AME 514 Applications of Combustion Paul D. Ronney Spring 2015

AME 514 - Basic information Instructor: Paul Ronney (ronney@usc.edu) Office: OHE 430J; Phone: (213) 740-0490; Fax: (213) 740-8071 Office hours: 9:00 am – 12:00 pm Thursdays, other times by appointment Website: http://ronney.usc.edu/AME514S15 Schedule: 1 lecture per week, Tuesdays 6:40 - 9:20 pm, RTH 109 Lectures: On campus, also webcast through the USC Distance Education Network Credit: 3 units Prerequisite: AME 513 or equivalent or permission of instructor Textbook: none required, but a good general text on combustion is S. R. Turns, "An Introduction to Combustion" http://www.mhprofessional.com/product.php?isbn=0073380199 AME 514 - Spring 2015 - Lecture 1

AME 514 - Basic information Grading: 5 homework assignments,1 for each section of the course (60%), final exam (40%) Each homework will consist of (1) report on a seminal paper in the field chosen from a list provided by PDR (others OK with approval in advance from me) (2) usual analytical / numerical problems Final exam will consist of 6 problems (1 per section, plus one "anything goes"), choose 4/6 AME 514 - Spring 2015 - Lecture 1

Helpful handy hints I'll hand out printed copies of lectures so you can annotate them, but for best results, download and use PowerPoint files (includes color, movies, hyperlinks, embedded spreadsheets, etc.) If you don't have PowerPoint, you can download a free PowerPoint viewer from Microsoft's website (but then you won't be able to use the embedded spreadsheets, etc.) Please ask questions in class - the goal of the lecture is to maintain a 2-way dialogue on the subject of the lecture Bringing your laptop allows you to download files from my website as necessary and play along in the studio audience AME 514 - Spring 2015 - Lecture 1

Tentative outline 1) Advanced fundamental topics (3 lectures) Flammability and extinction Ignition Emissions formation and remediation 2) Microscale reacting flows and power generation (3 lectures) i) Scaling considerations ii) Microscale internal combustion engines iii) Microscale gas turbine and rocket propulsion iv) Thermoelectrics v) Fuel cells 3) Turbulent combustion (3 lectures) i) Premixed-gas flames ii) Non premixed flames iii) Edge flames AME 514 - Spring 2015 - Lecture 1

Tentative outline 4) Advanced propulsion systems (3 lectures) i) Hypersonic propulsion ii) Pulse detonation engines 5) Emerging needs & technologies (3 lectures) i) Applications of combustion (aka "chemically reacting flow") knowledge to other fields Frontal polymerization Bacteria growth Inertial confinement fusion Astrophysical combustion ii) New technologies Transient plasma ignition HCCI engines Microbial fuel cells iii) Future needs in combustion research Optional after-class "field trips" to combustion labs (Egolfopoulos, Ronney) Other topics (for example, optical diagnostics) may be substituted by request of a majority of registered students AME 514 - Spring 2015 - Lecture 1

Alternative topics 1) Microgravity combustion (3 lectures) i) Premixed-gas flames ii) Particle-laden flames iii) Droplets iv) Flame spread over solid fuel beds 2) Optical diagnostics (3 lectures) Quantum physics of gases Absorption / transmission techniques (absorption spectroscopy, shadowgraphy, schlieren, interferometry) Scattering techniques (Rayleigh, Raman, Mie, LDV) Fluorescence techniques 3) Computational methods in combustion (3 lectures) Governing equations Numerical methods Applications AME 514 - Spring 2015 - Lecture 1

Assignment By Friday 1/16 (Optional) email me (ronney@usc.edu) your schedule to me so I can choose office hours (default: 12:30 - 3:30 Weds.) (Optional) send suggestions to me for other lecture topics and what could be deleted (if I don't hear from you I assume you approve the currently proposed syllabus) If you want to add a unit, you must state what unit should be removed (Optional) review material on premixed flames Turns Chapters 8 & 15 Egolfopoulos's AME 513 notes My AME 513 notes (http://ronney.usc.edu/courses/ame-513/, lectures 8 & 9) AME 514 - Spring 2015 - Lecture 1

Advanced fundamental topics (3 lectures) Why study combustion? (0.1 lectures) Quick review of AME 513 concepts (0.2 lectures) Flammability & extinction limits (1.2 lectures) Ignition (0.5 lectures) Emissions formation & remediation (1 lecture)

Why study combustion? > 80% of world energy production results from combustion of fossil fuels Energy sector accounts for 9% of US Gross Domestic Product Our continuing habit of burning things and our quest to find more things to burn has resulted in Economic booms and busts Political and military conflicts Global warming (or the need to deny its existence) Human health issues AME 514 - Spring 2015 - Lecture 1

US energy flow, 2010, units 1015 BTU/yr Each 1015 BTU/yr = 33.4 gigawatts http://www.eia.gov/totalenergy/data/annual/diagram1.cfm AME 514 - Spring 2015 - Lecture 1

What do we do with combustion? Power generation (coal, natural gas) Transportation (land, air, sea vehicles) Weapons (rapid production of high-pressure gas) Heating Lighting Cooking (1/3 of the world’s population still uses biomass-fueled open fires) Hazardous waste & chemical warfare agent destruction Production of new materials, e.g. nano-materials (Future?) Portable power, e.g. battery replacement Unintended / undesired consequences Fires and explosions (residential, urban, wildland, industrial) Pollutants – NOx (brown skies, acid rain), CO (poisonous), Unburned HydroCarbons (UHCs, catalyzes production of photochemical smog), formaldehyde, particulates, SOx Global warming from CO2 & other products AME 514 - Spring 2015 - Lecture 1

What do we want to know? From combustion device Power (thermal, electrical, shaft, propulsive) Efficiency (% fuel burned, % fuel converted to power) Emissions From combustion process itself Rates of consumption Reactants Intermediates Rates of formation Products Global properties Rates of flame propagation Rates of heat generation (more precisely, rate of conversion of chemical enthalpy to thermal enthalpy) Temperatures Pressures AME 514 - Spring 2015 - Lecture 1

Why do we need to study combustion? Chemical thermodynamics only tells us the end states - what happens if we wait “forever and a day” for chemical reaction to occur We need to know how fast reactions occur How fast depends on both the inherent rates of reaction and the rates of heat and mass transport to the reaction zone(s) Chemical reactions + heat & mass transport = combustion Some reactions occur too slowly to be observed, e.g. 2 NO  N2 + O2 has an adiabatic flame temperature of 2650K but no one has ever made a flame with NO because reaction rates are too slow! Chemical reaction leads to gradients in temperature, pressure and species concentration Results in transport of energy, momentum, mass Combustion is the study of the coupling between thermodynamics, chemical reaction and transport processes AME 514 - Spring 2015 - Lecture 1

