Radiation and Convection on Surfaces

Every solid surface in an FDS model defines convective and radiative flux thermal boundary conditions. What may not be immediately obvious is that each of the terms are always being calculated, sometimes using default parameters that may not have been explicitly specified by the user. The reason we are thinking about this is that we will likely redesign the PyroSim user interface to more clearly help the user understand what options are being selected when they create a surface.

The convective heat transfer flux is given by:

    \[\dot{q}_{\rm c}'' = h \, (T_{\rm g} - T_{\rm w})\]

where the default convective heat transfer coefficient h is based on a combination of natural and forced convection correlations, T_{\rm g} is the gas temperature, and T_{\rm w} is the wall temperature. Normally a user will not modify the convective heat transfer model h, but the user is responsible for how T_{\rm w} will be calculated, either as a fixed temperature or as part of thermal conduction into a solid.

The thermal radiation flux is conceptually more complicated. If it is assumed that the thermal radiation from the surrounding gases is absorbed within an infinitely thin layer at the surface of the solid obstruction, then the net radiative heat flux is the sum of incoming and outgoing components:

    \[\dot{q}_{r}'' = \dot{q}_{r,in}'' - \dot{q}_{r,out}''\]

with the incoming radiation a function of radiation intensity and geometry and the outgoing radiation given by:

    \[\dot{q}_{r,out}'' = \varepsilon\sigma T^4_{w}\]

where \varepsilon is the emissivity, \sigma is the Stefan-Boltzmann constant, and the wall temperature is raised to the fourth power. The user will typically only specify the emissivity and is again responsible for how the wall temperature will be calculated.

FDS provides some default surfaces (INERT, ADIABATIC, and OPEN) and PyroSim tries to help the user by further categorizing surface types (Burner, Heater/Cooler, Supply, Exhaust, and Layered). How each surface handles convection and radiation heat transfer is summarized in the table below.

surface type summary

Here is an example that exercises most of the above options. There is a supply inlet on the right with a temperature of 50.0 C. On the bottom, a heater at 500 C supplies heat by convection and radiation. On the left, some of the air is exhausted with the surface temperature value of 20 C. The top is OPEN and the front and back sides are INERT.

The velocity vectors are shown in the figure to the right.

test of surfaces velocity vectors

The calculated heat fluxes are consistent with the above discussion, with both convective and radiative components on all surfaces. The figure on the left shows the radiative flux for the heater (radiating into the enclosure) and on the right the radiative flux for the exhaust (the radiation removes heat from the enclosure).

heater rad flux exhaust rad flux

At the top OPEN surface we see that on the left side (where the flow is out of the model) the convective heat flux is zero, while on the right (where the flow is mostly tangent to the surface) the convective heat flux is significant.

top left conv flux top right conv flux

In summary, the user needs to be aware that even if they do not explicitly define convection or radiation parameters, these fluxes will still be calculated for all surfaces using the default values. For more detailed discussion, see the FDS User Manual and the FDS Technical Reference, available on the web at FDS-Smokeview.

Here is a listing of the FDS input file used in the example. PyroSim users: copy the text and save as a *.fds file. Then, on the File menu click Import FDS/CAD file… and select the file. This is an FDS 6 input file.

supply_tmpa20_heat500.fds
Generated by PyroSim - Version 2014.1.0331
Apr 23, 2014 3:56:40 PM

&HEAD CHID='supply_tmpa20_heat500'/
&TIME T_END=20.0/
&DUMP RENDER_FILE='supply_tmpa20_heat500.ge1'/
&MISC BAROCLINIC=.FALSE./

&MESH ID='MESH', IJK=20,20,30, XB=-1.0,1.0,-1.0,1.0,0.0,3.0/

&REAC ID='POLYURETHANE_REAC',
      FYI='SFPE Handbook, GM27',
      FUEL='REAC_FUEL',
      C=1.0,
      H=1.7,
      O=0.3,
      N=0.08,
      CO_YIELD=0.042,
      SOOT_YIELD=0.198/

