Why my calculated epsilon is different from FLUENT calculation?

minzhang · April 30, 2020, 22:48

Hello All,

For the "Velocity Inlet" boundary condition, I specified both Turbulent Intensity and Hydraulic Diameter.

For the "Solution Initialization", I chose to "Compute from inlet".

But the "Turbulent Dissipation Rate (epsilon)" calculated from FLUENT is different from my calculation. I am wondering why?

This is my calculation and my reference is here:
https://www.afs.enea.it/project/nept...ug/node238.htm

(1) I calculated Reynolds number at the inlet
Re = D_pipe*U/nu = 553852.1841

(2) I calculated Turbulence Intensity, I using equation (7.3-1)
I = 0.03063344 = 3.0633% which is the value I specified for my "Velocity Inlet"

(3) I calculated Turbulence length scale (L) using L=0.07*D_pipe (7.3-2)
L = 0.0072m which is the value I specified for my "Velocity Inlet"

(4) I calculated Turbulent Kinetic Energy using equation (7.3-4)
k = 0.0411m2/s2 (the same as FLUENT calculation = 0.04104477)

(5) I calculated Turbulence Dissipation Rate (epsilon) using eqaution (7.3-5)
epsilon = 0.1898 m2/s3

However, the value calculated by FLUENT is 2.711054 m2/s3.

vinerm · May 1, 2020, 15:59

It is because you might be using one of the current versions while referring the documentation, which is quite old. Current formulation is

$\varepsilon = \frac{k^{\frac{3}{2}}}{l}$

And $C_\mu$ is included in

.

minzhang · May 1, 2020, 18:01

Hello vinerm,

Could you give me more details about the expression for l, and how C_mu is included?

Could you point me to the current version of Ansys documentation?

Thanks!

vinerm · May 2, 2020, 17:07

Documentation is available at

https://ansyshelp.ansys.com

minzhang · May 3, 2020, 21:00

It seems that, as a free student academic version, I don't have the permission to access the document.

vinerm · May 4, 2020, 17:21

Yes, students do not have access to that. The formulation is still same, except that $C_\mu$ is considered within

. So, the value of

itself changes.

minzhang · May 4, 2020, 17:36

I am wondering whether you could post the formula for Turbulence length scale.
Thanks!

vinerm · May 5, 2020, 05:45

$l = \frac{0.07 L}{C_\mu^{3/4}}$

minzhang · May 5, 2020, 11:07

Based on the formula you gave, substitute l into epsilon, then it will be the same as equation (7.3-5) in the old documentation. Is that right?

vinerm · May 5, 2020, 11:35

Yes, the formula is still the same, however, the length scale is not.

minzhang · May 5, 2020, 11:37

But it won't affect the calculation for epsilon.
Therefore, my calculated epsilon is still different from the FLUENT calculation.

vinerm · May 5, 2020, 12:05

It does because the user supplies the value for

and not

.

minzhang · May 6, 2020, 18:49

This is my current calculation based on the latest formula you posted.

(1) I calculated Reynolds number at the inlet
Re = D_pipe*U/nu = 553852.1841

(2) I calculated Turbulence Intensity, I using equation (7.3-1)
I = 0.03063344 = 3.0633% which is the value I specified for my "Velocity Inlet"

(3) I calculated Turbulence length scale (L) using your equation L=0.07*D_pipe/C_mu^(3/4)
L = 0.0439m which is the value I specified for my "Velocity Inlet"
Here I have an assumption that Hydraulic Diameter == Turbulence length scale.

(4) I calculated Turbulence Dissipation Rate (epsilon) using your equation
epsilon = 0.1898 m2/s3 (same as my previous calculation since essentially the formula is the same)

However, the value calculated by FLUENT (this time) is 0.4446375 m2/s3.

vinerm · May 7, 2020, 06:33

Length Scale and Hydraulic Diameter are not same, otherwise you would not require different options.

minzhang · May 12, 2020, 23:53

Finally, I got to know why.
1. The reason is I assumed "Hydraulic Diameter == Turbulence length scale". When I use "Hydraulic Diameter =D_pipe", then I got the same epsilon value as FLUENT.
2. The formula in the old reference is consistent with the latest ones.
Thanks!

April 30, 2020, 22:48	Why my calculated epsilon is different from FLUENT calculation?	#1
minzhang Member Min Zhang Join Date: Mar 2017 Posts: 81 Rep Power: 9	Hello All, For the "Velocity Inlet" boundary condition, I specified both Turbulent Intensity and Hydraulic Diameter. For the "Solution Initialization", I chose to "Compute from inlet". But the "Turbulent Dissipation Rate (epsilon)" calculated from FLUENT is different from my calculation. I am wondering why? This is my calculation and my reference is here: https://www.afs.enea.it/project/nept...ug/node238.htm (1) I calculated Reynolds number at the inlet Re = D_pipeU/nu = 553852.1841 (2) I calculated Turbulence Intensity, I* using equation (7.3-1) I = 0.03063344 = 3.0633% which is the value I specified for my "Velocity Inlet" (3) I calculated Turbulence length scale (L) using L=0.07D_pipe (7.3-2) L = 0.0072m which is the value I specified for my "Velocity Inlet" (4) I calculated Turbulent Kinetic Energy* using equation (7.3-4) k = 0.0411m2/s2 (the same as FLUENT calculation = 0.04104477) (5) I calculated Turbulence Dissipation Rate (epsilon) using eqaution (7.3-5) epsilon = 0.1898 m2/s3 However, the value calculated by FLUENT is 2.711054 m2/s3.

