The simplest "complete models'' of turbulence are two-equation models in which
the solution of two separate transport equations allows the turbulent velocity
and length scales to be independently determined. The standard
FLUENT falls within this class of turbulence model and has become the
workhorse of practical engineering flow calculations in the time since it was
proposed by Launder and Spalding [
196]. Robustness, economy, and
reasonable accuracy for a wide range of turbulent flows explain its popularity
in industrial flow and heat transfer simulations. It is a semi-empirical model,
and the derivation of the model equations relies on phenomenological
considerations and empiricism.
As the strengths and weaknesses of the standard - model have become known, improvements have been made to the model to improve its performance. Two of these variants are available in FLUENT: the RNG - model [ 408] and the realizable - model [ 330].
The standard - model [ 196] is a semi-empirical model based on model transport equations for the turbulence kinetic energy ( ) and its dissipation rate ( ). The model transport equation for is derived from the exact equation, while the model transport equation for was obtained using physical reasoning and bears little resemblance to its mathematically exact counterpart.
In the derivation of the - model, the assumption is that the flow is fully turbulent, and the effects of molecular viscosity are negligible. The standard - model is therefore valid only for fully turbulent flows.
Transport Equations for the Standard - Model
The turbulence kinetic energy,
, and its rate of dissipation,
obtained from the following transport equations:
Modeling the Turbulent Viscosity
The turbulent (or eddy) viscosity
, is computed by combining
The model constants
have the following default values [