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

Abstract

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.

Impact of Boundary Parameters Accuracy on Modeling of Directed Energy Deposition Thermal Field

“…where k is the conduction coefficient, which depends on the temperature [40] with a neglected Marangoni effect within the melt pool [41,42]. However, it is possible to take it into account in a global way by multiplying the value of k by a factor [43] to artificially recover this effect.…”

The Impact of Marangoni and Buoyancy Convections on Flow and Segregation Patterns during the Solidification of Fe-0.82wt%C Steel

“…The validation process showcased a good agreement between the numerical predictions and the experimental measurements, enhancing the reliability of the outcomes study. Bobach et al [ 11 ] used the particle finite element method (PFEM) to simulate the phase-change process, taking into account the surface tension. The authors presented a series of test cases to validate their simulation method with temperature-driven convective flows in 2D.…”

Generalized‐α scheme in the PFEM for velocity‐pressure and displacement‐pressure formulations of the incompressible Navier–Stokes equations

“…The particle finite element method (PFEM) has drawn attention of the simulation community due to the possibility to formulate fluid flow equations in a Lagrangian framework, allowing the use of classical Lagrangian FEM and easing tracking of fluid boundaries, even in case of large and unpredictable boundary motions due to efficient remeshing algorithms. 1 The method has been extended to various materials and multi-physics problems with moving domains, such as plasticity, 2 fluid-structure interaction, 3,4 and phase change 5 among others. 6,7 In the PFEM, Lagrangian-based governing equations are solved using spatial FEM-Galerkin and temporal discretizations.…”

“…v n+1 , v n+1 , and x n+1 ), a time integration scheme must be used. For example, common schemes in the PFEM literature are the implicit Backward Euler, 3,5,[8][9][10][11][12] Trapezoidal, 13,14 Newmark, 15,16 and Newmark-Bossak. [17][18][19][20] Although explicit schemes can also be found.…”

“…To relate state variables with their time derivatives ($$$ {\dot{\mathrm{v}}}_{n+1} $$$, $$$ {\mathrm{v}}_{n+1} $$$, and $$$ {\mathrm{x}}_{n+1} $$$), a time integration scheme must be used. For example, common schemes in the PFEM literature are the implicit Backward Euler, 3,5,8‐12 Trapezoidal, 13,14 Newmark, 15,16 and Newmark–Bossak 17‐20 . Although explicit schemes can also be found 21 .…”