Study of an annular thermoacoustic prime mover, part (I) numerical analysis

This paper constitutes the first detailed numerical investigation of a thermoacoustic prime mover with periodic boundary conditions. The significant aspect to this research is to develop a new analysis program using MATLAB. The program implements shooting method because it appears to be a systematic way to solve this kind of nonlinear boundary value problem. This program is validated by comparing its solution to that using DeltaE[1-2] for a simple case. The overall agreement of resonance frequencies and the reciprocal of quality factor from the two methods are excellent. The agreement of the mode shapes is good in general. However the agreement of the low frequency mode is not as good as for the high frequency mode, particularly at high temperature difference. The reasons for this discrepancy at higher values of ΔT are not fully understood. The major advantages of the MATLAB program are the smooth mode shape curve and determination of the quality factor from the complex eigenfrequency.