Types of combustion Premixed - reactants are intimately mixed on the molecular scale before combustion is initiated; several flavors Deflagration Detonation Homogeneous reaction Nonpremixed - reactants mix only at the time of combustion - have to mix first then burn; several flavors Gas jet (Bic lighter) Liquid fuel droplet Liquid fuel jet (e.g. candle, Diesel engine) Solid (e.g. coal particle, wood) Type Chemical reaction Heat / mass transport Momentum transport Thermo-dynamics Deflagration ✔ ✗ Detonation Homogeneous reaction Nonpremixed flames AME 514 - Spring 2015 - Lecture 1

Deflagrations Subsonic propagating front sustained by conduction of heat from the hot (burned) gases to the cold (unburned) gases which raises the temperature enough that chemical reaction can occur; since chemical reaction rates are very sensitive to temperature, most of the reaction is concentrated in a thin zone near the high-temperature side May be laminar or turbulent Temperature increases in “convection-diffusion zone” or “preheat zone” ahead of reaction zone, even though no heat release occurs there, due to balance between convection & diffusion Reactant concentration decreases in convection-diffusion zone, even though no chemical reaction occurs there, for same reason How can we have reaction at the reaction zone even though reactant concentration is low there? (See diagram…) Because reaction rate is much more sensitive to temperature than reactant concentration, so benefit of high T outweighs penalty of low concentration AME 514 - Spring 2015 - Lecture 1

Schematic of deflagration Turbulent premixed flame experiment in a fan-stirred chamber (http://www.mech-eng.leeds.ac.uk/res-group/combustion/activities/Bomb.htm) Flame thickness () ~ /SL ( = thermal diffusivity) AME 514 - Spring 2015 - Lecture 1

Structure of deflagration Outside of the thin reaction zone, only convection and diffusion of enthalpy are present, thus energy conservation can be written as, for 1D steady flow from right to left (in -x direction, as in diagram on previous page) with boundary conditions T = Tf at x = 0 (flame front) T  T∞ as x  ∞ (far upstream of flame) T  Tf as x  -∞ (far downstream of flame) noting that due to mass conservation U = ∞SL = constant and assuming k and CP are constant, AME 514 - Spring 2015 - Lecture 1

Structure of deflagration Thus, the temperature profile is an exponential with decay length = flame thickness /SL Reactant concentration profile is essentially a mirror image of the temperature profile, at least for Lewis number  /D = 1 D = reactant diffusivity AME 514 - Spring 2015 - Lecture 1

Premixed flames - detonation Supersonic front sustained by heating of gas by shock wave After shock front, need time (thus distance = time x velocity) before reaction starts to occur ("induction zone") After induction zone, chemical reaction & heat release occur Pressure & temperature behavior coupled strongly with supersonic/subsonic gasdynamics Ideally only M3 = 1 "Chapman-Jouget detonation" is stable (M = Mach number = Vc; V = velocity, c = sound speed = (RT)1/2 for ideal gas) AME 514 - Spring 2015 - Lecture 1

Premixed flames - homogeneous reaction Model for knock in premixed-charge engines Fixed mass (control mass) with uniform (in space) T, P and composition No "propagation" in space but propagation in time In laboratory, we might heat the chamber to a certain T and see how long it took to react; in engine, compression of mixture (increases P & T, thus reaction rate) will initiate reaction Fuel + O2 AME 514 - Spring 2015 - Lecture 1

"Non-premixed" or "diffusion" flames Reactants mix at the time of combustion - mix then burn - only subsonic Many types - gas jet (Bic lighter), droplet, liquid fuel (e.g. Kuwait oil fire, candle), solid (e.g. coal particle, wood) Reaction zone must lie where fuel & O2 fluxes in stoichiometric proportion Generally assume "mixed is burned" - mixing slower than chemical reaction No inherent propagation rate (flame location determined by stoich. location) or thickness ( depends on mixing layer thickness ~ (/)1/2) ( = strain rate) - unlike premixed flames with characteristic propagation rate SL and thickness  ~ /SL that are almost independent of  Candle AME 514 - Spring 2015 - Lecture 1

"Non-premixed" or "diffusion" flames Candle Kuwait Oil fire Forest fire Diesel engine AME 514 - Spring 2015 - Lecture 1

AME 514 - Spring 2015 - Lecture 1

Diesel engine combustion Two extremes Droplet combustion - vaporization of droplets is slow, so droplets burn as individuals Gas-jet flame - vaporization of droplets is so fast, there is effectively a jet of fuel vapor rather than individual droplets Reality is in between, but in Diesels usually closer to the gas jet “with extras” – regions of premixed combustion P. F. Flynn, R. P. Durrett, G. L. Hunter, A. O. zur Loye, O. C. Akinyemi, J. E. Dec, C. K. Westbrook, SAE Paper No. 1999-01-0509. AME 514 - Spring 2015 - Lecture 1

Temperatures of non-premixed flames Adiabatic temperature of premixed flame, simplest approximation (const. CP, no dissociation, complete combustion, const. pressure): Tf = T∞ + YF,0QR/CP (YF,0 = fuel mass fraction far from front, QR = fuel heating value) Non-premixed not as simple, depends on transport of reactants to front & heat/products away from front Simplest approximation: diffusion dominated, no convection AME 514 - Spring 2015 - Lecture 1

Temperatures of non-premixed flames Mass flux (per unit cross-section area of flame) of fuel to flame front = DF(∂YF/∂x) = DF(0 - YF,0)/(xf - 0) = DFYF,0/xf Heat generation rate per unit area of flame front = QRDFYF,0/xf Mass flux of O2 to flame front = DoxYox,/( - xf) Heat conducted away from flame front per unit area = k(∂T/∂x)left + k(∂T/∂x)right = k(Tf - TF,0)/xf + k(Tf - Tox,)/( - xf) Unknowns Tf & xf Equations Heat generation rate = heat conduction rate away from front QRDFYF,0/xf = k(Tf - TF,0) + k(Tf - Tox,) Mass flux of O2 / fuel = stoichiometric O2 / fuel mass ratio =  DoxYox,/( - xf) / DFYF,0/xf =  Combine to obtain AME 514 - Spring 2015 - Lecture 1

Temperatures of non-premixed flames Implications - temperature Increasing either YF,0 or Yox, increases flame temperature Tf Increasing TF,0 or Tox, increases Tf Decreasing LeF or Leox increases Tf Above results very different from premixed flames LeF & Leox don't affect adiabatic Tf Only increasing Y of stoichiometrically deficient reactant increases Tf - increasing Y of other reactant decreases Tf If TF,0 = Tox, = T∞ AND LeF = Leox = 1, then Tf = T∞ + fstoichQR/CP where fstoich = YF,0/(1+) is the mass fraction of fuel in a stoichiometric mixture of fuel + inert (fuel mass fraction YF,0) and oxygen + inert (O2 mass fraction Yox,) Very much unlike premixed flames, where Tf is essentially independent of LeF & Leox, and only depends on Y of stoichiometrically deficient reactant AME 514 - Spring 2015 - Lecture 1

