Nonlinear two-dimensional model for thermoacoustic engines.

A two-dimensional model and efficient solution algorithm are developed for studying nonlinear effects in thermoacoustic engines. There is no restriction on the length or location of the stack, and the cross-sectional area of the resonator may vary with position along its axis. Reduced model equations are obtained by ordering spatial derivatives in terms of rapid variations across the pores in the stack, versus slow variations along the resonator axis. High efficiency is achieved with the solution algorithm because the stability condition for numerical integration of the model equations is connected with resonator length rather than pore diameter. Computation time is reduced accordingly, by several orders of magnitude, without sacrificing spatial resolution. The solution algorithm is described in detail, and the results are verified by comparison with established linear theory. Two examples of nonlinear effects are investigated briefly, the onset of instability through to saturation and steady state, and nonlinear waveform distortion as a function of resonator shape.