Towards a unified formulation for the simulation of thermo-fluid-solid problems with phase change

Industrial processes such as welding or additive manufacturing (AM) are driven by a concentrated heat source and involve phase change. Simulating these processes at the mesoscale presents a dilemma: It is challenging for classic coupled fluid-solid simulation strategies, due to the evolving melting front. Solid mechanics approaches may be insufficient, because it is well established in the literature that such processes can be sensitive to the convective flow in the liquid melt pool. Fluid dynamics approaches may be unable to reproduce the residual stresses that can cause warping and other defects. This work presents a simulation technique that is able to capture fluids and solids in the same framework with one single solver, i.e. without coupling fluid and solid solvers. The technique is based on the Lagrangian Particle Finite Element Method (PFEM), which has been shown to be able to simulate fluid dynamics and solid mechanics problems in the literature. The key development in this work is the unified formulation for fluids and elastic solids: A single set of governing equations is used to describe a material that can locally be in its solid or fluid state. The thermal solution step governs the heat transfer and the phase change. Everything combined, this simulation technique is able to capture phase change, the convective flow in the melt pool (driven by buoyancy and the Marangoni effect) and the evolution of stresses in the elastic solid due to non-uniform thermal expansion. This work outlines the mathematical formulation and algorithm of the simulation technique, then presents a series of verification test cases to finally demonstrate the capabilities claimed above. The demonstration test cases include a bird strike Fluid-Structure interaction (FSI) example, followed by two spot welding applications taken from the literature. While work remains to be done for the accurate simulation of welding or AM processes, the method is successfully proven to be able to capture the flow in the fluid and the residual stresses in the solid, the fluid-solid interaction and the phase change correctly

Towards a PFEM-based unified thermo-fluid-solid simulation tool for phase change problems

editorial reviewe

Phase change driven adaptive mesh refinement in PFEM

peer reviewedThe particle finite element method (PFEM) is used to simulate a simple phase change problem. This is a first step towards the simulation of additive manufacturing (AM) processes at the meso-scale, where the liquid melt pool interacts with the surrounding solid material and undergoes phase change. The focus of this paper lies on strategies to deal with the release or absorption of latent heat in the PFEM, especially with regard to mesh refinement. We briefly describe how mesh refinement in PFEM works and how it can be chosen specifically to achieve convergence despite the highly non-linear latent heat term. It is found that good agreement with the literature can be achieved on a simple 1D phase change test case, while using an automatic local mesh refinement

Simulation of the Marangoni Effect and Phase Change Using the Particle Finite Element Method

A simulation method is developed herein based on the particle finite element method (PFEM) to simulate processes with surface tension and phase change. These effects are important in the sim-ulation of industrial applications, such as welding and additive manufacturing, where concen-trated heat sources melt a portion of the material in a localized fashion. The aim of the study is to use this method to simulate such processes at the meso-scale and thereby gain a better under-standing of the physics involved. The advantage of PFEM lies in its Lagrangian description, al-lowing for automatic tracking of interfaces and free boundaries, as well as its robustness and flex-ibility in dealing with multiphysics problems. A series of test cases is presented to validate the simulation method for these two effects in combination with temperature-driven convective flows in 2D. The PFEM-based method is shown to handle both purely convective flows and those with the Marangoni effect or melting well. Following exhaustive validation using solutions reported in the literature, the obtained results show that an overall satisfactory simulation of the complex physics is achieved. Further steps to improve the results and move towards the simulation of ac-tual welding and additive manufacturing examples are pointed out

Simulation of the Marangoni Effect and Phase Change Using the Particle Finite Element Method

A simulation method is developed herein based on the particle finite element method (PFEM) to simulate processes with surface tension and phase change. These effects are important in the simulation of industrial applications, such as welding and additive manufacturing, where concentrated heat sources melt a portion of the material in a localized fashion. The aim of the study is to use this method to simulate such processes at the meso-scale and thereby gain a better understanding of the physics involved. The advantage of PFEM lies in its Lagrangian description, allowing for automatic tracking of interfaces and free boundaries, as well as its robustness and flexibility in dealing with multiphysics problems. A series of test cases is presented to validate the simulation method for these two effects in combination with temperature-driven convective flows in 2D. The PFEM-based method is shown to handle both purely convective flows and those with the Marangoni effect or melting well. Following exhaustive validation using solutions reported in the literature, the obtained results show that an overall satisfactory simulation of the complex physics is achieved. Further steps to improve the results and move towards the simulation of actual welding and additive manufacturing examples are pointed out

Mesh adaption for two-dimensional bounded and free-surface flows with the particle finite element method

peer reviewedThe particle finite element method (PFEM) is a Lagrangian method that avoids large mesh distortion through automatic remeshing when the computational grid becomes too distorted. The method is well adapted for flows with deforming interfaces and moving boundaries. However, the α-shape technique used to identify these boundaries presupposes a mesh of approximately uniform size. Moreover, the α-shape criterion is purely geometric and, thus, leads to violations of mass conservation at boundaries. We propose a new algorithm for mesh refinement and adaptation in two dimensions to improve the ratio accuracy to computational cost of the PFEM. A local target mesh size is prescribed according to geometric and/or physics-based criteria, and particles are added or removed to approximately enforce this target mesh size. Additionally, the new boundary recognition algorithm relies on the tagging of boundary nodes and a local α-shape criterion that depends on the target mesh size. The method allows thereby reducing mass conservation errors at free surfaces and improving the local accuracy through mesh refinement and simultaneously offers a new boundary tracking algorithm. The new algorithm is tested on four two-dimensional validation cases. The first two cases, i.e., the lid-driven cavity flow at Reynolds number 400 and the flow around a static cylinder at Reynolds numbers below 200, do not feature a free surface and mainly illustrate the mesh refinement capability. The last two test cases consist in the sloshing problem in a reservoir subjected to forced oscillations and the fall of a 2D liquid drop into a tank filled with the same viscous fluid. These last two cases demonstrate the more accurate representation of the free surface and a corresponding reduction of the error in mass conservation

A Unified Thermo-Fluid–Solid Formulation for FSI and Phase Change Problems Based on the Particle Finite Element Method

peer reviewedThe modeling of industrial processes that involve phase change (e.g., casting, welding or additive manufacturing) is challenging due to their multiscale and multiphysics nature. The coupling of the fluid and solid mechanics is difficult due to the unknown and evolving fluid–solid interface. To deal with the difficulty of the coupling, a unified approach has been developed where fluid and solid regions are represented in the same computational domain and solved by a single solver. The interaction of fluid and solid regions is therefore automatically captured and the material can locally undergo phase transition. This allows to capture the flow in the melt and the thermal stresses in the solid. The solid material model is currently limited to linear elasticity, but it opens the path to more complex material models with plasticity modeling, which already exist in the literature. The proposed method is based on the Particle Finite Element Method (PFEM), which has been shown to accurately handle both fluid and solid mechanics. In this work, we present the key aspects of this novel unified formulation and the treatment of the fluid–solid interface in the PFEM context. The methodology is presented and verified using a set of tests. A laser spot welding example test case demonstrates the potential of combining the unified formulation with the interface treatment and the phase change capabilities and is used for the validation of the present technique.ALFEWEL

Simulation of the Friction Melt Bonding (FMB) process using the FEM + PFEM

peer reviewe