Hostname: page-component-84b7d79bbc-dwq4g Total loading time: 0 Render date: 2024-07-30T00:03:17.108Z Has data issue: false hasContentIssue false
  • English
  • Français

A solution method for the three-dimensional compressible turbulent boundary-layer equations

Published online by Cambridge University Press:  04 July 2016

L. J. Johnston
L. J. Johnston*
Affiliation:
Aeronautics/Aerospace Department, von Karman Institute for Fluid Dynamics, B-1640 Rhode Saint Genèse-Belgium
Get access Rights & Permissions [Opens in a new window]

Summary

The development of a new calculation method for compressible 3D boundary layers is described. The method involves a finite-difference discretisation of the governing mean-flow equations. In particular, the differencing scheme used to discretise spanwise derivatives adapts automatically to the sign of the local crossflow within the boundary layer. A plane-by-plane solution procedure in the spanwise direction enables second-order accuracy to be maintained throughout the whole flowfield. A normal coordinate scaling with the local total momentum thickness removes most of the boundary layer growth in computational space. The Cebeci-Smith algebraic turbulence model is used for the initial validation of the calculation method. A simple modification to this model is tested, involving an explicit dependence of the outer eddy viscosity on the crossflow within the boundary layer. There results a significantly improved prediction of the NLR infinite swept wing flow experiment.

