Turbulence Modeling of Battery Cooling Channels When Both Turbulent and Laminar Flow Co-exist

Battery cooling channels are typically very long, with predominantly laminar flow. However, disturbances and separation at the inlet and outlet areas can sometimes introduce turbulence. Thus the main question: which aspects of turbulence modeling should be taken in consideration when simulating battery cooling channels? Here are some general suggestions:

• Generally speaking, recommending a specific turbulence model that will work universally is not an easy task. All turbulence models in Simcenter STAR-CCM+ have been thoroughly validated, using as reference the material provided by the NASA Turbulence Modelling Resource.
• However, for each specific application it is important to conduct a model comparison study, especially when experimental data is available. The choice of turbulence model is hence always a compromise, and in many cases, the most important factor is consistency - such as the chosen model consistently behaves for the specific analysis
• Additionally, setting the correct boundary conditions is just as crucial as selecting the turbulence model, especially for low-Reynolds-number flows.

For this specific application, some considerations are presented on two families of models:

• The K-Epsilon models 

Almost all K-Epsilon models have extensions that allows a correct solution in the viscous sub-layer as well. In addition, all these models are combined with an “All-y+ wall-treatment” that allows the use of the model with any type of mesh. The wall-treatment itself detects what is the current wall-resolution and adapts the production and dissipation in order to recover the solution obtained on a low y+- mesh. Nevertheless, one recommendation is to avoid meshes with the first point in the buffer layer (i.e. 10<y+<30), where the models will always struggle to give consistent results. 

In recent years, a new class of K-Epsilon models has been introduced in Simcenter STAR-CCM+: these are based on the elliptic-relaxation assumption and are inherently superior for the prediction of the correct near-wall asymptotic behavior of the turbulence quantities. The most notable example is the Lag Elliptic-Blending K-Epsilon model, which is also combined with an All-y+ wall-treatment.

• The SST K-Omega model 

A model that can predict the viscous (laminar) sub-layer is not inherently capable of predicting a transition region or even a laminar region. The best example is the SST K-Omega: the model is able to predict the correct velocity profile, even in the viscous sub-layer, but it will always return a fully turbulent solution, also for laminar cases. This is due to the use of the Omega equation, which only works under the assumption of fully turbulent behavior (e.g., it is independent of the Turbulent Kinetic Energy (TKE), and the boundary condition for Omega assumes a fully turbulent boundary layer). This is why this class of models must be combined with a transition model (Gamma, Gamma-ReTheta) to correctly predict transitional behaviors. In contrast, the Lag Elliptic-Blending K-Epsilon model works for both laminar and turbulent flows, because the boundary condition for epsilon is a finite value that also depends on TKE. This means that in situations where TKE=0, ε = 0, a full laminar solution is obtained.

To summarize, the suggested models to be considered for a comparative analysis of battery cooling channels are

• Lag Elliptic-Blending K-Epsilon
• SST K-Omega + Transition model (Gamma or Gamma-ReTheta)