Volume I - Section V - CFD Methodology 
Page V ° 19 
5.2.3. Near Wall Treatment 
Fluid velocity at a wall surface is zero, which is known as the no-slip condition. The type of flow 
between the wall and the bulk flow is known as a shear layer, in this case, a wall boundary layer. 
The boundary layer is a very complex region of high velocity gradient and diffusion dominated 
development. To model it precisely would necessitate an extremely fine grid. An empirical 
relationship is therefore used to describe the shape of the boundary layer so that only one grid 
cell near the wall is required. This empirical relationship describes the shape of the boundary 
layer in nondimensional terms. Two nondimensional terms are formulated. These are the friction 
velocity: 
f T V /2 
" Li 
u x = 
\ p 
(5.21) 
and a nondimensionalized distance from the wall (which can be viewed as a local Reynolds 
number): 
+ = P 
These formulae are based upon the established ‘universal’ relationships: 
u 1 
For y + > 1 1.5 (turbulent): 
u x 0.435 
In (V) 
(5.22) 
(5.23) 
For y + < 1 1.5 (laminar): — = y + (5.24) 
u x 
All that is required to deduce the wall shear stress from the near wall velocity is therefore the 
distance from the near wall cell center to the wall itself. 
5.2.4 Treatment of Contaminant 
A contaminant that is both advected and diffused by the fluid in which it is suspended can be 
modeled via the introduction of an additional transport equation. This concentration variable, C, 
has the units of kg of species/kg of fluid, and obeys the time averaged equation of the 
conservation of concentration flux such that: 
