction of homogeneous states in equilibrium turbulence. J. Fluid Mech. 209 (1989) 591–615.

    Google Scholar 

  27. Speziale, C.G., Sarkar, S. and Gatski, T.B., Modelling the pressure—strain correlation of turbulence: An invariant dynamical systems approach. J. Fluid Mech. 227 (1991) 245–272.

    Google Scholar 

  28. Taulbee, D.B., An improved algebraic Reynolds stress model and corresponding nonlinear stress model. Phys. Fluids A 4 (1992) 2555–2561.

    Article  Google Scholar 

  29. Tavoularis, S. and Corrsin, S., Experiments in nearly homogeneous turbulent shear flows with a uniform mean temperature gradient. J. Fluid Mech. 104 (1981) 311–367.

    Google Scholar 

  30. Wallin, S. and Johansson, A.V., A new explicit algebraic Reynolds stress turbulence model including an improved near-wall treatment. In: Chen, C., Shih, S., Lienau, J. and Kung, R. (eds.), Flow Modelling and Turbulence Measurements, Vol. VI. A.A. Balkema, Rotterdam (1996) pp. 309–406.

    Google Scholar 

  31. Yakhot, V., Orzag, S.A., Thangham, S., Gatski, T.B. and Speziale, C.G., Development of turbulence models for shear flows by a double expansion technique. Phys. Fluids A 4 (1992) 1510–1520.

    Article  Google Scholar 

  32. Yoshizawa, A., Statistical analysis of the deviation of the Reynolds stress from its eddy viscosity representation. Phys. Fluids 27 (1984) 1377–1387.

    Article  Google Scholar 

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Authors
  1. T. Rung
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  2. F. Thiele
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  3. S. Fu
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Rung, T., Thiele, F. & Fu, S. On the Realizability of Nonlinear Stress–Strain Relationships for Reynolds Stress Closures. Flow, Turbulence and Combustion 60, 333–359 (1998). https://doi.org/10.1023/A:1009966612158

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