Computational study of shock interaction with a vortex ring

1089-7666

AIP Digital Archive

Physics

The problem of shock interaction with a vortex ring is investigated within the framework of axisymmetric Euler equations solved numerically by a shock-fitted sixth-order compact difference scheme. The vortex ring, which is based on Lamb's formula, has an upstream circulation Γ=0.01 and its aspect ratio R lies in the range 8≤R≤100. The shock Mach number varies in the range 1.1≤M1≤1.8. The vortex ring/shock interaction results in the streamwise compression of the vortex core by a factor proportional to the ratio of the upstream and downstream mean velocity U1/U2, and the generation of a toroidal acoustic wave and entropy disturbances. The toroidal acoustic wave propagates and interacts with itself on the symmetry axis of the vortex ring. This self-interaction engenders high amplitude rarefaction/compression pressure peaks upstream/downstream of the transmitted vortex core. This results in a significant increase in centerline sound pressure levels, especially near the shock (due to the upstream movement of the rarefaction peak) and in the far downstream (due to the downstream movement of the compression peak). The magnitude of the compression peak increases nonlinearly with M1. For a given M1, vortex rings with smaller aspect ratios (R〈20) generate pressure disturbances whose amplitudes scale inversely with R, while vortex rings with larger aspect ratios (R〉40) generate pressure disturbances whose amplitudes are roughly independent of R. © 2001 American Institute of Physics.

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