Microgravity combustion lecture 2

1
Microgravity combustion - lecture 2

• Motivation
• Time scales (Lecture 1)
• Examples
• Premixed-gas flames
• Flammability limits (Lecture 1)
• Stretched flames (Lecture 1)
• Flame balls
• Nonpremixed gas flames
• Condensed-phase combustion
• Particle-laden flames
• Droplets
• Flame spread over solid fuel beds
• Reference Ronney, P. D., Understanding
  Combustion Processes Through Microgravity
  Research, Twenty-Seventh International Symposium
  on Combustion, Combustion Institute, Pittsburgh,
  1998, pp. 2485-2506

2
Nonpremixed-gas flames - counterflow

• Counterflow flames
• Nonpremixed flames less freedom of movement
  flame must lie where stoichiometric flux ratio
  maintained
• Radiating gas volume flame thickness ?
• Diffusion time scale ?2/? ?-1 ? ? (?/?)1/2
• Computations µg experiments simple C-shaped
  dual-limit response
• Conductive loss to burners at low ?? (?min)-1
  tcond d2/? (d burner spacing)
• Need larger burners to see true radiation limit

CH4-N2 vs. air (Maruta et al. 1998)
3
Nonpremixed-gas flames - gas-jet flames

• Roper (1977) Flame height (Lf) and residence
  time (tjet) determined by equating diffusion time
  (d2/D, d jet diameter, D oxygen diffusivity)
  to convection time (Lf/U)
• Mass conservation U(0)d(0)2 U(Lf)d(Lf)2
  (round jet) U(0)d(0) U(Lf)d(Lf) (slot jet)
• Buoyant flow U(Lf) (gLf)1/2 nonbuoyant
  U(Lf) U(0)
• Consistent with more rigorous model based on
  boundary-layer theory (Haggard Cochran, 1972)

4
Gas-jet flames - results

• Lf same at 1g or µg for round jet

Sunderland et al. (1999) - CH4/air
5
Flame widths at 1g and µg

• tjet larger at µg than 1g for round jet
• Larger µg flame width (Dtjet)1/2 - greater
  difference at low Re due to axial diffusion (not
  included in aforementioned models) buoyancy
  effects
• Greater radiative loss fraction at µg ( 50 vs.
  8, Bahadori et al., 1993), thus cooler
  temperatures, redder color from soot

Sunderland et al. (1999) - CH4/air
6
Gas-jet flames - radiative loss

• Estimate of radiative loss fraction (R)
  tjet/trad L/Utrad
• R do2/Dtrad (momentum-controlled) (µg)
• R (Udo2/gDtrad2)1/2 (buoyancy controlled)
  (low-speed 1g)
• R(1g)/R(µg) (Re/Gr)1/2 for gases with D ? ?
  (Re Ud/? Gr gdo3/?2)
• For typical do 1 cm, D 1 cm2/s (1 atm,
  T-averaged), R(1g)/R(µg) 1 at Re 1000
• Lower Re R(1g)/R(µg) Re1/2 - much higher
  impact of radiative loss at µg

7
Flame lengths at 1g and µg

• Low Re depends on Grashof or Froude number (Fr
  Re2/Gr)
• 1g (low Fr) buoyancy dominated, teardrop shaped
• µg (Fr 8) nearly diffusion-dominated, more
  like nonpremixed version of flame ball (similar
  to candle flame, fuel droplet flames discussed
  later)
• High Re results independent of Fr

do 3.3 mm, Re 21 d 0.42 mm, Re
291 Sunderland et al. (1999) - C2H6/air
8
Turbulent flame lengths at 1g and µg

• Turbulent flames (Hottel and Hawthorne, 1949)
• D uLI u Uo LI do ? Lf do
  (independent of Re)
• Bahadori et al. differences between 1g µg seen
  even at high Re - buoyancy effects depend on
  entire plume! (Cant get rid of buoyancy effects
  at high Re for turbulent flames!)

