[RabiArya]

What fluid properties are responsible for the K-€ model to be not convincing near the wall and which properties support or play a major role in K-W model being superior near wall and inferior away from wall. Please explain me this in terms of physical properties and their importances. Thank you.

[aero_head]

The k-ω model is a two-equation model that solves transport equations for turbulent kinetic energy and the specific dissipation rate (ω), which is the turbulent dissipation rate (ε), per unit turbulent kinetic energy. It belongs to the Reynolds-averaged Navier-Stokes (RANS) family of turbulence models where all the effects of turbulence are modeled.

It is a two-equation model. That means in addition to the conservation equations, it solves two transport equations (PDEs), which account for the history effects like convection and diffusion of turbulent energy. The two transported variables are turbulent kinetic energy (k), which determines the energy in turbulence, and specific turbulent dissipation rate (ω), which determines the rate of dissipation per unit turbulent kinetic energy. ω is also referred to as the scale of turbulence.

The standard k−ω model is a low Re model, i.e., it can be used for flows with low Reynolds number where the boundary layer is relatively thick and the viscous sublayer can be resolved.

Thus, the standard k−ω model is best used for near-wall treatment. Other advantages include a superior performance for complex boundary layer flows under adverse pressure gradients and separations (e.g., external aerodynamics and turbomachinery). On the contrary, this model has also shown to predict excessive and early separations.

SST stands for shear stress transport. The SST formulation switches to a k−ϵ behavior in the free-stream, which avoids the k−ω problem of being sensitive to the inlet free-stream turbulence properties.

The k−ω SST model provides a better prediction of flow separation than most RANS models and also accounts for its good behavior in adverse pressure gradients. It has the ability to account for the transport of the principal shear stress in adverse pressure gradient boundary layers. It is the most commonly used model in the industry given its high accuracy to expense ratio.

On the negative side, the SST model produces some large turbulence levels in regions with large normal strain, like stagnation regions and regions with strong acceleration. This effect is much less pronounced than with a normal k-epsilon model though.


The k-epsilon (k−ϵ) model for turbulence is the most common to simulate the mean flow characteristics for turbulent flow conditions. It belongs to the Reynolds-averaged Navier Stokes (RANS) family of turbulence models where all the effects of turbulence are modeled.

It is a two-equation model. That means that in addition to the conservation equations, it solves two transport equations (PDEs), which account for the history effects like convection and diffusion of turbulent energy. The two transported variables are turbulent kinetic energy (k), which determines the energy in turbulence, and turbulent dissipation rate (ϵ), which determines the rate of dissipation of turbulent kinetic energy.

The k−ϵ model is shown to be reliable for free-shear flows, such as the ones with relatively small pressure gradients, but might not be the best model for problems involving adverse pressure gradients, large separations, and complex flows with strong curvatures.


Now that we have discussed the above, we can rationalize that the k-omega model is best suited for near-wall flow region, due to the adverse pressure gradient developed there. Remember that the near-wall region of wall-bounded flows pose significant difficulties in turbulent flows. Since these regions involve steep gradients in velocity and temperature, the accurate treatment of this region is of utmost importance. The two main approaches to treat the near-wall regions are wall functions and wall-resolved methods.

[ghorrocks]

While aero_head's description is good and covers many applications, he is too general when he says "k-w model is best used for near-wall treatment". A more general description would be to say k-w can be integrated to the wall, whereas k-e requires wall functions for most applications. Now whether integrating to the wall is beneficial depends on what you are trying to do and what computing resources you have available to you.

This is just a quick view into why turbulence modelling is an extremely complex and not fully understood aspect of physics.

[RabiArya]

Thank you so much to both of you. It means a lot. I have got one more confusion which is actually what I am trying to find out. Why does the K-E model perform bad in adverse pressure gradient or high curvature zones unlike k-w model?

[ghorrocks]

Your statement is too general as well. In many applications with adverse pressure gradients, k-e leads to excessive turbulence generation and therefore too high turbulent viscosity. This tends to stabilise the flow, keep it attached too long and delay separations - but not always

And neither the k-e or k-w work well in high streamline curvature cases. The curvature correction model on the SST model in CFX helps in some cases, but in high streamline curvature cases you should be considering Reynold Stress models or LES approaches. But nothing is universal, it all depends on the application.