Combustion Theory

1
Combustion Theory Adiabatic Flame Temperature

• Brian Moore
• Shaun Murphy

2
Outline

• Flame Theory
• Combustion Chamber Chemistry
• Adiabatic Flame Temperature
• Example Problem

3
Types of Flames

• Two basic categories
• Pre-mixed
• Diffusion
• Both characterized as Laminar or Turbulent

4
Premixed

• Results from gaseous reactants that are mixed
  prior to combustion
• Flame propogates at velocities slightly less than
  a few m/s
• Considered constant pressure combustion
• Reacts quite rapidly

Example Spark Ignition Engine
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Diffusion

• Gaseous reactants are introduced separately and
  mix during combustion
• Energy release rate limited by mixing process
• Reaction zone between oxidizer and fuel zone

Example Diesel Engine
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Laminar

• Premixed
• Ex. Bunsen Burner
• Flame moves at fairly low velocity
• Mechanically create laminar conditions
• Diffusion
• Ex. Candle Flame
• Fuel Wax, Oxidizer Air
• Reaction zone between wax vapors and air

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Turbulent

• Premixed
• Heat release occurs much faster
• Increased flame propagation
• No definite theories to predict behavior
• Diffusion
• Can obtain high rates of combustion energy
  release per unit volume
• Ex. Diesel Engine
• Modeling is very complex, no well established
  approach

8
Flame Propagation

• Initial spark causes pressure wave formation
• Flame propagation considered constant pressure
• Burned and Unburned regions
• Unburned portion may undergo autoignition, known
  as Knock

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Chemistry Basics

• Reactants
• Fuel Hydro-Carbon
• Octane (C8H18)
• Oxidizer Dry Air (D.A)
• 21 O2
• 79 N2
• 1 mol O2 ? 3.76 mol N2

• Products
• CO2
• H2O
• N2

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Example Using Butane
Ideal Chemical Equation

• C4H10 O2 ? CO2 H2O
• Balancing the Equation
• Conservation of Mass
• C4H10 6.5O2 ? 4CO2 5H2O

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Example Cont.

• Practical Chemical Equation
• Air used as oxidizer, not pure oxygen
• C4H10 6.5(O23.76N2) ? 4CO2 5H2O24.44N2
• C4H10 31.03D.A. ? 4CO2 5H2O 31.03D.A -6.5O2

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Balancing Made Easy

• CaHb a(O23.76N2) ? bCO2 cH2O dN2
• a a(b/4) b a c b / 2 d
  3.76a

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Combustion Energy

• DU Q - W
• Q DU W
• W PDV
• Q DU PDV DH
• Q Hprod - Hreact

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Enthalpy

• Enthalpy of Formation (Dhf)
• Energy required to form the compound
• Change in Enthalpy (Dh)
• Difference in enthalpy between Product Temp. and
  Reference Temp.
• Dh h(Tprod) - h(Tref)
• Total Enthalpy (h)
• h Dhf Dh
• H S(nihi)

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Adiabatic Assumptions

• No heat transfer through cylinder walls
• All energy transferred to engine work exhaust
  products
• Allows Adiabatic Flame Temperature (AFT) to be
  calculated
• Q 0 Hreact Hprod

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Adiabatic Flame Temperature

• Highest possible temperature that can be achieved
  during combustion
• Never achieved in practice
• No realistic combustion chamber is adiabatic
• Dissociation lowers temperature
• Analagous to Carnot cycle for Heat Engines
• Useful design parameter
• Upper limit of exhaust temp. is known
• Calculation is an iterative process

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AFT Example Calculation

• Problem Statement Liquid Methane (CH4) is
  burned at a constant pressure. The air and fuel
  are supplied at 298 K and 1 atm. Determine the
  adiabatic flame temperature for these conditions
  assuming complete combustion.
• Balance Chemical Equation
• CH4 2(O23.76N2) ? CO2 2H2O7.52N2
• Energy Balance and Adiabatic Assumptions
• Q 0 Hprod Hreact Therefore,
  Hreact Hprod

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Calculations Cont.

• Determine Enthalpy of Reactants
• Dhf, CH4 -74.81 kJ/mol (from chart)
• Dhf, O2 Dhf, N2 0
• Hreact S(nihi) (n of moles)
• Hreact 1mol (-74.81 kJ/mol)
• Hreact -74.81 kJ

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Calculations Cont.

• Determine Enthalpies of Products
• Guess value for temperature required try 1000K
  
• hCO2 Dhf, CO2 (hCO2(Tprod) hCO2(Tref))
• hH2O Dhf, H2O (hH2O(Tprod) hH2O(Tref))
• hN2 Dhf, N2 (hN2(Tprod) hN2(Tref))
• Use tables provided to find hf and Dh

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Calculations Cont.

• Enthalpy of Formation values
• Dhf,CO2 -393.5 kJ/mol
• Dhf,H2O -241.8 kJ/mol
• Dhf,N2 0 kJ/mol
• Dh values
• hCO2(Tprod) hCO2(Tref) 33.41 kJ/mol
• hH2O(Tprod) hH2O(Tref) 25.98 kJ/mol
• hN2(Tprod) hN2(Tref) 21.46 kJ/mol

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Calculations Cont.

• Total Enthalpy of each molecule h Dhf Dh
• hCO2 -393.5 kJ/mol 33.41 kJ/mol -360.09
  kJ/mol
• hH2O -241.8 kJ/mol 25.98 kJ/mol -215.82
  kJ/mol
• hN2 0 kJ/mol 21.46 kJ/mol 21.46 kJ/mol
• Total Enthalpy of Products
• Hprod S(nihi)
• Hprod (1) -360.09 (2) -215.82 (7.5) 21.46
• Hprod -630.78 kJ

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Calculations Cont.

• Hprod ltlt Hreact Try Higher Temperature
  (2300 K)
• hCO2 -393.5 kJ/mol 109.67 kJ/mol -283.83
  kJ/mol
• hH2O -241.8 kJ/mol 88.29 kJ/mol -153.51
  kJ/mol
• hN2 0 kJ/mol 67.01 kJ/mol 67.01 kJ/mol
• Hprod S(nihi)
• Hprod 1( 283.83) 2( 153.51) 7.5( 67.01)
• Hprod -88.28 kJ

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Calculations Cont.

• Hprod lt Hreact Try Higher Temperature
  (2400 K)
• hCO2 -393.5 kJ/mol 115.79 kJ/mol -277.71
  kJ/mol
• hH2O -241.8 kJ/mol 93.60 kJ/mol -148.20
  kJ/mol
• hN2 0 kJ/mol 70.65 kJ/mol 70.62 kJ/mol
• Hprod S(nihi)
• Hprod (1) 302.05 (2) -169.11 (7.5) 56.14
• Hprod -44.46 kJ

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Calculations Cont.

• Interpolate to find proper value

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Summary

• Premixed and Diffusion Flames
• Laminar
• Turbulent
• Combustion Chemistry
• Balancing Chemical equations
• First Law Energy Balance
• Adiabatic Flame Temperature
• Assumptions
• Determination
• Iteration

26
Homework Problem

• Problem Statement Liquid Octane (C8H18) is
  burned at a constant pressure. The air and fuel
  are supplied at 298 K and 1 atm. Determine the
  adiabatic flame temperature for these conditions
  assuming complete combustion.