| Summary: | A<b> </b>2D computational fluid dynamics (CFD) model in consideration of nucleation characteristics (homogeneous/heterogeneous nucleation) using the volume of fluid (VOF) method and Lee model was proposed. The model was used to predict the process of a multiphase flow accompanied by freezing phase change during cryogenic fracturing. In this model, nucleation characteristic (homogeneous and heterogeneous nucleation) during the freezing process and the influence of the formed ice phase on the flowing behavior was considered. Validation of the model was done by comparing its simulation results to Neumann solutions for classical Stefan problem. The comparison results show that the numerical results are well consistent with the theoretical solution. The maximum relative differences are less than 7%. The process of multiphase flow accompanied by the freezing of water was then simulated with the proposed model. Furthermore, the transient formation and growth of ice as well as the evolution of temperature distribution in the computational domain was studied. Results show that the proposed method can better consider the difference between homogeneous nucleation in the fluid domain and heterogeneous nucleation on the wall boundary. Finally, the main influence factors such as the flow velocity and initial distribution of ice phase on the fracturing process were discussed. It indicates that the method enable to simulate the growth of ice on the wall and its effect on the flow of multiphase fluid.
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