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Computation of inviscid incompressible flow with rotation

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

The standard hyperbolic methods used to solve the compressible Euler equations are not effective in the limit of incompressible flow. The sound waves dominate the system and it becomes poorly conditioned for numerical solution. For steady flow governed by the incompressible Euler equations, artificial compressibility is a technique that removes the troublesome sound waves. It leads to a hyperbolic system of equations that we solve by finite-volume differences centred in space, and explicit multistage time-stepping. The stability of this novel system is analysed, its allowable discontinuities are described, and appropriate far-field and solid-wall boundary conditions are introduced. Results are presented for both two- and three-dimensional flows, including vorticity shed from a delta wing. Whether vorticity is produced or not depends very strongly on the body geometry, the accuracy of the solution method, and the transient discontinuities that evolve in the flow field. The results are analysed for the total-pressure losses in the flow fields, and for the diffusion of the vortex sheets.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 153 , April 1985 , pp. 275 - 312
Copyright
© 1985 Cambridge University Press

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References

Chorin, A. J. 1967 A numerical method for solving incompressible viscous flow problems. J. Comp. Phys. 2, 12–26.Google Scholar
Engqvist, B. & Majda, A. 1977 Absorbing boundary conditions for the numerical simulation of waves. Math. Comp. 31, 629–651.Google Scholar
Eriksson, L.-E. 1975 Calculation of two-dimensional potential flow wall interference for multicomponent airfoils in closed low speed wind tunnels. FFA TN AU-1116, Part 1, Stockholm.
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 Boundary conditions for artificial dissipation operators. FFA TN 1984-53, Stockholm.
Eriksson, L.-E. & Rizzi, A. 1983 Computer-aided analysis of the convergence to steady state of a discrete approximation to the Euler equations. AIAA Paper 83-1951 presented at 6th CFD Conf., Danvers, MA. (also J. Comp. Phys., in press).Google Scholar
Eriksson, L.-E., Rizzi, A. & Therre, J. P. 1984 Numerical solutions of the steady incompressible Euler equations applied to water turbines. AIAA Paper 84-2145.
Hoeijmakers, H. W. M. & Rizzi, A. 1984 Vortex-fitted potential solution compared with vortex-captured Euler solution for delta wing with leading edge vortex separation. AIAA Paper 84-2144.
Hoeijmakers, H. W. M. & Vaatstra, W. 1973 A higher-order panel method applied to vortex-sheet roll-up. AIAA J. 21, 516–523.Google Scholar
Hoeijmakers, H. W. M., Vaatstra, W. & Verhaagen, N. G. 1983 Vortex flow over delta and double-delta wings. J. Aircraft 21, 000–000.Google Scholar
Hummel, D. 1979 On the vortex formation over a slender wing at large incidence. AGARD CP-247.
Peyret, R. & Taylor, T. 1983 Computational Methods for Fluid Flow. Springer.
Rizzi, A. W. 1978 Numerical implementation of solid-body boundary conditions for the Euler equations. Z. angew. Math. Mech. 58, 301–304.Google Scholar
Rizzi, A. & Eriksson, L.-E. 1984 Computation of flow around wings based on the Euler equations. J. Fluid Mech. 148, 45–71.Google Scholar
Rizzi, A. & Eriksson, L.-E. 1985 Vortex-sheet capturing in numerical solutions of the incompressible Euler equations. SIAM J. Sci. Stat. Comp. (in press).
Wagner, H. 1925 Über die Entstehung des dynamischen Auftriebes von Tragflügeln. Z. angew. Math. Mech. 5, 17–35.Google Scholar