Temperatures of non-premixed flames Implications - flame position Increasing YF,0 or decreasing LeF moves flame AWAY from fuel source Increasing Yox, or decreasing Leox moves flame AWAY from ox. source Since Yox,/YF,0 << 1 for fuel-air mixtures (≈ 0.058 for CH4-air), flame lies very close to air side Since Yox,/YF,0 << 1, Leox affects Tf much more than LeF), but since Leox ≈ 1 for O2 in N2, Tf is hardly affected by fuel type even though LeF varies greatly between fuels AME 514 - Spring 2015 - Lecture 1

Law of Mass Action (LoMA) First we need to describe rates of chemical reaction For a chemical reaction of the form AA + BB  CC + DD e.g. 1 H2 + 1 I2  2 HI A = H2, A = 1, B = I2, B = 1, C = HI, C = 2, D = nothing, D = 0 the Law of Mass Action (LoMA) states that the rate of reaction [ i ] = concentration of molecule i (usually moles per liter) kf = "forward" reaction rate constant AME 514 - Spring 2015 - Lecture 1

Law of Mass Action (LoMA) How to calculate [ i ]? According to ideal gas law, the total moles of gas per unit volume (all molecules, not just type i) = P/T Then [ i ] = (Total moles / volume)*(moles i / total moles), thus [ i ] = (P/T)Xi (Xi = mole fraction of i) Minus sign on d[A]/dt and d[B]/dt since A & B are being depleted Basically LoMA states that the rate of reaction is proportional to the number of collisions between the reactant molecules, which in turn is proportional to the concentration of each reactant AME 514 - Spring 2015 - Lecture 1

Comments on LoMA AME 514 - Spring 2015 - Lecture 1 The reaction rate constant kf is usually of the Arrhenius form Z = pre-exponential factor, n = another (nameless) constant, E = "activation energy" (cal/mole);  = gas constant; working backwards, units of Z must be (moles per liter)1-A-vB/(K-nsec) With 3 parameters (Z, n, E) any curve can be fit! The exponential term causes extreme sensitivity to T for E/ >> T! AME 514 - Spring 2015 - Lecture 1

Comments on LoMA "Diary of a collision" Boltzman (1800's): fraction of molecules in a gas with translational kinetic energy greater than E is proportional to exp(-E/T), thus E represents the "energy barrier" that must be overcome for reaction to occur E has no relation to enthalpy of reaction hf (or heating value QR); E affects reaction rates whereas hf & QR affect end states (e.g. Tad), though hf & QR affect reaction rates indirectly by affecting T "Diary of a collision" AME 514 - Spring 2015 - Lecture 1

Comments on LoMA The full reaction rate expression is then H2 + I2  2HI is one of few examples where the actual conversion of reactants to products occurs in a single step; most fuels of interest go through many intermediates during oxidation; even for the simplest hydrocarbon (CH4) the "standard" mechanism (http://www.me.berkeley.edu/gri_mech/) includes 53 species and 325 individual reactions! The only likely reactions in gases, where the molecules are far apart compared to their size, are 1-body, 2-body or 3-body reactions, i.e. A  products, A + B  products or A + B + C  products In liquid or solid phases, the close proximity of molecules makes n-body reactions plausible AME 514 - Spring 2015 - Lecture 1

Comments on LoMA AME 514 - Spring 2015 - Lecture 1 Recall that the forward reaction rate is Similarly, the rate of the reverse reaction can be written as kb = "backward" reaction rate constant At equilibrium, the forward and reverse rates must be equal, thus This ties reaction rate constants (kf, kb) and equilibrium constants (Ki's) together AME 514 - Spring 2015 - Lecture 1

Deflagrations - burning velocity Since the burning velocity (SL) << sound speed, the pressure across the front is almost constant How fast will the flame propagate? Simplest estimate based on the hypothesis that Rate of heat conducted from hot gas to cold gas (i) = Rate at which enthalpy is conducted through flame front (ii) = Rate at which heat is produced by chemical reaction (iii) AME 514 - Spring 2015 - Lecture 1

Deflagrations - burning velocity Estimate of i Conduction heat transfer rate = -kA(T/) k = gas thermal conductivity, A = cross-sectional area of flame T = temperature rise across front = Tproducts - Treactants  = thickness of front (unknown at this point) Estimate of ii Enthalpy flux through front = (mass flux) x Cp x T Mass flux = VA ( = density of reactants = ∞, V = velocity = SL) Enthalpy flux = ∞CpSLAT Estimate of iii Heat generated by reaction = QR x (d[fuel]/dt) x Mfuel x Volume Volume = A QR = CPT/f [F]∞ = fuel concentration in the cold reactants AME 514 - Spring 2015 - Lecture 1

Deflagrations - burning velocity, thickness Combine (i) and (ii)  = k/CpSL = /SL ( = flame thickness)  = k/Cp = thermal diffusivity (units length2/time) For air at 300K & 1 atm,  ≈ 0.2 cm2/s For gases  ≈  ( = kinematic viscosity) For gases  ~ P-1T1.7 since k ~ P0T.7,  ~ P1T-1, Cp ~ P0T0 For typical stoichiometric hydrocarbon-air flame, SL ≈ 40 cm/s, thus  ≈ /SL ≈ 0.005 cm (!) (Actually when properties are temperature-averaged,  ≈ 4/SL ≈ 0.02 cm - still small!) Combine (ii) and (iii) SL = {w}1/2 w = overall reaction rate = (d[fuel]/dt)/[fuel]∞ (units 1/s) With SL ≈ 40 cm/s,  ≈ 0.2 cm2/s, w ≈ 1600 s-1 1/w = characteristic reaction time = 625 microseconds Heat release rate per unit volume = (enthalpy flux) / (volume) = (CpSLAT)/(A) = CpSL/k)(kT)/ = (kT)/2 = (0.07 W/mK)(1900K)/(0.0002 m)2 = 3 x 109 W/m3 !!! Moral: flames are thin, fast and generate a lot of heat! AME 514 - Spring 2015 - Lecture 1

Deflagrations - burning velocity More rigorous analysis (Zeldovich, 1940) Tad = adiabatic flame temperature; T∞ = ambient temperature Note same form SL ~ (aw)1/2 as simple estimate, where w ~ Z[F]∞-1e-b Still more rigorous (Bush and Fendell, 1970, n = 1) Note results are same to leading order for n = 1, Bush and Fendell added next order in expansion in powers of 1/b(1-e) AME 514 - Spring 2015 - Lecture 1