Type
Research Article
Information
The Aeronautical Journal , Volume 93 , Issue 924 , April 1989 , pp. 115 - 131
Copyright
Copyright © Royal Aeronautical Society 1989 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Kaynak, U. and Flores, J. Advances in the Computation of Transonic Separated Flows Over Finite Wings. AIAA Paper 87-1195, 1987.Google Scholar
2. Computation of Three Dimensional Boundary Layers Including Separation. AGARD R 741, Feb 1987.Google Scholar
3. Elsenaar, A. and Boelsma, S. H. Measurements of the Reynolds Stress Tensor in a Three Dimensional Turbulent Boundary Layer Under Infinite Swept Wing Conditions. NLR TR 74095U, 1974.Google Scholar
4. Rotta, J. C. A family of turbulence models for three dimensional thin shear layers. In: Proceedings of the Symposium on Turbulent Shear Flows, Pennsylvania State University, April 1977, 10.27-10.34.Google Scholar
5. Van Den Berg, B. Some Notes on Three Dimensional Turbulent Boundary Layer Data and Turbulence Modeling. NLR MP 82007U, 1982.Google Scholar
6. Smith, P. D. The numerical computation of three dimensional turbulent boundary layers. In: IUTAM Symposium on Three Dimensional Turbulent Boundary Layers, Berlin, March 1982. Springer Verlag, Berlin, 1982, 265–285.Google Scholar
7. Humphreys, D. A. and Lindhout, J. P. F. Calculation methods for 3D turbulent boundary layers. Prog Aerosp Sci, 1988, 25, (2), 107–129.Google Scholar
8. Wesseling, P. and Lindhout, J. P. F. A calculation method for three-dimensional incompressible turbulent boundary layers. In: AGARD CP 93 “Turbulent Shear Flows”, Jan 1972, Paper 8.Google Scholar
9. Rastogi, A. K. and Rodi, W. Calculation of general three dimensional turbulent boundary layers. AIAA J, 1978, 16, (2), 151–159.Google Scholar
10. Bradshaw, P. Calculation of three dimensional turbulent boundary layers. J Fluid Mech, 1971, 46, (3), 417–445.Google Scholar
11. Johnston, L. J. A numerical method for three dimensional compressible turbulent boundary layer flows. In: Proceedings of the 5th International Conference on Numerical Methods in Laminar and Turbulent Flow, Montreal, July 1987. Pineridge Press, 1987, 1421–1435.Google Scholar
12. Johnston, L. J. A Numerical Method to Compute Compressible Three Dimensional Turbulent Boundary Layer Flows. ARA Report 68, 1986.Google Scholar
13. Cebeci, T. and Smith, A. M. O. Analysis of Turbulent Boundary Layers. Academic Press, 1974.Google Scholar
14. Hassid, S. and Poreh, M. A turbulent energy model for flows with drag reduction. ASME Trans, J Fluids Eng, 1975, 97, 234–241.Google Scholar
15. Chien, K.-Y. Predictions of channel and boundary layer flows with a low Reynolds number turbulence model. AIAA J, 1982, 20, (1), 33–38.Google Scholar
16. Johnston, L. J. A Calculation Method for Compressible Three-Dimensional Turbulent Boundary-Layer Flows, von Karman Institute, Technical Note 167, July 1988.Google Scholar
17. Cebeci, T., Kaups, K. and Ramsey, J. A. A General Method for Calculating Three Dimensional Compressible Laminar and Turbulent Boundary Layers on Arbitrary Wings. NASA CR 2777, 1977.Google Scholar
18. Johnston, L. J. A calculation method for two dimensional wall bounded turbulent flows. Aeronaut J, May 1986, 90, (895), 174–184.Google Scholar
19. Cousteix, J., Aupoix, B. and Pailhas, G. Review of Theoretical and Experimental Results on Three Dimensional Turbulent Wakes and Boundary Layers. ESA TT 678, April 1981 (also ONERA NT 1980-4).Google Scholar
20. Tassa, A., Atta, E. H. and Lemmerman, L. A. A New Three Dimensional Boundary Layer Calculation Method. AIAA Paper 82-0224, 1982.Google Scholar
21. Lewkowicz, A. K. An improved universal wake function for turbulent boundary layers and some of its consequences. Z Flugwiss Weltraumforsch, 1982, 6, (4), 261–266.Google Scholar
22. East, L. F. A Prediction of the Law of the Wall in Compressible Three Dimensional Turbulent Boundary Layers. RAE TR 72178, 1972.Google Scholar
23. Mager, A. Generalization of Boundary Layer Momentum Integral Equations to Three Dimensional Flows Including Those of Rotating Systems. NACA TR 1067, 1952.Google Scholar
24. Lindhout, J. P. F., De Boer, E. and Van Den Berg, B. Three Dimensional Boundary Layer Calculations on Wings, Starting From the Fuselage. NLR MP 82060U, 1982.Google Scholar
25. Nash, J. F. and Scruggs, R. M. An Implicit Method for the Calculation of Three Dimensional Boundary Layers on Fuselage Configurations. Sybucon Inc., Report LG76ER0199, 1976.Google Scholar
26. Leonard, B. P. A survey of finite differences of opinion on numerical muddling of the incomprehensible defective confusion equation. In: ASME AMD 34 “Finite Element Methods for Convection Dominated Flows” , 1979, 1–17.Google Scholar
27. Delery, J. M. and Formery, M. J. A Finite Difference Method for Inverse Solutions of 3D Turbulent Boundary Layer Flow. AIAA Paper 83-0301, 1983. (also ONERA TP 1983-4).Google Scholar
28. Van Dalsem, W. R. and Steger, J. L. The Efficient Simulation of Separated Three Dimensional Viscous Flows Using the Boundary Layer Equations. AIAA Paper 85-4064, 1985.Google Scholar
29. Humphreys, D. A. Comparison of Boundary Layer Calculations for a Wing: the May 1978 Stockholm Workshop Test Case. FFA TN AE-1522, 1979.Google Scholar
30. Lindhout, J. P. F., Van Den Berg, B. and Elsenaar, A.: Comparison of Boundary Layer Calculations for the Root Section of a Wing. The September 1979 Amsterdam Workshop Test Case. NLR MP 80028U, 1981.Google Scholar
31. Van Den Berg, B. and Elsenaar, A. Measurements in a Three Dimensional Incompressible Turbulent Boundary Layer in an Adverse Pressure Gradient Under Infinite Swept Wing Conditions. NLR TR 72092U, 1972.Google Scholar
32. Abid, R., Delery, J. and Schmitt, R.: An Examination of Turbulence Models for a Separating Three Dimensional Turbulent Boundary Layer. ONERA TP 1985-74.Google Scholar
33. Cousteix, J. Three dimensional boundary layers. Introduction to calculation methods. In: AGARD R 741 “Computation of Three Dimensional Boundary Layers Including Separation“ , Feb. 1987, 1–1/1–49.Google Scholar
34. Van Den Berg, B. Three dimensional shear layer experiments and their use as test cases for calculation methods. In: AGARD R 741 “Computation of Three Dimensional Boundary Layers Including Separation” , Feb. 1987, 3–1/3–13.Google Scholar
35. Cook, P. H., Mcdonald, M. A. and Firmin, M. C. P. Wind Tunnel Measurements of the Mean Flow in the Turbulent Boundary Layer and Wake in the Region of the Trailing Edge of a Swept Wing at Subsonic Speeds. RAE TR 79062, 1979.Google Scholar
36. East, L. F. Measurements of the Three Dimensional Incompressible Turbulent Boundary Layer Induced on the Surface of a Slender Delta Wing by the Leading Edge Vortex. RAE TR 73141, 1974.Google Scholar
37. Smith, P. D. An Integral Prediction Method for Three Dimensional Compressible Turbulent Boundary Layers. ARC R&M 3739, 1974.Google Scholar