On the compressibility factor as a similarity parameter for steady single-phase isentropic expansions of organic vapors

This paper revisits similarity parameters for steady single-phase isentropic expansions of organic vapors. Building on earlier work that identified the compressibility factor in total conditions, Zt, as a convenient similarity parameter, this study defines the conditions under which Zt provides reliable similarity and those under which similarity deteriorates. Using a Helmholtz-energy-based equation of state within a steady quasi-one-dimensional isentropic expansion model, the evolution of flow property ratios and local thermodynamic and gasdynamic variables is examined over a broad range of stagnation states and fluids. Existing measurements of nozzle flows of siloxanes MDM and MM are processed in a geometry-independent form and complemented with theoretical calculations for additional organic vapors and operating conditions. A key outcome of this study is that the effectiveness of Zt as a similarity parameter depends on the thermodynamic region from which the expansion originates. In particular, static-to-total pressure-ratio profiles P/Pt(M) exhibit deviations typically below 1% for Zt≳0.6 when expansions originate from a thermodynamic region with dominant volumetric behavior, while larger discrepancies arise elsewhere. Grouping states by both Zt and thermodynamic region significantly reduces the spread in P/Pt compared to a classification based on Zt alone. The results show that a practical similarity approach can be obtained by combining Zt with information on the total state, improving the selection of experimental conditions and supporting the preliminary sizing of expansion components. The proposed similarity framework applies to different thermodynamic states of a given fluid. While equal values of Zt indicate a comparable degree of volumetric nonideality, they do not necessarily imply similar expansion behavior across different fluids. Overall, the framework applies over a broad range of operating conditions and identifies the limits of Zt-based similarity without requiring extensive thermodynamic analysis.