Low Reynolds K Epsilon Launder Sharma Model Functions Doubt...

RSilva · January 10, 2012, 12:58

Hi folks,

I am trying to implement the Low Reynolds K Epsilon Launder Sharma Turbulence Model in 3D from scratch because I will need to some changes later on to implement two phase modeling.

However I have some doubts about the E and D model functions, as seen in the wiki section: http://www.cfd-online.com/Wiki/Low-Re_k-epsilon_models.

I am unsure if these functions only apply to the YY axis, or do I need to use a gradient for them?? For D the gradient is pretty straightforward, but for E
I am struggling a bit? Do I have 3 or 6 terms for the gradient, because the partial derivatives change depending on which axis you differentiate first...

Hope it's clear and someone can help..

Cheers!

Rui

jola · January 10, 2012, 14:30

y in those formulas refers to the direction normal to the wall. Hence, in a 3D code it will be dependent on how the wall is oriented and will be a combination of x,y and z.

RSilva · January 10, 2012, 18:38

Thank you for your reply jola!

Could you suggest some articles or thesis or anyother source that has
those equation so that I can better understand?

Cheers!

Rui

RSilva · January 11, 2012, 11:23

Also, regarding the extra source terms:

for two dimensional pipe flow and assuming flow in the x-direction, the normal is y.

However, in 3D and pipe flow in the z-direction, both x and y are normal to the flow.

I am not quite understanding how to combine the three coordinates in the extra source terms.

Could you please provide some more details.

Thank you.

Best Regards,

Rui

RSilva · January 12, 2012, 12:45

I guess I have some progress...

So, I believe that for 3D the extra source term:

$E\epsilon =\left (\frac{\partial^{2} u }{\partial x^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} u }{\partial y^{2}} \right)^{^{2}}+\left (\frac{\partial^{2} u }{\partial z^{2}} \right )^{^{2}}$ + $\left (\frac{\partial^{2} v }{\partial x^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} v }{\partial y^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} v }{\partial z^{2}} \right )^{^{2}}$ + $\left (\frac{\partial^{2} w }{\partial x^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} w }{\partial y^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} w }{\partial z^{2}} \right )^{^{2}}$
+ $2 \left [ \left (\frac{\partial^{2} u }{\partial x \partial y} \right )^{^{2}} + \left (\frac{\partial^{2} u }{\partial x \partial y} \right )^{^{2}}+ \left (\frac{\partial^{2} u }{\partial z \partial y} \right )^{^{2}}\right ]$ + $2 \left [ \left (\frac{\partial^{2} v }{\partial x \partial y} \right )^{^{2}} + \left (\frac{\partial^{2} v }{\partial x \partial y} \right )^{^{2}}+ \left (\frac{\partial^{2} v }{\partial z \partial y} \right )^{^{2}}\right ]$ + $2 \left [ \left (\frac{\partial^{2} w }{\partial x \partial y} \right )^{^{2}} + \left (\frac{\partial^{2} w }{\partial x \partial y} \right )^{^{2}}+ \left (\frac{\partial^{2} w }{\partial z \partial y} \right )^{^{2}}\right ]$

Is this a correct assumption?
I think it's a bit long when compared with the two dimensional case, however it seems logical when I look at the general expression:

$2\mu \mu _{T}\left (\frac{\partial^{2} u_{i} }{\partial x_{j} \partial x_{k}} \right )^{2}$

I wonder if it's correct for the 3D case...

Can anyone provide some input?

Best Regards,

Rui

Kanarya · August 1, 2013, 07:55

hi Rui,

Did you manage to apple the model in two phase model?

Quote:

Originally Posted by RSilva

I guess I have some progress...

