Energy flow analysis of equivalent fluid models for porous media

Based on a heat conduction analogy that enables the energy flow analysis (EFA) to describe the smoothed energy variations, the EFA has been applied to a variety of structures to predict vibrational responses at high-frequency regions. In this paper, energy equations in the form of heat conduction laws are derived to represent dilatational waves in rigid- and limp-frame porous media using equivalent fluid models. Homogeneous and inhomogeneous waves are considered. Within the EFA framework, the group velocity and loss factor included in the energy models for structures are replaced with the energy velocity and effective loss factor, respectively. The capabilities of the energy models are illustrated using configurations in which the porous layer backed by a rigid wall is in a normal and oblique incident sound field. The results of the numerical simulations confirm the feasibility of the energy model. From an energy perspective, the adequacy of using rigid- and limp-frame equivalent fluid models is also discussed. It is shown that the use of a rigid-frame equivalent model for predicting the energy distribution is more restrictive than predicting acoustic performance such as sound absorption.