Quantitative methods in fire safety engineering 5 U01620 9. Introduction to combustion modelling

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Quantitative methods in fire safety engineering 5
(U01620) 9. Introduction to combustion
modelling

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

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Introduction to combustion Scope

• Combustion processes
• Premixed
• Diffusion flames
• Combustion chemistry
• Equilibrium
• Finite rate
• Combustion models
• Mixing controlled
• pdf methods

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Introduction to combustion Scope

• Toxic minor species
• Carbon monoxide
• Smoke
• Flame spread
• Solid-phase pyrolysis

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Example application
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Combustion processes

• Premixed flames
• Deflagration
• Detonation
• Diffusion flames
• Laminar
• Turbulent
• Typical of natural fire
• Fairly long time scales
• Buoyancy dominated

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Turbulent diffusion flames

• Combustion chemistry/heat release
• Essentially mixing controlled
• Chemical kinetics can be assumed fast
• Useful simplifying assumption
• Species yields (e.g. toxic emissions)
• Products of incomplete combustion
• Non-equilibrium/slow chemistry important
• High heat loss
• Thermal radiation from carbon particles
• May influence flame spread

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Combustion chemistry

• Equilibrium
• Thermodynamic equilibrium
• Unphysically high yields of intermediates
• Finite-rate chemistry
• Typically described by Arrhenius expressions
• EA is the activation energy (typically very
  high!)
• Even for simple fuels can be hundreds of
  reactions and dozens of intermediate species

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Methane mechanism

• Detailed scheme
• 149 elementary steps
• 144 reverse reactions
• 33 species

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Combustion modelling

• Want to describe
• Energy release
• Species yields, especially toxic products
• Distinguish controlling mechanisms
• Mixing control
• Chemical reaction rate
• Damkohler number
• Basis for simplified treatments
• Dagtgt1 (fast chemistry)

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Combustion modelling

• Transport equation for species
• Reynolds averaged form
• Chemical source term
• Highly non-linear in instantaneous gas
  temperature
• Problem of closure

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Chemical source term closure

• Consider simplified chemical reaction
• Fuel Oxidant Products
• k is rate constant for reaction
• Source term for fuel consumption
• If expanded get unknown cross-products

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Favre averaging

• Density-weighted time averaging
• simplifies mathematical description
• Reynolds average
• Favre average
• where

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Reynolds averaging

• Time averaging
• Reynolds (1895)

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Favre averaging

• Continuity equation
• Reynolds average
• Favre average

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Chemical source term closure

• Expand mean chemical source term

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Chemical source term closure

• Rate term can also be expanded
• cross correlations are unknown and highly
  non-linear!

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Does it matter?

• Consider
• temperature fluctuating between 500K and 2000K
  (e.g. reactants and products)
• Mean temperature 1250K
• Typical activation energy/R20,000K A1
• Rate from mean T
• Rate from exact T
• Ratio 0.5!

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Does it matter?

• Using mean temperatures
• Significant underestimate of reaction rates
• If we have to model finite-rate chemistry
• Need a method of accommodating influence of
  temperature fluctuations
• Solve additional transport equations for each
  species of interest
• Soon becomes intractable!

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Mixing controlled combustion

• If we cant model reaction rate, just assume its
  infinitely fast
• Constrained by microscopic mixing rate
• Need a model to describe mixing
• Eddy breakup (EBU version 1)
• Spalding (1971)
• k, ? turbulent kinetic energy and dissipation
• Yf fluctuation of fuel mass fraction
• CEBU empirical constant

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Mixing controlled combustion

• Eddy breakup (EBU version 2)
• Magnussen Hjertager (1976)
• For turbulent diffusion flame
• Assuming isotropic turbulence
• Usually taken to equal 4

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Eddy breakup models

• Reasonably successful across a range of
  combustion systems
• Relatively simple formulation
• Provides for distributed heat release
• e.g. flame lengthening under ventilation control
  arises automatically
• Tracks composition evolution in terms of
• Oxidant, reactant and products
• BUT, detailed chemistry neglected
• No good if require other minor species
• Toxic products of combustion, CO and smoke

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PDF methods

• Chemical source term closure requires
• Knowledge of all cross-correlations
• Can be solved using Monte Carlo method
• Introduce large number of fluid particles
• Track progress of each in time
• Adjust particle composition as it interacts
• Hence
• Obtain the joint-pdf numerically
• Hugely demanding computationally!

