Premixed flame propagation in Hele-Shaw cells: What Darrieus - PowerPoint PPT Presentation

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Premixed flame propagation in Hele-Shaw cells: What Darrieus

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Title: Premixed flame propagation in Hele-Shaw cells: What Darrieus


1
Premixed flame propagation in Hele-Shaw cells
What Darrieus Landau didnt tell you
  • http//ronney.usc.edu/research
  • Paul D. Ronney
  • Dept. of Aerospace Mechanical Engineering
  • University of Southern California
  • Los Angeles, CA 90089-1453 USA
  • National Tsing-Hua University
  • October 7, 2005

2
University of Southern California
  • Established 125 years ago this week!
  • jointly by a Catholic, a Protestant and a Jew -
    USC has always been a multi-ethnic,
    multi-cultural, coeducational university
  • Today 32,000 students, 3000 faculty
  • 2 main campuses University Park and Health
    Sciences
  • USC Trojans football team ranked 1 in USA last 2
    years

3
USC Viterbi School of Engineering
  • Naming gift by Andrew Erma Viterbi
  • Andrew Viterbi co-founder of Qualcomm,
    co-inventor of CDMA
  • 1900 undergraduates, 3300 graduate students, 165
    faculty, 30 degree options
  • 135 million external research funding
  • Distance Education Network (DEN) 900 students in
    28 M.S. degree programs 171 MS degrees awarded
    in 2005
  • More info http//viterbi.usc.edu

4
Paul Ronney
  • B.S. Mechanical Engineering, UC Berkeley
  • M.S. Aeronautics, Caltech
  • Ph.D. in Aeronautics Astronautics, MIT
  • Postdocs NASA Glenn, Cleveland US Naval
    Research Lab, Washington DC
  • Assistant Professor, Princeton University
  • Associate/Full Professor, USC
  • Research interests
  • Microscale combustion and power generation
  • (10/4, INER 10/5 NCKU)
  • Microgravity combustion and fluid mechanics
    (10/4, NCU)
  • Turbulent combustion (10/7, NTHU)
  • Internal combustion engines
  • Ignition, flammability, extinction limits of
    flames (10/3, NCU)
  • Flame spread over solid fuel beds
  • Biophysics and biofilms (10/6, NCKU)

5
Paul Ronney
6
Introduction
  • Models of premixed turbulent combustion dont
    agree with experiments nor each other!

7
Introduction - continued...
  • whereas in liquid flame experiments, ST/SL in
    4 different flows is consistent with Yakhots
    model with no adjustable parameters

8
Motivation (continued)
  • Why are gaseous flames harder to model compare
    (successfully) to experiments?
  • One reason self-generated wrinkling due to flame
    instabilities
  • Thermal expansion (Darrieus-Landau, DL)
  • Rayleigh-Taylor (buoyancy-driven, RT)
  • Viscous fingering (Saffman-Taylor, ST) in
    Hele-Shaw cells when viscous fluid displaced by
    less viscous fluid
  • Diffusive-thermal (DT) (Lewis number)
  • Needed simple apparatus for systematic study of
    DL, RT, ST DT instabilities their effects on
    burning rates

9
Hele-Shaw flow
  • Flow between closely-spaced parallel plates
  • Momentum eqn. reduces to linear 2-D equation
    (Darcys law)
  • 1000's of references
  • Practical application to combustion flame
    propagation in cylinder crevice volumes

10
Joulin-Sivashinsky (CST, 1994) model
  • Linear stability analysis of flame propagation in
    HS cells
  • Uses Euler-Darcy momentum eqn.
  • Combined effects of DL, ST, RT heat loss (but
    no DT effect - no damping at small l)
  • Dispersion relation effects of thermal expansion
    (?), viscosity change across front (F) buoyancy
    (G) on relationship between scaled wavelength (?)
    and scaled growth rate (?)
  • Characteristic wavelength for ST
    (?/6)(?uUw2/?av) smaller scales dominated by DL
    (no characteristic wavelength)

