Abstract

Acoustic Streaming in a Cylindrical Tube

M.Hamilton, Yu.A.Ilinskii, E.A.Zabolotskaya (Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas, USA)

e-mail: hamilton@mail.utexas.edu

Acoustic streaming in a cylindrical tube is studied analytically and numerically. Viscosity, thermal conductivity, and dependence of the viscosity coefficient on temperature are taken into account. There is no restriction on tube radius in relation to boundary layer thickness. Analytical solutions are obtained in the second order of approximation, and they are verified by comparison with numerical solutions. As in standing wave fields between parallel plates, both inner and outer streaming vortices are generated. The outer vortex, which corresponds to Rayleigh streaming in a viscous fluid, circulates in a direction opposite that of the inner vortex. Rayleigh streaming dominates in wide tubes, whose radii are several orders of magnitude greater than the boundary layer thickness. Only the inner vortex is observed when tube radius is comparable to boundary layer thickness, such as within the channels in thermoacoustic engine stacks. Both vortices are prominent for intermediate tube radii. Thermal conductivity is found to increase streaming velocity, while dependence of the viscosity coefficient on temperature partly offsets this increase. The net effect of including thermal effects is slight increase in streaming velocity, between 5% and 10%, over predictions based on viscous stresses alone.

Section : 7