Turbulent combustion Lecture 3

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Turbulent combustion (Lecture 3)

• Motivation (Lecture 1)
• Basics of turbulence (Lecture 1)
• Premixed-gas flames
• Turbulent burning velocity (Lecture 1)
• Regimes of turbulent combustion (Lecture 1)
• Flamelet models (Lecture 1)
• Non-flamelet models (Lecture 1)
• Flame quenching via turbulence (Lecture 1)
• Case study I Liquid flames (Lecture 2)
• (turbulence without thermal expansion)
• Case study II Flames in Hele-Shaw cells
  (Lecture 2)
• (thermal expansion without turbulence)
• Nonpremixed gas flames (Lecture 3)
• Edge flames (Lecture 3)

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Non-premixed flames

• Nonpremixed no inherent propagation rate (unlike
  premixed flames where propagation rate SL)
• No inherent thickness ? (unlike premixed flames
  where thickness ?/SL) - in nonpremixed flames,
  determined by equating convection time scale
  ?/U ?-1 to diffusion time scale ?2/? ? ?
  (?/?)1/2
• Have to mix first then burn
• Burning must occur near stoichiometric contour
  where reactant fluxes are in stoichiometric
  proportions (otherwise surplus of one reactant)
• Burning must occur near highest T since ?
  exp(-E/RT) is very sensitive to temperature (like
  premixed flames)
• Simplest approach mixed is burned - chemical
  reaction rates faster than mixing rates

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Nonpremixed turbulent jet flames

• Laminar Lf Uodo2/D
• Turbulent (Hottel and Hawthorne, 1949)
• D uLI u Uo LI do ? Lf do
  (independent of Re)
• High Uo ? high u ? Da small - flame lifts off
  near base (why base first?)
• Still higher Uo - more of flame lifted
• When lift-off height flame height, flame blows
  off (completely extinguished)

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Scaling of turbulent jets

• Determine scaling of mean velocity ( ), jet
  width (rjet) and mass flux through jet ( ) with
  distance from jet exit (x)
• Assume u(x) , LI(x) rjet(x)
• Note that mass flux is not constant due to
  entrainment!
• Conservation of momentum flux (Q)
• Kinetic energy flux (K) (not conserved -
  dissipated!)
• KE dissipation

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Scaling of turbulent jets

Uo
12
x
rjet(x)
do
entrainment
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Scaling of turbulent jets

• Combine

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Liftoff of turbulent jets

• Scaling suggests mean strain Redo3/2?/x2
• For fixed fuel ambient atmosphere (e.g. air),
  strain rate at flamelet extinction (?ext)
  constant
• Liftoff height (xLO) (?/?ext)1/2 Redo3/4
  uo3/4do3/4
• Experiments - closer to xLO uo1do0
• Alternative view
• Premixing at flame base causes flame to stabilize
  at point where ST (premixed, stoichiometric)
  mean velocity - more consistent

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EDGE FLAMES - motivation

• Reference Buckmaster, J., Edge flames, Prog.
  Energy Combust. Sci. 28, 435-475 (2002)
• Laminar flamelet model used to describe local
  interaction of premixed nonpremixed flames with
  turbulent flow
• Various regions of turbulent flow will be
  above/below critical extinction strain (?ext)
• Issues
• Can flame holes or edges persist?
• Will extinguishment in high-? region spread to
  other regions?
• Will burning region re-ignite extinguished
  region?
• Will ? at edge locate (?edge) be at higher or
  lower strain than extinction strain for uniform
  flame (?ext)?
• How is edge propagation rate affected by ??
• Lewis number effects?

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Edge flames

• Flame propagates from a burning region to a
  non-burning region, or retreats into the burning
  region
• Could be premixed or non-premixed

? FLOW ?
Non-premixed edge-flame in a counterflow
Kim et al., 2006
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Edge flames - nonpremixed - theory

• Daou and Linan, 1998
• Configuration as in previous slide
• No thermal expansion
• Non-dimensional stretch rate ? (??/SL2)1/2 or
  Damköhler number SL2/?? ?-2
• SL steady unstretched SL of stoichiometric
  mixture of fuel air streams
• Effects of stretch
• Low ? flame advances, triple flame structure
  - lean premixed, rich premixed trailing
  non-premixed flame branches
• Intermediate ? flame advances, but premixed
  branches weaker
• High ? flame retreats, only nonpremixed branch
  survives
• Note that stretch rate corresponding to zero edge
  speed is always less than the extinction stretch
  rate for the uniform (edgeless, infinite) flame
  sheet - edge flames always weaker than uniform
  flames - retreat in the presence of less strain
  than required to extinguish uniform flame
• Le effects as expected - lower Le yields higher
  edge speeds, broader extinction limits

