Calculating Temperatue from Radiation Flux

[robclay]

A frustrated electrical engineer writes:

I have a flare, and it emits radiation, and i have the radiation flux lines (Looks like a nyquist plot!)

So, basically... let's say i have a flux line close to the source, of 20 kW/m^2... and further out I have a line representing 10 kW/m^2. The medium is air, at 15 degC, so is there a straight forward equation for me to determine what the temperature would be. i.e. if i have a thermometer, and stuck it on that 20 flux line? Or 10 Flux line?

Thanks,
Robert

 

[IRstuff]

Temperature of what? The flame? The thermometer?

Your data is only useful for determining the temperature of the thermometer, which depends on the absorption/emission of the thermometer itself.

Temperature of the flame requires spectral measurements. The wavelength at the peak emission can be used to calculate a temperature using Wien's Law.

TTFN

FAQ731-376

 

[robclay]

Does it make sense if I say, what is the temperature of "Air" at the 20 or 10 flux line?

I am pretty sure I am trying to simplify something that shouldn't be this simple!

In the real application, it is a helicopter flying to close to the flare. The aviation guys are asking me, "What is the temperature at this point when it is flaring?"

Thanks

 

[IRstuff]

How long does the flare last? How long is the helicopter there? Why is he that close to a flare in the first place?

The air itself will not get heated from the radiation, only the actual convection.

Take a square area facing the flare. Assume 0.5 emissivity, so it absorbs 10 kW. Assume 0.5 emissivity on the other side that's emitting into a 295 K background. Assume both sides are forced air cooled by the rotors at 10W/m^2-K, results in about 340ºC, so pretty toasty.


The simple answer
The helicopter needs to stay at no more than 1 kW/m^2 flux for extended periods. 1kW/m^2 is about the maximum solar flux in an equatorial desert. Your helicopter's A/C is probably sized for something like that.


TTFN

FAQ731-376

 

[Flareman]

Robclay,
Basically, the air doesn't really change temperature very much at all because it will move around as soon as it warms up and be replaced by other atmospheric content.
Objects at a given location will change temperature according to their surface colors and conditions, shape, materials and so on. The temperature achieved depends on the mass of the object and its termal conductiveity and specific heat, as well as the duration of exposure.

My paper "Making the Flare Safe" (AIChE 1996) comes with with formulae which will help this solution.
David

http://www.flareman.com

 

[Flareman]

Robclay
If I had read the prior correspondence properly I wouldn't be sending a second message.
Your helicopter pilot may also be worried about the flue gas temperature, which is a completely different matter.

The flue gas temperature is the result of the adiabatic flame temperature calculation for the relief case in question, modified by the dilution effect of the ambient air. That dilution effect depends on the wind speed and the concurrent atmospheric stability category (basically where you are on the Earth's surface, whether the sun is shining and how hard the wind is blowing.
For that calculation you need a different paper "A proposed Comprehensive Model for Flare Flames and Plumes" (AIChE 206)

Or you tell the pilot to stay up wind.
I don't immediately have a good model for the localized updraft due to Radiant heat absorption of the surrounding air but on my only previous encounter with this as an issue, pilots apparently reported updraft to be beneficial.

David

http://www.flareman.com

 

[IRstuff]

Radiation absorption generally isn't from the adjacent air.

Disneyland Anaheim changed its nightly fireworks display to include some rather large gas flares, and even from several hundred feet away, you can instantly feel the radiated heat. It's radiated and not convected because it comes and goes synchronously with the duration of the flare, which would not be the case with convection, since there would be both a lag and a dispersively longer duration.

TTFN

FAQ731-376

 

[robclay]

Thanks Flareman and IRStuff.

I ended up modeling the 10% LFL. I used this as it is outlined in CAP 437, an aviation safety standard from overseas.

This seems more conservative than the radiation flux lines.

Flareman, do you have a copy of "Making the Flare Safe" available on your website?

Thanks so much,
Robert