Numerical study of the acoustic streaming and mean excess pressure produced in a small gap between a vibrating surface and a thin boundary

In this paper, a circular plane piston located horizontally and immersed in water is considered, and a rigid pipe is assumed to be placed vertically with its lower end very closed to the vibrating surface. The general objective of the work has been to investigate the acoustic streaming produced in the gap between the piston and the lower end of the pipe, and to study the associated spatial distribution of the mean excess pressure in the fluid and the flow of mass. For this purpose, the classical finite-difference time-domain method has been implemented, and the complete equations of conservation of mass and conservation of momentum were used together with the state equation to a second order approximation for an adiabatic process. Thermal effects were neglected to simplify the problem. The obtained numerical results illustrate the applicability of the method. The simulations show that a net flow of mass is produced in the gap between the piston and the end of the tube. The results illustrate the dependence of the flow on the size of the gap, the thickness of the wall of the pipe, and its inner radius.