The formulation presented in this paper is based on the boundary element method (BEM) and implements Kirchhoff's decomposition into viscous, thermal, and acoustic components, which can be treated independently everywhere in the domain except on the boundaries. The acoustic variables with losses are solved using extended boundary conditions that assume (i) negligible temperature fluctuations at the boundary and (ii) normal and tangential matching of the boundary's particle velocity. The proposed model does not require constructing a special mesh for the viscous and thermal boundary layers as is the case with the existing finite element method (FEM) implementations with losses. The suitability of this approach is demonstrated using an axisymmetrical BEM and two test cases where the numerical results are compared with analytical solutions.
An investigation on the resonance frequency shift for a plane-wave mode in a cylindrical cavity produced by a rigid sphere is reported in this paper. This change of the resonance frequency has been previously considered as a cause of oscillational instabilities in single-mode acoustic levitation devices. It is shown that the use of the Boltzmann-Ehrenfest principle of adiabatic invariance allows the derivation of an expression for the resonance frequency shift in a simpler and more direct way than a method based on a Green's function reported in literature. The position of the sphere can be any point along the axis of the cavity. Obtained predictions of the resonance frequency shift with the deduced equation agree quite well with numerical simulations based on the boundary element method. The results are also confirmed by experiments. The equation derived from the Boltzmann-Ehrenfest principle appears to be more general, and for large spheres, it gives a better approximation than the equation previously reported.
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