Computational study of shock interaction with a vortex ring

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 ba sed on Lamb's formula, has an upstream circulation Gamma =0.01 and its aspe ct ratio R lies in the range 8 less than or equal toR less than or equal to 100. The shock Mach number varies in the range 1. 1 less than or equal toM (1)less than or equal to1.8. The vortex ring/shock interaction results in t he streamwise compression of the vortex core by a factor proportional to th e ratio of the upstream and downstream mean velocity U-1/U-2, and the gener ation of a toroidal acoustic wave and entropy disturbances. The toroidal ac oustic wave propagates and interacts with itself on the symmetry axis of th e vortex ring. This self-interaction engenders high amplitude rarefaction/c ompression pressure peaks upstream/ downstream of the transmitted vortex co re. This results in a significant increase in centerline sound pressure lev els, especially near the shock (due to the upstream movement of the rarefac tion peak) and in the far downstream (due to the downstream movement of the compression peak). The magnitude of the compression peak increases nonline arly with M-1. For a given M-1, 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 di sturbances whose amplitudes are roughly independent of R. (C) 2001 American Institute of Physics.