Method of Determining a Nominal Index Value for the Polytropic Expansion Process of Supercritical Carbon Dioxide in Piston-Cylinder Devices

Abstract

The polytropic process is a widely used pressure model for predicting the nature of pressure and volume states in expansion and compression systems. The two variable nature of this model typically leads to an open ended approach with heavy reliance on mechanism evaluation and potential extended design iterations in the prototyping phase. Through a fundamental examination of the polytropic derivation from the energy transfer ratio assumption, in conjunction with repeated application of elementary thermodynamic principles, including First Law analysis, moving boundary work, and substance property evaluation, a solution to a refined nominal polytropic index can be found. The derivation can provide valuable insight to the polytropic process itself and address the issue of bounding a complex system with a reasonable choice of theoretical system input. With the aid of the method outlined in this paper, researchers will be enabled with a tool to better predict the polytropic expansion coefficient which finds widespread use in thermodynamic modeling and analysis. To this end, the method is used herein to predict a polytropic index of n = 1.306 and k = 1.615 for the specific heat ratio for a SCO2 expansion engine operating between 20 MPa and 9.2 MPa.