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Mixture fraction

• A variable can be defined as
• where, ?
• Assuming one-step chemistry
• the rate of change of each term is equal and
  opposite
• ? is not affected by chemical change

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Mixture fraction

• Call ? a conserved scalar
• Measure of the local mass which originated in
  fuel stream
• Value varies between 0 and 1
• Cannot be created or destroyed
• Affected by other mixing processes
• Convection and diffusion
• Can track in space by solving an additional
  transport equation for ?
• If we can relate other chemistry to this
  parameter alone there is no need to close
  chemical source term!

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Fast chemistry

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Laminar flamelet models

• Imagine the mixture consists of an ensemble of
  laminar flamelets
• Chemistry of each is defined for full range of
  mixture fraction values found in a laminar
  diffusion flame
• Obtain instantaneous species concentrations
• Y(?) defined by the state relationship
• Need only model the evolution of P(?)

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Laminar flamelet models

• How can we determine P(?)!?
• Solve additional transport equations
• Mean
• Variance
• Ties in effect of turbulence

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Laminar flamelet models

• Prescribed pdfs, of fixed general shape
• Beta function
• Gaussian
• Shape evolves with local conditions
• Expressed in terms of computed mean and variance
  of mixture fraction (beta function)

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Laminar flamelet models

• Flamelet chemistry
• Equilibrium (gross overprediction)
• Experimental measurements
• Opposed diffusion flame modelling
• Chemical kinetics limited only by knowledge of
  mechanisms and computer power

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Laminar flamelet - example

• Compared mechanisms
• Simple
• 41 species
• 274 reactions
• Held et al.
• Complex
• 160 species
• 1540 reactions
• Seiser et al.

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Toxic minor species

• Represent detailed chemistry in flamelet
• Obtain by quadrature
• OK provided chemistry is sufficiently fast
• Probably not true for CO
• Definitely not true for smoke

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Carbon Monoxide prediction

• Yield is a balance between
• Rate of formation (relatively slow)
• Turbulent transport
• Oxidation
• Flamelet methods robust for many cases
• May be necessary to parameterise to include
• Heat loss
• Strain rate
• Degree of vitiation
• Requires huge libraries of pre-computed
  flamelets!
• Only works for pure fuels

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Smoke prediction

• Fast chemistry assumption invalid
• Construct flamelet descriptions of the rate of
  formation
• Solve additional balance equations for soot
  particle number density and soot mass
• Flamelet rates provide source terms
• Consider oxidation where necessary
• May be a mixing-controlled rate

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Smoke prediction

• Heat loss very important
• Multiple radiative loss libraries
• Looks up appropriate flamelet according to
  overall energy balance
• Function of local soot concentration
• Coupled problem

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Flame spread modelling

• Ignition criterion
• Surface temperature
• Requires very accurate modelling of solid phase
  heat transfer
• Critical accumulated flux
• Requires some approximations for unknown heat
  losses from rear of specimen
• Cone calorimeter data
• Take HRR direct from cone test
• Will only apply to that flux
• Further complicated by radiation from flames

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Critical accumulated flux

• Defined as
• qmin is a minimum heat flux below which no
  ignition occurs

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Example application

• Flame spread over full-scale corner wall
• 10 different materials
• Cellulosics
• Plastics
• With/without fire retardant

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Heat release rate
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CO production rate
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Smoke production rate
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Sensitivity
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Sensitivity
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Sensitivity
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Sensitivity
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Summary (1)

• Eddy breakup
• Mixing controlled
• Laminar flamelet
• Relaxes fast chemistry assumption
• Overcomes problem of turbulent closure of
  chemical source terms
• Slow chemistry processes, e.g. for toxic products
  like CO and smoke, require solution of additional
  transport equations

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Summary (2)

• Flame spread predictions require
• Accurate smoke predictions
• Radiative feedback to surface controls
  volatilisation rate
• Need a comprehensive model which links all
  phenomena
• This is the strength of CFD over simpler models
  which are essentially more empirical

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References

• Chung, T.J. Computational Fluid Dynamics,
  Cambridge University Press, 2002
• Cox, G Combustion Fundamentals of Fire,
  Academic Press, 1995
• Moss, J.B. Turbulent diffusion flames, chapter
  4 in above, 1995
• Wilcox, D.C. Turbulence modelling for CFD, DCW
  Industries, 1998
• McGrattan, K. (ed.) Fire Dynamics Simulator
  (Version 4) Technical Reference Manual, NIST
  special publication 1018, 2004