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Numerical studies of supersonic flow over a compression corner

Published online by Cambridge University Press:  04 July 2016

S. C. Holmes  and
L. C. Squire
S. C. Holmes
Affiliation:
Cambridge University Engineering Department
L. C. Squire
Affiliation:
Cambridge University Engineering Department
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Summary

Numerical solutions of the Reynolds-averaged Navier-Stokes equations are presented for the shock/boundary-layer interaction which occurs with the attached, near-adiabatic, turbulent flow of air over a two-dimensional compression corner of 11° at a Mach number of 2·5.

It is shown that for this near-adiabatic flow, the isenthalpic and non-isenthalpic Navier-Stokes equations produce solutions which are very similar in respect of the velocity,pressure and density fields.

In the first part of the work, two different upstream, or approaching boundary-layer profiles are considered: one with a normal full velocity profile and the other with a less full velocity profile corresponding to a boundary layer that has developed in an adverse pressure gradient. Several turbulence models are compared using the isenthalpic form of the equations (because the computations are more economical). It is found that agreement with previous experiments (such as in the location of the shock and density profile predictions) is improved in the vicinity of the interaction using the non-equilibrium Johnson-King model compared to the equilibrium models of Baldwin-Lomax and Cebeci-Smith.

The second part of the work examines the effects of turbulent Prandtl number (Prt) modelling for this flow using the non-isenthalpic form of the Navier-Stokes equations. Three models for the turbulent Prandtl number are tested. It is found that modelling Prt affects the velocity, pressure and density fields only very slightly, and that the main impact is on the prediction of temperatures very close to the wall. The adiabatic wall temperature variation through the interaction has been measured experimentally and compared with the predictions. The best agreement was obtained using Wassel and Catton's model for Pr, rather than the familiar assumption that Prt = 0·9 everywhere in the flow.

Type
Research Article
Information
The Aeronautical Journal , Volume 96 , Issue 953 , March 1992 , pp. 87 - 95
Copyright
Copyright © Royal Aeronautical Society 1992 

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References

1. Dawes, W. N., Computation of viscous compressible flow in blade cascades using an implicit iteractive replacement algorithm, Proceedings of I. Mech. E. Conf. Computational Methods in Turbomachinery, Paper C55/84, 1984, pp 157–164.Google Scholar
2. Holmes, S. C., An Investigation of Supersonic Flow over a Compression Corner. Ph.D. Dissertation, Cambridge University, Cambridge, UK, 1991.Google Scholar
3. Benay, R., Coet, M. S., and Delery, J., Validation of turbulence models applied to transonic shock-wave-boundary- layer interaction, Rech Aerospatiale, 1987, 3, pp 1–16.Google Scholar
4. Baldwin, B. S., and Lomax, H., Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows, AIAA Paper 78-257, Jan. 1978.Google Scholar
5. Cebeci, T., and Smith, A. M. O., Analysis of Turbulent Boundary Layers, Academic Press, New York, 1974.Google Scholar
6. Stock, H. W., and Haase, W. Determination of length scales in algebraic turbulence models for Navier-Stokes Methods, AIAA J, Jan. 1989, 27, pp 5–15.Google Scholar
7. Martinelli, L., and Yakhot, V., RNG-based Turbulence TransportApproximations withApplications to Transonic Flows, AIAA Paper 89-1950, New York, 1989.Google Scholar
8. Johnson, D. A. and King, L. S. A mathematically simple turbulence closure model for attached and separated turbulent boundary layers, AIAA J, Nov. 1985, 23, pp 1684–1692.Google Scholar
9. Visbal, M., and Knight, D. The Baldwin-Lomax turbulence model for two-dimensional shock-wave/boundary-layer interactions, AIAA J, July 1984, 22, pp 921–928.Google Scholar
10. Granville, P. S. Baldwin-Lomax factors for turbulent boundary layers in pressure gradients, AIAA J, Dec. 1987, 25, pp 1624– 1627.Google Scholar
11. Yakhot, V., and Orszag, S. A., Renormalisation group analysis of turbulence, 1, Basic theory, J Sci Comput, 1986, 1,(1), pp 3–51.Google Scholar
12. Hayakawa, K., and Squire, L. C. The effect of upstream boundary layer state on the shock interaction at a compression corner, J Fluid Mech 1982, 122, pp 368–394.Google Scholar
13. Squire, L. C., Bryanston-Cross, P. J., and Liu, X. An interferometric study of the shock interaction at a compression corner, Aeronaut J, May 1991, 95, pp 143–151.Google Scholar
14. Squire, L. C. Eddy viscosity distributions in compressible turbulent boundary layers with injection, Aeronaut Q, May 1971, pp-169–182.Google Scholar
15. Marriott, P. G. Compressible Turbulent Boundary Layers with Discontinuous Injection, Ph.D. Dissertation, Cambridge University, Cambridge, UK, 1973.Google Scholar
16. Visbal, M. Numerical Simulation of Shock/Turbulent Boundary Layer Interaction over a 2-D Compression Corner, Ph.D. Dissertation, Rutgers University, NY, 1983.Google Scholar
17. Owen, F. K., Horstmann, C. C., and Kussoy, M. I. Mean and fluctuating flow measurements of a fully-developed, non-adiabatic hypersonic boundary layer, J Fluid Mech, 1975, 70, pp 393–413.Google Scholar
18. Cebeci, T. A model for eddy conductivity and turbulent Prandtl number, J Heat Transfer, 1973, 10 95 C, pp 227–234.Google Scholar
19. Wassel, A. T., and Catton, I. Calculation of turbulent boundary layers over flat plates with different phenomenological theories of turbulence and variable turbulent Prandtl number, Int J Heat Mass Transfer 1973, 16, pp 1547–1563.Google Scholar
20. Hammond, G. P. Turbulent Prandtl Number Distribution within the Constant Stress/Heat-Flux Region of a Near-Wall Flow, Cranfield SME Report No. 8401, Cranfield Institute of Technology, Bedford, UK, 1984.Google Scholar