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Numerical solution of Euler equations for aerofoils in arbitrary unsteady motion

Published online by Cambridge University Press:  04 July 2016

C. Q. Lin  and
K. Pahlke
C. Q. Lin
Affiliation:
Northwestern Polytechnical University Xi'an, China
K. Pahlke
Affiliation:
Institute for Design Aerodynamics, DLR Braunschweig, Germany
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Abstract

This paper is part of a DLR research programme to develop a three-dimensional Euler code for the calculation of unsteady flow fields around helicopter rotors in forward flight. The present research provides a code for the solution of Euler equations around aerofoils in arbitrary unsteady motion. The aerofoil is considered rigid in motion, and an O-grid system fixed to the moving aerofoil is generated once for all flow cases. Jameson's finite volume method using Runge-Kutta time stepping schemes to solve Euler equations for steady flow is extended to unsteady flow. The essential steps of this paper are the determination of inviscid governing equations in integral form for the control volume varying with time in general, and its application to the case in which the control volume is rigid with motion. The implementation of an implicit residual averaging with variable coefficients allows the CFL number to be increased to about 60. The general description of the code, which includes the discussions of grid system, grid fineness, farfield distance, artificial dissipation, and CFL number, is given. Code validation is investigated by comparing results with those of other numerical methods, as well as with experimental results of an Onera two-bladed rotor in non-lifting flight. Some numerical examples other than periodic motion, such as angle-of-attack variation, Mach number variation, and development of pitching oscillation from steady state, are given in this paper.

Type
Research Article
Information
The Aeronautical Journal , Volume 98 , Issue 976 , July 1994 , pp. 207 - 214
Copyright
Copyright © Royal Aeronautical Society 1994 

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References

1. Jameson, A., Schmidt, W. and Turkel, E. Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time stepping schemes, AIAA-Paper 81-1259, 1981.Google Scholar
2. Pahlke, K. Development of a numerical method solving the un steady Euler equations for oscillating airfoils, DLR-FB 129-90/35, 1990.Google Scholar
3. Kroll, N. and Jain, R.K. Solution of two-dimensional Euler equations- experience with a finite volume code, DLR-FB 129-90/35,1990.Google Scholar
4. Jorgenson, P.C.E. and Chima, R.V. An unconditionally stable Runge-Kutta method for unsteady flows, AIAA-89-0205, 27th Aero space Sciences Meeting, Reno, Nevada, 9-12 January, 1989.Google Scholar
5. Kroll, N. A finite volume method for solving Euler equations, DFVLR-IB, 1983.Google Scholar
6. Lin, C.Q. A fast-convergence iteration solution of incompressible potential flow around multi-element airfoils, Ada Aerodynamica Sinica, 1989, 7, (4), pp 394–399.Google Scholar
7. Jameson, A. and Baker, T.J. Solution of the Euler equations for complex configurations, AIAA-Paper 83-1929, 1983.Google Scholar
8. Lambourne, N.C. et al. Compendium of Unsteady Aerodynamic Measurements, AGARD Report No.702, 1982.Google Scholar
9. Garrick, I.E. Non steady wing characteristics. Section F of Aerodynamic Components of Aircraft at High Speed, Volume VII of High Speed Aerodynamics and Jet Propulsion, Princeton University Press, 1957.Google Scholar