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1 AME 514 - October 14, 2004 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 Ronney, P. D., “Understanding Combustion Processes Through Microgravity Research,” Twenty- Seventh International Symposium on Combustion, Combustion Institute, Pittsburgh, 1998, pp. 2485-2506Ronney, P. D., “Understanding Combustion Processes Through Microgravity Research,” Twenty- Seventh International Symposium on Combustion, Combustion Institute, Pittsburgh, 1998, pp. 2485-2506
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2 AME 514 - October 14, 2004 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 ≈ t cond ~ d 2 / (d = burner spacing) Need larger burners to see true radiation limit CH 4 -N 2 vs. air (Maruta et al. 1998)
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3 AME 514 - October 14, 2004 Nonpremixed-gas flames - gas-jet flames Roper (1977): Flame height (L f ) and residence time (t jet ) determined by equating diffusion time (d 2 /D, d = jet diameter, D = oxygen diffusivity) to convection time (L f /U) Mass conservation: U(0)d(0) 2 ~ U(L f )d(L f ) 2 (round jet); U(0)d(0) ~ U(L f )d(L f ) (slot jet) Buoyant flow: U(L f ) ~ (gL f ) 1/2 ; nonbuoyant: U(L f ) = U(0) Consistent with more rigorous model based on boundary-layer theory (Haggard & Cochran, 1972)
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4 AME 514 - October 14, 2004 Gas-jet flames - results L f ≈ same at 1g or µg for round jet Sunderland et al. (1999) - CH 4 /air
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5 AME 514 - October 14, 2004 Flame widths at 1g and µg Sunderland et al. (1999) - CH 4 /air t jet larger at µg than 1g for round jet Larger µg flame width ~ (Dt jet ) 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
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6 AME 514 - October 14, 2004 Gas-jet flames - radiative loss Estimate of radiative loss fraction (R) = t jet /t rad = L/Ut rad R = d o 2 /Dt rad (momentum-controlled) (µg) R = (Ud o 2 /gDt rad 2 ) 1/2 (buoyancy controlled) (low-speed 1g) R(1g)/R(µg) ≈ (Re/Gr) 1/2 for gases with D ≈ ≈ (Re = Ud/ ; Gr = gd o 3 / 2 ) For typical d o = 1 cm, D = 1 cm 2 /s (1 atm, T-averaged), R(1g)/R(µg) = 1 at Re ≈ 1000 Lower Re: R(1g)/R(µg) ~ Re 1/2 - much higher impact of radiative loss at µg
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7 AME 514 - October 14, 2004 Flame lengths at 1g and µg d o = 3.3 mm, Re = 21d = 0.42 mm, Re = 291 Sunderland et al. (1999) - C 2 H 6 /air Low Re: depends on Grashof or Froude number (Fr = Re 2 /Gr) 1g (low Fr): buoyancy dominated, teardrop shaped µg (Fr = ∞): 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
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8 AME 514 - October 14, 2004 Turbulent flame lengths at 1g and µg Hedge et al. (1997) - C 3 H 8 /air Turbulent flames (Hottel and Hawthorne, 1949) D ~ u’L I ; u’ ~ U o ; L I ~ d o L f ~ d o (independent of Re) D ~ u’L I ; u’ ~ U o ; L I ~ d o L f ~ d o (independent of Re) Bahadori et al.: differences between 1g & µg seen even at high Re - buoyancy effects depend on entire plume! (Can’t get rid of buoyancy effects at high Re for turbulent flames!)
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9 AME 514 - October 14, 2004 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) (beginning of test)
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10 AME 514 - October 14, 2004 Sooting gas-jet flames at 1g and µg
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11 AME 514 - October 14, 2004 Typically greater at µg due to larger t jet - outweighs lower T Smoke points seen at µg (Sunderland et al., 1994) - WHY??? » t jet ~ U o 1/2 for buoyant flames BUT... » t jet independent of U o for nonbuoyant flames ! » R (ideally) independent of U for nonbuoyant flames » Axial diffusion effects negligible at Re > 50 Thermophoresis effects - concentrates soot in annulus 1g µg n-butane in air, 10mm diameter jet, Re = 42 - Fujita et al., 1997 Sooting gas-jet flames at 1g and µg
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12 AME 514 - October 14, 2004 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
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13 AME 514 - October 14, 2004 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 Gravity force Thermophoretic force Combined effects:
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14 AME 514 - October 14, 2004 Expected behavior Particle-laden flames in stagnation flows Gravity effect on particle velocity (numerical):
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15 AME 514 - October 14, 2004 Note flow reversals Particle-laden flames in stagnation flows Gravity effect on particle velocity (numerical):
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16 AME 514 - October 14, 2004 Results can NOT be readily derived from simple arguments Particle-laden flames in stagnation flows Gravity effect on particle number density and flux (numerical)
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17 AME 514 - October 14, 2004 Results NOT “apparent” Particle-laden flames in stagnation flows Gravity effect on particle temperature (numerical)
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18 AME 514 - October 14, 2004 Premixed flame extinction by inert particles (1g expts.) Larger particles can more effectively cool down the flames - counter-intuitive result!
