1 AME 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 Ronney, P. D., “Understanding Combustion Processes Through Microgravity Research,” Twenty- Seventh International Symposium on Combustion, Combustion Institute, Pittsburgh, 1998, pp Ronney, P. D., “Understanding Combustion Processes Through Microgravity Research,” Twenty- Seventh International Symposium on Combustion, Combustion Institute, Pittsburgh, 1998, pp

2 AME 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)

3 AME 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)

4 AME October 14, 2004 Gas-jet flames - results  L f ≈ same at 1g or µg for round jet Sunderland et al. (1999) - CH 4 /air

5 AME 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

6 AME 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

7 AME 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

8 AME 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!)

9 AME 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)

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

11 AME 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

12 AME 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

13 AME 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:

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

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

16 AME 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)

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

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

19 AME 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

20 AME 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

21 AME 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

22 AME 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 

23 AME 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!

24 AME 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)

25 AME 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

26 AME 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

27 AME 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)

28 AME 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

29 AME 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)

30 AME 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)

31 AME 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…)

32 AME 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 ≈ Gr d 1/2  Experiment (Okajima & Kumagai, 1982): K/K g=0 ≈ Gr 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

33 AME October 14, 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)

34 AME 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

35 AME 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…)

36 AME 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 ,  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 ,  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  Buckmaster, J., Zhang, Y. (1999). “Oscillating Edge Flames,” Combustion Theory and Modelling 3,  Buckmaster, J., Hegap, A., Jackson, T. L. (2000). More results on oscillating edge flames. Physics of Fluids 12,  Chao, B.H., Law, C.K., T’ien, J.S., Twenty-Third Symposium (International) on Combustion, Combustion Institute, Pittsburgh, 1990, pp  Cheatham, S., Matalon, M., Twenty-Sixth Symposium (International) on Combustion, Combustion Institute, Pittsburgh, 1996, pp  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,  Godsave G.A.E, Fourth Symposium (International) on Combustion, Williams and Wilkins, Baltimore, 1953, pp  Haggard, J. B., Cochran, T. H., Combust. Sci. Tech. 5: (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  Hottel, H. C., Hawthorne, W. R., Third Symposium (International) on Combustion, Combustion Institute, Pittsburgh, Williams and Wilkins, Baltimore, 1949, pp

37 AME October 14, 2004 References  Kumagai, S., Isoda, H., Sixth Symposium (International) on Combustion, Combustion Institute, Pittsburgh, 1957, pp  Okajim, S., Kumagai, S., Nineteenth Symposium (International) on Combustion, Combustion Institute, Pittsburgh, 1982, pp  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: (1998).  Roper, F., Combust. Flame 29: (1977).  Spalding, D.B., Fourth Symposium (International) on Combustion, Williams and Wilkins, Baltimore, 1953, pp  Sunderland, P. B., Mendelson, B. J., Yuan, Z.-G., Urban, D. L., Combust. Flame 116: (1999).  Urban, D. L, et al., “Structure and soot properties of nonbuoyant ethylene/air laminar jet diffusion flames,” AIAA Journal, Vol. 36, pp (1998).