How exactly is the Mixture Fraction Calculated?

GeekCFD · August 5, 2024, 09:51

I am preparing a case setup for H2 combustion using reactingFoam.
However, I am seriously confused with how Mixture Fractions are calculated.

For example, suppose I have to calculate the Mixture Fraction for the below case (Non-reacting, Pure Mixing Only):

'N2' is the actual fuel.
So, Fuel Inlet Composition: Y_N2 = 1.0, Y_O2 = 0.0
Oxidizer Inlet Composition: Y_N2 = 0.79, Y_O2 = 0.21

N2 is coming from both the inlets, so how do I calculate the Mixture Fraction?? Also, of what quantity exactly do we calculate the Mixture Fraction?
I have read we calculate it for the fuel species (like, CH4/H2/C2H6, etc..); but here I have N2 as a fuel (suppose), but it is coming from both inlets, so how do I calculate the Mixture Fraction corresponding to the N2 which is coming from the fuel*inlet*only?

Regards,
GeekCFD

LuckyTran · August 5, 2024, 21:07

Fuel mixture fraction is mass flow of fuel/(fuel+oxidizer) regardless of whatever elemental composition you have defined as fuel and oxidizer.

The local mass fraction of N2 is the mixed sum of mass fraction from the fuel and from the oxidizer streams so Y_N2=Z*1.0+Z*0.79. There is always Z fraction coming from the fuel stream and 1-Z fraction coming from the oxidizer stream, hence why it is called appropriately called mixture fraction.

GeekCFD · August 6, 2024, 05:19

Thanks, Tran.
I think I got it. The mixture fraction treats the fuel and the oxidizer composition differently.
So, if I have the mass fraction of N2 coming from the fuel in each cell of the domain (say, ps) then, the Mixture Fraction can be calculated as:

Z = m_fuel/(m_fuel + m_air)
Z = ps * 28/(ps * 28 + (1 - ps) * 28.84)

Am I right here?

Regards,
GeekCFD

LuckyTran · August 6, 2024, 06:14

It's not helpful that you mix up popular nomenclature (in FVM CFD)

X is mole fraction
Y is mass fraction
Z is mixture fraction

Mixture fraction is fuel "mass" mixture fraction, you don't need to convert from molecular weights from mass fraction to mixture fraction. Mole mixture fractions are not a common definition in FVM-based CFD because you need to calculate mass flux on every face anyway that it makes it easier to do everything in mass fractions. And mixture fraction is (by convention) fuel-based

All of this is of course begging the question, why do you care what mixture fraction is if you have ReactingFoam which already has a transport equation for mass fraction? Just use the mass fractions... Every inlet has mass fractions of every species...

Inlet 1 Composition: Y_H2 = ?.?, Y_N2=1 - ?.? Y_O2 = 0.0
Inlet 2 Composition: Y_H2 = 0.0 Y_N2 = 0.79, Y_O2 = 0.21

And then why you are defining N2 as fuel when you are doing a H2 simulation, which has no H2. Please make it make sense!

August 5, 2024, 09:51	How exactly is the Mixture Fraction Calculated?	#1
GeekCFD New Member Harsh Anand Join Date: May 2024 Posts: 12 Rep Power: 2	I am preparing a case setup for H2 combustion using reactingFoam. However, I am seriously confused with how Mixture Fractions are calculated. For example, suppose I have to calculate the Mixture Fraction for the below case (Non-reacting, Pure Mixing Only): 'N2' is the actual fuel. So, Fuel Inlet Composition: Y_N2 = 1.0, Y_O2 = 0.0 Oxidizer Inlet Composition: Y_N2 = 0.79, Y_O2 = 0.21 N2 is coming from both the inlets, so how do I calculate the Mixture Fraction?? Also, of what quantity exactly do we calculate the Mixture Fraction? I have read we calculate it for the fuel species (like, CH4/H2/C2H6, etc..); but here I have N2 as a fuel (suppose), but it is coming from both inlets, so how do I calculate the Mixture Fraction corresponding to the N2 which is coming from the fuelinletonly? Regards, GeekCFD

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August 5, 2024, 21:07		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,762 Rep Power: 66	Fuel mixture fraction is mass flow of fuel/(fuel+oxidizer) regardless of whatever elemental composition you have defined as fuel and oxidizer. The local mass fraction of N2 is the mixed sum of mass fraction from the fuel and from the oxidizer streams so Y_N2=Z1.0+Z0.79. There is always Z fraction coming from the fuel stream and 1-Z fraction coming from the oxidizer stream, hence why it is called appropriately called mixture fraction.

August 6, 2024, 05:19		#3
GeekCFD New Member Harsh Anand Join Date: May 2024 Posts: 12 Rep Power: 2	Thanks, Tran. I think I got it. The mixture fraction treats the fuel and the oxidizer composition differently. So, if I have the mass fraction of N2 coming from the fuel in each cell of the domain (say, ps) then, the Mixture Fraction can be calculated as: Z = m_fuel/(m_fuel + m_air) Z = ps * 28/(ps * 28 + (1 - ps) * 28.84) Am I right here? Regards, GeekCFD

August 6, 2024, 06:14		#4
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,762 Rep Power: 66	It's not helpful that you mix up popular nomenclature (in FVM CFD) X is mole fraction Y is mass fraction Z is mixture fraction Mixture fraction is fuel "mass" mixture fraction, you don't need to convert from molecular weights from mass fraction to mixture fraction. Mole mixture fractions are not a common definition in FVM-based CFD because you need to calculate mass flux on every face anyway that it makes it easier to do everything in mass fractions. And mixture fraction is (by convention) fuel-based All of this is of course begging the question, why do you care what mixture fraction is if you have ReactingFoam which already has a transport equation for mass fraction? Just use the mass fractions... Every inlet has mass fractions of every species... Inlet 1 Composition: Y_H2 = ?.?, Y_N2=1 - ?.? Y_O2 = 0.0 Inlet 2 Composition: Y_H2 = 0.0 Y_N2 = 0.79, Y_O2 = 0.21 And then why you are defining N2 as fuel when you are doing a H2 simulation, which has no H2. Please make it make sense!