Numerical Simulation of Acoustic Streaming for Nonlinear Standing Ultrasonic Wave in Water Inside Axisymmetric Enclosure

Abstract

In this paper, acoustic streaming generated by standing waves in a cylindrical enclosure filled with water is simulated. The effects of geometry, vibrating amplitude and frequency on formation of streaming structures are numerically investigated. The vibrating source is located at the central region of the lower plate. This source generates a plane wave at the bottom of the cylinder. The complete Navier-Stokes equations are considered and an explicit finite-difference method is used to track the acoustic waves. Water in this simulation is assumed to be a Newtonian rotational compressible single-phase liquid with an accurate equation of state. Equations are derived in Lagrangian cylindrical coordinates, using the condition of axial symmetry. The variation of acoustic pressure demonstrates a periodic modulation. The shape of the mean flow field in a period of the modulation does not differ significantly from the second period and there is a steady state condition for all periods. Results showed stronger acoustic streaming because of a decrease in enclosure height and decrease in frequencies.In addition, the increase in the enclosure radius or radius of the vibrating plate and the increase in the maximum displacement of the vibrating plate caused higher acoustic streaming velocities.