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 and its aspect ratio R lies in the range The shock Mach number varies in the range 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 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 For a given vortex rings with smaller aspect ratios generate pressure disturbances whose amplitudes scale inversely with R, while vortex rings with larger aspect ratios generate pressure disturbances whose amplitudes are roughly independent of R.
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October 2001
Research Article|
October 01 2001
Computational study of shock interaction with a vortex ring
Z. Ding;
Z. Ding
School of Computational Science and Information Technology, Florida State University, Tallahassee, Florida 32306
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M. Y. Hussaini;
M. Y. Hussaini
School of Computational Science and Information Technology, Florida State University, Tallahassee, Florida 32306
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G. Erlebacher;
G. Erlebacher
School of Computational Science and Information Technology, Florida State University, Tallahassee, Florida 32306
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A. Krothapalli
A. Krothapalli
Department of Mechanical Engineering, Florida State University, Tallahassee, Florida 32310
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Physics of Fluids 13, 3033–3048 (2001)
Article history
Received:
October 09 2000
Accepted:
July 16 2001
Citation
Z. Ding, M. Y. Hussaini, G. Erlebacher, A. Krothapalli; Computational study of shock interaction with a vortex ring. Physics of Fluids 1 October 2001; 13 (10): 3033–3048. https://doi.org/10.1063/1.1399293
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