So, I believe that for 3D the extra source term:

$E\epsilon =\left (\frac{\partial^{2} u }{\partial x^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} u }{\partial y^{2}} \right)^{^{2}}+\left (\frac{\partial^{2} u }{\partial z^{2}} \right )^{^{2}}$ + $\left (\frac{\partial^{2} v }{\partial x^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} v }{\partial y^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} v }{\partial z^{2}} \right )^{^{2}}$ + $\left (\frac{\partial^{2} w }{\partial x^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} w }{\partial y^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} w }{\partial z^{2}} \right )^{^{2}}$
+ $2 \left [ \left (\frac{\partial^{2} u }{\partial x \partial y} \right )^{^{2}} + \left (\frac{\partial^{2} u }{\partial x \partial y} \right )^{^{2}}+ \left (\frac{\partial^{2} u }{\partial z \partial y} \right )^{^{2}}\right ]$ + $2 \left [ \left (\frac{\partial^{2} v }{\partial x \partial y} \right )^{^{2}} + \left (\frac{\partial^{2} v }{\partial x \partial y} \right )^{^{2}}+ \left (\frac{\partial^{2} v }{\partial z \partial y} \right )^{^{2}}\right ]$ + $2 \left [ \left (\frac{\partial^{2} w }{\partial x \partial y} \right )^{^{2}} + \left (\frac{\partial^{2} w }{\partial x \partial y} \right )^{^{2}}+ \left (\frac{\partial^{2} w }{\partial z \partial y} \right )^{^{2}}\right ]$

Is this a correct assumption?
I think it's a bit long when compared with the two dimensional case, however it seems logical when I look at the general expression:

$2\mu \mu _{T}\left (\frac{\partial^{2} u_{i} }{\partial x_{j} \partial x_{k}} \right )^{2}$

I wonder if it's correct for the 3D case...

Can anyone provide some input?

Best Regards,

Rui

RSilva · August 5, 2013, 10:05

Hello Kanarya,

yes I was. I am using it now in my simulations.

How can I help you?

Best Regards,

Rui

Kanarya · August 5, 2013, 10:40

Hi Rui,
do you have already publish some results?
Or do you have some comparison with the classical methods with wall function!
I already did it for single case but I have some difficulties to apply damping function to the wall with solid included case. Can you give me some reference about it?

thanks a lot

Quote:

Originally Posted by RSilva

Hello Kanarya,

yes I was. I am using it now in my simulations.

How can I help you?

Best Regards,

Rui

RSilva · August 5, 2013, 11:24

Hello Kanarya,

I'm finishing a paper on the subject but is not yet pusblished.

I can try and point in the right direction, but I cannot as of now provide you with some of the coding. I'm sure you understand.

So, the papers that helped me out were the following:

- C. M. Hrenya [1995] Comparison of low Reynolds number κ—ε turbulence models in predicting fully developed pipe flow

- J. J. Costa [1999] Test Of Several Version For The k-e Type Turbulence Modelling

- On the Mixture Model for Multiphase Flow

Also, remrmber that meshing is always an issue.

Hope this helps and let me know if you need anything.

Best Regards,

Rui

Kanarya · August 5, 2013, 11:48

Hi Rui,

Thanks for the quick answer!
Did you use mixture approach or dispersed one?
What is your application e.g gas-solid , gas-liquid, dense or dilute?
Because I am simulating gas solid CFB system and I want to include in both equation source term which includes the momentum interchange between two phases!

Thanks a lot again!

Quote:

Originally Posted by RSilva

Hello Kanarya,

I'm finishing a paper on the subject but is not yet pusblished.

I can try and point in the right direction, but I cannot as of now provide you with some of the coding. I'm sure you understand.

So, the papers that helped me out were the following:

- C. M. Hrenya [1995] Comparison of low Reynolds number κ—ε turbulence models in predicting fully developed pipe flow

- J. J. Costa [1999] Test Of Several Version For The k-e Type Turbulence Modelling

- On the Mixture Model for Multiphase Flow

Also, remrmber that meshing is always an issue.

Hope this helps and let me know if you need anything.

Best Regards,

Rui

RSilva · August 5, 2013, 11:52

Hi,

I'm using the Mixture Model because I´m modelling a solid-liquid dense suspension.

Since you are gas-solid, I recomend the works of Elghobashi (I believe it is spelled this way).

Best Regards,

Rui

Kanarya · August 5, 2013, 12:00

Hi Rui,

thanks for your time and patients!
did you get improvement near the wall without wall treatment (dense mesh) in comparison to classical models?
I am looking forward to read your paper!
thanks!
best!
kanarya

Quote:

Originally Posted by RSilva

Hi,

I'm using the Mixture Model because I´m modelling a solid-liquid dense suspension.

Since you are gas-solid, I recomend the works of Elghobashi (I believe it is spelled this way).

Best Regards,

Rui

RSilva · August 5, 2013, 12:10

Yes, I did.

