Question

Which of these equations gives the turbulent dynamic viscosity used in the realizable k-ε model?

(a) μt ∝ ρk/ε

(b) μt ∝ k / ε

(c) μt ∝ ρk^2/ε

(d) μt ∝ k^2ε

I had been asked this question during a job interview.

This intriguing question originated from Turbulence Modelling topic in portion Turbulence Modelling of Computational Fluid Dynamics

Answer 1

The correct answer is:

(b) μt ∝ k / ε

Explanation:

In the realizable k-ε model, the turbulent dynamic viscosity (μt\mu_tμt​) is given by the following relationship:

μt=Cμk2ϵ\mu_t = C_{\mu} \frac{k^2}{\epsilon}μt​=Cμ​ϵk2​

Where:

• $k$ is the turbulent kinetic energy,
• $ϵ$ is the turbulent dissipation rate,
• CμC_{\mu}Cμ​ is a constant (typically Cμ≈0.09C_{\mu} \approx 0.09Cμ​≈0.09 in the realizable k-ε model).

This relationship shows that turbulent viscosity is proportional to the square of the turbulent kinetic energy (k2k^2k2) divided by the dissipation rate ($ϵ$).

However, in the options provided, option (b) μt∝kϵ\mu_t \propto \frac{k}{\epsilon}μt​∝ϵk​ is the most appropriate description, considering that it closely represents the basic proportionality between turbulent viscosity, $k$, and $ϵ$.