Thermodynamics

H prod H react (15–16)Chapter 15 | 771The adiabatic flame temperature of a steady-flow combustion process isdetermined from Eq. 15–11 by setting Q 0 and W 0. It yieldsora N p 1h° f h h°2 p a N r 1h° f h h°2 r(15–17)Once the reactants and their states are specified, the enthalpy of the reactantsH react can be easily determined. The calculation of the enthalpy of the productsH prod is not so straightforward, however, because the temperature of the productsis not known prior to the calculations. Therefore, the determination of theadiabatic flame temperature requires the use of an iterative technique unlessequations for the sensible enthalpy changes of the combustion products areavailable. A temperature is assumed for the product gases, and the H prod isdetermined for this temperature. If it is not equal to H react , calculations arerepeated with another temperature. The adiabatic flame temperature is thendetermined from these two results by interpolation. When the oxidant is air,the product gases mostly consist of N 2 , and a good first guess for the adiabaticflame temperature is obtained by treating the entire product gases as N 2 .In combustion chambers, the highest temperature to which a materialcan be exposed is limited by metallurgical considerations. Therefore, the adiabaticflame temperature is an important consideration in the design of combustionchambers, gas turbines, and nozzles. The maximum temperaturesthat occur in these devices are considerably lower than the adiabatic flametemperature, however, since the combustion is usually incomplete, some heatloss takes place, and some combustion gases dissociate at high temperatures(Fig. 15–26). The maximum temperature in a combustion chamber can becontrolled by adjusting the amount of excess air, which serves as a coolant.Note that the adiabatic flame temperature of a fuel is not unique. Its valuedepends on (1) the state of the reactants, (2) the degree of completion of thereaction, and (3) the amount of air used. For a specified fuel at a specifiedstate burned with air at a specified state, the adiabatic flame temperatureattains its maximum value when complete combustion occurs with the theoreticalamount of air.FuelAirHeat loss• Incompletecombustion• DissociationProductsT prod < T maxFIGURE 15–26The maximum temperatureencountered in a combustion chamberis lower than the theoretical adiabaticflame temperature.EXAMPLE 15–8Adiabatic Flame Temperaturein Steady CombustionLiquid octane (C 8 H 18 ) enters the combustion chamber of a gas turbinesteadily at 1 atm and 25°C, and it is burned with air that enters the combustionchamber at the same state, as shown in Fig. 15–27. Determine theadiabatic flame temperature for (a) complete combustion with 100 percenttheoretical air, (b) complete combustion with 400 percent theoretical air,and (c) incomplete combustion (some CO in the products) with 90 percenttheoretical air.Solution Liquid octane is burned steadily. The adiabatic flame temperatureis to be determined for different cases.C 8 H 1825°C, 1 atmAir25°C, 1 atmCombustionchamberT P1 atmFIGURE 15–27Schematic for Example 15–8.CO 2H 2 ON 2O 2