The classic wall function behaves very poorly with particles, at least in solid-liquid case that I study.

Best Regards,

Rui

Kanarya · September 9, 2013, 05:26

Hi Rui,

what do you mean with "Also, remember that meshing is always an issue"?
do we need dense mesh near the wall for damping function as well (like Y+ =1 or Y+ =30). Y+ = 30 should be enough,right?

thanks in advance!

Best!

Kanarya

Quote:

Originally Posted by RSilva

Hello Kanarya,

I'm finishing a paper on the subject but is not yet pusblished.

I can try and point in the right direction, but I cannot as of now provide you with some of the coding. I'm sure you understand.

So, the papers that helped me out were the following:

- C. M. Hrenya [1995] Comparison of low Reynolds number κ—ε turbulence models in predicting fully developed pipe flow

- J. J. Costa [1999] Test Of Several Version For The k-e Type Turbulence Modelling

- On the Mixture Model for Multiphase Flow

Also, remrmber that meshing is always an issue.

Hope this helps and let me know if you need anything.

Best Regards,

Rui

RSilva · September 9, 2013, 07:00

Hi Kanarya,

I think that for Low Re models you should go for Y+=1.

This is due to the anisotropic behaviour near the wall.

The meshing issue comes from two points: 1) refine mesh until the results do not vary and 2) the RAM limitations for really dense meshes.

Hope this helps.

Best Regards,

Rui

Quote:

Originally Posted by Kanarya

Hi Rui,

what do you mean with "Also, remember that meshing is always an issue"?
do we need dense mesh near the wall for damping function as well (like Y+ =1 or Y+ =30). Y+ = 30 should be enough,right?

thanks in advance!

Best!

Kanarya

Kanarya · September 9, 2013, 07:17

Thanks a lot Rui!

Quote:

Originally Posted by RSilva

Hi Kanarya,

I think that for Low Re models you should go for Y+=1.

This is due to the anisotropic behaviour near the wall.

The meshing issue comes from two points: 1) refine mesh until the results do not vary and 2) the RAM limitations for really dense meshes.

Hope this helps.

Best Regards,

Rui

Kanarya · February 17, 2014, 06:59

Hi Rui,
Did you publish your paper about damping function in gas solid multiphase flows.
can you give me some referance about it?
thanks!

RSilva · February 17, 2014, 10:52

My paper is on Solid-liquid multiphase flows.
I'mm finalizing the paper and will submit it soon.

If I get accpeted for publication I'll share the link here.

I appologize if I gave the wrong impression.

Best Regards,

Rui

Quote:

Originally Posted by Kanarya

Hi Rui,
Did you publish your paper about damping function in gas solid multiphase flows.
can you give me some referance about it?
thanks!

January 10, 2012, 12:58	Low Reynolds K Epsilon Launder Sharma Model Functions Doubt...	#1
RSilva Member RCCS Join Date: Apr 2011 Posts: 40 Rep Power: 8	Hi folks, I am trying to implement the Low Reynolds K Epsilon Launder Sharma Turbulence Model in 3D from scratch because I will need to some changes later on to implement two phase modeling. However I have some doubts about the E and D model functions, as seen in the wiki section: http://www.cfd-online.com/Wiki/Low-Re_k-epsilon_models. I am unsure if these functions only apply to the YY axis, or do I need to use a gradient for them?? For D the gradient is pretty straightforward, but for E I am struggling a bit? Do I have 3 or 6 terms for the gradient, because the partial derivatives change depending on which axis you differentiate first... Hope it's clear and someone can help.. Cheers! Rui

February 17, 2014, 06:59	damping function in gas solid multiphase flows	#17
Kanarya Senior Member Join Date: May 2011 Posts: 231 Rep Power: 8	Hi Rui, Did you publish your paper about damping function in gas solid multiphase flows. can you give me some referance about it? thanks!

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January 10, 2012, 14:30		#2
jola Administrator Jonas Larsson Join Date: Jan 2009 Location: Gothenburg, Sweden Posts: 540 Rep Power: 10	y in those formulas refers to the direction normal to the wall. Hence, in a 3D code it will be dependent on how the wall is oriented and will be a combination of x,y and z.

