i*a £ e V - 14 
Ventilation Design Handbook on Animal Research Facilities Using Static Microisolators 
(5.8) 
So, if a fluid can have a laminar viscosity, fi, then a turbulent flow should have a turbulent or 
eddy viscosity, Ht. By using the eddy viscosity hypothesis that Boussinesq proposed, we can 
relate the Reynolds stress to the mean strain by: 
-pw'u' = \l T 
at/.. 
+ 
to,' 
dx, dx. 
-IP®,, 
(5.9) 
A zero-equation turbulence model simply sets a constant value of the eddy viscosity, or deduces 
it as an algebraic function of flow parameters. A one-equation model uses a differential equation 
to predict one part of the eddy viscosity while a two-equation model uses two differential 
equations. 
The main limitation imposed at this stage by equation 5.9 is that the eddy viscosity is the same in 
all directions at any point. Where this may be true of laminar viscosity, which is a property of the 
fluid, it may not be true of turbulent viscosity, which is effectively a property of the flow. 
Therefore, this eddy viscosity can have differing values in relation to differing Reynolds stresses. 
This occurs when the turbulence is said to be anisotropic. Conditions that may cause anisotropy, 
and thus could invalidate the isotropic assumption of equation 5.9, include extreme streamline 
curvature, swirl, adverse pressure gradients, and buoyancy. 
The two-equation approach including the standard k-e model and the RNG k-e model variant is 
presented first. Reynolds stress modeling is then discussed and, finally, the modeling of the 
Reynolds fluxes is briefly outlined. 
