A mixture of 32.5% urea and water, commercially known as AdBlue®, is conventionally used for Selective Catalytic Reduction (SCR) of NOx in diesel vehicles. AdBlue® freezes under cold winter conditions (below −11°C or 12°F). Complete freezing is detrimental to the tank in which it is stored, and exact knowledge of the freezing front (solid-liquid interface) propagation is key to mitigating complete freezing. However, modeling the solidification/melting process in the tank is made complicated by the fact that three phases have to be accounted for: gas (air), liquid (water) and solid (ice). Moreover, the effects of natural convection are important and cannot be neglected. Numerical constraints in modeling natural convection necessitate the use of very small time-step sizes, making full-blown Computational Fluid Dynamics (CFD) calculations of the freezing process computationally expensive, especially when the physical time scales of the problem are of several days. This thesis has two objectives: (1) to perform a CFD study of the freezing process in a partially-filled tank using the in-built modeling capabilities of the commercial CFD code ANSYS Fluent™ in order to establish the limits of such models and, (2) to develop and validate a computationally efficient reduced model for freeze/thaw.
The thesis begins with a systematic study to investigate the capabilities of the in-built physical models of Fluent pertaining to freezing/thawing, particularly with respect to computational efficiency. A canonical three-phase system was modeled using the Volume Of Fluid (VOF) method coupled with the solidification sub-model of Fluent. Results indicated that though Fluent was successfully able to capture the physical effects of solidification, extremely small time-step sizes (as low as 5×10-4 seconds) were needed to model the solidification process. This study successfully established the limits of Fluent’s in-built models to model freeze/thaw in actual tanks for SCR applications.
Following this preliminary CFD study, the development and validation of a reduced model for freeze/thaw was carried out. While the proposed model does not explicitly track the air-water interface, it offers a computationally efficient way of simulating the freezing process inside the tank. The model solves only for heat conduction in the system, while accounting for the effects of natural convection by enhancing the conductive heat fluxes using appropriate physical laws governing natural convection. Effects of solidification are accounted for by using a volumetric source term in the energy equation proportional to the latent heat of the solidifying phase. The reduced model was calibrated by matching temperature versus time data at various points inside the tank to experimentally measured temperature-time data for the freezing of a partially-filled tank of water. Following this, validation studies were carried out using combinations of three different fill levels—25%, 50% and 80% fill levels and two working liquids: water and AdBlue®. Results indicated good agreement with the experimental data, with correct predictions of the movement of the solid-liquid interface (solidification front) inside the tank. Wall-clock times for all simulations were found to be between 2-6 days, as compared to estimates of twelve months for full-blown CFD calculations.
Key contributions of this thesis include developing the mathematical models of the effects of solidification and natural convection in the reduced model, and implementing the reduced model into code using the various User-Defined Function (UDF) capabilities of ANSYS Fluent™.