Basic Fluid Mechanics and CFD

In this post i summarize the initial problem and the procedure to determine the wall function value (i.e., the solution) for given ,, and .

We looked for a solution to the problem:



with:

...

In the first part of this post we left with the problem of computing the following integral:



with:



I added all the explicit functional dependencies here because we know ...

In a previous post i wrote about an extension of the Reichardt law of the wall to pressure gradient effects. That was derived by assuming the Reichardt profile as a solution for the case without pressure gradient and using integration by parts. In particular, given the the Reichardt function ( is the Von Karman constant):



with:
...

I recently worked on wall functions, especially those based on simplified 1D numerical integration (e.g., http://link.springer.com/chapter/10....-642-14243-7_7) and i found a relatively simple, analytical, formulation that takes into account pressure gradient effects.

In practice, this is an extension of the Reichardt wall law to pressure gradient effects.

It is semi-analytical because it takes as assumption that the base Reichardt law is an exact solution of the...

y+ calculation is, possibly, the most pervasive topic among CFD practitioners and, certainly, anybody doing CFD for more than a month already has his own tool to compute it.

Still, all the y+ calculators i am aware of rely on a very specific flow condition, namely, a flat plate boundary layer. This is probably the most common practical case but not the only option. For example, the fully developed flow in a pipe is cretainly different and possibly requires a different input for the...