A quasi-one-dimensional nonlinear model of an open-closed standing-wave thermoacoustic engine

A quasi-one-dimensional nonlinear model of a standing-wave thermoacoustic engine with a quarter-wavelength resonator is presented. The model is based on cross-sectional averaged equations and is solved by high-order low-dispersion numerical schemes. Considering the acoustic reflection and radiation at the open end, broadband time-domain impedance boundary conditions are employed so that oscillation frequency can be self-adaptive. The impedance is expressed in the mathematical form of partial fraction expansion with complex-conjugate residues and poles, so that the convolution of the impedance with the velocity can be calculated by efficient and causal recursive convolution. Pole-residue pairs of the impedance can be optimized in the frequency domain. Critical temperature difference of an open-ended standing-wave thermoacoustic engine can be predicted and the time-domain simulation shows that the pressure oscillation undergoes a nonlinear amplifying process and eventually reaches saturation amplitude. Numerical results agree very well with the experiment for a small-scale thermoacoustic engine. The simulation results for different stack geometries are included.