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Computation of flow around wings based on the Euler equations

Published online by Cambridge University Press:  20 April 2006

Arthur Rizzi  and
Lars-Erik Eriksson
Arthur Rizzi
Affiliation:
FFA, The Aeronautical Research Institute of Sweden, S-161 11 Bromma, Sweden
Lars-Erik Eriksson
Affiliation:
FFA, The Aeronautical Research Institute of Sweden, S-161 11 Bromma, Sweden
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Abstract

Inviscid transonic flows containing either strong shock waves or complex vortex structure call for the Euler equations as a realistic model. We present here a computational procedure, termed WINGA2, for solving the Euler equations for transonic flow around aircraft upon a 0–0 mesh generated by transfinite interpolation. An explicit time-marching finite-volume technique solves the flow equations and features a non-reflecting far-field boundary condition and an internal mechanism for temporal damping together with a model for artificial viscosity. The method's convergence to a steady state is studied, and results computed on the CYBER 205 vector processor are presented. The Euler equation model is found to predict the existence of a tip vortex created by flow separating from the downstream region of the tip of the ONERA M6 wing where the radius of curvature approaches zero.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 148 , November 1984 , pp. 45 - 71
Copyright
© 1984 Cambridge University Press

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References

Agard Working Group 07 1984 Test cases for steady inviscid transonic and supersonic flows. AGARD Publ. (in preparation).
Engqvist, B. & Majda, A. 1977 Absorbing boundary conditions for the numerical simulation of waves. Math. Comp. 31, 629–651.Google Scholar
Eriksson, L.-E. 1982 Generation of boundary-conforming grids around wing—body configurations using transfinite interpolation. AIAA J. 20, 1313–1320.Google Scholar
Eriksson, L.-E. 1984 A study of mesh singularities and their effects on numerical errors. FFA TN 1984–10, Stockholm.
Eriksson, L.-E. & Rizzi, A. 1984 Computation of vortex flow around a canard—delta combination. J. Aircraft (in press).Google Scholar
Eriksson, L.-E. & Rizzi, A. 1984 Computer-aided analysis of the convergence to steady state of a discrete approximation to the Euler equations. J. Phys. (in press).Google Scholar
Gottlieb, D. & Gustafsson, B. 1976 On the Navier—Stokes equations with constant total temperature. Stud. Appl. Maths 55, 167–185.Google Scholar
Hirschel, E. H. & Fornasier, L. 1984 Flowfield and vorticity distribution near wing trailing edges. AIAA Paper 84–0421, New York.
Jameson, A. & Baker, T. J. 1984 Multigrid solution of the Euler equations for aircraft configurations. AIAA Paper 84–0093, New York.
Koeck, C. & Neron, M. 1984 Computations of three-dimensional transonic inviscid flows on a wing by pseudo-unsteady resolution of the Euler equations. In 5th GAMM Conf. Proc. Numer. Meth. Fluid Mech. (ed. M. Pandolfi & R. Piva). Vieweg.
Lomax, H. 1982 Some prospects for the future of computational fluid dynamics. AIAA J. 20, 1033–1043.Google Scholar
Lomax, H., Pulliam, T. H. & Jespersen, D. C. 1981 Eigensystem analysis techniques for finite-difference equations. AIAA Paper 81–1027.Google Scholar
MacCormack, R. W. & Paullay, A. J. 1974 The influence of the computational mesh on accuracy for initial value problems with discontinuous or nonunique solutions. Comp. Fluids 2, 339–361.Google Scholar
Rizzi, A. W. 1978 Numerical implementation of solid-body boundary conditions for the Euler equations. Z. angew. Math. Mech. 58, T301–T304.Google Scholar
Rizzi, A. W. 1981 Computation of rotational transonic flow. In Numerical Methods for the Computation of Inviscid Transonic Flow with Shocks, a GAMM Workshop (ed. A. W. Rizzi & H. Viviand). Notes on Numerical Fluid Mechanics. Vieweg.
Rizzi, A. 1982 Damped Euler-equation method to compute transonic flow around wing—body combinations. AIAA J. 20, 1321–1328.Google Scholar
Rizzi, A. 1983 Vector coding the finite-volume procedure for the CYBER 205. In Lecture Series Notes 1983–04, von Kármán Inst., Brussels.
Rizzi, A. & Eriksson, L.-E. 1984 The FFA aerodynamic flow code WINGA2 for CYBER 205: numerical software to solve the Euler equations. Adv. Engng Software (in press).Google Scholar