Combustion Physics (Day 4 Lecture) Chung K. Law Robert H. Goddard Professor Princeton University

Princeton-CEFRC-Combustion Institute Summer School on Combustion June 20-24, 2016

1 Day 4: Laminar Premixed Flames

1. The standard premixed flame 1. Phenomenological and asymptotic analyses 2. Parametric dependence 3. Chemical structure 2. Limit phenomena 1. The S-curve concept 2. Extinction through volumetric heat loss 3. Aerodynamics of flames 1. Hydrodynamic stretch 2. Flame stretch 3. Flamefront instabilities 2 1. The Standard Premixed Flame

3 Structure of (Standard) Premixed Flame

1. Hydrodynamic, Rankine-Hugoniot level (strong discontinuity): o Flame sheet o Uniform upstream and downstream states 2. Reaction-sheet level (weak discontinuity): o Additional preheat, diffusion zone of

o thickness D : reaction frozen due to large Ta , diffusion-convection controlling 3. Complete structure

oo o Additional reaction zone: RD  for large activation energy o Convection negligible relative to diffusion due 0 to small R , diffusion-reaction controlling • System is conservative

o o o c()T o  T q Y f   u   u u u   b u b , p b u c u 4 Flame Characteristics (1/5)

• Characteristic temperature change across reaction zone

(T )  [ TTxoo  ()]~[/( wdwdT / )]  ()/ T2 T R b fo b a T b w ~ exp( T / T ) a • Continuity of heat flux through preheat and reaction zones

oo()() TT2 R~ R b Ze 1   1 . (7.2.5) o o o DTTTTT b u() b u a

5 Flame Characteristics (2/5)

• Convection and diffusion balance in preheat zone:

ood d d d f~ [(/ cpp ) ], f ~(/ c ) d x d x d x d x

 / c p f o ~. o (7.2.6) D • Overall mass flux conservation:

Reactant mass flux entering flame ( o ) = Yfu Reaction flux through reaction zone ( oo ) Ywu b R

o o o (7.2.7)  fw~ bR

6 Flame Characteristics (3/5)

o 표 • Solving for f and ℓ퐷 from (7.2.6) and (7.2.7), using (7.2.5) o (/) cwpb (/) c (f o )2 ~, o 2 p (D ) ~ Ze (7.2.8, 9) Ze w o b • Results show three fundamental quantities governing flame response

o /cp : diffusion o o w b : reaction o o Ze : activation (Ta) and exothermicity (Tb )

7 Flame Characteristics (4/5)

o o • f ~ (  / c p ) w b : propagation rate, which is a response of the flame, is the geometric average of the diffusion and reaction rates, which are the driving forces in forming the flame.

• Dependence on transport: o o Nonpremixed flame: f ~  / c p ; diffusion dominating o o Premixed flame: f ~  / c p ; “diluted” by reaction • (7.2.8) and (7.2.9) can be alternately expressed as oo o fc Dp ~/  : depends only on transport

f o w o o ~ b : depends only on reaction o D Ze 8 Flame Characteristics: Summary (5/5)

• Since there are only two controlling processes (diffusion w o and reaction:  / c p , b ), flame characteristics are described by two independent relations, which can be expressed in three different ways to convey different messages o Balance of processes:

 / c p fo~ , f o ~ w o o o bR D o Explicit expressions for the responses:

o (/)(/)cp w b c p (fZoo e )22 ~ , ( ) ~ D o Z e w b o Explicit dependence on individual processes: f o w o fcoo~ / , ~ b Dpo D Ze 9 Specific Dependence on Pressure

on • w bp ~ pc ;  / pressure insensitive (n  1 ) o o1 / 2 o 1 / 2 n / 2 o o o 2 o f ~[(/)]~() cp w b w b ~ p , suu~ f / ~ f / p ~ p

oo~ ( /c n / w )1 / 2 ~ p  / 2 D p b • Implications:

o o For n = 2: s u  f () p ; cancellation between density and reaction; this is not a fundamental result f o o o For 0 < n < 2: increases and s u decreases with increasing p o Dependence of o on p is through reaction, not D diffusion 10 Asymptotic Analysis

