Modelling of compressible gas–liquid flow in a convergent–divergent nozzle

A two-fluid model for compressible flow of gas bubbles dispersed in liquid moving through a convergent–divergent nozzle, which is used for a gas-assisted atomization, is presented. The model is developed for flows with high values of the gas volume fraction—up to the phase inversion values. Drag and virtual mass forces are considered. A new method is proposed to correct the virtual mass coefficient for the high bubble loadings. The mixture kk–εε turbulence model is adapted for the nozzle flow. The particle number density equation is solved to calculate the distribution of the locally averaged bubble diameter. Curvilinear body fitted grids are utilized to represent the nozzle shape accurately. It is shown that for numerical stability it is necessary to discretize implicitly the virtual mass term and solve the momentum equations for two phases simultaneously in a coupled way. The comparison between the experimentally measured and the predicted pressure profiles along the nozzle wall demonstrated good overall agreement. Gravitational effects are analysed by modelling a three-dimensional case. The examination of the flow through the nozzle reveals the non-uniformities of the bubble size and volume fraction distributions. It is confirmed that the virtual mass force plays a major role in accelerating/decelerating flows with a relatively low interfacial drag.