Hedge et al. (1997) - C3H8/air
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Sooting gas-jet flames at 1g and µg

• Reference Urban et al., 1998
• Basic character of sooting flames same at 1g
  µg, but g affects temperature/time history (left)
  which in turn affects soot formation (right)

STS-94 space experiment (1997) Note soot emission
at high flow rate (beginning of test)
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Sooting gas-jet flames at 1g and µg
11
Sooting gas-jet flames at 1g and µg

• Typically greater at µg due to larger tjet -
  outweighs lower T
• Smoke points seen at µg (Sunderland et al.,
  1994) - WHY???
• tjet Uo1/2 for buoyant flames BUT...
• tjet independent of Uo for nonbuoyant flames !
• R (ideally) independent of U for nonbuoyant
  flames
• Axial diffusion effects negligible at Re gt 50
• Thermophoresis effects - concentrates soot in
  annulus

12
Particle-laden flames

• This section courtesy of Prof. F. N. Egolfopoulos
• Importance of particle-laden flows
• Intentional/unintentional solid particle addition
• Modification of ignition, burning, and extinction
  characteristics of gas phase
• Propulsion (Al, B, Mg)
• Power generation (coal)
• Material synthesis
• Explosions (lumber milling, grain elevators, mine
  galleries)
• Particles are used in laser diagnostics (LDV,
  PIV, PDA)
• Possible interactions between gas and particle
  phases
• Dynamic (velocity modification)
• Thermal (temperature modification)
• Chemical (composition modification)
• Parameters affecting these interactions
• Physico-chemical properties of both phases
• Fluid mechanics (strain rate)
• Long range forces on particles (e.g. electric,
  magnetic, centrifugal, gravitational)
• Phoretic forces on particles

13
Particle-laden flames - equations

• Egolfopoulos and Campbell, 1999
• Single particle momentum equation
• Single particle energy equation

F ma
Stokes drag with correction for velocity slip at
high Kn
Thermophoretic force
Combined effects
Gravity force
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Particle-laden flames in stagnation flows

• Gravity effect on particle velocity (numerical)

Expected behavior
15
Particle-laden flames in stagnation flows

• Gravity effect on particle velocity (numerical)

Note flow reversals
16
Particle-laden flames in stagnation flows

• Gravity effect on particle number density and
  flux (numerical)

Results can NOT be readily derived from simple
arguments
17
Particle-laden flames in stagnation flows

• Gravity effect on particle temperature
  (numerical)

Results NOT apparent
18
Premixed flame extinction by inert particles (1g
expts.)

• Larger particles can more effectively cool down
  the flames - counter-intuitive result!

19
Premixed flame extinction (1g simulations)

• Larger particles maintain larger temperature with
  the gas phase within the reaction zone!

Competition between surface and temperature
difference
20
Premixed flame extinction (1g simulations)

• At high strain rates smaller particles cool more
  effectively
• Reduced residence time for large particles
• Surface effect becomes important

21
Premixed flame extinction (1g and µg expts.)

• Extinction is facilitated at µg at 1g particles
  can not readily reach the top flame effect
  weaker for large particle loadings

22
Premixed flame extinction (1g µg simulations)

• Low loading Particles do not reach upper flame
  in 1g
• High loading Even at 1g particles penetrate the
  stagnation plane due to higher thermal expansion
  at higher ?

Low loading
High loading
23
Premixed flame extinction (1g µg expts)

• Extinction if facilitated at µg argument about
  reduced particle velocities not applicable in
  this case!

Note Single flame extinction
24
Premixed flame extinction (1g µg simulations)

• Extinction if facilitated at µg argument about
  reduced particle velocities not applicable in
  this case!
• Gravity affects the particle number density
• In µg particles possess more momentum and they
  are less responsive to thermal expansion that
  tends to decrease the particle number density ?
  more effective cooling

Note Single flame extinction
25
Premixed flame extinction (1g expts.)

