Combustion Calculation for Stoichiometry and Flame Properties

Combustion Stoichiometry

• To calculate the stoichiometric air requirement for combustion, we determine the amount of air (oxygen) needed to completely oxidize a given fuel without leaving any unburned fuel or excess oxygen.
• Let’s calculate this for a general fuel combustion process.

Steps for Stoichiometric Air Calculation

1. General Combustion Reaction:

For a hydrocarbon fuel of formula CxHy​:

      Cx Hy+νO2 →x CO2+y/2 *H2O

• νO2​​ (moles of oxygen) is given by:

             νO2=x+y/4

2. Mass of Oxygen Required:

Each mole of O2 has a molar mass of 32 g/mol  so the mass of oxygen required for one mole of fuel is:

   mO2​​=νO2​​×32g

3. Mass of Air Required:

Since air is 21% oxygen by volume (23.2% by mass), the mass of air required is:

Mair​=0.232*mO2​​​

Stoichiometric Air-to-Fuel Ratio (AFRst)

The air-to-fuel ratio at stoichiometry is the ratio of the mass of air required to the mass of the fuel:

AFRst = Mair_st/Mfuel​

Example  of Stoichiometric Air Calculations

Methane (CH4) Combustion

• Chemical Reaction:

        CH4+2O2→CO2+2H2O

• νO2=2
• Molar mass of CH4: 16 g/mol

Mass of Oxygen Required:

mO2=νO2×32=2×32=64 gm

Mass of Air Required:

Mair=mO2* 0.232=64* 0.232 ≈2 76 gm

Air-to-Fuel Ratio:

AFRst=mairmfuel=276/16≈17.25 

Hydrogen (CH4) Combustion

• Chemical Reaction:

            2H2+O2→2H2

• νO2=1
• Molar mass of H2​: 2 g/mol

Mass of Oxygen Required:

         mO2=νO2×32=1×32=32 gm

Mass of Air Required:

        mair=mO2* 0.232​=0.23*232​≈138g

Air-to-Fuel Ratio:

AFRs​=mfuel​mair​​=213/8​≈69.0

Ethanol (C2H5OH) Combustion

• Combustion reaction: C2H5OH+3O2→2CO2+3H2O
  • x=2, y=6
  • νO2​​=2+6/4​+/2​=3

Mass of oxygen required:

$$3\times 32=96\text{g}$$

Mass of air required:

        mair=96/0.232≈414 gm

Air-to-Fuel Ratio:

        AFRst=Mair/Mfuel=414/46≈9.0

Propane (C3H8) Combustion

• Combustion reaction: C3H8+5O2→3CO2+4H2O
  • x=3, y=8y
  • $=5$

Mass of oxygen required:

mO2=5×32=160 gm

Mass of air required:

mair=160*0.232≈690 g

Air-to-Fuel Ratio:

AFRst=Mair/Mfuel=446/90​≈15.7

 

Summary of Stoichiometric Air-to-Fuel Ratios:

• These values represent the mass of air required for the complete combustion of 1 unit of fuel at stoichiometric conditions.
  • Methane (CH4): AFRst≈17.25
  • Hydrogen (H2): AFRst≈69.0
• Stoichiometric Air-Fuel Ratios for Hydrocarbon Fuels

Stoichiometric Air-Fuel Ratios for Hydrocarbon Fuels

Fuel	Chemical Formula	Stoichiometric AFR (by mass)
Methane	CH4​	17.2
Ethane	C2H6​	16.0
Propane	C3H8​	15.6
Butane	C4H10​	15.5
Pentane	C5H12​	15.4
Hexane	C6H14​	15.2
Ethanol	C2H5OH	9.0
Gasoline	Approx. C8H18​	14.7
Diesel	Approx. C12H23​	14.5
Kerosene	Approx. C10H22​	14.6
Hydrogen	H2​	34.5

Stoichiometric Mixture Fraction Calculation

• The stoichiometric mixture fraction (Zst​) calculation depends on the stoichiometric air-fuel ratio, which defines the amount of air required for complete combustion of a given fuel.
• Let’s calculate it for methane (CH4​) and pure hydrogen (H2​) with air as the oxidizer.

