Gas radiation - verification with analytical solution

maciekstp · December 29, 2015, 08:00

Hi,
I am trying to simulate high temperature gas heat exchanger. The medium in an inner pipe is gas mixture which is a product of the combustion of natural gas (CO2~10%, H2O~18%). I would like to verify my results with analytical solution, based on Hottel charts. Calculated wall heat flux by radiation is 11 kW/m^2 (difference between flux emitted and absorbed by gas).

On the other hand, I made calculations in CFX. First I tried grey gas model - with one absorption coefficient, calculated by expressions based on Leckner correlations. Later, I chose Weighted Sum of Grey Gases, where absorption coefficient is based on Taylor and Foster correlations. In both cases, Discrete Transfer model was used.

Unfortunately, results from CFX are too high. I obtained Wall Radiative Heat Flux with value 28 kW/m^2 in both cases.

Please, let me know if you have any advice to solve my problem,

Best regards,
Maciek

ghorrocks · January 2, 2016, 01:18

I am not familiar with Hottel charts. But I suspect it is an empirical relation, not an analytical one. If it is empirical then significant errors can be expected, and it is not a good baseline result to compare against.

Also: Make sure you check the basics of simulation accuracy: http://www.cfd-online.com/Wiki/Ansys..._inaccurate.3F

maciekstp · January 2, 2016, 08:52

Glenn,
Thank you for your reply.
As you said, Hottel charts are empirical. However, my case is standard so I suspected at least similar results to this popular, simplified method.

I performed mesh sensitivity analysis. Also convergence is correct (RMS residual 1E-06). Now I am resolving the radiation matter. I will try to describe my calculations more specific, and maybe you will be able to find some mistake.

CFX needs a value for absorption coefficient. For a grey gas model there is an equation:

emissivity=1-exp(-k*L)

where the k is an absorption coefficient, and L is mean radiation beam length. So, k may be expressed as:

k=-ln(1-emissivity)/L

I defined some expressions in CFX, in order to calculate L and emissivity. L is calculated as:

L=3.6*V/A

where V is a volume, and A is a surface area of my geometry.

Emissivity is calculated from Leckner correlations, which are describing the Hottel charts. Calculated absorption coefficient is used in a radiation properties of my mixture.

In a second case, I used Weighted Sum of Grey Gases model. The most popular Taylor and Foster correlations let me calculate emissivity and total absorption coefficient.

My first check:
Emissivity read from Hottel charts, and calculated in CFX (both models) are very close (less than 5% error).

So I assume that problem is with calculating other radiation properties, for example wall radiative heat flux. In a manual method, I used the formula:

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

where gas absorptivity is estimated for a wall temperature. But the same parameter in CFX gives definitely different values (bigger by 2.5 factor).

I found in the CFX Reference Guide that Wall Radiative Heat Flux is computed as the difference between the radiative emission and the incoming radiative flux (Wall Irradiation Flux). Definitions of these values do not provide their dependence on absorption coefficient or emissivity.

Do you have any idea to improve my calculations?

Best regards,
Maciek

ghorrocks · January 3, 2016, 01:58

I do not use those radiation models much so cannot help you. Hopefully somebody else on the forum is more familiar with them than me.

Opaque · January 4, 2016, 12:22

I assume you are using the standard isothermal enclosed cylinder test case, i.e. all wall are isothermal at a different temperature as the gas, correct ?

How have you eliminated, or deactivated heat conduction in the ANSYS CFX Solver ? Did you use Thermal Conductivity = 0 [ W m-1 K^-1], and isothermal heat transfer model with thermal radiation active ?

If you do not eliminate heat conduction, and you get a temperature gradient in the fluid, you are comparing two very different cases.

Hope the above helps,

PS: Please refer to Hottel's solution as "reference solutions", they are not analytical (as in exactly solving a mathematical problem) solutions in any way or form. Perhaps, they are exact for the 1D-planar case only. As long as you have to define a mean beam length, you are getting an approximate solution.

