MAE 5310: COMBUSTION FUNDAMENTALS

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MAE 5310 COMBUSTION FUNDAMENTALS

• Laminar Premixed Flames Example, Applications and
  Comments
• Mechanical and Aerospace Engineering Department
• Florida Institute of Technology
• D. R. Kirk

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LAMINAR PRE-MIXED FLAME EXAMPLE

• Estimate the laminar flame speed, SL, of a
  stoichiometric propane (C3H8)-air mixture using
  the simplified theory of Spalding developed in
  class
• Make use of a global, one-step reaction mechanism
  to estimate the mean reaction rate

Laminar flame structure. Temperature and
heat-release rate profiles based on experiments
of Friedman and Burke Reference Turns An
Introduction to Combustion
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PRINCIPAL CHARACTERISTICS OF LAMINAR PREMIXED
FLAMES

• Definition of flame speed, SL
• Temperature profile through flame
• Product density is less than the reactant density
  so that by continuity the velocity of the burned
  gases is greater than the velocity of the
  unburned gases
• For a typical hydrocarbon-air flame at
  atmospheric pressure, the density ratio is about
  7
• Convenient to divide the flame into two zones
• Preheat zone little heat is released
• Reaction zone most of the chemical energy is
  released
• 2.a Thin region of fast chemistry
• Destruction of fuel molecules and creation of
  intermediate species
• Dominated by bimolecular reactions
• At atmospheric pressure, fast zone is usually
  less than 1 mm
• Temperature and species concentration gradients
  are very large
• The large gradients provide the driving forces
  for the flame to be self-sustaining, i.e.
  diffusion of heat and radical species from the
  reaction zone to the preheat zone
• 2.b Wider region of slow chemistry
• Chemistry is dominated by three-body radical
  recombination reactions, such as the final
  burn-out of CO via CO OH ? CO2 H
• At atmospheric pressure, this zone may extend
  several mm

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LAMINAR PREMIXED FLAMES SIMPLIFIED ANALYSIS

• Analysis couples principles of heat transfer,
  mass transfer, chemical kinetics, and
  thermodynamics to understand the factors
  governing
• Flame speed, SL
• Flame thickness, d (ANSWER, d2a/SL)
• Simplified approach using conservation relations
• Assumptions
• 1-D, constant area, steady flow
• Neglect kinetic and potential energy, viscous
  shear work, thermal radiation
• Constant pressure (neglect small pressure
  difference across flame)
• Diffusion of heat governed by Fouriers law
• Diffusion of mass governed by Ficks law (binary
  diffusion)
• Lewis number (Lea/D) unity
• Individual specific heats are equal and constant
• Fuel and oxidizer form products in a single-step
  exothermic reaction
• Oxidizer is present in stoichiometric or excess
  proportions thus, the fuel is completely
  consumed at the flame.

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VON KARMAN INTEGRAL ANALYSIS OF F.P.B.L.
Compare with development of Equation 8.7b
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USEFUL DATA AND EQUATIONS
Pay attention to units conversion (see WSR
example for C2H6)
Theoretical expression for laminar flame speed,
SL Premixed laminar flame thickness, d
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DETAILED ANALYSIS USING CHEMKIN CH4-AIR PREMIXED
LAMINAR FLAME

• Figure (a) shows principal C-containing species
  CH4, CO, and CO2.
• Note disappearance of fuel and appearance of
  intermediate CO, and burn-out of CO to form CO2
• CO concentration has peak value at approx same
  location where CH4 concentration goes to zero
• CO2 concentration at first lags CO concentration
  but then continues to rise as CO is oxidized
• Figure (b) shows C-containing intermediate
  species CH3, CH2O, and HCO, which are produced
  and destroyed in a narrow interval from
  approximately 0.4 mm 1.1 mm.
• Figure (d) shows same phenomena for the CH
  radical
• Figure (c) shows that H-intermediates, HO2 and
  H2O2 have somewhat broader profiles than
  C-intermediates. Peak concentrations appear
  slightly earlier in flame.
• H2O mole fractions reaches its 80 of equilibrium
  value (at about 0.9 mm) sooner than CO2 (at about
  2mm)
• All fuel has been destroyed in approx. 1 mm and
  most of total temperature rise ( 75) occurs in
  same interval
• Approach to equilibrium is relatively slow beyond
  this point (no equilibrium even at 3 mm)
• Slow approach toward equilibrium is a consequence
  of dominance of 3-body recombinations
• Figure (d) shows NO production
• Rapid rise in NO mole fraction in same region
  where CH radical is present in flame
• This is followed by a continual (almost linear)
  increase in NO mole fraction. In this later
  region NO formation is dominated by Zeldovich
  kinetics.
• Curve ultimately bends over as reverse reactions
  become more important and equilibrium is
  approached asymptotically

