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Eddy-Dissipation Model: production rates limiters equations

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Old   March 27, 2013, 13:12
Default Eddy-Dissipation Model: production rates limiters equations
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François Grégoire
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Let's say we have

v'_{CH_4}CH_4 + v'_{O_2}O_2 =v''_{CO_2}CO_2 + v''_{H_2O}H_2O\ \ \ \ \ (1)

from Fluent Theory Guide 14.0 or 14.5, section 7.1.2.3, equation (7-25), one of the two limiters for production rate of O2 is :

R_{O_2}=v'_{O_2}M_{w,O_2}A\rho\frac{\varepsilon}{\kappa}min\left(\frac{Y_{O_2}}{v'_{O_2}M_{w,O_2}},\frac{Y_{CH_4}}{v'_{CH_4}M_{w,CH_4}}\right)\ \ \ \ \ (2)

so that

R_{O_2}=A\rho\frac{\varepsilon}{\kappa}Y_{O_2}\ \ \ \ \ (3)

or

R_{O_2}=A\rho\frac{\varepsilon}{\kappa}\frac{v'_{O_2}M_{w,O_2}}{v'_{CH_4}M_{w,CH_4}}Y_{CH_4}\ \ \ \ \ (4)


Then I read the cited reference in Fluent Theory Guide [Magnussen and Hjertager, On Mathematical Modeling of Turbulent Combustion with Special Emphasis on Soot Formation and Combustion, 1976] and here is the limiting formula for the oxygen (equation (2) of the article):

R_{O_2}=A\rho Y_{O_2}\frac{\varepsilon}{\kappa}\frac{1}{r_f}\ \ \ \ \ (5)

where r_f is the stoichiometric oxygen-to-fuel mass ratio: r_f=\frac{v'_{O_2}M_{w,O_2}}{v'_{CH_4}M_{w,CH_4}}\ \ \ \ \ (6)

inserting (6) into (5) results in

R_{O_2}=A\rho Y_{O_2}\frac{\varepsilon}{\kappa}\frac{v'_{CH_4}M_{w,CH_4}}{v'_{O_2}M_{w,O_2}}\ \ \ \ \ (7)

Comparing (7) with (3) and (4), it looks like Fluent Theory Guide and Magnussen formulas don't match.

Did I go wrong somewhere? Or is there a typo in Fluent Theory Guide?

Last edited by macfly; March 28, 2013 at 12:49.
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