Numerical Simulation of Sound Radiated from a Turbulent Vortex Ring

The acoustic field radiated by a turbulent vortex ring is studied. Direct Numerical Simulations (DNS) of the fully compressible, three-dimensional Navier-Stokes equations are used to generate an axisymmetric vortex ring to which 3D stochastic disturbances are added. The disturbances cause instability and turbulent transition of the vortex ring. Detailed information about temporal evolution of sound pressure level, spectrum and directivity associated with each mode is investigated. The peak frequency agrees well with experiments, and the directivity of each azimuthal mode agrees well with predictions of vortex sound theory. Based on the self-similar decay of the turbulent near field, the selfsimilar decay of the sound field is investigated. We also explore the connections with jet noise by modeling the jet as a de-correlated train of vortex rings.