Fire Dynamics – Heat Fluxes in FDS

Various heat flux quantities can be used to output the heat flux to walls and surfaces in Fire Dynamics Simulator (FDS). This post will explain the difference between various heat flux output quantities.

The options for outputting heat fluxes (kW/m2) at a point location (on a surface) or boundary (along a wall or surface) are as follows:

  • Radiative heat flux – \dot q_{rad}''
  • Convective heat flux – \dot q_{conv}''
  • Net heat flux – \dot q_{net}''
  • Incident heat flux – \dot q_{inc}''
  • Gauge heat flux – \dot q_{gauge}''
  • Radiometer – \dot q_{radiometer}''
  • Radiative heat flux gas – \dot q_{rad}''

Radiative Heat Flux

Consider an energy balance on a surface or wall. The net radiative heat flux \dot q_{rad}'' is given by the sum of the incoming (or absorbed) \dot q_{rad,in}'' and outgoing (or reflected) \dot q_{rad,out}'' radiation:

\dot q_{rad}'' = \dot q_{rad,in}'' - \dot q_{rad,out}''

where \dot q_{rad,out}'' can be decomposed into

\dot q_{rad,out}'' = \dot q_{rad,in}'' - \varepsilon \sigma T_w^4

where \varepsilon is the emissivity, \sigma is the Stefan-Boltzmann constant, and T_w is the wall temperature.

The ‘RADIATIVE HEAT FLUX’ quantity can be used to output the net radiative heat flux to a surface.

Convective Heat Flux

The convective heat flux \dot q_{conv}'' is given by

\dot q_{conv}'' = h (T_g - T_w)

where h is the heat transfer coefficient, and T_g is the local gas temperature.

The ‘CONVECTIVE HEAT FLUX’ quantity can be used to output the convective heat flux to a surface.

Net Heat Flux

The net heat flux is the sum of the radiative heat flux and convective heat flux and is given by

\dot q_{net}'' = \dot q_{rad}'' + \dot q_{conv}''

The ‘NET HEAT FLUX’ quantity can be used to output the combined radiative and convective heat fluxes to a surface.

Incident Heat Flux

The incident heat flux is a diagnostic output and is the sum of the incoming radiation and convection. It does not include outgoing radiation and is given by

\dot q_{inc}'' = \dot q_{rad}''/\varepsilon + \sigma T_w^4 + \dot q_{conv}''

Substituting in the definition of the net radiative heat flux results in

\dot q_{inc}'' = (\dot q_{rad,in}'' - \dot q_{rad,out}'')/\varepsilon + \sigma T_w^4 + \dot q_{conv}''

Expanding the \dot q_{rad,out}'' term results in

\dot q_{inc}'' = (\dot q_{rad,in}'' - \varepsilon \sigma T_w^4)/\varepsilon - \sigma T_w^4 + \sigma T_w^4 + \dot q_{conv}''

Expanding the first term and simplifying results in

\dot q_{inc}'' = \dot q_{rad,in}''/\varepsilon - \sigma T_w^4 + \sigma T_w^4 + \dot q_{conv}''

Further simplification results in

\dot q_{inc}'' = \dot q_{rad,in}''/\varepsilon + \dot q_{conv}''

The ‘INCIDENT HEAT FLUX’ quantity can be used as a diagnostic to output the convective and incoming radiative heat fluxes to a surface.

Gauge Heat Flux

The gauge heat flux can be used when comparing experimentally measured heat fluxes for a gauge that is held at a fixed temperature. The gauge heat flux accounts for the incoming and outgoing radiation and convection and adjusts the heat fluxes based on a fixed (specified) wall temperature. The gauge heat flux is given by

\dot q_{gauge}'' = \dot q_{rad}''/\varepsilon + \dot q_{conv}'' + \sigma(T_w^4 - T_G^4) + h(T_w - T_G)

You must specify the gauge temperature T_G for this output.

The ‘GAUGE HEAT FLUX’ quantity can be used when comparing heat flux predictions to experimentally measured heat fluxes for a gauge at a fixed temperature.

Radiometer

The radiometer output quantity is similar to the gauge heat flux output quantity, but convection is neglected, which is given by

\dot q_{gauge}'' = \dot q_{rad}''/\varepsilon + \sigma(T_w^4 - T_\infty^4)

The ‘RADIOMETER’ quantity can be used when comparing heat flux predictions to experimentally measured heat fluxes from a radiometer.

Radiative Heat Flux Gas

The ‘RADIATIVE HEAT FLUX GAS’ quantity is the same as the radiative heat flux \dot q_{rad}'' except this device can be placed away from a solid surface to output the radiative heat flux if a surface was present at the specified location.

Example

An example case can be used to demonstrate the different heat flux output quantities in FDS. The source code for this example can be found on the fire-tools repository.

In this example, a 200 kW propane fire measuring 0.4 m by 0.4 m is placed 0.3 m from a single wall in a domain measuring 1 m by 1 m by 2 m. The grid cells are 10 cm on each side. The wall is divided vertically into two halves: one with thermal properties of gypsum (and an emissivity of 0.5 to exaggerate the results), and another specified as an ‘INERT’ surface with a fixed temperature of 20 °C. The other walls are open to ambient air. Two measurement locations are located on the wall at a height of 0.5 m: one located on the gypsum portion of wall, and one located on the INERT portion of the wall. The following snapshot from Smokeview shows the fire in front of the gypsum wall (left) and inert wall (right).

heat_flux_0423

Six heat flux output quantities were placed at the two measurement locations as follows: net heat flux, convective heat flux, radiative heat flux, incident heat flux, gauge heat flux, and radiometer.