11 Governing Equations (Le =1) (1/2)

d T d2 T fo c q w , • Dimensional: pc d x d x 2

d Y d2 Y fDwo   d x d x 2 d2 T d T o  TTa / • Nondimensional:    D aC Y e , d x2 d x (7.3.4)

d2 ()() T Y d T Y  0;Le  1 d x2 d x (7.3.5’)  / c o o p ~ f Da C  B C , x  x o 2  f   / c p

x  : T  T , Y  1, • B.C. : u o x : T  Tb , Y  0 , d T d Y x   :   0 . d x d x

12 Governing Equations (2/2)

• Integrating (7.3.5’) once; with b. c. at x    ,

d() T Y (TYT )   (  1). u (7.3.10’) dx x    TTo 1 T   ˆ o Evaluating (7.3.10’) at yields Tad : bu a d • Integrating (7.3.10’) again:

ˆ ()T Y  To  c e x  T o bb 1 for boundedness at xˆ 

ˆ o • Substituting YTT  b into (7.3.4) yields the single equation that needs to be solved:

d2 T d T oo  TTa /   D aCb T  T e (7.3.13) d x2 d x

o This is why   TY ˆ ˆ is called a (de-)coupling function

13 The Cold Boundary Difficulty

d2 T d T o  TTa / • Evaluating    D aC Y e , (7.3.4) d x2 d x at the x    freestream, where d2 T d T o 0 ,  00 LHS  d x2 d x o YTTRHS1,0    Thus the governing equation is unbalanced  ill posed • Difficulty exists for many steady-state problems with premixture at ambience: reactive ambience has infinite time to react  all reactants would be reacted before arrival of flame  unphysical posing of problem • Recourse o Artificial suppression of reaction term at x    o Asymptotic analysis: Rational freezing of reaction at due to large activation energy. 14 Distinguished Limit (1/2)

• Asymptotic analysis capitalizes on the largeness of activation energy which localizes reaction to a thin zone.

 TT/ • Consider reaction rate: a w~ D aC Y e

• For T a   1   and Dac푌 fixed, w 0  • No reaction in the reaction zone, obviously wrong!

• Thus the limit T a  must be taken rationally

15

o Thus the limit of must be taken rationally Distinguished Limit (2/2) • Distinguished limit:

T  requires D aw   such that is fixed . ac o TTab/ • Express D aC ~ D a e

Then 11 w~ D a e x pe x T p   D a  Z e To  T ab   TTo  b • Thus for w to remain fixed, Ze → ∞ requires

TTo thin reaction zone b

16 Procedure for Asymptotic Analysis

• Separately obtain (partial) solutions for the three zones: o Broad upstream, convective-diffusive, preheat zone, subject to b. c. at x    only. No downstream b. c. o Thin reactive-diffusive zone, without any b. c. o Broad downstream, equilibrium zone. • Partial solutions determined to leading order of reaction sheet ( Ze   ) and next order of broaden reaction zone (Ze >> 1, but finite) • Asymptotically match these partial solutions to determine the various boundary conditions, hence completing the solutions

17 Structure Equation for Inner, Reaction Zone (1/2)

• Define inner “stretched” variable and inner solution for reaction zone as ~ 2 exO/(1) T in     o  e 1    O e 

2 dd 2 o  eZe • Then G.E. becomes 11 1  e    eL eD a  1 e . dd2 • Observations: o Diffusion term: O(1); Convection term: O(e) o To retain exponential nonlinearity essential to chemical reaction: e Ze ~ O (1 )  e ~ Ze  1 identified o For reaction term to be O(1) in order to balance diffusion term:

e 2 Da o ~ O (1)  Da 0 ~ e  2 o e2: one e from thin zone, one e from reduced concentration 18

• Xxx • xx Structure Equation for Inner, Reaction Zone (2/2)

2 o o d     o 2 L e D a 1   e 1  . • Final structure equation: 1 , 2 (7.5.44,45) d  2 2 Ze 2

dd o   1  e 1 • Solution:  1 (7.5.16) dd1     Integrating with b. c.:  1  d  1 / d   0 at : 2

d  oo 1  e11 d   c   1.   e  c   1 1 in 1 in (7.5.47) d  o    1  1.   e 1  1  (7.5.48) Evaluating at :  cx     1  1  lim 111 e  lim 1  c  e  0 (7.5.49)       

