Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-22T10:12:24.038Z Has data issue: false hasContentIssue false
  • English
  • Français

A hybrid integral equation finite volume scheme for transonic potential flow about complex configurations

Published online by Cambridge University Press:  04 July 2016

A. K. Bhattacharya  and
N. L. Arora
A. K. Bhattacharya
Affiliation:
Indian Institute of Technology, Kanpur, India
N. L. Arora
Affiliation:
Indian Institute of Technology, Kanpur, India
Get access Rights & Permissions [Opens in a new window]

Abstract

A hybrid integral equation finite volume scheme has been developed for the calculation of transonic potential flow about complex configurations. A new technique has been used for evaluating the potential values in the field cells intersecting the body surface panels. These potential values then serve as Dirichlet boundary conditions for computing the potentials in the field by a finite volume Successive Line Over Relaxation (SLOR) scheme. In this approach there is no need to evaluate the potentials anywhere in the field by direct application of Green's third identity, thus significantly reducing computer processing time and storage requirement, while improving accuracy of surface pressure prediction and shock capture, as results indicate. The capability of tackling additional complex geometry with ease, the primary advantage of the integral equation approach, is demonstrated by using the same field grid for wing-alone and wing-body combination cases, while maintaining the solution accuracy.

Type
Research Article
Information
The Aeronautical Journal , Volume 98 , Issue 972 , February 1994 , pp. 35 - 48
Copyright
Copyright © Royal Aeronautical Society 1994 

