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about alpha in OPenfoam's sutherland part

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Old   October 17, 2011, 11:00
Question about alpha in OPenfoam's sutherland part
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yi Wang
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Hello, all
I want someone to help me on openfoam's sutherland part. It is as follows:

inline Foam::scalar Foam::sutherlandTransport<Thermo>::alpha
{
.......................
scalar CpBar =
(deltaT*(this->H(T) - this->H(specie::Tstd)) + Cp_)/(sqr(deltaT) + 1);
return mu(T)*Cv_*(1.32 + 1.77*this->R()/Cv_)/CpBar;
}
I am confused about Cp and alpha. In my opinion, alpha=mu(T)*Cp_.
Why use above fomula to calculate alpha?
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Old   October 17, 2011, 12:59
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Just I type the wrong fomula for alpha. it should be
alpha=kappa/Cp
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Old   October 18, 2011, 09:10
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Yes, but you need to compute Kappa first:

Kappa = mu(T)*Cv_*(1.32 + 1.77*this->R()/Cv_)
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Old   October 19, 2011, 03:37
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In my opinion, that is
Kappa=mu(T)*Cp_
=mu(T)*(Cv_+this->R())
=mu(T)*Cv_*(1. + this->R()/Cv_)
which is different from Kappa = mu(T)*Cv_*(1.32 + 1.77*this->R()/Cv_) .
Why?
How can I get 1.32 and 1.77?
if some would like, please give the details. thanks
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Old   October 19, 2011, 03:40
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Additionally, Why is CpBar used in this formula, not Cp? How to derive CpBar?
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Old   October 19, 2011, 09:03
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Quote:
Originally Posted by yiwang25 View Post
In my opinion, that is
Kappa=mu(T)*Cp_
You are making an assumption that Prandtl Number is 1, which is not general.

kappa is computed by modified Euchen Formula
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Old   October 19, 2011, 11:21
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Quote:
Originally Posted by jason_wy View Post
You are making an assumption that Prandtl Number is 1, which is not general.

kappa is computed by modified Euchen Formula

jason_wy, thank you very much!

Would you like to show me the details of modified Euchen Formula? or how can I get its reference?
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Old   October 19, 2011, 11:26
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This is the reference I have. I don't have it in hand. You proabably can find the formula elsewhere too. Good luck.

modified Euchen formula (Thermophysical Properties of Fluids: An Introduction to their prediction, Marc J. Assael, J. P. M. Trusler, Thomas F. Tsolakis, Imperial College Press, 1996)
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Old   October 19, 2011, 12:22
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Quote:
Originally Posted by jason_wy View Post
This is the reference I have. I don't have it in hand. You proabably can find the formula elsewhere too. Good luck.

modified Euchen formula (Thermophysical Properties of Fluids: An Introduction to their prediction, Marc J. Assael, J. P. M. Trusler, Thomas F. Tsolakis, Imperial College Press, 1996)

Thank you very much!
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Old   October 20, 2011, 05:16
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Additionally, I want to know where CpBar comes from? would you like to show me the reference?

CpBar =
(deltaT*(this->H(T) - this->H(specie::Tstd)) + Cp_)/(sqr(deltaT) + 1);
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Old   December 28, 2012, 20:58
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I don't understand the meaning of Cpbar too.

First of all, in this expression, the dimensions doesn't fit:

Cpbar = (deltaT*deltaH + Cp) / (sqr(deltaT) + 1)

Apparently it is a empirical correlation, because as deltaT -> 0 (or T -> Tstd), Cpbar -> Cp.

As described in Poling, B.E., Prausnitz, J.M., and O’Connell, J.P., “The Properties of Gases and Liquids”, McGraw-Hill, New York, 2001, the Modified Eucken Model does not fit very well as the temperature rises (the Eucken factor has in some cases a wrong behavior), so maybe Cpbar should "correct" this deviation.

But this expression for Cpbar I can't find it anywhere. Could someone help us?

By the way, the usage of Cpbar for alpha calculation imply that the kappa and alpha returned by sutherlandtransport does not satisfy the alpha = kappa/Cp condition, resulting perhaps in a poor adjustment.
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Old   March 27, 2013, 08:41
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In my opinion this whole Cpbar calculation is just wrong.

It might be somewhat justified for constantTransport, but I wouldn't even do it there.

In case of sutherlandTransport or polynomialTransport I think it's just a bug. Both of these transport models are usually used with a advanced model for Cp (e.g. janaf or polynomial) and therefore one gets an accurate Cp from there.

I guess I'm not the only one with that opinion, as the whole Cpbar thing was replaced in 2.2.x by a function call to the thermo class for all three transport models.
So correct Cp values are used there for the calculation of alpha.

-Armin
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