Cervenka, M., Bednarik, M.: Variety of acoustic streaming in 2D resonant channels, Wave Motion 66, 21-30, 2016.
Abstract: Acoustic streaming in 2D resonant channels with uniform or non-uniform cross-sections is studied within this work. An inertial force as well as a vibrating boundary are assumed for driving the acoustic field. The method of successive approximations is employed to derive linear equations for calculation of primary acoustic and time-averaged secondary fields including the radiation pressure and the mass transport velocity. The model equations have a standard form which allows their numerical integration using a universal solver; in this case, COMSOL Multiphysics was employed. As this software is based on the finite element method, it is simple and straightforward to perform the calculations with moderate computational costs even for complex geometries, which makes the proposed approach an operative tool for study of acoustic streaming. The numerical results are validated for the case of a rectangular channel by comparison with previously published analytical results; an excellent agreement is found. The numerical results show that the acoustic streaming can be quite complex even in rectangular channels and its structure depends on the manner of driving. Examples of acoustic streaming in wedged and elliptical channels are given to demonstrate a strong dependence of the acoustic streaming structure on the resonator shape.
Bednarik, M., Cervenka, M., Lotton, P., Penelet, G.: Behavior of plane waves propagating through a temperature-inhomogeneous region, Journal of Sound and Vibration 362, 292-304, 2016.
Abstract: Description and analysis of acoustic waves in ducts with a region containing temperature-inhomogeneous fluid represent a significant problem of scientific and practical interest. This interest is induced by the need of understanding how temperature fields affect acoustic processes which would lead to a more efficient design and control of systems involving thermoacoustic interactions. Most of the works addressing these problems limit themselves to the assumption of weak temperature profile gradients or to temperature profiles which do not connect neighboring temperature-homogeneous regions smoothly. In our work we investigate the behavior of plane acoustic waves that enter a region with an arbitrary temperature gradient. A polynomial character of the used temperature profile ensures smooth connection with constant-temperature regions. The one-dimensional wave equation for ducts with an axial mean temperature gradient is solved analytically. The derived solutions based on Heun functions extend the class of published exact analytical solutions of model wave equations taking into account the medium temperature gradient. Due to the property that our proposed polynomial temperature function has derivatives equal to zero at points which are connected with the surrounding temperature-homogeneous regions we can form more complex smooth temperature profiles for which it is possible to use the transfer matrix method.