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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");

-74600.000

 

0.

 

0.

 

-241826.000

 

-393510.000

(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);

-380601.4217

 

-231324.6170

 

8894.01326

 

9245.04858

(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)

-74600.000

(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)

1727.525390

(3.2)

 

 

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