&DEVC ID='temp 1.5 m', QUANTITY='TEMPERATURE', XYZ=0.0,0.0,1.5/
&DEVC ID='Heater Adiabatic Temp', QUANTITY='ADIABATIC SURFACE TEMPERATURE', XYZ=0.0,0.0,0.1, IOR=3/
&DEVC ID='Heater Wall Temp', QUANTITY='WALL TEMPERATURE', XYZ=0.0,0.0,0.1, IOR=3/
&DEVC ID='Heater Rad Flux', QUANTITY='RADIATIVE HEAT FLUX', XYZ=0.0,0.0,0.1, IOR=3/
&DEVC ID='Heater Conv Flux', QUANTITY='CONVECTIVE HEAT FLUX', XYZ=0.0,0.0,0.1, IOR=3/
&DEVC ID='Left Adiabatic Temp', QUANTITY='ADIABATIC SURFACE TEMPERATURE', XYZ=-1.0,0.0,1.5, IOR=1/
&DEVC ID='Left Wall Temp', QUANTITY='WALL TEMPERATURE', XYZ=-1.0,0.0,1.5, IOR=1/
&DEVC ID='Left Rad Flux', QUANTITY='RADIATIVE HEAT FLUX', XYZ=-1.0,0.0,1.5, IOR=1/
&DEVC ID='Left Conv Flux', QUANTITY='CONVECTIVE HEAT FLUX', XYZ=-1.0,0.0,1.5, IOR=1/
&DEVC ID='Right Adiabatic Temp', QUANTITY='ADIABATIC SURFACE TEMPERATURE', XYZ=1.0,0.0,1.5, IOR=-1/
&DEVC ID='Right Wall Temp', QUANTITY='WALL TEMPERATURE', XYZ=1.0,0.0,1.5, IOR=-1/
&DEVC ID='Right Rad Flux', QUANTITY='RADIATIVE HEAT FLUX', XYZ=1.0,0.0,1.5, IOR=-1/
&DEVC ID='Right Conv Flux', QUANTITY='CONVECTIVE HEAT FLUX', XYZ=1.0,0.0,1.5, IOR=-1/
&DEVC ID='Top Adiabatic Temp', QUANTITY='ADIABATIC SURFACE TEMPERATURE', XYZ=0.9,0.0,3.0, IOR=-3/
&DEVC ID='Top Wall Temp', QUANTITY='WALL TEMPERATURE', XYZ=0.9,0.0,3.0, IOR=-3/
&DEVC ID='Top Rad Flux', QUANTITY='RADIATIVE HEAT FLUX', XYZ=0.9,0.0,3.0, IOR=-3/
&DEVC ID='Top Conv Flux', QUANTITY='CONVECTIVE HEAT FLUX', XYZ=0.9,0.0,3.0, IOR=-3/
&DEVC ID='Back Adiabatic Temp', QUANTITY='ADIABATIC SURFACE TEMPERATURE', XYZ=0.0,1.0,1.5, IOR=-2/
&DEVC ID='Back Wall Temp', QUANTITY='WALL TEMPERATURE', XYZ=0.0,1.0,1.5, IOR=-2/
&DEVC ID='Back Rad Flux', QUANTITY='RADIATIVE HEAT FLUX', XYZ=0.0,1.0,1.5, IOR=-2/
&DEVC ID='Back Conv Flux', QUANTITY='CONVECTIVE HEAT FLUX', XYZ=0.0,1.0,1.5, IOR=-2/
&DEVC ID='Top Left Adiabatic Temp', QUANTITY='ADIABATIC SURFACE TEMPERATURE', XYZ=-0.9,0.0,3.0, IOR=-3/
&DEVC ID='Top Left Wall Temp', QUANTITY='WALL TEMPERATURE', XYZ=-0.9,0.0,3.0, IOR=-3/
&DEVC ID='Top Left Rad Flux', QUANTITY='RADIATIVE HEAT FLUX', XYZ=-0.9,0.0,3.0, IOR=-3/
&DEVC ID='Top Left Conv Flux', QUANTITY='CONVECTIVE HEAT FLUX', XYZ=-0.9,0.0,3.0, IOR=-3/
&SURF ID='Supply',
      RGB=26,204,26,
      TMP_FRONT=50.0,
      VEL=-1.0,
      VEL_T=0.0,-1.0/
&SURF ID='Heater',
      RGB=255,102,0,
      TMP_FRONT=500.0/
&SURF ID='Exhaust',
      RGB=26,204,26,
      VEL=0.5/

&OBST XB=-1.0,1.0,-1.0,1.0,0.0,0.1, SURF_IDS='Heater','INERT','INERT'/ Base

&VENT SURF_ID='Supply', XB=1.0,1.0,-1.0,1.0,0.0,3.0/ Supply
&VENT SURF_ID='OPEN', XB=-1.0,1.0,-1.0,1.0,3.0,3.0/ Exhaust
&VENT SURF_ID='Exhaust', XB=-1.0,-1.0,-1.0,1.0,0.0,3.0/ Near zero supply

&BNDF QUANTITY='ADIABATIC SURFACE TEMPERATURE'/
&BNDF QUANTITY='WALL TEMPERATURE'/

&SLCF QUANTITY='TEMPERATURE', PBY=0.0/
&SLCF QUANTITY='VELOCITY', VECTOR=.TRUE., PBY=0.0/

&TAIL /

Comments or Questions

This post was written by Daniel Swenson. For comments or questions, send email to support@thunderheadeng.com.

 

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