• Final result:  o  1 as eigenvalue • In physical terms: 2 ( / c ) B o o 2 p c  T / T ( f )  e a b Ze 2 • Phenomenological derivation only missed the term 2 Le / Ze 19 Dependence on Tad

• Correlates well with Tad through heat of combustion o Equivalence ratio o C/H ratio

20 Dependence on Le

• More rigorous derivation shows (fo )2 ~ L e o Concentration effect

o Tf  Tad is not affected for the standard flame, hence weak

effect; exaggerated for hydrogen (Lelean0.3, Lerich2.3) o Effects are more significant for stretched flames for which

Tf is affected

21 Dependence on Molecular Structure

• Flame speed increases with ethane (C2H6),

ethylene (C2H4), and acetylene (C2H2)

Air as oxidizer Modified air to match Tad

22 Dependence on Pressure

• Dependence of flame speed on pressure is through o Chemistry o Density • Observed decreasing trend of flame speed with pressure is density effect, not chemistry effect • f o is the proper parameter because it is only affected by chemistry • f o usually increases with increasing pressure

23 Dependence on Transport Properties

• Flame speed can be manipulated through inert substitution, while keeping oxygen mole fraction fixed

o N2 and Ar have similar molecular weights and hence diffusivities, but different cp, which affects the flame temperature.

o Ar and He have the same cp but different diffusivities and densities

24 Extraction of Global n and Ea

 ln f o  ln f o n  2. ER2.o  a   ln p  (1 /T ) T ad ad p

• Results demonstrate the role of pressure on two-body branching (promoting with pressure) and three-body termination (retarding with pressure) reaction • Note: possible n < 0 25 Chemical Structure of Flames

26 Asymptotic versus Chemical Structure

• Asymptotic Structure o Broad, convective-diffusive, nonreactive zone followed by: o Narrow, diffusive-reactive zone at downstream end of flame o One-step overall reaction accounts for both activation and heat release o Chemical activation is thermal in nature

27 Asymptotic versus Chemical Structure

• Chemical Structure (with chain mechanism) o Termination reaction is temperature insensitive  can occur in upstream diffusive zone  reactions take place throughout entire flame structure o Termination reactions can be highly exothermic  substantial heat release in preheat zone o Chemical activation through radicals produced at downstream, high-temperature end that back diffuse to the preheat zone o In homogeneous system initiating radicals are produced by original fuel-oxidizer species.

28 Premixed H2-Air Flame: Diffusive Structure

• H2 diffusion layer is thicker than those of O2 and heat (T) because of its high diffusivity.

• Rapid reduction in H2 concentration (due to diffusion, not reaction) causes a bump in mole fraction of O2. This is not physical, just definitional (on mole basis)

29 Chain Structure

• Active reaction zone: 0.04 cm to 0.1 cm; two zone structure • Trailing, H production zone

o O+H2→OH+H; OH+H2 →H2O+H o H back diffuses • Leading, H consumption zone

o Back-diffused H reacts with O2 at low temperature through H+O2+M →HO2+M. o HO2 subsequently forms H2O2,

o Contrasts with H2+O2 →HO2+H in homogeneous system.

• Maximum consumption rates of H2:O2 = 2:1; occurring at same location

• H2O generated through entire reaction zone. 30 Thermal Structure

• Major exothermic reactions o H consumption layer,

H+O2+M →HO2+M o H production layer

OH+H2 →H2O+H • Major endothermic reaction

o H+O2→OH+O which is the major branching step • Maximum heat release occurs at 800 K ! • 30% heat released in H consumption layer, at 1000 K • Chemical activation, indicated by maximum H production rate, occurs around 1400 K. 31 Summary of Contrasts with Asymptotic Structure

• Important reactions occur throughout flame structure • H radical needed for initiation at leading edge is produced in the downstream and back diffuses • Maximum heat release occur at front of the active reaction zone • Substantial heat evolved in the moderately low temperature region of the flame

32 2. Limit Phenomena

33 Concepts of Ignition & Extinction

• Thermal runaway: Feedback loop involving nonlinear Arrhenius heat generation and linear heat loss • Radical runaway: Radical proliferation through chain branching • Unsteady (ignition) analysis: Tracking the temporal evolution of a reacting mixture upon application of ignition stimulus • Steady, S-curve analysis: Identify states at which steady solution does not exist for a non-reacting situation, signaling ignition, or a strongly burning situation, signaling extinction • Ultimate (extinction) consideration: system adiabaticity