11
Objectives
  • Measure
  • Propagation rates
  • Wrinkling characteristics
  • of premixed flames in Hele-Shaw cells
  • as a function of
  • Mixture strength (thus SL) (but density ratio (?)
    viscosity change (fb - fu) dont vary much over
    experimentally accessible range of mixtures)
  • Cell thickness (w)
  • Propagation direction (upward, downward,
    horizontal)
  • Lewis number (vary fuel inert type)
  • and compare to JS model predictions

12
Apparatus
  • Aluminum frame sandwiched between Lexan windows
  • 40 cm x 60 cm x 1.27 or 0.635 or 0.32 cm test
    section
  • CH4 C3H8 fuel, N2 CO2 diluent - affects Le,
    Peclet
  • Upward, horizontal, downward orientation
  • Spark ignition (3 locations, plane initiation)
  • Exhaust open to ambient pressure at ignition end
    - flame propagates towards closed end of cell

13
Results - video - baseline case
  • 6.8 CH4-air, horizontal, 12.7 mm cell

14
Results - video - upward propagation
  • 6.8 CH4-air, upward, 12.7 mm cell

15
Results - video - downward propagation
16
Results - video - high Lewis number
  • 3.0 C3H8-air, horizontal, 12.7 mm cell (Le 1.7)

17
Results - video - low Lewis number
  • 8.6 CH4 - 32.0 O2 - 60.0 CO2, horizontal, 12.7
    mm cell (Le 0.7)

18
Results - stoichiometric, baseline thickness
19
Results - stoichiometric, thinner cell
20
Results - stoichiometric, very thin cell
21
Broken flames at very low Pe, Le lt 1
  • 6.0 CH4- air, downward, 6.3 mm cell (Pe 30(!))

22
Results - qualitative
  • Orientation effects
  • Horizontal propagation - large wavelength wrinkle
    fills cell
  • Upward propagation - more pronounced large
    wrinkle
  • Downward propagation - globally flat front
    (buoyancy suppresses large-scale wrinkles)
    oscillatory modes, transverse waves
  • Thinner cell transition to single large tulip
    finger
  • Consistent with Joulin-Sivashinsky predictions
  • Large-scale wrinkling observed even at high Le
  • Broken flames observed near limits for low Le but
    only rarely not repeatable
  • For practical range of conditions, buoyancy
    diffusive-thermal effects cannot prevent
    wrinkling due to viscous fingering and/or thermal
    expansion
  • Evidence of preferred wavelengths, but selection
    mechanism unclear

23
Lewis number effects
3.0 C3H8 - 97.0 air Horizontal propagation 12.7
mm cell, Pe 166
8.6 CH4 - 34.4 O2 - 57.0 CO2 Horizontal
propagation 12.7 mm cell, Pe 85
6.8 CH4 - 93.2 air Horizontal propagation 12.7
mm cell, Pe 100
24
Results - propagation rates
  • 3-stage propagation
  • Thermal expansion - most rapid, propagation rate
    (?u/?b)SL
  • Quasi-steady (slower but still gt SL)
  • Near-end-wall - slowest - large-scale wrinkling
    suppressed

25
Results - quasi-steady propagation rates
  • Horizontal, CH4-air (Le 1)
  • Quasi-steady propagation rate (ST) always larger
    than SL - typically ST 3SL even though u/SL
    0!
  • Independent of Pe SLw/? ? independent of heat
    loss
  • Slightly higher ST/SL for thinner cell despite
    lower Pe (greater heat loss) (for reasons to be
    discussed later)

26
Results - quasi-steady propagation rates
  • Horizontal, C3H8-air
  • Very different trend from CH4-air - ST/SL depends
    significantly on Pe cell thickness (why? see
    next slide)
  • STILL slightly higher ST/SL for thinner cell
    despite lower Pe (greater heat loss)

