Efficient exact solution procedure for quasi-one-dimensional nozzle flows with stiffened-gas equation of state

Abstract

We propose an efficient and accurate exact solution procedure for the converging–diverging nozzle flows of compressible liquids governed by a stiffened-gas equation of state (SG-EOS). First, we elaborate on how to formulate a complete SG-EOS and suggest a new method to determine the parameters of SG-EOS. Next, we derive the relations for the quasi-one-dimensional nozzle flow of the SG-EOS liquids and propose an efficient solution procedure to obtain the exact solution at various boundary conditions. The proposed solution procedure can accurately calculate the position of the shock wave regardless of the number of computational grid points. We then verify the solution procedure against the previous results for the air and water nozzle flows. We also investigate the influence of the SG-EOS parameters on the nozzle flow of liquid water containing a shock wave. The proposed solution procedure can be used for the basic design of a compressible liquid nozzle and the validation of compressible two-phase flow model.