34 Principle of Well-Stirred Reactor

• In steady-state operation: • Using: ˆ T Ta d c F

 TT/  TT/ V c() T T V Q B c e af T T  D a(), T  T e af o p f o c F f o Cad f B Characteristic flow time Da  C (8.1.23) VV/ Characteristic collision time

• Solutions: 1: Weakly-reactive state 2: Strong-burning state I: Ignition state E: Extinction state 3: Triple solution nonmonotonicity and hysteresis

35 Concept of S-Curve

• Ignition/extinction turning points defined by

 dln D a C  0  dT f cr • (8.1.23) yields the two roots

1 / 2 (TTTTTa do ){1   4( o a d / a )} T f , c r  . (8.1.29) 2 (1 1 /T ) a • Folding possible when {·} > 0 in (8.1.29). Otherwise S-curve is stretched for: o Low activation energy reactions o High initial temperatures 36 Premixed Flame Extinction (through Heat Loss) (1/3)

• The standard flame, being adiabatic, does not exhibit any extinction o behavior, i.e. finite f for finite Yu. • Heat loss lowers flame temperature

from Tad, leading to abrupt extinction, at finite Yu. System becomes non-conservative • Radiation from flame is an inherent heat loss mechanism • Assume loss occurs only in the preheat zone, and with L being a loss coefficient, then amount of loss is  / c  D p q L d x D L  L 0 f 37 Premixed Flame Extinction (2/3) • Overall energy conservation

 / c p o fc p()(). Tad  T u  fc p T f  T u  L (8.4.4) f  / c 2 p 2 Tfa d Tad (1  L )  T (1  L '/ f ) (8.4.4’) fT2 ad 2  / c p o L ';/ L f f f o o 2 (A) ()fT ad • In analogy to standard flame result (/) cwo oo20p (f ) ; w  e x p (  Ea / R T a d ) (B) Ze we can write

(/) cwp (f )20 ; w  e x p (  E / R T ) af Ze (C) • Using (8.4.4’) in w

0 2 0 2 w~exp[( Eaa / R )/(1  L '/ f )]  exp(  E / R )exp(  L / f ) 0 (D) LERL (/)'a 38 Premixed Flame Extinction (3/3) • C/B using D: o f 2  (/ f f oo ) 22  w / w  exp(  L / f ),

from which f22ln. fL  (8.4.9) • (8.4.9) is the generalized equation governing flame propagation with loss. o For L0 , f  1, f  f 0 o Extinction, turning point: dL ( )ex  0 df 2 1 1 / 2 o Solving: LEE e, f e

39 Other Limit Phenomena

• Flammability Limits: o For given mixture temperature and pressure, the leanest and richest concentrations beyond which flame propagation is absolutely not possible o Set the ultimate boundaries for extinction

• Blowoff and Flashback o Consequence of lack of dynamic balance between flame speed and flow speed o Has nothing to do with extinction and ignition

40 Flammability Limit

• Simulation for methane/air mixtures shows o Extinction f = 0.493 empirical: f = 0.48 o f/fo = e-1/2 ≈ 0.6

o (Tf)ext ≈ 1,450 K • Extinction temperature result corroborates with the concept of limit temperature for hydrocarbon fuels Stabilization Mechanism of Premixed Flame at Burner Rim Triple-Flame Stabilization Mechanism of Nonpremixed Flame at Burner Rim 3. Aerodynamics of Laminar Flames

44 Standard Flame vs. Real Flame (1/2)

Hydrodynamic Limit

Reaction-Sheet Limit

45 Standard Flame vs. Real Flame (2/2)

• Standard 1D Planar Flame foo f(,,) q L e w o c i, j k

oo o System is conservative, Tb T b() q c fo ~ L e o ij, • General Stretched Flame

o f f(,,;,) qc L e i, j w k K a L . Ka: Karlovitz number, representing aerodynamic effects of flow nonuniformity, flame curvature, flame/ flow unsteadiness . L: Generalized loss parameter o System could become locally or globally nonconservative

Tb T b(,,;,) q c L e i, j w k K a L o O(e) modification of flame temperature leads to O(1) change in flame speed  locally intensified burning or extinction

46

The Stretch Rate

• Definition: Lagrangian time derivative of the logarithm of

area A of a surface 1 dA   A d t

A(p,q,t) = (epdp) × (eqdq) = (dpdq)n

• Letting Vv f,, ts t    v ()() V  n   n t s, t f vs, t n ( v s  n ) • Sources of stretch:

Flow nonuniformity: vs Flame curvature: n

Flame oblique to flow vns 0.

