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Modelling 2D separation from a high lift aerofoil with a non-linear eddy-viscosity model and second-moment closure

Published online by Cambridge University Press:  04 July 2016

F. S. Lien
Affiliation:
University of ManchesterInstitute of Science and TechnologyManchester, UK
M. A. Leschziner
Affiliation:
University of ManchesterInstitute of Science and TechnologyManchester, UK

Abstract

A computational study is presented, which examines the performance of variants of second-moment closure and non-linear eddy-viscosity models when used to predict attached and separated flows over a high lift aerofoil for a range of incidence angles. The capabilities of both model types, especially in respect of resolving the onset of suction-side separation at high incidence, are contrasted with those of a low-Re k-ε model based on the linear Boussinesq stress-strain relationship. The second-moment model contains a conventional linear approximation of the pressure straining process; a cubic (realisable) variant has been investigated in an earlier study and found to offer no advantages. The quadratic eddy-viscosity model features coefficients which are sensitised to the strain and vorticity invariants. While both models, in the form originally proposed, are superior to the linear eddy-viscosity variant, neither performs well in respect of resolving separation, unless modified so as to return the requisite low level of shear stress in the boundary layer approaching separation. Once separation is resolved with sufficient realism, the near wake aft of the trailing edge is also well represented. All models return poor representations of the far wake which is characterised by low levels of turbulence production to dissipation ratio.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 1995 

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References

1. Smith, A.M.O. and Gamberoni, N. Transition, pressure gradient and stability theory, Proceedings 9th International Congress Applied Mechanics, Brussels, 1956, 4, p 234.Google Scholar
2. Launder, B.E., Reece, G.J. and Rodi, W. Progress in the development of a Reynolds stress turbulent closure, J Fluid Mech, 1975, 68, p537.Google Scholar
3. GIBSON, M.M. and Launder, B.E. Ground effects on pressure fluctuations in the atmospheric boundary layer, J Fluid Mech, 1978, 86, p 491.Google Scholar
4. Wolfshtein, M.W. The velocity and temperature distribution in one-dimensional flow with turbulence augmentation and pressure gradient, Int J Heat Mass Trans, 1969, 12, p 301.Google Scholar
5. Obi, S., Peric, M. and Scheuerer, G. A finite-volume calculation procedure for turbulent flows with second order closure and collocated variable arrangement, Proceedings 7th Symposium Turbulent Shear Flows, Stanford University, p 17.4,1989.Google Scholar
6. Davidson, L. High lift airfoil flow simulation using a two-layer Reynolds stress transport model, Proceedings 5th Int IAHR Symposium on Refined Flow Modelling and Turbulence Measurement, Paris, p 777, 1993.Google Scholar
7. Masson, B., Huang, P.G. and Bradshaw, P. Compressible Navier-Stokes calculations of the flow over airfoil sections: comparison of 1st and 2nd order turbulence models, SAE Paper 932510, 1993.Google Scholar
8. Lien, F.S. and Leschziner, M.A. Modelling 2D and 3D separation from curved surfaces with variants of second-moment closure combined with low-Re near wall formulations, Proceedings 9th Symposium Turbulent Shear Flows, Kyoto, p 13.1, 1993.Google Scholar
9. Lien, F.S. and Leschziner, M.A. Assessment of turbulence-transport models including non-linear RNG eddy-viscosity formulation and second-moment closure for flow over a backward-facing step, Computers and Fluids, 1994, 23, p 983.Google Scholar
10. Launder, B.E. Second-moment closure: present… and future?, Int J Heat Fluid Flow, 1989, 10, p 282.Google Scholar
11. Leschziner, M.A. Refined turbulence modelling for engineering flows, Computational Fluid Dynamics 1994 (Wagner, S., Periaux, J. and Hirschel, E.H. eds.), John Wiley and Sons, p 33, 1994.Google Scholar
12. Gatski, T.B. and Speziale, C.G. On explicit algebraic stress models for complex turbulent flows, J Fluid Mech, 1993, 254, p 59.Google Scholar
13. Yoshizawa, A. Statistical analysis of the deviation of the Reynolds stress from its eddy viscosity representation, Phys Fluids, 1984, 27, p 1377.Google Scholar
14. Speziale, C.G. On non-linear k-l and k-ε models of turbulence, J Fluid Mech, 1987, 178, p 459.Google Scholar
15. Rubinstein, R. and Barton, J.M. Non-linear Reynolds stress models and the renormalisation group, Phys Fluids A, 1990, 2, p 1472.Google Scholar
16. Yakhot, V. and Orszag, S.A. Renormalisation group analysis of turbulence: 1. Basic theory, J Sci Comput, 1986, 1, p 3.Google Scholar
17. Shih, T.H., Zhu, J. and Lumley, J.L. A realisable reynolds stress algebraic equation model, NASA TM-105993, 1993.Google Scholar
18. Suga, K., Craft, T.J. and Launder, B.E. Development and application of a non-linear k-ε model, Proceedings 6th Biennial Colloquium on CFD, UMIST, p 1.2, 1994.Google Scholar
19. Piccin, O. and Cassoudesalle, D. Etude Dans la Soufflerie Fl Des Profiles AS239 et AS240, ONERA Technical Report PV 73/1685 AYG, 1987.Google Scholar
20. Lien, F.S. and Leschziner, M.A. Computational modelling of 3D turbulent flow in S-diffuser and transition ducts, Engineering Turbulence Modelling and Measurements 2, 1993, Elsevier, p 217.Google Scholar
21. Yap, C. Turbulent Heat and Momentum Transfer in Recirculating and Impinging Flows, PhD Thesis, University of Manchester, 1987.Google Scholar
22. Craft, T.J. and Launder, B.E. New wall reflection model applied to the turbulent impinging jet, AIAA J, 1992, 30, p 2970.Google Scholar
23. Daly, B.J. and Harlow, F.H. Transport equation in turbulence, Phys Fluids, 1970, 13, p 2634.Google Scholar
24. Fu, S., Launder, B.E. and Tselepidakis, D.P. Accommodating the Effects of High Strain Rates in Modelling the Pressure-Strain Correlation, Report TFD/87/5, Dept of Mech Eng, UMIST, 1987.Google Scholar
25. Craft, T.J. Calculations of separated flow in a staggered tube- assembly of G. McGrath, contributed to 3rd ERCOFTAC-IAHR Workshop on Refined Flow Modelling, Lisbon, 1994.Google Scholar
26. Lien, F.S. and Leschziner, M.A. A general non-orthogonal finite- volume algorithm for turbulent flow at all speed incorporating second-moment closure, Part 1: Numerical implementation and Part 2: Application, Comp Meth Appl Mech Eng, 1994, 114, p 123 and p 149.Google Scholar
27. Lien, F.S. and Leschziner, M.A. Upstream monotonic interpolation for scalar transport with application to complex turbulent flows, Int J Num Meth Fluids, 1994, 19, p 527.Google Scholar
28. Leonard, B.P. A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comp Meth Appl Mech Eng, 1979, 19, p 59.Google Scholar
29. Rhie, C.M. and Chow, W.L. Numerical study of the turbulent flow past an airfoil with trailing edge separation, AIAA J, 1983, 21, p 1525.Google Scholar
30. Stock, H.W. and Haase, W. Determination of length scales in algebraic turbulence models for Navier-Stokes methods, AIAA J, 1989, 27, p 5.Google Scholar
31. Haase, W., Brandsma, F., Elsholz, E., Leschziner, M. and Schwamborn, D. (Eds), EUROVAL — a European initiative on validation of CFD codes, Notes Num Fluid Mech, 1993, 42, p 263.Google Scholar