Revisiting the difference between traveling-wave and standing-wave thermoacoustic engines - A simple analytical model for the standing-wave one

摘要

There are two major categories in a thermoacoustic prime-mover. One is the traveling-wave type and the other is the standing-wave type. A simple analytical model of a standing-wave thermoacoustic prime-mover is proposed at relatively low heat-flux for a stack much shorter than the acoustic wavelength, which approximately describes the Brayton cycle. Numerical simulations of Rott's equations have revealed that the work flow (acoustic power) increases by increasing of the amplitude of the particle velocity (|U|) for the traveling-wave type and by increasing cosI broken vertical bar for the standing-wave type, where I broken vertical bar is the phase difference between the particle velocity and the acoustic pressure. In other words, the standing-wave type is a phase-dominant type while the traveling-wave type is an amplitude-dominant one. The ratio of the absolute value of the traveling-wave component (|U|cosI broken vertical bar) to that of the standing-wave component (|U|sinI broken vertical bar) of any thermoacoustic engine roughly equals the ratio of the absolute value of the increasing rate of |U| to that of cosI broken vertical bar. The different mechanism between the traveling-wave and the standing-wave type is discussed regarding the dependence of the energy efficiency on the acoustic impedance of a stack as well as that on omega I"(alpha), where omega is the angular frequency of an acoustic wave and tau(alpha) is the thermal relaxation time. While the energy efficiency of the traveling-wave type at the optimal omega I"(alpha) is much higher than that of the standing-wave type, the energy efficiency of the standing-wave type is higher than that of the traveling-wave type at much higher omega I"(alpha) under a fixed temperature difference between the cold and the hot ends of the stack.