Thermodynamics of Combustion

Abstract

Although combustion processes often involve chemical reactions that may be far from equilibrium, the equilibrium state provides a useful guide on the ultimate combustion state if sufficient time is given. Chemical compositions of the combustion products at equilibrium, heating value of a fuel, and flame temperature can be determined from thermodynamics. In comparison to the thermodynamics of a pure substance, the thermodynamics of combustion systems are complicated by the change of components during combustion. That is, the components in the final state are different from those in the initial state. With the introduction of enthalpy of formation, the general approach normally used to solve thermodynamic problems of a pure substance can be extended to combustion systems. The following topics will be discussed in this chapter: (1) properties of mixtures, (2) combustion stoichiometry, (3) heating values and enthalpy of formation, (4) adiabatic flame temperatures, and (5) equilibrium state (Cantera Program).

Exercises

• 2.1 Consider an isentropic combustion system with a total of K species. Assuming constant specific heats, show that the mixture temperature and pressure at two different states are related to the respective pressures as

  $$ \frac{{{T_2}}}{{T{}_1}} = {\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^{(\gamma - 1)/\gamma }} $$

  where

  $$ \gamma = \frac{{\sum\limits_{i = 1}^K {{m_i}{c_{p,i}}} }}{{\sum\limits_{i = 1}^K {{m_i}{c_{v,i}}} }}. $$

• 2.2 Measurements of exhaust gases from a methane-air combustion system show 3% of oxygen by volume (dry base) in the exhaust. Assuming complete combustion, determine the excess percentage of air, equivalence ratio, and fuel/air ratio.

• 2.3 There has been a lot of interest about replacing gasoline with ethanol, but is this really a good idea? We’re going to compare a blend of ethanol (70% ethanol and 30% gasoline by volume) to gasoline. Calculate the lower heating value (LHV) of a 70% ethanol/30% isooctane mixture in terms of kJ/mol of fuel. Assume complete combustion. How does this compare to the tabulated value for gasoline (isooctane)? Assuming a 20% thermal efficiency, if you need to get 100 kW of power from an engine, how much of each fuel (in mol/s) do you need? If you have a stoichiometric mixture of the ethanol/gasoline blend and air in your 100 kW engine, how much CO₂ are you emitting in g/s? How does this compare to the same engine running a stoichiometric mixture of 100% gasoline and air?

• 2.4 Gasoline is assumed to have a chemical composition of C_8.26 H_15.5.

  • (a) Determine the mole fractions of CO₂ and O₂ in the exhaust for an engine with normalized air/fuel ratio λ = 1.2 with the assumption of complete combustion.

  • (b) The enthalpy of formation of C_8.26 H_15.5 is −250 MJ/kmol. Determine the LHV of gasoline in terms of MJ/kg. The molecular mass of C_8.26 H_15.5 is 114.62 kg/kmol.

  • (c) Using an average c _p for the products at 1,200 K, estimate the adiabatic flame temperature at constant pressure of 1 atm for the lean (λ = 1.2) mixture.

• 2.5 A mixture of methane gas and air at 25°C and 1 atm is burned in a water heater at 150% theoretical air. The mass flow rate of methane is 1.15 kg/h. The exhaust gas temperature was measured to be 500°C and approximately 1 atm. The volumetric flow rate of cold water (at 22°C) to the heater is 4 L/min.

  • (a) Draw a schematic of the water heater and name its most important elements.

  • (b) Using Cantera, determine the amount of heat generated from burning of 1 kg of methane.

  • (c) Calculate the temperature of the hot water if the heat exchanger were to have an efficiency of 1.0, i.e., perfect heat transfer.

• 2.6 An acetylene-oxygen torch is used in industry for cutting metals.

  • (a) Estimate the maximum flame temperature using average specific heat c _p .

  • (b) Measurements indicate a maximum flame temperature of about 3,300 K. Compare with the result from (a) and discuss the main reasons for the discrepancy.

• 2.7 A space heater burns propane and air with intake temperature at T₀ = 25°C and pressure at 1 atm (see Fig. 2.5). The combustible mixture enters the heater at an equivalence ratio φ = 0.8. The exhaust gases exit at temperature T₁ = 500 K and contain CO₂, H₂O, O₂, and N₂ only at station 1. In order to use a 3-way catalyst for exhaust treatment, additional propane is injected into the exhaust to consume all the remaining oxygen in the exhaust such that the gases entering the catalyst contain only CO₂, H₂O, and N₂ at station 2. Assume that the entire system is at P = 1 atm and complete combustion occurs in both the heater and in the exhaust section.

  Fig. 2.5

  

  Exercise 2.7

  • (a) The volumetric flow rate of propane entering the heater is 1 L/min. Determine the injection rate of propane into the exhaust between station 1 and station 2 (see Fig. 2.5). Note that the propane at the injection station is at the same conditions as heater inlet, i.e., T = 25°C and P = 1 atm.

  • (b) With the assumption of constant specific heats for the gases, estimate the temperature at station 2, T ₂ . The specific heat can be approximated by that of N₂ at 700 K as ${\hat{c}_p} = 30.68\,kJ/kmol - K$,

• 2.8 Two grams of solid carbon, C(s), are combusted with pure oxygen in a 500 cm³ bomb calorimeter initially at 300 K. After the carbon is placed inside the bomb, the chamber is evacuated and then filled with gaseous oxygen from a pressurized tank.

  • (a) Determine the minimum O₂ pressure inside the bomb necessary to allow complete combustion of the solid carbon.

  • (b) When the bomb is cooled back to its initial temperature of 300 K, determine the pressure inside the bomb.

• 2.9 Consider the combustion chamber in a jet engine at cruising altitude. For simplicity, the combustor is operated at 1 atm of pressure and burns a stoichiometric (φ = 1) mixture of n-heptane (C₇H₁₆) and air. The intake conditions are as indicated in Fig. 2.6.

  Fig. 2.6

  

  Exercise 2.9

  • (a) Write the stoichiometric chemical reaction for the fuel with air.

  • (b) If the mass flow rate of fuel is 1 kg/s, what is the mass flow rate of air?

  • (c) What is the rate of heat loss from the combustion chamber if 10% of the LHV (heat of combustion) of the fuel is lost to surroundings?

  • (d) What is the temperature of the products?

  • (e) How does the temperature change if we burn fuel rich (φ > 1)? How about fuel lean (φ < 1)? (Hint: Easiest to show with a plot)

• 2.10 An afterburner is a device used by jet planes to increase thrust by injecting fuel after the main combustor. A schematic of this system is shown in Fig. 2.7. In the main combustor, hexane is burned with air at an equivalence ratio of φ = 0.75. The products of the main combustor are CO₂, H₂O, O₂ and N₂, all of which enter the afterburner. In the afterburner, additional hexane is injected such that the equivalence ratio is φ = 1.25. In the afterburner the hexane reacts with the excess O₂ from the main combustor to form CO, H₂O, and CO₂ only. Combined with the products of the main combustor, the gases exiting the afterburner are CO, CO₂, H₂O, O₂ and N₂. The entire system is insulated, and the pressure everywhere is atmospheric. The inlet temperature of the hexane and air is 20°C. Determine the temperature of the exhaust gases at each stage (Fig. 2.7). Note: An approximate answer is sufficient and it can be assumed that the specific heats for the gases are constant and approximately equal to that of N₂ at 1,000 K.

  Fig. 2.7

  

  Exercise 2.10