A boundary element analysis on acoustic dissipation by wall visco-thermal boundary layer

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On acoustic energy dissipation at wall surfaces, especially at the solid surfaces of the apertures of resonators of Helmholtz type, the viscosity and thermal conductance there plays the leading role. By using the Stokes theory for the viscous mode and the Kirchhoff theory for the thermal mode, explicit expressions can been given for the acoustic resistance of the aperture of simple shape such as a long round tube. However for n neck of general shape with finite length, we have to solve implicit relationships between acoustic mode wave and the visco-thermal boundary layer.We employed a boundary element numerical approach along with the substructure techniques for the acoustic mode fields, and implemented a computer code to combine the acoustic mode and the visco-thermal mode through the effective acoustic mode admittance for the visco-thermal boundary layer. This admittance was derived from the Stokes and Kirchhoff theories, and includes the Laplacian of the acoustic pressure over the acoustic mode boundary. We took a finite difference approach for the Laplacian operation by employing the constant boundary element.To investigate the effectiveness of the numerical simulation, we conducted a series of numerical simulations and experiments for the dissipation factors of slit resonators, and compared the results. In the experiments, rigid specimens of highly precise dimensions are used. Consequently, the agreement between the dissipation factor by the numerical simulation and that by the experiment was excellent, as far as boundary element dimension was 0.1 mm or finer. To reduce the requirement of this fine element size, the use of a third order approximation element is under investigation.