Law of the Wall in Free-Surface Flows
 

Hi Dear Friends. To me, here is a difficult problem.

Let us consider an impinging jet onto a flat plate, in high Reynolds number. In this case, the fluid spread out in a thin layer on the plate. In general, in order to apply the log-law, we need of the parallel velocity in EMPTY cells just above of the first cell in the inner-layer. Also, in order to conserve the momentum, we need to discretize the transport equation for the velocity in the constant-stress layer, but in EMPTY cells we not apply the Reynolds-averaged Navier-Stokes equations. So, I have two questions: a) If you use a uniform grid to simulate this free-surface problem, how to use the law of the wall? b) How we determine the ghost value for the velocity?

Thank you very much. Valdemir.

Re: Law of the Wall in Free-Surface Flows
 

(1).First of all, you can read the previously posted messages related to the use of the wall function, through the search key in this forum. (2). I can only give you a brief description once again here. (3). In the region where you are trying to solve numerically, you must use a turbulence model which can reproduce the law of the wall log-profile solution. (4). Since the law of the wall log-profile is valid (or has been shown experimentally) for boundary layer flows with small adverse pressure gradient (including favorable pressure gradient) over a large portion of the boundary layer, this commonly valid region can be served as the matching region for the numerical solution and the analytical log-law profile wall function. This is the key to the use of the wall function. (5). The analytical wall function has one unknown, the skin friction coefficient.(or the wall shear stress) Once the skin friction is known, the velocity can be calculated from the law of the wall with the matching point location measured from the wall. The velocity calculated can then be used in the numerical solution as a boundary condition. From the numerical solution, you can evaluate the shear stress at the boundary, which is taken as a constant throughout the law of the wall region. Therefore, it is the same as the wall shear stress or the skin friction, this numerically updated skin friction can be used to update the velocity at the matching point again, until the process converges. (6). The actual implementation of this matching process varies depending on the school of thought, the problem formulation, etc.. It also routinely involves the turbulence quantity such as TKE (k) at the matching point. (7). The wall function approach has nothing to do with free-surface issue at all.

Re: Law of the Wall in Free-Surface Flows
 

Hi Dr. John. Thanks for your considerations. I completely agree with you. But, your comments are only valid in the context of confined flows. Valdemir.

Re: Law of the Wall in Free-Surface Flows
 

(1). I guess, we are probably talking about two different things. (2). Sorry, anyone wishes to comment on this problem please continue.

Re: Law of the Wall in Free-Surface Flows
 

Are you using Fluent? If yes I cant help. If no I will try.

Gs

Re: Law of the Wall in Free-Surface Flows
 

No I am not. I am using the SMAC method.