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 lfgmarc September 15, 2011 13:13

inconsistency in the chemical reactions in Reacting Foam?

Hi foamers, I try to simulate a diffusion flame with reactingfoam, but I have some doubts. First in the tutorial case reactions file have this information:

species
(
O2
H2O
CH4
CO2
N2
);

reactions
(
irreversibleArrheniusReaction
CH4 + 2O2 = CO2 + 2H2O
(5.2e16 0 14906)
);

This is a global one-step reaction of methane and air, in which the reaction rate is:

q=A_o*T^n*exp(-Ea/(Ru*T))[fuel]^a*[O_2]^b

If I understand correctly then the parameters of the last equation are:

A_0=5.2e16 // pre-exponential factor

Ta=(Ea/Ru)= 14906 // activation temperature

and exponents a, b = 1 because the format of input is:

species
(
species list
);

reactions
(
reaction type
Reaction Equation (A^a+b^b==>C+D)
(A n Ta)
);

In the book of Chemical Kinetic Modeling of Hydrocarbon Combustion (Westbrook and Dryer) I found that the parameters of the reaction rate equation for methane-air reaction are:

A_0=1.3e9 [[mol/cm^3]^(1-a-b)]*s^-1

Ea=48.4e3 [kcal/mol]

a=-0.3

b=1.3

Accordingly the activation temperature result: Ta=24358.32K. To test the consistency of units I use the application chemkinToFoam, I made a reaction file in the chemkin format:

ELEMENTS
H O C N
END
SPECIE
CH4 O2 CO2 H2O N2
END
REACTIONS

CH4 +2O2 => CO2 +2H2O 1.3e9 0.0 48.4e3
FORD /CH4 -0.3/
FORD /O2 1.3/
END

using chemkinToFoam the result was:

species
5
(
CH4
O2
CO2
H2O
N2
)
;

reactions
1
(
irreversibleArrheniusReaction
CH4^-0.3 + 2O2^1.3 = CO2 + 2H2O
(1.3e+09 0 24354.5)

);

In the case of the activation temperature is clear that the units are K, but in the case of the pre-exponential factor I not be very sure about its units, from chemkintoFoam the units of this parameter apparently are:

[[mol/cm^3]^(1-a-b)]*s^-1

My question is: what is the meaning of the difference between the values ​​of the parameters?. I tried a case with the parameters from Westbrook and Dryer, but the results were not good. If anyone has information about the source from which the parameters were taken for the tutorial case it was very helpful, maybe I can be wrong with my analysis in that case I'll be very grateful with some advice.

Best regards

 megacrout October 10, 2011 11:11

Hi Luis,

First of all I will refer in the following to the cases you described using bold OF code as case 1, 2, 3 and 4 respectively.

I think most of your questions result from one missing piece of information, namely the fact that parameters a and b in the equation

q=A_o*T^n*exp(-Ea/(Ru*T))[fuel]^a*[O_2]^b

are USUALLY taken as equal to the stoichiometric coefficients. That is, in the first case you described, b=2 (not 1), a=1. However, this does not NECESSARILY have to be the case, as the description of Westbook and Dryer you gave shows.

Btw, you wrote: Ea=48.4e3 [kcal/mol] which is a ridiculously big activation energy. But you then wrote in your third case CH4 +2O2 => CO2 +2H2O 1.3e9 0.0 48.4e3 where the activation energy has to be given in [cal/mol] so I take it the first occurence has a typo.

The conversion to foamChemistry format (case 4) is "obviously" right, since OF did it. The fact that the value of the preexponential factor remained unchanged shows that - using your formula for its units: [[mol/cm^3]^(1-a-b)]/s - OF computed units of 1/s. This means it uses the given exponents for computing the reaction rate when stoichiometric coefficients AND kinetic exponents are specified. Else, the stoichiometric coefficients are used as exponents a and b.

As for you last question, the discrepancy between given parameters in the tutorial and in the literature can result from many sources: assumptions (it is usually ASSUMED that the stoichiometric coefficients can be used as kinetic exponents), measurement conditions (catalyzed reactions for example might lead to negative exponents), aso. Measured values usually apply to one very specific case (p, T, geometry, concentrations ratios... have to be met) and canīt be used to run ANY simulation.

I think I answered all your questions. Please read a few books about chemical kinetics. What I explained is about basics and will appear in any book on this topic. Please also have a look at http://www.cfd-online.com/Forums/ope...ions-file.html. This might help further too.

Best regards.

Tibo

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