Numerical Study on the Effect of Stack Radii on the Low Onset Heating Temperature and Efficiency of 4-Stage Thermoacoustic Engine

The thermoacoustic engine can convert low-grade thermal energy into acoustic energy. Applying the 4-stage engine could have higher efficiency in recovering the heat at lower-grade waste heat. Since the narrow channel radii of the stack are the heart of the thermoacoustic engine, this paper aims to indicate the optimum radii of the 4-stage thermoacoustic engine and predict the suitable low-temperature using the 4-stage engine stacks. The calculation procedure starts with setting the engine geometry and changing the hot end, assuming the ambient temperature to be 27 °C. The stability limit condition under which the spontaneous gas oscillation becomes neutral is calculated using the transfer method. The heating temperature, the angular frequency, the ratio of oscillatory pressure and velocity at the second, third, and fourth ambient end of the engine stack, and the ratio of oscillatory pressure and velocity at the last hot end of the engine stack have been calculated. Then, the obtained combination of the pressure and velocity is used to calculate the acoustic power at the ends of the engines. Finally, the second law of efficiency is applied to determine the engine performance. The results revealed that the onset heating temperature T_h drops from 82 to 43 °C when r/ δ rises from 0.5 to 1.2, while, by applying the 4-stage engine, the optimum r/ δ shifted to be close to 1.2. The lowest onset temperature was 43 °C with 8% of the Carnot efficiency.