Combustion Efficiency Calculation after Preheating

1. Effect of preheating on AFT

CODE:

import cantera as ct
import matplotlib.pyplot as plt

gas = ct.Solution(\'gri30.cti\')

A = ct.Quantity(gas)
A.TPX = 298.15,ct.one_atm,\'CH4:1\'
A.moles = 1

Tm = 298
Tma = 600

B = ct.Quantity(gas)

for T in range (Tm,Tma):

B.TPX = T,ct.one_atm,{\'O2\':0.21 , \'N2\':0.79}
B.moles = 9.52

M = A + B
M.equilibrate(\'HP\',\'auto\')
plt.plot(T,M.T,\'+\', color = \'blue\')

plt.title(\'Effect of preheating on AFT\')
plt.xlabel(\'Preheating temperature\')
plt.ylabel(\'Adiabatic flame temperature\')
plt.show()

Here 2 instances A &B of the Quantity class has been created, A is for the fuel which is at 298k, 1 atm and 1 mole, whereas B is used for the air which will take the pre-heating temperature ranging from 298k - 600k, at 1 atm and for 9.62 moles.

After this two moles are added and equilibrate function is used to get the AFT of this reaction.

AFT increases with pre-heating temperature. This is because pre-heating helps to increases the temperature of the system which in turn causes the combustion to take place efficiently by using less amount of the fuel. Therefore, from the above graph, we can conclude that preheating helps to save fuel and improves fuel economy.

2. Effect of preheating temp on combustion efficiency

Formula:

Q = Mass of air*enthalpy of Air + Mass of fuel*Enthalpy of fuel - Mass of product*Enthalpy of product

Qsp = Q/Mass of Fuel

efficiency = Qsp/LHV

where LHV is the lower heating value for the fuel which is given as 50 MJ/Kg.

CODE:

import cantera as ct
import matplotlib.pyplot as plt

gas = ct.Solution(\'gri30.cti\')

reac = ct.Quantity(gas)
reac.TPX = 298.15 , ct.one_atm , {\'CH4\': 0.095 , \'O2\': 0.1901 , \'N2\': 0.7148}
reac.moles = 10.52

p = ct.Quantity(gas)
p.TPX = 298.15,ct.one_atm,{\'CO2\':0.095 , \'H2O\':0.1901 , \'N2\': 0.7148}
p.moles = 10.52

fuel = ct.Quantity(gas)
fuel.TPX = 298.15 , ct.one_atm , \'CH4:1\'
fuel.moles = 1
M_fuel = fuel.mass

prod = ct.Quantity(gas)
prod.TPX = 1700,ct.one_atm,{\'CO2\':0.095 , \'H2O\':0.1901 , \'N2\': 0.7148}
prod.moles = 10.52
M_prod = prod.mass

Tpre_low = 298
Tpre_high = 600
Lower_Heating_Value = 50e6

for T_pre in range (Tpre_low,Tpre_high):

Air = ct.Quantity(gas)
Air.TPX = T_pre , ct.one_atm , {\'O2\':0.21 , \'N2\': 0.79}
Air.moles = 9.52
M_air = Air.mass

H_Air = Air.enthalpy_mass
H_fuel = fuel.enthalpy_mass
H_prod = prod.enthalpy_mass

Air_to_fuel = M_air/M_fuel

Q = M_air*H_Air + M_fuel*H_fuel - M_prod*H_prod
Qsp = Q/M_fuel
eff = Qsp/Lower_Heating_Value
plt.plot(T_pre,eff,\'+\',color = \'brown\')

plt.xlabel(\'Pre-Heating Temperature [K]\')
plt.ylabel(\'Combustion Efficiency\')
plt.title(\'Effect of the Pre-Heating in Combustion Efficiency\')
plt.show()

We can conclude from the graph that combustion efficiency increases with pre-heating temperature.

Yes, it is right to assume that the furnace\'s exit temperature remains constant. Although realistically speaking, there may be very small variations in the exit temperature due to external conditions, it is generally not significant enough to have an impact. If the recuperators exit temperatures fluctuated significantly, it would have a detrimental impact on the efficiency and the life of the recuperator. A lower exit temperature will reduce the combustion efficiency whereas a higher temperature will lead to increased stress corrosion on the boiler components which may end failing after a particular threshold. Therefore, it is vital to keep the recuperator\'s exhaust temperature constant.