Solid/Gas thermal equilibrium with radiative heat transfer

[PyroMind-code]

Describe the bug
FDS version : FDS-6.10.1-0-g12efa16

I am testing thermal energy exchange between gas and solid phases in a closed, adiabatic system in order to verify convergence toward thermal equilibrium while conserving total energy. Both convection and radiation heat transfer mechanisms are investigated.

The configuration consists of an adiabatic cubic chamber of dimensions 10 × 10 × 10 cm³, filled with air at 800°C. A solid cube of dimensions 2 × 2 × 2 cm³ is centered inside the chamber with a temperature of 20°C.

Two cases are considered:

• Heat transfer by convection only
• Heat transfer by convection and radiation

Expected behavior
In an adiabatic, closed, energy-conservative system, gas and solid temperatures should converge toward the analytically computed equilibrium temperature of 189.3 °C, independently of the heat transfer mechanism.

This behavior is correctly observed when only convection is enabled. However, when radiation is included, the system does not converge toward the expected equilibrium temperature.

Following the FDS User Guide recommendations (Section 8.3.2), I also tested adiabatic walls with the wall temperature set to the initial gas temperature (TMP_FRONT_INITIAL = 800 °C). In this case, the discrepancy is even larger, and the results deviate further from the expected equilibrium.

To Reproduce
Here are the input file:

Thermal_equilibrium_fds_with_rad.fds.txt
Thermal_equilibrium_no_rad.fds.txt

[mcgratta]

I am going to look first at the green curve (Conv + rad). For the red curve where T_init =T_adi I am not sure that the problem is well-posed because we have this hot exterior wall at the start and it's not clear to me where that energy belongs in the overall scheme of things.

[drjfloyd]

Reading the issue, with the problem showing up for radiation, I wondered if it was a time accuracy issue. Set ANGLE and TIME increments for radiation to 1, and the end temperature dropped to 193. WALL_INCREMENT=1 and dropped to 191.

[mcgratta]

Yes, I just reached that same conclusion. I cannot type that fast.

[PyroMind-code]

Thank you for this suggestion, adjusting these parameters significantly improves the results !
I was, however, expecting the radiative solver to remain globally energy conservative. I expected convergence toward the same equilibrium temperature, independently of the radiation update frequency.
Is this non‑conservative behavior at coarse radiation ANGLE/TIME increments expected in FDS? Is the radiative solver not intrinsically energy conservative?

[drjfloyd]

Numerical methods have errors that depend on temporal and spatial resolution.

The cube and gas temperatures change fairly quickly. With no strong flow field the timestep size is ~0.1 s. You are getting to 90 % of the final cube temperature in about 150 time steps or 10 full update of the radiation solver with the default parameters. Any angles that are not updated in a timestep keep their value from their last update which in your case is a significant fraction of the time that conditions are changing rapidly.

In a typical fire simulation, timesteps are 10 to 100 times smaller and the impact of updating over 15 timesteps is not a significant source of error. Run your case with DT=0.01 and 0.001 and you will see how improving time accuracy helps in this case.