Deflagrations - burning velocity How does SL vary with pressure? Define order of reaction (n) = A+ B; since Thus SL ~ {w}1/2 ~ {P-1Pn-1}1/2 ~ P(n-2)/2 For typical n = 2, SL independent of pressure For "real" hydrocarbons, working backwards from experimental results, we find typically SL ~ P-0.4, thus n ≈ 1.2 AME 514 - Spring 2015 - Lecture 1

Deflagrations - temperature effect Since Zeldovich number () >> 1 For typical hydrocarbon-air flames, E ≈ 40 kcal/mole  = 1.987 cal/mole, Tf ≈ 2200K if adiabatic   ≈ 10, at T close to Tf, w ~ T10 !!!  Thin reaction zone concentrated near highest temp.  In Zeldovich (or any) estimate of SL, overall reaction rate  must be evaluated at Tad, not T∞ How can we estimate E? If reaction rate depends more on E than concentrations [ ], SL ~ {w}1/2 ~ {exp(-E/T)}1/2 ~ exp(E/2T) - Plot of ln(SL) vs. 1/Tad has slope of -E/2 If  isn't large, then w(T∞) ≈ w(Tad) and reaction occurs even in the cold gases, so no control over flame is possible! Since SL ~ w1/2, SL ~ (T)1/2 ~ T5 typically! AME 514 - Spring 2015 - Lecture 1

Deflagrations - summary These relations show the effect of Tad (depends on fuel & stoichiometry),  (depends on diluent gas (usually N2) & P), w (depends on fuel, T, P) and pressure (engine condition) on laminar burning rates Re-emphasize: these estimates are based on an overall reaction rate; real flames have 1000's of individual reactions between 100's of species - but we can work backwards from experiments or detailed calculations to get these estimates for the overall reaction rate parameters AME 514 - Spring 2015 - Lecture 1

Deflagrations Schematic of flame temperatures and laminar burning velocities Real data on SL (Vagelopoulos & Egolfopoulos, 1998) AME 514 - Spring 2015 - Lecture 1

Advanced fundamental topics Flammability & extinction limits Description of flammability limits Chemical kinetics of limits Time scales Mechanisms of limits Buoyancy effects - upward & downward Conduction heat loss to tube walls (Sidebar) more about flames in tubes Radiation heat loss Optically thin limit (Sidebar) reabsorption effects Aerodynamic stretch Chemical fire suppressants AME 514 - Spring 2015 - Lecture 1

Flammability and extinction limits Reference: Ju, Y., Maruta, K., Niioka, T., "Combustion Limits," Applied Mechanics Reviews, Vol. 53, pp. 257-277 (2001) Too lean or too rich mixtures won't burn - flammability limits Even if mixture is flammable, still won't burn in certain environments Small diameter tubes Strong hydrodynamic strain or turbulence High or low gravity High or low pressure Understanding needed for combustion engines & industrial combustion processes (leaner mixtures  lower Tad  lower NOx); fire & explosion hazard management, fire suppression, ... AME 514 - Spring 2015 - Lecture 1

Flammability limits - basic observations Limits occur for mixtures that are thermodynamically flammable - theoretical adiabatic flame temperature (Tad) far above ambient temperature (T∞) Limits usually characterized by finite (not zero) burning velocity at limit Models of limits due to losses - most important prediction: burning velocity at the limit (SL,lim) - better test of limit predictions than composition at limit AME 514 - Spring 2015 - Lecture 1

Premixed-gas flames – flammability limits 2 limit mechanisms, (1) & (2), yield similar fuel % and Tad at limit but very different SL,lim AME 514 - Spring 2015 - Lecture 1

Flammability limits in vertical tubes Most common apparatus - vertical tube (typ. 5 cm in diameter) Ignite mixture at one end of tube, if it propagates to other end, it's "flammable" Limit composition depends on orientation - buoyancy effects Upward propagation Downward propagation AME 514 - Spring 2015 - Lecture 1

Chemical kinetics of limits Lean hydrocarbon-air flames: main branching reaction (promotes combustion) is H + O2  OH + O; d[O2]/dt = -1016.7[H][O2]T-0.8e-16500/RT [ ]: mole/cm3; T: K; R: cal/mole-K; t: sec Depends on P2 since [ ] ~ P, strongly dependent on T Why important? Only energetically viable way to break O=O bond (120 kcal/mole), even though [H] is small Main H consumption reaction H + O2 + M  HO2 + M; {M = any molecule} d[O2]/dt = -1015.2[H][O2][M]T0e+1000/RT for M = N2 (higher rate for CO2 and especially H2O) Depends on P3, nearly independent of T Why important? Inhibits combustion by replacing H with much less active HO2 Branching or inhibition may be faster depending on T and P AME 514 - Spring 2015 - Lecture 1

Chemical kinetics of limits Rates equal ("crossover") when [M] = 101.5T-0.8e-17500/RT Ideal gas law: P = [M]RT thus P = 103.4T0.2e-17500/RT (P in atm)  crossover at 950K for 1 atm, higher T for higher P …but this only indicates that chemical mechanism may change and perhaps overall W drop rapidly below some T Computations show no limits without losses – no purely chemical criterion (Lakshmisha et al., 1990; Giovangigli & Smooke, 1992) - for steady planar adiabatic flames, burning velocity decreases smoothly towards zero as fuel concentration decreases (domain sizes up to 10 m, SL down to 0.02 cm/s) …but as SL decreases, d increases - need larger computational domain or experimental apparatus Also more buoyancy & heat loss effects as SL decreases …. AME 514 - Spring 2015 - Lecture 1

Chemical kinetics of limits Ju, Masuya, Ronney (1998) Ju et al., 1998 AME 514 - Spring 2015 - Lecture 1

Aerodynamic effects on premixed flames Aerodynamic effects occur on a large scale compared to the transport or reaction zones but affect SL and even existence of the flame Why only at large scale? Re on flame scale ≈ SL/ ( = kinematic viscosity) Re = (SL/)() = (1)(1/Pr) ≈ 1 since Pr ≈ 1 for gases Reflame ≈ 1  viscosity suppresses flow disturbances Key parameter: stretch rate () Generally  ~ U/d U = characteristic flow velocity d = characteristic flow length scale AME 514 - Spring 2015 - Lecture 1

Aerodynamic effects on premixed flames Strong stretch ( ≥ w ~ SL2/ or Karlovitz number Ka  /SL2 ≥ 1) extinguishes flames Moderate stretch strengthens flames for Le < 1 Buckmaster & Mikolaitis, 1982a (Ze = b in my notation), cold reactants against adiabatic products SL/SL(unstrained, adiabatic flame) ln(Ka) AME 514 - Spring 2015 - Lecture 1

