AME 514 Applications of Combustion

1
AME 514Applications of Combustion

• Paul D. Ronney
• Fall 2008

2
AME 514 - Fall 2008

• Instructor Paul Ronney (ronney_at_usc.edu)
  Office OHE 430J Phone [phone] Fax
  [phone]
• Office hours 100 - 330 Wednesdays, other
  times by appointment
• Website http//ronney.usc.edu/AME514F08
• Schedule 1 lecture per week, Tuesdays 630 -
  910 pm, OHE 132
• Lectures On campus, also webcast through the
  USC Distance Education Network
• Credit 3 units
• Prerequisite AME 513 or equivalent or
  permission of instructor
• Grading 5 homework assignments,1 for each
  section of the course (60), final exam (40)
• Each homework will consist of
• (1) report on a seminal paper in the field chosen
  from a list provided by PDR (others OK with
  approval in advance from me)
• (2) usual analytical / numerical problems
• Final exam will consist of 6 problems (1 per
  section, plus one anything goes), choose 4/6

3
Supplemental texts (not required)

• S. R. Turns, An Introduction to Combustion
  http//www.mhprofessional.com/product.php?isbn007
  235044X
• F. A. Williams, Combustion Theory
  (Benjamin-Cummins, 1985, ISBN 0-8053-9801-5)
• Turns and Williams are on reserve in the Science
  and Engineering Library

4
Helpful handy hints

• Ill hand out printed copies of lectures so you
  can annotate them, but for best results, download
  and use powerpoint files (includes color, movies,
  hyperlinks, imbedded spreadsheets, etc.)
• If you dont have Powerpoint, you can download a
  free powerpoint viewer from Microsofts website
• Please provide (polite) feedback/comments on the
  production aspects of the course
• Please ask questions in class - the goal of the
  lecture is to maintain a 2-way dialogue on the
  subject of the lecture
• Bringing your wireless-equipped laptop allows you
  to download files from my website as necessary
  and play along in the studio audience

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Tentative outline

• 1) Advanced fundamental topics (3 lectures)
• Flammability and extinction
• Ignition
• Emissions formation and remediation
• 2) Microscale reacting flows and power generation
  (3 lectures)
• i) Scaling considerations
• ii) Microscale internal combustion engines
• iii) Microscale gas turbine and rocket
  propulsion
• iv) Thermoelectrics
• v) Fuel cells
• 3) Turbulent combustion (3 lectures)
• i) Premixed-gas flames
• ii) Non premixed flames
• iii) Edge flames

6
Tentative outline

• 4) Advanced propulsion systems (3 lectures)
• i) Hypersonic propulsion
• ii) Pulse detonation engines
• 5) Emerging needs technologies (3 lectures)
• i) Applications of combustion (aka chemically
  reacting flow) knowledge to other fields
• Frontal polymerization
• Bacteria growth
• Inertial confinement fusion
• Astrophysical combustion
• ii) New technologies
• Transient plasma ignition
• HCCI engines
• Microbial fuel cells
• iii) Future needs in combustion research
• Optional after-class field trips to combustion
  labs (Egolfopoulos, Ronney, Wang)
• Other topics (for example, optical diagnostics)
  may be substituted by request of a majority of
  registered students

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Alternative topics

• 1) Microgravity combustion (3 lectures)
• i) Premixed-gas flames
• ii) Particle-laden flames
• iii) Droplets
• iv) Flame spread over solid fuel beds
• 2) Optical diagnostics (3 lectures)
• Quantum physics of gases
• Absorption / transmission techniques (absorption
  spectroscopy, shadowgraphy, schlieren,
  interferometry)
• Scattering techniques (Rayleigh, Raman, Mie, LDV)
• Fluorescence techniques
• 3) Computational methods in combustion (3
  lectures)
• Governing equations
• Numerical methods
• Applications

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Assignment

• By Friday 8/29
• (Optional) Email me (ronney_at_usc.edu) your
  schedule to me so I can choose office hours
  (default 100 - 330 Weds.)
• (Optional) send suggestions to me for other
  lecture topics and what could be deleted (if I
  dont hear from you I assume you approve the
  currently proposed syllabus)
• If you want to add a unit, you must state what
  unit should be removed
• (Optional) review material on premixed flames
• Turns Chapters 8 15
• Williams Chapter 8
• Egolfopouloss AME 513 notes

9
Advanced fundamental topics

• Quick review of AME 513 concepts
• Flammability extinction limits (1.5 lectures)
• Ignition (.5 lecture)
• Emissions formation remediation (1 lecture)

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Why do we need to study combustion?

• Chemical thermodynamics only tells us the end
  states (temperature, product composition) - what
  happens if we wait forever and a day for
  chemical reaction to occur
• I assume you know chemical thermodynamics, if not
  refer to AME 513 or AME 436 (lectures 2, 3) notes
• We also need to know how fast reactions occur
• Need to couple chemistry to heat, mass momentum
  transport to determine properties of real
  combustion systems
• Chemical reactions heat mass transport
  combustion
• Some reactions occur too slowly to be of any
  consequence, e.g. 2 NO ? N2 O2 has an adiabatic
  flame temperature of 2869K (no dissociation) or
  2650K (with dissociation, mostly NO O) but no
  one has ever made a flame with NO because
  reaction rates are too slow! (Why?)
• What kinds of things do we do with this
  information?
• Determine rates of flame propagation and heat
  generation
• Determine conditions for knock in IC engines
• Determine rates of pollutant formation and
  destruction
• Determine ignition and extinction conditions

11
Types of flames - premixed

• Premixed - reactants are intimately mixed on the
  molecular scale before combustion is initiated
  several flavors
• Deflagration
• Detonation
• Homogeneous reaction
• Deflagration - propagating subsonic front
  sustained by conduction of heat from the hot
  (burned) gases to the cold (unburned) gases which
  raises the temperature enough that chemical
  reaction can occur since chemical reaction rates
  are very sensitive to temperature, most of the
  reaction is concentrated in a thin zone near the
  high-temperature side
• May be laminar or turbulent
• Temperature increases in convection-diffusion
  zone or preheat zone ahead of reaction zone,
  even though no heat release occurs there, due to
  balance between convection diffusion (see
  analysis 2 slides ahead)
• Reactant concentration decreases in
  convection-diffusion zone, even though no
  chemical reaction occurs there, for the same
  reason
• How can we have reaction at the reaction zone
  even though reactant concentration is low there?
  (See diagram) Because reaction rate is much
  more sensitive to temperature than reactant
  concentration, so benefit of high T outweighs
  penalty of low concentration

