A combustion engineer increases the fuel-air equivalence ratio from 1.0 (stoichiometric) to 1.2 (rich) while keeping the reactant inlet temperature and pressure constant. What happens to the adiabatic flame temperature?
AIt increases, because more fuel releases more total chemical energy
BIt stays the same, because total enthalpy of combustion is conserved
CIt decreases, because unburned excess fuel absorbs heat without contributing combustion energy
DIt increases up to equivalence ratio 1.2 before decreasing at higher ratios
At stoichiometric (φ = 1.0), all fuel burns and the released energy heats only the minimum product mass — AFT is maximized. Above stoichiometric (rich), the excess fuel cannot burn due to insufficient oxygen. This unburned fuel is still present in the products and absorbs sensible heat without releasing combustion energy, diluting the temperature. The intuitive error is thinking 'more fuel = more energy = higher temperature' — but the temperature depends on energy per unit product mass, not total energy.
Question 2 Multiple Choice
Why is the adiabatic flame temperature calculation typically iterative rather than solvable in a single step?
ABecause the stoichiometric air-fuel ratio changes with flame temperature
BBecause the heat of combustion (ΔH_combustion) is temperature-dependent and must be updated each iteration
CBecause the specific heats (cp) of product species like CO₂ and H₂O vary significantly with temperature, so H_products(T) is nonlinear in T
DBecause dissociation at all temperatures introduces unknown product concentrations that must be solved simultaneously
The energy balance H_products(T_flame) = H_reactants requires evaluating ∫cp dT for each product species from reference to T_flame. Because cp for CO₂ and H₂O varies significantly over the relevant temperature range (500–3000 K), H_products is a nonlinear function of T_flame with no closed-form inverse. The procedure is therefore: guess T_flame, compute H_products, compare to H_reactants, adjust, repeat. Dissociation (option D) introduces additional complexity at very high temperatures, but even without dissociation the cp variation alone necessitates iteration.
Question 3 True / False
At flame temperatures above approximately 1800 K, molecular dissociation of CO₂ and H₂O causes the actual flame temperature to exceed the simple adiabatic flame temperature prediction.
TTrue
FFalse
Answer: False
Dissociation is endothermic — breaking chemical bonds absorbs energy. When CO₂ and H₂O partially dissociate into CO, O₂, H₂, OH, and atomic species at high temperatures, they consume energy that would otherwise go into raising the temperature. This acts as a thermostatic effect, limiting peak temperature. The actual AFT is lower than the simple cp-based prediction, not higher. Correctly accounting for dissociation requires solving chemical equilibrium equations simultaneously with the energy balance, typically reducing AFT by 100–300 K.
Question 4 True / False
Preheating the combustion air (e.g., using exhaust gas in a recuperator) increases the adiabatic flame temperature for a stoichiometric mixture.
TTrue
FFalse
Answer: True
Preheating the air raises the enthalpy of the reactants entering the combustion process. Since energy balance requires H_products(T_flame) = H_reactants(T_preheat), a higher reactant enthalpy means the products must reach a higher temperature to satisfy the balance. Physically: less of the combustion energy must be 'spent' heating the air from ambient to flame temperature, so more is available to push the products to a higher final temperature. This is why recuperators improve efficiency in industrial furnaces and gas turbines.
Question 5 Short Answer
Why is the adiabatic flame temperature maximized at the stoichiometric mixture ratio, and why does both excess air and excess fuel reduce it?
Think about your answer, then reveal below.
Model answer: At stoichiometric, all fuel burns completely and the released energy heats exactly the minimum product mass — the ratio of energy released to mass heated is at its maximum. Excess air introduces additional N₂ and O₂ into the products that must be heated by the same combustion energy but contribute none themselves, reducing energy per unit mass and thus temperature. Excess fuel leaves unburned hydrocarbons in the products that absorb sensible heat without contributing combustion energy, also diluting the temperature. Only stoichiometric combustion avoids both dilution effects.
This question tests whether students understand AFT as energy per unit product mass, not total energy. Adding more air adds more mass to heat; adding more fuel adds unreacted material that acts as a heat sink. The stoichiometric point is a maximum because it is the only ratio where every molecule of oxidizer and fuel is consumed productively. In practice, engines often run slightly lean (excess air) to ensure complete combustion and reduce emissions, accepting the AFT penalty in exchange for reliability.