Flame unsteadiness (Vf ≠0), with curvature  n  0

47 Examples of Stretched Flames

a • Stagnation Flame: v x,  a y , 0 ,  a  0 (k  1)

2 dR f • Expanding Spherical Flame:  0 Rf d t wasin 2 • Bunsen Flame:  0 2 R f • Each of above has its opposite analog

48 Effects of Stretch (1/2)

• Hydrodynamic stretch: Flame-sheet limit o Tangential velocity gradient: changes flame surface area and hence total burning rate, ∫ f dA o Normal velocity: Balances flame speed o Net effect: Distortion of flame geometry Modifies total burning rate (e.g. higher burning rate in turbulent flame through surface wrinkling)

49 Effects of Stretch (2/2)

• Flame stretch: reaction-sheet limit

o Tangential velocity affects normal mass flux f b entering reaction zone o For Le≠1, modifies temperature and concentration profiles differently  modifies total enthalpy and flame temperature  locally non-conservative • Hydrodynamic stretch and flame stretch strongly coupled • Stretch (i.e. convection) in thin reaction zone is unimportant

50 Example of Hydrodynamic Stretch: Corner Formation in Landau Propagation

o • Landau propagation: ssuu • Concave segment develops into a corner; convex segment flattens • Positive curvature and hence stretch dominate • Mathematically described by Burgers equation, similar to that for shock formation

51 Flame Stretch due to Flow Straining: The Stagnation Flame (1/2)

• Stretch is positive,  >0; situation reversed for  <0 • Consider total energy conservation in control volume o Diffusion: normal to reaction sheet o Convection: along (divergent,  >0) streamline • Le>1: More heat loss than reactant mass gain system sub-adiabatic • With increasing  : o Flame temperature decreases, until extinction o Flame at finite distance from stagnation surface at extinction o Complete reactant consumption at extinction

52 The Stagnation Flame (2/2) • Le<1: More reactant mass gain than heat loss  system super-adiabatic • With increasing  : o Flame temperature increases, extinction not possible as long as the flame is away from surface o Eventually flame is pushed to the stagnation surface, leading to incomplete reaction and eventually extinction

53 Flame Stretch due to Flame Curvature: The Bunsen Flame • For the concave flame curvature,  <0; expect opposite response from the  >0 stagnation flame • (Negative) flame curvature focuses heat and defocuses mass in the diffusion zone o Le>1: Super-adiabatic, burning at flame tip intensified relative to shoulder o Le<1: Sub-adiabatic, burning at tip weakens, lead to extinction (i.e. tip opening)

54 Flame Stretch due to Flame Motion: the Unsteady Spherical Flame

• For the expanding flame,  >0 ; expect similar behavior as the stagnation flame.

• An increase in flame radius Rf by dRf leads to an 2 increased amount (4 d RR Tf ) of heat transferred to the 2 preheat zone, and (4 d RR Mf ) of mass transferred. o Le>1: Sub-adiabatic, more heat transferred away o Le<1: Super-adiabatic, less heat transferred away

• Stretch rate,  = (2/Rf)(dRf/dt) continuously decreases

with increasing Rf ,

approaching the planar limit

55 Analysis (1/2) (Based on Stagnation Flame Analogy) • Energy loss/ gain in control volume TT fu Y u fu c p()()()()() T a d Tq fc  D   ss// T u T M u M

o  () TT / f  u T Normal heat flux; loss ()q /  D Y o c u M Normal chemical energy flux; gain

o  /(/) su Fraction of flux diverted out of control volume due to stretch • In nondimensional form

T T   K a0( L e 1  1) / f 2   S 0 / f 2 (A) a d f o S0 K a 0( L e  1 1) 0 0 0 o Karlovitz number, K a   /(/); s uT nondimensional stretch rate

