Motion characteristics of particles around the cylindrical tube in a standing wave sound field

A calculation method combining the acoustic radiation force around the cylinder and the acoustic streaming Stokes force is proposed to calculate the motion of fluid and granular media outside a cylindrical tube. Using the acoustic streaming equation outside the cylinder, the external vortex is obtained as the main body of flow when Rem ≥ 325.27, where Rem is the dimensionless parameter that depends on the structure of the vortex. On this basis, the limit slip velocity of the acoustic streaming outside the tube is calculated by using Nyborg's boundary slip velocity theory, and the acoustic radiation force formula near the cylinder. The expression of particle critical diameter is derived when the particle velocity is zero and the acoustic radiation force and the acoustic streaming Stokes force are in equilibrium. The movement of particles outside the cylinder at different positions is simulated, and the results are consistent with the theoretical formula: the particles’ critical diameter is related to the acoustic frequency. When the particle diameter is less than the critical diameter, the Stokes force of the acoustic streaming is dominant, and the particles move with the acoustic streaming. When the particle diameter is greater than or equal to the critical diameter, the acoustic radiation force is dominant, and the particles gradually congregate at the node of the acoustic radiation force under the action of the acoustic radiation force. Theoretical and simulation results show that the proposed method can be used to examine the distribution of particles outside the tube, and the results are helpful to solve the problems of tube scaling and reduction of the heat exchange rate of heat exchangers and steam generators in power stations.