Multi-Parameter Coupled Thermodynamic Analysis and Optimization of a Free-Piston Stirling Air Conditioner

To enhance the thermal performance of a Stirling air conditioner, this study applies Schmidt-based dimensionless analysis to systematically investigate the influence of key structural parameters on its cooling and heating characteristics. A dimensionless thermodynamic framework is established under the ideal isothermal assumptions of the Schmidt model to investigate the effects of temperature ratio, swept volume ratio, dead volume ratio, and phase angle on a Stirling system. The results indicate that increasing the temperature ratio enhances the thermodynamic driving potential; however, excessive temperature ratios introduce stronger irreversibilities, resulting in saturation or even degradation of effective cooling performance. The dimensionless cooling capacity increases significantly with phase angle, rising from 0.25 at α = 50° to 0.65 at α = 120°, while heating capacity peaks at α ≈ 71.6° with εe = 0.18. The p–v diagram analysis reveals optimal work output at α ≈ 75°, where the cycle area reaches 20.8, representing a 44.4% increase from the value at 15°. Performance saturation occurs at τ > 3 and κ > 6 for cooling and beyond κ > 4 for heating. Within the assumptions of the ideal Schmidt model, the results suggest that medium-to-high temperature ratios (τ ≈ 3–4) combined with moderate swept volume ratios (κ ≈ 6–8) provide the optimal balance between thermodynamic performance and structural compactness; these parameter combinations should be regarded as theoretical design references for ideal operating conditions rather than directly applicable engineering optimization guidelines.