27
Results - quasi-steady propagation rates
  • C3H8-air (lean) Le 1.7, lower ST/SL
  • C3H8-air (rich) Le 0.9, higher ST/SL ( 3),
    independent of Pe, similar to CH4-air

28
Results - quasi-steady propagation rates
  • Horizontal, CH4-O2-CO2 (Le 0.7)
  • Similar to CH4-air, no effect of Pe
  • Slightly higher average ST/SL 3.5 vs. 3.0,
    narrow cell again slightly higher

29
Results - quasi-steady propagation rates
  • Upward, CH4-air (Le 1)
  • Higher ST/SL for thicker cell - more buoyancy
    effect, increases large-scale wrinkling - no
    effect of orientation for 1/8 cell
  • More prevalent at low Pe (low SL) - back to ST/SL
    3 for high Pe

30
Results - quasi-steady propagation rates
  • Downward, CH4-air (Le 1)
  • Higher ST/SL for thinner cell - less buoyancy
    effect - almost no effect for 1/8 cell
  • More prevalent at low Pe (low SL) - back to ST/SL
    3 for high Pe
  • How to correlate ST/SL for varying orientation,
    SL, w ???

31
Results - quasi-steady propagation rates
  • Upward, CH4-O2-CO2 (Le 0.7)
  • Higher ST/SL for thicker cell - more buoyancy
    effect, increases large-scale wrinkling - less
    effect of orientation for 1/8 cell
  • More prevalent at low Pe (low SL) - back to ST/SL
    4 for high Pe

32
Results - pressure characteristics
  • Initial pressure rise after ignition
  • Pressure constant during quasi-steady phase
  • Pressure rise higher for faster flames
  • Slow flame Fast flame

33
Scaling analysis
  • How to estimate driving force for flame
    wrinkling?
  • Hypothesis use linear growth rate (?) of
    Joulin-Sivashinsky analysis divided by wavenumber
    (k) (i.e. phase velocity ?/k) scaled by SL as a
    dimensionless growth rate
  • Analogous to a turbulence intensity)
  • Use largest value of growth rate, corresponding
    to longest half-wavelength mode that fits in
    cell, i.e., k (2?/L)/2
  • (L width of cell 39.7 cm)
  • Small L, i.e. L lt ST length (?/6)(?uUw2/?av)
  • DL dominates - ?/k constant
  • Propagation rate should be independent of L
  • Large L, i.e. L gt (?/6)(?uUw2/?av)
  • ST dominates - ?/k increases with L
  • Propagation rate should increase with L
  • Baseline condition (6.8 CH4-air, SL 15.8
    cm/s, w 12.7 mm) ST length 41 cm gt L -
    little effect of ST

34
Scaling analysis
  • ST length smaller (thus more important) for
    slower flames and smaller w - but these
    conditions will cause flame quenching - how to
    get smaller ST length without quenching?
  • ST length w (?/6)(?u/?av)(1/Pr)Pe for fixed
    cell width, minimum Pe 40 set by quenching -
    easier to get smaller ST length without quenching
    in thinner cells

35
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36
Effect of JS parameter
  • Results correlate reasonably well with relation
  • ST/SL 1 0.64 (?/kSL)
  • - suggests dimensionless JS parameter IS the
    driving force

37
Effect of JS parameter
  • Very similar for CH4-O2-CO2 mixtures

38
Effect of JS parameter
  • but propane far less impressive

39
Image analysis - flame position
  • Determine flame position
  • Video frames digitized, scaled to 256 pixels in x
    (spanwise) direction
  • Odd/even video half-frames separated
  • For each pixel column, flame position in y
    (propagation) direction (yf) is 1st moment of
    intensity (I) w.r.t. position, i.e.
  • Contrast brightness adjusted to obtain good
    flame trace

40
Flame front lengths
  • Front length / cell width - measure of wrinkling
    of flame by instabilities
  • Relatively constant during test
  • Higher/lower for upward/downward propagation
  • Front length / cell width AT/AL lt ST/SL - front
    length alone cannot account for observed flame
    acceleration by wrinkling
  • Curvature in 3rd dimension must account for
    wrinkling
  • Assume ST/SL (AT/AL)(U/SL), where U speed of
    curved flame in channel, flat in x-y plane

41
Flame front lengths
  • Even for horizontally-propagating flames, AT/AL
    not constant - decreases with increasing Pe - but
    (inferred) U/SL increases to make (measured)
    ST/SL constant!

