The heat released as a fire burns is distributed to the environment primarily through convection and radiation. In a simulation, you specify the fraction of the fire total heat release rate that should be assigned to radiation. But, when you check the FDS output files you may see a different fractional amount of radiation in the Q_RADI column of data. This post will explain why these values are different, and what you should expect the Q_RADI data to represent.
As described in the SFPE Handbook of Fire Protection Engineering (Section Three, Chapter 4), “The chemical (fire) heat release rate distributes itself into a convective component and into a radiative component. The convective component is carried upward in a plume and the radiative component is incident on the bounding surfaces of the compartment.”
In the FDS User Guide (SVN 20596) section “13.1.1 Radiative Fraction”, it states:
“The most important radiation parameter is the fraction of energy released from the fire as thermal radiation, commonly referred to as the radiative fraction. It is a function of both the flame temperature and chemical composition, neither of which are reliably calculated in a large scale fire calculation because the flame sheet is not well-resolved on a relatively coarse numerical grid. In calculations in which the mesh cells are on the order of a centimeter or larger, the temperature near the flame surface cannot be relied upon when computing the source term in the radiation transport equation, especially because of the T4 dependence. As a practical alternative, the parameter RADIATIVE_FRACTION on the REAC line allows you to specify explicitly the fraction of the total combustion energy that is released in the form of thermal radiation. Some of that energy may be reabsorbed elsewhere, yielding a net radiative loss from the fire or compartment that is less than the RADIATIVE_FRACTION, depending mainly on the size of the fire and the soot loading.”
By default, the radiative fraction is 35%, meaning that in mesh cells with combustion, 35% of the Heat Release Rate per Unit Volume (HRRPUV) will be released as thermal radiation. As described above, once radiation is released, based on the radiative fraction setting, the energy can then be absorbed by gas species in the domain atmosphere which defaults to ‘AIR’. Some of the most significant species in the gas can be Soot, Droplets/Particles, Water Vapor (Humidity) and CO2.
We demonstrate this using a simple model of a burner in an open box. For this example the HRR of the fire is 25 kW and the Radiative Fraction value is set to the default of 35%, which means that an ideal Q_RADI without any losses to absorption would be 8.75 kW. (Note that starting with FDS 6.3.0, the Radiative Fraction is specified as part of the reaction. In PyroSim, this is located on the Byproducts tab of the Edit Reactions dialog.) This model illustrates the effect of ambient gas species on how radiation is absorbed and the effect on the Q_RADI output.
The output data shown in the Q_RADI column of the jobname_hrr.csv file, is the integration of radiative HRR (q″r) over the entire simulation domain, plus bulk elements that can absorb radiation (e.g. droplets/particles). The radiative fraction only ensures that the fire emits at least the specified radiative fraction. Q_RADI shows the net result of emission and absorption of radiation in the domain, along with any numerical error in either the transport of the radiation or in the integration for the Q_RADI term.
See Figure 2 for a comparison of the HRR from the fire, compared to the Q_RADI output. Keep in mind that the orange line in Figure 2 is showing the portion of the total HRR that is released as thermal radiation. The ratio of Q_RADI and HRR is shown in Figure 3. (Note that the initial oscillation is due to a combination of boundary conditions and the mesh size. If mesh is refined, the oscillation disappears.)
As shown in Figure 3, the calculated Q_RADI/HRR ratio is somewhat less than the specified radiative fraction value of 35%. This difference is primarily a result of absorption by CO2 and water in the air. We can demonstrate this by setting the Ambient Carbon Dioxide Mass Fraction (Y_CO2_INFTY) and Relative Humidity (HUMIDITY) to zero (in PyroSim this is set on the Environment tab of the Simulation Parameters dialog). When this is done, the ratio is very close to 35%.
Radiation output from soot in the upper layer and surfaces which are warming up and radiating energy can increase the difference between the specified radiative fraction and calculated Q_RADI/HRR ratio.
For more information regarding the treatment of Radiation in FDS, please see sections 13.1.1 and 16.10.1 in the FDS User Guide, and in the FDS Technical Guide refer to sections 2.6.2, 6.1.2, 6.1.3 and 6.3.
Special thanks to Jason Floyd from Jensen Hughes for clarifying some information for this post.
PyroSim File – Q_RADI.psm
FDS Input Text
&HEAD CHID='Q_RADI'/ &TIME T_END=10.0/ &DUMP RENDER_FILE='Q_RADI.ge1', DT_RESTART=300.0/ &MESH ID='Mesh01', IJK=40,40,40, XB=-0.5,1.5,-0.5,1.5,0.0,2.0/ &REAC ID='METHANE', FYI='AFT NIST Multi-Floor FDS5 Validation', FUEL='REAC_FUEL', FORMULA='C1H4', HEAT_OF_COMBUSTION=5.56E4/ &SURF ID='Fire', COLOR='RED', HRRPUA=100.0, ADIABATIC=.TRUE./ &OBST XB=0.25,0.75,0.25,0.75,0.0,0.0033462, SURF_IDS='Fire','INERT','INERT'/ Obstruction &VENT SURF_ID='OPEN', XB=1.5,1.5,-0.5,1.5,0.0,2.0/ Mesh Vent: Mesh01 [XMAX] &VENT SURF_ID='OPEN', XB=-0.5,-0.5,-0.5,1.5,0.0,2.0/ Mesh Vent: Mesh01 [XMIN] &VENT SURF_ID='OPEN', XB=-0.5,1.5,1.5,1.5,0.0,2.0/ Mesh Vent: Mesh01 [YMAX] &VENT SURF_ID='OPEN', XB=-0.5,1.5,-0.5,-0.5,0.0,2.0/ Mesh Vent: Mesh01 [YMIN] &VENT SURF_ID='OPEN', XB=-0.5,1.5,-0.5,1.5,2.0,2.0/ Mesh Vent: Mesh01 [ZMAX] &VENT SURF_ID='OPEN', XB=-0.5,1.5,-0.5,1.5,0.0,0.0/ Mesh Vent: Mesh01 [ZMIN] &TAIL /