12
Schematic of deflagration
Turbulent premixed flame experiment in a
fan-stirred chamber (http//www.mech-eng.leeds.ac.
uk/res-group/combustion/activities/Bomb.htm)
Flame thickness (?) ?/SL (? thermal
diffusivity)
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Structure of deflagration

• Outside of the thin reaction zone, only
  convection and diffusion of enthalpy are present,
  thus energy conservation can be written as, for
  1D steady flow from right to left (in -x
  direction, as in diagram on previous page)
• with boundary conditions
• T Tf at x 0 (flame front)
• T ? T8 as x ? 8 (far upstream of flame)
• T ? Tf as x ? -8 (far downstream of flame)
• noting that due to mass conservation
• ?U ?8SL constant
• and assuming k and CP are constant,
• thus, the temperature profile is an exponential
  with decay length flame thickness ?/SL
• Reactant concentration profile is essentially a
  mirror image of the temperature profile, at least
  for Lewis number ? ?/D 1
• D reactant diffusivity

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Premixed flames - detonation

• Supersonic front sustained by heating of gas by
  shock wave
• After shock front, need time (thus distance
  time x velocity) before reaction starts to occur
  (induction zone)
• After induction zone, chemical reaction heat
  release occur
• Pressure temperature behavior coupled strongly
  with supersonic/subsonic gasdynamics
• Ideally only M3 1 Chapman-Jouget detonation
  is stable
• (M Mach number Vc V velocity, c sound
  speed (?RT)1/2 for ideal gas)

15
Premixed flames - homogeneous reaction

• Model for knock in premixed-charge engines
• Fixed mass (control mass) with uniform (in space)
  T, P and composition
• No propagation in space but propagation in time
• In laboratory, we might heat the chamber to a
  certain T and see how long it took to react in
  engine, compression of mixture (increases P T,
  thus reaction rate) will initiate reaction

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Non-premixed or diffusion flames

• Reactants mix at the time of combustion - mix
  then burn - only subsonic
• Many types - gas jet (Bic lighter), droplet,
  liquid fuel (e.g. Kuwait oil fire, candle), solid
  (e.g. coal particle, wood)
• Reaction zone must lie where fuel O2 fluxes in
  stoichiometric proportion
• Generally assume mixed is burned - mixing
  slower than chemical reaction
• No inherent propagation rate (flame location
  determined by stoich. location) or thickness (?
  depends on mixing layer thickness (?/?)1/2) (?
  strain rate) - unlike premixed flames with
  characteristic propagation rate SL and thickness
  ? ?/SL that are almost independent of ?

Candle
Kuwait Oil fire
Forest fire
Diesel engine
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(No Transcript)
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Temperatures of non-premixed flames

• Adiabatic temperature of premixed flame, simplest
  approximation (const. CP, no dissociation,
  complete combustion, const. pressure)
• Tf T8 YF,0QR/CP
• (YF,0 fuel mass fraction far from front, QR
  fuel heating value)
• Non-premixed not as simple, depends on transport
  of reactants to front heat/products away from
  front
• Simplest approximation diffusion dominated, no
  convection

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Temperatures of non-premixed flames

• Mass flux (per unit cross-section area of flame)
  of fuel to flame front ?DF(?YF/?x)
  ?DF(0-YF,0)/(xf-0) ?DFYF,0/xf
• Heat generation rate per unit area of flame front
  QR?DFYF,0/xf
• Mass flux of O2 to flame front ?DoxYox,?/(?-xf)
• Heat conducted away from flame front per unit
  area
• k(?T/?x)left k(?T/?x)right k(Tf-TF,0)/xf
  k(Tf-Tox,?)/(?-xf)
• Unknowns Tf xf
• Equations
• Heat generation rate heat conduction rate away
  from front
• k(Tf-TF,0) k(Tf-Tox,?) QR?DFYF,0/xf
• Mass flux of O2 / fuel stoichiometric O2 / fuel
  mass ratio ?
• ?DoxYox,?/(?-xf) / ?DFYF,0/xf ?
• Combine to obtain

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Temperatures of non-premixed flames

• Implications - temperature
• Increasing either YF,0 or Yox,? increases flame
  temperature Tf
• Increasing TF,0 or Tox,? increases Tf
• Decreasing LeF or Leox increases Tf
• Above results very different from premixed flames
• LeF Leox dont affect adiabatic Tf
• Only increasing Y of stoichiometrically deficient
  reactant increases Tf - increasing Y of other
  reactant decreases Tf
• If TF,0 Tox,? T8 AND LeF Leox 1, then
• Tf T8 fstoichQR/CP
• where fstoich YF,0/(1?) is the mass fraction
  of fuel in a stoichiometric mixture of fuel
  inert (fuel mass fraction YF,0) and oxygen
  inert (O2 mass fraction Yox,?)
• Very much unlike premixed flames, where Tf is
  essentially independent of LeF Leox, and only
  depends on Y of stoichiometrically deficient
  reactant

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Temperatures of non-premixed flames

• Implications - flame position
• Increasing YF,0 or decreasing LeF moves flame
  AWAY from fuel source
• Increasing Yox,? or decreasing Leox moves flame
  AWAY from ox. source
• Since Yox,?/?YF,0 ltlt 1 for fuel-air mixtures (
  0.058 for CH4-air), flame lies very close to air
  side
• Since Yox,?/?YF,0 ltlt 1, Leox affects Tf much more
  than LeF), but since Leox 1 for O2 in N2, Tf is
  hardly affected by fuel type even though LeF
  varies greatly between fuels

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Law of Mass Action (LoMA)

