A general one-equation turbulence model for free shear and wall-bounded flows

Flow, Turbulence and Combustion

Volumn 73, Issue 3-4, 2005, Pages 187-215

  Fares, Ehab ^a   Schröder, Wolfgang ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Model; One equation; Turbulence

Indexed keywords

BOUNDARY CONDITIONS; DAMPING; EQUATIONS OF MOTION; PRANDTL NUMBER; SHEAR STRESS; TURBULENCE;

CLASSICAL TWO-EQUATION MODELS; DAMPING EQUATIONS; ONE-EQUATION; SPALART-ALLMARAS;

WALL FLOW;

EID: 18844415830     PISSN: 13866184     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10494-005-8625-y     Document Type: Article

References (65)

1. Baldwin, B.S. and Lomax, H., Thin layer approximation and algebraic model for separated turbulent flows. AIAA Paper (1978) 78-257.
2. Baldwin, B.S. and Barth, T.J., A one-equation turbulence transport model for high reynolds number wall-bounded flows. AIAA Paper (1991) 91-0610.
3. Bardina, J.E., Huang, P.G. and Coakly, T.J., Turbulence modeling validation, testing and development. NASA Technical Memorandum (1997) 110446.
4. Batchelor, G.K., Axial flow in trailing line vortices. J. Fluid Mech. 20 (1964) 645-658.
5. Bradbury, J.S., The structure of a self-preserving turbulent plane jet. J. Fluid Mech. 23 (1965) 31-64.
6. Bradshaw, P., Ferriss, D.H. and Atwell, N.P., Calculation of boundary layer development using the turbulent energy equation. J. Fluid Mech. 23 (1976) 31-64.
7. Cook, P.H., McDonald, M.A. and Firmin, M.C.P., Aerofoil RAE 2822 - Pressure distributions, and boundary layer and wake measurements. AGARD AR-138 (1979).
8. Durbin, P., A Reynolds stress model for the near-wall turbulence. J. Fluid Mech. 249, pp. 465ff (1993).
9. Emmons, H.W., Shear Flow Turbulence. In: Proceedings of the 2nd U.S. Congress of Applied Mechanics, ASME (1954).
10. Page, A. and Falkner, V.M., Note on Experiments on the Temperature and Velocity in the Wake of a Heated Cylidrical Obstacle. In: Proceedings Royal Society (London), ser. A, vol. 135 (1932) pp. 702-705.
11. Fares, E. and Schröder, W., A differential equation for approximate wall distance. Intern. J. Numer. Methods Fluids 39 (2002) 743-762.
12. Gersten, K. and Herwig, H., Strömungsmechanik. Grundlagen der Impuls-, Wärme und Stoffübertragung aus asymptotischer Sicht. Vieweg-Verlag, Braunschweig/Wiesbaden (1992).
13. Godin, P. and Zingg, D.W., High-lift aerodynamic computations with one- and two-equation turbulence models. AIAA J. 35(2) (1997) 238-243.
14. Govindarajiu, S.P. and Saffman, P.O., Flow in a turbulent trailing vortex. Phys. Fluids 14 (1971) 2074-2080.
15. Grasso, F., Pirozzoli, S. and Gatski, T.B., Analysis and simulation of a turbulent, compressible starting vortex. Phys. of Fluids 11 (1999) 356-367.
16. Heskestad, G., Hot-wire measurements in a plane turbulent jet. J. Appl. Mech. 32(4) (1965) 721-734.
17. Hoffmann, E.R. and Joubert, P.N., Turbulent line vortices. J. of Fluid Mechanics 16 (1963) 395-411.
18. Jones, W.P. and Launder, B.E., The predicition of laminarization with a two-equation model of turbulence. Intern. J. Heat Mass Trans. 15 (1972) 301-314.
19. Kline, S.J., Morkovin, M.V., Sovran, G. and Cockrell, D.J., Computation of turblent boundary layers. 1968 AFOSR-IFP-Stanford Conference Proceedings, vol. I, Thermoscience Division, Stanford University, California (1969).
20. Launder, B.E., Reece, G.J. and Rodi, W., Progress in the development of a Reynolds-Stress Turbulence Closure. J. Fluid Mech. 68 (pt. 3) (1975) 537-566.
21. van Leer, B., Toward the ultimate conservative ddifference scheme V. A second-order J. Comput. Phys. 32 (1979) 101-136.
22. Liepmann, H.W. and Laufer, J., Investiations of free turbulent mixing. NACA TN, 1257 (1947).
23. +. J. Comput. Phys. 129 (1996) 164-382.
24. Ludwieg, H. and Tillmann, W., Untersuchungen über die Wandschubspannung in turbulenten Reibungsschichten. Ing.-Archiv 17 (1949) 288-299.
25. Mellor, G.L. and Herring, H.J., Two Methods of calculating turbulent boundary layer behavior based on numerical solution of the equation of motion. Proc. Conf. Turb. Boundary Layer Pred., Stanford (1968).
26. Menter, F.R., Influence of freestream values on k-ω turbulence model predictions. AIAA J. 30(6) (1992) 1657-1659.
27. Menter, F.R., Zonal two equation k-ω turbulence models for aerodynamic flows. AIAA Paper (1993)93-2906.
28. Menter, F.R., Eddy viscosity transport equations and their relation to the k-ε model. NASA-TM, 108854 (1994).
29. Moir, I.R.M., Measurements on a two-dimensional aerofoil with high-lift devices. AGARD AR-303, 2 (1994) 58-59.
