Premixed, Nonpremixed and Partially Premixed Flames

Premixed, Nonpremixed and Partially Premixed Flames Flame (Reaction Zone) Flame (Reaction Zone) Flame (Reaction Zone) Fuel Air Fuel + Air φ 1 Products Fuel + Air φ > 1 F + A Air (+ F?) NONPREMIXED PREMIXED PARTIALLY (Local Quenching) (Incomplete Mixing) PREMIXED

Diffusion Flames Video images of ethane jet diffusion flames in quiescent air in 1g and µg. Burner tube inside diameter= 2.87 mm; mean fuel jet velocity=7.5 cm/sec. Takahashi and Katta: Proc. Combust. Inst., Vol. 29, 2002, pp. 2509-2518. Computed Images (from 1 to 200 msec) in terms of temperature field (contours) of a propagating edge diffusion flame in an ethane jet in quasi-quiescent air in 0g. Burner tube diameter= 3 mm; mean fuel jet velocity=6.86 cm/sec.

Flame Images Propane torch Turbulent diffusion Flame

Premixed Flame Images Bunsen Burner Methane-Air Premixed Flame LPG (liquified petroleum gas)-air premixed flames for different φ and inlet velocity in a diverging channel Akram et al. Energy & Fuels, 2012, 26, 3267 3274

Propagating premixed flame in SI engine Flame Images

Partially Premixed Flame n-heptane PPF * Rich premixed zone Non-premixed zone Diesel Engine Combustion **. * P. Berta, S. Aggarwal, I. Puri. Combustion and Flame. 145 (2006) 740-764 ** Quasi-steady Diesel combustion plume as presented by DEC (1997).

Flame Images: Partially Premixed (Double) Flames Partially Premixed Flames Established on a Slot Burner (Methane/Air) (Propane/Air) NP RP φ = 1.4 V in = 30cms -1 V out = 30cms -1 φ = 1.6 V in = 30cms -1 V out = 30cms -1 φ = 1.7 V in = 30cms -1 V out = 30cms -1 φ = 1.9 V in = 30cms -1 V out = 30cms -1 Le 1 Le<1

Nonpremixed and Partially Premixed (Double) Flames Flames Established in a Counterflow Burner strain rate 50 s -1 φ = 10 φ = 5 φ = 3.5 φ = 2.5 Image of syngas (50%H 2-50%CO) /air nonpremixed flame established at p=1atm, strain rate a s = 65s -1. N-Heptane PPFs showing the double flame structure: characteristic of non-premixed and premixed reaction zones. The fuel enters at the bottom and the oxidizer at the top.

A Schematic of Premixed Flame Structure Henry A. Becker, "Flame," in AccessScience, McGraw-Hill Companies, 2008, http://www.accessscience.com

Burner Stabilized Premixed H2-O2-N2 Flame Species profiles in a burner-stabilized flame of a mixture with H2 = 18.8%, O2 = 4.6%, and N2 = 76.6% at 1 atm. Symbols represent experimental data from Dixon- Lewis et al., solid lines: present model; dashed lines: model of Li et al. Burke et al. Int. J. Chemical Kinetics (2011)

Counterflow N-heptane-air Premixed Flame Temperature and velocity 2500 2000 Stagnation plane 300 200 T (K) 1500 1000 100 0-100 v (cm) T(K) V(cm/s) 500-200 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Distance from the nozzle (cm) -300 Φ=0.8, inlet velocity v=70cm/s, inlet temperature T 0 =400K, distance between the two nozzles d=1cm. Stretched flame speed=62 cm/s Flame thickness=0.8 mm

Counterflow N-heptane-air Premixed Flame 0.25 Fuel, oxidizer, and products 0.2 Mole fraction 0.15 0.1 O2 CO2 H2O n-heptane * 10 O2 CO H2 * 10 H2O 0.05 H2 CO2 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Distance from the nozzle (cm) Φ=0.8, inlet velocity v=70cm/s, inlet temperature T 0 =400K, distance between the two nozzles d=1cm.

