Time-Domain Impedance Boundary Conditions in Computational Fluid Dynamics for use in Thermoacoustic Modeling

Thermoacoustic devices convert heat to work or vice versa using acoustic waves, and consist of several parts that partially reflect acoustic waves. These reflections can be represented by an acoustic impedance, which is a complex quantity that takes into account a phase difference between the pressure and velocity oscillation. Usually one is only interested in a single part of the thermoacoustic device, but to correctly numerically predict these wave phenomena the whole device should be modeled. As solving acoustics using Computational Fluid Dynamics (CFD) requires comparatively high computational resources, using the complete computational domain of the whole device is unattractive. The reduction of the computational domain might be possible with a so-called Time-Domain Impedance Boundary Condition (TD-IBC), which relates the inward traveling acoustic wave to the outward traveling acoustic wave. Standard commercial CFD software does not feature such a boundary condition as of yet. This master thesis discusses the feasibility, theory and implementation of both a non-reflective boundary condition (NRBC) and a TD-IBC. The NRBC and TD-IBC are implemented in ANSYS CFX CFD software using FORTRAN subroutines. The results showed that for a complex reflection coefficient R=0.5+0.5i and an excitation frequency of f=100 Hz the measured absolute reflection coefficient IRI was off 1.05%, and the phase differed phi = 0.0334 rad. From the work done it can be concluded that it is indeed possible to implement a TD-IBC for application in thermoacoustics.