56 Analysis (2/2)

• Following same analysis as that for premixed flame with heat loss, yields

22 o o o o 1 o ffln s , s Z e S  Z e( L e  1) K a uu • -so has the same role as L in (8.4.9), showing extinction for s<0 (i.e. loss due to stretch) • Further define Markstein number as M aoo Z e L e  1 1 • Then: s o M a o K a o

57 Response of Stretched Flame

o • From (A): Tf (>,<) Tad for S (<, >) 0 Since So= (Le-1-1)Kao, influence is lumped for nonequidiffusion and stretch. o Tf > Tad for (Ka > 0, Le < 1) or (Ka < 0, Le > 1) o Tf < Tad for (Ka > 0, Le > 1) or (Ka < 0, Le < 1) o Tf  Tad for either Ka = 0 (Le ≠ 1) or Le = 1 (Ka≠0) • Super-lumped parameter for flame speed: so= Zeo(Le-1-1)Kao:

Reactivity ╳ nonequidiffusivity ╳ stretch • Markstein number, Mao=Zeo(Le-1-1) :

Reactivity ╳ nonequidiffusivity; a property of the mixture.

58 Results on Stretched Equidiffusive Flame • Stretched flame ( ≠ 0) for equidiffusive mixture (Le = 1) is not affected by stretch: So=(Le-1-1) 0

59 Nonequidiffusive Mixtures

60 Results on Stretched Nonequidiffusive Flame

(a)Counterflow flame (b) Outwardly (c) Inwardly propagating flame propagating flame

61 Flame Images

 > 0

 < 0

62 Further Implications of Stretched Flame Phenomena

• Determination • Concentration • Flame of laminar and temperature stabilization flame speeds modifications in and blowoff flame chemistry

50

45

40

35

30

25 1920 1940 1960 1980 2000 BurningVelocity 298at (cm/s) K Year of Publication 63 Flame Front Instabilities (1/2)

Diffusional Thermal Instability Hydrodynamic Instability (Flame sheet, constant flame speed; density jump)

64 Flame Front Instabilities (2/2)

Diffusional-Thermal DL Diffusional-Thermal DL Le<1 Le>1 Le>1 Le>1 Le<1 Le>1 65 Closing Remarks of Day 4 Lecture (1/2) • The standard premixed flame o Concepts introduced: asymptotic analysis; cold boundary difficulty; distinguished limit; flame structure based on one-step and detailed chemistry; extraction of global kinetic parameters • Further studies: o Need chemical structure of hydrocarbon flames o Explain the lack of influence on laminar flame speed by: (a) low-temperature chemistry, and (b) molecular size for large n-alkanes o Is it possible to derive a semi-empirical expression for

the laminar flame speed based on Tad and extracted global kinetic parameters? 66 Closing Remarks of Day 4 Lecture (2/2) • Limit phenomena: Extinction is due to insufficient reaction time while flame blowoff/out is due to imbalance between flame and flow speeds • Extinction is in general caused by enthalpy loss in the preheat zone, leading to O(e) reduction in flame temperature and O(1) reduction in flame speed • Need to distinguish flame stabilization by auto-ignition or flame holding • What is the fate of a freely-propagating flame to increasing strength of imposed strain rate? • Need detailed study of the chemical structure of stretched flames 67 ! Daily Specials !

68 Day 4 Specials

1. Low-temperature, NTC flames 2. Pulsations in premixed and diffusion flames: a. Extinction b. Spiral patterns 3. Pulsation in self-propagating high- temperature synthesis 69

1. Low-temperature, NTC Flames

70 The Issue

5 10

4 10

• NTC behavior observed for 3

10

(ms) g

i 1 atm homogeneous mixtures in  2 3 atm 10 low- to intermediate- 5 atm 1 10

temperature range Ignition delay 0 10 atm 10 20 atm 50 atm -1 10 0.8 1 1.2 1.4 1.6 1.8 2 1000/T (1/K) • NTC behavior not observed o in extensive counterflow experiments & simulations o Finite residence time shifts ignition temperature to >1000K, hence moves ignition chemistry out of the NTC regime o Can NTC behavior be manifested for: . Low strain rate flows? . High pressures?

