[pavlossemelides]

I've been reading up on wall functions in turbulent CFD and all explanations I've seen state, in one way or another, that wall-functions are needed to rectify the near-wall flow behavior when our y+ lies outside the laminar sublayer. My question is: can I run a simulation without using wall functions and with a y+ outside the laminar sublayer if I don't care about near-wall flow behavior? Let's say that I just care about the velocity and pressure profiles in the main flow (outside the boundary layer). Thanks in advance.

[sbaffini]

Nope, you indeed need to use wall functions when you don't care for the near wall behavior (yet you expect it to kind of obey to the wall function prescription) in order for the wall error to not pollute the main flow.

To see why, consider that when you have wall functions your wall stress can be balanced with a velocity profile that is nearly flat, almost inviscid for very high Re. A regular no slip bc would inevitably force the near wall velocity profile to linearly go to 0. The result would be an artificially enlarged boundary layer and a much larger bulk velocity to preserve the mass flow.

[pavlossemelides]

Thanks for your reply. So just to see if I interpret the following statement correctly

Originally Posted by sbaffini

To see why, consider that when you have wall functions your wall stress can be balanced with a velocity profile that is nearly flat, almost inviscid for very high Re.

A wall function imposes a large velocity gradient at the wall (as expected in turbulent flow), whereas if there was no wall function the arising CFD solution would give a much smaller velocity gradient at the wall resulting in a much larger boundary layer? Would the boundary layer with no wall functions be akin to a laminar one?

[sbaffini]

Yes, but I would not use the term "impose". A more correct one is "sustain".

You have to think of wall functions as just more elaborate interpolations than the simple linear one used in general. Now, for a given velocity at a given distance, a wall function interpolation to the wall is such that, for turbulent cases, will give a much larger wall derivative than the corresponding linear interpolation. That is, the wall function interpolation for turbulent cases is always more flat toward the wall than the laminar one.

The result of this difference is that, if the wall function interpolation was the correct one, the smaller wall derivative of the linear interpolation will give a smaller stress, and the flow will accelerate to reach a larger velocity that will give the correct stress.

It is in this sense that wall functions can sustain larger velocity gradients at wall. However, a solution obtained with a wall function, especially at large Re, won't show you any gradient in the solved velocity field. Actually, your solution will resemble an inviscid one, as indeed the nearest velocity to the wall can be much larger than with linear interpolation.

Of course, if the hypotheses underlying the wall function are not fullfilled, the wall function interpolation is just wrong as well, but typically still better than nothing.

[piu58]

Wall functions realize the effect that the fluid gets more viscose near the walls. This drags the flow. Without wall funktions the flow would have a much too large velocity in the near of walls, and therewith in the free stream too.