[bumper]

Hello everybody,


i'm trying to understand the usage of the near wall treatment. It is clear that the values of velocity are changing fast in ther near of the wall, so there is a special way to handle this region. Let's take the k-epsilon model for example. With the help of the model, you calculate the turbulent viscosity and than you can solve the reynolds stress tensor and the governing equations. Now i want to solve the problem near a wall, so i need a special behaviour. There is the logarithmic law as you can see in the attached picture. Which value is calculating with the help of this law? Is it the velocity u? At which step takes the equation place ? In the free stream, i understand the way of calculation (as described above), but how is it at near wall treatment. I hope i described my problem in a good way. I have already read the documentation, but I didn't get through it.



Thank for your help,


bumper

[Seps]

Hi there bumper,
Check this video out, he explains it pretty well:
https://www.youtube.com/watch?v=fJDYtEGMgzs

[Far]

Part 1 : General Discussion

Originally Posted by bumper

Hello everybody,


i'm trying to understand the usage of the near wall treatment. It is clear that the values of velocity are changing fast in ther near of the wall, so there is a special way to handle this region. Let's take the k-epsilon model for example. With the help of the model, you calculate the turbulent viscosity and than you can solve the reynolds stress tensor and the governing equations. Now i want to solve the problem near a wall, so i need a special behaviour. There is the logarithmic law as you can see in the attached picture. Which value is calculating with the help of this law? Is it the velocity u? At which step takes the equation place ? In the free stream, i understand the way of calculation (as described above), but how is it at near wall treatment. I hope i described my problem in a good way. I have already read the documentation, but I didn't get through it.



Thank for your help,


bumper

There are three things : Reynolds Averaged Navier Stokes Equations aka RANS, Stress tensor and Turbulent viscosity.


In RANS you have average or mean velocity terms in every part of it. Also it contains the combination of laminar and turbulent viscosity term shear stress part of RANS. So your goal is to calculate the turbulent viscosity.

Here comes the role of turbulence modeling. Turbulence modeling is used to solve the six unknowns (fluctuations in velocity). There are actually nine unknown in stress tensor, but due to symmetry in tensor there are only six unknown (for example u12 = u21).

In K-Epsilon model they are using K and Epsilon to replace these six unknowns. After solving for K and Epsilon we can find out the value of unknown turbulent viscoisty.

Once we have the value of turbulent viscosity we will put it back in the RANS




Definitely it is iterative procedure. And this will stop once it will achieve the required convergence level. Keep in mind that Main RANS equations and turbulence model are solved in sequential way, even for the coupled solvers.

[Far]

Near wall modeling or modeling in the boundary layer is concerned with getting the appropriate values of viscosity terms near the wall.

In turbulence modeling there are various terms for example very very near wall , near wall modeling and away from wall. You can refer to good books on fluid dynamics or refer to wilcox book.

But in nutshell, we want to use the appropriate method/model to estimate these values correctly.

In boundary layer there are three zones, generally speaking, linear region, buffer zone, and log law region.

In linear region u+ and Y+ are directly proportional. However in this zone laminar effects are dominating the turbulence effects. This region is from Y+ = 1-5

In buffer zone the both effects balances each other. This zone is from Y+ = 5 - 30. You can imagine that towards Y+= 30 turbulence effects will be dominating the laminar effects.

In log region, turbulence effects are dominating. This region extends from Y+= 30 to 100 or may be upto 300. The upper limit varies from flow to flow condition. So safe bait would be values near to 30

When you want to solve the linear region for accurately solving for the skin friction coefficient. This is main component of the drag for aerodynamic bodies such as airfoils. You need to use the specially function which can cater for this region. This is also known as Low Reynolds number modeling. This does not mean that the global Reynolds number is low, it means that in this region flow velocities are so low that Reynolds number bases on these velocities will be low. But keep in mind we will always use global Reynolds number to calculate values of Y+ etc

[Far]

i'm trying to understand the usage of the near wall treatment. It is clear that the values of velocity are changing fast in ther near of the wall, so there is a special way to handle this region.

This is done by software it self. You have to just understand it and use appropriate setting in Fluent.

Let's take the k-epsilon model for example. With the help of the model, you calculate the turbulent viscosity and than you can solve the Reynolds stress tensor and the governing equations.

Explained already.

There is the logarithmic law as you can see in the attached picture. Which value is calculating with the help of this law? Is it the velocity u? At which step takes the equation place ? In the free stream, i understand the way of calculation (as described above), but how is it at near wall treatment.

Dont confuse it. It is CFD jargon.

We are trying to get the values of Pressure, velocity components, temperature etc from CFD. Only thing is that, we dont provide any boundary condition at wall. So in order to correctly predict the effect of wall we have these models.

If you just to solve the log law, means you are only interested in the fully turbulent region (Y+ >30) you can do it. For it you will use wall functions. But keep in mind, if there is any separation, velocity will go to zero and Y+ will approach zero. Which is viscous sub layer or linear law profile. In this case you are using wrong (wall functions) to calculate the flow variables.

New wall treatment

New wall treatment uses hybrid wall functions. In these wall functions, linear profile and log profile are blended. Buffer zone is modeled by giving appropriate weight age to both zones based on Y+ values.


Last thing, when you are comparing u+ and y+, they are same for all type of flow. Whether you are solving it or any one else. But just u or y will give you alot of variation. Thats why we call them universal law or profiles.

[bumper]

Wow,


thanks a lot for this really good answer


To sum it up and to check if i understand it in the rigth way.



You use the near wall treatment to calculate the shear stress near the wall due to the fluid viscosity ?

[Far]

Originally Posted by bumper

Wow,


thanks a lot for this really good answer


To sum it up and to check if i understand it in the rigth way.



You use the near wall treatment to calculate the shear stress near the wall due to the fluid viscosity ?

From fluent theory guide

Turbulent flows are significantly affected by the presence of walls. Obviously, the mean velocity field is affected through the no-slip condition that has to be satisfied at the wall. However, the turbulence is also changed by the presence of the wall in non-trivial ways. Very close to the wall, viscous damping reduces the tangential velocity fluctuations, while kinematic blocking reduces the normal fluctuations. Toward the outer part of the near-wall region, however, the turbulence is rapidly augmented by the production of turbulence kinetic energy due to the large gradients in mean velocity.

The near-wall modeling significantly impacts the fidelity of numerical solutions, inasmuch as walls are the main source of mean vorticity and turbulence. After all, it is in the near-wall region that the solution variables have large gradients, and the momentum and other scalar transports occur most vigorously. Therefore, accurate representation of the flow in the near-wall region determines successful predictions of wall-bounded turbulent flows.