Soot absorption coefficient

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Hosein Sadeghi

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Sep 20, 2022, 5:47:34 AMSep 20
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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 
Capture.PNG

while the equation in the reference is

Capture02.PNG

Could you please check it?


BR,
Hosein



dr_jfloyd

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Sep 20, 2022, 8:37:38 AMSep 20
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The RADCAL in FDS has been updated since the original version.  See the notes on the current soot model:

Hosein Sadeghi

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Sep 20, 2022, 8:57:49 AMSep 20
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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

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Sep 20, 2022, 9:12:56 AMSep 20
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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

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Sep 20, 2022, 9:15:46 AMSep 20
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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

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Sep 20, 2022, 9:56:17 AMSep 20
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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

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Sep 20, 2022, 10:28:10 AMSep 20
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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

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Sep 20, 2022, 10:45:35 AMSep 20
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Yes, the note is incorrect. The equations are in the following papers as well,


Thank you.


BR,
Hosein

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