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DETAILED ANALYSIS USING CHEMKIN CH4-AIR PREMIXED
LAMINAR FLAME

• Plot shows molar production / destruction rates
  for various species and provides more insight
  into CH4 ? CO ? CO2 sequence
• Peak fuel destruction rate nominally corresponds
  with peak CO production rate
• CO2 production rate initially lags that of CO
• Even before location where there is no longer any
  CH4 to produce additional CO, the net CO
  production rate becomes negative (CO is being
  destroyed)
• Maximum rate of CO destruction occurs just
  downstream of peak CO2 production rate
• Bulk of chemical activity is contained in an
  interval extending from about 0.5 mm to 1.5 mm

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DETAILED ANALYSIS USING CHEMKIN CH4-AIR PREMIXED
LAMINAR FLAME

• Plot shows NO production rate through flame
• Figure shows that early appearance of NO within
  flame (0.5 mm 0.8 mm see Figure (d)) is result
  of passive diffusion since production rate is
  essentially zero in that region.
• First chemical activity associated with NO is a
  destructive process in region approximately 0.8
  mm 0.9 mm.
• NO production reaches a maximum at an axial
  location between CH and O-atom concentrations. It
  is likely that both Fenimore and Zeldovich
  pathways are important (see p.168-171 or Turns.
• Beyond O-atom peak at a distance of 1.2 mm
  (Figure (d)), NO production rate falls. Since
  temperature continues to rise in this region,
  decline in net NO production rate must be a
  consequence of decaying O-atom concentration and
  building strength of reverse reactions.

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STOICHIOMETRIC METHANOL-AIR FLAME
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FACTORS INFLUENCING SL AND d

• Scaling relation developed on p. 274-275
• Laminar flame speed has a strong temperature
  dependence
• Global reaction orders for HC 2
• EA 1.67x108 J/kmol
• Example CASE A vs. CASE B
• SL increases by a factor of 3.64 when the
  unburned gas temperature is increased from 300 K
  to 600 K
• Increasing unburned gas temperature will also
  increase the burned gas temperature by the same
  amount (neglect dissociation and variable
  specific heats)
• Example CASE A vs. CASE C
• Case C forces a lower Tb
• Captures the effect of heat transfer of changing
  equivalence ratio, either rich or lean, from the
  maximum-temperature condition.

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LAMINAR FLAME SPEED (TP) SCALING USEFUL DATA
Experimental measurements generally show a
negative pressure dependence Plot is for CH4 -
Air SL (cm/s) 43P-0.5 (atm)
Plot is for CH4 Air f1.0 P1 atm
Primary effect of f is through flame
temperature Max slightly rich of f1.0
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LAMINAR FLAME SPEED FOR VARIOUS FUELS
Laminar flame speeds for pure Fuels burning in
air at f 1.0 P 1 atm, Tu 300K

• Comment on H2
• Thermal diffusivity of H2 is many times greater
  than HC fuels
• Mass diffusivity of H2 is much greater than HC
  fuels
• Reaction kinetics for H2 are very rapid (no slow
  CO ? CO2 step)

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FLAME SPEED CORRELATIONS FOR SELECTED FUELS

• One of most useful correlations for laminar flame
  speed, SL, given by Metghalchi and Keck
• Determined experimentally over a range of
  temperatures and pressures typical of those found
  in reciprocating IC engines and gas-turbine
  combustors

• EXAMPLE Employ correlation of Metghalchi and
  Keck to compare laminar flame speed gasoline
  (RMFD-303)-air mixtures with f 0.8 for 3 cases
• At reference conditions of T 298 K and P 1
  atm
• At conditions typical of a spark ignition engine
  operating at T 685 K and P 18.38 atm
• At same conditions as (2) but with 15 percent (by
  mass) exhaust gas recirculation

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TRANSIENT BEHAVIOR

• 3 important aspects to consider
• Quenching distance
• Critical diameter of a circular tube where a
  flame extinguishes, rather than propagates
• Flammability limits
• Lower limit leanest mixture (flt1) that will
  allow steady flame propagation
• Upper limit richest mixture (fgt1) that will
  allow steady flame propagation
• Minimum ignition energy
• In each of these, heat loss is the controlling
  phenomena
• Ignition and Quenching Criteria (also called
  Williams criteria)
• Ignition will only occur if enough energy is
  added to the gas to heat a slab about as thick as
  a steadily propagating laminar flame to the
  adiabatic flame temperature
• The rate of liberation of heat by chemical
  reactions inside the slab must approximately
  balance the rate of heat loss from the slab by
  thermal conduction
• Keep in mind that (1) and (2) are just
  rules-of-thumb

