The Effects of Heat Transfer through the Ends of a Cylindrical Cavity on Acoustic Streaming and Gas Temperature

Abstract

The longitudinal vibrational motion of a cylindrical cavity with gas, in which the acoustic streaming occurs, is considered. The motion is described by the system of equations for the dynamics and thermal conductivity of a viscous perfect gas, written in a cylindrical coordinate system associated with the cavity. The system of equations is solved numerically by the finite volume method with an implicit staggered grid scheme, while the convective–diffusion fluxes are approximated by the power law scheme. According to the boundary conditions, the lateral surface of the cavity is maintained at a constant equal initial temperature. The effects of heat transfer through the ends of the cavity are studied. Heat transfer is given by isothermal boundary conditions. The obtained solutions are compared with the solutions under adiabatic boundary conditions. It is shown for the first time that the effects of heat transfer manifest themselves with an increase in the nonlinearity of the process; when the frequency and amplitude of vibration increase, this is also facilitated by an increase in the radius of the cavity. The effects of heat transfer on the period average temperature, on the streaming velocity and on structure are established.

Keywords

• heat transfer
• isothermal boundary condition
• adiabatic boundary condition
• period average temperature
• acoustic streaming
• nonlinear effects