Enhanced Wall Treatment
Posted April 11, 2014 at 16:53 by diamondx
Useful near wall treatments informations:
Quote:
This is completely wrong
If this is true then they would have used the simple elseif command which was used in the previous version of SA and KOmega 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 Kepsilon and Komega models.
First question comes into mind why two approaches used for the same effect i.e. implementing the smooth transition between the loglaw and viscous sublayer implementation. This is because:
1. Kepsilon models were not designed for the near wall flow, therefore they require the damping functions to simulate the near wall effects.
2. Komega 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 komega and SA model with hybrid wall functions here
http://num.math.unigoettingen.de/ba...ings/knopp.pdf
http://num.math.unigoettingen.de/ba...ngs/alrutz.pdf
But whether it is two layer approach (Kepsilon) or single model implementation approach (Komega 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 Kepsilon model) or Y+<2 (Komega model, I am not writing low reynolds number komega becuase Komega is originally a low Reynolds number model, so no need to define the Rose) and similarly the Y+ > 30 for high Reynolds number Komega and KEpsilon 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 Kepsilon model of M. Wolfstein.
"The Velocity and Temperature Distribution of OneDimensional Flow with Turbulence Augmentation and Pressure Gradient.
Int. J. Heat Mass Transfer, 12:301318, 1969."
Put in simple words:
1. With Y+~1 , you are solving the low Reynolds number Kepsilon 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 komega model because they are already applicable upto viscous sublayer.
Now the question is how does the enhanced (hybrid) wall function work.
They work like
Uplus = (1blending function) * Uplus (of viscous sublayer) + blending function * Uplus (of log law)
Blending function = 0 for y+ < 6
Blending function =~ 1 for Y+ > 3040
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.unigoettingen.de/ba...ings/knopp.pdf
Blending functions has the following values (Equation 7 of reference http://num.math.unigoettingen.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.
If this is true then they would have used the simple elseif command which was used in the previous version of SA and KOmega 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 Kepsilon and Komega models.
First question comes into mind why two approaches used for the same effect i.e. implementing the smooth transition between the loglaw and viscous sublayer implementation. This is because:
1. Kepsilon models were not designed for the near wall flow, therefore they require the damping functions to simulate the near wall effects.
2. Komega 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 komega and SA model with hybrid wall functions here
http://num.math.unigoettingen.de/ba...ings/knopp.pdf
http://num.math.unigoettingen.de/ba...ngs/alrutz.pdf
But whether it is two layer approach (Kepsilon) or single model implementation approach (Komega 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 Kepsilon model) or Y+<2 (Komega model, I am not writing low reynolds number komega becuase Komega is originally a low Reynolds number model, so no need to define the Rose) and similarly the Y+ > 30 for high Reynolds number Komega and KEpsilon 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 Kepsilon model of M. Wolfstein.
"The Velocity and Temperature Distribution of OneDimensional Flow with Turbulence Augmentation and Pressure Gradient.
Int. J. Heat Mass Transfer, 12:301318, 1969."
Put in simple words:
1. With Y+~1 , you are solving the low Reynolds number Kepsilon 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 komega model because they are already applicable upto viscous sublayer.
Now the question is how does the enhanced (hybrid) wall function work.
They work like
Uplus = (1blending function) * Uplus (of viscous sublayer) + blending function * Uplus (of log law)
Blending function = 0 for y+ < 6
Blending function =~ 1 for Y+ > 3040
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.unigoettingen.de/ba...ings/knopp.pdf
Blending functions has the following values (Equation 7 of reference http://num.math.unigoettingen.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.
Total Comments 1
Comments

Hello I am a beginner to CFD and currently a student. I was wondering where a good place to start to learn CFD is such as websites, books, and tutorials, so that i can learn to code for simple flows over an object.
Posted November 30, 2016 at 22:12 by stefcfd