# Enhanced Wall Treatment

Posted April 11, 2014 at 16:53 by diamondx

Useful near wall treatments informations:

If this is true then they would have used the simple else-if command which was used in the previous version of SA and K-Omega model. Still you can observe in the theory guide of Fluent (I am talking about SA model) they are using the integration to wall approach for the Y+< 2 and wall function approach for the Y+>30 and strongly recommend to make the meshes either with Y+< 2 or Y+> 30 so that they can use the either IWT or wall function approach. Although the actual switch is implemented at the intersection of two profiles i.e. 11.225 (previously it was implemented at 11.06 in version 6.3).

First question comes into mind why two approaches used for the same effect i.e. implementing the smooth transition between the log-law and viscous sub-layer implementation. This is because:

1. K-epsilon models were not designed for the near wall flow, therefore they require the damping functions to simulate the near wall effects.

2. K-omega based models were designed originally for the near wall region and therefore does not require the damping functions, hence the hybrid wall functions (blending of near wall and log law function) were implemented directly and same is true for SA model. You can find the details of latest work here for the k-omega and SA model with hybrid wall functions here

http://num.math.uni-goettingen.de/ba...ings/knopp.pdf

http://num.math.uni-goettingen.de/ba...ngs/alrutz.pdf

But whether it is two layer approach (K-epsilon) or single model implementation approach (K-omega or SA model) the purpose is same i.e. to remove the short comings of the both models. i.e. the low reynolds number is valid for the Y+ < 0.2 (low reynolds number K-epsilon model) or Y+<2 (K-omega model, I am not writing low reynolds number k-omega becuase K-omega is originally a low Reynolds number model, so no need to define the Rose) and similarly the Y+ > 30 for high Reynolds number K-omega and K-Epsilon model.

To be continued....

Now consider this http://en.wikipedia.org/wiki/Law_of_the_wall

It is clearly written that U+ = Y+ for the Y+ < 5 (you can consider the sublayer up 11.225 but at the Y+ = 12 the error is around 25%) http://en.wikipedia.org/wiki/Law_of_the_wall

Log law is for Y+> 30.

Buffer zone is Y+ = 5 to Y+ = 30 This is problem area where both models (low Reynolds number and high Reynolds number ) don't work.

This is the reason why the hybrid or enhanced wall treatment model was came into existence.

Here is the some material from Fluent user guide:

In other words the with Y+ ~ 1, you are solving the low reynolds number K-epsilon model of M. Wolfstein.

"The Velocity and Temperature Distribution of One-Dimensional Flow with Turbulence Augmentation and Pressure Gradient.

Int. J. Heat Mass Transfer, 12:301-318, 1969."

Put in simple words:

1. With Y+~1 , you are solving the low Reynolds number K-epsilon model

2. In original form Wolfstein model is not applicable for the Y+ > 0.2

3. So to over come this we have to use the hybrid wall functions.

4. Enhanced wall treatment is method to implement the hybrid (or enhanced) wall functions for the varying Y+ in the CFD model.

5. Enhanced wall treatment is not needed to implement hybrid (enhanced) wall functions in k-omega model because they are already applicable up-to viscous sub-layer.

Now the question is how does the enhanced (hybrid) wall function work.

They work like

Uplus = (1-blending function) * Uplus (of viscous sub-layer) + blending function * Uplus (of log law)

Blending function = 0 for y+ < 6

Blending function =~ 1 for Y+ > 30-40

So for Y+< 6 you have viscous sub layer and you are using the low Reynolds number model

for Y+> 30 You are using the log law implement ion (aka wall functions)

Between Y+ ~ 6 and 30 one is using the linear some of both profiles according to the relative weightage.

For example in reference http://num.math.uni-goettingen.de/ba...ings/knopp.pdf

Blending functions has the following values (Equation 7 of reference http://num.math.uni-goettingen.de/ba...ings/knopp.pdf)

Y+ = 1 , BF = 0

Y+ = 10, BF = 0.018

Y+ = 12, BF = 0.038

Y+ = 15, BF = 0.094

Y+ = 20, BF = 0.2922

Y+ = 25, BF = 0.626

Y+ = 27, BF = 0.761

Y+ = 30 , BF = 0.909

Y+ = 35, BF = 0.9929

Y+ = 38, BF = 0.9992

Y+ = 40, BF = 0.9998

Blending function is different for different terms. For example in above example, BF was calculated for U+ and Y+. But which ever function is used the basic theory is same.

PS : I have already mentioned in one thread that the enhanced wall treatment is good for the Y+ < 10, because for higher values you have increasing weitage of log law and which is not good at predicting the separation.