Lewis number tutorial Le affects flame temperature in curved (shown below) or stretched flames When Le < 1, additional thermal enthalpy loss in curved/stretched region is less than additional chemical enthalpy gain, thus local flame temperature in curved region is higher, thus reaction rate increases drastically, local burning velocity increases Opposite behavior for oppositely curved flames AME 514 - Spring 2015 - Lecture 1

TIME SCALES - premixed-gas flames See Ronney (1998) Chemical time scale tchem ≈ /SL ≈ (a/SL)/SL ≈ a/SL2 a = thermal diffusivity [typ. 0.2 cm2/s], SL = laminar flame speed [typ. 40 cm/s] Conduction time scale tcond ≈ Tad/(dT/dt) ≈ d2/16a d = tube or burner diameter Radiation time scale trad ≈ Tad/(dT/dt) ≈ Tad/(L/rCp) (L = radiative heat loss per unit volume) Optically thin radiation: L = 4sap(Tad4 – T∞4) ap = Planck mean absorption coefficient [typ. 2 m-1 at 1 atm] L ≈ 106 W/m3 for HC-air combustion products trad ~ P/sap(Tad4 – T∞4) ~ P0, P = pressure Buoyant transport time scale t ~ d/V; V ≈ (gd(Dr/r))1/2 ≈ (gd)1/2 (g = gravity, d = characteristic dimension) Inviscid: tinv ≈ d/(gd)1/2 ≈ (d/g)1/2 (1/tinv ≈ Sinv) Viscous: d ≈ n/V Þ tvis ≈ (n/g2)1/3 (n = viscosity [typ. 0.15 cm2/s]) AME 514 - Spring 2015 - Lecture 1

Time scales (hydrocarbon-air, 1 atm) Conclusions Buoyancy unimportant for near-stoichiometric flames (tinv & tvis >> tchem) Buoyancy strongly influences near-limit flames at 1g (tinv & tvis < tchem) Radiation effects unimportant at 1g (tvis << trad; tinv << trad) Radiation effects dominate flames with low SL (trad ≈ tchem), but only observable at µg Small trad (a few seconds) - drop towers useful Radiation > conduction only for d > 3 cm Re ~ Vd/n ~ (gd3/n2)1/2 Þ turbulent flow at 1g for d > 10 cm AME 514 - Spring 2015 - Lecture 1

Flammability limits due to losses Golden rule: at limit Why 1/b not 1? T can only drop by O(1/b) before extinction - O(1) drop in T means exponentially large drop in , thus exponentially small SL (could also say heat generation occurs only in /b region whereas loss occurs over  region) AME 514 - Spring 2015 - Lecture 1

Flammability limits due to losses Heat loss to walls tchem ~ tcond  SL,lim ≈ (8)1/2a/d at limit or Pelim  SL,limd/a ≈ (8)1/2 ≈ 9 Actually Pelim ≈ 40 due to temperature averaging - consistent with experiments (Jarosinsky, 1983) Upward propagation in tube Rise speed at limit ≈ 0.3(gd)1/2 due to buoyancy alone (same as air bubble rising in water-filled tube (Levy, 1965)) Pelim ≈ 0.3 Grd1/2; Grd = Grashof number  gd3/n2 Causes stretch extinction (Buckmaster & Mikolaitis, 1982b): tchem ≈ tinv or 1/tchem ≈ Sinv Note f(Le) < 1 for Le < 1, f(Le) > 1 for Le > 1 - flame can survive at lower SL (weaker mixtures) when Le < 1 AME 514 - Spring 2015 - Lecture 1

Difference between S and SL long flame skirt at high Gr or with small f (low Lewis number, Le) (but note SL not really constant over flame surface!) AME 514 - Spring 2015 - Lecture 1

Flammability limits due to losses Downward propagation – sinking layer of cooling gases near wall outruns & "suffocates" flame (Jarosinsky et al., 1982) tchem ≈ tvis Þ SL,lim ≈ 1.3(ga)1/3 Pelim ≈ 1.65 Grd1/3 Can also obtain this result by equating SL to sink rate of thermal boundary layer = 0.8(gx)1/2 for x =  Consistent with experiments varying d and a (by varying diluent gas and pressure) (Wang & Ronney, 1993) and g (using centrifuge) (Krivulin et al., 1981) More on limits in tubes… AME 514 - Spring 2015 - Lecture 1

Flammability limits in vertical tubes Upward propagation Downward propagation AME 514 - Spring 2015 - Lecture 1

Flammability limits in tubes Upward propagation - Wang & Ronney, 1993 AME 514 - Spring 2015 - Lecture 1

Flammability limits in tubes Downward propagation - Wang & Ronney, 1993 AME 514 - Spring 2015 - Lecture 1

Flammability limits – losses - continued… Big tube, no gravity – what causes limits? Radiation heat loss (trad ≈ tchem) (Joulin & Clavin, 1976; Buckmaster, 1976) What if not at limit? Heat loss still decreases SL, actually 2 possible speeds for any value of heat loss, but lower one generally unstable AME 514 - Spring 2015 - Lecture 1

Flammability limits – losses - continued… Doesn't radiative loss decrease for weaker mixtures, since temperature is lower? NO! Predicted SL,lim (typically 2 cm/s) consistent with µg experiments (Ronney, 1988; Abbud-Madrid & Ronney, 1990) AME 514 - Spring 2015 - Lecture 1

Reabsorption effects Is radiation always a loss mechanism? Reabsorption may be important when aP-1 < d Small concentration of blackbody particles - decreases SL (more radiative loss) More particles - reabsorption extend limits, increases SL Abbud-Madrid & Ronney (1993) AME 514 - Spring 2015 - Lecture 1

Reabsorption effects on premixed flames Gases – much more complicated because absorption coefficient depends strongly on wavelength and temperature & some radiation always escapes (Ju, Masuya, Ronney 1998) Absorption spectra of products different from reactants Spectra broader at high T than low T Dramatic difference in SL & limits compared to optically thin AME 514 - Spring 2015 - Lecture 1

Stretched flames - spherical Spherical expanding flames, Le < 1: stretch allows flames to exist in mixtures below radiative limit until flame radius rf is too large & curvature benefit too weak (Ronney & Sivashinsky, 1989) Adds stretch term (2S/R) (R = scaled flame radius; R > 0 for Le < 1; R < 0 for Le > 1) and unsteady term (dS/dR) to planar steady equation Dual limit: radiation at large rf, curvature-induced stretch at small rf (ignition limit) AME 514 - Spring 2015 - Lecture 1

Stretched flames - spherical Theory (Ronney & Sivashinsky, 1989) Experiment (Ronney, 1985) AME 514 - Spring 2015 - Lecture 1

