Velocity of Mass Transport to Model Acoustic Streaming: Numerical Application to Annular Resonators

The acoustic wave propagation in thermo-viscous fluid can generate slow phenomena such as acoustic streaming, by non-linear processes that are mainly confined in the acoustical boundary layers. Considering the fundamental conservation equations for mass, momentum and energy, and splitting the different time scales for acoustic propagation and acoustic streaming, the equations governing the acoustic streaming are presented in a standard form for a weakly compressible flow. The formulation is based upon the velocity of mass transport as variable. The force responsible for acoustic streaming is composed of quadratic terms that account for the combined acoustical density variation or viscosity variation, and particle velocity. The numerical computation of the unsteady Gedeon streaming flow in annular resonator is done as a validation of this formulation.