Temperature dependent Cp in Perfect Gas

Yuval · August 29, 2014, 16:24

Hi there Foamers!

A long time reader, a first-time writer in these forums.

My question is regarding the thermophysicalProperties dictionary.
As OpenFoam implements only an ideal gas EoS, I was wondering how it can allow temperature-dependent models for Cp and Cv, such as janaf and hPolynomial.
Doesn't that contradict the ideal-gas assumption in which Cp and Cv are taken as constants?
I guess I'm missing something here. Would be forever grateful to whoever enlightens me.

Thanks in advance!
Yuval.

Matt_B · September 3, 2014, 15:26

Hi Yuval, and welcome to this Forum.
I go straight to the answer to your question, I hope I have understood what you meant.
A gas is defined as "ideal" just because at low pressure its behavior is very close to an "Ideal Gas" and its properties are easily predictable. Cp and Cv for an Ideal Gas are just considered depending on T whilst for a "Real Gas" it shall be also accounted a contribution by means of pressure variation.
Thus, it's common that an "Ideal Gas" has Cp and Cv temperature-dependent; it means that Cp and Cv are never a constant, when temperature varies, but they usually have a linear or quadratic correlation with temperature.

Bye.

Matteo

Yuval · September 3, 2014, 20:47

Hi Matteo,

Thanks a lot for your answer!
I admit that I'm a bit confused by the different definitions of an ideal gas you find in different sources. In some places "Ideal Gas" and "Perfect Gas" are synonymous while in others they are said to exhibit different behaviors. For instance here: http://yidnekachew.files.wordpress.c...ronaldplus.pdf an "ideal gas" is defined just like you said (pg. 376), while a "perfect gas" is a gas that obeys the ideal gas law and has a constant specific heat capacity.

I guess that in openFoam, although the equation of state is named "perfect gas" it is meant as "ideal gas", with temperature-dependent heat capacities.

Anyway, thanks again for your answer!

Yuval.

August 29, 2014, 16:24	Temperature dependent Cp in Perfect Gas	#1
Yuval New Member Yuval Join Date: Jul 2014 Location: Munich, Germany Posts: 3 Rep Power: 12	Hi there Foamers! A long time reader, a first-time writer in these forums. My question is regarding the thermophysicalProperties dictionary. As OpenFoam implements only an ideal gas EoS, I was wondering how it can allow temperature-dependent models for Cp and Cv, such as janaf and hPolynomial. Doesn't that contradict the ideal-gas assumption in which Cp and Cv are taken as constants? I guess I'm missing something here. Would be forever grateful to whoever enlightens me. Thanks in advance! Yuval. Last edited by Yuval; September 1, 2014 at 09:09.

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September 3, 2014, 15:26		#2
Matt_B Member Join Date: Feb 2012 Posts: 35 Rep Power: 14	Hi Yuval, and welcome to this Forum. I go straight to the answer to your question, I hope I have understood what you meant. A gas is defined as "ideal" just because at low pressure its behavior is very close to an "Ideal Gas" and its properties are easily predictable. Cp and Cv for an Ideal Gas are just considered depending on T whilst for a "Real Gas" it shall be also accounted a contribution by means of pressure variation. Thus, it's common that an "Ideal Gas" has Cp and Cv temperature-dependent; it means that Cp and Cv are never a constant, when temperature varies, but they usually have a linear or quadratic correlation with temperature. Bye. Matteo

September 3, 2014, 20:47		#3
Yuval New Member Yuval Join Date: Jul 2014 Location: Munich, Germany Posts: 3 Rep Power: 12	Hi Matteo, Thanks a lot for your answer! I admit that I'm a bit confused by the different definitions of an ideal gas you find in different sources. In some places "Ideal Gas" and "Perfect Gas" are synonymous while in others they are said to exhibit different behaviors. For instance here: http://yidnekachew.files.wordpress.c...ronaldplus.pdf an "ideal gas" is defined just like you said (pg. 376), while a "perfect gas" is a gas that obeys the ideal gas law and has a constant specific heat capacity. I guess that in openFoam, although the equation of state is named "perfect gas" it is meant as "ideal gas", with temperature-dependent heat capacities. Anyway, thanks again for your answer! Yuval.