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# Temperature in a Combustion Chamber Burning Methane

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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");
 (2.1)

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);
 (2.2)

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)
 (3.1)
 > 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)
 (3.2)
 >

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