Polytropic Change of State Calculations

Polytropic change of state calculations are used within many thermodynamic cycle analysis tasks for turbomachinery like gas turbines or compressors. The typical approach is using formulas, which are theoretically valid for ideal gas conditions only. But often gases are used, which do certainly not behave like ideal gases. This is motivation to check how and which polytropic change of state algorithms can be used for real gases or corresponding mixtures. There is a vast experience on polytropic efficiencies achievable with existing turbomachinery. Manufacturers calibrate their performance analysis with real test results for compensating potential deviations from their analysis approach. But they normally do not disclose their approaches for the thermodynamic calculation and the corrections made based on their test results. But for investigations of new thermodynamic cycles before the stage of development with an available demonstrator a best possible prediction of the performance is desired. In this paper the assumptions and formulas for calculating polytropic changes of state and polytropic efficiencies are gathered from literature. The most fundamental assumption is based on a constant dissipation rate during the polytropic change of state. It could be tracked back to Zeuner, Stodola and Dzung. A numerically convenient approximation is the “polytropic exponent approach”. It fulfills the first assumption for an ideal gas but it is only an approximation for real gases. The temperature after a polytropic change of state is defined by its initial condition, the pressure ratio and the polytropic efficiency. Three different calculation algorithms are compared here: The recursive “constant dissipation rate algorithm” suggested by the author, the most used “ideal gas formula” and the “polytropic exponent formula” as the most used approximation for real gases. Numeric results for compression from 1bar to up to 100bar are shown for dry air, Argon, Neon, Nitrogen, Oxygen and CO2. The deviations of the different calculation approaches are considerable.