A thermodynamic model for thermo-acoustic heat transfer within closed cavities that includes soft wall acoustic resistance

Abstract

The Navier-Stokes and energy equations modeling the propagation and reflection of acoustic waves generated by wall heating within closed cavities, also known as hydrodynamic model, can only adequately capture the predicted experimental trends when wall impedance is included in the model to take into account wave amplitude (resistance) and phase (reactance) losses upon wall reflection. These simulations are often restricted to one-dimension due to stiffness, since the extreme disparity between the smallest (acoustic) and largest (thermal diffusion) time scales lead to very large CPU times. Hence, thermodynamic models are often preferred instead, since they filter out the acoustic scales and model their effect, thus requiring much smaller CPU times. The present paper shows for the first time how soft wall resistance effects can be included in a thermodynamic model, leading to a significant improvement in their ability to predict experimental trends while still maintaining their low CPU times. This, in turn, led to the discovery that soft wall resistance turns the piston effect negligible even near the thermodynamic critical point.