## Conclusions

Mathematical modeling of multi-phase Stirling engine systems was presented in this chapter. A symmetric three-phase system was discussed in detail based on eigen-analysis of the corresponding linearization. This analysis proved the self-starting potential of multi-

 Figure 5.21: Implementation of reverser mechanism within the fabricated three-phase Stir­ling engine prototype.

Phase systems relying on Hartman-Grobman theorem and indirect method of Lyapunov. The start-up temperature of the heater at which the system starts its operation was derived based on the same modal analysis.

Design, fabrication, and test of a symmetric three-phase free-piston Stirling engine sys­tem were discussed as well. The system was designed to operate with moderate-temperature heat input that is consistent with solar-thermal collectors. Diaphragm pistons and nylon flexures are considered for this prototype to eliminate surface friction and provide appropri­ate seals. The experimental results were presented and compared with design calculations. Tests confirmed the design models for heat exchanger flow friction losses and gas spring hysteresis dissipation. However, it was revealed that gas spring hysteresis loss was an im­portant dissipation phenomenon for low-power systems, and should be carefully addressed in design as it hindered the operation of the symmetric three-phase prototype.

Analysis showed that the gas hysteresis dissipation could be reduced drastically by increasing the number of phases in a system with a little compromise on the operating frequency and, hence, the output power. It was further shown that for an even number of phases (greater than 5), half of the pistons could be eliminated by utilizing a reverser. By introducing a reverser to the fabricated system, the system proved its self-starting capability in engine mode and validated the derived expression for computing the start-up temperature.

 Time, s

 Time, s

 Figure 5.22: Recorded acceleration signals of the three phases in the revised three-phase Stirling engine system.

 Figure 5.23: Fundamental frequency components of the three acceleration signals. Compare to Figure 5.20(b).

 Figure 5.24: Acceleration signal of one piston at full-amplitude ascillation.