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Law of the Wall curve and Y+..for those of you who are bored.

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Old   September 9, 2011, 13:21
Default Law of the Wall curve and Y+..for those of you who are bored.
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I'm a aero engineering student trying to put a bunch of things together...I am using Fluent with a K-e model for drag analysis over a vehicle.

I still have numerous questions about y plus, even after searching these forums and confusion mainly comes from applying the technical equations and definitions to how Fluent uses them.

Ok so I guess there's no quick way around explaining my questions without sounding really basic, so I'll just have to tell you everything I think I understand so far.
  • I get that Y+ is nondimesional and gives you an idea of how far your closest gridpoint is to the surface.
  • For k-e models (used for fully turbulent flow) with no enhanced wall treatment, we want Y+ to be between 30-500.
  • shows me a graph of U+ (average velocity) vs Y+
I'm trying to make sense out of the graph, how it relates to my solutions in Fluent and the basic idea of what calculations are being carried out in CFD.

Looking at the graph, I'm going to refer to Y+ as a "distance" even though it's a nondimensional give you an idea of a scaled distance i guess...right? Ok so the curve in red shows me what the average velocity should be for a given "distance" from the wall. We need to use an average velocity because the flow is turbulent with lots of velocity fluctuations.

The "Log-Law" blue curve is formed from the equation u+=(1/k)ln(y+)+C+. I see that for y+ from 30-500, the red and blue lines are very close.

Ok so here's where I wonder what's going on. First off, for y+ values of 30-500, where are we in relation to the boundary layer? We are still inside the boundary layer right? We have not traveled far enough out to reach the freestream? So CFD will now know this average velocity, from using the Log-Law relation at that point/distance from the wall. Given this value, how does it approximate the underlying viscous sublayer/buffer layer? Does it approximate the nice red curve in the graph by using U+=y+ for Y+<5, and somehow guess the values for the buffer layers? Or, does it take the known avg velocity associated with the y+=30-500 and just take the du/dy slope at that point and interpolate all the way down to the wall?

For example, if my y+ value for the k-e with no EWT is 20, and Fluent uses the log law relation, then my computed average U will be higher than it should be, so drag computed will be overestimated. OOOOrrrrrr, does fluent know that y+ is 20, so it knows it must lie within the buffer layer, and it does some kind of calculation from there...

As if that wasn't enough, I heard that when you use enhanced wall treatment (EWT) you want y+ from 1-5. Is this because EWT is really solving what the boundary layer looks like, so you just need close enough grid points to model the viscous sublayer?

And hey, what about if I were to be doing something else, and I wanted to use k-w, maybe for flow over an airfoil with Re=3e6? Does k-w or transition sst need different target y+ values (not in the 30-500 range) to model the boundary layer? If so, what are those values and why those numbers?

One more thing...what the hell is y-star and how does that play in to any of this? Sounds like y+ takes care of alot.

Alright well if anyone had the patience to read my ranting, I'll really appreciate any clarification on this stuff!
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Old   September 12, 2011, 08:36
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Nevermind, I found an explanation that helps alot on this forum:

Here's what you can find at that link:
In terms of boundary layer theory, y+ is simply a local thickness Reynolds number. In terms of CFD y+ is a nondimensional distance from the wall to the first grid point. In a practical sense, we don't resolve the solutions of turbulent flow by direct numercial simulation. This would require a very fine mesh near the wall in order to resolve the turbulent eddies in the boundary layer. Also, turbulence is time varying and random, so EVERY CFD model would need to be run as transient, even if the mean flow is steady state. Modern computers can't handle this except for the simplest flow, and the most powerful computing available when CFD was developed couldn't even match what most people have on their home PC today. Maybe in the future it will be possible to solve the turbulent Navier Stokes equations by direct numercial simulation right down to the wall.

In order to deal with the temporal fluctuation of turbulence, we time average the governing equations. This is why you often hear CFD referred to as RANS (Reynolds-Averaged-Navier-Stokes) analysis. But this is too good to be true. While on one hand we simplify the equations, on the other, the Reynolds averaging process introduces a new variable, so now we have a steady state problem with more unknowns than equations, and we all know that we can't solve a set of equations if we have more unknowns than we have equations. So we need another equation(s) to close the Reynolds equations. The variable is known as the Reynolds Stress, and the closing equation(s) are known as turbulence models.

Turbulence models deal with the flow in the boundary layer. The boundary layer is divided into an inner and outer region, and the inner region can be further subdivided into a laminar (viscous) sublayer and a fully turbulent region. For flow over a smooth flat plate with no adverse pressure gradients or other funky stuff going on, the inner region stretches from the wall out to about y+=150. The inner region is referred to as the "law of the wall zone" The fully turbulent part of the inner region is known as the "log-law of the wall zone", and is characerized by a log-linear variation of the nondimensional velocity u+. In the viscous sublayer, it is assumed the u+=y+, and when plotted on log-linear graphs, it looks like the familiar Couette flow velocity profile that you see in an undergraduate fluids course.

Now CFD codes assume that this viscous sublayer where u+=y+ happens between the wall and the first grid point. The first grid point is where code switches from the log-law to the viscous sublayer. Generally this switch should occur at a value of y+ somewhere around 30. If your mesh is too fine near the wall, you will get a low value of y+. This will result in overprediction of the near wall velocity. On the other extreme, if y+ is too high, it will cause the code to apply the law of the wall to the outer wake where it is not valid.

Okay, so I gave you a simplistic description. Things such as Reynolds number, surface roughness, adverse pressure gradient, etc will change the value of y+ where the velocity profile swicthes from the viscous sublayer to the log law of the wall. The value of y+ for the transition can range anywhere from about 10.8 up to 50.

Further complicating matters is that some turbulence models employed by modern CFD codes can account for very low or high values of y+ and supposedly still give you reasonable accuracy.
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Old   September 12, 2011, 15:25
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