Similarity Parameters for Non-Ideal One-Dimensional Isentropic Expansions

This paper reports an investigation into similarity parameters for one-dimensional isentropic expansions of compressible flows in the non-ideal regime involving thermodynamic conditions in the close proximity of the vapor-liquid saturation curve and the critical point. Several expansions having different total pressure and temperature but sharing the same compressibility factor evaluated at total conditions were calculated using an Helmoltz energy-based fundamental relation of Span-Wagner type for several pure fluids of varying complexity and from different fluid classes. The total compressibility factor was found to be a suitable similarity parameter for characterizing isentropic expansions of complex fluids in moderately high non-ideal conditions because it is associated with similar evolution of compressibility factor and fundamental derivative of gasdynamics along the process, thanks to the particular shape of their isolines in the temperature - entropy thermodynamic plane. Compressibility factor and fundamental derivative of gasdynamics can be seen as representative of information contained in thermal and caloric equations of state, respectively. Expansions sharing similar trends in these two parameters were found to be similar since similar volumetric and caloric behaviours rule the evolution of thermodynamic properties. The use of the total compressibility factor as similarity parameter for isentropic expansions could allow to reduce the number of design parameters in preliminary sizing of thermodynamic cycles and components operating in the non-ideal compressible regime and could significantly decrease the experimental effort in wind tunnel calibration of probes employed in such flows.