A Theory of the Wilson Line for Steam at Low Pressures

Abstract

An algebraic method for determining the onset of condensation—the position of the Wilson line on a Mollier diagram—in steam at low pressures is presented. The method is based on the assumptions that the exponent of the nucleation rate expression is large and that the nucleation pulse duration is small. Under these conditions the growth integrals can be evaluated for specific rate expressions for the formation of stable droplets and their subsequent growth. The onset of condensation for a specified expansion rate is then determined by the solution to a system of algebraic equations. The method is illustrated using the classical nucleation rate and the droplet growth rate expression of Gyarmathy. The analytical solution agrees well with a published exact numerical solution by Gyarmathy. An extensive comparison of the predictions of the present method with the experimental results of Yellot (1933), Gyarmathy and Meyer (1965), Barschdorff (1965), and Moses and Stein (1978) is presented. The favorable comparison suggests that the method provides an efficient means for predicting the onset of condensation for various initial states and various expansion rates. The predictions of the theory on the role of the expansion rate, the initial stagnation conditions, and the history of the expansion are discussed.