• First we need to describe rates of chemical
  reaction
• For a chemical reaction of the form
• ?AA ?BB ? ?CC ?DD
• e.g. 1 H2 1 I2 ? 2 HI
• A H2, ?A 1, B I2, ?B 1, C HI, ?C 2, D
  nothing, ?D 0
• the Law of Mass Action (LoMA) states that the
  rate of reaction
• i concentration of molecule i (usually
  moles per liter)
• kf forward reaction rate constant
• How to calculate i ?
• According to ideal gas law, the total moles of
  gas per unit volume (all molecules, not just type
  i) P/?T
• Then i (Total moles / volume)(moles i /
  total moles), thus
• i (P/?T)Xi (Xi mole fraction of i)
• Minus sign on dA/dt and dB/dt since A B are
  being depleted
• Basically LoMA states that the rate of reaction
  is proportional to the number of collisions
  between the reactant molecules, which in turn is
  proportional to the concentration of each reactant

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Comments on LoMA

• The reaction rate constant kf is usually of the
  Arrhenius form
• Z pre-exponential factor, n another
  (nameless) constant, E activation energy
  (cal/mole) ? gas constant working backwards,
  units of Z must be (moles per liter)1-?A-vB/(K-nse
  c)
• With 3 parameters (Z, n, E) any curve can be fit!
• The exponential term causes extreme sensitivity
  to T for E/? gtgt T!

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Comments on LoMA

• Boltzman (1800s) showed that the fraction of
  molecules in a gas with translational kinetic
  energy greater than some value E is proportional
  to exp(-E/?T), thus E represents the energy
  barrier that must be overcome for reaction to
  occur
• Diary of a collision

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Comments on LoMA

• The full reaction rate expression is then
• H2 I2 ? 2HI is one of few examples where the
  actual conversion of reactants to products occurs
  in a single step most fuels of interest go
  through many intermediates during oxidation even
  for the simplest hydrocarbon (CH4) the standard
  mechanism (http//www.me.berkeley.edu/gri_mech/)
  includes 53 species and 325 individual reactions!
• The only likely reactions in gases, where the
  molecules are far apart compared to their size,
  are 1-body, 2-body or 3-body reactions, i.e. A ?
  products, A B ? products or A B C ?
  products
• In liquid or solid phases, the close proximity of
  molecules makes n-body reactions plausible

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Comments on LoMA

• Recall that the forward reaction rate is
• Similarly, the rate of the reverse reaction can
  be written as
• kb backward reaction rate constant
• At equilibrium, the forward and reverse rates
  must be equal, thus

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Deflagrations - burning velocity

• Since the burning velocity (SL) ltlt sound speed,
  the pressure across the front is almost constant
• How fast will the flame propagate? Simplest
  estimate based on the hypothesis that
• Rate of heat conducted from hot gas to cold gas
  (i)
• Rate at which enthalpy is conducted through flame
  front (ii)
• Rate at which heat is produced by chemical
  reaction (iii)

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Deflagrations - burning velocity

• Estimate of i
• Conduction heat transfer rate -kA(?T/?)
• k gas thermal conductivity, A cross-sectional
  area of flame
• ?T temperature rise across front Tproducts -
  Treactants
• ? thickness of front (unknown at this point)
• Estimate of ii
• Enthalpy flux through front (mass flux) x Cp x
  ?T
• Mass flux ?VA (? density of reactants ?8, V
  velocity SL)
• Enthalpy flux ?8CpSLA?T
• Estimate of iii
• Heat generated by reaction QR x (dfuel/dt) x
  Mfuel x Volume
• Volume A?
• QR CP?T/f

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Deflagrations - burning velocity, thickness

• Combine (i) and (ii)
• ? k/?CpSL ?/SL (? flame thickness)
• ? k/?Cp thermal diffusivity (units
  length2/time)
• For air at 300K 1 atm, ? 0.2 cm2/s
• For gases ? ? (? kinematic viscosity)
• For gases ? P-1T1.7 since k P0T.7, ? P1T-1,
  Cp P0T0
• For typical stoichiometric hydrocarbon-air flame,
  SL 40 cm/s, thus ? ?/SL 0.005 cm (!)
  (Actually when properties are temperature-averaged
  , ? 4?/SL 0.02 cm - still small!)
• Combine (ii) and (iii)
• SL ??1/2
• ? overall reaction rate (dfuel/dt)/fuel8
  (units 1/s)
• With SL 40 cm/s, ? 0.2 cm2/s, ? 1600 s-1
• 1/? characteristic reaction time 625
  microseconds
• Heat release rate per unit volume (enthalpy
  flux) / (volume)
• (?CpSLA?T)/(A?) ?CpSL/k)(k?T)/? (k?T)/?2
• (0.07 W/mK)(1900K)/(0.0002 m)2 3 x 109 W/m3
  !!!
• Moral flames are thin, fast and generate a lot
  of heat!

30
Deflagrations - burning velocity

• More rigorous analysis (Zeldovich, 1940)
• Tad adiabatic flame temperature T8 ambient
  temperature
• Same functional form as simple estimate (SL
  ??1/2, where ? is an overall reaction rate)
  with some additional constants
• How does SL vary with pressure? Define order of
  reaction (n) ?A ?B since
• Thus SL ??1/2 P-1Pn-11/2 P(n-2)/2
• For typical n 2, SL independent of pressure
• For real hydrocarbons, working backwards from
  experimental results, we find typically SL
  P-0.1, thus n 1.8

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Deflagrations - temperature effect

• Since Zeldovich number (?) gtgt 1
• For typical hydrocarbon-air flames, E 40
  kcal/mole
• ? 1.987 cal/mole, Tf 2200K if adiabatic
• ? ? 10, at T close to Tf, ? T10 !!!
• ? Thin reaction zone concentrated near highest
  temp.
• ? In Zeldovich (or any) estimate of SL, overall
  reaction rate ? must be evaluated at Tad, not T8
• How can we estimate E? If reaction rate depends
  more on E than concentrations , SL ??1/2
  exp(-E/?T)1/2 exp(?E/2?T) - Plot of ln(SL)
  vs. 1/Tad has slope of -E/2?
• If ? isnt large, then ?(T8) ?(Tad) and
  reaction occurs even in the cold gases, so no
  control over flame is possible!
• Since SL ?1/2, SL (T?)1/2 T5 typically!

