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An eddy-viscosity limited algebraic stress model for shock-boundary-layer interaction

Published online by Cambridge University Press:  04 July 2016

G. Richardson  and
N. Qin
G. Richardson
Affiliation:
Centre for Computational Aerodynamics, College of Aeronautics, Cranfield University, Bedford, UK
N. Qin
Affiliation:
Centre for Computational Aerodynamics, College of Aeronautics, Cranfield University, Bedford, UK
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Abstract

This paper presents a μt-limited explicit algebraic stress model for shock-wave-turbulent boundary-layer interactions based on an investigation of various two-equation turbulence models. The results of the κ-ω model, the shear stress transport (SST) model, and a quadratic explicit algebraic stress model are presented and analysed for the Delery channel bump, and the Bachalo and Johnson axisym-metric bump test cases. While the κ-ω model failed to give good predictions, the SST model proved reasonably successful in predicting strong interaction problems. The non-linear quadratic explicit algebraic stress model gave improved results (when compared with the original κ-ω model) for the channel bump test cases, but was not as good as the SST model. Inspired by this investigation, a model formulation is proposed in which Bradshaw's assumption for eddy-viscosity limiting (as used in the SST model) is applied to a quadratic explicit algebraic stress model. The QSST model further improves the SST model for strong shock-boundary-layer interactions.

Type
Research Article
Information
The Aeronautical Journal , Volume 105 , Issue 1045 , March 2001 , pp. 105 - 118
Copyright
Copyright © Royal Aeronautical Society 2001 

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References

1. Pope, S.B. A more general effective-viscosity hypothesis, J Fluid Mech, 1975, 72, Part 2. pp 331–340.Google Scholar
2. Suga, K. Development and application of a non-linear eddy-viscosity model sensitised to stress and strain invariants, 1995, PhD Thesis. UMIST.Google Scholar
3. Craft, T.J., Launder, B.E. and Suga, K. Development and application of a cubic eddy-viscosity model of turbulence. Int J of Heat and Fluid Flow, 1996, 17, pp 108–115.Google Scholar
4. Craft, T.J., Launder, B.E. and Suga, K. Prediction of turbulent transitional phenomena with a nonlinear eddy-viscosity model, Int J of Heat and Fluid Flow. 1997, 18, pp 15–28.Google Scholar
5. Abid, R., Rumsey, C. and Gatski, T. Prediction of non-equilibrium flows with explicit algebraic stress models. AlAA J, 1995, 33, (11), p 2026.Google Scholar
6. Abid, R., Morrison, J.H., Gatski, T.B. and Speziale, C.G. Prediction of complex aerodynamic flows with explicit algebraic stress models, 1996, AlAA Paper 96-0565, 34th Aerospace Sciences Meeting and Exhibit.Google Scholar
7. Gatski, T.B. and Speziale, C.G. On explicit algebraic stress models for complex turbulent flows. J Fluid Mech, 1993, 254, pp 59–78.Google Scholar
8. Launder, B.E., Reece, G.J. and Rodi, W. Progress in the development of a Reynolds stress turbulence closure, J Fluid Mech, 1975, 68, pp 537–566.Google Scholar
9. Leschziner, M.A., Dimitriadis, K.P. and Page, G. Computational modelling of shock wave/boundary layer interaction with a cell-vertex scheme and transport models of turbulence. Aeronaut J, 1993, 97, (962), pp 43–61.Google Scholar
10. Speziale, C.G. and Gatski, T.B. Comparison of explicit and traditional algebraic stress models of turbulence, AlAA J, 35, pp 1506–1509.Google Scholar
11. Speziale, C.G., Sarkar, S. and Gatski, T.B. Modelling the pressure-strain correlation of turbulence: an invariant dynamical system approach, J Fluid Mech, 1991, 227, pp 245–272.Google Scholar
12. Rizzetta, D.P. Evaluation of algebraic Reynolds stress models for separated high-speed flows, 1997, AlAA Paper 97-2125, 28th AlAA Fluid Dynamics Conf.Google Scholar
13. Qin, N., Ludlow, D.K., Shaw, S.T. and Richardson, G. A unified high resolution approach for two equation turbulence modelling, 1997, Proceedings of the 3rd Pacific (nt Conf on Aerospace Sci and Tech, p 219-226.Google Scholar
14. Richardson, G. and Qin, N. Linear and non-linear turbulence modelling for shock-wave/turbulent boundary-layer interactions using a strongly coupled approach, 1998, AlAA Paper 98-0324, 36th Aerospace Sciences Meeting.Google Scholar
15. Delery, J. Experimental investigation of turbulence properties in transonic shock-boundary-layer interactions. AlAA J, 1983, 21, pp 180–185.Google Scholar
16. Bachalo, W. and Johnson, D. Transonic, turbulent boundary-layer separation generated on an axi symmetric flow model. A/AAV, 1986, 24, p 437.Google Scholar
17. Bradshaw, P., Ferriss, D.H., and Atwell, N.P. Calculation of boundary-layer development using the turbulent energy equation, J Fluid Mech. 1967, 28, pp593–616.Google Scholar
18. Qin, N., Scriba, K.W. and Richards, B.E. Shock-shock, shock-vortex interaction and aerodynamic heating in hypersonic corner flow, Aeronaut J, 199l, 95, (945),pp.l52–l60.Google Scholar
19. Osher, S. and Soloman, F. Upwind difference schemes for hyperbolic systems of conservation laws, Mathematics of Comp. 1982, 38, (158), pp 339–374.Google Scholar
20. Van Leer, B. Towards the ultimate conservation difference scheme: A second order sequel toGodunov's method, J Comput Phvsics. 1979,32, pp 101–136.Google Scholar
21. Menter, F.R. Zonal two-equation κ-ω turbulence models for aerodynamic (lows, 1993, AIAA Paper 93-2906.Google Scholar
22. Champagne, F.H., Harris, V.G., and Corrsin, S. Experiments on nearly homogeneous turbulent shear flow, J Fluid Meek, 1970, 41, pp 81–139.Google Scholar
23. Tavoularis, S. and Corrsin, S. Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient, J Fluid Mech. 1981,104, pp 311–347.Google Scholar
24. Rogers, M.M. and Moin, P. The structure of the vorticity field in homogeneous turbulent flows, J Fluid Mech, 1987, 176, pp 33–66.Google Scholar
25. Lee, M.J., Kim, J. and Moin, P. Structure of turbulence at high shear rate, J Fluid Mech, 1990, 216, pp 561–583.Google Scholar
26. Shih, T.H., Zhu, J. and Lumley, J.L. A new Reynolds stress algebraic equation model. Computer Methods in App Mech and Engg, 1995, 125, (1-4), pp 287–302.Google Scholar
27. Wilcox, D.C, Turbulence modelling for CFD, 1993, DCW Industries.Google Scholar
28. Menter, F.R. Influence of free-stream values on κ-ω model predictions, 1992, AAIA J., 30(6), pp 1657–1659.Google Scholar