NUMERICAL-SIMULATION OF A THERMOACOUSTIC REFRIGERATOR .1. UNSTEADY ADIABATIC FLOW AROUND THE STACK

A low Mach-number compressible flow model for the simulation of acoust ically driven flow in a thermoacoustic stack is constructed. The model is based on the assumption that the acoustic wavelength is much large r than the characteristic hydrodynamic lengthscale. Thus, a simplified description of the flow is obtained which still retains the essential features of acoustically induced velocity oscillations near solid bou ndaries. A vorticity-based formulation of the governing equation is de rived which relies on the Helmholtz decomposition of the velocity vect or into irrotational and divergence-free components. Irrotational moti on is used to represent the action of acoustic waves. Meanwhile the di vergence-free velocity component is used to capture the nonlinear vort ical perturbations due to no-slip boundaries. A simplified version of the model is applied to analyze unsteady flow in the neighborhood of a n idealized thermoacoustic stack which consists of a periodic array of thin plates placed in an acoustic standing wave. Computed results are used to analyze, for different stack configurations, the nonlinear re sponse of the flow to different acoustic driving amplitudes and freque ncies. In particular, it is shown that the flow is dominated by the mo tion of vortices which result from the shedding of boundary layers fro m the edges of the stack. The dependence of energy losses on stack con figuration and operating conditions is also examined. (C) 1996 Academi c Press, Inc.