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Deflagrations - summary

• These relations show the effect of Tad (depends
  on fuel stoichiometry), ? (depends on diluent
  gas (usually N2) P), ? (depends on fuel, T, P)
  and pressure (engine condition) on laminar
  burning rates
• Re-emphasize these estimates are based on an
  overall reaction rate real flames have 1000s of
  individual reactions between 100s of species -
  but we can work backwards from experiments or
  detailed calculations to get these estimates for
  the overall reaction rate parameters

33
Deflagrations
Schematic of flame temperatures and laminar
burning velocities
Real data on SL (Vagelopoulos Egolfopoulos,
1998)
34
Advanced fundamental topics

• Flammability extinction limits
• Description of flammability limits
• Chemical kinetics of limits
• Time scales
• Mechanisms of limits
• Buoyancy effects - upward downward
• Conduction heat loss to tube walls
• (Sidebar) more about flames in tubes
• Radiation heat loss
• Optically thin limit
• (Sidebar) reabsorption effects
• Aerodynamic stretch
• Chemical fire suppressants

35
Flammability and extinction limits

• Reference Ju, Y., Maruta, K., Niioka, T.,
  Combustion Limits, Applied Mechanics Reviews,
  Vol. 53, pp. 257-277 (2001)
• Too lean or too rich mixtures wont burn -
  flammability limits
• Even if mixture is flammable, still wont burn in
  certain environments
• Small diameter tubes
• Strong hydrodynamic strain or turbulence
• High or low gravity
• High or low pressure
• Understanding needed for combustion engines
  industrial combustion processes (leaner mixtures
  ? lower Tad ? lower NOx) fire explosion hazard
  management, fire suppression, ...

36
Flammability limits - basic observations

• Limits occur for mixtures that are
  thermodynamically flammable - theoretical
  adiabatic flame temperature (Tad) far above
  ambient temperature (T8)
• Limits usually characterized by finite (not zero)
  burning velocity at limit
• Models of limits due to losses - most important
  prediction burning velocity at the limit
  (SL,lim) - better test of limit predictions than
  composition at limit

37
Premixed-gas flames flammability limits
2 limit mechansims, (1) (2), yield similar fuel
and Tad at limit but very different SL,lim
38
Flammability limits in vertical tubes

• Most common apparatus - vertical tube (typ. 5 cm
  in diameter)
• Ignite mixture at one end of tube, if it
  propagates to other end, its flammable
• Limit composition depends on orientation -
  buoyancy effects

• Upward propagation Downward
  propagation

39
Chemical kinetics of limits

• Lean hydrocarbon-air flames main branching
  reaction (promotes combustion) is
• H O2 ? OH O dO2/dt -1016.7HO2T-0.8e-1
  6500/RT
• mole/cm3 T K R cal/mole-K t sec
• Depends on P2 since P, strongly dependent
  on T
• Why important? Only energetically viable way to
  break OO bond (120 kcal/mole), even though H
  is small
• Main H consumption reaction
• H O2 M ? HO2 M M any molecule
• dO2/dt -1015.2HO2MT0e1000/RT for M
  N2
• (higher rate for CO2 and especially H2O)
• Depends on P3, nearly independent of T
• Why important? Inhibits combustion by replacing
  H with much less active HO2
• Branching or inhibition may be faster depending
  on T and P

40
Chemical kinetics of limits

• Rates equal (crossover) when
• M 101.5T-0.8e-17500/RT
• Ideal gas law P MRT thus
• P 103.4T0.2e-17500/RT (P in atm)
• ? crossover at 950K for 1 atm, higher T for
  higher P
• but this only indicates that chemical mechanism
  may change and perhaps overall W drop rapidly
  below some T
• Computations show no limits without losses no
  purely chemical criterion (Lakshmisha et al.,
  1990 Giovangigli Smooke, 1992) - for steady
  planar adiabatic flames, burning velocity
  decreases smoothly towards zero as fuel
  concentration decreases (domain sizes up to 10 m,
  SL down to 0.02 cm/s)
• but as SL decreases, d increases - need larger
  computational domain or experimental apparatus
• Also more buoyancy heat loss effects as SL
  decreases .

41
Chemical kinetics of limits

• Ju, Masuya, Ronney (1998)

Ju et al., 1998
42
Aerodynamic effects on premixed flames

• Aerodynamic effects occur on a large scale
  compared to the transport or reaction zones but
  affect SL and even existence of the flame
• Why only at large scale?
• Re on flame scale SL?/? (? kinematic
  viscosity)
• Re (SL?/?)(?/?) (1)(Pr) 1 since Pr 1 for
  gases
• Reflame  1 ? viscosity suppresses flow
  disturbances
• Key parameter stretch rate (?)
• Generally ? U/d
• U characteristic flow velocity
• d characteristic flow length scale

43
Aerodynamic effects on premixed flames

• Strong stretch (? ? SL2/? or Karlovitz number
  Ka ? ??/SL2 1) extinguishes flames
• Moderate stretch strengthens flames for Le lt 1

44
Lewis number tutorial

• Le affects flame temperature in curved (shown
  below) or stretched flames
• When Le lt 1, additional thermal enthalpy loss in
  curved/stretched region is less than additional
  chemical enthalpy gain, thus local flame
  temperature in curved region is higher, thus
  reaction rate increases drastically, local
  burning velocity increases
• Opposite behavior for oppositely curved flames

45
TIME SCALES - premixed-gas flames

• See Ronney (1998)
• Chemical time scale
• tchem ?/SL (a/SL)/SL a/SL2
• a thermal diffusivity typ. 0.2 cm2/s,
• SL laminar flame speed typ. 40 cm/s
• Conduction time scale
• tcond Tad/(dT/dt) d2/16a
• d tube or burner diameter
• Radiation time scale
• trad Tad/(dT/dt) Tad/(L/rCp)
• Optically thin radiation L 4sap(Tad4 T84)
• ap Planck mean absorption coefficient typ. 2
  m-1 at 1 atm
• L 106 W/m3 for HC-air combustion products
• trad P/sap(Tad4 T84) P0, P pressure
• Buoyant transport time scale
• t d/V V (gd(Dr/r))1/2 (gd)1/2
• (g gravity, d characteristic dimension)
• Inviscid tinv d/(gd)1/2 (d/g)1/2 (1/tinv
  Sinv)
• Viscous d n/V Þ tvis (n/g2)1/3 (n
  viscosity typ. 0.2 cm2/s)

