JetFlame -1 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Laminar Nonpremixed Combustion

JetFlame -2 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Laminar Jet Flames Reacting jet will be “similar” to nonreacting/mixing flow except 1.Fuel and oxidizer must react at some f 2.Heat release   = constant probably not a good assumption –buoyancy effects (body force term) –Thermal expansion driven flow fields 3.Must include diffusion of products (and intermediates/radicals) 4.Now there will be source and sink terms in the species conservation (and energy) equations

JetFlame -3 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Diffusion Flame – Fast Kinetics Where will flame “sit” in terms of  ? For Da >> 1 (  chem small; very fast chemistry) –reaction zone should be very thin as soon as fuel and oxidizer meet, they will react Consider 1-d diffusion of fuel into air  >>1  <<1 fueloxid.  <1  <<1  >>1 fueloxid.  >1 For fast (infinite rate), single-step reaction, flame sits at stoichiometric surface: Flame Sheet Approx.  >>1  <<1 fueloxid.  =1

JetFlame -4 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Jet Flame Description Overventilated vs. underventilated flames –overall excess fuel, underventilated –overall excess air, overventilated (always the case for open air flame) overventilated under- ventilated

JetFlame -5 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Fuel, oxidizer diffuse toward flame sheet Products (T) diffuse away Jet Flame Description r 2R2R x x=x 1 x=x 2 flame sheet r 1 x 1 x2x2 f Flame tip –final fuel burnout –buoyancy r=0 Y Ox YPYP YFYF x1x1 YPYP LfLf Flame Length YFYF (f=fstoich) Mixture fraction –continuous

JetFlame -6 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Mixture Fraction Contours With no heat release, flame would follow f stoich contour from nonreacting solution x r f

JetFlame -7 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Historical Development Burke & Schumann (1928) –“classical” analytic solution (Lewis&von Elbe, Kuo) –assumed u x =const, u r =0 so mom. equation not needed (can’t account for buoyancy) –assumed flame sheet, single D –reasonable results for L f of circular flames Roper (1977) –removed u x =const. limitation –results improved for buoyant and non-circular jets Numerical solutions (e.g., Kee & Miller, AIAA J. 16,1978) –can include finite rate kinetics, differential diffusion

JetFlame -8 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Conservation Equations Examine conservation equations for simplest case Assumptions –as for nonreacting case: laminar, steady, axisymmetric, quiescent/infinite reservoir, Fickian diffusion, no axial diffusion (  const) –for flame: normal thermal diffusion, no radiative transfer, negl. viscous dissipation, constant pressure, flame sheet approx., Le=1 Mass (1)

JetFlame -9 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Conservation Equations Axial momentum axial conv.radial conv.radial diffusion body force (buoyancy) (2) Species/Energy –next we could write 2 species conservation eq’ns. e.g., Y F, Y Ox with Y P =1  Y F  Y Ox –energy equation in terms of T –BUT run into problems with boundary conditions (at flame)

JetFlame -10 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Flame Boundary Conditions Example –species conservation axial conv.radial conv.radial diffusion source/sink –chemical term is 0 everywhere except at flame sheet –so flame is boundary between 2 solutions (inside/outside) but don’t know where the flame is! all we know is the mass fluxes into the flame governed by stoichiometric proportions Same problem for energy equation in terms of T

JetFlame -11 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Conserved Scalars Solution to this problem - write equations in terms of scalars that have no sources or sinks in the flow –scalar that “exists” on both sides of flame and whose “integral” is constant (like mass flow rate of jet fluid in nonreacting case) Examples  ij = mass proportion of element i in species j –total enthalpy, h sens +h chem, if negligible radiation, viscous dissipation, body force work (+ no conduction to bodies) –mixture fraction, f –elemental (atom) mass fraction

JetFlame -12 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Conserved Scalar Equations Species  Mixture fraction –only need 1 “species” equation to determine composition (flame sheet approximation) e.g., if f > f stoich (inside flame) only fuel and products, Y F + Y P = 1 Le=1,  =D (3) (4) Energy  Total enthalpy

JetFlame -13 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Summary So we have four conservation equations with no source/sink terms –except in momentum eq’n. if body force important buoyancy effects –equations similar except different diffusion coeffients (  =D, ) Schmidt number effects (Sc  /D) Next normalize (2) – (4) and B.C

JetFlame -14 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Normalization Self-similar type solution (like nonreacting case) r 2R2R x =0 in pure ambient =1 in pure jet fluid  fraction of product mass that comes from “fuel” –same normalization as f (0  1)

JetFlame -15 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Boundary Conditions General axisymmetric jet r * = 0, any x * r * =  x * = 0, r * > 1 For top hat/uniform exit profile x * = 0, r *  1 r*r* 1 x*x* 

