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Caracteristic length used for Peclet number

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Old   June 2, 2015, 10:00
Default Caracteristic length used for Peclet number
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Laurent DASTUGUE
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Hi foamers,
Does anybody know what is the caracteristic length used when OpenFOAM calculate the Peclet number ?
I don't have access these days to OpenFOAM and i have to answer this question.
Thanks a lot.
Laurent
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Old   June 2, 2015, 10:38
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Alexey Matveichev
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Hi,

It seems you have access to the Internet.

https://github.com/OpenFOAM/OpenFOAM...d/Pe/Pe.C#L118

https://github.com/OpenFOAM/OpenFOAM...olation.C#L136

So, Pe is calculated in assumption Sct = 1 and length scale is cell size.
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Old   June 2, 2015, 10:51
Default Sct ?
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Hi Alexey,
thank you for the links, and for your answer concerning the length scale.
Just one question : What is Sct ?
Laurent
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Old   June 2, 2015, 11:00
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Alexey Matveichev
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Sct is turbulent Schmidt number (https://en.wikipedia.org/wiki/Schmidt_number). As you can see, in Pe.C everything is divided by viscosity, yet for Peclet one has to divide by diffusivity. If we assume that Sc = 1, we can just divide by viscosity (for turbulent case we have to assume that Sc = 1 and Sct = 1, so nuEff( = nu + nut) == Deff( = nu/Sc + nut/Sct)).
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Old   June 3, 2015, 04:56
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Laurent DASTUGUE
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Ok i understand now.
Is the Peclet number calculated here a massic one ? (Pe=Re*Sc) or a thermic one (Pe=Re*Pr).
If this is a massic one, can i say that Pe = Re, since Sc = 1 ?
Laurent
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Old   June 3, 2015, 05:08
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Alexey Matveichev
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Hi,

If you assume Pr = Prt (turbulent Prandtl number) = 1, then it becomes "termic" And yes, you can call the value calculated by Pe utility Reynolds number.
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Old   June 3, 2015, 05:18
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In fact what i want to do is the calculation of the convection coefficient h.
I know that there is a relation between h and the Nusselt number, and i know a relation letting me to have Nusselt, by the use of Re and Pr values.
Since i have the value of Prandtl number easily, knowing the fluid caracteristics, i just need the value of Re to have Nu and to have finally the value of h.
So reading your posts, i understand the following :
using Pe utility, i can do the operation Re = Pe/Pr to have Reynolds number.
Am i right ? Or must i apply some operations on Pe utility results before having the Peclet number value which will let me calculate Re ?
Laurent
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Old   June 3, 2015, 07:54
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Alexey Matveichev
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Hi,

Short answer: it depends.

Pe field produced by Pe utility is surfaceScalarField and its value is

\text{Pe}_{\text{calculated by Pe utility}} = \frac{Lu}{\nu}

where L is of order of cell size, u is in fact

u = \frac{\vec{u}\times\vec{S}}{|\vec{S}|}

where S is face normal vector with module equal to the surface of the face.

So, in fact Pe is Re.

If you are happy with h as a surfaceScalarField, then yes, you just manipulate result of Pe utility; if, for example, you need convection coefficient as volume field, you need additional steps.
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Old   June 3, 2015, 08:07
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Laurent DASTUGUE
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Hi,
thank you very much for your help.
So what we have is : Pe = Pe / Pr, isn't it ?
Why is this utility not called Re ???
Laurent
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Old   June 3, 2015, 09:37
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Alexey Matveichev
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Hi,

Quote:
Originally Posted by laurentD View Post
So what we have is : Pe = Pe / Pr, isn't it ?
Yes, though not sure if I get the notation right.

Quote:
Why is this utility not called Re ???
I don't know. Due to certain historical reasons?
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Old   June 3, 2015, 10:14
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Laurent DASTUGUE
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Thank you very much Alexey for your time. Have a good day.
Maybe this utility will be called Re in a next future thanks to your explanations ;-)
Laurent
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