Stoichiometric Mixture Fraction Formula:

       Zst=1/(1+So/Sf)​

Where:

• $So$: Stoichiometric mass of oxidizer per unit mass of fuel.
• Sf​: Stoichiometric mass of fuel per unit mass of oxidizer.

Breaking it Down:

sO=Air-to-Fuel Ratio at Stoichiometry (AFRst)

For air:

sO=(Mass of air/Mass of fuel)=(4.76*νO2*MWair)/(νF⋅MWF)

Where:

• νO2​​: Stoichiometric oxygen requirement.
• νF​: Fuel coefficient in the reaction.
• MWF​: Molar mass of the fuel (g/mol).
• MWair​: Molar mass of air, approximately 28.97 g/mol
• The factor 4.76 accounts for the ratio of air to oxygen (79%N2+21%O2)

Methane (CH4) Combustion

Combustion Reaction:

     CH4+2 O2→CO2+2 H2O

• νO2=2
• νF=1
• MWCH4=16 g

Stoichiometric Air-to-Fuel Ratio (AFRst)

AFRst=4.76*2*28.97/1⋅16=17.19

Mixture Fraction:

Zst=1/(1+AFRst)=1/(1+17.19)​≈0.055

For Hydrogen (H2) Combustion

Combustion Reaction:

2 H2+O2→2 H2O2 

• νO2=1
• νF​=2
• MWH2=2 g/mol

Stoichiometric Air-to-Fuel Ratio (AFRst)

AFRst=4.76*1*28.97/(2*2)=​=34.49

Mixture Fraction:

Zst=1/(1+AFRst_=​=1/(1+34.491​)≈0.028

Summary of Stoichiometric Mixture Fractions:

• Methane (CH4​): Zst​≈0.055
• Hydrogen (H2): $\approx 0.028$

These values are specific to the stoichiometric combustion of these fuels with air.

 

Scope of stichometry for CFD Simulations

• The stoichiometry of combustion plays a critical role in providing input data for Computational Fluid Dynamics (CFD) simulations, especially in modeling chemical reactions, energy transfer, and pollutant formation in combustion systems.
• Here’s an overview of its scope as a CFD data

Defining Combustion Chemistry

• Stoichiometric calculations define the chemical reaction equations for fuels and oxidizers, which are crucial in CFD models that simulate:
  • Combustion reactions.
  • Species transport (e.g., CO, CO2_22​, H2O, NOx.
  • Energy release and heat transfer.
• Example: For a hydrocarbon fuel, the stoichiometric air-to-fuel ratio helps establish the oxygen consumption and product formation for equilibrium calculations.

Setting Boundary Conditions

• Stoichiometric ratios influence key boundary condition parameters in CFD simulations:
• Inlet Conditions:
  • Air-fuel mixture composition at the inlets.
  • Equivalence ratio
• Outlet Conditions:
  • • Expected species concentrations (e.g., excess oxygen, unburned hydrocarbons) depend on stoichiometry.

Energy Source Term

Stoichiometric calculations provide the heat release rate, which is a function of:

• Fuel type and lower heating value (LHV).
• Combustion efficiency.
• Extent of reaction (stoichiometric or otherwise).

CFD uses this data to model thermal dynamics, such as:

• Temperature rise in the combustor.
• Heat transfer to walls or surroundings.

Application-Specific Scope

• Gas Turbines: Stoichiometry defines lean-premixed conditions for low-emission designs.
• IC Engines: Helps in simulating stratified charge combustion or fuel injection strategies.
• Industrial Boilers: Used for optimizing fuel-air supply for efficiency and minimal pollutants.
• Burners and Furnaces: Guides flame stability and energy efficiency analysis.

Uses Stoichiometry for CFD Simulations

1. ANSYS Fluent: Utilizes stoichiometric data for premixed, non-premixed, and partially premixed combustion models.
2. OpenFOAM: Uses mixture fraction and equivalence ratio in reacting flow solvers.
3. COMSOL Multiphysics: Employs stoichiometric relationships for chemical species transport and energy balance in combustion simulations.