Method of moments and its application in phase transition of water

By introducing the moments of the droplet size distribution over the internal coordinates, the method of moments (MOM) tracks the time dependence of the lower order moments to solve the evolution of droplet phase in flow. Among all the available numerical methods, MOM is widely applied to model the phase transition of water vapor because of its good balance of simulation efficiency and accuracy. The concept and development of the classical MOM for homogeneous condensation were introduced firstly. The method was used to investigate the Prandtl-Meyer corner expansion flow with homogeneous condensation of water vapor and it is found that the condensation wave changes from steady to unsteady when saturation ratio is increasing. Then, a simplified model of instantaneous-wetting for heterogeneous nucleation on solid particle surface was introduced and nucleation rate based on the particle size distribution was derived. So, the classic MOM was extended to unsteady flows with heterogeneous condensation. As a demonstration, the heterogeneous condensation in closed shock tube problem was simulated by the extended MOM. The waves induded by the heterogeneous condensation within expansion fan and evaporation behind trans-metted shock were observed clearly and the influence of phase transition on fluid flow could not be neglected. Finally, the classic MOM was extended to account the slips of velocity and temperature between the liquid phase and the gas phase in condensing flows. The interphase interaction is realized through source terms which include the mass, momentum and energy exchanges. As an example, the method was used to simulate the homogeneous homogeneous condensation in vortex flow. Due to the very strong velocity slip, a dry zone is found in the vortex core region, which confirms the experimental observation, but not discovered by the classic MOM.