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EXAMPLE FLAME ARRESTERS
Flame arresters on boat motor
Davey Miners Safety Lamp
The screen's ability to dissipate heat and
prevent combustion while allowing flammable
mixtures of gases to pass through has been used
in practical applications.  Sir Humphrey Davy
used this principle in his invention of the
miner's safety lamp in 1815.  Flammable gases
from the mine could pass through the screen
and burn in the enclosed flame with a 'colored
haze' while the screen prevented the open flame
from causing a mine explosion
Flame arresters are used to prevent propagation
of flame fronts in process piping
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QUENCHING DISTANCE, FLAMMABILITY LIMITS, AND
MINIMUM IGNITION ENERGY
CH4-Air at 1 atm
Laminar flame speeds for pure Fuels burning in
air at f 1.0 P 1 atm, Tu 300K
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FLAMMABILITY LIMITS

• Experiments show that a flame will propagate only
  within a range of mixture compositions (sometimes
  called mixture strengths in this context) between
  lower and upper limits of flammability
• Lower limit is leanest mixture (f lt 1) that will
  allow steady flame propagation
• Upper limit is richest mixture (f gt 1) that will
  allow steady flame propagation
• Flammability limits are frequently quoted as
  percent fuel by volume in mixture, or as a
  percentage of the stoichiometric fuel requirement
• Experimental determination Tube Method
• Determine whether or not a flame initiated at the
  bottom of a vertical tube (approximately 50 mm
  diameter and 1.2 m long) propagates the length of
  tube
• A mixture that sustains the flame is said to be
  flammable and by adjusting the mixture strength,
  flammability limit can be ascertained
• In addition to mixture properties, experimental
  flammability limits are related to heat losses
  from the system, and hence, are generally
  apparatus dependent

• Example A full propane cylinder from a stove
  leaks contents of 1.02 lb (0.464 kg) into a 12 x
  14 x 8 (3.66 m x 4.27 m x 2.44 m) room at 20 ºC
  and 1 atm. After a long time, the fuel gas and
  the room air are well mixed. Is mixture in room
  flammable?

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IGNITION

• GOAL Estimate minimum ignition energy, Eign, as
  a function of T P
• CRITERIA Volume of gaseous reactants heated
  during ignition must be large enough so that when
  ignition source is removed, heat loss to the
  surroundings will not exceed the chemical energy
  release rate.

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FLAME STABILIZATION COMMENTS

• Both Flashback and Liftoff are related to
  matching local laminar flame speed to local flow
  velocity
• Flashback occurs when the flame enters and
  propagates through the burner tube without
  quenching
• Can be dangerous and can lead to explosions
• Can be useful as a flash tube from pilot flame
  to a burner
• Occurs when local flame speed exceeds local flow
  velocity (when fuel flow is being decreased or
  turned off transient event)
• Controlling parameters fuel type, equivalence
  ratio, flow velocity, and burner geometry (same
  parameters that control quenching)
• Liftoff is the condition where the flame is not
  attached to the burner tube but is stabilized at
  some distance from the port
• Can lead to escape or loss of unburned gases
• Can lead to incomplete combustion
• Ignition is often difficult above lifting limit
• Tough to accurately control position of flame
• Poor heat transfer
• Flame can be noisy

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FLAME STABILIZATION COMMENTS

• Liftoff depends on local flame and flow
  properties near the edges of the burner port
• Liftoff and blowoff can be explained by the
  countervailing effects of decreased heat and
  radical loss to burner and increased dilution
  with ambient air, both occur when flow velocity
  is increased
• Consider a flame that is stabilized close to
  burner rim
• Local flow velocity at stabilization location is
  small because of boundary layer (Vwall0)
• Because flame is close to cold wall, both heat
  and reactive species diffuse to wall, which leads
  to small SL
• With SL and flow velocities small and equal,
  flame edge lies close to burner tube
• When flow velocity is increased, flame anchor
  point moves downstream
• SL increases since heat/radical losses are less
  because flame is now not as close to cold wall
• Increase in SL results in only a small downstream
  adjustment
• Flame remains attached
• Now increase flow velocity further
• New effect is important dilution of mixture with
  ambient air as a result of diffusion
• Dilution tends to offset effects of heat loss and
  flame lifts
• With further increases in flow velocity, a point
  is reached at which there is no location across
  the flow at which the SL matches the flow
  velocity, and the flame blows off the tube

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FLAME STABILIZATION
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