Numerical Calculation of Speed of Sound for Vapor-Liquid Critical Flow from Pipe with Granular Layer

摘要

The dynamics of the critical vapor-liquid flow at the outlet from a pipe filled with granular backfill is studied. The cases of critical outflow at homogeneous filling of spherical shape with diameters of 2 and 4 mm are considered. The values of critical mass flow rates at different levels of vapor content in a two-phase mixture are obtained. Based on the method of smoothed particles hydrodynamics, a model of the critical flow of a vapor-liquid mixture from a channel filled with granular backfill has been developed which allows to obtain characteristics of the critical flow, such as mass flow, vapor content, and sound velocity of the vapor-liquid flow. An area of low vapor content characterized by low sound velocity was studied. The dependence of the vapor content at the outlet of the pipe is determined depending on the initial vapor content for the case of a pipe without filling and for a pipe filled with a granular layer. For the output vapor content, the corresponding values of the sound velocity at the outlet of the pipe were calculated. Obtained results were compared with the available data in the literature for channels without backfill and a satisfactory consistency of results was obtained. It is shown that the addition of granular backfill leads to a decrease in the speed of sound compared to the case of a pipe without backfill, which is consistent with experimental studies.