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November 17, 2007, 18:48 
Question on Sutherland's Relation and Viscosity

#1 
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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 highspeed 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?


November 17, 2007, 23:10 
Re: Question on Sutherland's Relation and Viscosit

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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


November 17, 2007, 23:23 
Re: Question on Sutherland's Relation and Viscosit

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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 = 1.899e7 * 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. 

November 18, 2007, 02:33 
Re: Question on Sutherland's Relation and Viscosit

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> viscosity = 1.899e7 * 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. 

November 18, 2007, 02:57 
Re: Question on Sutherland's Relation and Viscosit

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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? 

November 18, 2007, 09:45 
Re: Question on Sutherland's Relation and Viscosit

#6 
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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


November 18, 2007, 09:51 
Re: Question on Sutherland's Relation and Viscosit

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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 highspeed aerodynamics from one of my colleagues (it was from Delft TU and had no references)


November 19, 2007, 07:51 
Re: Question on Sutherland's Relation and Viscosit

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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


November 20, 2007, 04:24 
Re: Question on Sutherland's Relation and Viscosit

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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). 

November 21, 2007, 06:09 
Re: Question on Sutherland's Relation and Viscosit

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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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