# Choice of Turbulence Model

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# Choice of Turbulence Model

Posted May 3, 2023 at 14:13 by wa\$\$im
Updated May 3, 2023 at 16:23 by wa\$\$im
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Turbulence is a complex phenomenon that occurs in most engineering applications involving fluid dynamics. It is characterized by the irregular and chaotic motion of fluid particles, which can cause significant fluctuations in velocity and pressure. Until now, there has not been a single and practical turbulence model that can reliably predict all turbulent flows with sufficient accuracy. whereas many turbulence models have been developed from the perspective of finding different compromises between solution accuracy and computational cost. Going from DNS to RANS models, passing through DES, LES, and many others, the computational cost decreases significantly due to the cost of more and more flow averaging, which in some cases may lead to the loss of relatively important flow features.

In the following discussion, we will mainly focus on the use of RANS models since they are the most widely used approach for calculating industrial flows and can be found in most commercial CFD softwares (noting StarCCM+ and Fluent) and non-commercial CFD softwares (like OpenFOAM).

RANS stands for Reynolds-averaged Navier-Stokes equations. The main advantage of the method is its capacity to simulate complex geometries at a relatively low computational cost. This was possible due to the small number of degrees of freedom resulting from flow averaging. The three most popular turbulence models using the RANS approach are, to my knowledge :
• k-epsilon model
• k-omega model
• Spalart-Allmaras model

k-epsilon : The k-epsilon model is a two-equation model that solves for turbulent kinetic energy and dissipation rate. It is the most widely-used engineering turbulence model for industrial applications. It is robust, reasonably accurate, and contains submodels for compressibility, buoyancy, combustion, and many others. Its main limitations are that the epsilon equation contains a term which cannot be calculated at the wall (therefore, wall functions must be used), and that it generally performs poorly for flows with strong separation, large streamline curvature, and large pressure gradient. k-epsilon models are best suited to applications that contain complex recirculation, with or without heat transfer.

k-omega : The k-omega model is similar to the k-epsilon model in that two transport equations are solved, but differs in the choice of the second transported turbulence variable. Indeed, it solves for the specific dissipation rate in addition to the turbulent kinetic energy. The added value of this substitution is that the specific dissipation rate can be integrated at the wall, so there is no obligation of using wall functions. It is accurate and robust for a wide range of boundary layer flows with pressure gradient. It is, thus, best suited for aerospace and turbo-machinery applications.
An interesting variation of the standard k-omega model, is the k-omega SST, where SST stands for Shear Stress Transport. The k-omega SST contains a blending function to gradually transition from the standard k–ω model near the wall to a high Reynolds number version of the k–ε model in the outer portion of the boundary layer. In other terms, it uses the standard k-omega formulation in the inner parts of the boundary layer, and switches to a k-epsilon behaviour in the free-stream. This ensures that the appropriate model is utilized throughout the flow field. Although this model comes with many advantages, its main disadvantage is that it is harder to convegre compared to the standard models, and thus is more numerically expensive.

Spalart-Allmaras : The Spalart-Allmaras model is relatively new compared to the first two discussed models. It maily differs by being a single equation model that solves for a modified eddy viscosity. It is thus also relativaly less expensive, especially that the transport of the modified eddy viscosity is easy to resolve near the wall. It is best suited for aerospace and turbo-machinery applications where boundary layers are largely attached and separation is mild if it occurs. This is for example the cas of flows over airfoils or boundary-layers flows. The Spalart-Allmaras model is gaining in popularity, but faces some limitations since it is not suited for flows where complew recirculation occurs. It also usually over-predicts the boundary layer thickness which mainly deterior the accuray of heat transfer solution.

For more curious readers, i would suggest the following book, from which i would suggest reading the following book : Rodriguez, Sal. (2019). Applied Computational Fluid Dynamics and Turbulence Modeling: Practical Tools, Tips and Techniques. 10.1007/978-3-030-28691-0.

or watch the following video : RANS Turbulence Models: Which Should I Choose?

You can also dowload my open source calculator of initial values and boundary conditions of some of the most common turbulence models : github.com/wassim-abdelnour/Turbulence-Calculator

The following animation shows the velocity profile of an air flow over NACA 4415 airfloil, free-stream velocity is 1 m/s.