Shall I go for ‘Low-Reynolds-Number Models’ or ‘Wall Functions’?

One challenge in any CFD simulation is how to treat the thin near-wall sublayer, where viscous effects become important.

• In flows with heat transfer, an accurate resolution of this layer can be crucial because most of the temperature change occurs across it.

• The most reliable way is to use a fine grid and a low-Re-number model.

• This can be very expensive, particularly in 3D.

• Slow convergence can also be a problem – as a result of model source terms and high aspect ratio cells.

• An alternative method used to deal with the wall effects is based on so-called ‘wall functions’. The idea of the wall function approach is to apply boundary conditions (based on the log-law[1]) some distance away from the wall, thus eliminating the need to have a fine mesh all the way down to the wall. This approach is used in conjunction with a high-Reynolds-number turbulence model. Some of the usual assumptions of a conventional wall function approach are:

- The first near-wall grid node is located far enough from the wall (at a distance yp) to ensure that the first cell is placed in the inner region of the boundary layer. The first near-wall cell should usually be at y+ ≥ 30, where y+ is a dimensionless wall distance, defined as:

- The flow over this region is assumed to obey the inner law of the wall (i.e. log-law).

[1] In fluid dynamics, the law of the wall states that the average velocity of a turbulent flow at a certain point is proportional to the logarithm of the distance from that point to the "wall", or the boundary of the fluid region.