SutherlandTransport setting for air

tangd · July 20, 2006, 08:52

Could somebody tell me what are the values of Sutherland coefficient As and Sutherland temperature Ts for air? Thanks!

elmorsli · July 20, 2006, 13:04

For viscosity:
mu=1.4584E-6*pow(T,3./2.)/(T+110.33);

and for thermal conductivity:
lambda=2474.7264e-6*pow(T,3./2.)/(T+194.4)

tangd · July 26, 2006, 01:21

Thanks for your reply. What are the coefficients As and Ts for N2? Is there a table including the coefficient of all gases?

TomP · July 24, 2009, 05:29

When using constTransport the conductivity can be calculated based on the viscosity, the heat capacity and the Prandtl number. When using sutherlandTransport there is no mention of the conductivity constant (at least not in the manual). You also give the sutherland coefficients for the conductivity, but then my question is where do I use them? Right after those of the viscosity?

Quote:

Originally Posted by elmorsli

For viscosity:
mu=1.4584E-6*pow(T,3./2.)/(T+110.33);

and for thermal conductivity:
lambda=2474.7264e-6*pow(T,3./2.)/(T+194.4)

mohsen cheraghi · October 26, 2012, 04:24

I have the same question. can any one explain more?

okroud · October 30, 2012, 05:05

Quote:

Originally Posted by elmorsli

For viscosity:
mu=1.4584E-6*pow(T,3./2.)/(T+110.33);

and for thermal conductivity:
lambda=2474.7264e-6*pow(T,3./2.)/(T+194.4)

I am also interested in the calculation of the thermal conductivity. Is there any more information? Which numbers in the second equation are coefficients, that I have to set in OpenFOAM? Hope anyone can help us!

immortality · December 6, 2012, 07:00

I don't think conductivity coefficients to be necessary.only As and Ts are important.

camille131 · April 23, 2013, 16:37

Hi,
could you tell me where I can find the sutherland coefficients As and Ts for natural gas (ie: methane). And where can I find a table of these coef. for any gas?
Thank you very much

Daniel_P · April 3, 2014, 10:20

Hej everyone!

Sorry for reactivating this old post, but it is still not clear to me how the thermal conductivity is calculated by OF when using Sutherland's law.

For my calculations I use chtMultiRegionSimpleFoam (OF 2.2.x) and experimented with the transport models in thermophysicalProperties of a fluid region. The thermo model I set is heRhoThermo and the fluid is air.

When I set transport to "const", I define a constant dynamic viscosity mu and the Prandtl number Pr. The thermal conductivity k is then calculated by Pr=mu*cp/k.

In a second example I set transport to "sutherland". Now I define only the two input parameters As=1.4792e-06 and Ts=116 for Sutherland's law. Since there is no error message when starting a calculation, I guess that no other input is needed.

But how does the solver calculate the thermal conductivity then?

Thank you for any help,
Daniel

GRAUPS · July 16, 2014, 15:46

Quote:

Originally Posted by Daniel_P

But how does the solver calculate the thermal conductivity then?
Daniel

Daniel, sorry this is a bit late, but I was just looking into this very thing today and I believe I found the answer. I'll post here in case anyone else needs the info.

The OpenFOAM sutherland viscosity model appears to use the modified Euken Model (based on kinetic theory) for the thermal conductivity calculation. I found the equation being used on line 149 of the sutherlandTransportI.H file ($FOAM_SRC/thermophysicalModels/specie/transport/sutherland/sutherlandTransportI.H)

I identified it as the modified Euken Model based on section 1.4.7.2.2 of this doc...

http://www.arc.vt.edu/ansys_help/cfx_mod/i1299744.html

Brock

Daniel_P · July 18, 2014, 06:00

Hej Brock!

Thank you very much for your precise answer!
I think you are right, the solver uses the modified Eucken equation in order to calculate the thermal conductivity if the Sutherland transport model is selected.
However, I am not sure how good the accuracy of this model is? From what I read, the thermal conductivity calculated from the modified Eucken equation differs up to 25% from experimental values. Anyway, the accuracy is another question. It is good to know what OpenFOAM does!
Thanks again for your help!

