A path-specific isentropic exponent for non-ideal compressible fluids

Abstract

Isentropic processes are crucial in engineering as they represent idealized processes and serve as reference conditions for thermodynamic analyses. Existing methods for calculating isentropic processes in non-ideal fluids are either too slow for practical engineering applications [equation of state (EOS) approach] or inaccurate (classic modified polytropic isentrope equation: Pvj ¼ Const: where exponent j is the isentropic expansion coefficient). This paper proposes a novel isentrope equation, Pvk ¼ Const:, with a path-specific exponent k correcting for j variation in generic non-ideal fluid isentropic processes. The benefit of this approach is that it maintains the isentrope equation’s polytropic form, so that the explicit isentropic relations can be derived, enabling straightforward and rapid calculations and a better physical understanding. Using supercritical carbon dioxide as the fluid to test the hypothesis, the proposed isentropic relations accurately calculate the stagnation state within 2% of the exact EOS calculation, whereas the classic isentropic relations have errors up to 50%. Additionally, the fitted k function is explicit and can calculate the stagnation state approximately 15–20 times faster than the EOS approach. Moreover, the results of two other non-ideal fluids, hexamethyldisiloxane and R-143a, are included to prove the robustness and general applicability of the proposed equations. This method strikes a balance between accuracy, simplicity, and computational speed for calculating isentropic processes in nonideal fluids, offering greatly simplified expressions for thermodynamics modeling in engineering applications such as turbomachinery reduced-order models and design optimizations.