Nonpremixed-gas flames - counterflow. Research, TwentySeventh International Symposium on Combustion,

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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)» balls Nonpremixed gas flames Condensed-phase combustion» Particle-laden flames» Droplets» spread over solid fuel beds Reference: Ronney, P. D., Understanding Combustion Processes Through Microgravity Research, Research, TwentySeventh International Symposium on Combustion, Combustion Institute, Pittsburgh, 1998, pp AME October 14, 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 δ Diffusion time scale δ2/α ~ Σ-1 δ ~ (α/σ)1/2 Computations & µg experiments simple Cshaped dual-limit response Conductive loss to burners at low Σ? (Σ (Σmin)-1 tcond ~ d2/α (d = burner spacing) Need larger burners to see true radiation limit CH4-N2 vs. vs. air (Maruta et al. 1998) AME October 14,

2 Nonpremixed-gas flames - gas-jet flames Roper (1977): 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) AME October 14, Gas-jet flames - results L f same at 1g or µg for round jet L f /d o Sunderland et al. (1g) Sunderland et al. (µg, 1 atm) Sunderland et al. (µg, 0.5 atm) Sunderland et al. (µg, 0.25 atm) Cochran and Masica (µg) Bahadori et al. (µg) Bahadori & Stocker (µg) Reynolds number (Re) Sunderland et al. (1999) - CH 4 /air AME October 14,

3 widths at 1g and µg 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 10 w/d o 1 Sunderland et al. (1g) Sunderland et al. (µg, 1 atm) Sunderland et al. (µg, 0.5 atm) Sunderland et al. (µg, 0.25 atm) Cochran and Masica Bahadori et al Reynolds number (Re) Sunderland et al. (1999) - CH 4 /air AME October 14, Gas-jet flames - radiative loss Estimate of radiative loss fraction (R) = t jet /t rad = L/Ut rad R = d o2 /Dt rad (momentum-controlled) (µg) R = (Ud o2 /gdt rad2 ) 1/2 (buoyancy controlled) (low-speed 1g) R(1g)/R(µg) (Re/Gr) 1/2 for gases with D α ν (Re = Ud/ν; Gr = gd o3 /ν 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 AME October 14,

4 lengths at 1g and µg 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 d o = 3.3 mm, Re = 21 d = 0.42 mm, Re = 291 Sunderland et al. (1999) - C 2 H 6 /air AME October 14, Turbulent flame lengths at 1g and µg Turbulent flames (Hottel( and Hawthorne, 1949) 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 t get rid of buoyancy effects at high Re for turbulent flames!) length / nozzle diameter Earth gravity Microgravity Blow-off limits Jet Reynolds number Hedge et al. (1997) - C 3 H 8 /air AME October 14,

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

6 Sooting gas-jet flames at 1g and µg 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 1/2 o 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 AME October 14, 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 October 14,

7 Particle-laden flames - equations Egolfopoulos and Campbell, 1999 Single particle momentum equation: m p! " du p dt #$ = F PX = F SDX + F TPX + F GRX F SDX = %3 & µ g d p (u p % u g ) C F TPX = " %6&µ g ' g d p C ) g $ s! ( + C t Kn +T g * ) p # T g (1 + 3C m Kn)! " (1 + 2 ) g ) p + 2C t Kn # $ * F = ma (1+0.15Re 0687 p ), C = fn(kn) F GRX = %m p g Gravity force Combined effects: du p Single particle energy equation: dx = A 1 A 2 "T g " dt p m p c par! dt # $ u p d 2 (u g!u p ) + p u p d 2 + g T g u p p % Q p + Q p,rad % Q g,rad%p = 0 Q p = 4 & d p ' g (T g % T p ) C Nu, C Nu = fn(re p ) Stokes drag with correction for velocity slip at high Kn Thermophoretic force AME October 14, Particle-laden flames in stagnation flows Gravity effect on particle velocity (numerical): Particle Flow Velocity, cm/s 20 Gas Flow Particle Flow -g Fuel/Oxidizer 15 0-g H 2/Air, p=1 atm!=0.25 d =20 m p µ g -0.2 Spatial Distance, cm Expected behavior Fuel/Oxidizer/Particles AME October 14, x r 7

8 Particle-laden flames in stagnation flows Gravity effect on particle velocity (numerical): Velocity, cm/s Gas Flow Particle Flow GSP 0-g -g T, K Fuel/Oxidizer g Spatial Distance, cm H /Air, p=1 atm 2!=0.25 d =100 m p µ x r Fuel/Oxidizer/Particles Note flow reversals AME October 14, Particle-laden flames in stagnation flows Gravity effect on particle number density and flux (numerical) g +g Fuel/Oxidizer Normalized number density g H 2/Air, p=1 atm!=0.25 d p =20 µ m T, K Normalized particle flux Gas Flow Particle Flow +g -g (a) (b) T, K x r Fuel/Oxidizer/Particles g Spatial Distance, cm Results can NOT be readily derived from simple arguments AME October 14,