Stretched counterflow or stagnation flames Mass + momentum conservation, 2D, const. density () (ux, uy = velocity components in x, y directions) admit an exact, steady (∂/∂t = 0) solution which is the same with or without viscosity (!!!):  = rate of strain (units s-1) Similar result in 2D axisymmetric geometry: Very simple flow characterized by a single parameter , easily implemented experimentally using counter-flowing round jets… AME 514 - Spring 2015 - Lecture 1

Stretched counterflow or stagnation flames S = duz/dz – flame located where uz = SL Increased stretch pushes flame closer to stagnation plane - decreased volume of radiant products Similar Le effects as curved flames z AME 514 - Spring 2015 - Lecture 1

Premixed-gas flames - stretched flames Stretched flames with radiation (Ju et al., 1999): dual limits, flammability extension even for Le >1, multiple solutions (which ones are stable?) AME 514 - Spring 2015 - Lecture 1

Premixed-gas flames - stretched flames Dual limits & Le effects seen in µg experiments, but evidence for multivalued behavior inconclusive Guo et al. (1997) AME 514 - Spring 2015 - Lecture 1

Chemical fire suppressants Key to suppression is removal of H atoms H + HBr  H2 + Br H + Br2  HBr + Br Br + Br + M  Br2 + M -------------------------------- H + H  H2 Why Br and not Cl or F? HCl and HF too stable, 1st reaction too slow HBr is a corrosive liquid, not convenient - use CF3Br (Halon 1301) - Br easily removed, remaining CF3 very stable, high CP to soak up heat Problem - CF3Br very powerful ozone depleter - banned! Alternatives not very good; best ozone-friendly chemical alternative is probably CF3CH2CF3 or CF3H Other alternatives (e.g. water mist) also being considered AME 514 - Spring 2015 - Lecture 1

Chemical fire suppressants AME 514 - Spring 2015 - Lecture 1

References AME 514 - Spring 2015 - Lecture 1 Abbud-Madrid, A., Ronney, P. D., "Effects of Radiative and Diffusive Transport Processes on Premixed Flames Near Flammability Limits," Twenty Third Symposium (International) on Combustion, Combustion Institute, 1990, pp. 423-431. Abbud-Madrid, A., Ronney, P. D., "Premixed Flame Propagation in an Optically-Thick Gas," AIAA Journal, Vol. 31, pp. 2179-2181 (1993). Buckmaster, J. D. (1976). The quenching of deflagration waves, Combust. Flame 26, 151 -162. Buckmaster, J. D., Mikolaitis, D. (1982a). The premixed flame in a counterflow, Combust. Flame 47, 191-204 . Buckmaster, J. D., Mikolaitis, D. (1982b). A flammability-limit model upward propagation through lean methan-air mixtures in a standard flammability tube. Combust. Flame 45, pp 109-119. Giovangigli, V. and Smooke, M. (1992). Application of Continuation Methods to Plane Premixed Laminar Flames, Combust. Sci. Tech. 87, 241-256. Guo, H., Ju, Y., Maruta, K., Niioka, T., Liu, F., Combust. Flame 109:639-646 (1997). Jarosinsky, J. (1983). Flame quenching by a cold wall, Combust. Flame 50, 167. Jarosinsky, J., Strehlow, R. A., Azarbarzin, A. (1982). The mechanisms of lean limit extinguishment of an upward and downward propagating flame in a standard flammability tube, Proc. Combust. Inst. 19, 1549-1557. Joulin, G., Clavin, P. (1976). Analyse asymptotique des conditions d'extinction des flammes laminaries, Acta Astronautica 3, 223. Ju, Y., Masuya, G. and Ronney, P. D., "Effects of Radiative Emission and Absorption on the Propagation and Extinction of Premixed Gas Flames" Twenty-Seventh International Symposium on Combustion, Combustion Institute, Pittsburgh, 1998, pp. 2619-2626. Ju, Y., Guo, H., Liu, F., Maruta, K. (1999). Effects of the Lewis number and radiative heat loss on the bifurcation of extinction of CH4-O2-N2-He flames, J. Fluid Mech. 379, 165-190. AME 514 - Spring 2015 - Lecture 1

References Krivulin, V. N., Kudryavtsev, E. A., Baratov, A. N., Badalyan, A. M., Babkin, V. S. (1981). Effect of acceleration on the limits of propagation of homogeneous gas mixtures, Combust. Expl. Shock Waves (Engl. Transl.) 17, 37-41. Lakshmisha, K. N., Paul, P. J., Mukunda, H. S. (1990). On the flammability limit and heat loss in flames with detailed chemistry, Proc. Combust. Inst. 23, 433-440. Levy, A. (1965). An optical study of flammability limits, Proc. Roy. Soc. (London) A283, 134. Ronney, P.D., "Effect of Gravity on Laminar Premixed Gas Combustion II: Ignition and Extinction Phenomena," Combustion and Flame, Vol. 62, pp. 120-132 (1985). Ronney, P.D., "On the Mechanisms of Flame Propagation Limits and Extinction Processes at Microgravity," Twenty Second Symposium (International) on Combustion, Combustion Institute, 1988, pp. 1615-1623. Ronney, P. D., "Understanding Combustion Processes Through Microgravity Research," Twenty-Seventh International Symposium on Combustion, Combustion Institute, Pittsburgh, 1998, pp. 2485-2506 Ronney, P.D., Sivashinsky, G.I., "A Theoretical Study of Propagation and Extinction of Nonsteady Spherical Flame Fronts," SIAM Journal on Applied Mathematics, Vol. 49, pp. 1029-1046 (1989). Wang, Q., Ronney, P. D. (1993). Mechanisms of flame propagation limits in vertical tubes, Paper no. 45, Spring Technical Meeting, Combustion Institute, Eastern/Central States Section, March 15-17, 1993, New Orleans, LA. AME 514 - Spring 2015 - Lecture 1

Advanced fundamental topics End of flammability limits notes - sidebar topics from here on …

Effects of radiative emission and absorption on the propagation and extinction of premixed gas flames Yiguang Ju and Goro Masuya Department of Aeronautics & Space Engineering Tohoku University, Aoba-ku, Sendai 980, Japan Paul D. Ronney Department of Aerospace & Mechanical Engineering University of Southern California Los Angeles, CA 90089-1453 Published in Proceedings of the Combustion Institute, Vol. 27, pp. 2619-2626 (1998)

Background Microgravity experiments show importance of radiative loss on flammability & extinction limits when flame stretch, conductive loss, buoyant convection eliminated – experiments consistent with theoretical predictions of Burning velocity at limit (SL,lim) Flame temperature at limit Loss rates in burned gases …but is radiation a fundamental extinction mechanism? Reabsorption expected in large, "optically thick" systems Theory (Joulin & Deshaies, 1986) & experiment (Abbud-Madrid & Ronney, 1993) with emitting/absorbing blackbody particles Net heat losses decrease (theoretically to zero) Burning velocities (SL) increase Flammability limits widen (theoretically no limit) … but gases, unlike solid particles, emit & absorb only in narrow spectral bands - what will happen? AME 514 - Spring 2015 - Lecture 1