30. Morkovin, M.V. and Favre A. (Eds.). Effects of compressibility on turbulent flows. In: Méchanique de la Turbulence, Centre National de la Recherche Scientific, Paris (1962), pp. 367-380.
31. Musker, A.J., Explicit expression for the smooth wall velocity distribution in a turbulent boundary layer. AIAA J. 17 (1979) 655-657.
32. Nagano, Y., Pei, C.Q. and Hattori, H., A new low-reynolds-number one-equation model of turbulence. Flow, Turbulence and Combust. 63 (1999) 135-151.
33. Nee, V.W. and Kovasznay, L.S.G., The calculation of the incompressible turbulent boundary layer by a simple theory. Phys. Fluids 12 (1968) 473ff.
34. Pantano, C. and Jacquin, L., Differential rotation effects within a turbulent batchelor vortex. In: Direct and Large-Eddy Simulation-IV Workshop Proceedings, Enschede, The Netherlands, 2001.
35. Phillips, W.R.C., The turbulent trailing vortex during Roll-up. J. Fluid Mech. 105 (1981) 451-467.
36. Phillips, W.R.C. and Graham, J.A.H., Reynolds stress measurements in a turbulent trailing vortex. J. Fluid Mech. 147 (1984) 451-467.
37. Pope, S.B., An explanation of the turbulent round-jet/plane-jet anomaly. AIAA J. 16(3) (1978) 279-281.
38. Prandtl, L., Über die ausgebildete Turbulenz. ZAMM 5 (1925) 136-139.
39. Prandtl, L., Über ein neues Formelsystem für die ausgebildete Turbulenz. Nachr. Akad. Wiss. Göttingen, Math. Phys. (1945) 6-19.
40. Qin, J.H., Numerical Simulations of a Turbulent Axial Vortex. Ph.D. Thesis, Purdue University (1998).
41. Rodi, W., A new method for analyzing how-wire signals in highly turbulent flows and its evaluation on round jets. Disa Information 17 (1975) 9-18.
42. Rogers, S.E., Menter, F., Durbin, P.A. and Mansour, N.M., A comparison of turbulence models in computing multi-element airfoil flows. AIAA Paper (1994) 94-0291.
43. Rumsey, C.L. and Vasta, V.N., A comparison of the predictive capabilities of several turbulence models using upwind and central-difference computer codes. AIAA Paper (1993) 93-0192.
44. Saffman, P.G., Structure of turbulent line vortices. Phys. Fluids 16(8) (1973) 1181-1188.
45. Saffman, P.G., Vortex Dynamics. Cambridge Monographs on Mech. and Appl. Math., Cambridge (1992).
46. Sai, V.A. and Lutfy, F.M., Analysis of the Baldwin-Barth and Spalart-Allmaras one-equation turbulence models. AIAA J. 33(10) (1995) 1971-1974.
47. Samuel, A.E. and Joubert, P.N., A boundary layer developing in an increasingly adverse pressure gradient. J. Fluid Mech. 66 (1974) 481-505.
48. Schlichting, H. and Gersten, K., Grenzschicht-Theorie. 9th ed. Springer-Verlag, Berlin/Heidelberg (1997).
49. Schubauer, G.B. and Klebanoff, P.S., Contributions on the mechanics of boundary layer transition. NASA-TN (1955) 3489,
50. also NASA-TR (1956) 1289.
51. Secundov, A.N., Application of the differential equation for turbulent viscosity to the analysis of plane nonself-similar flows. Akademiya Nauk, SSSR, Izvestiia, Mekhanika Zhidkosti i Gaza (1971) 114-127.
52. Shur, M., Strelets, M., Zaikov, L., Gulyaev, A.N., Kozlov, V. E. and Secundov, A.N., A comparative numerical testing of one- and two-equation turbulence models for flows with separation and reattachment. AIAA Paper (1995) 95-0863.
53. Spalart, P.R. and Allmaras, S.R., A one-equation turbulence model for aerodynamic flows. AIAA Paper (1992) 92-0439.
54. Spalart, P.R. and Shur, M., On the sensitization of turbulence models to rotation and curvature. Aerosp. Sci. Tech. (5) (1997) 297-302.
55. Spalart, P.R., Personal communication (2002).
56. Spalding, D.B., A single formula for the "law of the wall." ASME J. Appl. Mech. 28 (1961) 455-457.
57. Sreedhar, M. Ragab, S., Large eddy simulation of longitudinal stationary vortices. Phys. Fluids 6 (1994) 2501-2514.
58. Townsend, A.A., The structure of turbulent shear flow. Cambridge University Press, 2nd ed., Cambridge, England (1976).
59. Van Driest, E.R., Turbulent boundary layer in compressible fluids. J. Aeronau. Sci. 18 (1951) 145-160.
60. Wang, Q., Massey, S.J. and Abdol-Hamid, K.S., Solving Navier-stokes equations with advanced turbulence models on three-dimensional unstructured grids. AIAA Paper (1999) 99-0156.
61. Weygandt, J.H. and Mehta, R.D., Three-dimensional structure of straight and curved plane wakes. J. Fluid Mech. 282 (1995) 279.
62. Wilcox, D.C., Reassessment of the scale-determining equation for advanced turbulence models. AIAA J. 26(11) (1988) 1299-1310.
63. Wilcox, D.C., Turbulence Modeling for CFD. 2nd ed., DCW Industries (1998).
64. Wygnanski, I., and Fiedler, H.E., Some Measurements in Self-Presering Jet. J. Fluid Mech. 38 (1969) 577-612.
65. Zeman, O., The presistence of trailing vortices: A modeling study. Phys. Fluids 7(1) (1995) 135-143.