The importance of pseudo-polytropic analysis for supercritical CO2 turbomachinery and power systems

This work demonstrates that pseudo-polytropic analysis performs better than polytropic analysis when nonlinear thermodynamic properties are involved, such as those found in supercritical CO2 turbomachinery problems. Pseudo-polytropic is the name given for a thermodynamic analysis in which the polytropic index is updated in each pressure step of a simulation. An analytical derivation of the polytropic indexes (n and m) reveals that the polytropic analysis is a simplified version of the pseudo-polytropic analysis. The derivations presented in this work are based on fundamental energy, mass, and entropy balances, and simulations are done using Python-Coolprop interfaces. In addition, isentropic simulations were done comparing results obtained directly from the EoS with results derived from polytropic and pseudo-polytropic analysis. Despite the high accuracy of the mathematical formula derived for the polytropic indexes, when those properties are used in a thermodynamic simulation, error propagation may lead to cumulative deviations as large as 8.8 %, for a pressure step size of 10 kPa.