46
Time scales (hydrocarbon-air, 1 atm)

• Conclusions
• Buoyancy unimportant for near-stoichiometric
  flames
• (tinv tvis gtgt tchem)
• Buoyancy strongly influences near-limit flames at
  1g
• (tinv tvis lt tchem)
• Radiation effects unimportant at 1g (tvis ltlt
  trad tinv ltlt trad)
• Radiation effects dominate flames with low SL
• (trad tchem), but only observable at µg
• Small trad (a few seconds) - drop towers useful
• Radiation gt conduction only for d gt 3 cm
• Re Vd/n (gd3/n2)1/2 Þ turbulent flow at 1g
  for d gt 10 cm

47
Flammability limits due to losses

• Golden rule at limit
• Why 1/b not 1? T can only drop by O(1/b) before
  extinction - O(1) drop in T means exponentially
  large drop in ?, thus exponentially small SL.
  Could also say heat generation occurs only in ?/b
  region whereas loss occurs over ? region

48
Flammability limits due to losses

• Heat loss to walls
• tchem tcond ? SL,lim (8?)1/2a/d at limit
• or Pelim ? SL,limd/a (8?)1/2 9
• Actually Pelim 40 due to temperature averaging
  - consistent with experiments (Jarosinsky, 1983)
• Upward propagation in tube
• Rise speed at limit 0.3(gd)1/2 due to buoyancy
  alone (same as air bubble rising in water-filled
  tube (Levy, 1965))
• Pelim 0.3 Grd1/2 Grd Grashof number ?
  gd3/n2
• Causes stretch extinction (Buckmaster
  Mikolaitis, 1982)
• tchem tinv or 1/tchem Sinv
• Note f(Le) lt 1 for Le lt 1, f(Le) lt 1 for Le lt 1
  - flame can survive at lower SL (weaker mixtures)
  when Le lt 1

49
Difference between S and SL

• long flame skirt at high Gr or with small f (low
  Lewis number, Le)
• (but note SL not really constant over flame
  surface!)

50
Flammability limits due to losses

• Downward propagation sinking layer of cooling
  gases near wall outruns suffocates flame
  (Jarosinsky et al., 1982)
• tchem tvis Þ SL,lim 1.3(ga)1/3
• Pelim 1.65 Grd1/3
• Can also obtain this result by equating SL to
  sink rate of thermal boundary layer 0.8(gx)1/2
  for x ?
• Consistent with experiments varying d and a (by
  varying diluent gas and pressure) (Wang Ronney,
  1993) and g (using centrifuge) (Krivulin et al.,
  1981)
• More on limits in tubes

51
Flammability limits in vertical tubes

• Upward propagation Downward
  propagation

52
Flammability limits in tubes

• Upward propagation - Wang Ronney, 1993

53
Flammability limits in tubes

• Downward propagation - Wang Ronney, 1993

54
Flammability limits losses - continued

• Big tube, no gravity what causes limits?
• Radiation heat loss (trad tchem) (Joulin
  Clavin, 1976 Buckmaster, 1976)
• What if not at limit? Heat loss still decreases
  SL, actually 2 possible speeds for any value of
  heat loss, but lower one generally unstable

55
Flammability limits losses - continued

• Doesnt radiative loss decrease for weaker
  mixtures, since temperature is lower? NO!
• Predicted SL,lim (typically 2 cm/s) consistent
  with µg experiments (Ronney, 1988 Abbud-Madrid
  Ronney, 1990)

56
Reabsorption effects

• Is radiation always a loss mechanism?
• Reabsorption may be important when aP-1 lt d
• Small concentration of blackbody particles -
  decreases SL (more radiative loss)
• More particles - reabsorption extend limits,
  increases SL

Abbud-Madrid Ronney (1993)
57
Reabsorption effects on premixed flames

• Gases much more complicated because absorption
  coefficient depends strongly on wavelength and
  temperature some radiation always escapes (Ju,
  Masuya, Ronney 1998)
• Absorption spectra of products different from
  reactants
• Spectra broader at high T than low T
• Dramatic difference in SL limits compared to
  optically thin

58
Stretched flames - spherical

• Spherical expanding flames, Le lt 1 stretch
  allows flames to exist in mixtures below
  radiative limit until flame radius rf is too
  large curvature benefit too weak (Ronney
  Sivashinsky, 1989)
• Adds stretch term (2S/R) (R scaled flame
  radius R gt 0 for Le lt 1 R lt 0 for Le gt 1) and
  unsteady term (dS/dR) to planar steady equation
• Dual limit radiation at large rf,
  curvature-induced stretch at small rf (ignition
  limit)

59
Stretched flames - spherical

• Theory (Ronney Sivashinsky, 1989)
• Experiment
• (Ronney, 1985)

60
Stretched counterflow or stagnation flames

• Mass momentum conservation, 2D, const. density
  (?)
• (ux, uy velocity components in x, y
  directions)
• admit an exact, steady (?/?t 0) solution which
  is the same with or without viscosity (!!!)
• ? rate of strain (units s-1)
• Similar result in 2D axisymmetric geometry
• Very simple flow characterized by a single
  parameter ?, easily implemented experimentally
  using counter-flowing round jets

61
Stretched counterflow or stagnation flames

• S duz/dz flame located where uz SL
• Increased stretch pushes flame closer to
  stagnation plane - decreased volume of radiant
  products
• Similar Le effects as curved flames

62
Premixed-gas flames - stretched flames

• Stretched flames with radiation (Ju et al.,
  1999) dual limits, flammability extension even
  for Le gt1, multiple solutions (which ones are
  stable?)