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Edge flames - nonpremixed - theory

• Daou et al., 2002

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Edge flames - nonpremixed - theory

• Daou and Linan, 1998 (lF ?(LeFuel - 1))

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Edge flames - nonpremixed - theory

• Thermal expansion effect (Ruetsch et al., 1995)
  U/SL (?8/?f)1/2 with proportionality constant
  shown

(?8/?f)1/2
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Edge flames - nonpremixed - with heat loss

• Daou et al., 2002
• ? dimensionless heat loss 7.5?/Pe2 Pe ?
  SLd/? (see Cha Ronney, 2006)
• With heat loss trailing non-premixed branch
  disappears at low ? - nonpremixed flame
  extinguishes because mixing layer thickness
  (?/?)1/2 (thus volume, thus heat loss) increases
  while burning rate decreases

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Edge flames - premixed - theory

• Daou and Linan, 1999 - similar response of Uedge
  to stretch as nonpremixed flames - also note
  spots

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Experiments - nonpremixed edge-flames

• Cha Ronney (2006)
• Use parallel slots, not misaligned slots
• Use jet of N2 to erase flame, then remove jet
  to watch advancing edge, or establish flame, then
  zap with N2 jet to obtain retreating flame

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Edge flames - nonpremixed - experiment
Propagating
Retreating
Tailless
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Edge flames - nonpremixed - experiment

• Behavior very similar to model predictions with
  heat loss - negative at low or high ?, positive
  at intermediate ? with Uedge/SL 0.7(?8/?f)1/2
  (prediction 1.8)
• Propagation rates same for different gaps when
  scaled by strain rate ? except at low ? (thus low
  Vjet) where smaller gap ? more heat loss (higher
  ?)

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Edge flames - nonpremixed - experiment

• Dimensional Uedge vs. stretch (?) can be mapped
  into scaled Uedge vs. scaled stretch rate (?) for
  varying mixtures
• Little effect of mixture strength when results
  scaled by ?, except at low ?, where weaker
  mixture ? lower SL ? higher ?
• Dimensional Dimensionless

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Edge flames - nonpremixed - experiment

• High stretch (?) or heat loss (?) causes
  extinction - experiments surprising consistent
  with experiments, even quantitatively
• Very difficult to see tailless flames in
  experiments
• Model assumes volumetric heat loss (e.g.
  radiation) - mixing layer thickness can increase
  indefinitely, get weak non-premixed branch that
  can extinguish when premixed branches do not
• Experiment - heat loss mainly due to conduction
  to jet exits, mixing layer thickness limited by
  jet spacing
• Experiment (Cha Ronney, 2006)
  Prediction (Daou et al., 2002)

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Edge flames - nonpremixed - experiment

• Lewis number effects VERY pronounced - at low Le,
  MUCH higher Uedge than mixture with same SL (thus
  ?) with Le 1
• Opposite trend for Le gt 1
• Low Le (CH4-O2-CO2) High Le (C3H8-O2-N2)
• (Lefuel 0.74 LeO2 0.86) (Lefuel 1.86
  LeO2 1.05)

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Edge flames - nonpremixed - experiment

• Zst stoichiometric mixture fraction
  fraction of fuel inert in a stoichiometric
  mixture of (fuelinert) (O2inert) (1 gt Zst gt
  0)
• High Zst flame sits near fuel side low Zst
  flame sits near O2 side
• but results not at all symmetric with respect to
  Zst 0.5!
• Due to shift in O2 concentration profile as Zst
  increases to coincide more closely with location
  of peak T, increases radical production (Chen
  Axelbaum, 2005) (not symmetrical because most
  radicals on fuel side, not O2 side)

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Edge flames - nonpremixed - experiment

• Heat loss limit (low ?, thus low strain) -
  relationship between ? and ? independent of
  mixture strength, gap, Le, Zst, etc.
• Recall high ? (high strain) limit depends
  strongly on Le but almost independent of ? (page
  21)
• Suggests relatively simple picture of
  non-premixed edge flames