January 10, 2012, 18:38		#3
RSilva Member RCCS Join Date: Apr 2011 Posts: 40 Rep Power: 8	Thank you for your reply jola! Could you suggest some articles or thesis or anyother source that has those equation so that I can better understand? Cheers! Rui

January 11, 2012, 11:23		#4
RSilva Member RCCS Join Date: Apr 2011 Posts: 40 Rep Power: 8	Also, regarding the extra source terms: for two dimensional pipe flow and assuming flow in the x-direction, the normal is y. However, in 3D and pipe flow in the z-direction, both x and y are normal to the flow. I am not quite understanding how to combine the three coordinates in the extra source terms. Could you please provide some more details. Thank you. Best Regards, Rui

January 12, 2012, 12:45		#5
RSilva Member RCCS Join Date: Apr 2011 Posts: 40 Rep Power: 8	I guess I have some progress... So, I believe that for 3D the extra source term: $E\epsilon =\left (\frac{\partial^{2} u }{\partial x^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} u }{\partial y^{2}} \right)^{^{2}}+\left (\frac{\partial^{2} u }{\partial z^{2}} \right )^{^{2}}$ + $\left (\frac{\partial^{2} v }{\partial x^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} v }{\partial y^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} v }{\partial z^{2}} \right )^{^{2}}$ + $\left (\frac{\partial^{2} w }{\partial x^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} w }{\partial y^{2}} \right )^{^{2}}+\left (\frac{\partial^{2} w }{\partial z^{2}} \right )^{^{2}}$ + $2 \left [ \left (\frac{\partial^{2} u }{\partial x \partial y} \right )^{^{2}} + \left (\frac{\partial^{2} u }{\partial x \partial y} \right )^{^{2}}+ \left (\frac{\partial^{2} u }{\partial z \partial y} \right )^{^{2}}\right ]$ + $2 \left [ \left (\frac{\partial^{2} v }{\partial x \partial y} \right )^{^{2}} + \left (\frac{\partial^{2} v }{\partial x \partial y} \right )^{^{2}}+ \left (\frac{\partial^{2} v }{\partial z \partial y} \right )^{^{2}}\right ]$ + $2 \left [ \left (\frac{\partial^{2} w }{\partial x \partial y} \right )^{^{2}} + \left (\frac{\partial^{2} w }{\partial x \partial y} \right )^{^{2}}+ \left (\frac{\partial^{2} w }{\partial z \partial y} \right )^{^{2}}\right ]$ Is this a correct assumption? I think it's a bit long when compared with the two dimensional case, however it seems logical when I look at the general expression: $2\mu \mu _{T}\left (\frac{\partial^{2} u_{i} }{\partial x_{j} \partial x_{k}} \right )^{2}$ I wonder if it's correct for the 3D case... Can anyone provide some input? Best Regards, Rui

August 5, 2013, 10:05		#7
RSilva Member RCCS Join Date: Apr 2011 Posts: 40 Rep Power: 8	Hello Kanarya, yes I was. I am using it now in my simulations. How can I help you? Best Regards, Rui

August 5, 2013, 11:24		#9
RSilva Member RCCS Join Date: Apr 2011 Posts: 40 Rep Power: 8	Hello Kanarya, I'm finishing a paper on the subject but is not yet pusblished. I can try and point in the right direction, but I cannot as of now provide you with some of the coding. I'm sure you understand. So, the papers that helped me out were the following: - C. M. Hrenya [1995] Comparison of low Reynolds number κ—ε turbulence models in predicting fully developed pipe flow - J. J. Costa [1999] Test Of Several Version For The k-e Type Turbulence Modelling - On the Mixture Model for Multiphase Flow Also, remrmber that meshing is always an issue. Hope this helps and let me know if you need anything. Best Regards, Rui

August 5, 2013, 11:52		#11
RSilva Member RCCS Join Date: Apr 2011 Posts: 40 Rep Power: 8	Hi, I'm using the Mixture Model because I´m modelling a solid-liquid dense suspension. Since you are gas-solid, I recomend the works of Elghobashi (I believe it is spelled this way). Best Regards, Rui

August 5, 2013, 12:10		#13
RSilva Member RCCS Join Date: Apr 2011 Posts: 40 Rep Power: 8	Yes, I did. The classic wall function behaves very poorly with particles, at least in solid-liquid case that I study. Best Regards, Rui