Colloquia

Samenvatting

The modern study of solidification began in the 1940s, when engineers used analytical methods to examine phase transitions in casting and welding. Since then, the principles behind solid-liquid phase transition has become crucial for the further development of latent heat thermal energy storage, phase-change materials, food preservation, and even medical procedures like cryosurgery. Understanding heat transfer problems involving solid–liquid phase transitions is therefore essential.

This work presents a numerical model for solving heat transfer problems involving phase transitions. The main challenge stems from time-dependent boundary conditions, known as the Classical Stefan problem. This occurs because the domain includes regions corresponding to both solid and liquid, whose boundaries evolves over time. Conventional methods explicitly track the moving boundaries, requiring an adaptive mesh, which increases computational complexity and cost.

The model in this work uses the Enthalpy Method, reformulating the problem in terms of enthalpy, defined as the sum of sensible and latent heat. The temperature is recovered from the enthalpy field using an appropriate enthalpy–temperature relation. This allows the simulation to run on a fixed grid, simplifying implementation and lowering computational demands.

Instead of developing from scratch, the model is implemented in the OpenFOAM framework to leverage existing infrastructure. It uses a fully implicit time-integration scheme with a dual-loop structure: an outer loop for Newton linearization and an inner loop that solves the linear system of equations. A custom algorithm recovers temperature from enthalpy, handling both isothermal and non-isothermal transitions. Convergence is reached when enthalpy and temperature fields are consistent.

To include the effects of natural convection, the velocity field must be obtained by solving the Navier–Stokes equations. The medium is assumed to be pseudo-porous which makes it possible to solve the Navier-Stokes equations on a multiphase domain where solid and liquid phases coexist. The momentum equations includes a Darcy source term that suppresses the local velocity field in (partially) solidified cells. Buoyancy-driven flow is modeled via the Boussinesq approximation, which assumes that density variations are temperature induced and only affect the gravity term of the momentum equations.

The solver was implemented as a custom OpenFOAM solver and verified against benchmark cases. Results show good accuracy and efficiency for conduction-dominated problems. Though minor errors appear with strong natural convection, the model remains quite accurate.