The following snapshot shows the convective heat flux on the wall. If the radiative, net, or convective heat flux quantities are visualized via a boundary file, there is a difference between the heat flux values on the two materials because the gypsum material is warmer than ambient air, which results in a negative convective heat flux (heat transfer from the wall to the air), whereas the inert (cold) wall does not heat up, which results in a positive convective heat flux (heat transfer from the air to the wall):

heat_flux_0500

The following snapshot shows the gauge heat flux on the wall. Note that the incident heat flux and gauge heat flux do not depend on the emissivity or properties of the materials, so the two different wall materials show no difference in the incident and radiative heat flux quantities. In other words, this is the heat flux “incident” upon the material and does not depend on the properties of the material (a similar effect is observed for the ‘WALL TEMPERATURE’ vs. the ‘ADIABATIC SURFACE TEMPERATURE’ output quantities):

heat_flux_0498

The following plot shows the different heat fluxes on the inert wall:

heat_flux_inert

The highest heat fluxes are the incident and gauge heat flux, which are between 10 kW/m2 and 15 kW/m2, followed closely by the radiometer. This is expected because the incident and gauge heat fluxes do not account for radiative losses, the gauge heat flux is the heat flux to an inert (cold) wall, and the wall and gauge temperatures for the inert wall are fixed at 20 °C. The radiative and net heat fluxes are the next highest heat fluxes between 8 kW/m2 and 14 kW/m2, and they are overlapping because the convective heat flux is close to 0 kW/m2.

The following plot shows the different heat fluxes on the gypsum wall:

heat_flux_gypsum

The various heat flux quantities are in the same order as the inert wall. The incident heat flux, gauge heat flux, and radiometer are overlapping from 10 kW/m2 to 15 kW/m2. Because the gypsum material has an emissivity of 0.5, the radiative heat flux is lower (approximately 5 kW/m2) because half of the radiation is reflected away. As the gypsum wall heats up, it begins to transfer heat outwards via convection, hence the negative convective heat flux of approximately -1 kW/m2. Because of the reduced radiative heat flux and the negative heat flux, the net heat flux (sum of the radiative and convective heat fluxes) is less than the inert wall and is approximately 5 kW/m2.

Conclusion

Use the ‘RADIATIVE HEAT FLUX’, ‘CONVECTIVE HEAT FLUX’, or ‘NET HEAT FLUX’ output quantities to obtain the heat flux to a surface that accounts for both incoming and outgoing radiative and convective heat transfer and uses the actual wall temperature in the heat transfer calculations.

Use the ‘GAUGE HEAT FLUX’ or ‘RADIOMETER’ output quantities when comparing to experimental measurements. Specify a gauge temperature when using the gauge heat flux output quantity.

Use the ‘INCIDENT HEAT FLUX’ output quantity as a diagnostic output to check the heat flux value (neglecting radiative losses).

Walls with the default ‘INERT’ boundary condition should not be used in a realistic scenario because they remain at a fixed temperature. They should only be used for diagnostic purposes.

The source code for this heat flux example can be found on the fire-tools repository, including the FDS input file and the Python script to generate the plots.

Posted in FDS, fire

Forward and Inverse Modeling of Fire Physics Towards Fire Scene Reconstructions

dissertation

My PhD dissertation on “Forward and Inverse Modeling of Fire Physics Towards Fire Scene Reconstructions” has been made available and can be downloaded from:

http://repositories.lib.utexas.edu/handle/2152/21971

Posted in Research, The University of Texas at Austin

Flame Heights, 3D Smoke, and Circular Vents in FDS

An FDS user from Japan writes in with a couple of questions regarding my flame height and fire plume video on YouTube:

I am using FDS to do some study in fire simulation, and very interested in your Videos on your homepage. As you showed the flame heights and fire plumes calculated by FDS (on the following URL), I have 2 questions and wonder if you could help me out?

1. The flame color

In your video, it seems that there is no soot smoke around the plumes. But in my calculation, there is some soot smoke, as shown in the following figure. I am using FDS6 now, and the &REAC ID is required. SOOT_YIELD was set to be 0.0, why there was the soot smoke?

2. The diameter of the fire

The diameter of the fire in your calculation is 1.5m, but it seems to be 1m in the SMV animation. I wonder how long is the fire width in your calculation? As it is not easy to make a circle object in FDS, could you tell me the details of your model in FDS.

My response:

Thank you for your questions.

1) In my flame height video, I loaded the 3D smoke option to show heat release rate per unit volume (HRRPUV), but I did not load the 3D smoke option to show soot density (or smoke). You are correct that in FDS 6 the default soot yield is 0.00. So, you are not seeing a visualization of smoke, but you are seeing a different colormap being used in FDS 6 for the HRRPUV quantity.

The colorbar for HRRPUV in FDS 6 ranges from black to orange, and you can view and edit the colormap by going to the appropriate option in Smokeview. So, to answer your question, we are both looking at the same quantity (HRRPUV) in Smokeview, but the colormaps are slightly different.

2) The base of my fuel in the video is indeed 1.5 m on each side, but you are seeing a perspective shift in Smokeview because our view is centered on the base of the flame, which makes it difficult to see exactly where the edges of the fuel base line up with the tick marks in Smokeview. If you “slide” the view to the left or right in Smokeview, then you will see that the edges of the fuel base line up with the tick marks for -0.75 m and 0.75 m.

Additionally, in FDS 6, you can specify circular vents for fires and/or openings. Take a look at the section for Special Vents > Circular Vents in the FDS User’s Guide to see how you can specify a circular vent using the XYZ and RADIUS parameters on a VENT line.

Posted in FDS