Volume I - Section V - CFD Methodology 
Page V - 17 
This model has been tried and tested for a whole range of engineering applications. It is simple, 
but more importantly, it is stable. Only two extra differential equations are introduced. The 
convergence process is less prone to divergence than other, higher order turbulence models. This 
approach has been adopted for the present research. 
5.22.2 Re-normalized group theory (RNG) ke turbulence model 
Essentially, this model has much the same form as the standard model. It is part empirical and 
part analytical. The only changes are a modified term relating to the production of energy 
dissipation in the £ equation and a different set of model constants. This RNG model is typical of 
those offered by some commercial, general purpose CFD codes. The new equations for k and £ 
become: 
dpU t k 
d ( 
dx t 
dx , , 
M + 
Pr 
dk 
'k 7 
dx, 
i 
dpU ,£ _ d 
dx, dx. 
(( 
p + 
p T 
' de ^ 
e 
dx, 
‘ 7 
The new function Cirng is given 
+ P + G- pe 
+ (C,-C, RNO )f(P + C 3 G)-C 2 pf- 
k k 
by the equations: 
C 
1RNG 
{<-%.) 
(l + /fr? 3 ) 
and: 
(5.15) 
(5.16) 
(5.17) 
(5.18) 
In this case rjo and P are additional model constants. The latter should not be confused with the 
coefficient of thermal expansion. The main modification is to the £ equation, where the rate of 
strain of the flow has been incorporated into the model constants. Under conditions of extreme 
strain, the eddy viscosity is reduced. It is this feature of the RNG model that is said to 
accommodate strong anisotropy in regions of large shear, i.e., the treatment of massive 
separation and anisotropic large-scale eddies. Most validation of this model has been only under 
extremely high strain conditions, such as internal flow in a 180° bend and flow within a 
contracting-expanding duct. Accurate prediction of separation regions seems to be the grail of the 
