FINITE-AMPLITUDE SATURATION OF SELF-SUSTAINED OSCILLATIONS IN A STANDING WAVE THERMOACOUSTIC ENGINE

By introducing the natural angular frequency as a complex value, this report estimates the finite-amplitude saturation of the sound waves in a standing wave thermoacoustic engine having a stacked-screen regenerator. The eigenvalue of complex angular frequency is calculated from a transfer matrix that models the whole engine. In the eigenvalue, the imaginary part exponentially characterizes the attenuation/growth constant for instantaneous amplitudes of sound oscillations. By an effective radius that models the tortuous flow channels of the stacked-screen regenerator as a bundle of cylindrical tubes, this report theoretically involve the nonlinear dissipations of the regenerator into the framework of the linear thermoacoustic theory in the frequency domain for numerically accounting for the attenuation/growth constant in the time domain. Therefore, this calculation suppresses the growth rate of the thermoacoustic amplification by nonlinear effects, which allows to analytically estimate the finite amplitude of the spontaneous oscillations. For verifying the calculation, this study experimentally investigated a 2.15-meter-long standing wave thermoacoustic engine consisting of a 40 mm-inner-diameter cylindrical tube. The standing wave engine contained a regenerator unit consisting of a stacked-screen regenerator sandwiched by a cold and a hot-heat exchanger with a thermal buffer tube, at 3/8 length of the engine. Serval kinds of metallic woven mesh screens have experimented with 0.6 MPa of nitrogen gas. Oscillation amplitude growths from onset to saturation states of the standing wave engine were measured to compare with calculations. The comparisons indicate that the effective radius is capable of qualitatively evaluating the start-up temperature ratio and predicting the evolutions of steady oscillations of the standing wave engine.