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An Euler correction method for computing two-dimensional unsteady transonic flows

Published online by Cambridge University Press:  04 July 2016

D. Das  and
S. Santhakumar
D. Das
Affiliation:
Aerodynamics DivisionVikram Sarabhai Space Centre, ISRO, Trivandrum, India
S. Santhakumar
Affiliation:
Department of Aerospace EngineeringIndian Institute of Technology, Madras, India
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Abstract

An Euler correction method is developed for unsteady, transonic inviscid flows. The strategy of this method is to treat the flow-field behind the shock as rotational flow and elsewhere as irrotational flow. The solution for the irrotational flow is obtained by solving the unsteady full-potential equation using Jameson's rotated time-marching finite-difference scheme. Clebsch's representation of velocity is followed for rotational flow. In this representation the velocities are decomposed into a potential part and a rotational part written in terms of scalar functions. The potential part is computed from the unsteady full potential equation with appropriate modification based on Clebsch's representation of velocity. The rotational part is obtained analytically from the unsteady momentum equation written in terms of Clebsch variables. This method is applied to compute the unsteady flow-field characteristics for an oscillating NACA 64A010 aerofoil. The results of the present calculation are found to be in good agreement with both Euler solution and experimental results.

Type
Research Article
Information
The Aeronautical Journal , Volume 103 , Issue 1020 , February 1999 , pp. 85 - 94
Copyright
Copyright © Royal Aeronautical Society 1999 

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References

1. Simpson, L.B. and Whitefield, D.L. A flux-difference split algorithm for unsteady thin-layer Navier-Stokes solutions, AIAA paper 89-1995-CP, June 1989.Google Scholar
2. Yoon, S. and Kwak, D. Implicit methods for the Navier-Stokes equations, Comp Systems in Engineering, 1, (2–4), 1990, pp 535–547.Google Scholar
3. Ekaterinaris, J.A. and Menter, F.R. Computation of oscillating airfoil flows with one and two equation turbulence models, AIAA J, 1994, 32, (12), pp 2359–2365.Google Scholar
4. Ko, S. and McCroskey, W.J. Computation of unsteady separating flows over an oscillating airfoil, AIAA paper 95–0312, 1995.Google Scholar
5. Song, W.P. and Pahlke, K. Unsteady N-S calculations for NACA 0012 airfoil oscillating at high angle-of-attack, Technical Report IB 129-96/18, DLR, 1996.Google Scholar
6. Magnus, R. and Yoshihara, H. The transonic oscillating flap, AIAA Paper 76–327, 1976.Google Scholar
7. Steger, J.L. and Warming, R.L. Flux vector splitting of the inviscid gas dynamics equations with application to finite-difference methods, J Comp Phys, 1981, 40, pp 263–293.Google Scholar
8. Belk, D.M. Unsteady Three-Dimensional Euler Equation Solutions on Dynamic Blocked Grids, PhD Dissertation, Mississippi State University, 1986.Google Scholar
9. Harten, A., Lax, P.D. and Van Leer, B. On upstream differencing and Godunov-type schemes for hyperbolic conservative laws, SIAM Review, 1983, 25, pp 35–61.Google Scholar
10. Chakravarthy, S. and Osher, S. A New class of high accuracy TVD schemes for hyperbolic conservation laws, AIAA Paper 85–0363, January 1985.Google Scholar
11. Thomas, J.L., Van Leer, B. and Walters, R.W. Implicit split-flux schemes for the Euler equations, AIAA Paper 85–1680, July 1985.Google Scholar
12. Sides, J. Compulation of unsteady transonic flows with an implicit numerical method for solving the Euler equation, Recherche Aerospatiale, 1985, 2, pp 17–39.Google Scholar
13. Batina, J.T. Unsteady Euler airfoil solutions using unstructured dynamic meshes, AIAA J, 1990, 28, (8), pp 1381–1388.Google Scholar
14. Davis, G.A. and Bendikson, O.O. Unsteady transonic two-dimensional Euler solutions using finite elements, AIAA J, 31. (6). June 1993.Google Scholar
15. Collyer, M.R., and Lock, R.C. Prediction of viscous effects in steady transonic flow past an aerofoil. Aeronaut Q, August 1979, 30, (3), pp 485–505.Google Scholar
16. Metrens, J., Klevenhusen, K.D. and Jacob, H. Accurate transonic wave drag prediction using simple physical models, AIAA J, 1987, 25, (6), pp 799–805.Google Scholar
17. Zi-Giang, Z. and Xue-Song, B. Numerical computation of improved transonic potential method, J Aircr, March-April 1992, 29, (2), pp 799–805.Google Scholar
18. Tai, T.C. Hybrid approach to transonic inviscid flow with moderate to strong shock wave, Transonic Aerodynamics, Nixon, D. (Ed), Vol 21, Progress in Astronautics and Aeronautics, NY, AIAA, 1982.Google Scholar
19. Sokhey, J.J. Transonic flow around axisymmetric inlets including rotational flow effects, AIAA paper 80–0341, January 1980.Google Scholar
20. Dang, T.Q. and Chen, L.T. An Euler correction method for two and three-dimensional transonic flows, AIAA paper 87–522, January 1987.Google Scholar
21. Lamb, H. Hydrodynamics, Dover, Newyark, 1960.Google Scholar
22. Devasia, K.J. and Ashok, V. Personal communication on the use of SALE-3D code to transient problems.Google Scholar
23. Roychowdhury, A.P. and Parthan, S. Personal communication on the use of a version of ARC 2D code to unsteady problems.Google Scholar
24. Das, D. An unsteady 3D full potential method to estimate flow field characteristics, VSSC-AFDG-ARD-089, November l993.Google Scholar
25. Magnus, R.J. Calculations of some unsteady transonic flows about the NACA 64A010 and 64A010 airfoils, AFFDL TR-77-46, July 1977.Google Scholar
26. Chyu, W.J. and Davis, S.S. Numerical studies of unsteady transonic flows over an oscillating airfoil, AGARD CP-374.Google Scholar
27. Davis, S.S. Experimental studies of scale effects on oscillating airfoils at transonic speeds, AGARD-CP-296, February 1981, pp 9–1 to 9–6.Google Scholar
28. Davis, S.S. and Malcolm, G.W. Experiments in unsteady transonic flows, AIAA paper 79–0769, 17th Aerospace Sciences Meeting, New Orleans, USA, 15–17 January 1979.Google Scholar
29. McCroskey, W.J., Kutler, P. and Bridgeman, J.O. Status and prospect of computational fluid dynamics for unsteady transonic viscous flows, AGARD CP-374.Google Scholar