Soot absorption coefficient

[Hosein Sadeghi]

Hi,

It seems the calculation of soot absorption coefficient in rcal.f90 does not match the equation in the mentioned reference [Dalzell and Sarofim (1969)]. The equation in the code is 

while the equation in the reference is

Could you please check it?

BR,

Hosein

[dr_jfloyd]

The RADCAL in FDS has been updated since the original version.  See the notes on the current soot model:

https://github.com/firemodels/radcal/blob/master/Documentation/SootModel_Modification_RadCal_HadiBordbar_May2020.pdf

[Hosein Sadeghi]

Hello,

Thank you for sharing the link. Comparing the equations, they seem different to me. I am using the latest version of FDS, not the original RADCAL. In rcal.f90,

It is 

FF = 36.0_EB*PI*RIN*RIK/LAMBDA/((RIN**2-RIK**2+2.0_EB)**2+(2.0_EB*RIN*RIK)**2)

while based on the document you sent, it should be 

FF = 36.0_EB*PI*RIN*RIK/((RIN**2-RIK**2+2.0_EB)**2+PI*(2.0_EB*RIN*RIK)**2)

and the constant wavenumber of omega=1e06 has been used in the code (ABCO       = FF*SOOT_VOLUME_FRAC*1.E6_EB). It should be variable based on the equation, kappa= c*omega*f_v.

BR,

Hosein

[Randy McDermott]

As discussed in the notes and in code, lambda[mu-m] = 10,000/omega[cm^-1].  ABCO is in [1/m].  1e6 is just converting mu-m to m.  So, the notes and the code look fine to me.  

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[dr_jfloyd]

Line 1879:

LAMBDA = 10000._EB/OMEGA

which means

Line 1897:

FF = 36.0_EB*PI*RIN*RIK/LAMBDA/((RIN**2-RIK**2+2.0_EB)**2+(2.0_EB*RIN*RIK)**2)

is really just:

FF = C * OMEGA

Line 1899:

ABCO = FF*SOOT_VOLUME_FRAC*1E6 = C * OMEGAE * F_V = kappa

The 1E6 isn't OMEGA. It is converting the volume fraction to ppm.

[Hosein Sadeghi]

Thank you. So you have considered ppm=1E10*F_v ?

And a PI is still missing in the second term of the denominator, (2.0_EB*RIN*RIK)**2  shouldn't be PI*(2.0_EB*RIN*RIK)**2 ?

BR,

Hosein

[dr_jfloyd]

Randy had it right I goofed. The 1E6 is the wavelength conversion.

It looks like the notes have an error, and the FDS code is correct.  Eq 4 in the notes is Eq 12.53 in Ref 2. In Ref 2 there is no pi in the denominator.

[Hosein Sadeghi]

Yes, the note is incorrect. The equations are in the following papers as well,

https://www.sciencedirect.com/science/article/pii/S1290072914001057  (Eq. 4)

https://www.tandfonline.com/doi/full/10.1080/00102202.2014.883221  (Eq. 2)

Thank you.

BR,

Hosein