Week 4 - Combustion Efficiency Calculation after Preheating

1) Effect of preheating on the adiabatic flame temperature

The effect of preheating air on Adiabatic Flame Tempreature (AFT) of CH4 was calculated. The Quantity class method of Cantera was used to created a Mixture Methane/Air to determine the AFT.

Combustion efficiency is a measurement of how well the fuel burned is being utilized in the combustion process. We used air temerature from 298 to 600K. From the graph we conclude that, AFT increses linearly with increasing air temperature. This means that, a larger amount of useful heat is available for a given amount of fuel, that implies that for a desired amount of usuful heat or work, the amount of fuel required is lesser. Hence, preheating air helps with fuel saving.

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Effect of preheating air on AFT.Methane
Program by-Susana Maldonado 
\"\"\"
import cantera as ct
import matplotlib.pyplot as plt

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

#CH4 + 2(O2 + 3.76N2) = CO2 + 2H20 + 7.52N2

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

#Air
air = ct.Quantity(gas)
T_min = 289 #K
T_max = 600 #K
 
plot_interval = 5 #if its divited in 5 shows the point

for T_preheating in range(T_min,T_max):
	air.TPX= T_preheating,ct.one_atm,{\'O2\':0.21,\'N2\':0.79}
	air.moles =(2*3.76)/0.79

	M=fuel+air
	M.equilibrate(\'HP\',\'auto\')
	
	if T_preheating%plot_interval is 0:
		plt.plot(T_preheating,M.T,\'.\',color = \'grey\')

plt.grid()
plt.title(\'Effect of preheating air on AFT-CH4\')
plt.xlabel(\'Preheating air temperature [K]\')
plt.ylabel(\'Adiabatic Flame Temperature [K]\')
plt.show()

2) Effect of pre-heat temeprature on combustion efficiency

Combustion efficiency is a measure of how much of the maximum available heat is generated in the combustion process i.e., it is a ratio of available heat generated in combustion to the maximum possible heat generated by combustion.

Assuming an adiabatic furnance and the furnace exit temperature as 1700K:

`eta=Q/(dotm underset(f)() * LHV)`

LHV=50MJ/kg

`Q=dotm underset(A)()*doth underset(A)()+ dotm underset(f)()*doth underset(f)()-(dotm underset(A)()+dotm underset(f)())*doth underset(p)()`

Assuming `phi=1`

if `(A/F)=((dotm underset(A)())/(dotm underset(f)()))`

`eta=((A/F)doth underset(A)() + doth underset(f)()-((A/F)+1)*doth underset(p)())/(LHV)`

Using the Quantity calss to create our mixture

Products: CO2, 2H2O, 7.52N2

`COunderset(2)()=1/10.52=0.095`

`Hunderset(2)()O=2/10.52=0.1901`

`Nunderset(2)()=7.52/10.52=0.7148`

\"\"\"
Effect of preheating air on combustion efficiency
Program by-Susana Maldonado 
\"\"\"

import cantera as ct
import matplotlib.pyplot as plt

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

#CH4 + 2(O2 + 3.76N2) = CO2 + 2H20 + 7.52N2

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

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


#Air
air = ct.Quantity(gas)
T_min = 289 #K
T_max = 600 #K
LHV = 50e6 #J/kg
 
plot_interval = 5 #if its divited in 5 shows the point

for T_preheating in range(T_min,T_max):
	air.TPX= T_preheating,ct.one_atm,{\'O2\':0.21,\'N2\':0.79}
	air.moles =(2*3.76)/0.79
	mass_air = air.mass

	h_air = air.enthalpy_mass
	h_fuel = fuel.enthalpy_mass
	h_products = products.enthalpy_mass

	air_fuel=mass_air/mass_fuel

	#Total heat transfer
	Q = (air_fuel*h_air) + (h_fuel) - ((air_fuel +1)*h_products)
	
	#Efficiency
	efficiency=(Q/LHV)*100
	
	if T_preheating%plot_interval is 0:
		plt.plot(T_preheating,efficiency,\'.\',color = \'grey\')

plt.grid()
plt.title(\'Effect of preheating air on combustion efficiency-CH4\')
plt.xlabel(\'Preheating air temperature [K]\')
plt.ylabel(\'Efficiency [%]\')
plt.show()

Combustion efficiency increases linearly with preheated air. Preheating temperature depends on the temperature of the products after the combustion, if the output temperature goes on increasing as the cycle proceeds could leads to the damage of the recuperator. So, it is theoretically correct to assume a fixed furnace exit temperature if the input fuek quantity or the work extracted is not constant.