Quantitative methods in fire safety engineering 5 U01620 10' Introduction to radiation modelling

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Quantitative methods in fire safety engineering 5
(U01620) 10. Introduction to radiation
modelling

• Stephen Welch
• S.Welch_at_ed.ac.uk
• School of Engineering and Electronics
• University of Edinburgh

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Introduction to radiation Scope

• Radiation processes
• Geometrical effects
• Optical properties
• Radiation models
• Flux methods
• DTRM (RANS)
• RTE solution
• Absorption coefficient
• FVM (LES)
• Example application

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Radiative exchanges

• Two major issues
• Geometrical relationship (configuration factors)
• Optical properties of the gas
• Emissive powers
• Absorptivities

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Radiation models

• Flux methods
• Typified by the 6-flux method
• Patankar Spalding (1973)
• Integrates fluxes along orthogonal axes
• Uses same techniques as other solved variables
• Poor description of oblique transfers
• Should not be used near fire source
• Should not be used for flame spread

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Radiation models

• Discrete Transfer Radiation Method (DTRM) in
  SOFIE/JASMINE/CFX
• Pre-compute general radiation rays
• Lockwood Shah (1981)
• Integrates fluxes along arbitrary axes
• Uses special solver
• Loosely coupled so do not have to compute on
  every step of fluid flow solution

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Radiation models

• Finite volume method (FVM) in FDS
• Solved in manner similar to convective transport
• Hostikka McGrattan (2002)
• Uses 100 solid angles
• Some cases use wide band model

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DTRM ray discretization

• Hemisphere divided into solid angles
• Polar (?)
• Azimuthal (? )

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Radiative transfer equation

• Radiative intensity along line of sight evaluated
  from integrated form of RTE
• where ?? and ib,? are spectral transmissivity and
  black body intensity, respectively

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Radiative transfer equation

• If medium is grey and homogeneous
• Recurrence relation
• Can be expanded along entire path

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Radiative transfer equation

• Solution process is iterative
• Over elemental solid angle
• Incident flux for nth ray is
• Total incident flux obtained by summation

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Optical properties

• A range of models available
• Differ in treatment of spectral variation
• Single grey gas/band
• Modak
• Homogeneous isothermal gas/soot mixture
• Mixed grey gas (WSGG)
• Truelove
• Taylor Foster
• Smith

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Optical properties (cont.)

• Narrow band
• Consider detailed spectral dependence
• Grosshandler Nguyen (1985)
• Computationally intensive
• Not tractable in general calculations
• Can be used for checking performance of simpler
  models

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Optical properties

• Mixed grey gas model (WSGG)
• Considers radiative transfer over a finite number
  of spectral bands (often only 4)
• clear gas
• optically thin
• optically intermediate
• optically thick
• Compromise between
• Accuracy
• Tractability

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Absorption coefficient

• Effective absorption coefficient per band
• k absorption constant for band b
• p partial pressure
• Hence, local emissivity
• l path length
• Various simplifications can be made for
  computational expediency
• Hierarchy of models of different complexity

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Radiation model hierarchy
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Computational requirements
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Errors

• All radiation models suffer from numerical errors
• DTRM/FVM models affected by the ray effect
• Insufficient rays crossing each relevant control
  volume
• Hot spots appear on receiving surfaces
• Other systematic errors arise from compromises in
  representation of spectral dependencies
• Cross-check results for simplified case against
  those of detailed narrow band models

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Example application

• Heat transfer to a steel beam BRI beam

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Example application

• Flowfield

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Parametric Study
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Parametric Study
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Parametric Study
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Summary

• Flux methods
• Crude
• DTRM
• Flexible method independent of grid
• Can accommodate different degrees of complexity
  in spectral representations
• Take care over numerical errors
• Ray effect
• Spectral lumping

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References

• Chung, T.J. Computational Fluid Dynamics,
  Cambridge University Press, 2002
• Cox, G Combustion Fundamentals of Fire,
  Academic Press, 1995
• Lockwood, F.C. and Shah, N.G. (1981) "A new
  radiation solution method or incorporation in
  general combustion prediction procedures", 18th
  Symp (Int.) on Comb., pp. 1405-1414
• Hostikka, S. et al. Numerical Modeling of Pool
  Fires using Large Eddy Simulation and Finite
  Volume Method for Radiation, Proc. 7th IAFSS,
  2002
• McGrattan, K. (ed.) Fire Dynamics Simulator
  (Version 4) Technical Reference Manual, NIST
  special publication 1018, 2004
• Grosshandler, W.L. Nguyen, H.D. J. Heat Trans.,
  107, 445, 1985