Transient Numerical Analysis of a Dissipative Expansion Chamber Muffler

Expansion chamber mufflers are commonly applied to reduce noise in HVAC. Dissipative materials, such as microperforated plates (MPPs), are often applied to achieve a more broadband mitigation effect. Such mufflers are typically characterized in the frequency domain, assuming time-harmonic excitation. From a computational point of view, transient analyses are more challenging. A transformation of the equivalent fluid model or impedance boundary conditions into the time domain induces convolution integrals. We apply the recently proposed finite element formulation of a time domain equivalent fluid (TDEF) model to simulate the transient response of dissipative acoustic media to arbitrary unsteady excitation. As most time domain approaches, the formulation relies on approximating the frequency-dependent equivalent fluid parameters by a sum of rational functions composed of real-valued or complex-conjugated poles. The arising convolution integrals are indirectly computed by solving a set of ordinary ODEs coupled to the scalar wave equation, according to the auxiliary equation (ADE) method. The numerical study of a dissipative expansion chamber muffler with an MPP reveals that the characteristics of transient excitation fundamentally differ from the known time-harmonic behavior because the typical quarter-wavelength resonance cannot evolve. Furthermore, it is shown that viscous effects dominate the dissipation in the MPP, while thermal losses are insignificant. Therefore, a constant, real-valued equivalent bulk modulus can be used. The low rational approximation order of the equivalent density entails an increase of computational degrees of freedom induced by the TDEF approach by less than 7% for the given problem.