Nonequilibrium Modeling of Two-Phase Critical Flows in Tubes

Abstract

A nonequilibrium two-phase flow model is described for the analysis of critical flows in variable diameter tubes. Modeling of the two-phase flow mixture in the tube is accomplished by utilizing a one-dimensional form of conservation and balance equations of two-phase flow which account for the relative velocity and temperature differences between the phases. Closure of the governing equations was performed with the constitutive equations which account for different flow regimes, and the solution of the nonlinear set of six differential equations was accomplished by a variable step numerical procedure. Computations were carried out for a steam-water mixture with varying degrees of liquid subcooling and stagnation pressures in the vessel upstream of the tube and for different tube lengths. The numerical results are compared with the experimental data involving critical flows with variable liquid subcoolings, stagnation pressures, and tube lengths, and it is shown that the nonequilibrium model predicts well the critical flow rate, pressure distribution along the tube, and the tube exit pressure.