Steady Flow Boundary Layer in Acoustic Streaming

Abstract

The observed configuration of sonically induced flow in the vicinity of solid objects may depart significantly from predictions based on first-order perturbation theory whenever the acoustic particle displacement amplitude s exceeds in magnitude the acoustic boundary-layer thickness δAC. This change in the flow pattern seems to be intimately connected with two related physical effects: The observed increase in heat transfer from heated objects subjected to intense sound; the observed increase in drag experienced by an object subjected simultaneously to a steady unidirectional flow and to an intense sound field. An attempt is being made to understand these effects by extending the conventional perturbation theory to higher orders, a formidable task unless analytic solutions are available for the first-order perturbations. In connection with an attempt to find analytic solutions for the streaming in the vicinity of a right-circular cylinder, a formula has been obtained for the streaming boundary layer thickness δDC divided by the cylinder radius a, δDCa = [(1 − 13√3 δACa)−12 −1] + [2 − 13√6]δACa. (This work has been supported by the Air Research and Development Command, U. S. Air Force.)