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19 AME 514 - October 14, 2004 Premixed flame extinction (1g simulations) Larger particles maintain larger temperature with the gas phase within the reaction zone! Competition between surface and temperature difference
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20 AME 514 - October 14, 2004 Premixed flame extinction (1g simulations) At high strain rates smaller particles cool more effectively Reduced residence time for large particles Surface effect becomes important
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21 AME 514 - October 14, 2004 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
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22 AME 514 - October 14, 2004 Low loading High loading 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
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23 AME 514 - October 14, 2004 Note: Single flame extinction Premixed flame extinction (1g & µg expts) Extinction if facilitated at µg; argument about reduced particle velocities not applicable in this case!
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24 AME 514 - October 14, 2004 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 Premixed flame extinction (1g & µg simulations)
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25 AME 514 - October 14, 2004 Note: Single flame extinction 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
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26 AME 514 - October 14, 2004 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
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27 AME 514 - October 14, 2004 Droplet combustion Spherically-symmetric model (Godsave, Spalding 1953) Steady burning possible - similar to flame balls (large radii: transport is diffusion-dominated) Mass burning rate = (π/4) d d d K; K = (8k/ d C P ) ln(1+B) Flame diameter d f = d d ln(1+B) / ln(1+f) Regressing droplet: d do 2 - d d (t) 2 = Kt if quasi-steady 1st µg experiment - Kumagai (1957) - K(µg) < K(1g)
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28 AME 514 - October 14, 2004 Droplet combustion ... But large droplets NOT quasi-steady K & d f /d d not constant - depend on d do & time Large time scale for diffusion of radiative products to far-field & O 2 from far-field (like flame ball) Soot accumulation dependent on d do Absorption of H 2 O from products by fuel (alcohols) Marchese et al. (1999), heptane in O 2 -He
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29 AME 514 - October 14, 2004 Droplets - extinction limits Dual-limit behavior Residence-time limited (small d d ): t drop = d f 2 / ≤ t chem Heat loss (large d d ) (Chao et al., 1990): t drop ≥ t rad Radiative limit at large d d confirmed by µg experiments Extinction occurs at large d d, but d d decreases during burn - quasi-steady extinction not observable Marchese, et al. (1999)
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30 AME 514 - October 14, 2004 Droplets - extinction limits Note flame never reaches quasi-steady diameter d f = d d ln(1+B)/ ln(1+f) due to unsteadiness & radiative loss effects Extinguishment when flame diameter grows too large (closer to quasi-steady value) Marchese, et al. (1999)
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31 AME 514 - October 14, 2004 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(1+B) term; radiation not affected by flow Add radiative flux (q r ) to droplet surface Crude estimates indicate important for practical flames, especially with exhaust-gas recirculation / reabsorption, but predictions never tested (PDR’s proposals keep getting rejected…)
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32 AME 514 - October 14, 2004 Droplets - buoyancy effects How important is buoyancy in droplet combustion? Buoyant O 2 transport / diffusive O 2 transport ≈ “effective diffusivity” / D O2 ≈ V buoy *d f / D O2 ≈ 0.3(gd f ) 1/2 d f /D O2 d f ≈ 10d d, D O2 ≈ “effective diffusivity” / D O2 ≈ 3.7Gr d 1/2 (Gr d gd d 3 / 2 ) K/K g=0 ≈ 1 + 3.7Gr d 1/2 Experiment (Okajima & Kumagai, 1982): K/K g=0 ≈ 1 + 0.53Gr d.52 - scaling ok Scaling Gr 1/2 since d f determined by stoichiometry, ≈ independent of V If instead d f ~ /V then V ~ (gd f ) 1/2 ~ (g /V) 1/2 V ~ (g ) 1/3, d f ~ ( 2 /g) 1/3 D eff ~ no change in K with Gr! Moral: need characteristic length scale that is independent of buoyancy to see increase in transport due to buoyancy Buoyancy effectsG-jitter effects on KC-135 aircraft
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33 AME 514 - October 14, 2004 0 sec 0.4 sec 0.2 sec 0.3 sec 0.5 sec 0.6 sec 0.7 sec 0.8 sec 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 n-heptane in air (Manzello et al., 2000)
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34 AME 514 - October 14, 2004 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 > d f 2 / Eventual extinguishment - probably due to O 2 depletion 1g µg 1g µg
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35 AME 514 - October 14, 2004 Candle flames - oscillations Oscillations before extinguishment, except for small d f 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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36 AME 514 - October 14, 2004 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., T’ien, 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. 5:291-298 (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.
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37 AME 514 - October 14, 2004 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, 1079–1086. 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 116:432–459 (1999). Maruta, K., Yoshida, M., Guo, H., Ju, Y., Niioka, T., Combust. Flame 112:181-187 (1998). Roper, F., Combust. Flame 29:219-226 (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 116:376-386 (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).
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