Visibility vs optical density

[Victor Shestopal]

Dear Colleagues,

 

FDS5 produces "soot visibility" parameter. How does it correlate with optical density or extinction coefficient? 

 

Victor Shestopal
Australia

 

[dr_jfloyd]

The User's Manual defines each of these quantities in 14.3.2

On Mar 22, 7:20 pm, "Victor Shestopal" <firec...@optusnet.com.au>
wrote:

>  MYLOGO.bmp
> 3KViewDownload

[fde]

From time to time I get confused about visibility calculation and I try to remember/understand again and I have a question. 

According to FDS User Guide eq. 21.23, Optical density is D= - 1/L  log(I/I_0){base10}. OPTICAL DENSITY unit is given as 1/m  (Table 21.4 FDS User Guide). 

I find the same equation in this paper paper (eq 4) as in D_L,log. which has a unit of [Bel/m] =  Optical density pr. meter (10-based logarithm)

It appears the unit is not consistent for identical equations.

 

Visibility in FDS is given as S = C / K and D=K/2.3 therefore for C=3 (reflecting surfaces) S = 3/(2.3*D) = 1.3/D

According to the abovementioned paper, S = 1/D (reflecting surface)  (D definition in FDS User guide is equal to D_L,log in the abovementioned paper). 

I cannot see C factors in the paper, so I am not sure if the paper uses different C factors or they are the same but I make an error in my calculation. 

Could anyone help me with this conversion please?

[dr_jfloyd]

Visibility is challenging. There are mulitple terms with similar names, you see the same term being used in slightly different ways in diffrerent publications, and values assumed for converting a smoke density to an obscuration or visibility can differ as well. For visbility this is in part that conversion factors for getting visibility are not fundamental physical constants but rather values based on some assessment of human visual acuity over some population of test subjects.

In the paper you referenced, FDS would be Eq. 10 or 11, the first term:

ln(10)/D_L or 2.5 ln(10)/D_L where D_L would be the same as K in Eq. 21.21 in the User's Guide.  Why this paper uses ln(10) and 2.5 ln(10) is not referenced. 

ln(10) is 2.3 so this gives C values of 2.3 and 5.8 which are similiar to the 3 and 8 suggested in the FDS User's Guide. The 3 and 8 are from the SFPE Handbook and represent midpoint values over a group of tests (the Handbook gives ranges of 2 to 4 and 5 to 10. The values 2.3 and 5.8 are within those ranges).

[fde]

Thank you for the response. 

So I understand that FDS and this paper uses slightly different C values although both are within the range of the tests (as shown in SFPE Handbook). 

You referred to Eq 10 and 11. I think it should have been 11 and 12 (light reflecting and emitting objects)

You note that D_L is the same term in the Eq. 21.21 in User Guide but I see that Eq. 21.21 is the equation of K (light extinction coefficient) and it does not contain D (optical density). 

If I try to match the optical density equations, Eq21.23 in User Guide is identical to Eq.4 in the paper which has a unit of Bel/m which differs from the optical density unit in FDS user guide (1/m). 

A side note: In normative British fire safety standard PD7974-2:2019, visibility is expressed as S=1/D in Eq. 73 for light reflecting objects. So there is a slight difference in calculation of visibility due to selected C factor between PD7974-2 and FDS default. Yet, in my experience, the reviewers in UK always accept the FDS defaults in CFD assessments (e.g. C factor). 

[dr_jfloyd]

Yes, I mistyped. 11 and 12.

The first part of 11 and 12 uses D_L. In Eq 7 in the paper:

D_L = 1/L ln (I/I0)

or

I/I0 = exp (-D_L _L)

This is the same as Eq 21.20 in the  guide only FDS uses K rather than D_L

[fde]

Thank you for your clarification.