Alexander Gary Zimmerman

arXiv2020

Mixed finite elements for convection-coupled phase-change in enthalpy form: Open software verified and applied to 2D benchmarks

Melting and solidification processes are often affected by natural convection of the liquid, posing a multi-physics problem involving fluid flow, convective and diffusive heat transfer, and phase-change reactions. Enthalpy methods formulate this convection-coupled phase-change problem on a single computational domain. The governing equations can be solved accurately with a monolithic approach using mixed finite elements and Newton's method. Previously, the monolithic approach has relied on adaptive mesh refinement to regularize local nonlinearities at phase interfaces. This contribution instead separates mesh refinement from nonlinear problem regularization and provides a continuation procedure which robustly obtains accurate solutions on the tested 2D uniform meshes. A flexible and extensible open source implementation is provided. The code is formally verified to accurately solve the governing equations in time and in 2D space, and convergence rates are shown. Two benchmark simulations are presented in detail with comparison to experimental data sets and corresponding results from the literature, one for the melting of octadecane and another for the freezing of water. Sensitivities to key numerical parameters are presented. For the case of freezing water, effective reduction of numerical errors from these key parameters is successfully demonstrated. Two more simulations are briefly presented, one for melting at a higher Rayleigh number and one for melting gallium.

physics.comp-ph↗

arXiv2019

Modeling and simulation of heat source trajectories through phase-change materials

The modeling and simulation of heat source trajectories through phase-change materials is a relevant problem both for space exploration and for terrestrial climate research, among other fields. In space, the DLR and NASA are both interested in exploring beneath the surfaces of icy moons, primarily Enceladus and Europa, where conditions may alloy for extraterrestrial life. On Earth, unique sub-glacial aquatic ecosystems offer potential for geo-biological discoveries. Unfortunately, existing ice-drilling technology is dirty and cumbersome. Melting probes are a clean and compact alternative technology which use heaters to melt through the ice. A melting probe's trajectory can be controlled with differential heating. Successful trajectory control requires advancements not only in the modeling and simulation of the ambient dynamics, but also of the probe's coupled rigid body dynamics. Fundamentally, the rigid body dynamics can be modeled by the equations of motion; but this approach is prohibitively complex. This work proposes an approach which exploits that the motion of the probe is driven by contact with the evolving liquid-solid interface. From this perspective, an energy minimization problem is formulated. The general mathematical problem is formulated as two split operators, respectively for the rigid body dynamics and the ambient dynamics. These operators are coupled with feasibility constraints which ensure that the probe does not penetrate the solid. Concrete examples are shown both for the energy minimization problem and for the unsteady ambient dynamics. Finally, an algorithm is presented for the temporal coupling of the split operators, which is implemented using Python and C++. Example trajectories are shown, including the dynamic response of the probe velocity to a rapid change in the heat flux.

cs.CE↗