Supercritical flow in rectangular expansions

Abstract

In recent years the occasions for design of channels to contain supercritical flow has increased considerably. Consequently there has developed a need for a method of predicting the physical characteristics of such flow based on theory. Accordingly, use has been made of the analogy between supersonic gas flow and supercritical fluid flow to apply the method of characteristics, originally developed for gas dynamics, to fluid dynamics. Herbich and Bagge have used this method in the development of a set of equations for predicting the profile of flow passing through an expansion. These equations were converted to a form suitable for numerical solution by computer. An experimental model was constructed in the Hydromechanics Laboratories and the resultant profiles obtained for different sets of parameters compared to those predicted by the mathematical model. The tests indicated that the equations were somewhat limited in use because of the assumptions made in the original analysis. For angles of expansion greater than 5⁰ separation occurs with the result - a non-hydrostatic pressure distribution. For steep slopes vertical acceleration has a significant effect and for slopes greater than 15 percent air entrainment becomes a significant problem. While friction affects the profile in the experimental apparatus, it was felt that on larger models, the relative size of this term would decrease and accordingly its relative effect on the profile.