MAE 5310: COMBUSTION FUNDAMENTALS

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MAE 5310 COMBUSTION FUNDAMENTALS

• Coupled Thermodynamic and Chemical Systems
• September 29, 2009
• Mechanical and Aerospace Engineering Department
• Florida Institute of Technology
• D. R. Kirk

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MOTIVATION

• Calculation of flame temperature given only
  initial and final states as determined by
  equilibrium, but no requirements on chemical
  rates (Chapter 1)
• Development of chemical rate equations and
  chemical time scales (Chapter 2)
• Couple chemical kinetics with fundamental
  conservation principles (mass and momentum) for 4
  archetypal thermodynamic systems
• Constant-pressure, fixed mass reactor
• Constant-volume, fixed-reactor
• Well-Stirred reactor
• Plug-flow reactor
• Coupling allows description of the detailed
  evolution of a reacting system from its initial
  reactant state to final product state
• System may or may not be in chemical equilibrium
• Goal Calculate the system temperature and
  various species concentrations as functions of
  time as the system proceeds from reactants to
  products

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4 USEFUL REACTOR MODELS
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2
4
3
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SUMMARY OF USEFUL RELATIONS
ci mole fraction Yi mass fraction Xi molar
concentration
Mole / mass fraction relation Mass fraction /
molar concentration Mole fraction / molar
concentration Mass concentration MWmix
defined in terms of mass fractions MWmix defined
in terms of mole fractions MWmix defined in
terms of molar concentrations
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1. CONSTANT PRESSURE, FIXED MASS REACTOR
1st Law Differentiation of enthalpy Note that
enthalpys are on per mole basis Calorically
perfect gas short hand notation for net
production rate for complete mechanism Substituti
on into 1st Law Volume expression Expression
for rate of change of molar concentrations
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2. CONSTANT VOLUME, FIXED MASS REACTOR
1st Law Substitution into 1st Law In
terms of molar enthalpys (instead of internal
energy) Expression for time rate of change of
pressure Very useful for explosion calculations
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EXAMPLE ENGINE KNOCK (LECTURE 1)

• In internal combustion engines, compressed
  gasoline-air mixtures have a tendency to ignite
  prematurely rather than burning smoothly
• This creates engine knock, a characteristic
  rattling or pinging sound in one or more
  cylinders.
• Octane number of gasoline is a measure of its
  resistance to knock (or its ability to wait for a
  spark to initiate a flame).
• Octane number is determined by comparing the
  characteristics of a gasoline to isooctane
  (2,2,4-trimethylpentane) and heptane.
• Isooctane is assigned an octane number of 100. It
  is a highly branched compound that burns
  smoothly, with little knock.
• Heptane is given an octane rating of zero. It is
  an unbranched compound and knocks badly.

Flame Mode
Non-Flame Mode
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EXAMPLE ENGINE KNOCK

• In spark ignition engines, knock occurs when
  unburned fuel-air mixture ahead of flame reacts
  homogeneously, i.e., it autoignites
• Rate of pressure rise is a key parameter in
  determining knock intensity and propensity for
  mechanical damage to piston-crank engine assembly
• Pressure vs. time traces for normal and knocking
  combustion in a spark-ignition engine shown below
• Note very rapid pressure rise in case of heavy
  knock.

Piston exposed to long terms effects of
knock http//www-cms.llnl.gov/s-t/int_combustion_e
ng.html
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EXAMPLE ENGINE KNOCK

• Create a simple constant volume model of
  autoignition process and determine temperature,
  pressure and fuel and product concentrations as a
  function of time
• Assume that initial conditions corresponding to
  compression of a fuel-air mixture from 300 K and
  1 atm to TDC for a compression ratio of 101.
  Initial volume before compression is 3.68x10-4 m3
  which corresponds to an engine with both bore and
  a stroke of 75 mm. Use ethane, C2H6, as fuel.
• Other assumptions
• One-step global kinetics using rate parameters
  for ethane
• Fuel, air and products all have equal molecular
  weights, MW29
• Specific heats for the fuel, air, and products
  are constant and equal, cp1,200 J/kg K
• Enthalpy of formation of air and products is zero
  and enthalpy of formation of fuel is 4x107 J/kg
• Stoichiometric air-fuel ratio is 16, and
  combustion is restricted to stoichiometric or
  lean cases

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SOLUTION MATLAB SIMULATION, CONSTANT VOLUME
Products
Oxidizer
Fuel
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SOLUTION EXPANDED SCALE ON TOP PLOT
Oxidizer
Products
Fuel
Large temperature increase in 0.1 ms
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EXAMPLE RESULTS AND COMMENTS

• Equations are integrated numerically using MATLAB
• Coupled ODEs are stiff
• Temperature increases only about 200 K in first 3
  ms, then T rises extremely rapidly to adiabatic
  flame temperature, Tad 3300 K, in less than 0.1
  ms
• This rapid temperature rise and rapid consumption
  of fuel is characteristic of a thermal explosion,
  where the energy released and temperature rise
  from reaction feeds back to produce
  ever-increasing reaction rates because of the
  (-Ea/RT) temperature dependence of the reaction
  rate.
• It can also be shown that huge pressure
  derivatives are associated with exploding stage
  of reaction, with peak values of dP/dt 1.9x1013
  Pa/s !!!
• Although this model predicted explosive
  combustion of mixture after an initial period of
  slow combustion, as is observed in real knocking
  combustion, single-step kinetics mechanism does
  not model true behavior of autoigniting mixtures
• In reality, induction period, or ignition delay,
  is controlled by formation of intermediate
  species (radicals)
• To accurately model knock, a more detailed
  mechanism would be required

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HOMEWORK 3 PART 1

• Explicitly derive all relevant equations and
  initial conditions shown in class for the
  constant volume engine knock simulation
• Calculate the actual value of the specific heat
  ratio, g(T), for ethane C2H6
• Use an program to solve the set of coupled
  differential equations
• If possible make your code intelligent using a
  variable time step based on some convergence
  criteria related to temperature gradient
• Generate plots of fuel, oxidizer and product
  molar concentrations versus time
• Generate a plot of temperature versus time
• Generate a plot of dP/dt versus time
• Repeat for f 0.7 and comment on results
• Repeat with methane fuel, C2H4 with f1.0 and
  f0.7 and comment on results
• Discuss the following issues in detail
• How would you modify your code to account for
  variable molecular weights and specific heats,
  i.e. which governing ODEs change and how?
• How would you update your code to utilize the
  4-step quasi-global mechanism on page 156?