科研之友
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摘要
Temperature variations associated with acoustic pressure are known to be quasi-adiabatic in the bulk of the fluid and quasi-isothermal at the walls of relatively thick bodies, developing thermal acoustic boundary layers. For thin rigid bodies, of sufficiently small characteristic length, the thermal boundary condition may differ from isothermal condition. The acoustic field, with particle velocity normal to the boundary near the wall, is studied for both plane geometry (a thin membrane) and a cylindrical one (a fibre): thus, avoiding shear viscosity effects, these analytical models focus on thermal boundary layers effects with the thermal conduction inside the solid body and the heat flow between the fluid and the solid both taken into account. For both geometries, the complex local polytropic coefficient, which is related to the complex local compressibility of the fluid, is used to account for the local condition for the fluid in the neighbourhood of the solid-fluid interface inside the thermal boundary layer. Then, to compare the thermal effects implied by each geometry, both the complex local polytropic coefficient (calculated at the wall) and the acoustic specific admittance of the boundary are used to describe the transition between isothermal and adiabatic thermal conditions as a function of the frequency. Results show that the temperature boundary condition depends significantly on the geometry of the solid body. The boundary condition on the surface of a cylinder can differ significantly from an isothermal one, while it remains isothermal on the surface of a plate with the thickness equal to the cylinder diameter. Results would be of interest in several applications involving fibres, and also confirm the isothermal boundary condition commonly used in the literature when considering plane or shell geometries.
- 出版日期2013-8
