Vorticity Dynamics in Isobarically Closed Porous Channels Part I: Standard Perturbations

Abstract

When acoustic pressure oscillations are induced in a porous channel of the closed ‐open type, the linearized Navier‐Stokes equations can be solved analytically to obtain an accurate description of the temporal e owe eld corresponding to laminar conditions. The channel considered herehas a rectangularcross section, has two equally permeablewalls,andisopenatthedownstreamend.Thecurrentmethodologyparallelstheclosed ‐closedboundary analysis carried out previously for a channel with both ends closed. Limiting our scope to laminar conditions, we apply standard perturbation tools to present a closed-form solution that becomes asymptotically exact for large kinetic Reynolds numbers. Verie cations are materialized by way of numerical simulations and quantie cation of the maximum absolute error entailed in the e nal formulations. Note that the error is found to exhibit a clear asymptotic behavior. Furthermore, the analytical formulation reveals vortical structures and explains the direct ine uence of acoustic pressure oscillations on the rotational waves generated in the closed ‐open cone guration. Finally, the explicit roles of variable injection, viscosity, and oscillation frequency are explained.