Laminar Premixed Flames Refs: Turns (Chapter 8), Law (Chapter 7), Kuo (Chapter 5) Introduction Scale analysis for laminar flame speed and flame thickness Simplified analysis due to Spalding Detailed analysis; numerical solution Effects of important parameters on the flame speed and thickness Counterflow flames Partially Premixed Flames

Laminar Premixed Flames Introduction Ø In premixed flames, the reaction zone separates the reactants (i.e. a mixture of fuel and oxidizer that are mixed at the molecular level) and products. Ø Safety is a major concern for premixed flames. Consequently, such flames are not as common as the nonpremixed and partially premixed flames. Nevertheless, they are still very important in numerous combustion systems. Examples include: Gas turbine combustors using lean premixed combustion Spark ignition engines Fires in coal mines Numerous other systems, such as residential burners, furnaces, diesel engines, rocket engines in which the combustion is characterized by a partially premixed flame containing multiple reaction zones Ø A premixed flame is characterized by the propagation of a wave. Broadly speaking, there are two types of combustion waves; detonation waves and deflagration waves. A detonation wave is a shock wave, which propagates at a supersonic speed, accompanied by combustion. A deflagration wave or a laminar flame on the other hand is a relatively low-speed wave, and pressure change across it is negligible.

Laminar Premixed Flames Ø A laminar flame is of fundamental importance in most practical systems. Even in systems that involve nonpremixed flames, the laminar flame speed is important with regards to flame liftoff and stabilization. Ø Commonly used premixed flame configurations for fundamental studies include: Bunsen burner flame Flame stabilized on a flat flame burner Propagating flame in a tube Spherical flames Counterflow premixed flame Flame stabilized on a rod Ø This chapter deals with the fundamental aspects of laminar premixed flames. In particular, we will discuss: Laminar flame speed and flame thickness Flame structure Fundamental analysis of a laminar premixed flame Effects of important parameters Flame stretch and flame stability (advanced topic, not covered)

Laminar Premixed Flames Laminar flame speed represents a fundamental property of fuel-oxidizer mixtures. It is defined as the mixture velocity normal to the flame surface. It provides the mixture burning rate in the flame. Scale Analysis: Laminar Flame Speed and Thickness In a 1-D, steady, laminar flame, there is a balance between convection, diffusion and reaction processes. Then a simple scale (dimensional) analysis can be used to obtain approx. expressions for laminar flame speed (S L ) and thickness (δ). Conservation of mass: Equating thermal diffusion time to reaction time: ( ) 1/2 S L = ( ωα / ρ u ) 1/2 = ( ωdl e / ρ u ) 1/2 = (1/ ρ u ) ωλ / c p ( ) 1/ 2 δ = α /S L = λ /(c p ω ) ρ u S L = ω δ Also equating convection and reaction times δ 2 /α ρ u / ω Laminar premixed flame speed and structure are governed by both the chemical kinetics and transport. The laminar flame speed is fundamental to the flame shape and stabilization, including flashback and flame blowout. Laminar flames are also of fundamental importance to turbulent premixed flames.

Laminar Premixed Flames Bunsen Burner Methane-Air Premixed Flame S L = v u,n = v u sinα It is important to know the laminar flame speed for any given fuel for a range of equivalence ratios, temperatures, pressures, etc.

Laminar Premixed Flames Simplified Analysis (Due to Spalding) ρ t = (ρv x) x = 0 ρ u S L = ρ b U b ρ u S L δ ρ b U b ρ i = ( m % i) + m % i % = 0 t x m " i = m " Y i ρd i ( Y i / x) dp dx = 0 Using energy equation as derived in the Shvab Zeldovich Formulation dt m!! c p dx d T (λ dx T 0 dx ) = h f,i!!! m i Two extra boundary conditions for δ and S L dt dx δ d δ r T(x ) = T u T(x ) = T b (x ) = dt dx x (x + ) = 0

Simplified Analysis: Thermal Theory of Spalding 1. A planar steady, one-dimensional, adiabatic flame, which is either stationary or propagating at a fixed speed of S L. 2. p=constant 3. Constant transport properties. Also constant and equal specific heats, and Le=1. 4. Three species with a single global reaction. The Spalding analysis provides the following results: m!! c p (T b T u ) = δδh c m!!! F Δh c = (ν +1)c p (T b T u ) δ = 2α /S L S L = ( (υ +1)2α. m % F % /ρ u ) 1/ 2 m!!! F = average fuel consumption rate / volume Here ν is the stoichiometric air-fuel ratio by mass, α is thermal diffusivity,. These equations can be used to examine qualitatively the effects of various parameters, such as pressure, equivalence ratio, fuel type, temperature, diluent, etc. See Turns: An Introduction to Combustion (pp. 266-287) Kuo: Principles of Combustion (449-458)

Laminar Premixed Flames Detailed Analysis and Numerical Solution Detailed analysis of one-dimensional premixed flames: see Kuo, p. 461-468. Freely propagating premixed flames using Chemkin and Premix: See Kuo, p. 468-471 Counterflow premixed flames using Chemkin and Oppdif. Flame Stretch and Flame Speed (More advanced course) Introduction to flame stretch Derivation of flame stretch and flame speed in curvilinear coordinated for this flame. Effect of stretch and Lewis number on flame speed and extinction Effect of stretch and Lewis number on flame stability.

