Heat radiation - how to handle

[Gregor2019]

Dear Delphin-Team,
I am modelling a 380 kV power cable in a soil body. The power cable is protected by a protection pipe and the space between protection pipe and power cable is filled by air. As far as I know concerning heat transport, heat conduction and heat convection by air is included in the software, but not heat radiation. The heat conductivity of air is associated with values between 0.030 and 0.313 W/mK in Delphin. However, the real heat conductivity of dry air is 0.025 W/mK. Therefore, I would like to know on the one hand on what the heat conductivity values are based on (as there is no information in the source column) and on the other hand if those values much higher than 0.025 W/mK therefore include heat radiation.

Solving the problem that Delphin does not include heat radiation, I thought of an option how to integrate it into Delphin.One could calculate the heat radiation that would be radiated from a current carrying power cable to its surrounding (air and protection pipe). This heat radiation could be thought of as being a heat flux. Inserting this into the equation Lamda = ( Q * (ln radius(protection pipe)/ radius(power cable) ) ) / ( 2*Pi* 1m* delta T ), the corresponding heat conductivity of air that is required to guarantee the heat flux Q could be calculated.


This value could then be added to the real heat conductivity of air. Always referring my calculation to a reference temperature of the protection pipe of 0 degree C, my results for cable temperatures from 1 degree C to 100 degree C result in heat conductivities of air between 0.167 and 0.265 W/mK. These values resemble the once that are given in Delphin, which is why I asked above whether the values in Delphin already include heat radiation to some extent.

For being on the safe side, I would generally like to know whether my approach seems to be reasonable to include heat radiation in Delphin.

I am looking forward to hearing from you and wish you the best!

- Markus

[ghorwin]

Hi Markus,

you may not be aware of the "Long wave radiation exchange" model in DELPHIN (Field condition = source/sink model). You may approximate your pipe as a rectangle and then assign the LW field condition across the parallel air gaps.

Also, you could just linearize the Boltzmann radiation equation (Take (T1-T2) out of (T1^4-T2^4)) and then have a rough supplement to the heat conduction value in the gap.

-Andreas

[fechner]

Hi Gregor,

The thermal conductivities of air in the Delphin material database are calculated by using the values from the standard ISO 6946. It includes convection and radiation.
I would suggest, as Andreas said, to use our source model for the longwave radiation exchange. The convective part can be modeled by an additional thermal conductivity. A possible method to calculate this is described in the standard EN 673.

[Gregor2019]

Dear Andreas and Mr. Fechner,
I finally had time to implement the adaptations and follow your approaches.

Thank you very much, it helped a lot!
Markus =)

[fechner]

I splitted the theme. All answers to the high temperature topic you will find in another theme 'High temperatures limit?'