Improved solution for the vortical and acoustical mode coupling inside a two-dimensional cavity with porous walls.
This work presents an improved solution to a former study that analyzes the oscillatory motion of gases prescribed by vortico-acoustical mode coupling inside a two-dimensional porous cavity. The physical problem arises in the context of an oscillating gas inside a rectangular enclosure with wall transpiration, sublimation, or sweating. Previously, a multiple-scale solution was derived for the temporal field. The asymptotic formulation was based on an unconventional choice of scales. Its accuracy was also commensurate with the size of epsilon, a parameter that captured the effect of small viscosity. Currently, an exact solution is derived and compared to the previous formulation. A simple WKBJ solution is also constructed for validation purposes. Unlike both asymptotic formulations, the exact solution remains accurate regardless of the range of physical parameters.
Mechanical and Industrial Engineering Department, Marquette University, Milwaukee, Wisconsin 53233, USA.
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Majdalani