Serco Assurance

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Serco Assurance
Modelling of Radiation Heat Transfer across
Narrow Gas Gaps Chris Fry
FEAT Technical User Group Meeting
June 19 2003
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Gas gaps can be important in thermal problems

• Gas gaps are very common
• Clearance gaps
• Contact gaps
• Gas gaps can have a significant effect upon heat
  transfer
• Thermal conductivity of air 2000 times smaller
  than that of mild steel.

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Heat transfer across narrow gas gaps

• Heat transfer by radiation and conduction
• Gap assumed too narrow for convection
• Rate of heat transfer across gap given by

Where
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Current modelling of narrow gaps in FEAT

• Heat transfer by both conduction and radiation
  can already be modelled in FEAT
• Use of RADSOL cumbersome for such a simple
  radiation problem
• Narrow width of gaps makes all rays hit in first
  box
• Use of RADSOL can require significant CPU time.

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Modelling of narrow gas gaps in TAU

• TAU is an old heat transfer Finite Element code
  which is owned by Serco Assurance
• Contains explicit gap element type
• Gap element consists of two surfaces
• Heat transfer between surfaces calculated from
  surface temperatures
• Gap width determined automatically
• Heat conservation ensured
• Gap element is very useful!

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New modelling of narrow gas gaps in FEAT

• Avoid use of RADSOL
• Include radiation heat transfer in an effective
  thermal conductivity.
• Effective conductivity approximated by

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Simple test cases

• Test model - two mild steel plates separated by a
  narrow gas gap
• Transient calculation with right hand plate
  exposed to a fire
• Five different cases considered
• 3mm gap - conduction only
• 3mm gap - radiation only
• 3mm gap - radiation and conduction
• 1mm gap - radiation and conduction
• Varying gap ( 1-3mm) - radiation and conduction
• Results validated against TAU

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The test case model
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Results - case 1 - 3mm gap - conduction only
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Results - case 2 - 3mm gap - radiation only
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Results - case 3 - 3mm gap - radiation and
conduction
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Results - case 4 - 1mm gap - radiation and
conduction
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Results - case 5 - gap of varying width
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Automatic determination of gap width

• Useful to be able to automatically determine gap
  width
• But not essential
• Can be easily done using using DISTANCE
• At all positions inside the gap, width of gap is
  equal to sum of distances to two opposite sides
  of the gap

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Conclusions

• Effective conductivity method for narrow gas gaps
  has been tested
• Method was shown to work effectively
• Method did not produce any instability or
  timestep limitation.
• Accuracy of method demonstrated by comparison
  against TAU
• Advantages over RADSOL
• Energy conservation is guaranteed
• Generally less complicated to implement
• Uses less CPU time
• Full report available on FEAT website

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Closing remark - uncertainties in the real world

• Considerable uncertainty in practice
• Uncertain gap width
• Uncertain surface emissivity
• Modelling errors probably much smaller than real
  uncertainties