How to calculate 'scattering coefficient' in combustion gases? Any references and ideas are very much appreciated.

Manosh

If you are asking how to calculate the scattering coefficient for the gaseous species (not solid or liquid species), my answer is that this that scattering from a gas molecule is neglible (relative to gas-phase absorption or scattering by a solid particle, if present), so just use

scattering coefficient = 0

for all gaseous species

Hi

Yes, I am asking how to calculate the scattering coefficient for the gaseous species. Can you please write me details 'why scattering from a gas molecule is neglible'?

If I dont know the scattering coefficient how do I compare this with absorption?

Any references please?

Regards

Manosh

Here is an example using some data from Siegel & Howell, Thermal Radiation Transfer, 2nd ed.

Let the medium be air at standard T and P (T=300 K and P = 101325 Pa)

The spectral blackbody emissive power has maximum value at

lambda_max = 2898 microns K / 300 K = 9.7 microns

T average scattering cross-section (s_lambda) versus wavelength for this case is shown in Fig 16-12, p.588 of Siegel & Howell for air and has approximately a 1/lambda^4 dependence (ie, Rayleigh scattering).

Let's assume the blackbody emissive power is significant in the range 0.2 to 100 microns (I just went a generous portion on each side of lambda_max).

The maximum s_lambda in this wavelength range is thus at 0.2 microns, which from data in Fig 16-12 is

s_lambda = 3.0e-25 cm^2 = 3.0e-29 m^2

The scattering coefficient sigma = s_lambda * n

where n = # particles/m^3 = P/(kT)

= 101325/(1.38e-23 * 300)

= 2.45e+25 particles/m^3

Thus, sigma = 3.0e-29 * 2.45e+25 = 7.35e-04 1/m

Optical thickness based on scattering only would be

tau = sigma * L

where L = some characteristic length of your problem

(maybe mean beam lenght)

For tau > some value, you could consider scattering important. I'll use the following criteria

tau > 0.01

which means you need a length L

L > 0.01/7.35e-04 = 14 meters

for scattering from air at standard conditions to have any significant effect on radiative intensity.

The above is just an order of magnitude example. Also, even if you had an L large enough for scattering to cause any significant change in the radiative intensity, if the absorption coefficient is much larger than the scattering coefficient, (say 100 times or more), you can still safely neglect scattering.

I imagine except for the case of a very large domain in which absorption is small that scattering due to gas molecules is neglible. (If you want to show why the sky is blue, okay you should not neglect scattering in your atmospheric simulation, but if you are trying to predict radiation source terms in your energy equation or radiative heat fluxes to your domain boundaries, I doubt you will encounter many situations in which gas-phase scattering is important).

DEar Jeff

Thank you very much for your details discussion.

Manosh