CFD Online Discussion Forums - Low Reynolds k-epsilon model

I had the same questions and the learning curve is rather steep. There is a lot to sort through and understand the numerous tubulence models without taking a turbulence course or being given the time to extensively read the turbulence books.

I've assimilated a lot of information over the last several months and the following are excerpts about the standard k-epsilon and k-omega models.

* Standard k-e
The baseline two-transport-equation model solving for kinetic energy k and turbulent dissipation ε. Turbulent dissipation is the rate at which velocity fluctuations dissipate. This is the default k–ε model. Coefficients are empirically derived; valid for fully turbulent flows only. In the standard k-e model, the eddy viscosity is determined from a single turbulence length scale, so the calculated turbulent diffusion is that which occurs only at the specified scale, whereas in reality all scales of motion will contribute to the turbulent diffusion. The k-e model uses the gradient diffusion hypothesis to relate the Reynolds stresses to the mean velocity gradients and the turbulent viscosity. Performs poorly for complex flows involving severe pressure gradient, separation, strong streamline curvature. The most disturbing weakness is lack of sensitivity to adverse pressure gradients; another shortcoming is numerical stiffness when equations are integrated through the viscous sublayer which are treated with damping functions that have stability issues [F. R. Menter, “Zonal Two Equation k-w Turbulence Models for Aerodynamic Flows,” AIAA Paper #93-2906, 24th Fluid Dynamics Conference, July 1993; F. R. Menter, “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA Journal, vol. 32, no. 8, pp. 1598-1605, 1994]. {Notes: The author’s self-investigation for flow through a pipe is consistent with the statements that this model is valid for flows without separation and for fully turbulent flow. Compared to a finned problem which had separation and which predicted erroneous results with the k-e model, this pipe flow did not have separation and results of k-e and k-w models showed good agreement for high Reynolds numbers. In this pipe flow, as Reynolds number was decreased, the difference between the inlet pressures predicted by the k-e and k-w models increased. Note that, based on the author’s limited experience, results for temperature are less sensitive to model choice and for velocity seem indifferent. Pressure results seem highly sensitive to both the model choice and the mesh. Be careful to check all results before deciding that results are valid. For additional details, see section entitled “Comparison of k-e and k-w Models.”}

* Standard k-w
A two-transport-equation model solving for kinetic energy k and turbulent frequency ω. This is the default k–ω model. This model allows for a more accurate near wall treatment with an automatic switch from a wall function to a low-Reynolds number formulation based on grid spacing. Demonstrates superior performance for wall-bounded and low Reynolds number flows. Shows potential for predicting transition. Options account for transitional, free shear, and compressible flows. The k-e model uses the gradient diffusion hypothesis to relate the Reynolds stresses to the mean velocity gradients and the turbulent viscosity. Solves one equation for turbulent kinetic energy k and a second equation for the specific turbulent dissipation rate (or turbulent frequency) w. This model performs significantly better under adverse pressure gradient conditions. The model does not employ damping functions and has straightforward Dirichlet boundary conditions, which leads to significant advantages in numerical stability. This model underpredicts the amount of separation for severe adverse pressure gradient flows.

About the low-Re k-epsilon formulation, CFX has developed an approach to avoid the problems associated with the low-Re formulation. CFX uses Scalable Wall Functions which avoids the problems associated with the lower valid limit for y+. This approach uses wall functions, ignoring the near-wall mesh if y+ drops below 11.

I would actually recommend the SST model, largely based on the following advice from an ANSYS engineer
Most flows have some laminar regions. The transition to turbulence can happen very rapidly and, in many cases, effects of transition are insignificant. In many cases, the issue is whether the laminar region is significant. There are a couple of possible approaches:
• Always run SST with the turbulence transition model and conduct a turbulence model sensitivity study, which would mean run the same case with k-epsilon, SST, and SST with transition. This will give a feel for which turbulence model gives the best results for the least amount of computational overhead and then apply that to future studies.
• Practically speaking, the vast majority of users today simply start with SST. If results are not good, then try SST with transition enabled. If transition is enabled, the recommended transition model for general-purpose applications is the Gamma Theta Model. This model has been extensively validated with the SST turbulence model for a wide range of transitional flows.

For information about y+, the following link may be useful
http://www.cfd-online.com/Forums/cfx...tml#post253330

Please feel free to look at other posts listed below
http://www.cfd-online.com/Forums/mai...tml#post256730
http://www.cfd-online.com/Forums/flu...ce-models.html

I hope this helps. Good luck!