Abstract
Liquid water–urea mixtures are used in diesel vehicles for exhaust after treatment. In cold weather, the entire liquid may freeze and the process may span over a day. Traditional computational fluid dynamics and heat transfer (CFD/CHT) methodologies are impractical for modeling such freezing processes because of restrictions in the time-step size—typically milliseconds—posed by numerical stability and physical timescale considerations. Preliminary investigations revealed that the primary constraint for using small time-steps is the fine-scale motion generated by natural convection in both the liquid and the gas. A new model is proposed and demonstrated for efficient prediction of the propagation of the solidification front. In this model, heat transfer due to natural convection is modeled as a diffusive process analogous to how turbulent transport is modeled using an eddy diffusivity. The model enables the use of large time-steps since the fine-scale motions due to natural convection are not resolved. It was validated against experimental data for pure water, which were also collected as part of the study. Each experiment collected data at intervals of 6 s for a total duration of about 24 h. Several different tank fill levels were considered, and a good agreement with experimental data was noted, especially for shallow fill levels. Large-scale parallel three-dimensional calculations were conducted for the freezing of pure water in a few days of computational time as opposed to a year (projected) of computational time using traditional CFD/CHT models and the same computational resources.
