Lewis number calculation

[Francis Oppong]

Good day all,

a) Please I am trying to calculate the Lewis number  but the plot I am getting is not what I am expecting. From the attached image the tendency of the curve should be in the descending order of Lewis number for the equivalence ratio, which is right but it shouldn't be a straight line like in the plot. However, the Lewis numbers are too high from equivalence ratios 0.9-1.4. 

b) Also, I want to compute the effective Lewis number. Therefore, I have to compute the Lewis numbers of the fuel and the oxidizer separately. Since I am treating the oxidizer as single ideal gas I used the binary mass diffusion coefficients to calculate the Lewis number of the oxidizer and I end up getting higher Le's in the range of 4. 

Please can someone kindly advise on what I am doing wrong. Attached is the cti and the code.

Thanks

FO

[Jeff Santner]

The mass diffusivity should not be the average diffusivity of all species. Instead, the Lewis number of the fuel is based on the diffusivity of the fuel in the mixture, and the Lewis number of the oxidizer is based on the diffusivity of oxygen in the mixture. 

[Francis Oppong]

Jeff,

Thanks.  I get a messy plot for not using the average mass diffusivity. I am unable to get what you suggested in Cantera. Please can you kindly give a small demonstration (code form) of what you mean by looking at my code or you can recommend a cantera documentation that will give me a cue about how to obtain the mass diffusivity of the fuel and oxidizer.

Regards

Francis

[Jeff Santner]

Francis,

This is how I've been calculating the Lewis number of the fuel and of the oxidizer. "gas" is a cantera Solution object of the unburned mixture.

    thermal_diff = gas.thermal_conductivity/gas.cp_mass/gas.density_mass

    Le_O2 = (thermal_diff /

             gas.mix_diff_coeffs_mole[gas.species_index('O2')])

    Le_F = 0

    sum_fuel = sum([x[1] for x in mixture_list if x[0] in fuel_list])  # Find the total mole fraction of fuel species. There may be multiple "fuel"s

    for component in mixture_list:

        #Use molar weighting as found in Yu, Hu, Cheng, Yang, Zhang, Huang (2015)

        if component[0] in fuel_list:

            Le_F += (component[1]/sum_fuel) * (thermal_diff /

                     gas.mix_diff_coeffs_mole[gas.species_index(component[0])])

    # Using equation from Bechtold and Matalon (2001)

    if phi < 1:

        PHI = 1/phi     # capital phi

        Le_E = Le_O2    # excess reactant

        Le_D = Le_F    # deficient reactant

    else:

        PHI = phi

        Le_E = Le_F

        Le_D = Le_O2

    A = 1 + beta * (PHI - 1)

    Le_eff = 1+((Le_E - 1) + (Le_D - 1) * A) / (1 + A)

    # Above equation can be rearranged to (Le_E + A*Le_D ) / (1 + A).

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[Francis Oppong]

Jeff, 

Thanks. Trying to go through to understand it.

Regards

Francis.

[Francis Oppong]

Jeff, 

Sorry to worry you. I don't really understand this line 'sum_fuel = sum([x[1] for x in mixture_list if x[0] in fuel_list])'. I specified the mixture_list as the fuel and oxidizer, and the fuel_list as the fuel but it doesn't work. The fuel is a single fuel.

Regards

Francis 

[Jeff Santner]

Sorry, that code is a snippet from something I wrote that doesn't really work on its own. Since you have a single fuel (let's say the species is called 'fuel'), you can just replace all the lines regarding Le_F with:

    Le_F = (thermal_diff / gas.mix_diff_coeffs_mole[gas.species_index('fuel')])

[dailim...@gmail.com]

Hi Jeffrey,

how did you determine the beta, Zeldovich number? particularly, how you determine the activation energy when calculating the Zeldovich number?

Best,

Liming

[Francis]

Liming,

Check here 'https://doi.org/10.1016/j.proci.2016.06.194 '

All the best.

Francis

[dailim...@gmail.com]

Thanks Francis.

Best,

Liming

[Jeff Santner]

First I found the activation temperature (or energy) using a polynomial fit of ln(flame speed) against 1/(T_adiabatic), while perturbing the unburned temperature +/- 10 K. I usually had results with perturbations of -10K, -5K, unperturbed, +5K, and +10K that I used to create the fit. If I remember correctly, the activation temperature = -2 x d(ln(Su)) / d(1/T_ad).

Then, the Zeldovich number is calculated as Ze = T_act * (T_ad - T_u)/(T_ad**2)

You should check the paper that Francis attached for more information.

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[Gan Xiao]

Hi Jeffrey:

             I am also very interested in your work about how to calculate the Lewis number in Cantera. Could you share the code about how to implement it?

             Thanks.

Regards

Shawn

         

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