Modeling Phase Change in a Thermosiphon with a Pseudofluid Approach using COMSOL Multiphysics®

Introduction:

Thermosiphons that operate near the phase change temperature of the fluid provide considerable advantages. The reason being the amount of heat absorbed that causes phase change is much higher than the heat required to change the temperature. Additionally, Phase change offers a significant change in density, enabling natural fluid flow in the thermosiphon.

Modeling Approach:

Modeling a thermosiphon involves modeling of fluid/gas flow, heat transfer, and phase change. Instead of using interface tracking approach, a typical phase change model that comes with drawbacks like having higher computational complexity and inability to consider topological changes, our approach involves using a single domain. We call it a pseudofluid. The properties of the psedofluid are dependent on temperature and pressure. The properties change from liquid to vapor, over a small phase transition window. In the figure below, we see how a cross-phase density function is defined to indicate the transition of state from liquid to vapor.

Figure 1: Representative images of density as a function of temperature and pressure.

In this modeling approach, there are no domain boundaries, enabling topological changes between phases. This overcomes one of the major drawbacks of the interface tracking approach. Our solution could now have plenty of pockets of fluid transitioning from one phase to another, which is in line with our everyday observations of fluids brought to a boil, for instance.

The pseudofluid approach for modeling fluid flow with phase change has been implemented using COMSOL Multiphysics®. The model uses the boundary conditions defined based on the operating conditions. The fluid velocity, pressure and temperature are obtained by solving the coupled governing equations. These results can be post- processed to obtain other derived quantities of interest. As an example, the image below shows the formation of different phases of fluid (represented by their density), as well as the local velocity of the convection currents in a tilted tube, which represents the thermosiphon flask.

Figure 2: Density distribution and velocity arrow field of the pseudofluid in a thermosiphon. Rise of vapor along the top of the tilted thermosiphon is observed in the zoomed image on the right.

Approximations:

There are two approximations inherent in the pseudofluid approach. It doesn’t take surface tension forces into account; so even though topological changes are handled, a big contributing factor in bubble formation during boiling is still left out. Also, phase transition occurs over a small range of temperatures instead of a specific value. The smaller this range is, the more accurate the phase change phenomenon. Ideally, we would choose a range that represents the intermediate slushy stage well. However, a smaller range causes more difficulties in convergence of the solutions.