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Edge flames in low Le mixtures

• Diffusive-thermal instability for Lewis number ltgt
  1
• High Le - imaginary growth rates - pulsating,
  travelling waves
• Low Le - real growth rates with maximum value at
  finite wave number - cellular flames
• Low-Le instability well known for premixed flames
• Encouraged by heat losses (Joulin Clavin,
  1979), but near extinction conditions (high ? or
  low Da) not required
• Discouraged by stretch (Sivashinsky et al., 1981)
• Computations (Buckmaster Short 1999 Daou
  Liñán 1999) (premixed)
• Le ltlt 1 Instabilities not suppressed (or
  reappear) at high ?
• Sequence of behavior as ? increased wrinkled
  continuous flames, travelling flame tubes,
  isolated tubes
• Analogous to flame balls - curvature/stretch
  induced enhancement of flame temperature at low
  Le
• Similar for nonpremixed flames (Thatcher Dold,
  2000)

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Edge flames in low Lewis number mixtures

• Computations by Buckmaster Short (1999)

Stationary single tube

• Moving train of tubes

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Edge flames with low Lewis number

• Kaiser et al., 2000
• Twin premixed, single premixed, nonpremixed
• H2-N2 vs. O2-N2

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Edge flames with low Lewis number
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Results - twin premixed - high Da

• Nearly flat (low ?) or moderately wrinkled
  (higher ?) flames

• Moderately wrinkled flame
• 8.10H2, ? 120 s-1 (high Da, high ?)

• Nearly flat flame 8.77H2
• ? 45 s-1 (high Da, low ?)

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Results - twin premixed - lower Da

• Moving tubes emanating from center
• Still lower Da - stationary multiple tubes

• Moving tubes

• Stationary multiple tubes
• 6.96H2, ? 60 s-1

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Schematic of tube formation
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Results - twin premixed - very near limit

• Very low Da - stationary single or twin tubes
• High s - near wall - lower ? - slightly farther
  from limit
• Low s - near center - higher ? - slightly farther
  from limit

Stationary twin tube near center (low ?)
(6.68H2, ? 60 s-1)
Stationary single tube near center (low ?)
(6.64H2, ? 60 s-1)

• Stationary single tube near wall (high ?)
  (6.11H2, ? 100 s-1)

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Results - twin premixed - orthogonal view

• Verifies tube-like character of flames
• Upward curvature due to buoyancy much weaker than
  flame tube curvature

Single tube standard view (6.64H2, ? 60 s-1)

• Single tube orthogonal view
• (6.50H2, ? 100 s-1)

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Results - twin premixed - turbulence

• High s - sudden transition to turbulent flow
• Occurs for all flame structures
• Rejet Vw/n 600 (w jet width), ? 140 s-1
• Re at transition independent of gap (d)
• Similar results found for inert counterflowing
  jets
• Slightly lower Re for single premixed
  nonpremixed ( 500)
• Prevents examination of lower Da via higher ?

6.9H2, ? 158 s-1
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Results - single premixed, decreasing H2
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Results - single premixed

• High Da - attached flames (low ?) or partially
  attached V-flames (lower ?)
• Apparent lower second flame due to shear layer
  between hot burned gas cold unburned stream -
  not a flame - same with air or N2

• Fuel/air side

• Fuel/air side

• Inert side

• Inert side

Attached flame (high Da, low ?)
Partially attached V-flame (high Da, high ?)
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Results - single premixed

• Lower Da - bridging tubes
• Still lower Da - moving tubes

• Fuel/air side

• Fuel/air side

• Inert side

• Inert side

• Bridging tubes

• Moving tubes

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Results - single premixed

• Very low Da - flat single flames (!) attached to
  nozzle exit
• Considerable hysteresis - behavior different for
  increasing vs. decreasing fuel conc.

• Fuel/air side

• Fuel/air side

• Inert side

• Inert side

• Transition from moving tubes to flat flame -
  standard view

Flat flame(s) - orthogonal view
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Results - non-premixed
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Results - non-premixed

• Flat flames at high Da - Burke-Schumann
  (infinite-rate chemistry, mixing limited)
  solution unconditionally stable
• but why is there an apparent second flame???