Detailed Analysis:1-D Equations Used in CHEMKIN d m " i dx = m " " i dm " dx = 0 dt m!!! c p dx d # % dx λ dt $ dx Boundary conditions: " " m = ρv = C m " dy i dx + d ( dx ρyv i d,i) = ω i M i dp dx = 0 & dt (+ ρy i V di c pi ' dx = T(x ) = T u and Y i (x ) = Y i,o Unknowns: ρ, v, Y i, T, S L or m!! = ρ u S L h0 fi! ω i M i dt dx (x ) = dy i dx (x ) = 0 Equations for reaction rates using a detailed kinetic mechanism Equations for diffusion velocities, mass diffusivities, specific heats, thermal conductivity S L. Ideal gas equation to compute density Mass flux or flame speed is an eigenvalue; it is determined as part of the solution.

Laminar Flame Speed and Structure Propane-air Φ=1

Laminar Premixed Flames Effects of Various Parameters on Flame Speed and Thickness Considering global 1-step reaction Fuel +υ.ox (1+υ).Pr S L = ( (υ +1)2α. m % F % /ρ u ) 1/ 2 δ = 2α /S L ω F = m # F # = Ae (E / R u T ) [ F] a [ O x ] b M X F [ ] = ρy / M ρ pm /T ω F ρ u T u e (E / R ut ) p n 1 ρc p T b n (Y F )a (Y Ox ) b α = k S L (T ) c / 2 T u (T b ) n / 2 e (E / 2R u T b ) p (n 2)/ 2 T u p (T )c δ (T ) c / 2 (T b ) n / 2 e (E / 2R ut ) p n / 2

Effect of Various Parameters S L (T ) c / 2 T u (T b ) n / 2 e (E / 2R u T b ) p (n 2)/ 2 δ (T ) c / 2 (T b ) n / 2 e (E / 2R u T ) p n / 2 Global reaction order (n) is often assumed as 2, which implies that S L is independent of p, and δ decreases with p. Note that the reaction rate increases with pressure, but the mixture also becomes denser, such that S L is nearly independent of p. Reaction rate p 2, ==> S L p 0 α 1/p and ρ p, ==> δ 1/p Effect of p on δ is mainly due to the fact p increases the reaction rate Actual data indicates that n has a complex variation with p Reaction order varies with pressure due to chemistry effects; for example diffusion to wall becomes important at low pressures, and 3-body reactions (H +O 2 + M==>HO 2 + M) become important at high pressure. Flame temperature may also vary somewhat with pressure due to dissociation effects Both T u and T b have strong influence on S L ; S L increases with T u since T b T u + Δh c /c p Effect of T b occurs mainly through the exponential term, as the activation energy is relatively high.

Effects of Various Parameters S L = ( (υ +1)2α. m % F % /ρ u ) 1/ 2 δ = 2α /S L The effect of equivalence ratio (φ) on flame speed and thickness appears mainly through its effect on T b, and also through its effect on Y F and Y o. Thus flame speed and thickness are, respectively maximum and minimum near φ =1 for hydrocarbon flames. Effect of molecular weight of reactant (M): α 1/M and ρ M, ==> S L 1/M Shifts the peak in S L to richer mixture (φ >1) for lighter fuels, such as H 2 Flame speed can also be modified by using diluents, which mainly affect the specific heat and thereby the flame temperature in the order: Cp CO2 >Cp N2 >Cp Ar ( Cp He ) Some diluents such as He can also modify the transport property (thermal conductivity or diffusivity), and molecular weight

Methane-Air Flames Effect of pressure on the predicted and measured laminar flame speed and overall reaction order Som and Aggarwal, CST, Vol. 179 (2007)

N-Heptane-Air Flames Good agreement between the predicted and measured laminar flame speeds Xue and Aggarwal, AIAA Journal, Vol. 40 (2002)

Premixed Flame Speed for Hydrogen-Air Mixture Computed Using Different Mechanisms H2/air flames at 1 atm H2/O2/He flames O2/(O2+He) = 0.125 at 5 atm O2/(O2 +He) = 0.080 at 15 atm Briones et al., C&F, Vol. 140 (2005)

