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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A fully coupled finite element formulation for liquid-solid-gas thermo-fluid flow with melting and solidification
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A fully coupled finite element formulation for liquid-solid-gas thermo-fluid flow with melting and solidification

机译：具有熔融和凝固功能的液固气热流体全耦合有限元配方

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摘要

Many important industrial processes, such as additive manufacturing, involve rapid mass, flow and heat transport between gas, liquid and solid phases. Various associated challenges, such as the large density ratio between gas and condensed phases, make accurate, robust thermal multi-phase flow simulations of these processes very difficult. In order to address some of the associated challenges, a computational framework for thermal multi-phase flows is developed based on the finite element method (FEM). A unified model for thermal multi-phase flows similar to the models widely used in the manufacturing community is adopted. The combination of the level-set method and residual-based variational multi-scale formulation (RBVMS) is used to solve the governing equations of thermal multi-phase flows. Phase transitions between solid and liquid phases, i.e., melting and solidification, are considered. Interfacial forces, including surface tension and Marangom stress, are taken into account and handled by a density-scaled continuum surface force model. A robust fully coupled solution strategy is adopted to handle various numerical difficulties associated with thermal multi-phase flow simulations, and implemented by means of a matrix-free technique using Flexible GMRES. The mathematical formulation and its algorithmic implementation are described in detail. Four numerical test cases are presented to demonstrate the capability of the proposed formulation. The first case is a benchmark example of solidification of aluminum in a graphite mold, the second case is a thermo-capillary droplet migration problem, the third case is a spot laser melting problem, and the fourth case is the melting of metal with an interior gas bubble. The computational results are compared with analytical, experimental and simulation data from other researchers, with good agreement in cases where such data is available. (C) 2018 Elsevier B.V. All rights reserved.
机译：许多重要的工业过程（例如增材制造）都涉及在气相，液相和固相之间快速的质量，流量和热传递。各种相关的挑战，例如气相和冷凝相之间的高密度比，使得这些过程的精确，鲁棒的热多相流模拟非常困难。为了解决一些相关的挑战，基于有限元方法（FEM）开发了用于热多相流的计算框架。采用与制造界广泛使用的相似的热多相流统一模型。水平集方法和基于残差的变分多尺度公式（RBVMS）的组合用于求解热多相流的控制方程。考虑固相和液相之间的相变，即熔融和固化。包括表面张力和Marangom应力在内的界面力已考虑在内，并由密度缩放的连续表面力模型进行处理。采用鲁棒的完全耦合解决方案策略来处理与热多相流模拟相关的各种数值难题，并通过使用无弹性GMRES的无矩阵技术来实现。详细描述了数学公式及其算法实现。提出了四个数值测试案例，以证明所提出配方的功能。第一种情况是铝在石墨模具中凝固的基准示例，第二种情况是热毛细管液滴迁移问题，第三种情况是点激光熔化问题，第四种情况是内部金属的熔化气泡。将计算结果与其他研究人员的分析，实验和模拟数据进行比较，并且在可获得此类数据的情况下具有很好的一致性。 （C）2018 Elsevier B.V.保留所有权利。

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