help with wall functions

Nick Georgiadis

I am trying to use the wall-function approach of Ota and Goldberg, in which none of the flow variables are reset, and in fact, a no-slip surface is used. The essence of the model is that you use a law of the wall (they propose using the White-Cristoph compressible law of the wall) to solve for the wall shear stress, and then simply use this shear stress in the solution scheme. Any turbulence model (even an algebraic model like I am using, Cebeci-Smith) may then be employed with this method.

My questions to anyone familiar with this (or a similar) approach is:

(1) When solving the law of the wall expression, the iterated quatity is friction velocity. This quantity is then squared and multiplied by the density to get the wall shear stress. How can this (especially through the squaring process) be expected to get an accurate wall shear stress?

(2) Apart from solving for the wall shear stress, the (solved) shear stress throughout the rest of the bdy. layer should be constant, particularly near the wall. Can this happen in practice when using such a wall function? especially with a higher order scheme that would use the flow variables at the wall point and one off the wall?

This wall function approach has been used with success by several authors, so I am sure my doubts are due to my ignornace on the topic. As a result, any explanations to my 2 questions will be very appreciated.