15.18. Providing an Initial Guess for k and ε (or k and ω)

For flows using one of the - models, one of the - models, or the RSM, the converged solutions or (for unsteady calculations) the solutions after a sufficiently long time has elapsed should be independent of the initial values for and (or and ). For better convergence, however, it is beneficial to use a reasonable initial guess for and (or and ).

In general, it is recommended that you start from a suitable state of turbulence. When using a -insensitive wall treatment, it is critically important to specify suitable turbulence fields. Guidelines are provided below:

  • If you were able to specify reasonable boundary conditions at the inlet, it may be a good idea to compute the initial values for and (or and ) in the whole domain from these boundary values. See Initializing the Solution for details.

  • For more complex flows (for example, flows with multiple inlets with different conditions) it may be better to specify the initial values in terms of Turbulent Intensity and Turbulent Viscosity Ratio, which can both be specified at the inlet(s). For Turbulent Intensity, , typical values lie in the range of 1-10%. For Turbulent Viscosity Ratio, typical values lie in the range of 1-100.

    • The value of can then be computed from the Turbulent Intensity and the characteristic mean velocity magnitude of your problem (note that in the following calculation for , must be given as a fraction):

      (15–6)

    • You should specify an initial guess for so that the resulting eddy viscosity () is sufficiently large in comparison to the molecular viscosity. Suitable levels of turbulent viscosity are typically in the range of 1-100 times larger than the molecular viscosity. From this, you can compute :

      (15–7)

      where is the Turbulent Viscosity Ratio which can be prescribed at the inlet and then used for the domain initialization.

    • Similarly, for the specific dissipation rate, :

      (15–8)

    Note that, for the RSM, Reynolds stresses are initialized automatically using Equation 15–4 and Equation 15–5.