Background (continued) Objectives Model premixed-gas flames computationally with detailed radiative emission-absorption effects Compare results to experiments & theoretical predictions Practical applications Combustion at high pressures and in large furnaces IC engines: 40 atm - Planck mean absorption length (LP) ≈ 4 cm for combustion products ≈ cylinder size Atmospheric-pressure furnaces - LP ≈ 1.6 m - comparable to boiler dimensions Exhaust-gas or flue-gas recirculation - absorbing CO2 & H2O present in unburned mixture - reduces LP of reactants & increases reabsorption effects AME 514 - Spring 2015 - Lecture 1

Numerical model Steady planar 1D energy & species conservation equations CHEMKIN with pseudo-arclength continuation 18-species, 58-step CH4 oxidation mechanism (Kee et al.) Boundary conditions Upstream - T = 300K, fresh mixture composition, inflow velocity SL at x = L1 = -30 cm Downstream - zero gradients of temperature & composition at x = L2 = 400 cm Radiation model CO2, H2O and CO Wavenumbers (w) 150 - 9300 cm-1, 25 cm-1 resolution Statistical Narrow-Band model with exponential-tailed inverse line strength distribution S6 discrete ordinates & Gaussian quadrature 300K black walls at upstream & downstream boundaries Mixtures CH4 + {0.21O2+(0.79-g)N2+ g CO2} - substitute CO2 for N2 in "air" to assess effect of absorbing ambient AME 514 - Spring 2015 - Lecture 1

Results - flame structure Adiabatic flame (no radiation) The usual behavior Optically-thin Volumetric loss always positive Maximum T < adiabatic T decreases "rapidly" in burned gases "Small" preheat convection-diffusion zone - similar to adiabatic flame With reabsorption Volumetric loss negative in reactants - indicates net heat transfer from products to reactants via reabsorption Maximum T > adiabatic due to radiative preheating - analogous to Weinberg's "Swiss roll" burner with heat recirculation T decreases "slowly" in burned gases - heat loss reduced "Small" preheat convection-diffusion zone PLUS "Huge" convection-radiation preheat zone AME 514 - Spring 2015 - Lecture 1

Flame zone detail Radiation zones (large scale) Flame structures Flame zone detail Radiation zones (large scale) Mixture: CH4 in "air", 1 atm, equivalence ratio (f) = 0.70; g = 0.30 ("air" = 0.21 O2 + .49 N2 + .30 CO2) AME 514 - Spring 2015 - Lecture 1

Radiation effects on burning velocity (SL) CH4-air (g = 0) Minor differences between reabsorption & optically-thin ... but SL,lim 25% lower with reabsorption; since SL,lim ~ (radiative loss)1/2, if net loss halved, then SL,lim should be 1 - 1/√2 = 29% lower with reabsorption SL,lim/SL,ad ≈ 0.6 for both optically-thin and reabsorption models - close to theoretical prediction (e-1/2) Interpretation: reabsorption eliminates downstream heat loss, no effect on upstream loss (no absorbers upstream); classical quenching mechanism still applies g = 0.30 (38% of N2 replaced by CO2) Massive effect of reabsorption SL much higher with reabsorption than with no radiation! Lean limit much leaner (f = 0.44) than with optically-thin radiation (f = 0.68) AME 514 - Spring 2015 - Lecture 1

Comparisons of burning velocities g = 0 (no CO2 in ambient) g = 0.30 Note that without CO2 (left) SL & peak temperatures of reabsorbing flames are slightly lower than non-radiating flames, but with CO2 (right), SL & T are much higher with reabsorption. Optically thin always has lowest SL & T, with or without CO2 Note also that all experiments lie below predictions - are published chemical mechanisms accurate for very lean mixtures? AME 514 - Spring 2015 - Lecture 1

Mechanisms of extinction limits Why do limits exist even when reabsorption effects are considered and the ambient mixture includes absorbers? Spectra of product H2O different from CO2 (Mechanism I) Spectra broader at high T than low T (Mechanism II) Radiation reaches upstream boundary due to "gaps" in spectra - product radiation that cannot be absorbed upstream Absorption spectra of CO2 & H2O at 300K & 1300K AME 514 - Spring 2015 - Lecture 1

Mechanisms of limits (continued) Flux at upstream boundary shows spectral regions where radiation can escape due to Mechanisms I and II - "gaps" due to mismatch between radiation emitted at the flame front and that which can be absorbed by the reactants Depends on "discontinuity" (as seen by radiation) in T and composition at flame front - doesn't apply to downstream radiation because T gradient is small Behavior cannot be predicted via simple mean absorption coefficients - critically dependent on compositional & temperature dependence of spectra Spectrally-resolved radiative flux at upstream boundary for a reabsorbing flame (πIb = maximum possible flux) AME 514 - Spring 2015 - Lecture 1

Effect of domain size Limit f & SL,lim decreases as upstream domain length (L1) increases - less net heat loss Significant reabsorption effects seen at L1 = 1 cm even though LP ≈ 18.5 cm because of existence of spectral regions with L(w) ≈ 0.025 cm-atm (!) L1 > 100 cm required for domain-independent results due to band "wings" with small L(w) Downstream domain length (L2) has little effect due to small gradients & nearly complete downstream absorption Effect of upstream domain length (L1) on limit composition (o) & SL for reabsorbing flames. With-out reabsorption, o = 0.68, thus reabsorption is very important even for the smallest L1 shown AME 514 - Spring 2015 - Lecture 1

Effect of g (CO2 substitution level) f = 1.0: little effect of radiation; f = 0.5: dominant effect - why? (1) f = 0.5: close to radiative extinction limit - large benefit of decreased heat loss due to reabsorption by CO2 (2) f = 0.5: much larger Boltzman number (defined below) (B) (≈127) than f = 1.0 (≈11.3); B ~ potential for radiative preheating to increase SL Note with reabsorption, only 1% CO2 addition nearly doubles SL due to much lower net heat loss! Effect of CO2 substitution for N2 on SL AME 514 - Spring 2015 - Lecture 1

Effect of g (continued) Effect of CO2 substitution on flammability limit composition Effect of CO2 substitution on SL,lim/SL,adiabatic Limit mixture much leaner with reabsorption than optically thin Limit mixture decreases with CO2 addition even though CP,CO2 > CP,N2 SL,lim/SL,ad always ≈ e-1/2 for optically thin, in agreement with theory SL,lim/SL,ad up to ≈ 20 with reabsorption! AME 514 - Spring 2015 - Lecture 1

