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Why my calculated epsilon is different from FLUENT calculation?

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Old   April 30, 2020, 21:48
Default Why my calculated epsilon is different from FLUENT calculation?
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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.
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Old   May 1, 2020, 14:59
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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 l.
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Old   May 1, 2020, 17:01
Default Current version of Ansys documentation
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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!
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Old   May 2, 2020, 16:07
Default Documentation
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Documentation is available at

https://ansyshelp.ansys.com
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Old   May 3, 2020, 20:00
Default Don't have access to the Documentation
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It seems that, as a free student academic version, I don't have the permission to access the document.
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Old   May 4, 2020, 16:21
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Yes, students do not have access to that. The formulation is still same, except that C_\mu is considered within l. So, the value of l itself changes.
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Old   May 4, 2020, 16:36
Default Formula of Turbulence length scale
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I am wondering whether you could post the formula for Turbulence length scale.
Thanks!
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Old   May 5, 2020, 04:45
Default Length Scale
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l = \frac{0.07 L}{C_\mu^{3/4}}
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Old   May 5, 2020, 10:07
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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?
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Old   May 5, 2020, 10:35
Default Epsilon
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Yes, the formula is still the same, however, the length scale is not.
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Old   May 5, 2020, 10:37
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But it won't affect the calculation for epsilon.
Therefore, my calculated epsilon is still different from the FLUENT calculation.
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Old   May 5, 2020, 11:05
Default Epsilon
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It does because the user supplies the value for l and not L.
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Old   May 6, 2020, 17:49
Default I still could not get the same epsilon value as FLUENT?
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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.
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Old   May 7, 2020, 05:33
Default Hydraulic Diameter
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Length Scale and Hydraulic Diameter are not same, otherwise you would not require different options.
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Old   May 12, 2020, 22:53
Default Now I know why!
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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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