NTC Behavior Predicted at Low Strain Rates !

k = 200/s k = 100/s

Pressure:1 Atm. NTC Behavior Exaggerated with Increasing Pressure

2500 2500

2000 2000 1 atm 1500 1500 3 atm

1000 1000

Two-

Maximumtemperature (K) Maximumtemperature (K)

500 500 stage 0 500 Tair (K) 1000 1500 0 500 1000 1500 Tair (K) ignition k = 100/s 2500

• At lower pressures, ignition occurs in 2000 two stages, final ignition controlled by high-temperature chemistry 1500 10 atm • At higher pressures, ignition occurs 1000 in one stage, controlled by low- One-stage ignition Maximumtemperature (K) 500 temperature chemistry 0 500 Tair (K) 1000 1500 Experimental Observation of Nonpremixed LTC Flame

Infrared Images at Ignition Ignition Temperature (1 atm, strain rate: 60 /s)

A: Air vs DME

B: N2 vs DME C: Ignition (Air vs DME)

D: Ignition (N2 vs DME)

• Detailed chemical structure study shows that such flames are governed by LTC Experimental Observation of Premixed LTC Flame 0.8 1.0 1.2

1.4 1.6 1.8 • Different behavior from hot flames • Insensitive of flame location, implying small variation in flame speed with Φ variation

• Stronger chemiluminescence for richer cases 18 2a. Pulsating Extinction of Premixed and Diffusion Flames

76 The Issue: Heightened Sensitivity Near Extinction • S-curve analysis is based on steady-state considerations, showing on-off states • Near state of extinction, the burning intensity of flame is reduced, implying larger effective activation energies • Flamefront pulsating instabilities ae also promoted with increasing activation energy • Could extinction occurs in a pulsating manner, especially for Le > 1 flames?

77 The Issue: Intrinsic Chemical Influence Near Diffusion Flame Extinction

• Finite-rate chemistry plays no role in the reaction-sheet limit of diffusion flames • Flamefront (pulsating) instability intrinsically requires consideration of finite-rate chemistry • Since finite-rate chemistry is responsible for extinction, then could extinction occur in a pulsating manner even for diffusion flames, if Le > 1 for one of the reactants?

78 Oscillatory Extinction of Le > 1 Premixed Flame

Calculated extinction Calculated S- Experimental dynamics; extinction curve, showing observation of controlled by steady- earlier extinction oscillatory luminosity due to pulsation state extinction temperature

79 Oscillatory Extinction of Diffusion Flames: Computation

Calculated S-curve, Calculated extinction showing earlier dynamics; extinction extinction due to controlled by steady-state pulsation extinction temperature 80 Oscillatory Extinction of Diffusion Flames: Experiment

Steady and oscillatory extinction of diffusion flames experimentally observed

81 2b. Observations of Spirals over Flame Surfaces

82 Target Patterns (Le > 1)

Experimental conditions: • Lean butane-air, f = 0.59 • 30 atm. pressure • Consecutive frames at framing rate of 15000 fps • Frame dimension: 2.73cm × 5.46cm

Regular Spirals

70 Hydrogen, f=4.30, p=20 atm 60

50

40

Pixels 30

Starting Point 20 End Point

10 94 pixels/cm

0 0 20 40 60 80 100 120 Pixels • Rich hydrogen-air flame (f = 4.30) at 20 atm. • Spirals confined within hydrodynamic cells • Spiral can be either clockwise or counter- clockwise a b

Magnified View of the Spirals

c

Disordered Spirals

• Hydrogen-oxygen flame at 30 atm. and f = 6.00 • Disordered spirals

3. Pulsation in Self-propagating High-temperature Synthesis

87 Pulsation in Condensed-Phase Flames

• A curious result: o Propagation of solid flames exhibit temperature-sensitive Arrhenius behavior, e.g. pulsation o But reaction for individual particles is in diffusion flame- sheet limit  no finite rate chemistry

Laminated product structure due to pulsation 88 Pulsation in Condensed-Phase Flame

• Explanation: Arrhenius behavior from temperature- sensitive solid-phase diffusivity

2 TTTTaa//a d a d • Gas-phase flame speed: fg a s ~ ( D )gg  ~ (  D ) e ~ e • Condensed-phase flame speed: f2 ~ ( DD )  K ~ (  ) SHS s S H S s c

22 Since Kc (2 B D /  A )ln(1 s  Y B / s O )~ D s  fSHS ~ D s

TTTTdd//ad But Ds ~ e , therefore: fSHS ~ e

89