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f_sizer August 26, 2010 07:03

Blottner Coefficients
 
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I have been working with a CFD code that requires Blottner coefficients as an input. These are not easy to come by, but I've written a simple program in Scilab that calculates the coefficients for you.

The user inputs required are three temperatures and their corresponding viscosities, which are available on the NIST website.

http://webbook.nist.gov/chemistry/fluid/

The output is given in the x vector as the Blottner Coefficients A,B and C. (x(1)=A, x(2)=B etc.)

As an example I have included data for Helium at 1bar.

//Blottner
T1=100;
T2=800;
T3=1500;
u1=6.9644e-06;
u2=3.5932e-05;
u3=5.4056e-05;
//Calculating Blottner viscosity coefficients for He at 1bar
A=[(log(T1))^2 log(T1) 1 ; (log(T2))^2 log(T2) 1; (log(T3))^2 log(T3) 1];
u=[log(u1)-log(0.1); log(u2)-log(0.1); log(u3)-log(0.1)];
x=lusolve(sparse(A),u);
T=[10:10:1500]';
mu=0.1*exp((log(T)*x(1)+x(2)).*log(T)+x(3));
//Calculating Sutherland Viscosity
eta = ((mu0*(T0+C)).*((T./T0)^(3/2)))./(T+C);
//Import Helium data from NIST file
HEV=fscanfMat('HeliumNISTonebar.txt');
plot(T,mu,HEV(:,1),HEV(:,2))

The attached .txt file was taken from the NIST site by simply copying the html output option into excel, deleting not needed columns, and saving as .txt.

Matlab users will need to exchange the lusolve function for the gaussian elimination equivalent in Matlab.

I hope it helps someone!


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