In the k- ε model and its variants, two turbulence-specific quantities are used: turbulent kinetic energy and turbulent dissipation. Turbulent kinetic energy is defined using the three turbulence intensities Ix,Iy, and Iz as follows:
With the ratios from section B2.1.2, the factor α depends solely on the longitudinal turbulence intensity:
Turbulent dissipation correlates with an integral length scale Lt, turbulent energy k, and a constant Cμ :
Some implementations use the mixing length Lt-mix instead of the integral length scale. In applying the k-ε model to atmospheric flows, turbulent viscosity is typically limited to a maximum of κ⋅z (Karman constant κ=0.41 and height z ) to avoid unrealistically high values of turbulent viscosity. The characteristic vortex with a horizontal axis should not exceed twice the distance to the ground.
The k-ε model is one of the most commonly used methods in flow simulation due to its numerical stability and the ability to use relatively large cells near walls. Despite its popularity, it has known weaknesses that can often be mitigated by modifications:
- Stagnation Point Problem:
The model tends to overestimate turbulent kinetic energy and pressure at stagnation points, which can affect simulations of separations at leading edges. Improved variants, such as the RNG model, the "realizable k-ε" model, or the MMK model, address this issue.
- Rotating Flows:
The standard model shows weaknesses in accuracy when simulating rotating flows.
- Near-Wall Resolution:
Limited resolution near walls requires using wall laws to bridge the viscous sublayer. However, this method can be inadequate in cases of separation, especially if tangential pressure gradients are not considered.