Effect of inhomogeneous temperature fields on acoustic streaming structures in resonators

Abstract

Acoustic streaming in 2D rectangular resonant channels filled with a fluid with a spatial temperature distribution is studied within this work. An inertial force is assumed for driving the acoustic field; the temperature inhomogeneity is introduced by resonator walls with prescribed temperature distribution. The method of successive approximations is employed to derive linear equations for calculation of primary acoustic and time-averaged secondary fields including the streaming velocity. The model equations have a standard form which allows their numerical integration using a universal solver; in this case, COMSOL Multiphysics was employed. The numerical results show that fluid temperature variations in the direction perpendicular to the resonator axis influence strongly the streaming field if the ratio of the channel width and the viscous boundary layer thickness is big enough; the streaming in the Rayleigh vortices can be supported as well as opposed, which can ultimately lead to the appearance of additional vortices.

Numerical study of the influence of the convective heat transport on acoustic streaming in a standing wave

“…The streaming profile distortion described within this work is of the same type as it has been found in experiments. 11,12,15,16 The results described within this work cannot be obtained using the previous theoretical models dealing with acoustic streaming in temperature-inhomogeneous fluids, 3,5,6,13 as these models do not capture the effect of the acoustic-streamingdriven convective heat transport.…”

“…It has been shown recently 13 that the acoustic streaming structure is particularly influenced by the mean temperature gradient in the direction perpendicular to the resonator axis. If D r T m (z) ¼ T m (0, z) À T m (R, z) < 0, acoustic streaming near the resonator axis is locally supported, if D r T m (z) > 0, it is locally opposed which may even result in the development of additional outer vortices.…”

“…If D r T m (z) ¼ T m (0, z) À T m (R, z) < 0, acoustic streaming near the resonator axis is locally supported, if D r T m (z) > 0, it is locally opposed which may even result in the development of additional outer vortices. 13 If the streaming velocity is small enough for the convective heat transport to be effective, it can be approximately written 21 [for the wall temperature distribution Eq. (12)] that…”

“…The normalized streaming velocity along the axis reaches the maximum value of U mz /U R ¼ 1.009; the distribution slightly differs from the sinusoidal one, 2 which is also in line with the observations made earlier. 13 If the streaming velocity increases, its distribution quickly gets distorted, and the value of the normalized streaming velocity in maxima decreases; the maxima are shifted toward the acoustic velocity nodes (resonator end-walls). For example, for Re nl ¼ 0.2, the maximum value of U mz /U R ¼ 0.771.…”

“…Cervenka and Bedna r ık 13 have recently shown that (a) the slow-streaming profile is particularly sensitive to the temperature variation in the direction perpendicular to the resonator axis, (b) this variation can be caused by the wall-temperature gradient if the resonator is wide enough, and (c) additional outer streaming cells can appear like in the case of the fast streaming in resonators with isothermal walls. 10,11 The underlying mathematical model does not take into account acoustic streaming as a means of heat transport which means that the results are only valid for small streaming velocities.…”