Laminar Flame Thickness and Quenching Distance for Methane-Air Flames Turns-An Introduction to Combustion

Syngas-Air Flames: Fuel Effect Measured and predicted laminar burning velocities for syngas-air mixtures Laminar Burning Velocity [cm/s] 210 180 150 120 90 60 a) McLean et al. [1994] Mueller et al. Mechanism Davis et al. Mechanism GRI-3.0 mechanism Flame A: 50%CO - 50%H 2 30 Flame B: 95%CO - 5%H 2 0 0 1 2 3 4 5 6 Equivalence Ratio Flame A: 50% CO- 50% H 2 Flame B: 95% CO- 5% H 2 Variation of laminar burning velocity with volume percent of CO in syngas at φ = 2.0 Som et al., Fuel (2008) 319 334

Syngas Flames: Effect of Pressure Measured and predicted laminar burning velocities for CO-H 2 -O 2 -He mixture Curran et al., C&F Vol. 160 (2013) 95% CO + 5% H 2 in (O 2 + 7 He) mixture, T u = 298 K

Premixed NG Flames: Effect of Hydrogen Laminar Flame Speed: S L ~ (D ω i ) Flame Thickness: δ D =D/ S L Flame speed increases while flame thickness decreases with H2 addition Peak in burning velocity occurs at richer conditions Huang et al., Combust Flame, 2006, Vol. 146

Hydrogen-Air Flames: Effect of Diluents Measured and predicted laminar burning velocities for H 2 -O 2 -Diluent mixtures He: λ = 0.25 W/m/K Ar: λ = 0.032 λ S L Diluents modify mainly the specific heat and thereby the flame temperature in the order: Cp CO2 >Cp N2 >Cp Ar ( Cp He ) Qiao et al., C&F Vol. 143 (2005)

Limit Combustion Phenomena Ignition and flame extinction represent limit combustion phenomenon and involve transient processes. Ignition can be defined as the initiation of rapid exothermic reactions leading to the appearance of a flame in a combustible mixture; it may be caused with an external source such as an electric spark, or without any external source such as autoignition in a compression ignition engine. It is of practical interest in numerous applications, including the need to prevent fires and unwanted explosions, and to initiate controlled combustion in furnaces and engines. Extinction of flames may be achieved in various ways, including the addition of a flame suppressants (inert or chemical), passing the flame through tubes of small diameter (basis for flame arrestor design), or blowing the flame away using high gas velocity. It is of interest from the considerations of fire suppression, and controlling combustion processes in various propulsion and power generation systems. Flammability limits are generally expressed in terms of mixture compositions (equivalence ratio or fuel concentration by volume), for fixed temperature and pressure, beyond which a fuel-air mixture cannot be made to burn. Most of these phenomena are inherently transient. However, we will analyze them from energy considerations (i.e., heat loss), and discuss the limit behavior, i.e., conditions under which a flame will extinguish or not, or ignition will occur or not. Turns, Law, Williams

Minimum Quenching Distance Consider a flame propagating in a tube. If the tube diameter is sufficiently small, it will cause flame to extinguish. This quenching diameter can be experimentally determined by observing whether a flame stabilized above the tube does or does not flashback when the reactant flow is suddenly shutoff. Here we determine a quenching distance (d) by considering a long slot burner of a given width (L), and using the criterion that rate of heat generation due to chemical reactions is balanced by the rate of heat loss to by thermal conduction. #!QV =!m F Δh c V = λa% dt $ dx & ( ' wall δ Here V=dδL is the gas volume, A=2δL! # " Approximating dt dx $ & % wall = T w T b d / b This leads to: with b>2 d 2 = 2λb(T b T w )!m F Δh c q cond V d Schematic of flame quenching between two parallel walls q cond

Minimum Quenching Distance Using equations for fuel consumption rate and heat of combustion derived earlier, assuming Le-1, and T w T u, the above equation becomes: d = 2α b / S L δ = 2α /S L d = b.δ These equations provide results that are qualitatively in agreement with experimental data, such as shown in Fig. 8.16 (Turns), indicating quenching distance to be greater than flame thickness. See data in Table. Note X values are in percentage.