December 29, 2015, 08:00	Gas radiation - verification with analytical solution	#1
maciekstp New Member Join Date: Oct 2014 Posts: 5 Rep Power: 12	Hi, I am trying to simulate high temperature gas heat exchanger. The medium in an inner pipe is gas mixture which is a product of the combustion of natural gas (CO2~10%, H2O~18%). I would like to verify my results with analytical solution, based on Hottel charts. Calculated wall heat flux by radiation is 11 kW/m^2 (difference between flux emitted and absorbed by gas). On the other hand, I made calculations in CFX. First I tried grey gas model - with one absorption coefficient, calculated by expressions based on Leckner correlations. Later, I chose Weighted Sum of Grey Gases, where absorption coefficient is based on Taylor and Foster correlations. In both cases, Discrete Transfer model was used. Unfortunately, results from CFX are too high. I obtained Wall Radiative Heat Flux with value 28 kW/m^2 in both cases. Please, let me know if you have any advice to solve my problem, Best regards, Maciek Last edited by maciekstp; December 29, 2015 at 17:42.

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January 2, 2016, 01:18		#2
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,872 Rep Power: 144	I am not familiar with Hottel charts. But I suspect it is an empirical relation, not an analytical one. If it is empirical then significant errors can be expected, and it is not a good baseline result to compare against. Also: Make sure you check the basics of simulation accuracy: http://www.cfd-online.com/Wiki/Ansys..._inaccurate.3F

January 2, 2016, 08:52		#3
maciekstp New Member Join Date: Oct 2014 Posts: 5 Rep Power: 12	Glenn, Thank you for your reply. As you said, Hottel charts are empirical. However, my case is standard so I suspected at least similar results to this popular, simplified method. I performed mesh sensitivity analysis. Also convergence is correct (RMS residual 1E-06). Now I am resolving the radiation matter. I will try to describe my calculations more specific, and maybe you will be able to find some mistake. CFX needs a value for absorption coefficient. For a grey gas model there is an equation: emissivity=1-exp(-kL) where the k is an absorption coefficient, and L is mean radiation beam length. So, k may be expressed as: k=-ln(1-emissivity)/L I defined some expressions in CFX, in order to calculate L and emissivity. L is calculated as: L=3.6V/A where V is a volume, and A is a surface area of my geometry. Emissivity is calculated from Leckner correlations, which are describing the Hottel charts. Calculated absorption coefficient is used in a radiation properties of my mixture. In a second case, I used Weighted Sum of Grey Gases model. The most popular Taylor and Foster correlations let me calculate emissivity and total absorption coefficient. My first check: Emissivity read from Hottel charts, and calculated in CFX (both models) are very close (less than 5% error). So I assume that problem is with calculating other radiation properties, for example wall radiative heat flux. In a manual method, I used the formula: q_rad=sigma(gas emissivityT_gas^4 - gas absorptivity*T_wall^4) where gas absorptivity is estimated for a wall temperature. But the same parameter in CFX gives definitely different values (bigger by 2.5 factor). I found in the CFX Reference Guide that Wall Radiative Heat Flux is computed as the difference between the radiative emission and the incoming radiative flux (Wall Irradiation Flux). Definitions of these values do not provide their dependence on absorption coefficient or emissivity. Do you have any idea to improve my calculations? Best regards, Maciek

January 3, 2016, 01:58		#4
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,872 Rep Power: 144	I do not use those radiation models much so cannot help you. Hopefully somebody else on the forum is more familiar with them than me.

January 4, 2016, 12:22		#5
Opaque Senior Member Join Date: Jun 2009 Posts: 1,880 Rep Power: 33	I assume you are using the standard isothermal enclosed cylinder test case, i.e. all wall are isothermal at a different temperature as the gas, correct ? How have you eliminated, or deactivated heat conduction in the ANSYS CFX Solver ? Did you use Thermal Conductivity = 0 [ W m-1 K^-1], and isothermal heat transfer model with thermal radiation active ? If you do not eliminate heat conduction, and you get a temperature gradient in the fluid, you are comparing two very different cases. Hope the above helps, PS: Please refer to Hottel's solution as "reference solutions", they are not analytical (as in exactly solving a mathematical problem) solutions in any way or form. Perhaps, they are exact for the 1D-planar case only. As long as you have to define a mean beam length, you are getting an approximate solution.