MAE 5310: COMBUSTION FUNDAMENTALS

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MAE 5310 COMBUSTION FUNDAMENTALS

• Lecture 5 Chemical Equilibrium
• September 1, 2008
• Mechanical and Aerospace Engineering Department
• Florida Institute of Technology
• D. R. Kirk

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CHEMICAL EQUILIBRIUM

• So far we have calculated adiabatic flame
  temperature assuming complete combustion
• All fuel is completely oxidized to form CO2, H2O
  and excess O2 and N2 are carried through
  unaffected
• This assumption is fine for T lt 1250 K, but most
  combustion systems operate at higher T
• Species that are normally stable at ambient
  conditions dissociate
• Concentration is determined by a balance between
  oxidation and formation
• Balance is a function of T, P and concentration
• Note The chemical equilibrium relations we will
  use still only approximate the species
  concentrations in a combustion process. That is,
  they rest on the assumption that the conditions
  are constant for a sufficiently long time for all
  the reactions to reach equilibrium

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ADDITIONAL PRODUCT FORMATION

• NO Dissociation Complete Combustion
• Equivalence ratio less than or equal unity, f 1
• The products formed are CO2, H2O, O2, and N2
• Equivalence ratio greater than unity, f gt 1
• The products formed are CO2, CO, H2O, H2, and N2
• WITH Dissociation
• Products formed include CO2, CO H2O, H2, H, OH,
  O2, O, NO, N2, and N
• Concentration is dependent on T, P and f

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CHEMICAL EQUILIBRIUM FOR A FIXED-MASS SYSTEM

• If final temperature of combustion reaction is
  high enough, CO2 will dissociate
• Can calculate adiabatic flame temperature as
  function of a (a fraction of CO2 dissociated)
• Must consider second law dS 0
• Composition of system will shift toward point of
  maximum entropy when approaching from either
  side, since dS is positive
• Once maximum entropy is reached no further
  changes since would violate second law
• (dS)U,V,m 0

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PROPANE-AIR COMBUSTION AT 1 ATMAdopted From
Turns, S.R., Introduction to Combustion
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2nd LAW OF THERMODYNAMICS GIBBS FREE ENERGY

• To arrive at equilibrium relations, employ 2nd
  Law of Thermodynamics
• State 2nd Law in terms of the Gibbs Free Energy,
  GH-TS
• For a closed system at constant T and P, the
  Gibbs free energy is minimum at thermodynamic
  equilibrium

Basic Thermodynamic Relations
Criteria for Equilibrium
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MORE USEFUL FORMS

• GiHi-TSi
• Separate Gi into a pressure dependent and term
  and pressure independent term
• Recall that Cpi is not a function of pressure
• The more negative DGº is, the larger Kp is and
  the more spontaneous the reaction is

Another useful form
Equation 40
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COMMENTS ON KP

• The Kp of a reaction depends on temperature only
• Independent of pressure of the equilibrium
  mixture
• Not affected by presence of inert gases
• The Kp of the reverse reaction is 1/ Kp
• The larger the Kp, the more complete the reaction
• If Kp gt 1,000 (or ln Kp gt 7) reaction assumed
  complete
• If Kp lt 0.001 (or ln Kp lt -7) reaction assumed
  not to occur
• Mixture pressure affects the equilibrium
  composition (but not Kp)
• Presence of inert gases affects the equilibrium
  composition
• When stoichiometric coefficients are doubled, the
  value of Kp is squared
• Free electronic in the equilbrium composition can
  be treated as an ideal gas
• Equilibrium calculations provide information on
  the equilibrium composition of a reaction, not on
  the reaction rate.