Gas Radiaition Properties, Absoprtion Coefficent

MH_Engineer · June 8, 2015, 12:03

Hello

I am trying to calculate the absorption coefficient for H2O and CO2 mixture for a radiation problem in Fluent.

According to the Fluent manual they want it in the units 1/m.

Past posts bring up such references as Hottel Charts or using text books such as Thermal Radiation Heat Transfer by Howell & Siegel.

Using Hottel Charts, you need to provide mean beam length which is shape dependent and the coefficient it calculates is unitless. Should I assume a 1m sphere when using these charts to get my coefficient in units 1/m???

Or in Thermal Radiation 5th Ed., there is the Leckner equation which is an algebraic equation of Hottel's charts. Once again it solves the coefficient as unitless, so should I just plug in 1m as Le to get the coefficient on a 1/m units?

The equations and charts aren't linear so I am having a hard time trying to represent them in units of 1/m.

maciekstp · December 30, 2015, 09:21

Hi,
Mean radiation beam length can be calculated approximately with formula:

L=3.6*V/A

where V is a volume, and A is a surface area of your geometry. For a simple "flow in a duct" case, you can get that L=0.9*diameter.

Using Hottel charts, you can estimate gas emissivity for your case. As you said, Leckner equations can be used to calculate the emissivity.

Emissivity is unitless and it is equal to absorptivity. However, absorption coefficient is something different, and it is expressed in units [m^-1].

For a grey gas model, there is a popular equation:

emissivity=1-exp(-k*L)

where k is an absorption coefficient. After doing some math, you can obtain:

k=-ln(1-emissivity)/L

I am working in CFX and I did it by defining some expressions to calculate absorption coefficient. I tried to simulate simple flow of combustion gas in a duct. To verify my results, I calculated this case analytically. I estimated emissivity and absorptivity from Hottel charts and I used this formula:

q_rad=sigma*(gas emissivity*T_gas^4 - gas absorptivity*T_wall^4)

to calculate wall radiative heat flux. Unfortunately, value from CFX is much bigger than value from analytical solution. Does anyone have a similar problem? I will be grateful for any advice,

Best regards,
Maciek

Runtowhere · January 28, 2016, 18:13

Hi, I think the q_rad formulation that you used for calculating the radiative heat flux is not
appropriate for this problem.
You can use the Fluent with the WSGG model to solve this problem to see if there is any difference between it with CFX.
Hope this works for you.

June 8, 2015, 12:03	Gas Radiaition Properties, Absoprtion Coefficent	#1
MH_Engineer New Member James O Join Date: May 2015 Posts: 4 Rep Power: 11	Hello I am trying to calculate the absorption coefficient for H2O and CO2 mixture for a radiation problem in Fluent. According to the Fluent manual they want it in the units 1/m. Past posts bring up such references as Hottel Charts or using text books such as Thermal Radiation Heat Transfer by Howell & Siegel. Using Hottel Charts, you need to provide mean beam length which is shape dependent and the coefficient it calculates is unitless. Should I assume a 1m sphere when using these charts to get my coefficient in units 1/m??? Or in Thermal Radiation 5th Ed., there is the Leckner equation which is an algebraic equation of Hottel's charts. Once again it solves the coefficient as unitless, so should I just plug in 1m as Le to get the coefficient on a 1/m units? The equations and charts aren't linear so I am having a hard time trying to represent them in units of 1/m.

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December 30, 2015, 09:21		#2
maciekstp New Member Join Date: Oct 2014 Posts: 5 Rep Power: 12	Hi, Mean radiation beam length can be calculated approximately with formula: L=3.6V/A where V is a volume, and A is a surface area of your geometry. For a simple "flow in a duct" case, you can get that L=0.9diameter. Using Hottel charts, you can estimate gas emissivity for your case. As you said, Leckner equations can be used to calculate the emissivity. Emissivity is unitless and it is equal to absorptivity. However, absorption coefficient is something different, and it is expressed in units [m^-1]. For a grey gas model, there is a popular equation: emissivity=1-exp(-kL) where k is an absorption coefficient. After doing some math, you can obtain: k=-ln(1-emissivity)/L I am working in CFX and I did it by defining some expressions to calculate absorption coefficient. I tried to simulate simple flow of combustion gas in a duct. To verify my results, I calculated this case analytically. I estimated emissivity and absorptivity from Hottel charts and I used this formula: q_rad=sigma(gas emissivityT_gas^4 - gas absorptivityT_wall^4) to calculate wall radiative heat flux. Unfortunately, value from CFX is much bigger than value from analytical solution. Does anyone have a similar problem? I will be grateful for any advice, Best regards, Maciek

January 28, 2016, 18:13		#3
Runtowhere New Member sunrunw Join Date: Sep 2013 Posts: 2 Rep Power: 0	Hi, I think the q_rad formulation that you used for calculating the radiative heat flux is not appropriate for this problem. You can use the Fluent with the WSGG model to solve this problem to see if there is any difference between it with CFX. Hope this works for you.