Comparison to analytic theory Joulin & Deshaies (1986) - analytical theory Comparison to computation - poor Better without H2O radiation (mechanism (I) suppressed) Slightly better still without T broadening (mechanism (II) suppressed, nearly adiabatic) Good agreement when L(w) = LP = constant - emission & absorption across entire spectrum rather than just certain narrow bands. Drastic differences between last two cases, even though both have no net heat loss and have same Planck mean absorption lengths! Effect of different radiation models on SL and comparison to theory AME 514 - Spring 2015 - Lecture 1

Comparison with experiment No directly comparable expts., BUT... Zhu, Egolfopoulos, Law (1988) CH4 + (0.21O2 + 0.79 CO2) (g = 0.79) Counterflow twin flames, extrapolated to zero strain L1 = L2 ≈ 0.35 cm chosen since 0.7 cm from nozzle to stagnation plane No solutions for adiabatic flame or optically-thin radiation (!) Moderate agreement with reabsorption Abbud-Madrid & Ronney (1990) (CH4 + 4O2) + CO2 Expanding spherical flame at µg L1 = L2 ≈ 6 cm chosen (≈ flame radius) Optically-thin model over-predicts limit fuel conc. & SL,lim Reabsorption model underpredicts limit fuel conc. but SL,lim well predicted - net loss correctly calculated Comparison of computed results to experiments where reabsorption effects may have been important AME 514 - Spring 2015 - Lecture 1

Conclusions Reabsorption increases SL & extends limits, even in spectrally radiating gases Two loss mechanisms cause limits even with reabsorption (I) Mismatch between spectra of reactants & products (II) Temperature broadening of spectra Results qualitatively & sometimes quantitatively consistent with theory & experiments Behavior cannot be predicted using mean absorption coefficients! Can be important in practical systems AME 514 - Spring 2015 - Lecture 1

Planck mean absorption coefficient AME 514 - Spring 2015 - Lecture 1

More on flammability limits in tubes Experiments show that the flammability limits are wider for upward than downward propagation, corresponding to SL,lim,down > SL,lim,up since SL is lower for more dilute mixtures …but note according to the models, SL,lim,down > SL,lim,up when Gr < 10,000 f12 but also need Pe > 40 (not in heat-loss limit) Gr > 18,000  at high Le (high f) & 18,000 < Gr < 10,000 f12, upward limits may be narrower than downward limits (?!?) Never observed, but appropriate conditions never tested - high Le, moderate Gr AME 514 - Spring 2015 - Lecture 1

Turbulent limit behavior? Burned gases are turbulent if Re > 2000 Upward limit: Re ≈ S(r∞/rad-1)d/n  Gr > 300 x 106 Downward limit: Re ≈ SL(r∞/rad-1)d/n  Gr > 40 x 109 - not accessible with current apparatus "Standard" condition (5 cm tube, air, 1 atm): Gr ≈ 3.0 x 106 : always laminar! AME 514 - Spring 2015 - Lecture 1

Approach Study limit mechanisms by measuring Sb,lim for varying Tube diameter  = (diluent, pressure) Le  = Le(diluent, fuel) and determine scaling relations (Pelim vs. Gr & Le) Apparatus Tubes with 0.5 cm < D < 20 cm; open at ignition end He, Ne, N2, CO2, SF6 diluents 0.1 atm < P < 10 atm 2 x 102 < Gr < 2 x 109 Absorption tank to maintain constant P during test Thermocouples Procedure Fixed fuel:O2 ratio Vary diluent conc. until limit determined Measure Sb,lim & temperature characteristics at limit AME 514 - Spring 2015 - Lecture 1

Results - laminar flames Upward limit Low Gr Pelim ≈ 40 ± 10 at low Gr Highest T near centerline of tube High Gr Pelim ≈ 0.3 Gr1/2 at high Gr Highest T near centerline (low Le) Highest T near wall (high Le) Indicates strain effects at limit Downward Pelim ≈ 1.5 Gr1/3 at high Gr Upward limits narrower than downward limits at high Le & moderate Gr, e.g. lean C3H8-O2-Ne, P = 1 atm, D = 2.5 cm, Le ≈ 2.6, Gr ≈ 19,000: fuel up / fuel down ≈ 0.83 AME 514 - Spring 2015 - Lecture 1

Limit regimes - upward propagation AME 514 - Spring 2015 - Lecture 1

Limit regimes - downward propagation AME 514 - Spring 2015 - Lecture 1

Flamelet vs. distributed combustion Abdel-Gayed & Bradley (1989): distributed if Ka > 0.3 Ka  0.157 ReT-1/2U2; ReT  u'LI/n, U  u'/SL LI  integral scale of turbulence Estimate for pipe flow u' ≈ 0.05S(r∞/rad-1); LI ≈ d SL,lim from Buckmaster & Mikolaitis (1982) model  Ka ≈ 0.0018/f2 Gr1/4 ≈ 0.3/f2 at Gr = 700 x 106 Distributed combustion probable at high Gr, moderate Le Away from limit - wrinkled, unsteady skirt AME 514 - Spring 2015 - Lecture 1

Limit flame - distributed combustion C3H8-O2-CO2, P = 2.5 atm, d = 10 cm, Le ≈ 1.3, Gr ≈ 6 x 108 AME 514 - Spring 2015 - Lecture 1

Farther from limit - wrinkled skirt C3H8-O2-CO2, P = 2.5 atm, d = 10 cm, Le ≈ 1.3, Gr ≈ 6 x 108 AME 514 - Spring 2015 - Lecture 1

Lower Le - boiling tip, no tip opening C3H8-O2-SF6, P = 2.5 atm, d = 10 cm, Le ≈ 0.7, Gr ≈ 5 x 109 AME 514 - Spring 2015 - Lecture 1

Turbulent flame quenching Why does distributed flame exist at  ≈ 4d, whereas laminar flame extinguishes when  ≈ 1/40 d (Pe = 40)? Analysis Nu = hd/k ≈ 0.023 Re.8 Pr.3 (turbulent heat transfer in pipe) Qloss ≈ hAT; A = πd; let  = n D (n is unknown) Qgen ≈ oSbπd2CpT; Sb = 0.3(gd)1/2 Qloss/Qgen ≈ 1/b at quenching limit  n ≈ 5Gr0.1/b at quenching limit Gr = 600 x 106,  = 10  n = 3.9 at limit !!! But low Le  SL low at tip opening  n > 4 at tip opening  distributed flame not observable AME 514 - Spring 2015 - Lecture 1

Conclusions Probable heat loss & buoyancy-induced limit mechanisms observed Limit behavior characterized mainly by Lewis & Grashof numbers Scaling analyses useful for gaining insight Transition to turbulence & distributed-like combustion observed High-Gr results may be more applicable to "real" hazards (large systems, turbulent) than classical experiments at low Gr AME 514 - Spring 2015 - Lecture 1