Daniel

dappe · November 3, 2015, 08:38

Sorry if I'm witless

but I can't understand how to get As and Ts from mu and lambda equations posted at the top of the thread! In particular in my case I'm interested in values for air.
Thanks for your help.
Alessandro

Alexee · November 18, 2015, 09:00

Quote:

Originally Posted by dappe

Sorry if I'm witless

but I can't understand how to get As and Ts from mu and lambda equations posted at the top of the thread! In particular in my case I'm interested in values for air.
Thanks for your help.
Alessandro

As and Ts are the constants in mu formula, namely:

As = 1.4584E-6
Ts = 110.33

Heat80 · November 23, 2015, 15:12

Hi,
Does anybody know how to include thermal conductivity of individual species (not for mixture) in the Fluent results. I know how to get Cp and species gradients but still struggling with thermal conductivity.
Thank you in advance

amin_jalalian · April 10, 2016, 08:00

Hi
I am working with methane-air 2-step combustion. In later versions of openfoam there was no need to file 'transportProperties' but in openfoam3.0+ there is need to that. In openfoam3.0+ tutorial in 'transportProperties' it was As and Ts. What values must I write for these parameters in methane combustion?

ebringley · September 13, 2017, 13:00

Quote:

Originally Posted by GRAUPS

Daniel, sorry this is a bit late, but I was just looking into this very thing today and I believe I found the answer. I'll post here in case anyone else needs the info.

The OpenFOAM sutherland viscosity model appears to use the modified Euken Model (based on kinetic theory) for the thermal conductivity calculation. I found the equation being used on line 149 of the sutherlandTransportI.H file ($FOAM_SRC/thermophysicalModels/specie/transport/sutherland/sutherlandTransportI.H)

I identified it as the modified Euken Model based on section 1.4.7.2.2 of this doc...

http://www.arc.vt.edu/ansys_help/cfx_mod/i1299744.html

Brock

Here is an updated link:
CFX Documentation:
https://www.sharcnet.ca/Software/Ans...cfx_intro.html

Specifically:
https://www.sharcnet.ca/Software/Ans.../i1299744.html

Benito · October 16, 2018, 05:31

Hi

I am trying to simulate heat transfer around a cylinder for air with thermal expansion in the gas with OpenFoam 3.1.

My thermoType is :

>thermoType hPsiThermo<pureMixture<sutherlandTransport<specieT hermo<hConstThermo<perfectGas>>>>>;
>mixture air 1 28.9 1007 0 1.458e-06 110.4;

for the mixture, I set to two parameters of Sutherland model (As= 1.458e-06and Ts=110.4).

How I do it for the heat conductiity?

Thanks

Henrinavier · November 22, 2022, 07:55

Since I just stumbled across this problem, here are my take-aways:

The formulation of Sutherland's law to calculate the viscosity $\mu$ in OpenFOAM deviates from the original or common formulation:
Original/Common: $\mu_{0}\frac{T_{0}+C}{T+C} \left ( \frac{T}{T_{0}} \right ) ^{3/2}$ , with reference viscosity $\mu_{0}$ at the reference temperature

and the Sutherland coefficient

.
OpenFOAM: $\frac{A_{s} T^{3/2}}{T+T_{s}}$ , with $A_{s} = \mu_{0} \frac{T_{0} + C}{T_0^{3/2}}$ (and $T_{s} = C$ just to make it a bit more complicated).

Therefore, you can use the values from literature but you'll have to calculate

for each substance.

Hope that helps someone some time.

July 20, 2006, 08:52	Could somebody tell me what ar	#1
tangd Member Dihao Tang Join Date: Mar 2009 Posts: 78 Rep Power: 17	Could somebody tell me what are the values of Sutherland coefficient As and Sutherland temperature Ts for air? Thanks!

July 20, 2006, 13:04	*For viscosity: mu=1.4584E-6p**	#2
elmorsli New Member mbark elmorsli Join Date: Mar 2009 Location: Sherbrooke, quebec, canada Posts: 1 Rep Power: 0	For viscosity: mu=1.4584E-6pow(T,3./2.)/(T+110.33); and for thermal conductivity: lambda=2474.7264e-6pow(T,3./2.)/(T+194.4)

July 26, 2006, 01:21	Thanks for your reply. What ar	#3
tangd Member Dihao Tang Join Date: Mar 2009 Posts: 78 Rep Power: 17	Thanks for your reply. What are the coefficients As and Ts for N2? Is there a table including the coefficient of all gases?

