Theoretical Analysis of Vuilleumier's Hypothetical Engine and Cooler

Vuilleumier machines are a promising technology for heating. Respective performances of Vuilleumier's engine and cooler are generally unclear. In Stirling machines, performances can be determined based on PV power flow and heat flow methods. In this work, respective performances based on two methods in current Vuilleumier models were investigated. It was found that PV power flow and heat flow methods in current Vuilleumier models were ineffective for analysis of respective performances due to there being no piston as a boundary between Vuilleumier's engine and cooler. Then, a virtual piston was assumed, and a virtual piston based Vuilleumier model (VPBVM) was developed. The relative Carnot efficiencies of the obtained engine and cooler were 53 similar to 64% and 43 similar to 49%, respectively, at conditions of 550 degrees C hot temperature, 50 similar to 70 degrees C warm temperature, and -20 similar to 10 degrees C cold temperature. The results indicated that respective performances obtained in VPBVM were reasonable. Moreover, the engine's compression ratios could be obtained in VPBVM and were 1.2 similar to 1.24. Thus, VPBVM could be effective for the analysis of the Vuilleumier machine's engine and cooler.

Automated summary

In this study, performances of Vuilleumier engine and cooler were investigated using two methods, resulting in the development of the VPBVM model with reasonable results. The relative Carnot efficiencies of the obtained engine and cooler were found to be between 53% to 64% and 43% to 49% respectively at certain conditions. Additionally, the engine's compression ratios could also be obtained, demonstrating the effectiveness of VPBVM for analyzing Vuilleumier machine's engine and cooler.