This research was motivated by thermoacoustic refrigeration, the cooling effect achieved from the interaction of sound waves and solid boundaries. Systems that have produced sound from a temperature difference, and cooling generated from sound waves have been successfully built. Linear inviscid theory that has been used to explain these effects, however, is incapable of dealing with the nonlinear processes observed even at low oscillation amplitudes. A numerical simulation on an entire thermoacoustic resonator was completed with finite difference methodology. The method involved the solution to the compressible, two-dimensional, unsteady, nonlinear, viscous continuity, momentum, and energy equations. The derivatives are approximated with a finite difference scheme accurate to second order both spatially and temporally. A membrane which models a loudspeaker generally used in most thermoacoustic systems generates acoustic waves on one wall. Numerical computations are completed for various Reynolds number. The time-dependent simulation of acoustic waves within a rectangular domain showed that beating or subharmonic oscillations, and cross-waves are among the complex behaviors observed.
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