63
Premixed-gas flames - stretched flames

• Dual limits Le effects seen in µg experiments,
  but evidence for multivalued behavior
  inconclusive
• Guo et al. (1997)

64
Chemical fire suppressants

• Key to suppression is removal of H atoms
• H HBr ? H2 Br
• H Br2 ? HBr Br
• Br Br M ? Br2 M
• --------------------------------
• H H ? H2
• Why Br and not Cl or F? HCl and HF too stable,
  1st reaction too slow
• HBr is a corrosive liquid, not convenient - use
  CF3Br (Halon 1301) - Br easily removed, remaining
  CF3 very stable, high CP to soak up heat
• Problem - CF3Br very powerful ozone depleter -
  banned!
• Alternatives not very good best ozone-friendly
  chemical alternative is probably CF3CH2CF3 or
  CF3H
• Other alternatives (e.g. water mist) also being
  considered

65
Chemical fire suppressants
66
References

• Abbud-Madrid, A., Ronney, P. D., "Effects of
  Radiative and Diffusive Transport Processes on
  Premixed Flames Near Flammability Limits," Twenty
  Third Symposium (International) on Combustion,
  Combustion Institute, 1990, pp. 423-431.
• Abbud-Madrid, A., Ronney, P. D., "Premixed Flame
  Propagation in an Optically-Thick Gas," AIAA
  Journal, Vol. 31, pp. 2179-2181 (1993).
• Buckmaster, J. D. (1976). The quenching of
  deflagration waves, Combust. Flame 26, 151 -162.
• Buckmaster, J. D., Mikolaitis, D. (1982b). The
  premixed flame in a counterflow, Combust. Flame
  47, 191-204 .
• Giovangigli, V. and Smooke, M. (1992).
  Application of Continuation Methods to Plane
  Premixed Laminar Flames, Combust. Sci. Tech. 87,
  241-256.
• Guo, H., Ju, Y., Maruta, K., Niioka, T., Liu,
  F., Combust. Flame 109639-646 (1997).
• Jarosinsky, J. (1983). Flame quenching by a cold
  wall, Combust. Flame 50, 167.
• Jarosinsky, J., Strehlow, R. A., Azarbarzin, A.
  (1982). The mechanisms of lean limit
  extinguishment of an upward and downward
  propagating flame in a standard flammability
  tube, Proc. Combust. Inst. 19, 1549-1557.
• Joulin, G., Clavin, P. (1976). Analyse
  asymptotique des conditions dextinction des
  flammes laminaries, Acta Astronautica 3, 223.
• Ju, Y., Masuya, G. and Ronney, P. D., Effects of
  Radiative Emission and Absorption on the
  Propagation and Extinction of Premixed Gas
  Flames Twenty-Seventh International Symposium on
  Combustion, Combustion Institute, Pittsburgh,
  1998, pp. 2619-2626.
• Ju, Y., Guo, H., Liu, F., Maruta, K. (1999).
  Effects of the Lewis number and radiative heat
  loss on the bifurcation of extinction of
  CH4-O2-N2-He flames, J. Fluid Mech. 379, 165-190.
• Krivulin, V. N., Kudryavtsev, E. A., Baratov, A.
  N., Badalyan, A. M., Babkin, V. S. (1981).
  Effect of acceleration on the limits of
  propagation of homogeneous gas mixtures, Combust.
  Expl. Shock Waves (Engl. Transl.) 17, 37-41.

67
References

• Lakshmisha, K. N., Paul, P. J., Mukunda, H. S.
  (1990). On the flammability limit and heat loss
  in flames with detailed chemistry, Proc. Combust.
  Inst. 23, 433-440.
• Levy, A. (1965). An optical study of
  flammability limits, Proc. Roy. Soc. (London)
  A283, 134.
• Ronney, P.D., "Effect of Gravity on Laminar
  Premixed Gas Combustion II Ignition and
  Extinction Phenomena," Combustion and Flame, Vol.
  62, pp. 120-132 (1985).
• Ronney, P.D., "On the Mechanisms of Flame
  Propagation Limits and Extinction Processes at
  Microgravity," Twenty Second Symposium
  (International) on Combustion, Combustion
  Institute, 1988, pp. 1615-1623. Ronney, P. D.,
  Understanding Combustion Processes Through
  Microgravity Research, Twenty-Seventh
  International Symposium on Combustion, Combustion
  Institute, Pittsburgh, 1998, pp. 2485-2506
• Ronney, P.D., Sivashinsky, G.I., "A Theoretical
  Study of Propagation and Extinction of Nonsteady
  Spherical Flame Fronts," SIAM Journal on Applied
  Mathematics, Vol. 49, pp. 1029-1046 (1989).
• Wang, Q., Ronney, P. D. (1993). Mechanisms of
  flame propagation limits in vertical tubes, Paper
  no. 45, Spring Technical Meeting, Combustion
  Institute, Eastern/Central States Section, March
  15-17, 1993, New Orleans, LA.

68
Advanced fundamental topics

• End of flammability limits notes - sidebar topics
  from here on

69
Effects of radiative emission and absorption on
the propagation and extinction of premixed gas
flames

• Yiguang Ju and Goro Masuya
• Department of Aeronautics Space Engineering
• Tohoku University, Aoba-ku, Sendai 980, Japan
• Paul D. Ronney
• Department of Aerospace Mechanical Engineering
• University of Southern California
• Los Angeles, CA 90089-1453
• Published in Proceedings of the Combustion
  Institute, Vol. 27, pp. 2619-2626 (1998)

70
Background

• Microgravity experiments show importance of
  radiative loss on flammability extinction
  limits when flame stretch, conductive loss,
  buoyant convection eliminated experiments
  consistent with theoretical predictions of
• Burning velocity at limit (SL,lim)
• Flame temperature at limit
• Loss rates in burned gases
• but is radiation a fundamental extinction
  mechanism? Reabsorption expected in large,
  "optically thick systems
• Theory (Joulin Deshaies, 1986) experiment
  (Abbud-Madrid Ronney, 1993) with
  emitting/absorbing blackbody particles
• Net heat losses decrease (theoretically to
  zero)
• Burning velocities (SL) increase
• Flammability limits widen (theoretically no
  limit)
• but gases, unlike solid particles, emit
  absorb only in narrow spectral bands - what will
  happen?