Flammability Limits Flammability limits are generally expressed in terms of mixture compositions (equivalence ratio or fuel fraction by volume), for fixed temperature and pressure, beyond which a fuel-air mixture cannot be made to burn. These limits can be determined experimentally by igniting a fuel-air mixture at one end of a long tube. If the mixture is within flammability limit, the ignition leads to a flame propagating in the tube. However, there are equivalence ratios (outside the flammability limits) that will not lead to propagating flame after the ignition source is removed. Using a large-diameter tube provides more consistent results. Table shows flammability limits for some fuels, expressed in terms of lean and rich equivalence ratios (or fuel mole fractions for lean and rich mixtures). These limits are strongly influenced by temperature, pressure, and other conditions, such as oxygen fraction, and gravity for upward/downward propagating flames. Figure depicts the effect of gravity on the lower flammability limit. Note that the fuel-air mixture gets preheated due to hot buoyant gases in case of upward propagating flame.

Flammability Limits Turns 760 torrs=1 atm

Flame Stability (Advanced Topic) Flashback When the flame enters and propagates upstream in the burner tube without quenching Serious safety hazard; flame arresters (such as wire mesh) are designed to quench flame Liftoff and Blowout For low velocities, the flame is attached, or the flame edge is close to burner lip. As V is increased, the flame lift off and its liftoff height increases until the flame blows out (or extinguished). Flame response to stretch Premixed flames characteristics (speed, structure, emission, instability, etc.) are also strongly influenced by aerodynamic effects, such as aerodynamic straining, flame curvature and unsteadiness. (1) Turns, (2) Lewis and Von Elbe

Flame Stability: Flashback Flame stabilized on a vertical tube Flame flashback is a serious safety hazard. It refers to the situation when the flame enters and propagates upstream in the burner tube without quenching. It occurs as the mixture flow is reduced or turned off. In a gas appliance, it can potentially ignite a large volume of gas in the mixture, leading to explosion. A flame arrester (such as wire mesh) is designed to quench flame propagation by absorbing heat from the flame, and reducing the temperature below the ignition temperature. Conditions in terms of safe mixture speed for a range of equivalence ratios (φ) for a given flame can be estimated from the plot of laminar flame speed versus φ. Important parameters for flashback to be essentially the same as those affecting quenching, e.g., φ, fuel type, mixture velocity, and burner geometry. For example, slightly rich mixtures provide the highest propensity for flashback, and flashback stability for CH4 is much greater than that of H2-rich fuels. Textbooks by (1) Turns, (2) Glassman

Flame Stability: Liftoff and Blowout Flame Stabilized on a vertical tube Flame liftoff generally involves uncontrolled and unsteady combustion, and can lead to blowout. It is also a safety hazard. It depends strongly on flame and flow properties near the edge of the burner. For low mixture velocities (V), the conical flame is attached, as the flame edge lies close to burner lip. As V is increased, the flame cone angle decreases, and the flame edge moves slightly downstream. As V is increased further, the flame jumps to a downstream location at a critical V, With further increase in V, the liftoff height increases until the flame blowout. When the flame is attached near the burner rim, the flow velocity in the stabilization region is relatively low. However, the flame speed (S L ) in this region is also low due to the diffusion of heat and radical species to the rim. As V is increased, the flame edge moves downstream, which increases S L, since the loss of heat and radical species is reduced. Thus the flame remains close to the burner. However with further increase in V causes dilution of the mixture with ambient fluid, which compensates for the decrease in heat and radical species loss. (1) Turns, (2) Lewis and Von Elbe

Turns Flashback and Liftoff

Thermo-Diffusive Instability Lean hydrogen flames: Le<1 Flame speed increases with stretch Lean propane flames: Le>1 Flame speed decreases with stretch Law & Sung, Prog. Energy Combus. Sci. 26, 2000

Partially Premixed (Double) Flames on a Slot Burner NP (Methane/Air) (Propane/Air) RP φ = 1.4 V in = 30cms -1 V out = 30cms -1 Le 1 φ = 1.6 V in = 30cms -1 V out = 30cms -1 φ = 1.7 V in = 30cms -1 V out = 30cms -1 Le<1 φ = 1.9 V in = 30cms -1 V out = 30cms -1 Flame tip is negatively stretched, and L b is positive for rich propane flames Burning rate decreases with stretch

Thermal-Diffusive Instability: H 2 -C 3 H 8 Blend Hydrogen (Le<1) Propane (Le>1) Spherically expanding premixed flames Law et al., 30th Int Combust Sym, 2005

Flame Liftoff and Blowout Blowout of methane jet flame using CO2 dilution Aggarwal, Prog. Energy Combust Sci., 35, 528 570, 2009