MAE 5310: COMBUSTION FUNDAMENTALS

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MAE 5310 COMBUSTION FUNDAMENTALS

• Introduction to Chemical Kinetics
• September 10, 2009
• Mechanical and Aerospace Engineering Department
• Florida Institute of Technology
• D. R. Kirk

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CHEMICAL KINETICS OVERVIEW

• In many combustion processes, chemical reaction
  rates control rate of combustion
• Chemical reaction rates determine pollutant
  formation and destruction
• Ignition and flame extinction are dependent on
  rate processes
• Overall reaction of a mole of fuel, F, with a
  moles of oxidizer, O, to form b moles of
  products, P, can be expressed by a global
  reaction mechanism as
• From experimental measurements, rate at which the
  fuel is consumed expressed as
• ci is molar concentration of ith species in
  mixture
• Equation states that rate of disappearance of
  fuel is proportional to each of reactants raised
  to a power
• Constant of proportionality, kglobal, is called
  global rate coefficient, which is a strong
  function of temperature and minus sign indicates
  that fuel concentration decreases with time
• Exponents n and m relate to reaction order
• Reaction is nth order with respect to fuel
• Reaction is mth order with respect to oxidizer
• Reaction is (nm)th order overall

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EXAMPLE OF INTERMEDIATE SPECIES

• Consider global reaction of conversion of
  hydrogen and oxygen to water
• The following elementary reactions are important
• First reaction produces hydroperoxy, HO2 and a
  hydrogen atom, H
• HO2 and H are called radicals
• Radicals, or free radicals, are reactive
  molecules, or atoms, that have unpaired electrons
• To have a complete picture of hydrogen and oxygen
  combustion over 20 elementary reactions are
  necessary
• Collection of elementary reactions necessary to
  describe an overall reaction is called a
  mechanism

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MOLECULAR KINETIC AND COLLISION THEORY
OVERVIEWBIMOLECULAR REACTIONS

• Molecular collision theory an be used to provide
  insight into form of bimolecular reaction rates
  and to suggest the temperature dependence of the
  bimolecular rate coefficient
• Consider a single molecule of diameter s
  traveling at constant speed v and experiencing
  collisions with identical, but stationary,
  molecules
• If distance between traveled between collisions
  (mean free path, l) is large then moving molecule
  sweeps out a cylindrical volume in which
  collisions are possible vps2Dt in a time
  interval Dt.
• At ambient conditions for gases
• Time between collisions O(10-9 s)
• Duration of collisions O(10-12 10-13 s)
• If stationary molecules distributed randomly and
  have a number density, n/V, the number of
  collisions experienced by the traveling molecule
  per unit time is Z collisions per unit time
  (n/V)vps2
• In actual gas all molecules are moving
• Assuming a Maxwellian distribution for all
  molecules, the collision frequency, Zc, is given
  by

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MOLECULAR KINETIC AND COLLISION THEORY
OVERVIEWBIMOLECULAR REACTIONS

• So far theory applies to identical molecules
• Extend analysis to collisions between unlike
  molecules have diameters sA and sB. Diameter of
  collision volume is then given as sAB(sA sB)/2
• This is an expression for the frequency of
  collision of a single A molecule with all B
  molecules
• Ultimately we want collision frequency associated
  with all A and B molecules
• Total number of collisions per unit volume and
  per unit time is obtained by multiplying
  collision frequency of a single A molecule by the
  number of A molecules per unit volume and using
  the appropriate mean molecular speed (RMS)
• ZAB/V Number of collisions between all A and
  all B / Unit volume Unit time

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MOLECULAR KINETIC AND COLLISION THEORY
OVERVIEWBIMOLECULAR REACTIONS

• NAvogadro 6.022x1023 molecules/mol or
  6.022x1026 molecules/kmol
• Probability, P, that a collision leads to
  reaction can be expressed as product of two terms
• Energy factor, exp-EA/RT
• Expresses the fraction of collisions that occur
  with an energy above the threshold level
  necessary for reaction, EA, or activation energy
• Geometrical or steric factor, p
• Takes into account the geometry of collisions
  between A and B

More common curve fit A, n and EA are empirical
parameters
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EXAMPLE H2 OXIDATION AND NET PRODUCTION RATES
Global reaction
Partial mechanism Find dO2/dt, dH/dt, etc.
System of 1st order, ordinary differential
equations
Initial conditions for each participating species
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GENERAL NOTATION
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EXAMPLE

• Determine the collision-theory steric factor for
  the reaction O H2 ? OH H at T2000 K give the
  sphere diameters, sO3.050 and sH22.827 Å using
  the data in Appendix 2 of Glassman
• Comments
• Pay attention to units
• kb1.381x10-23 J/K 1.381x10-16 g cm2/s2 K