about alpha in OPenfoam's sutherland part
 

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?

Just I type the wrong fomula for alpha. it should be
alpha=kappa/Cp

Yes, but you need to compute Kappa first:

Kappa = mu(T)*Cv_*(1.32 + 1.77*this->R()/Cv_)

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

Additionally, Why is CpBar used in this formula, not Cp? How to derive CpBar?

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?

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!

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);

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.

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

Dear OF users,

I would like to revive this old thread.

I know, that in last OpenFOAM versions CpBar is not used any more. Instead they use alpha = kappa/Cp(p, T).

In foam-extend it is still alpha = kappa/CpBar, where CpBar = [deltaT*{H(T) – H(Tstd)} + Cp(T)]/[sqr(deltaT) + 1].

When I use e.g. Janaf for calculating Cp and H, then I use the thermally perfect gas model, which is not the same as calorically perfect gas model.

In my opinion, when I calculate alpha by alpha = kappa/Cp, I use the calorically perfect gas model, even when I calculated Cp with Janaf.

So, I think here is an inconsistency.

I can’t calculate H by Janaf thermophysical model (therally perfect gas) and then calculate alpha for my energy conservation equation by assuming that the gas is calorically perfect.

Is there anybody who has the same doubts?

Regards

Alex