
[Sponsors] 
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<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? 

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 

October 19, 2011, 11:21 

#7 
New Member
yi Wang
Join Date: Feb 2011
Posts: 15
Rep Power: 7 

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) 

October 19, 2011, 12:22 

#9  
New Member
yi Wang
Join Date: Feb 2011
Posts: 15
Rep Power: 7 
Quote:
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”, McGrawHill, 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 

Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
alphaEqn.H in twoPhaseEulerFoam  cheng1988sjtu  OpenFOAM Bugs  15  May 1, 2016 16:12 
TwoPhaseEulerFoam and Boundary conditions  raagh77  OpenFOAM Running, Solving & CFD  98  September 23, 2013 06:31 
about bounded alpha equation for bubbleFoam and twoPhaseEulerFoam  kaifu  OpenFOAM  2  May 6, 2011 05:33 
settlingFoam fails with timeVarying conditions on U  alberto  OpenFOAM Bugs  1  April 21, 2010 14:16 
Determining alpha and beta for porous baffle  Liaqat Khan  CDadapco  1  October 27, 2000 04:44 