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Microgravity combustion - lecture 2

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

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Microgravity combustion - lecture 2

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  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 AME 514 - October 14, 2004

  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) AME 514 - October 14, 2004

  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) AME 514 - October 14, 2004

  4. Gas-jet flames - results • Lf ≈ same at 1g or µg for round jet Sunderland et al. (1999) - CH4/air AME 514 - October 14, 2004

  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 AME 514 - October 14, 2004

  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 AME 514 - October 14, 2004

  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 = ∞): 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 AME 514 - October 14, 2004

  8. Turbulent flame lengths at 1g and µg • Turbulent flames (Hottel and Hawthorne, 1949) • D ~ u’LI; 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! (Can’t get rid of buoyancy effects at high Re for turbulent flames!) Hedge et al. (1997) - C3H8/air AME 514 - October 14, 2004

  9. 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) AME 514 - October 14, 2004

  10. Sooting gas-jet flames at 1g and µg AME 514 - October 14, 2004

  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 > 50 • Thermophoresis effects - concentrates soot in annulus 1g µg n-butane in air, 10mm diameter jet, Re = 42 - Fujita et al., 1997 AME 514 - October 14, 2004

  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 AME 514 - October 14, 2004

  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 AME 514 - October 14, 2004

  14. Particle-laden flames in stagnation flows • Gravity effect on particle velocity (numerical): Expected behavior AME 514 - October 14, 2004

  15. Particle-laden flames in stagnation flows • Gravity effect on particle velocity (numerical): Note flow reversals AME 514 - October 14, 2004

  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 AME 514 - October 14, 2004

  17. Particle-laden flames in stagnation flows • Gravity effect on particle temperature (numerical) Results NOT “apparent” AME 514 - October 14, 2004

  18. Premixed flame extinction by inert particles (1g expts.) • Larger particles can more effectively cool down the flames - counter-intuitive result! AME 514 - October 14, 2004

  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 AME 514 - October 14, 2004

  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 AME 514 - October 14, 2004

  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 AME 514 - October 14, 2004

  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 AME 514 - October 14, 2004

  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 AME 514 - October 14, 2004

  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 AME 514 - October 14, 2004

  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 AME 514 - October 14, 2004

  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 AME 514 - October 14, 2004

  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 = (π/4)dddK; K = (8k/dCP) ln(1+B) • Flame diameter df = dd ln(1+B) / ln(1+f) • Regressing droplet: ddo2 - dd(t)2 = Kt if quasi-steady • 1st µg experiment - Kumagai (1957) - K(µg) < K(1g) AME 514 - October 14, 2004

  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 AME 514 - October 14, 2004

  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) AME 514 - October 14, 2004

  30. Droplets - extinction limits • Note flame never reaches quasi-steady diameter df = dd 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) AME 514 - October 14, 2004

  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(1+B) 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 (PDR’s proposals keep getting rejected…) AME 514 - October 14, 2004

  32. Droplets - buoyancy effects • How important is buoyancy in droplet combustion? • Buoyant O2 transport / diffusive O2 transport ≈ “effective diffusivity” / DO2 ≈ Vbuoy*df / DO2 ≈ 0.3(gdf)1/2df/DO2 • df ≈ 10dd, DO2 ≈   “effective diffusivity” / DO2 ≈ 3.7Grd1/2 (Grd  gdd3/2)  K/Kg=0 ≈ 1 + 3.7Grd1/2 • Experiment (Okajima & Kumagai, 1982): K/Kg=0 ≈ 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 Buoyancy effects G-jitter effects on KC-135 aircraft AME 514 - October 14, 2004

  33. 0 sec 0.2 sec 0.3 sec 0.4 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) AME 514 - October 14, 2004

  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 > df 2/ • Eventual extinguishment - probably due to O2 depletion 1g µg AME 514 - October 14, 2004

  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…) AME 514 - October 14, 2004

  36. 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. AME 514 - October 14, 2004

  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, 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). AME 514 - October 14, 2004

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