Historical Review of Real-Fluid Isentropic Flow Models

The analysis of steady, one-dimensional, isentropic flow of nonideal compressible fluids is simplified greatly by the use of an approximate model for the PV or P_ρ relation, this relation being called the isentrope equation. The simplest isentrope model is the perfect-gas or polytrope equation PVⁿ = constant. During the past 80 years, five isentrope equations have evolved: the polytrope, Walker, van der Waals, Rayleigh, and Callendar models. The historical development and limitations of each model are discussed. Only the polytrope and Rayleigh model yield simple, closed-form, analytic solutions for isentropic flow properties. A comparison with calculated data for sonic flow properties reveals the superiority of the Rayleigh model for the prediction of isentropic flow.