Analytical model of the pulse tube engine

• An analytical expression for the pV-work of the pulse tube engine is derived.
• The irreversible nature of the pulse tube engine is shown mathematically.
• The temperature ratio above which the engine operates is calculated and measured.
• An upper limit for the pulse tube engine's efficiency is derived.

The pulse tube engine represents the thermodynamic inversion of the pulse tube refrigerator used in cryogenic cooling applications. It has a high potential to be used as a prime mover for the conversion of low grade waste heat into mechanical or electrical energy. This paper describes an analytical analysis of the pulse tube engine based on a zero-dimensional model. During compression and expansion, the engine components are considered as isothermal with characteristic temperatures. At the piston's dead centers, a thermal relaxation model is used to switch between these temperatures. Analytical relations for the pV–work developed by the pulse tube engine and its efficiency are derived. The irreversible nature of the pulse tube engine is studied by calculating the entropy production in the components. Furthermore, the thermodynamic cycle is investigated analytically under variation of design features and operating conditions. The results are compared to prior numerical studies. The minimal temperature ratio above which the engine provides a work output is derived analytically and compared to experimental observations. Fundamental characteristics and application limitations of the pulse tube engine are disclosed. An upper limit for the efficiency of the pulse tube engine is derived theoretically and confirmed experimentally as well as through numerically calculations.