Sound generation by a vortex ring collision with a wall

Abstract

Sound generation by a collision of a vortex ring with a free-slip/no-slip wall is investigated by using a direct numerical simulation. The three-dimensional, unsteady, compressible Navier–Stokes equations are solved by a finite difference method, not only for a near-vortical flow field but also for a far-acoustic field. By comparing free-slip and no-slip problems, we discuss the effects of the no-slip boundary condition at the wall surface on the near and far fields. In addition, a new three-dimensional expression to predict the far-field sound pressure is proposed based on the theory of vortex sound. Then, by using the new expression, we discuss the relation between the vortical phenomenon and the acoustic wave modes. For normal collision with a no-slip wall, a secondary vorticity layer is produced on the wall surface because of the no-slip condition, and then forms secondary and tertiary vortex rings. The mutual interaction between the primary and secondary/tertiary vortex rings induces a rebounding motion of the primary vortex ring. The sound pressure radiated by the collision has a quadrupolar nature, and its generation is closely related to the rebounding motion. For oblique collision with a no-slip wall, the secondary vortical structure consists of helical vortex lines. The variations in vorticity moment associated with the formation of the helical vortex lines affect the quadrupole emission. In this case, in addition to the quadrupole and octupole modes, the dipole mode is also observed which is not observed in the free-slip case. The new expression proposed shows that the generation of the dipole in the no-slip case is related to the wall shear stress and the velocity distribution.