Water-urea mixtures are used in diesel vehicles for exhaust aftertreatment. The liquid mixture, stored in a tank, is susceptible to freezing in cold weather. Depending on weather conditions, the tank size and the liquid fill level, the freezing of the entire liquid may span over a day. Mitigation strategies require understanding of the freezing history. 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 time-scale considerations. The primary constraint for using small time-step sizes is the fine-scale motion generated by natural convection in both the liquid and the gas (unoccupied space). 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 and a gradient diffusion model. The model enables use of large time-steps since the fine-scale motions due to natural convection are no longer resolved. The model was validated against experimental data, which were also collected as part of the study. Each experiment collected data at intervals of 6 seconds for a total duration of about 24 hours. Several different tank fill levels were considered, and good agreement with experimental data was noted, especially for shallow fill levels. Large-scale parallel three-dimensional calculations were conducted in a few days of computational time using the proposed model as opposed to a year (projected) of computational time using traditional CFD/CHT models and the same computational resources.

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