A Transient Numerical Analysis of a Dissipative Expansion Chamber Muffler

Expansion chamber mufflers are commonly applied to reduce noise in heating, ventilation, and air-conditioning (HVAC) or exhaust systems. In dissipative mufflers, sound-absorptive materials, such as microperforated plates (MPP), are applied to achieve an enhanced and more broadband mitigation effect. Computational acoustics (CA) analyses of mufflers are usually carried out in the frequency domain, assuming time-harmonic excitation. However, certain applications require time-domain simulations. From a computational point of view, such transient analyses are more challenging. A transformation of the governing equations involving frequency-dependent material parameters into the time domain induces convolution integrals. We apply the recently proposed finite element (FE) formulation of a time-domain equivalent fluid (TDEF) model to simulate the transient response of dissipative acoustic media to arbitrary unsteady excitation. Like 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 and complex-conjugated poles. The arising convolution integrals are computed indirectly by solving a set of ordinary auxiliary differential equations (ADE) coupled to the scalar wave equation, according to the 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 characteristic quarter-wavelength resonance cannot evolve. Negligible thermal losses allow the use of a constant, real-valued equivalent bulk modulus. The low rational approximation order of the equivalent density entails an increase of computational degrees of freedom induced by the proposed TDEF approach for the given problem by less than 7% compared to the frequency domain formulation.