A compact wall model for CFD simulations

It is often necessary to model both internal and external walls in CFD simulations, especially at the room level. Actual walls are generally composed of multiple (thin) layers and may be exposed to solar irradiance. Modeling the wall construction explicitly can be tedious (because of complexities at wall intersections) and also problematic, as the computational grid required in the wall may be much finer than that of the adjacent fluid region. This is an issue particularly in preliminary design applications where a coarse grid is most efficient. The disparity in grid length scale can dramatically increase solution times and negatively impact robustness, resulting in the need for a large overall cell count to achieve low-aspect-ratio cells. To avoid these liabilities, we introduce a compact (steady-state and transient) mathematical model that accounts for solar heat flux and three-dimensional heat transfer, and requires no physical grid cells in the thickness-direction of the wall. We validate the compact wall model's predictions against detailed numerical benchmarks and find that it accurately predicts both temporal and spatial temperature variations. The primary value of the model is that it can be built into application-specific CFD tools (e.g., for analyzing modular systems) so that wall heat transfer and thermal mass can be accurately modeled with minimum user effort or modeling skill.