IV.3 The k - model
The standard model used for turbulence is to solve additional transport equations for k and .
These equations relate transport of k (or ) to diffusion (2 term) and net production terms.
Production and Removal terms actually very similar between the two equations - regions of
high k are also regions of high dissipation of k, i.e. of high . The model includes 5
adjustable constants (C = 0.09 is one) - values for which have been derived by
fitting the model for a range of flows, and are taken to be(more or less) universal
constants.
Having solved these equations to find k and , and thus found a value of t, we are now in a
position to close the Reynolds equations. The eddy viscosity concept is usually taken to
mean
We are now solving for 3 scalars (p, k, ) and the 3 components of mean velocity . We have 6
equations in all, so we can find solutions to this problem.