AME514-F06-lecture2

AME514-F06-lecture2 - Advanced fundamental topics Ignition...

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Unformatted text preview: Advanced fundamental topics Ignition Basic concepts Mathematical theory Dynamics of ignition Effects of the state of the combustible mixture Effects of the characteristics of the ignition source Effects of the flow environment More detailed information: http://ronney.usc.edu/Lecture2/AME514F06/AME514.ignition.review.pdf AME 514 - Fall 2006 - Lecture 2 1 Basic concepts Experiments (Lewis & von Elbe, 1961) show that a minimum energy (Emin) (not just minimum T or volume) required to ignite a flame Emin lowest near stoichiometric (typ. 0.2 mJ) but minimum shifts to (typ. mJ) richer mixtures for higher HCs (why? Stay tuned...) tuned... Prediction of Emin relevant to energy conversion and fire safety applications Minimum ignition energy (mJ) (mJ) AME 514 - Fall 2006 - Lecture 2 2 1 Basic concepts Emin related to need to create flame kernel with dimension () large ( enough that chemical reaction () can exceed conductive loss rate ( (/2), thus > (/)1/2 ~ /()1/2 ~ /SL ~ ( /( Emin ~ energy contained in volume of gas with T Tad and radius 4/SL 4 4$ 3 4$ 2 k (T ' T ) " E min # % &C p (Tad ' T( ) # 0.3 % 3 &(C p (Tad ' T( ) # 34) ( ( ad 3 ( 3 3 SL Successful ignition Initial profile Initial profile TEMPERATURE TEMPERATURE ! Unsuccessful ignition ! Later Still later Later Still later SL DISTANCE DISTANCE AME 514 - Fall 2006 - Lecture 2 3 Predictions of simple Emin formula Since ~ P-1, Emin ~ P-2 if SL is independent of P Emin 100,000 times larger in a He-diluted than SF6diluted mixture with same SL, same P (due to and differences) Stoichiometric CH4-air @ 1 atm: predicted Emin 0.010 mJ 30x times lower than experiment (due to chemical kinetics, heat losses, shock losses ...) ... but need something more (Lewis number effects): (Lewis effects): 10% H2-air (SL 10 cm/sec): predicted Emin 0.3 mJ = 2.5 times 10 0.3 higher than experiments Lean CH4-air (SL 5 cm/sec): Emin 5 mJ compared to 5000mJ 5 for lean C3H8-air with same SL - but prediction is same for both AME 514 - Fall 2006 - Lecture 2 4 2 Predictions of simple Emin formula Emin ~ 3 hard to measure, but quenching distance (q ) (min. tube diameter through which flame can propagate) should be ~ since Pelim = SL,lim q/ ~ q/ 40 constant, thus should have L,lim Emin ~ q3P 2 10 Correlation so-so Hydrogen (lean) Minimum ignition energy (mJ) 10 10 10 10 10 1 0 Hydrogen (rich) Methane (lean) Methane (rich) Ethane (lean) Ethane (rich) Propane (lean) Propane (rich) Best fit to all data Slope = 0.739 -1 -2 Slope = 1 -6 -5 -4 -3 -2 3 -1 0 -3 10 10 10 10 10 10 10 3 Pressure * (quenching distance) (atm cm ) AME 514 - Fall 2006 - Lecture 2 5 More rigorous approach Assumptions: 1D spherical; ideal gases; adiabatic (except for ignition source Q(r,t)); 1 limiting reactant (e.g. very lean or rich); 1-step overall reaction; D, , CP, etc. constant; low Mach #; no body forces Governing equations for mass, energy & species conservations (y = limiting reactant mass fraction; QR = its heating value) ! ! "# 1 " 2 + (r #v ) = 0 "T = "#T# = constant "t r 2 "r #T 1 # k # $ #T ' "C p + "C p 2 ( r 2vT ) = 2 & r 2 ) + "QR yZ exp #t r #r r #r % # r ( ! #y 1 # "D # $ #y ' *E " + "v 2 ( r 2 y ) = 2 & r 2 ) * "yZ exp +T #t r #r r #r % #r ( ( ) + Q(r,t) *E +T ( ) ! AME 514 - Fall 2006 - Lecture 2 6 3 More rigorous approach Non-dimensionalize (note Tad = T + YQR /CP) "# T Ze% & v E ;$ # tAe% & ;R # r ;U # ;& # %& Tad '( )Tad ' ( Ze "# ! T$ y k Q(r,t) ;Y # ;Le # ;& # Tad y$ %C p D %$C p T$ Ze' ( leads to, for mass, energy and species conservation ! " (1/# ) 1 " % 2 1 ( + 2 'R U* = 0 "$ R "R & # ) "Y 1 " 1 $ 1 " & "Y ) +U 2 (R 2Y ) = Le % R 2 "R ( R 2 "R + , Yexp ' * "# R "R ( ,- ( )) 1 ,1 $ ! with boundary conditions "# 1 " # 1 " & "# ) +U 2 (R 2# ) = % R 2 "R ( R 2 "R + + (1, %)Yexp ' * "$ R "R ! ( ,- ( )) + .(R,$ )# 1 ,1 # ! ! " (R,0) = #;Y (R,0) = 1;U(R,0) = 0 for all R (Initial condition: T = T, y = y, U = 0 everywhere) (At infinite radius, T = T, y = y, U = 0 for all times) (Symmetry condition at r = 0 for all times) " (R, # ) = $;Y (R, # ) = 1;U(R, # ) = 0 as R % & "# "Y "U = = = 0 at R = 0 and as R $ % "R "R "R ! ! AME 514 - Fall 2006 - Lecture 2 7 Steady (?!?) solutions If reaction is confined to a thin zone near r = RZ (large ) 1# $ Rz R R > Rz : " = + $; Y = 1# z T* 1% $ T %T R "* # =$+ or T * = T& + ad & Le R Tad Le Le R < Rz : " = " * = constant; Y = 0 Rz = &# & 1 )) & %# ) 2-Le, . Z " , exp( ( * %1++;" = ;SL = exp( + ** ' 2 * Le SL ! # ' 2 '$ ! ! This is a flame ball solution - note for Le < > 1, T* > < Tad; for Le = 1, T* = Tad and RZ = Generally unstable R < RZ: shrinks and extinguishes R > RZ: expands and develops into steady flame RZ related to requirement for initiation of steady flame - expect Emin ~ Rz3 ... but stable for a few carefully (or accidentally) chosen mixtures AME 514 - Fall 2006 - Lecture 2 8 4 Steady (?!?) solutions How can a spherical flame not propagate??? 1.2 C ~ 1-1/r Fuel concentration T ~ 1/r Normalized temperature (T - T ) / (T f - T ) T* Temperature 1 0.8 0.6 0.4 0.2 0 0.1 Flame ball Propagating flame (!/r f = 1/10) T! Interior filled with combustion products Reaction zone ! ! 1 10 Radius / Radius of flame 100 Fuel & oxygen diffuse inward Heat & products diffuse outward Space experiments show ~ 1 cm diameter flame balls possible Movie: 500 sec elapsed time AME 514 - Fall 2006 - Lecture 2 9 Lewis number effects Energy requirement very strongly dependent on Lewis number! 1000 100 ! = 1/7 " = 10 R 3 / R 3(Le = 1) 10 1 0.1 0.01 z z 0.001 0 0.5 1 1.5 2 Lewis number From the relation Rz = &# & 1 )) " exp( ( * %1++ ** Le ' 2 '$ From computations by Tromans and Furzeland, 1986 Furzeland, ! AME 514 - Fall 2006 - Lecture 2 10 5 Lewis number effects Ok, so why does min. MIE shift to richer mixtures for higher HCs? HCs? Leeffective = effective/Deffective Deff = D of stoichiometrically limiting reactant, thus for lean mixtures Deff = Dfuel; rich mixtures Deff = DO2 Lean mixtures - Leeffective = Lefuel Mostly air, so eff air; also Deff = Dfuel CH4: DCH4 > air since MCH4 < MN2&O2 thus LeCH4 < 1, thus Leeff < 1 Higher HCs: Dfuel < air, thus Leeff > 1 - much higher MIE HCs: Rich mixtures - Leeffective = LeO2 CH4: CH4 > air since MCH4 < MN2&O2, so adding excess CH4 INCREASES Leeff Higher HCs: fuel < air since Mfuel > MN2&O2, so adding excess fuel HCs: DECREASES Leeff Actually adding excess fuel decreases both and D, but decreases more " eff = " mix ~ Const1 ;DO2 ~ M mix Const 2 Const 3 + M mix MO 2 AME 514 - Fall 2006 - Lecture 2 11 ! Dynamic analysis RZ is related (but not equal) to an ignition requirement Joulin (1985) analyzed unsteady equations for Le < 1 " (# ) ln ( " (# )) + ! # q(# ) d" (s) ds = " (# ) % 2 d# # $ s 0 2 + &* 2 ( ) Le . 