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Turbulent combustion Lecture 3

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Regimes of turbulent combustion (Lecture 1) Flamelet models (Lecture 1) ... flames at high Da - Burke-Schumann (infinite-rate chemistry, mixing limited) ... – PowerPoint PPT presentation

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Title: Turbulent combustion Lecture 3


1
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)

2
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

3
(No Transcript)
4
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)

5
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

6
Scaling of turbulent jets

Uo
12
x
rjet(x)
do
entrainment
7
Scaling of turbulent jets
  • Combine

8
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

9
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?

10
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
11
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

12
Edge flames - nonpremixed - theory
  • Daou et al., 2002

13
Edge flames - nonpremixed - theory
  • Daou and Linan, 1998 (lF ?(LeFuel - 1))

14
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
15
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

16
Edge flames - premixed - theory
  • Daou and Linan, 1999 - similar response of Uedge
    to stretch as nonpremixed flames - also note
    spots

17
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

18
Edge flames - nonpremixed - experiment
Propagating
Retreating
Tailless
19
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
    ?)

20
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

21
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)

22
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)

23
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)

24
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

25
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)

26
Edge flames in low Lewis number mixtures
  • Computations by Buckmaster Short (1999)

Stationary single tube
  • Moving train of tubes

27
Edge flames with low Lewis number
  • Kaiser et al., 2000
  • Twin premixed, single premixed, nonpremixed
  • H2-N2 vs. O2-N2

28
Edge flames with low Lewis number
29
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 ?)

30
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

31
Schematic of tube formation
32
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)

33
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)

34
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
35
Results - single premixed, decreasing H2
36
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 ?)
37
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

38
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
39
Results - non-premixed
40
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
41
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
42
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
43
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.

44
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.
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