Lumped parameter model for resonant frequency estimation of a thermoacoustic engine with gas-liquid coupling oscillation

Gas-liquid coupling oscillation is a novel approach to reducing the resonant frequency and to elevating the pressure amplitude of a thermoacoustic engine. If a thermoacoustic engine is used to drive low-frequency pulse tube refrigerators, the frequency matching between the thermoacoustic engine and the refrigerator plays an important role. Based on an acoustic-electric analogy, a lumped parameter model is proposed to estimate the resonant frequency of a standing-wave thermoacoustic engine with gas-liquid coupling oscillation. Furthermore, a simplified lumped parameter model is also developed to reduce the computation complexity. The resonant frequency dependence on the mean pressure, the gas space volume, and the water column length is computed and analyzed. The impact of different working gases on the resonant frequency is also discussed. The effectiveness of the models is validated by comparing the computed results with the experimental data of the gas-liquid coupling oscillation system. An increase in the mean working pressure can lead to a rise in the resonant frequency, and a lower resonant frequency can be achieved by elongating the liquid column. In comparison with nitrogen and argon, carbon dioxide can realize a lower frequency due to a smaller specific heat ratio.