sutherland temperature computing

Anna Tian · December 19, 2012, 06:27

Hi,

May I ask how to compute sutherland temperature? Shall I always use 110 K?

Thank you very much.

leebro61 · December 20, 2012, 00:17

In my solver for air properties I use:

mu = C1*pow(T, 3/2)/(T+C2)
k = C3*pow(T, 3/2)/(T+C4)

where;

1.458e-06 !C1 - Sutherland's Law Dynamic Viscosity Constant
110.4 !C2 - Sutherland's Law Dynamic Viscosity Constant
2.495e-03 !C3 - Sutherland's Law Thermal Conductivity Constant
194.0 !C4 - Sutherland's Law Thermal Conductivity Constant

I am also curious if there are better values to be using based on the temperature ranges I am simulating...

lukasf · May 25, 2022, 05:26

Hi,

OpenFOAM and ANSYS Fluent use T_s = S = C2 = 110.4 K for air.

However, in the paper of Sutherland it gives a value of 113 K.

Where does the difference come from?

The value of 110.4 K is not even mentioned.

Paper of Sutherland:

https://www.google.com/url?sa=t&rct=...GPpKK5dGrLzoaL

LuckyTran · May 25, 2022, 08:33

I don't know the origin of any of those numbers but to me, if I am just trying to calculate viscosity then Sutherland's formula is just the form of the equation and I never have any expectation that there is 1 set of correct coefficients unless I am writing specifically about the history of the viscosity of air. The difference is expected (at least in my opinion).

Sutherland's formula doesn't take into account pressure and is really just a curve fit of the viscosity vs temperature at some arbitrarily set reference temperature (which is also one of the coefficients).

Best accuracy is obtained when the curve fitting is done at the reference temperature and pressure that you are simulating. If I am doing combustion at 24 bar, I wouldn't use a set of Sutherland's coefficients at room temperature and pressure, I would do my own curve fitting and generate my own coefficients vs a fluids database that I trust. Also, fluid properties databases have changed significantly since the time of Sutherland.

lukasf · May 25, 2022, 09:35

I think you are right. It is better to use your own function derived from a property tool.

I compared the results of a property tool and sutherland with both coefficients and the results are very similiar in the temperature and pressure range I have.

Good to check, though.

December 19, 2012, 06:27	sutherland temperature computing	#1
Anna Tian Senior Member Meimei Wang Join Date: Jul 2012 Posts: 494 Rep Power: 15	Hi, May I ask how to compute sutherland temperature? Shall I always use 110 K? Thank you very much. __________________ Best regards, Meimei

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December 20, 2012, 00:17		#2
leebro61 New Member Join Date: Nov 2012 Posts: 3 Rep Power: 13	In my solver for air properties I use: mu = C1pow(T, 3/2)/(T+C2) k = C3pow(T, 3/2)/(T+C4) where; 1.458e-06 !C1 - Sutherland's Law Dynamic Viscosity Constant 110.4 !C2 - Sutherland's Law Dynamic Viscosity Constant 2.495e-03 !C3 - Sutherland's Law Thermal Conductivity Constant 194.0 !C4 - Sutherland's Law Thermal Conductivity Constant I am also curious if there are better values to be using based on the temperature ranges I am simulating...

May 25, 2022, 05:26		#3
lukasf Senior Member Lukas Fischer Join Date: May 2018 Location: Germany, Munich Posts: 117 Rep Power: 7	Hi, OpenFOAM and ANSYS Fluent use T_s = S = C2 = 110.4 K for air. However, in the paper of Sutherland it gives a value of 113 K. Where does the difference come from? The value of 110.4 K is not even mentioned. Paper of Sutherland: https://www.google.com/url?sa=t&rct=...GPpKK5dGrLzoaL

May 25, 2022, 08:33		#4
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,674 Rep Power: 65	I don't know the origin of any of those numbers but to me, if I am just trying to calculate viscosity then Sutherland's formula is just the form of the equation and I never have any expectation that there is 1 set of correct coefficients unless I am writing specifically about the history of the viscosity of air. The difference is expected (at least in my opinion). Sutherland's formula doesn't take into account pressure and is really just a curve fit of the viscosity vs temperature at some arbitrarily set reference temperature (which is also one of the coefficients). Best accuracy is obtained when the curve fitting is done at the reference temperature and pressure that you are simulating. If I am doing combustion at 24 bar, I wouldn't use a set of Sutherland's coefficients at room temperature and pressure, I would do my own curve fitting and generate my own coefficients vs a fluids database that I trust. Also, fluid properties databases have changed significantly since the time of Sutherland.

May 25, 2022, 09:35		#5
lukasf Senior Member Lukas Fischer Join Date: May 2018 Location: Germany, Munich Posts: 117 Rep Power: 7	I think you are right. It is better to use your own function derived from a property tool. I compared the results of a property tool and sutherland with both coefficients and the results are very similiar in the temperature and pressure range I have. Good to check, though.