• Fuel/N2 side

• Fuel/N2 side

• Air side

• Air side

• Normal view

Orthogonal view
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Results - non-premixed

• Moving tubes at lower Da - similar to premixed
  flames
• How can non-premixed flames exhibit premixed
  flame instabilities? Near extinction, fuel or O2
  leaksthrough flame front, causing partial
  premixing of fuel and O2, creating
  quasi-premixed-flame behavior

• Fuel/N2 side

• Fuel/N2 side

• Air side

• Air side

• Normal view

Orthogonal view
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Results - non-premixed

• Stationary multiple or single tubes at still
  lower Da

• Fuel/N2 side

• Fuel/N2 side

• Air side

• Air side

3 tubes
1 tube
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References

• Buckmaster, J. D., Combust. Sci. Tech. 115, 41
  (1996).
• Buckmaster, J., Edge flames, Prog. Energy
  Combust. Sci. 28, 435-475 (2002).
• Buckmaster, J. D. and Short, M. (1999). Cellular
  instabilities, sub-limit structures and
  edge-flames in premixed counterflows. Combust.
  Theory Modelling 3, 199-214.
• M. S. Cha and S. H. Chung (1996).
  Characteristics of lifted flames in nonpremixed
  turbulent confined jets. Proc. Combust. Inst.
  26, 121128
• M. S. Cha and P. D. Ronney, Propagation rates of
  non-premixed edge-flames, Combustion and Flame,
  Vol. 146, pp. 312 - 328 (2006).
• R. Chen, R. L. Axelbaum, Combust. Flame 142
  (2005) 6271.
• R. Daou, J. Daou, J. Dold (2002). Effect of
  volumetric heat-loss on triple flame propagation
  Proc. Combust. Inst., Vol. 29, pp. 1559 - 1564.
• J. Daou, A Liñán (1998). The role of unequal
  diffusivities in ignition and extinction fronts
  in strained mixing layers, Combust. Theory
  Modelling 2, 449477
• J. Daou and A. Liñán (1999). Ignition and
  extinction fronts in counterflowing premixed
  reactive gases, Combust. Flame. 118, 479-488.
• Hottel, H. C., Hawthorne, W. R., Third Symposium
  (International) on Combustion, Combustion
  Institute, Pittsburgh, Williams and Wilkins,
  Baltimore, 1949, pp. 254-266.
• Joulin, G. and Clavin, P. (1979). Linear
  stability analysis of nonadiabatic flames
  diffusional-thermal model. Combust. Flame 35,
  139.
• Kaiser, C., Liu, J.-B. and Ronney, P. D.,
  Diffusive-thermal Instability of Counterflow
  Flames at Low Lewis Number, Paper No. 2000-0576,
  38th AIAA Aerospace Sciences Meeting, Reno, NV,
  January 11-14, 2000.
• N. I. Kim, J. I. Seo, Y. T. Guahk and H. D. Shin
  (2006). The propagation of tribrachial flames
  in a confined channel, Combustion and Flame,
  Vol. 146, pp. 168 - 179.

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References

• Liu, J.-B. and Ronney, P. D., Premixed
  Edge-Flames in Spatially Varying Straining
  Flows, Combustion Science and Technology, Vol.
  144, pp. 21-46 (1999).
• Ruetsch, G. R., Vervisch, L. and Linan, A.
  (1995). Effects of heat release on triple flames.
  Physics of Fluids 7, 1447.
• Shay, M. L. and Ronney, P. D., "Nonpremixed
  Flames in Spatially-Varying Straining Flows,"
  Combustion and Flame, Vol. 112, pp. 171-180
  (1998).
• Sivashinsky, G. I., Law, C. K. and Joulin, G.
  (1982). On stability of premixed flames in
  stagnation-point flow. Combustion Science and
  Technology 28, 155-159.
• R. W. Thatcher and J. W. Dold (2000). Edges of
  flames that do not exist flame-edge dynamics in
  a non-premixed counterflow. Combust. Theory
  Modelling 4, 435-457.
• Vedarajan, T. G., Buckmaster, J. D. and Ronney,
  P. D., Two-dimensional Failure Waves and
  Ignition Fronts in Premixed Combustion,
  Twenty-Seventh International Symposium on
  Combustion, Combustion Institute, Pittsburgh,
  1998, pp. 537-544.