Derivation:
Viscosity was calculated using the Chapman-Enskog theory:
Diffusivity was calculated using dcalc, which utilizes the start301 database and the Chapman-Enskog formula.
Example:
In order to test the accuaracy of our gas Schmidt number program, we calculated the Schmidt number of chlorine in air at 297 K, 1 atm, and at mole fractions of .5 for both compounds. The following is the output from start301. --------------------------------------------------------------------------------------------------------------------------------------------------------------
Enter the name of compound # 1: chlorine
Enter the name of compound # 2: air
Here are your compounds' formulae and names:
No. Formula Name
----------------------------------------
1 Cl2 chlorine
2 N1.58O.42 air
>> gschmidt(1, 297, 1, [.5, .5])
Sc =
0.6100
This Schmidt number value of 0.6100 corresponds very well to the Bird, Stewart, and Lightfoot value of 0.6200.
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Gas Schmidt Number Program:
function gschmidt = sccalc(p, T, Tdeg, z, index)
% Calculates the dimensionless Schmidt number for low density binary gas
% mixtures. For most gas mixtures, the Schmidt number can range from .2-3.
% Mixmu and dcalc are used to calculate viscosity and diffusivity
% of the mixture.
% The Chapman-Enskog formula is used in the matlab function dcalc to
% calculate diffusivity in m^2/s
% In order to calculate viscosity in kg/m/s, the Matlab function mixmu is
% used. Mixmu uses equations 1.4-15 and 1.4-16 from BS&L, 3rd ed.
% The ideal gas law is used to calculate density in kg/m^3.
% Argument List:
% p [=] pressure in kPa
% T [=] temperature in the units of Tdeg
% z [=] vector of mole fractions of chosen compounds
% Tdeg [=] chosen temperature scale
% 1 - 'kelvin'
% 2 - 'celsius'
% 3 - 'rankine'
% 4 - 'farenheit'
% index [=] index of compounds from start301
% Returns:
% Sc [=] Schmidt
global mw
if nargin==4
index= [1,2];
end
pkPa=p*101.33
DAB=dcalc(pkPa, T, index)
mu=mixmu(z,T,index)
if Tdeg==2
T=(T+273.15);
end
if Tdeg==3
T=(T*.55556);
end
if Tdeg==4
T=(T+459.67)*.55556;
end
j=index(1);
k=index(2);
mixmw=z(1)*mw(j)+z(2)*mw(k);
R=.08206;
rho = p*mixmw/R/T;
Sc=mu/rho/DAB |