Question

Let Cμ be a dimensionless constant and ρ be the density of the flow. Express the eddy dynamic viscosity in terms of k and ε.

(a) ρCμk^2/ε

(b) ρCμ k/ε

(c) ρCμ ε/k

(d) ρCμ ε^2/k

I have been asked this question in final exam.

The origin of the question is Turbulence Modelling topic in portion Turbulence Modelling of Computational Fluid Dynamics

Answer 1

The correct option is (a) ρCμk^2/ε

Explanation: Using dimensional analysis, the turbulent dynamic viscosity can be given as

μt = Cμ ρϑl

Where,

ϑ → Velocity scale of large eddies

l → Length scale of large eddies

Substituting these two in k and ε terms, we get

μt = Cμ ρ\(\frac{k^2}{\varepsilon}\)

Where, Cμ is a dimensionless constant which is adjustable. The standard k-ε model uses Cμ=0.09.