71
Background (continued)

• Objectives
• Model premixed-gas flames computationally with
  detailed radiative emission-absorption effects
• Compare results to experiments theoretical
  predictions
• Practical applications
• Combustion at high pressures and in large
  furnaces
• IC engines 40 atm - Planck mean absorption
  length (LP) 4 cm for combustion products
  cylinder size
• Atmospheric-pressure furnaces - LP 1.6 m -
  comparable to boiler dimensions
• Exhaust-gas or flue-gas recirculation - absorbing
  CO2 H2O present in unburned mixture - reduces
  LP of reactants increases reabsorption effects

72
Numerical model

• Steady planar 1D energy species conservation
  equations
• CHEMKIN with pseudo-arclength continuation
• 18-species, 58-step CH4 oxidation mechanism (Kee
  et al.)
• Boundary conditions
• Upstream - T 300K, fresh mixture composition,
  inflow velocity SL at x L1 -30 cm
• Downstream - zero gradients of temperature
  composition at x L2 400 cm
• Radiation model
• CO2, H2O and CO
• Wavenumbers (w) 150 - 9300 cm-1, 25 cm-1
  resolution
• Statistical Narrow-Band model with
  exponential-tailed inverse line strength
  distribution
• S6 discrete ordinates Gaussian quadrature
• 300K black walls at upstream downstream
  boundaries
• Mixtures CH4 0.21O2(0.79-g)N2 g CO2 -
  substitute CO2 for N2 in air to assess effect
  of absorbing ambient

73
Results - flame structure

• Adiabatic flame (no radiation)
• The usual behavior
• Optically-thin
• Volumetric loss always positive
• Maximum T lt adiabatic
• T decreases rapidly in burned gases
• Small preheat convection-diffusion zone -
  similar to adiabatic flame
• With reabsorption
• Volumetric loss negative in reactants - indicates
  net heat transfer from products to reactants via
  reabsorption
• Maximum T gt adiabatic due to radiative preheating
  - analogous to Weinbergs Swiss roll burner
  with heat recirculation
• T decreases slowly in burned gases - heat loss
  reduced
• Small preheat convection-diffusion zone PLUS
• Huge convection-radiation preheat zone

74
Flame structures

• Flame zone detail Radiation zones
  (large scale)
• Mixture CH4 in air, 1 atm, equivalence ratio
  (f) 0.70 g 0.30 (air 0.21 O2 .49 N2
  .30 CO2)

75
Radiation effects on burning velocity (SL)

• CH4-air (g 0)
• Minor differences between reabsorption
  optically-thin
• ... but SL,lim 25 lower with reabsorption since
  SL,lim (radiative loss)1/2, if net loss halved,
  then SL,lim should be 1 - 1/v2 29 lower with
  reabsorption
• SL,lim/SL,ad 0.6 for both optically-thin and
  reabsorption models - close to theoretical
  prediction (e-1/2)
• Interpretation reabsorption eliminates
  downstream heat loss, no effect on upstream loss
  (no absorbers upstream) classical quenching
  mechanism still applies
• g 0.30 (38 of N2 replaced by CO2)
• Massive effect of reabsorption
• SL much higher with reabsorption than with no
  radiation!
• Lean limit much leaner (f 0.44) than with
  optically-thin radiation (f 0.68)

76
Comparisons of burning velocities

• g 0 (no CO2 in ambient) g 0.30
• Note that without CO2 (left) SL peak
  temperatures of reabsorbing flames are slightly
  lower than non-radiating flames, but with CO2
  (right), SL T are much higher with
  reabsorption. Optically thin always has lowest
  SL T, with or without CO2
• Note also that all experiments lie below
  predictions - are published chemical mechanisms
  accurate for very lean mixtures?

77
Mechanisms of extinction limits

• Why do limits exist even when reabsorption
  effects are considered and the ambient mixture
  includes absorbers?
• Spectra of product H2O different from CO2
  (Mechanism I)
• Spectra broader at high T than low T (Mechanism
  II)
• Radiation reaches upstream boundary due to gaps
  in spectra - product radiation that cannot be
  absorbed upstream

Absorption spectra of CO2 H2O at 300K 1300K
78
Mechanisms of limits (continued)

• Flux at upstream boundary shows spectral regions
  where radiation can escape due to Mechanisms I
  and II - gaps due to mismatch between radiation
  emitted at the flame front and that which can be
  absorbed by the reactants
• Depends on discontinuity (as seen by radiation)
  in T and composition at flame front - doesnt
  apply to downstream radiation because T gradient
  is small
• Behavior cannot be predicted via simple mean
  absorption coefficients - critically dependent on
  compositional temperature dependence of spectra

Spectrally-resolved radiative flux at upstream
boundary for a reabsorbing flame (pIb maximum
possible flux)
79
Effect of domain size

• Limit f SL,lim decreases as upstream domain
  length (L1) increases - less net heat loss
• Significant reabsorption effects seen at L1 1
  cm even though LP 18.5 cm because of existence
  of spectral regions with L(w) 0.025 cm-atm (!)
• L1 gt 100 cm required for domain-independent
  results due to band wings with small L(w)
• Downstream domain length (L2) has little effect
  due to small gradients nearly complete
  downstream absorption

Effect of upstream domain length (L1) on limit
composition (?o) SL for reabsorbing flames.
With-out reabsorption, ?o 0.68, thus
reabsorption is very important even for the
smallest L1 shown
80
Effect of g (CO2 substitution level)

• f 1.0 little effect of radiation
• f 0.5 dominant effect - why?
• (1) f 0.5 close to radiative extinction
  limit - large benefit of decreased heat loss due
  to reabsorption by CO2
• (2) f 0.5 much larger Boltzman number
  (defined below) (B) (127) than f 1.0 (11.3)
  B potential for radiative preheating to
  increase SL
• Note with reabsorption, only 1 CO2 addition
  nearly doubles SL due to much lower net heat
  loss!

Effect of CO2 substitution for N2 on SL
81
Effect of g (continued)
Effect of CO2 substitution on SL,lim/SL,adiabatic
Effect of CO2 substitution on flammability limit
composition

• Limit mixture much leaner with reabsorption than
  optically thin
• Limit mixture decreases with CO2 addition even
  though CP,CO2 gt CP,N2
• SL,lim/SL,ad always e-1/2 for optically thin,
  in agreement with theory
• SL,lim/SL,ad up to 20 with reabsorption!

82
Comparison to analytic theory

• Joulin Deshaies (1986) - analytical theory
• Comparison to computation - poor
• Better without H2O radiation (mechanism (I)
  suppressed)
• Slightly better still without T broadening
  (mechanism (II) suppressed, nearly adiabatic)
• Good agreement when L(w) LP constant -
  emission absorption across entire spectrum
  rather than just certain narrow bands.
• Drastic differences between last two cases, even
  though both have no net heat loss and have same
  Planck mean absorption lengths!