9 Particle-laden flames in stagnation flows Gravity effect on particle temperature (numerical) Gas Flow Particle Flow Gas Phase Gas Flow Fuel/Oxidizer T, K H 2/Air, p=1 atm!=0.25 u exit =30 cm/s d p =100 µ m 0-g g x r Fuel/Oxidizer/Particles Spatial Distance, cm Results NOT apparent AME October 14, Premixed flame extinction by inert particles (1g expts.) Larger particles can more effectively cool down the flames - counter-intuitive result! Fuel/Oxidizer x r Fuel/Oxidizer/Particles AME October 14,

10 Premixed flame extinction (1g simulations) Larger particles maintain larger temperature with the gas phase within the reaction zone! Fuel/Oxidizer x r Fuel/Oxidizer/Particles Competition between surface and temperature difference AME October 14, Premixed flame extinction (1g simulations) At high strain rates smaller particles cool more effectively Reduced residence time for large particles Surface effect becomes important Fuel/Oxidizer x r Fuel/Oxidizer/Particles AME October 14,

11 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 Fuel/Oxidizer x r Fuel/Oxidizer/Particles AME October 14, 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 φ Low loading Fuel/Oxidizer High loading x r Fuel/Oxidizer/Particles AME October 14,

12 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 Air Fuel+Air+Particles Premixed AME October 14, 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 Air Premixed Fuel+Air+Particles AME October 14,

13 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 0.95 (a) (b) n p,inj = 0 part/cm 3 Note: Single flame extinction Equivalence Ratio at Extinction,! ext n p,inj = 0 part/cm 3 n p,inj! 4000 part/cm 3 n p,inj! 4000 part/cm 3 Air CH 4 /Air Global Strain Rate, K glb, s C 3 H 8 /Air Fuel+Air+Particles Premixed AME October 14, 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 October 14,

14 Droplet combustion Spherically-symmetric model (Godsave( Godsave,, Spalding 1953) Steady burning possible - similar to flame balls (large radii: transport is diffusion-dominated) Mass burning rate = (π/4)( /4)ρ d d d K; ; K = (8k/ρ d C P ) ln(1+b) diameter d f = d d ln(1+b) / ln(1+f) Regressing droplet: d 2 do - d d (t) 2 = Kt if quasi-steady 1st µg experiment - Kumagai (1957) - K(µg) < K(1g) Normalized T or product mass fraction (T-T )/(T -T ) or (Y-Y )/(Y -Y )! f!! f! Droplet (dashed line) (B = 3) ball (solid line) Radius / Radius of flame AME October 14, 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 AME October 14,

15 Droplets - extinction limits Dual-limit behavior Residence-time limited (small d d ): t drop = d f2 /α 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) AME October 14, 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) AME October 14,

16 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 ) $ B ' " = ln& 1+ ); % 1# R /"( R * q rd d C P ; " * K, dc P 2+L V 8+ Normalized burning rate! K/K R=0 5 4 B = 3 3 B = R! q d C /2"L r d P v AME October 14, 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 ν effective diffusivity / D O2 3.7Gr 1/2 d (Gr d gd d3 /ν 2 ) K/K g= Gr 1/2 d Experiment (Okajima( & Kumagai,, 1982): K/K g= Gr.52 d - scaling ok Scaling Gr 1/2 since d f determined by stoichiometry, independent of V If instead d f ~ α/v then V ~ (gd( f ) 1/2 ~ (gα/v) 1/2 V ~ (gα) 1/3, d f ~ (α 2 /g) 1/3 D eff ~ α 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 October 14,

17 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 shell to form 0 sec 0.2 sec 0.5 sec 0.6 sec 0.3 sec 0.7 sec 0.4 sec 0.8 sec n-heptane in air (Manzello (Manzello et al., 2000) AME October 14, Candle flames Similar to quasi-steady droplet but near-field not spherical Space experiments (Dietrich et al., al., 1994, 1997) Nearly hemispherical at µg Steady for many minutes - probably > df 2/α Eventual extinguishment - probably due to O2 depletion 1g µg AME October 14,

18 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 ) AME October 14, References M. G. Andac,, F. N. Egolfopoulos,, and C. S. Campbell, ''Premixed flame extinction by inert particles in normal- and micro-gravity,'' Combustion and 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 s, 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 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 AME October 14,

19 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, Marchese,, A. J., Dryer, F. L., Nayagam,, V., Numerical Modeling of Isolated n-alkane Droplet s: Initial Comparisons With Ground and Space-Based Microgravity Experiments, Combust. 116: (1999). Maruta, K., Yoshida, M., Guo,, H., Ju, Y., Niioka,, T., Combust. 112: (1998). Roper, F., Combust. 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. 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). AME October 14,