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On the computation of transonic leading-edge vortices using the Euler equations

Published online by Cambridge University Press:  21 April 2006

Arthur Rizzi  and
Charles J. Purcell
Arthur Rizzi
Affiliation:
FFA, The Aeronautical Research Institute of Sweden, S-161 11 Bromma, Sweden and Royal Institute of Technology, S-100 44 Stockholm, Sweden
Charles J. Purcell
Affiliation:
ETA Systems, Inc., St Paul, MN 55108, USA
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Abstract

Separation from the leading edge of a delta wing with the subsequent roll-up into a vortex has been simulated in numerical solutions to the Euler equations. Such simulations raise a number of questions that are still outstanding, including the process of inviscid separation from a smooth edge, the role of artificial viscosity in the creation and capturing of vortex sheets, the roll-up mechanism and core features, losses in total pressure, and the stability of the vortical flow structures to three-dimensional disturbances. These matters are discussed in the context of two numerical experiments, both carried out in a sequence of three simulations that starts with a coarse-mesh discretization and ends with a fine mesh of over one million cells. The first experiment is for transonic flow, M∞ = 0.7, α = 10°, around a pure delta wing. The sequence converges to the expected classical steady vortex flow. In the second experiment, transonic flow, M∞ = 0.9, α = 8°, past a twisted cranked-and-cropped delta wing, the sequence does not converge. Instead the crank is observed in the fine-mesh solution to set off an instability in the vortex sheet that causes the vortex to burst into a thin chaotic vortical layer embedded in laminar flow. The mesh sequence suggests that it is the shortest waves resolved that are most unstable, but the energy contained in them comes from the large-scale motion and seems to be small.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 181 , August 1987 , pp. 163 - 195
Copyright
© 1987 Cambridge University Press

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