Guideline for Adopting the Local Reaction Assumption for Porous Absorbers in Terms of Random Incidence Absorption Coefficients

Room surfaces have been extensively modeled as locally reacting in room acoustic predictions although such modeling could yield significant errors under certain conditions. Therefore, this study aims to propose a guideline for adopting the local reaction assumption by comparing predicted random incidence acoustical characteristics of typical building elements made of porous materials assuming extended and local reaction. For each surface reaction, five well-established wave propagation models, the Delany-Bazley, Miki, Beranek, Allard-Champoux, and Biot model, are employed. Effects of the flow resistivity and the absorber thickness on the difference between the two surface reaction models are examined and discussed. For a porous absorber backed by a rigid surface, the assumption of local reaction always underestimates the random incidence absorption coefficient and the local reaction models give errors of less than 10% if the thickness exceeds 120 mm for a flow resistivity of 5000 Nm^–4s. As the flow resistivity doubles, a decrease in the required thickness by 25 mm is observed to achieve the same amount of error. For an absorber backed by an air gap, the thickness ratio between the material and air cavity is important, since the thicker the cavity, the more extendedly reacting the absorber. If the absorber thickness is approximately 40% of the cavity depth, the local reaction models give errors below 10% even for a low flow resistivity case.