April 3, 2014, 10:20		#9
Daniel_P New Member Join Date: Dec 2013 Posts: 11 Rep Power: 12	Hej everyone! Sorry for reactivating this old post, but it is still not clear to me how the thermal conductivity is calculated by OF when using Sutherland's law. For my calculations I use chtMultiRegionSimpleFoam (OF 2.2.x) and experimented with the transport models in thermophysicalProperties of a fluid region. The thermo model I set is heRhoThermo and the fluid is air. When I set transport to "const", I define a constant dynamic viscosity mu and the Prandtl number Pr. The thermal conductivity k is then calculated by Pr=mu*cp/k. In a second example I set transport to "sutherland". Now I define only the two input parameters As=1.4792e-06 and Ts=116 for Sutherland's law. Since there is no error message when starting a calculation, I guess that no other input is needed. But how does the solver calculate the thermal conductivity then? Thank you for any help, Daniel immortality likes this.

November 23, 2015, 15:12	Thermal conductivity for each species	#14
Heat80 New Member Younis Najim Join Date: Apr 2013 Location: Michigan State University Posts: 12 Rep Power: 13	Hi, Does anybody know how to include thermal conductivity of individual species (not for mixture) in the Fluent results. I know how to get Cp and species gradients but still struggling with thermal conductivity. Thank you in advance

October 26, 2012, 04:24		#5
mohsen cheraghi New Member mohsen cheraghi Join Date: Jun 2010 Location: Switzerland Posts: 28 Rep Power: 15	I have the same question. can any one explain more?

December 6, 2012, 07:00		#7
immortality Senior Member Ehsan Join Date: Oct 2012 Location: Iran Posts: 2,208 Rep Power: 26	I don't think conductivity coefficients to be necessary.only As and Ts are important.

April 23, 2013, 16:37		#8
camille131 Member Camille Join Date: Oct 2012 Posts: 54 Rep Power: 13	Hi, could you tell me where I can find the sutherland coefficients As and Ts for natural gas (ie: methane). And where can I find a table of these coef. for any gas? Thank you very much

July 18, 2014, 06:00		#11
Daniel_P New Member Join Date: Dec 2013 Posts: 11 Rep Power: 12	Hej Brock! Thank you very much for your precise answer! I think you are right, the solver uses the modified Eucken equation in order to calculate the thermal conductivity if the Sutherland transport model is selected. However, I am not sure how good the accuracy of this model is? From what I read, the thermal conductivity calculated from the modified Eucken equation differs up to 25% from experimental values. Anyway, the accuracy is another question. It is good to know what OpenFOAM does! Thanks again for your help! Daniel

November 3, 2015, 08:38		#12
dappe New Member Join Date: Sep 2015 Posts: 15 Rep Power: 10	Sorry if I'm witless but I can't understand how to get As and Ts from mu and lambda equations posted at the top of the thread! In particular in my case I'm interested in values for air. Thanks for your help. Alessandro

April 10, 2016, 08:00	As and Ts in methan combustion	#15
amin_jalalian Member amin jalalian Join Date: Mar 2014 Posts: 34 Rep Power: 12	Hi I am working with methane-air 2-step combustion. In later versions of openfoam there was no need to file 'transportProperties' but in openfoam3.0+ there is need to that. In openfoam3.0+ tutorial in 'transportProperties' it was As and Ts. What values must I write for these parameters in methane combustion?

October 16, 2018, 05:31		#17
Benito New Member Join Date: Oct 2018 Posts: 1 Rep Power: 0	Hi I am trying to simulate heat transfer around a cylinder for air with thermal expansion in the gas with OpenFoam 3.1. My thermoType is : >thermoType hPsiThermo<pureMixture<sutherlandTransport<specieT hermo<hConstThermo<perfectGas>>>>>; >mixture air 1 28.9 1007 0 1.458e-06 110.4; for the mixture, I set to two parameters of Sutherland model (As= 1.458e-06and Ts=110.4). How I do it for the heat conductiity? Thanks

November 22, 2022, 07:55		#18
Henrinavier New Member Adrian Join Date: Dec 2015 Location: Germany Posts: 6 Rep Power: 10	Since I just stumbled across this problem, here are my take-aways: The formulation of Sutherland's law to calculate the viscosity $\mu$ in OpenFOAM deviates from the original or common formulation: Original/Common: $\mu_{0}\frac{T_{0}+C}{T+C} \left ( \frac{T}{T_{0}} \right ) ^{3/2}$ , with reference viscosity $\mu_{0}$ at the reference temperature and the Sutherland coefficient . OpenFOAM: $\frac{A_{s} T^{3/2}}{T+T_{s}}$ , with $A_{s} = \mu_{0} \frac{T_{0} + C}{T_0^{3/2}}$ (and $T_{s} = C$ just to make it a bit more complicated). Therefore, you can use the values from literature but you'll have to calculate for each substance. Hope that helps someone some time.

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