1t # R(( ) 0 q" ;' " ;( " 4 $ * 2 - 1) * 1) Le 0 Rz2 Rz 4 $%RzTad (& ) , / (, and q are the dimensionless radius, time and heat input) and found at the optimal ignition duration ! E min 2 & 1$ % )&1$ Le ) 3 " 14 #( +( + - C (T $ T ) R ' % *' , * Le * ad p ad . z which has the expected form Emin ~ {energy per unit volume} x {volume of minimal flame kernel} ~ {adCp(Tad - T)} x {Rz3} { AME 514 - Fall 2006 - Lecture 2 ! 12 6 Dynamic analysis Joulin (1985) Radius vs. time vs. Minimum ignition energy vs. ignition duration vs. AME 514 - Fall 2006 - Lecture 2 13 Effect of spark gap & duration Expect "optimal" ignition duration ~ ignition kernel time scale ~ RZ2/ optimal" Duration too long - energy wasted after kernel has formed and propagated away - Emin ~ t1 Duration too short - larger shock losses, larger heat losses to electrodes due to high T kernel Expect "optimal" ignition kernel size ~ kernel length scale ~ RZ optimal" Size too large - energy wasted in too large volume - Emin ~ R3 Size too small - larger heat losses to electrodes Sloane & Ronney, 1990 Detailed chemical model Kono et al., 1976 1-step chemical model AME 514 - Fall 2006 - Lecture 2 14 7 Effect of flow environment Mean flow or random flow (i.e. turbulence) (e.g. inside IC engine or gas turbine) increases stretch, thus Emin Kono et al., 1984 DeSoete, 1984 DeSoete, AME 514 - Fall 2006 - Lecture 2 15 Effect of ignition source Laser ignition sources higher than sparks despite lower heat losses, less asymmetrical flame kernel - maybe due to higher shock losses with shorter duration laser source? Minimum ignition energy (mJ) 10 1 ps laser ns laser Lewis & von Elbe Sloane & Ronney Ronney Kingdon & Weinberg 0.1 4 5 6 7 8 9 10 11 12 Mole percent CH in air 4 Lim et al., 1996 AME 514 - Fall 2006 - Lecture 2 16 8 References De Soete, G. G.: 20th Symposium (International) on Combustion, Combustion Institute, 1984, p. 161. Dixon-Lewis, G., Shepard, I. G.: 15th Symposium (International) on Combustion, Combustion Institute, 1974, p. 1483. Frendi, A., Sibulkin, M.: "Dependence of Minimum Ignition Energy on Ignition Parameters," Combust. Sci. Tech. 73, 395-413, 1990. Joulin, G.: Combust. Sci. Tech. 43, 99 (1985). Kingdon, R. G., Weinberg, F. J.: 16th Symposium (International) on Combustion, Combustion Institute, 1976, p. 747.9924. Kono, M., Kumagai, S., Sakai, T.: 16th Symposium (International) on Combustion, Combustion Institute, 1976, p. 757. Kono, M., Hatori, K., Iinuma, K.: 20th Symposium (International) on Combustion, Combustion Institute, 1984, p. 133. Lewis, B., von Elbe, G.: Combustion, Flames, and Explosions of Gases, 3rd ed., Academic Press, 1987. Lim, E. H., McIlroy, A., Ronney, P. D., Syage, J. A., in: Transport Phenomena in Combustion (S. H. Chan, Ed.), Taylor and Francis, 1996, pp. 176-184. Ronney, P. D., Combust. Flame 62, 120 (1985). Sloane, T. M., Ronney, P. D., "A Comparison of Ignition Phenomena Modelled with Detailed and Simplified Kinetics," Combustion Science and Technology, Vol. 88, pp. 1-13 (1993). Tromans, P. S., Furzeland, R. M.: 21st Symposium (International) on Combustion, Combustion Institute, 1986, p. 1891. AME 514 - Fall 2006 - Lecture 2 17 9 ...
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