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.