Temperature in a Combustion Chamber Burning Methane
Introduction
A gas turbine burns methane in 200% stoichiometric air.
CH4 + 4 O2 + 15.04 N2 # CO2 + 2 H2O + 7.52 N2 + 15.04 N2 + 4 O2
The air and the fuel enter the combustion chamber at 600 K. This application will determine the adiabatic flame temperature of the system by equating the enthalpy of the reactants to the enthalpy of the products.
Thermodynamic data is calculated using the empirical correlations built into Maple's ThermophysicalData:-Chemicals package.
restart: with(ThermophysicalData:-Chemicals):
Physical Parameters
Enthalpies of formation
h_f_CH4 := Property("HeatOfFormation", "CH4"); h_f_O2 := Property("HeatOfFormation", "O2"); h_f_N2 := Property("HeatOfFormation", "N2"); h_f_H2O := Property("HeatOfFormation", "H2O"); h_f_CO2 := Property("HeatOfFormation", "CO2");
Enthalpies
h_CH4 := Property("Hmolar", "CH4", "temperature" = T): h_CO2 := Property("Hmolar", "CO2", "temperature" = T): h_H2O := Property("Hmolar", "H2O", "temperature" = T): h_O2 := Property("Hmolar", "O2", "temperature" = T): h_N2 := Property("Hmolar", "N2", "temperature" = T):
Reference enthalpies
h_r_CO2 := eval(h_CO2, T = 600); h_r_H2O := eval(h_H2O, T = 600); h_r_N2 := eval(h_N2, T = 600); h_r_O2 := eval(h_O2, T = 600);
Heat Balance and Numerical Solution
At constant pressure, H_reactants = H_products
H_reactants := 1 * h_f_CH4 + 4 * (h_f_O2 + 3.76 * h_f_N2)
H_products := 2 * (h_f_H2O + h_H2O - h_r_H2O) + 1 * (h_f_CO2 + h_CO2 - h_r_CO2) + 15.02 * (h_f_N2 + h_N2 - h_r_N2) + 2 * (h_f_O2 + h_O2 - h_r_O2):
Hence the adiabatic flame temperature is
fsolve(H_reactants = H_products,T=1000)
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