7.2 Initialisation of the k-epsilon model

Initial values and boundary conditions must be specified for eqn and to solve their respective transport equations. The ideal specification of boundary conditions for eqn and follows those for eqn described in Sec. 4.3 .

PICT\relax \special {t4ht=

Turbulence fields require: a fixed value condition at inlets; zero gradient or inlet-outlet at outlets; and, a more complex specification at solid walls, introduced in Sec. 7.7 .

Inlet values eqn and must therefore be specified. There may be industry standards, published recommendations or measured data to help select these values for the specific problem being simulated.

But more often than not, eqn and must be estimated. Inlet and initial estimates of are usually based on a Prandtl mixing length eqn from the expression

This relation can be derived by considering a planar boundary layer. In the “log law” region (see Sec. 7.7 ) which can be combined with the mixing length Eq. (6.21 ) to give
Substituting eqn from Eq. (6.31 ) yields Eq. (7.4).

A value for eqn must then be specified in order to calculate inlet and initial values of from Eq. (7.4 ). Procedures to estimate eqn are described in Sec. 7.3 .

Inlet and initial estimates for eqn can be calculated by

kin = 3-(jujI)2; 2 \relax \special {t4ht=
from a specified turbulent intensity eqn, the ratio of the root-mean-square (RMS) of turbulent fluctuations eqn to the mean flow speed eqn. The expression is derived from the definition eqn .

A value for eqn must then be specified in order to calculate the inlet and initial values of eqn from Eq. (7.6 ). Procedures to estimate eqn are also described in Sec. 7.3 . The values of eqn and at inlet boundaries influence the solution throughout the CFD simulation, so should be estimated as accurately as possible.

The accuracy of the initial (internal) values is not so critical, since they do not influence the solution beyond a short period at the beginning of a simulation.

Initial values can, however, affect stability during the early steps of a CFD simulation. The flow boundary conditions generally cause sudden impulses which can generate large forces, causing fluctuations in the solution of eqn. Higher eqn, based on initial eqn and values, tends to cause larger fluctuations, which may make the solution of the eqn-equation unstable.

Notes on CFD: General Principles - 7.2 Initialisation of the k-epsilon model