42
Flame front lengths
  • AT/AL similar with propane - but (inferred) U/SL
    lower at low Pe to make (measured) ST/SL lower!

43
Flame front lengths
  • AT/AL correlates reasonably well with JS growth
    parameter for CH4-air and CH4-O2-CO2
  • Less satisfying for C3H8-air (high Le)
  • Expected trend - AT/AL increases as JS parameter
    increases
  • but AT/AL gt 1 even when JS parameter lt 0

44
Results - wrinkling characteristics
  • Individual images show clearly defined wavelength
    selection

45
Results - wrinkling characteristics
  • but averaging make them hard to see - 1/2 wave
    mode dominates spectra

46
Results - wrinkling characteristics
  • Because relative amplitudes of modes evolve over
    time

47
Results - wrinkling characteristics
  • Shows up better in terms of amplitude x
    wavenumber

48
Wrinkling - different mixture strengths
  • Modes 3 - 5 are very popular for a range of SL

49
Wrinkling - different cell thicknesses
  • Characteristic wavelength for ST 103 cm, 26 cm,
    6.4 cm in 12.7, 6.35, 3.2 mm thick cells - for
    thinner cells, ST dominates DL, more nearly
    monochromatic behavior (ST has characteristic
    wavelength, DL doesnt)

Run 108 9.5 CH4-air Horizontal propagation 6.35
mm cell
50
Wrinkling - different orientations
  • Upward more wrinkling at large scales (RT
    encouraged) downward less wrinkling at large
    scales smaller scales unaffected (RT dominant at
    large wavelengths)

51
Wrinkling - different fuel-O2-inerts, same SL
  • Slightly broader spectrum of disturbances at low
    Le, less at high Le

52
Conclusions
  • Flame propagation in quasi-2D Hele-Shaw cells
    reveals effects of
  • Thermal expansion - always present
  • Viscous fingering - narrow channels, high U
  • Buoyancy - destabilizing/stabilizing at long
    wavelengths for upward/downward propagation
  • Lewis number affects behavior at small
    wavelengths but propagation rate large-scale
    structure unaffected
  • Heat loss (Peclet number) little effect, except
    U affects transition from DL to ST controlled
    behavior

53
Remark
  • Most experiments conducted in open flames
    (Bunsen, counterflow, ...) - gas expansion
    relaxed in 3rd dimension
  • but most practical applications in confined
    geometries, where unavoidable thermal expansion
    (DL) viscous fingering (ST) instabilities cause
    propagation rates 3 SL even when heat loss,
    Lewis number buoyancy effects are negligible
  • DL ST effects may affect propagation rates
    substantially even when strong turbulence is
    present - generates wrinkling up to scale of
    apparatus
  • (ST/SL)Total (ST/SL)Turbulence x
    (ST/SL)ThermalExpansion ?

54
Remark
  • Computational studies suggest similar conclusions
  • Early times, turbulence dominates
  • Late times, thermal expansion dominates
  • H. Boughanem and A. Trouve, 27th Symposium, p.
    971.

55
Future work
  • Examine phase information, mode coupling
  • Obstacles of specified wavenumber - examine
    forced response
  • Linear growth behavior - need to suppress
    instabilities until specified time / location
    (e.g. acoustics, Clanet Searby PRL 1998)
  • Radial growth from point ignition (Sivashinsky
    others)

56
Thanks to
  • National Tsing-Hua University
  • Prof. C. A. Lin, Prof. T. M. Liou
  • Combustion Institute (Bernard Lewis Lectureship)
  • NASA (research support)
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