MECH3260 Chap.5 Combustion and Stoichiometry
Combustion and Stoichiometry
Week 5 turns the gas-mixture analysis of Chapter 3 on a chemical reaction.
It starts with the atom balance that fixes the reaction, then describes mixtures that are not stoichiometric using either excess air or the equivalence ratio, and finds the dew point of the combustion products by reapplying the psychrometry tool from Chapter 4. It then values a fuel through its enthalpy of formation and its higher and lower heating values.
The second half is energy accounting: the standardised enthalpy that lets a first-law balance close when the substances leaving are not the substances that arrived, and the adiabatic flame temperature, the ceiling a reaction reaches when no heat or work leaves, found by iterating the product temperature until the two sides of the balance agree.
What this chapter covers
- 01
Writing a stoichiometric reaction with the fuel coefficient set to 1 and every atom balanced
- 02
Non-stoichiometric combustion described as % theoretical air (100% = stoichiometric) or % excess air
- 03
Air-fuel ratio A/F, the mass of air supplied per unit mass of fuel burned, and equivalence ratio phi = (F/A)actual / (F/A)stoich -- rich if phi>1, lean if phi<1
- 04
Product dew point: partial pressure of water in the gaseous products, then saturation temperature at that pressure -- the corrosion-risk temperature for exhaust equipment
- 05
Enthalpy of formation h_f (zero for elements by convention, negative for exothermic formation)
- 06
Higher vs lower heating value (HHV vs LHV) -- LHV used for power-system calculations
Propane burned with 30% excess air
- +2Stoichiometric: C3H8 + 5(O2+3.76N2) -> 3CO2 + 4H2O + 18.8N2.
- +230% excess air: supply 6.5 mol O2 -> 3CO2 + 4H2O + 1.5O2 + 24.44N2.
- +2A/F by mass = 892.3/44 = 20.3.
- +2Equivalence ratio phi = 15.6/20.3 = 0.77 (lean).
- +2Product dew point: P_v=12.27 kPa, T_dp ~ 49.8-49.9°C by interpolation.
Key terms
- Stoichiometric air
- Exactly the air required for complete combustion of the fuel supplied, with no oxygen left over. It is the reference against which every real combustor is described as running rich or lean.
- Air-fuel ratio
- The mass of air supplied per unit mass of fuel. The fuel-air ratio is its reciprocal, and mixing the two up is a fast way to invert an answer without noticing.
- Equivalence ratio
- The actual fuel-to-air ratio scaled against the stoichiometric fuel-to-air ratio. Above one the mixture is rich and above stoichiometric fuel, below one it is lean, and the molar masses cancel out of the definition.
- Excess air
- Air supplied beyond the stoichiometric requirement, quoted as a percentage above one hundred percent theoretical air. It leans the mixture, and because it must still be heated to the product temperature, it also lowers the flame temperature.
- Enthalpy of formation
- The energy accounting for making a substance from its elements at the reference state. It is negative for an exothermic formation and zero for elemental substances in their stable form, which is why oxygen and nitrogen carry only a temperature term.
- Standardised enthalpy
- The enthalpy of formation plus the change from the reference temperature to the actual temperature, summed over the moles of each species. It is what allows an energy balance to close across a reaction.
- Lower heating value
- The energy released by complete combustion when the product water is left as vapour. The higher value assumes it condenses and so exceeds it by the latent heat, and power-system calculations normally quote the lower one.
- Adiabatic flame temperature
- The product temperature reached when no heat and no work leave the combustor, making the product enthalpy equal the reactant enthalpy. It is a maximum that real flames do not reach because combustion is incomplete and products dissociate.
Combustion and Stoichiometry FAQ
Why do more excess air and a higher equivalence ratio mean opposite things?
They are measured from different sides of the same balance. Excess air counts air above the theoretical requirement, so adding it leans the mixture. Equivalence ratio compares actual fuel-to-air against stoichiometric fuel-to-air, so adding fuel or removing air raises it and richens the mixture. Supply more air and one number goes up while the other goes down.
This is the single highest-frequency mix-up in the topic, and writing both definitions out once at the top of your notes is usually enough to stop it.
Why does the products dew point matter for a real combustor?
Because combustion products carry water vapour, and if the exhaust cools below the temperature at which that vapour saturates, liquid condenses inside the flue or the heat exchanger. That water is acidic in the presence of sulphur and it corrodes.
The calculation is the same partial-pressure argument used for moist air, run on the product mixture, which is why this chapter reuses the psychrometry tool rather than introducing a new one.
Which heating value should I use?
Whichever one matches the state the water leaves in. If the exhaust is hot enough that the water stays a vapour, its latent heat was never recovered and the lower value is the honest figure, which is the usual case for engines and gas turbines. Condensing appliances do recover it, and there the higher value applies. Quoting the higher value for a system that vents hot exhaust overstates the available energy by several percent.
How do I find a flame temperature when I need its own value to look up the enthalpies?
By searching rather than solving. The reactant side is computable straight away from the given inlet temperature and never changes again. Then guess a product temperature, sum the product standardised enthalpies at that guess, and compare. Find one guess that lands above the reactant total and one below, then interpolate between them.
Two or three trials is normally enough, and showing the bracketing pair is part of the method the marks follow.
Exam move
Treat this chapter as an integration exercise rather than new territory. Writing the products as a mixture reuses the mole-fraction tools from Chapter 3, and finding when the exhaust water condenses reuses the dew-point argument from Chapter 4, so the genuinely new content is short: the atom balance and the two ratios that describe how far from stoichiometric a combustor runs.
Get the atom balance mechanical first, because every later step depends on the product mole numbers being right. Then write the two ratio definitions side by side and check you can say which way each moves when the air supply changes. Save the standardised-enthalpy bookkeeping for a separate session and work it on a mole basis throughout, since converting to mass part way through is where the sign errors get in.
Finish with one full flame-temperature iteration, written out including the failed first guess, so the search feels routine rather than alarming under exam conditions.
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