Session: 11-46-01: Methods and Algorithms in Computational Heat Transfer

Paper Number: 95217

95217 - A Reduced Three-Phase Model for Solidification of Liquid in Large Tanks 

Selective Catalytic Reduction (SCR) systems in diesel vehicles commonly reduce emissions of NOx by adding a water-urea solution to the exhaust gas. This solution is stored onboard in large plastic tanks and has a freezing point around -11°C. The solution therefore freezes in regions with sufficiently cold climates and expands during this process. This leads to a rise in pressure within the tank, which can damage both the tank and the components within. Mitigation strategies are developed to avoid such an occurrence. This requires an understanding of the long (spread over several hours to days) freezing process. Using traditional computational fluid dynamics and heat transfer (CFD/CHT) methods to simulate this slow freezing process results in extremely long simulation times due to the (contrastingly) small time step sizes required by natural convection time scales. This is also compounded by the large tank sizes involved. In our previous work, we proposed and validated a reduced natural convection model which models the heat transfer due to natural convection as a diffusive process. The primary advantage of this model was that it allowed the use of large time step sizes to greatly improve simulation times. While this model tracked the solid-liquid solidification front, it did not account for expansion of urea ice and the movement of the gas-(solid/liquid) interface.

As a continuation of the previous work, a new model is presented to track the gas-(solid/liquid) interface during freezing of partially filled tanks. Similar to the traditional volume-of-fluid method, the gas-(solid/liquid) interface is described by a scalar called volume fraction, representing the fraction of (solid+liquid) volume in each cell, The volume fraction is obtained by solving a conservation equation for excess volume created due to expansion. This conservation equation is derived from a diffusion model (analogous to the approach used for the energy equation), as opposed to an advection model.  It is assumed that the volume equilibrates instantaneously at each time step. Since the diffusive volume flux across cell faces is dependent on the gradient of the volume fractions themselves, sub time stepping is used to capture this behavior. Additionally, the solution to the volume transport equation is only calculated once every few time steps of the energy equation.

The volume transport equation was discretized using the unstructured Finite Volume Method (FVM) and then solved using a parallel Conjugate-Gradient Squared (CGS) solver implemented via User-Defined Functions (UDFs) in the commercial CFD software ANSYS-Fluent^TM. Freezing simulations using different liquids (water, urea solution) and fill levels (25%, 50% and 80%) were performed and results were validated against experimental data. Temperature data at several thermocouple locations was compared for each fill level and good agreement with experimental data was found in most cases, particularly for shallow fill levels.

Presenting Author: Shashank Terala Ohio State University

Presenting Author Biography: Graduate student.

Authors:

Shashank Terala Ohio State University
Sandip Mazumder Ohio State Univ
Gurpreet Matharu Ford Motor Company
Dhaval Vaishnav Ford Motor Company
Syed Ali Ford Motor Company