• Low strain rates reacting particles augment
  overall reactivity
• High strain rates reacting particles act as
  inert cooling the gas phase and facilitating
  extinction

Note Single flame extinction
26
Summary - particle-laden flames

• Direct effect on the trajectory of slow-moving
  particles
• Indirect effects on particle
• Number density
• Temperature
• Chemical activity
• For inert particles, gravity has a noticeable
  effect on flame propagation and extinction
  through its modification of the particle dynamic
  and thermal states as well as on the particle
  number density
• For reacting particles, gravity can render the
  solid phase inert thorugh its effect on the
  particle dynamic behavior

27
Droplet combustion

• Spherically-symmetric model (Godsave, Spalding
  1953)
• Steady burning possible - similar to flame balls
• (large radii transport is diffusion-dominated)
  
• Mass burning rate (p/4)?dddK K (8k/?dCP)
  ln(1B)
• Flame diameter df dd ln(1B) / ln(1f)
• Regressing droplet ddo2 - dd(t)2 Kt if
  quasi-steady
• 1st µg experiment - Kumagai (1957) - K(µg) lt K(1g)

28
Droplet combustion

• ... But large droplets NOT quasi-steady
• K df/dd not constant - depend on ddo time
• Large time scale for diffusion of radiative
  products to far-field O2 from far-field (like
  flame ball)
• Soot accumulation dependent on ddo
• Absorption of H2O from products by fuel
  (alcohols)

Marchese et al. (1999), heptane in O2-He
29
Droplets - extinction limits

• Dual-limit behavior
• Residence-time limited (small dd) tdrop df2/?
  tchem
• Heat loss (large dd) (Chao et al., 1990) tdrop
  trad
• Radiative limit at large dd confirmed by µg
  experiments
• Extinction occurs at large dd, but dd decreases
  during burn - quasi-steady extinction not
  observable

Marchese, et al. (1999)
30
Droplets - extinction limits

• Note flame never reaches quasi-steady diameter
• df dd ln(1B)/ ln(1f) due to unsteadiness
  radiative loss effects
• Extinguishment when flame diameter grows too
  large (closer to quasi-steady value)

Marchese, et al. (1999)
31
Droplets - radiation effects

• Radiation in droplet flames can be a loss
  mechanism or can increase heat feedback to
  droplet (increased burning rate)
• Problem of heat feedback severe with droplets -
  Stefan flow at surface limits conductive flux,
  causes ln(1B) term radiation not affected by
  flow
• Add radiative flux (qr) to droplet surface
• Crude estimates indicate important for practical
  flames, especially with exhaust-gas recirculation
  / reabsorption, but predictions never tested
  (PDRs proposals keep getting rejected)

32
Droplets - buoyancy effects

• How important is buoyancy in droplet combustion?
• Buoyant O2 transport / diffusive O2 transport
  effective diffusivity / DO2
• Vbuoydf / DO2 0.3(gdf)1/2df/DO2
• df 10dd, DO2 ? ? effective diffusivity /
  DO2 3.7Grd1/2 (Grd ? gdd3/?2)
• ? K/Kg0 1 3.7Grd1/2
• Experiment (Okajima Kumagai, 1982) K/Kg0 1
  0.53Grd.52 - scaling ok
• Scaling Gr1/2 since df determined by
  stoichiometry, independent of V
• If instead df ?/V then V (gdf)1/2
  (g?/V)1/2
• ? V (g?)1/3, df (?2/g)1/3 ? Deff ? ? no
  change in K with Gr!
• Moral need characteristic length scale that is
  independent of buoyancy to see increase in
  transport due to buoyancy

33
Soot formation in µg droplet combustion

• Thermophoresis causes soot particles to migrate
  toward lower T (toward droplet), at some radius
  balances outward convection causes soot
  agglomeration shell to form

34
Candle flames

• Similar to quasi-steady droplet but near-field
  not spherical
• Space experiments (Dietrich et al., 1994, 1997)
• Nearly hemispherical at µg
• Steady for many minutes - probably gt df 2/?
• Eventual extinguishment - probably due to O2
  depletion

1g µg
35
Candle flames - oscillations

• Oscillations before extinguishment, except for
  small df
• Near-limit oscillations of spherical flames?
  (Cheatham Matalon)
• Edge-flame instability? (Buckmaster et al., 1999,
  2000)
• Both models require high Le near-extinction
  conditions
• Some evidence in droplets also (Nayagam et al.,
  1998)
• Predicted but not seen in flame balls! (see
  STS-107 results)

