In the present study, a consistent and conservative Phase-Field model is developed to study thermo-gas-liquid-solid flows with liquid-solid phase change. The proposed model is derived with the help of the consistency conditions and exactly reduces to the consistent and conservative Phase-Field method for incompressible two-phase flows, the fictitious domain Brinkman penalization (FD/BP) method for fluid-structure interactions, and the Phase-Field model of solidification of pure material. It honors the mass conservation, defines the volume fractions of individual phases unambiguously, and therefore captures the volume change due to phase change. The momentum is conserved when the solid phase is absent, but it changes when the solid phase appears due to the no-slip condition at the solid boundary. The proposed model also conserves the energy, preserves the temperature equilibrium, and is Galilean invariant. A novel continuous surface tension force to confine its contribution at the gas-liquid interface and a drag force modified from the Carman-Kozeny equation to reduce solid velocity to zero are proposed. The issue of initiating phase change in the original Phase-Field model of solidification is addressed by physically modifying the interpolation function. The corresponding consistent scheme is developed to solve the model, and the numerical results agree well with the analytical solutions and the existing experimental and numerical data. Two challenging problems having a wide range of material properties and complex dynamics are conducted to demonstrate the capability of the proposed model.
翻译:在本研究中,开发了一个一致和保守的阶段-实地模型,以研究液-固态流动的热气-液-液体-固体流动,进行液-固化阶段变化;拟议的模型是在一致性条件帮助下产生的,并完全减少对压缩两阶段流动的一致和保守的阶段-现场方法、对流体结构互动的虚构的域布林克曼惩罚方法(FD/BP)和纯材料固化的阶段-实地模型;它尊重质量保护,明确界定单个阶段的数量部分,从而捕捉因阶段变化而产生的数量变化;当固态阶段不存在时,即保持势头,但在固态阶段似乎由于固态边界的无翻转状态而改变时,则完全减少;拟议的模型还保存能源,保持温度平衡,是加利利安的动态;新的连续表面紧张力量,将其贡献限制在气体-液体界面上,从拟议的卡曼-库泽尼方程式模型修改为将固态速度降低到零的模型;提议在初始阶段-实地模型启动阶段变化,但当固化阶段阶段阶段阶段阶段阶段阶段阶段阶段阶段阶段阶段阶段阶段因固态阶段条件而出现变化时,但当固体阶段阶段阶段阶段阶段阶段阶段阶段因固态阶段性阶段性阶段性变化而出现变化时,该阶段,该阶段性阶段性阶段性阶段性阶段性变化,该阶段性阶段性阶段性变化到固化状态状态状态因固化状态状态状态状态因固态状态状态状态因固态性状态状态因固化状态因固态状态因固态状态因固态性状态状态因固化状态因固态性状态而变化而变化而变化而变化;还因固态性变,通过实际调整后,同时调整后,通过机能和数值分析结果,通过实际调整后,通过机能和数值分析性变后,通过机能和数值分析性变后,即调整后,通过机能,通过机能和数值分析性变变后变后变现的机能性变后变后变现的机变现的机变现的机变制制制制制制制制制,通过机变数制变数制,将调整后变数制制制制制制制制制制制制制制制制制制制制算。。