JetFlame -16 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion General Normalized Eq’n. In terms of generalized variable,  axial momentum species/energy =1/Fr, Froud # local if Fr <<  /   buoyancy controlled Since we used Le=1, h * =h * ( f ) –same for axial velocity if Sc=1 and negl. buoyancy Still need to relate  *, h * to p, T

JetFlame -17 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion State Relationships Virial state eq.  Need to get cp cp Y i =? –for f > f stoich –for f < f stoich

JetFlame -18 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion State Relationships –for f = f stoich YFYF Y ox YPYP Simple, linear relations for flame sheet approx. Le=1 T if c p =constant Flame broadening h=? YiYi f 1 1 f st f h 1 for pure fuel jet, pure ox ambient hF,ehF,e h ox, 

JetFlame -19 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Summary of Equations Conservation equations for simple jet Mass Momentum (axial) Species, Energy (Le=1) =1/Fr, Froud #

JetFlame -20 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Solution to determine  (r,x) Start with simplest case Sc=1 (Le=1), Constant Density, Const. “Properties” – ,  =  D =  = const –then all conservation equations become –which gives identical solution as for nonreacting jet

JetFlame -21 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Solutions (Constant Density) Flame Location –at f = f stoich –for diluted oxygen, pure fuel x r f stoich stoich. oxygen/ fuel mass ratio Discussion: why? f=0 f=1 –f stoich  if you dilute oxidizer (flame gets bigger) –similarly f stoich  as dilute fuel (flame gets smaller)

JetFlame -22 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Solutions (Constant Density) Flame Length –use flame width –when r flame =0 Discussion: why? x r f f=0 f=1 L f  for Q e /D  or f stoich  (dilute ox.) volumetric flowrate  function (p) –for given mass flowrate reduce combustor length by having distributed nozzles

JetFlame -23 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Solutions (Variable Density) Fay extended Burke-Schumann approach –still Sc=Le=1 but with momentum equation,  const –limited to Fr large (no buoyancy)   = density in cold oxidizer  f = density at flame  F = density in cold fuel I u = mometum integral (>1) Roper –includes buoyancy (see Turns) /f/f   /  ref Iu(/f)Iu(/f) after Turns Table 9.2

JetFlame -24 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Problems with the Mixture Fraction Approach Problems with the Mixture Fraction Approach Multistep Chemistry –even with fast chemistry (equilibrium chemistry) will still have fuel and oxidizer coexisting –changes f  Y, h state relations - > use elemental (atom) conserved scalars Finite Rate Chemistry –solution will depend on chemical time scales and flow time scales (diffusion, residence time) Differential diffusion

JetFlame -25 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Scalar Dissipation Definition –units of 1/s Essentially inverse of characteristic diffusion time in the flame Non zero scalar dissipation causes departures from equilibrium –Large enough values lead to flame extinction

JetFlame -26 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion also harder for H 2 to diffuse against high velocities to get to flame ft/s ft/s Finite Rate Kinetic Effects Can see effect of Da=  flow /  chem in opposed jet flow –higher velocity gives less flow time (time to react) u fuel u ox Equilibrium H 2 /air STP f stoich f=1 f=0

JetFlame -27 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Partially Premixed Combustion Practical systems involve combination of nonpremixed and premixed combustion –partially premixed combustion –stratified combustion Example, premixed flames usually anchor diffusion flames –finite time for reactions required –triple point flame air fuel f=f stoich lean premixed rich premixed SLSL diffusion flame

JetFlame -28 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Nonpremixed Lifted Flames Higher flowrate, longer distance to ignition point –less diffusion flame, more premixed As get to too high a jet velocity –can reach point where either nonflammable –or even stoichiometric flame too slow to propagate  blowoff of nonpremixed flame air fuel f=f stoich lean premixed rich premixed

JetFlame -29 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion 60 mm 20 mm 40 mm Radius, R (mm) Soot Volume Fraction (ppm) Primary Particle Diameter (nm) flamesheet air fuel Soot in Diffusion Flames Typical results, ethylene-air

JetFlame -30 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Soot – What is it? Mostly graphitic carbon Nucleation  growth  dehydrogenation  graphitization Branchy aggregates of primary particles Primary particle diameter d p dpdp 500 nm 5 nm

JetFlame -31 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Soot Formation Soot primarily forms due to “heating” (pyrolysis) of HC fuel species in oxygen deficient regions Large ring HC condense Particles grow and agglomerate Soot oxidizes in high T, oxygen regions

JetFlame -32 School of Aerospace Engineering Copyright © by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion Soot Emissions So soot primarily produced in regions of –“high” fuel concentration (less oxidizer: O 2, OH,...) –high temperature (promotes pyrolysis and growth) Soot oxidized in regions of –high temperature –high oxidizer concentration So most soot made in combustor is subsequently destroyed (oxidized) unless –rich region remains unmixed –gases cooled (mixing, walls, soot radiation)