Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-05-03T01:40:54.169Z Has data issue: false hasContentIssue false
  • English
  • Français

The prediction of separated flow using a viscous-inviscid interaction method

Published online by Cambridge University Press:  04 July 2016

B.R. Williams
B.R. Williams*
Affiliation:
Aerodynamics Department, Royal Aircraft Establishment, Farnborough
Get access Rights & Permissions [Opens in a new window]

Summary

The separation of boundary-layer flow from a wing or in a diffuser usually defines the limit of efficient operation, so it is important that the onset and development of separated flow can be predicted. The calculation of the interaction of the shear layout close to an aerofoil with the external inviscid flow has offered an attractive alternative to solving the Reynoldsaveraged Navier Stokes equations for attached flow: the interaction method is much faster. In this paper it is shown how the interaction approach can be extended for use with separated flows and the development of a practical method is described. The calculation of the shear layer through the singularity at separation is accomplished by using an inverse mode. Beyond separation the empirical definition of a new family of velocity profiles allows an integral calculation of the shear layer to proceed up to the reattachment. The solutions for the shear layer close to the aerofoil are matched to the external inviscid flow by a ‘semi-inverse’ method. A careful examination of the stability of this method leads to rapid convergence for separated and attached flows. As an illustration the stall and post stall behaviour of a twodimensional aerofoil is predicted and compared with experimental results.

Type
Research Article
Information
The Aeronautical Journal , Volume 89 , Issue 885 , May 1985 , pp. 185 - 197
Copyright
Copyright © Royal Aeronautical Society 1985 

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. Lock, R. C. and Firmin, M. C. P. Survey of techniques for estimating viscous effects in external aerodynamics. Proceedings of IMA Conference on Numerical Methods in Aeronautical Fluid Dynamics, 30th March-lst April 1981, edited by Roe, P., Academic Press, 1983.Google Scholar
2. Catherall, D. and Mangler, K. W. The integration of the two-dimensional laminar boundary-layer equations past the point of vanishing skin friction. J. Fluid Mech. 1966, 26, Pt 1, 63–182.Google Scholar
3. East, L.F., Smith, P. D. and Merryman, P. J. Prediction of the development of separated turbulent boundary layers by the lagentrainment method. RAE Technical Report 77046,1977,.Google Scholar
4. Green, J. E., Weeks, D. J. and Brooman, J. W. F. Prediction of turbulent boundary layers and wakes in compressible flow by a lag-entrainment method. RAE Technical Report 72231,1972.Google Scholar
5. Le Balleur, J. C. Strong matching method for computing transonic viscous flows including wakes and separations. La Recherche Aerospatiale No 1981-3, 21–45, English translation.Google Scholar
6. Lock, R. C. Private communication.Google Scholar
7. Mahgoub, H. E. H. and Bradshaw, P. Calculation of turbulent-inviscid flow interactions with large normal pressure gradients. AIAA Journal, 1979,17,10,1025-29.Google Scholar
8. East, L. F. A representation of second-order boundary-layer effects in the momentum integral equation and in viscousinviscid interactions. RAE Techical Report 81002,1981.Google Scholar
9. Wigton, L. B. and Holt, M. Viscous-inviscid interaction in transonic flow. AIAA Paper No 81-1003,1981.Google Scholar
10. Hastings, R. C. Private communication.Google Scholar
11. Wadcock, A. J. Flying hot-wire study of two-dimensional turbulent separation on a NACA 4412 airfoil at maximum lift. PhD Thesis, California Institute of Technology, 1978.Google Scholar
12. Newling, J. C. An improved two-dimensional multi-aerofoil program. HSA-MAE-R-FDM-0007,1977.Google Scholar
13. Weeks, D. J. RAE unpublished paper.Google Scholar
14. Green, J. E. Application of Head’s entrainment method to the prediction of turbulent boundary layers and wakes in compressible flow. RAE Technical Report 72079,1972.Google Scholar
15. Green, J. E. The prediction of turbulent boundary-layer development in compressible flow. J. Fluid Mech., 1968, 31, 753–778.Google Scholar
16. Thwaites, B. Incompressible aerodynamics. 1960, Clarendon Press.Google Scholar
17. Granville, P. S. The calculation of viscous drag of bodies of revolution. David Taylor Model Basin, Report 849,1953.Google Scholar
18. Horton, H. P. A semi-empirical theory for thegrowth and bursting of laminar separation bubbles. ARC CP10/3,1967.Google Scholar
19. Garner, H. C., Rogers, E. W. E., Acum, W. E. A. and Maskell, E. C. Subsonic wind tunnel wall corrections. AGARDograph 109,1966.Google Scholar
20. Hess, J. L. and Smith, A. M. O. Calculation of potential flow about arbitrary bodies. Progress in Aeronautical Sciences, 1967, 8, 1–139, Pergamon Press.Google Scholar