ESAIM: Proceedings, Vol. 7, 1999, 369-377
Third International Workshop on Vortex Flows
and Related Numerical Methods
http://www.emath.fr/proc/Vol.7/
Sound Generation by the Interaction of a Vortex
Ring with a Rigid Sphere
E. RIVOALEN ,
S. HUBERSON ,
O.M. KNIO
Laboratoire de Mécanique, Université
du Havre, BP 540, 76058 Le Havre, France
Department of Mechanical Engineering, The Johns
Hopkins University,
Baltimore, MD 21218-2686, USA
Abstract:
High-Reynolds-number interactions between a vortex ring and a stationary
rigid sphere are computed using two Lagrangian particle models. The first
is a 3D slender vortex filament scheme which tracks the motion of the filament
centerline. The centerline velocity is expressed as the sum of a self-induced
velocity and potential velocity added to satisfy potential boundary conditions
on the surface of the sphere. The self-induced velocity is computed numerically
from the line Biot-Savart integral, which is carefully desingularized so
as to provide the correct behavior of the vorticity distribution in the
asymptotic thin-core limit. The second model is a particle scheme for the
simulation of axisymmetric viscous flow. The scheme is based on discretization
of the vorticity field into desingularized vortex elements that are advected
in a Lagrangian frame. The velocity of the particles is expressed as the
sum of a vortex interaction velocity expressed in terms of a desingularized
Biot-Savart law, a potential velocity expressed in terms of the image of
vortex elements, and a diffusion velocity. The filament and the particle
schemes are applied to compute the passage of axisymmetric vortex rings
over a stationary rigid sphere in the high-Reynolds-number limit, and to
analyze the far-field sound generated by this interaction. Both models
show that as the ring passes over the sphere, its radius increases while
its core shrinks due stretching. In the parameter regime considered, the
two models yield very close predictions of vortex trajectories and speeds.
The filament model indicates that the passage leads to the generation of
a pressure spike in the acoustic far-field. Meanwhile, the particle computations
reveal that in addition to a pressure spike the far-field sound can also
exhibit a substantial high-frequency quadrupole emission. Analysis of the
computations reveals that this high-frequency noise emission is due to
filamentation within the vortex core. The results also show that the high-frequency
quadrupole noise may be dominant, especially when the vortex core is thin
and the Mach number is not very small.
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