Quote:

**This is completely wrong**

If this is true then they would have used the simple else-if command which was used in the previous version of SA and K-Omega model. Still you can observe in the theory guide of Fluent (I am talking about SA model) they are using the integration to wall approach for the Y+< 2 and wall function approach for the Y+>30 and strongly recommend to make the meshes either with Y+< 2 or Y+> 30 so that they can use the either IWT or wall function approach. Although the actual switch is implemented at the intersection of two profiles i.e. 11.225 (previously it was implemented at 11.06 in version 6.3).

**Now lets discuss the theory behind the enhanced wall treatment for K-epsilon and K-omega models.**

First question comes into mind why two approaches used for the same effect i.e. implementing the smooth transition between the log-law and viscous sub-layer implementation. This is because:

1. K-epsilon models were not designed for the near wall flow, therefore they require the damping functions to simulate the near wall effects.

2. K-omega based models were designed originally for the near wall region and therefore does not require the damping functions, hence the hybrid wall functions (blending of near wall and log law function) were implemented directly and same is true for SA model. You can find the details of latest work here for the k-omega and SA model with hybrid wall functions here

http://num.math.uni-goettingen.de/ba...ings/knopp.pdf

http://num.math.uni-goettingen.de/ba...ngs/alrutz.pdf

But whether it is two layer approach (K-epsilon) or single model implementation approach (K-omega or SA model) the purpose is same i.e. to remove the short comings of the both models. i.e. the low reynolds number is valid for the Y+ < 0.2 (low reynolds number K-epsilon model) or Y+<2 (K-omega model, I am not writing low reynolds number k-omega becuase K-omega is originally a low Reynolds number model, so no need to define the Rose) and similarly the Y+ > 30 for high Reynolds number K-omega and K-Epsilon model.

To be continued....

Now consider this http://en.wikipedia.org/wiki/Law_of_the_wall

It is clearly written that U+ = Y+ for the Y+ < 5 (you can consider the sublayer up 11.225 but at the Y+ = 12 the error is around 25%) http://en.wikipedia.org/wiki/Law_of_the_wall

Log law is for Y+> 30.

Buffer zone is Y+ = 5 to Y+ = 30 This is problem area where both models (low Reynolds number and high Reynolds number ) don't work.

This is the reason why the hybrid or enhanced wall treatment model was came into existence.

Here is the some material from Fluent user guide:

In other words the with Y+ ~ 1, you are solving the low reynolds number K-epsilon model of M. Wolfstein.

"The Velocity and Temperature Distribution of One-Dimensional Flow with Turbulence Augmentation and Pressure Gradient.

Int. J. Heat Mass Transfer, 12:301-318, 1969."

Put in simple words:

1. With Y+~1 , you are solving the low Reynolds number K-epsilon model

2. In original form Wolfstein model is not applicable for the Y+ > 0.2

3. So to over come this we have to use the hybrid wall functions.

4. Enhanced wall treatment is method to implement the hybrid (or enhanced) wall functions for the varying Y+ in the CFD model.

5. Enhanced wall treatment is not needed to implement hybrid (enhanced) wall functions in k-omega model because they are already applicable up-to viscous sub-layer.

Now the question is how does the enhanced (hybrid) wall function work.

They work like

Uplus = (1-blending function) * Uplus (of viscous sub-layer) + blending function * Uplus (of log law)

Blending function = 0 for y+ < 6

Blending function =~ 1 for Y+ > 30-40

So for Y+< 6 you have viscous sub layer and you are using the low Reynolds number model

for Y+> 30 You are using the log law implement ion (aka wall functions)

Between Y+ ~ 6 and 30 one is using the linear some of both profiles according to the relative weightage.

For example in reference http://num.math.uni-goettingen.de/ba...ings/knopp.pdf

Blending functions has the following values (Equation 7 of reference http://num.math.uni-goettingen.de/ba...ings/knopp.pdf)

Y+ = 1 , BF = 0

Y+ = 10, BF = 0.018

Y+ = 12, BF = 0.038

Y+ = 15, BF = 0.094

Y+ = 20, BF = 0.2922

Y+ = 25, BF = 0.626

Y+ = 27, BF = 0.761

Y+ = 30 , BF = 0.909

Y+ = 35, BF = 0.9929

Y+ = 38, BF = 0.9992

Y+ = 40, BF = 0.9998

Blending function is different for different terms. For example in above example, BF was calculated for U+ and Y+. But which ever function is used the basic theory is same.

PS : I have already mentioned in one thread that the enhanced wall treatment is good for the Y+ < 10, because for higher values you have increasing weitage of log law and which is not good at predicting the separation.

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