On a generalized nonlinear K-ε model for turbulence that models relaxation effects

Theoretical and Computational Fluid Dynamics

Volumn 8, Issue 4, 1996, Pages 275-288

  Huang, Y N ^a   Rajagopal, K R ^a  

^a University of Pittsburgh   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039712687     PISSN: 09354964     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf00639696     Document Type: Article

References (28)

1. Bardina, J., Ferziger, J.H., and Reynolds, W.C. (1983). Improved turbulence models based on large-eddy simulation of homogeneous, incompressible turbulent flows. Technical Report No. TF-19, Stanford University, Stanford, CA, 1983.
2. Crow, S.C. (1968). Viscoelastic properties of fine grained incompressible turbulence. J. Fluid Mech. 33(1), 1-20.
3. Friedrichs, K.O., and Lax, P.D. (1971). Systems of conservation equations with a convex extension. Proc. Nat. Acad. Sci. U.S.A., 68, 1686-1688.
4. Gatski, T.B., and Speziale, C.G. (1993). On explicit algebraic stress models for complex turbulent flows. J. Fluid Mech., 254, 59-78.
5. Huang, Y.-N., and Rajagopal, K.R. (1995). On necessary and sufficient conditions for fully-developed turbulent secondary flow in a straight tube. Math. Models Methods Appl. Sci., 1(5), 111-123.
6. Huang, Y.-N., and Rajagopal, K.R. (1994). On the origin of laminar steady secondary flow of non-Newtonian fluids in straight tubes. Submitted for publication.
7. Kremer, G.M. (1985). Zur erweiterten Thermodynamik idealer und dichter Gase. Dissertation, Technische Universität, Berlin.
8. Kremer, G.M. (1987). Extended thermodynamics of non-ideal gases. Phys. A, 144, 156-178.
9. Kremer, G.M., and Beevers, C. (1984). Extended thermodynamics of dense gases. In Recent Developments in Non-Equilibrium Thermodynamics (J. Casas-Vâzque, D. Jou, and G. Lebon, eds.), pp. 429-436. Lecture Notes in Physics, Vol. 199. Springer-Verlag, Berlin.
10. Launder, B.E., and Spalding, D.B. (1974). The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Engrg., 3. 269-289.
11. Lax, P.D. (1972). Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves. Regional Conference Series in Applied Mathematics. SIAM, Philadelphia, PA.
12. Liu, I.-S. (1972). Method of Lagrange multipliers for exploitation of entropy principle. Arch. Rational Mech. Anal., 46, 131-148.
13. Liu, I.-S., and Müller, I. (1983). Extended thermodynamics of classical and degenerate ideal gases. Arch. Rational Mech. Anal., 83, 285-331.
14. Marshall, J., and Naghdi, P.M. (1989), Philos. Trans. Roy. Soc. London. Ser. A, 327, 415-435.
15. Müller, I. (1966). Zur Ausbreitungsgeschwindigkeit von Störungen in kontinuierlichen Medien. Dissertation, Technische Hochschule, Aachen.
16. Müller, I., and Wilmanski, K. (1986). Extended thermodynamics of a non-Newtonian fluid. Rheol. Acta, 25, 335-349.
17. Nikuradse, J. (1926). Untersuchungen über die Geschwindigkeitsverteilung in turbulente Strömungen. Thesis, V.D.I.-Forsch. 76, Göttingen.
18. Nikuradse, J. (1930). Turbulente Strömung in nicht-kreisförmigen Rohren. Ing. Arch., 1. 306-332.
19. Pope, S.B. (1975). A more general effective viscosity hypothesis. J. Fluid Mech., 72, 331-340.
20. Rivlin, R.S. (1957). The relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids. Quart. Appl. Math., 15, 212-214.
21. Smith, G.F. (1970). On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Internat. J. Engrg. Sci., 9, 889-916.
22. Speziale. C.G. (1987). On nonlinear K-I and K-ε models of turbulence. J. Fluid Mech., 178, 459-475.
23. Speziale, C.G. (1991). Ann. Rev. Fluid Mech., 23, 107-130.
24. Taulbee, D.B. (1992). An improved algebraic Reynolds stress model and corresponding non-linear stress model. Phys. Fluids A, 4, 2555-2561.
25. Wang, C.C. (1970). A new representation theorem for isotropic functions, I and II. Arch. Rational Mech. Anal., 36, 166-223.
26. Wang, C.C. (1971). Corrigendum to "Representations for isotropic functions." Arch. Rational Mech. Anal., 43, 392-395.
27. Yakhot, Y., Orszag, S.A., Thangam, S., Gatski, T.B., and Speziale, C.G. (1992). Development of turbulence models for shear flows by a double expansion technique. Phys. Fluids A, 4(7), 1510-1520.
28. Yoshizawa, A., and Nisizima, S. (1993). A nonequilibrium representation of the turbulent viscosity based on a two-scale turbulence theory. Phys. Fluid A, 5(12), 3302-3304.