Turbulent flows are significantly affected by the presence of walls. Obviously,
the mean velocity field is affected through the no-slip condition that has to
be satisfied at the wall. However, the turbulence is also changed by the
presence of the wall in non-trivial ways. Very close to the wall, viscous
damping reduces the tangential velocity fluctuations, while kinematic blocking
reduces the normal fluctuations. Toward the outer part of the near-wall region,
however, the turbulence is rapidly augmented by the production of turbulence
kinetic energy due to the large gradients in mean velocity.
The near-wall modeling significantly impacts the fidelity of numerical solutions, inasmuch as walls are the main source of mean vorticity and turbulence. After all, it is in the near-wall region that the solution variables have large gradients, and the momentum and other scalar transports occur most vigorously. Therefore, accurate representation of the flow in the near-wall region determines successful predictions of wall-bounded turbulent flows.
The - models, the RSM, and the LES model are primarily valid for turbulent core flows (i.e., the flow in the regions somewhat far from walls). Consideration therefore needs to be given as to how to make these models suitable for wall-bounded flows. The Spalart-Allmaras and - models were designed to be applied throughout the boundary layer, provided that the near-wall mesh resolution is sufficient.
Numerous experiments have shown that the near-wall region can be largely subdivided into three layers. In the innermost layer, called the "viscous sublayer'', the flow is almost laminar, and the (molecular) viscosity plays a dominant role in momentum and heat or mass transfer. In the outer layer, called the fully-turbulent layer, turbulence plays a major role. Finally, there is an interim region between the viscous sublayer and the fully turbulent layer where the effects of molecular viscosity and turbulence are equally important. Figure 12.10.1 illustrates these subdivisions of the near-wall region, plotted in semi-log coordinates.
Wall Functions vs. Near-Wall Model
Traditionally, there are two approaches to modeling the near-wall region. In
one approach, the viscosity-affected inner region (viscous sublayer and buffer
layer) is not resolved. Instead, semi-empirical formulas called "wall
functions'' are used to bridge the viscosity-affected region between the wall
and the fully-turbulent region. The use of wall functions obviates the need to
modify the turbulence models to account for the presence of the wall.
In another approach, the turbulence models are modified to enable the viscosity-affected region to be resolved with a mesh all the way to the wall, including the viscous sublayer. For purposes of discussion, this will be termed the "near-wall modeling'' approach. These two approaches are depicted schematically in Figure 12.10.2.
Wall functions are a collection of semi-empirical formulas and functions that in effect "bridge'' or "link'' the solution variables at the near-wall cells and the corresponding quantities on the wall. The wall functions comprise