Effect of different radiation models on SL and
comparison to theory
83
Comparison with experiment

• No directly comparable expts., BUT...
• Zhu, Egolfopoulos, Law (1988)
• CH4 (0.21O2 0.79 CO2) (g 0.79)
• Counterflow twin flames, extrapolated to zero
  strain
• L1 L2 0.35 cm chosen since 0.7 cm from nozzle
  to stagnation plane
• No solutions for adiabatic flame or
  optically-thin radiation (!)
• Moderate agreement with reabsorption
• Abbud-Madrid Ronney (1990)
• (CH4 4O2) CO2
• Expanding spherical flame at µg
• L1 L2 6 cm chosen ( flame radius)
• Optically-thin model over-predicts limit fuel
  conc. SL,lim
• Reabsorption model underpredicts limit fuel conc.
  but SL,lim well predicted - net loss correctly
  calculated

Comparison of computed results to experiments
where reabsorption effects may have been important
84
Conclusions

• Reabsorption increases SL extends limits, even
  in spectrally radiating gases
• Two loss mechanisms cause limits even with
  reabsorption
• (I) Mismatch between spectra of reactants
  products
• (II) Temperature broadening of spectra
• Results qualitatively sometimes quantitatively
  consistent with theory experiments
• Behavior cannot be predicted using mean
  absorption coefficients!
• Can be important in practical systems

85
Planck mean absorption coefficient

86
More on flammability limits in tubes

• Experiments show that the flammability limits are
  wider for upward than downward propagation,
  corresponding to SL,lim,down gt SL,lim,up since SL
  is lower for more dilute mixtures
• but note according to the models, SL,lim,down gt
  SL,lim,up when
• Gr lt 10,000 f12
• but also need Pe gt 40 (not in heat-loss limit)
• Gr gt 18,000
• ? at high Le (high f) 18,000 lt Gr lt 10,000
  f12, upward limits may be narrower than downward
  limits (?!?)
• Never observed, but appropriate conditions never
  tested - high Le, moderate Gr

87
Turbulent limit behavior?

• Burned gases are turbulent if Re gt 2000
• Upward limit Re S(r8/rad-1)d/n ? Gr gt 300 x
  106
• Downward limit Re SL(r8/rad-1)d/n ? Gr gt 40 x
  109 - not accessible with current apparatus
• "Standard" condition (5 cm tube, air, 1 atm)
• Gr 3.0 x 106 always laminar!

88
Approach

• Study limit mechanisms by measuring Sb,lim for
  varying
• Tube diameter
• ? ?(diluent, pressure)
• Le ? Le(diluent, fuel)
• and determine scaling relations (Pelim vs. Gr
  Le)
• Apparatus
• Tubes with 0.5 cm lt D lt 20 cm open at ignition
  end
• He, Ne, N2, CO2, SF6 diluents
• 0.1 atm lt P lt 10 atm
• 2 x 102 lt Gr lt 2 x 109
• Absorption tank to maintain constant P during
  test
• Thermocouples
• Procedure
• Fixed fuelO2 ratio
• Vary diluent conc. until limit determined
• Measure Sb,lim temperature characteristics at
  limit

89
Results - laminar flames

• Upward limit
• Low Gr
• Pelim 40 10 at low Gr
• Highest T near centerline of tube
• High Gr
• Pelim 0.3 Gr1/2 at high Gr
• Highest T near centerline (low Le)
• Highest T near wall (high Le)
• Indicates strain effects at limit
• Downward
• Pelim 40 10 at low Gr
• Pelim 1.5 Gr1/3 at high Gr
• Upward limits narrower than downward limits at
  high Le moderate Gr, e.g. lean C3H8-O2-Ne, P
  1 atm, D 2.5 cm, Le 2.6, Gr 19,000 fuel up
  / fuel down 0.83

90
Limit regimes - upward propagation
91
Limit regimes - downward propagation
92
Flamelet vs. distributed combustion

• Abdel-Gayed Bradley (1989) distributed if Ka
  gt 0.3
• Ka ? 0.157 ReT-1/2U2 ReT ? uLI/n, U ? u/SL
• LI ? integral scale of turbulence
• Estimate for pipe flow
• u' 0.05S(r8/rad-1) LI d
• SL,lim from Buckmaster Mikolaitis (1982)
  model
• ? Ka 0.0018/f2 Gr1/4 0.3/f2 at Gr 700
  x 106
• Distributed combustion probable at high Gr,
  moderate Le
• Away from limit - wrinkled, unsteady skirt

93
Limit flame - distributed combustion

• C3H8-O2-CO2, P 2.5 atm, d 10 cm, Le 1.3, Gr
  6 x 108

94
Farther from limit - wrinkled skirt

• C3H8-O2-CO2, P 2.5 atm, d 10 cm, Le 1.3, Gr
  6 x 108

95
Lower Le - boiling tip, no tip opening

• C3H8-O2-SF6, P 2.5 atm, d 10 cm, Le 0.7, Gr
  5 x 109

96
Turbulent flame quenching

• Why does distributed flame exist at ? 4d,
  whereas laminar flame extinguishes when ? 1/40
  d (Pe 40)?
• Analysis
• Nu hd/k 0.023 Re.8 Pr.3 (turbulent heat
  transfer in pipe)
• Qloss hA?T A pd? let ? n D (n is unknown)
• Qgen ?oSbpd2Cp?T Sb 0.3(gd)1/2
• Qloss/Qgen 1/b at quenching limit
• ?? n 5Gr0.1/b at quenching limit
• Gr 600 x 106, ? 10 ? n 3.9 at limit !!!
• But low Le ? SL low at tip opening ? n gt 4 at tip
  opening ? distributed flame not observable

97
Conclusions

• Probable heat loss buoyancy-induced limit
  mechanisms observed
• Limit behavior characterized mainly by Lewis
  Grashof numbers
• Scaling analyses useful for gaining insight
• Transition to turbulence distributed-like
  combustion observed
• High-Gr results may be more applicable to "real"
  hazards (large systems, turbulent) than classical
  experiments at low Gr