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Old   November 17, 2007, 18:48
Default Question on Sutherland's Relation and Viscosity
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Pradu
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Sutherland's relation gives the viscosity for air as a function of temperature only. Can this relation still be used in high-speed compressible flow? If not, are there any known relations at high speeds and temperatures for air's viscosity, heat generated due to viscosity, and thermal conduction?
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Old   November 17, 2007, 23:10
Default Re: Question on Sutherland's Relation and Viscosit
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Ahmed
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both relations (for viscosity and thermal conductivity) are valid as long as the air does not reach the limit of dissociation
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Old   November 17, 2007, 23:23
Default Re: Question on Sutherland's Relation and Viscosit
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Anton Lyaskin
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Application of Sutherland relation is actually limited by temperature. The limit is about 1700..1900K (different sources give different values). There are some papers about modifications to Sutherland relation for higher temperature, but most of them are not publicly available. From annotations to them I've got the idea that the trick is to change the exponent. So I've used the formula like this

viscosity = 1.899e-7 * T ^ 1.74 / (T - 296.7)

It gives you more or less smooth transition from Sutherland and fits pretty well with experimental data. The problem is that if you go for even higher temperature, like 3000K or more, you'll get chemical reactions (dissociation of O2, formation of NO and NO2 and etc). So if you'll need precise viscosity calculation, you should calculate it as for a mixture of different gases, taking into the account local concentration of all these species.
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Old   November 18, 2007, 02:33
Default Re: Question on Sutherland's Relation and Viscosit
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Pradu
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> viscosity = 1.899e-7 * T ^ ( 1.74 / (T - 296.7) )

Nice. What are the units for T and viscosity? If I assume Kelvin and kg/(m*s) it doesn't come out to be very close to Sutherland's relation at low temperatures.

Also the given formula will peak at T=296.7 Tunits, so after what temperature is the given formula valid.
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Old   November 18, 2007, 02:57
Default Re: Question on Sutherland's Relation and Viscosit
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Pradu
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Sorry, it does correspond to Sutherland's. I guess one can start using your proposed relation after 1900K:

http://www.prism.gatech.edu/~gtg365v.../Viscosity.png

Where did you get the experimental data for the fit? Is it accessible to the public?
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Old   November 18, 2007, 09:45
Default Re: Question on Sutherland's Relation and Viscosit
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Anton Lyaskin
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Yes, you're right about units. It's for use at high temperatures only (above 1700...1900K) - at lower temperatures it will of course differ from Sutherland
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Old   November 18, 2007, 09:51
Default Re: Question on Sutherland's Relation and Viscosit
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Anton Lyaskin
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As for the data source - I'll have to search my archives, because it was 4 years ago. Either it was something publicly available found by googling, or it was a Dutch textbook on high-speed aerodynamics from one of my colleagues (it was from Delft TU and had no references)
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Old   November 19, 2007, 07:51
Default Re: Question on Sutherland's Relation and Viscosit
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George
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You can also use the polyonims data fits from NASA. They also give the coefficiens, and they follow the same methodology as for calculating Cp
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Old   November 20, 2007, 04:24
Default Re: Question on Sutherland's Relation and Viscosit
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Anton Lyaskin
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I have polynomial approximation found here

http://users.wpi.edu/~ierardi/FireTools/air_prop.html

but it also has a limitation at 1600K.

George, could you please give a link to NASA polynomials?

As for my approximation, now I remember where it came from - I found the idea in the publicly available annotation to a classified paper (my request for this paper should be somewhere at the forum). In the annotation there was a new value of the exponent (i.e 1.74), so I've just adjusted the other coefficients to have smooth transition from Sutherland at 1900.

Anyway, 1900K is pretty close to the point where chemistry starts to play a big part (it will depend upon pressure also).
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Old   November 21, 2007, 06:09
Default Re: Question on Sutherland's Relation and Viscosit
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George
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I am on holidays at the moment and I have no idea where I found them. I just remember that it was a .pdf file containing coefficients for hundreds of chemical species. When I return home next week I will let you know.
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