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. Wu, J.C. and Thompson, J.F. Numerical solutions of time dependent incompressible Navier-Stokes equations using an integro-differential formulation, J Computers Fluids, 1973, 1, (2), pp 197–215.Google Scholar
2. Wu, J.C. Numerical boundary conditions for viscous flow problems, AIAA J, 1976, 14, (8), pp 1042–1049.Google Scholar
3. El Refaee, M.M., Wu, J.C. and Lekoudis, S.G. Solutions of the compressible Navier-Stokes equations using the integral method, AIAA J, 1982, 20, (3), pp 356–362.Google Scholar
4. Morino, L. Scalar/vector potential formulation for compressible viscous unsteady flows, NASA CR-3921, 1985.Google Scholar
5. Morino, L. and Beauchamp, P. A potential-vorticity decomposition for the boundary-element analysis of viscous flows, In: Boundary Element Methods in Applied Mechanics 1, Tanaka, M. and Cruse, T.A. (eds), 1988, Pergamon Press, New York.Google Scholar
6. Morino, L. Helmholtz and Poincare potential-vorticity decompositions for the analysis of unsteady compressible viscous flows, In: Developments in Boundary Element Methods Vol. 6, Banerjee, P.K. and Morino, L. (Eds), 1990, Elsevier Science Publishers, London.Google Scholar
7. Hess, J.L. and Smith, A.M.O. Calculation of potential flow about arbitrary bodies, Progress Aeronaut Sci, 1966, 8, pp 1–138.Google Scholar
8. Morino, L. and Kuo, C.C. Subsonic potential aerodynamics for complex configurations, a general theory, AIAA J, 1974, 12, (2).Google Scholar
9. Hess, J.L. The problem of three-dimensional lifting flow and its solution by means of surface singularity distribution, Comput Meth Appl Mech Eng, 1974, 4,(3).Google Scholar
10. Johnson, F.T. A general panel method for the analysis and design of arbitrary configurations in incompressible flows, NASA CR 3079, 1980.Google Scholar
11. Maskew, B. Prediction of subsonic aerodynamic characteristics: a case for low-order panel methods, J Aircr, 1982, 19, (2), pp 157–163.Google Scholar
12. Luu, T.S. and Coulmy, G. Method of calculating the compressible flow around an aerofoil or a cascade up to the shockfree transonic range, Comput Fluid, 1977, 5, pp 261–275.Google Scholar
13. Piers, W.J. and Sloof, J.W. Calculation of transonic flow by means of a shock-capturing field panel method, AIAA Paper 79-1459, 1979.Google Scholar
14. Hounjet, M.H.L. Transonic panel method to determine loads on oscillatory airfoils with shocks, AIAA J, 1981, 19, (5), pp 559–566.Google Scholar
15. Johnson, F.T., James, R.M., Bussoletti, J.E., Woo, A.C. and Young, D.P. A transonic rectangular grid embedded panel method, AIAA Paper 82-0953, June 1982.Google Scholar
16. Tseng, K. and Morino, L. Nonlinear Green's function method for unsteady transonic flows, In: AIAA Progress in Astronautics and Aeronautics — Transonic Aerodynamics I, 1982, Nixon, D. (Ed), AIAA, New York, pp 565–603.Google Scholar
17. Ravichandran, K.S., Arora, N.L. and Singh, R. Transonic full potential solutions by an integral equation method, AIAA J, 1984, 22, (7), pp 882–888.Google Scholar
18. Oskam, B. Transonic panel method for full potential equation applied to multi-component airfoils, AIAA J, 1985, 23, (9), pp 1327–1334.Google Scholar
19. Erickson, L.L. and Strande, S.M. A theoretical basis for extending surface-panelling methods to transonic flow, AIAA J, 1985, 23, (12), pp 1860–1867.Google Scholar
20. Kandil, O.A. and Hu, H. Integral equation solution for transonic and subsonic aerodynamics, In: Notes on Numerical Fluid Mechanics 1, Ballman, J., Eppler, R. and Hackbusch, W. (Eds), Vieweg, 1988, pp 101–109.Google Scholar
21. Arora, N.L. and Agarwal, J.P. Three dimensional transonic full potential solution by an integral equation method, Proceedings of 17th ICAS Congress, Stockholm vol 2, 1990, pp 2055–2064.Google Scholar
22. Samant, S.S., Bussoletti, J.E., Johnson, F.T., Burkhart, R.H., Everson, B.L., Melvin, R.G., Young, D.P., Erickson, L.L., Madson, M.D. and Woo, A.C. Tranair: a computer code for transonic analyses of arbitrary configurations, AIAA Paper 87-0034, January 1987.Google Scholar
23. Sinclair, P.M. A three-dimensional field integral method for the calculation of transonic flow on complex configurations theory and preliminary results, Aeronaut J, June/July 1988, 92, (916), pp 235–241.Google Scholar
24. Sinclair, P.M. Integral methods in British Aerospace Brough, In: Computational Methods in Aeronautical Fluid Dynamics 1, Stow, P. (ed), Oxford, 1990, pp 23–37.Google Scholar
25. Bhattacharya, A.K. and Arora, N.L. A hybrid integral equation finite volume scheme for transonic potential flow past arbitrary configurations, Proceedings of the Fifth Asian Congress of Fluid Mechanics, Taejon, 1992, pp 618–621.Google Scholar
26. Hafez, M.M., Murman, E.M. and South, J.C. Artificial compressibility methods for numerical solution of transonic full potential equation, AIAA J, 1979, 17, (8), pp 838–844.Google Scholar
27. Osher, S., Hafez, M. and Whitlow, W. Entropy condition satisfying approximations for the full potential equation of transonic flow, Math Comp January 1985, 44, 169, pp 1–29.Google Scholar
28. Holst, T.L. Fast conservative algorithm for solving the transonic full potential equation, AIAA J, 1980, 18, (12), pp 1431–1439.Google Scholar
29. Baker, T.J. Computations of transonic potential flow, In: Computational Methods for Turbulent, Transonic and Viscous Flows I, Essar, J.A. (ed), Hemisphere, 1983, pp 213–289.Google Scholar
30. Ahmed, S. Pressure Measurements in the Heatshield Region of PSLV Model at Transonic Speeds, NAL TWT-1-33-84, August 1984.Google Scholar
31. Schmitt, V. and Charpin, F. Pressure distributions on the Onera M6 wing at transonic Mach numbers, AGARD-AR-138, May 1979, Chapter B1.Google Scholar
32. Sacher, P. Numerical solutions for three dimensional cases-swept wings, AGARD-AR-211, May 1985, Chapter 7.Google Scholar
33. Treadgold, D.A., Jones, A.F. and wilson, K.H. Pressure distribution measured in RAE transonic wind tunnel on RAE wing A in combination with axisymmetric body, AGARD-AR-138, May 1979, Chapter B4.Google Scholar
34. Keener, E.R. Pressure distribution measurements on a transonic low aspect ratio wing, NASA TM-86683, September 1985.Google Scholar
35. Hinson, B.L. and Burdges, K.P. Acquisition and Application of Transonic Wing and Far-Field Test Data for Three Dimensional Computational Method Evaluation, Air Force Office of Scientific Research TR-80-0421, March 1980.Google Scholar