May 1, 2020, 15:59	Version	#2
vinerm Senior Member Vinerm Join Date: Jun 2009 Location: Nederland Posts: 2,946 Blog Entries: 1 Rep Power: 36	It is because you might be using one of the current versions while referring the documentation, which is quite old. Current formulation is $\varepsilon = \frac{k^{\frac{3}{2}}}{l}$ And $C_\mu$ is included in . __________________ Regards, Vinerm PM to be used if and only if you do not want something to be shared publicly. PM is considered to be of the least priority.

May 1, 2020, 18:01	Current version of Ansys documentation	#3
minzhang Member Min Zhang Join Date: Mar 2017 Posts: 81 Rep Power: 9	Hello vinerm, Could you give me more details about the expression for l, and how C_mu is included? Could you point me to the current version of Ansys documentation? Thanks!

May 2, 2020, 17:07	Documentation	#4
vinerm Senior Member Vinerm Join Date: Jun 2009 Location: Nederland Posts: 2,946 Blog Entries: 1 Rep Power: 36	Documentation is available at https://ansyshelp.ansys.com minzhang likes this. __________________ Regards, Vinerm PM to be used if and only if you do not want something to be shared publicly. PM is considered to be of the least priority.

May 3, 2020, 21:00	Don't have access to the Documentation	#5
minzhang Member Min Zhang Join Date: Mar 2017 Posts: 81 Rep Power: 9	It seems that, as a free student academic version, I don't have the permission to access the document.

May 4, 2020, 17:21	Help Manual	#6
vinerm Senior Member Vinerm Join Date: Jun 2009 Location: Nederland Posts: 2,946 Blog Entries: 1 Rep Power: 36	Yes, students do not have access to that. The formulation is still same, except that $C_\mu$ is considered within . So, the value of itself changes. __________________ Regards, Vinerm PM to be used if and only if you do not want something to be shared publicly. PM is considered to be of the least priority.

May 4, 2020, 17:36	Formula of Turbulence length scale	#7
minzhang Member Min Zhang Join Date: Mar 2017 Posts: 81 Rep Power: 9	I am wondering whether you could post the formula for Turbulence length scale. Thanks!

May 5, 2020, 05:45	Length Scale	#8
vinerm Senior Member Vinerm Join Date: Jun 2009 Location: Nederland Posts: 2,946 Blog Entries: 1 Rep Power: 36	$l = \frac{0.07 L}{C_\mu^{3/4}}$ __________________ Regards, Vinerm PM to be used if and only if you do not want something to be shared publicly. PM is considered to be of the least priority.

May 5, 2020, 11:07		#9
minzhang Member Min Zhang Join Date: Mar 2017 Posts: 81 Rep Power: 9	Based on the formula you gave, substitute l into epsilon, then it will be the same as equation (7.3-5) in the old documentation. Is that right?

May 5, 2020, 11:35	Epsilon	#10
vinerm Senior Member Vinerm Join Date: Jun 2009 Location: Nederland Posts: 2,946 Blog Entries: 1 Rep Power: 36	Yes, the formula is still the same, however, the length scale is not. __________________ Regards, Vinerm PM to be used if and only if you do not want something to be shared publicly. PM is considered to be of the least priority.

May 5, 2020, 11:37		#11
minzhang Member Min Zhang Join Date: Mar 2017 Posts: 81 Rep Power: 9	But it won't affect the calculation for epsilon. Therefore, my calculated epsilon is still different from the FLUENT calculation.

May 5, 2020, 12:05	Epsilon	#12
vinerm Senior Member Vinerm Join Date: Jun 2009 Location: Nederland Posts: 2,946 Blog Entries: 1 Rep Power: 36	It does because the user supplies the value for and not . __________________ Regards, Vinerm PM to be used if and only if you do not want something to be shared publicly. PM is considered to be of the least priority.

May 6, 2020, 18:49	I still could not get the same epsilon value as FLUENT?	#13
minzhang Member Min Zhang Join Date: Mar 2017 Posts: 81 Rep Power: 9	This is my current calculation based on the latest formula you posted. (1) I calculated Reynolds number at the inlet Re = D_pipeU/nu = 553852.1841 (2) I calculated Turbulence Intensity, I* using equation (7.3-1) I = 0.03063344 = 3.0633% which is the value I specified for my "Velocity Inlet" (3) I calculated Turbulence length scale (L) using your equation L=0.07D_pipe/C_mu^(3/4) L = 0.0439m which is the value I specified for my "Velocity Inlet" Here I have an assumption that Hydraulic Diameter == Turbulence length scale. (4) I calculated Turbulence Dissipation Rate* (epsilon) using your equation epsilon = 0.1898 m2/s3 (same as my previous calculation since essentially the formula is the same) However, the value calculated by FLUENT (this time) is 0.4446375 m2/s3.

May 7, 2020, 06:33	Hydraulic Diameter	#14
vinerm Senior Member Vinerm Join Date: Jun 2009 Location: Nederland Posts: 2,946 Blog Entries: 1 Rep Power: 36	Length Scale and Hydraulic Diameter are not same, otherwise you would not require different options. minzhang likes this. __________________ Regards, Vinerm PM to be used if and only if you do not want something to be shared publicly. PM is considered to be of the least priority.

May 12, 2020, 23:53	Now I know why!	#15
minzhang Member Min Zhang Join Date: Mar 2017 Posts: 81 Rep Power: 9	Finally, I got to know why. 1. The reason is I assumed "Hydraulic Diameter == Turbulence length scale". When I use "Hydraulic Diameter =D_pipe", then I got the same epsilon value as FLUENT. 2. The formula in the old reference is consistent with the latest ones. Thanks!

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