# about alpha in OPenfoam's sutherland part

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 October 17, 2011, 11:00 about alpha in OPenfoam's sutherland part #1 New Member   yi Wang Join Date: Feb 2011 Posts: 15 Rep Power: 7 Hello, all I want someone to help me on openfoam's sutherland part. It is as follows: inline Foam::scalar Foam::sutherlandTransport::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?

 October 17, 2011, 12:59 #2 New Member   yi Wang Join Date: Feb 2011 Posts: 15 Rep Power: 7 Just I type the wrong fomula for alpha. it should be alpha=kappa/Cp

 October 18, 2011, 09:10 #3 New Member   Yi Wang Join Date: Mar 2009 Posts: 17 Rep Power: 9 Yes, but you need to compute Kappa first: Kappa = mu(T)*Cv_*(1.32 + 1.77*this->R()/Cv_)

 October 19, 2011, 03:37 #4 New Member   yi Wang Join Date: Feb 2011 Posts: 15 Rep Power: 7 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

 October 19, 2011, 03:40 #5 New Member   yi Wang Join Date: Feb 2011 Posts: 15 Rep Power: 7 Additionally, Why is CpBar used in this formula, not Cp? How to derive CpBar?

October 19, 2011, 09:03
#6
New Member

Yi Wang
Join Date: Mar 2009
Posts: 17
Rep Power: 9
Quote:
 Originally Posted by yiwang25 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

October 19, 2011, 11:21
#7
New Member

yi Wang
Join Date: Feb 2011
Posts: 15
Rep Power: 7
Quote:
 Originally Posted by jason_wy 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?

 October 19, 2011, 11:26 #8 New Member   Yi Wang Join Date: Mar 2009 Posts: 17 Rep Power: 9 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) hajott likes this.

October 19, 2011, 12:22
#9
New Member

yi Wang
Join Date: Feb 2011
Posts: 15
Rep Power: 7
Quote:
 Originally Posted by jason_wy 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!

 October 20, 2011, 05:16 #10 New Member   yi Wang Join Date: Feb 2011 Posts: 15 Rep Power: 7 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);

 December 28, 2012, 20:58 #11 New Member   Yuri Almeida Join Date: Jan 2012 Location: Rio de Janeiro, Brazil Posts: 21 Rep Power: 6 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.

 March 27, 2013, 08:41 #12 Senior Member     Armin Join Date: Feb 2011 Location: Helsinki, Finland Posts: 156 Rep Power: 11 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 Lisandro Maders likes this.

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