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References

• M. G. Andac, F. N. Egolfopoulos, and C. S.
  Campbell, ''Premixed flame extinction by inert
  particles in normal- and micro-gravity,''
  Combustion and Flame 129, pp. 179-191, 2002.
• M. G. Andac, F. N. Egolfopoulos, C. S. Campbell,
  and R. Lauvergne, ''Effects of inert dust clouds
  on the extinction of strained laminar flames,''
  Proc. Comb. Inst. 28, pp. 2921-2929, 2000.
• Bahadori, M. Y., Stocker, D. P., Vaughan, D. F.,
  Zhou, L., Edelman, R. B., in Modern Developments
  in Energy Combustion and Spectroscopy, (F. A.
  Williams, A. K. Oppenheim, D. B. Olfe and M.
  Lapp, Eds.), Pergamon Press, 1993, pp. 49-66.
• Buckmaster, J., Zhang, Y. (1999). Oscillating
  Edge Flames, Combustion Theory and Modelling 3,
  547-565.
• Buckmaster, J., Hegap, A., Jackson, T. L. (2000).
  More results on oscillating edge flames.
  Physics of Fluids 12, 1592-1600.
• Chao, B.H., Law, C.K., Tien, J.S., Twenty-Third
  Symposium (International) on Combustion,
  Combustion Institute, Pittsburgh, 1990, pp.
  523-531.
• Cheatham, S., Matalon, M., Twenty-Sixth Symposium
  (International) on Combustion, Combustion
  Institute, Pittsburgh, 1996, pp. 1063-1070.
• Egolfopoulos, F. N., Campbell, C. S. (1999).
  Dynamics and structure of dusty reacting flows
  Inert particles in strained, laminar, premixed
  flames, Combustion and Flame 117, 206-226.
• Godsave G.A.E, Fourth Symposium (International)
  on Combustion, Williams and Wilkins, Baltimore,
  1953, pp. 818-830.
• Haggard, J. B., Cochran, T. H., Combust. Sci.
  Tech. 5291-298 (1972).
• Hegde, U., Yuan, Z. G., Stocker, D., Bahadori, M.
  Y., in Proceedings of the Fourth International
  Microgravity Combustion Workshop, NASA Conference
  Publication 10194, 1997, pp. 185-190.
• Hottel, H. C., Hawthorne, W. R., Third Symposium
  (International) on Combustion, Combustion
  Institute, Pittsburgh, Williams and Wilkins,
  Baltimore, 1949, pp. 254-266.

37
References

• Kumagai, S., Isoda, H., Sixth Symposium
  (International) on Combustion, Combustion
  Institute, Pittsburgh, 1957, pp. 726-731.
• Okajim, S., Kumagai, S., Nineteenth Symposium
  (International) on Combustion, Combustion
  Institute, Pittsburgh, 1982, pp. 1021-1027.
• S. L. Manzello, M. Y. Choi, A. Kazakov, F. L.
  Dryer, R. Dobashi, T. Hirano (2000). The
  burning of large n-heptance droplets in
  microgravity, Proceedings of the Combustion
  Institute 28, 10791086.
• Marchese, A. J., Dryer, F. L., Nayagam, V.,
  Numerical Modeling of Isolated n-Alkane Droplet
  Flames Initial Comparisons With Ground and
  Space-Based Microgravity Experiments, Combust.
  Flame 116432459 (1999).
• Maruta, K., Yoshida, M., Guo, H., Ju, Y., Niioka,
  T., Combust. Flame 112181-187 (1998).
• Roper, F., Combust. Flame 29219-226 (1977).
• Spalding, D.B., Fourth Symposium (International)
  on Combustion, Williams and Wilkins, Baltimore,
  1953, pp. 847-864.
• Sunderland, P. B., Mendelson, B. J., Yuan, Z.-G.,
  Urban, D. L., Combust. Flame 116376-386 (1999).
• Urban, D. L, et al., Structure and soot
  properties of nonbuoyant ethylene/air laminar jet
  diffusion flames, AIAA Journal, Vol. 36, pp.
  1346-1360 (1998).