Combustion

Combustion is a rapid exothermic chemical reaction between a fuel and an oxidizer that converts chemical energy into heat and reaction products. In engineering practice combustion is analyzed using stoichiometry (to determine theoretical oxidizer required), energy balances (to compute heat release and adiabatic flame temperatures), and transport/kinetic concepts (flame propagation, ignition, pollutant formation). Key distinctions: complete vs incomplete combustion (CO2 + H2O vs CO, H2, soot), premixed vs diffusion flames, laminar vs turbulent regimes, and pollutant formation pathways (thermal NOx via Zeldovich mechanisms at high temperature, fuel-Nox from fuel-bound nitrogen, and prompt NOx). Practical design accounts for equivalence ratio, excess air, flame stability, ignition energy, residence time, and heat losses which affect efficiency and emissions.

Governing FormulaUseful relations and assumptions (SI units): - Stoichiometric reaction balance: sum of stoichiometric coefficients of reactants = products. Example: CH4 + 2 O2 -> CO2 + 2 H2O. - Air composition (by mole): O2 = 0.21, N2 = 0.79; O2:N2 molar ratio ≈ 1:3.76. One mole O2 is accompanied by 3.76 mol N2 in dry air. - Theoretical (stoichiometric) air per mole fuel: n_air,stoich = n_O2,stoich * (1 + 3.76). - Equivalence ratio: phi = (fuel/oxidizer)_actual / (fuel/oxidizer)_stoichiometric. phi < 1 = fuel-lean, phi = 1 stoichiometric, phi > 1 fuel-rich. - Air–fuel ratio (mass basis): AF_stoich = (molar air per mole fuel * M_air) / M_fuel, where M_air ≈ 28.97 g/mol. - Heat of reaction (at reference T): Delta_H_rxn = sum(n_i * Delta_Hf,products) - sum(n_j * Delta_Hf,reactants). - Adiabatic flame temperature (approximate constant-cp): Q_release = sum(n_prod * cp_prod) * (T_ad - T_initial). Solve T_ad = T_initial + Q_release / (sum n_prod * cp_prod). (Assumes constant average molar heat capacity cp over temperature range.) - Heating value per mass: LHV or HHV (J/kg) = (|Delta_H_rxn| per mole) / molar mass (kg/mol) using appropriate product state (water vapor for LHV). (When numerical values are needed in quiz problems, necessary standard constants and formation enthalpies will be provided in each question.)

Knowledge Check

10 Questions

1.Compute the stoichiometric amount of dry air (in moles) required to completely combust 1.00 mol of methane (CH4) to CO2 and H2O at standard composition of dry air (O2 mole fraction = 0.21, N2 = 0.79). Reaction: CH4 + 2 O2 -> CO2 + 2 H2O. Use O2:N2 = 1:3.76.

2.Which expression correctly defines the equivalence ratio (phi) for a premixed fuel–oxidizer mixture?

3.For 1.00 mol CH4 mixed with 6.00 mol of dry air (O2 mole fraction 0.21), determine the equivalence ratio phi. Use the stoichiometric air for CH4 as 9.52 mol air per mol CH4 (from Q1).

4.Estimate the adiabatic flame temperature for complete stoichiometric combustion of 1.00 mol CH4 with stoichiometric air using a simple constant-molar-heat-capacity model. Use: reaction enthalpy (products gas) Delta_H_rxn = -802.3 kJ/mol CH4 (i.e., 802.3 kJ released per mol CH4), assume average molar heat capacity of the product mixture cp,avg = 30.0 J/(mol·K), and total products after stoichiometric combustion = 10.52 mol (1 CO2 + 2 H2O + 7.52 N2). Take initial temperature 298 K. What is the approximate adiabatic flame temperature (T_ad)?

5.Which set of conditions most strongly favors formation of carbon monoxide (CO) and soot (particulate carbon) during hydrocarbon combustion?

6.Using the formation enthalpy of gaseous water Delta_Hf,H2O(g) = -241.8 kJ/mol, compute the lower heating value (LHV) in MJ/kg of hydrogen fuel (reaction H2 + 0.5 O2 -> H2O(g)). Use molar mass H2 = 2.016 g/mol.

7.Which parameter most strongly controls the rate of thermal NOx formation (the Zeldovich mechanism) in high-temperature air combustion?

8.Approximately what is the lower flammability limit (LFL) by volume in air at 1 atm and 298 K for methane (CH4)? (Use well-known empirical data.)

9.Calculate the theoretical (stoichiometric) air–fuel mass ratio (AF_stoich) for liquid octane approximated by C8H18. Use reaction stoichiometry and assume dry air molar mass M_air = 28.97 g/mol and octane molar mass M_C8H18 = 114.23 g/mol. Reaction: C8H18 + (25/2) O2 -> 8 CO2 + 9 H2O. Use O2:N2 = 1:3.76 to convert O2 moles to air moles.

10.For a premixed methane–air mixture at fixed initial temperature and pressure, the laminar flame speed typically reaches its maximum value near which equivalence-ratio condition?