Week 4 - Combustion Efficiency Calculation after Preheating

Aim

To Find the Combustion Efficiency of the Furnace with respect to Preheating.

Recuperator

It is a type of heat exchanger has separate flow paths for each fluid along their own passages and heat is transferred through the separating walls. Recuperators are often used in power engineering, to increase the overall efficiency of thermodynamic cycles. For example, in a gas turbine engine. The recuperator transfers some of the waste heat in the exhaust to the compressed air, thus preheating it before entering the combustion chamber. Many recuperators are designed as counter-flow heat exchangers.

Adiabatic Flame Temperature

The Final Temperature that is obtained after the fuel is completely burnt.

Case: 1

#PreHeat Temperature VS Adiabatic Flame Temperature

""""
The stoichiometric mixture of combustion of methane looks like the following :-

CH4 + 2(O2+3.76N2)  -> CO2 + 2H2O + 7.52N2

"""

import cantera as ct 
import matplotlib.pyplot as plt 


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

air = ct.Quantity(gas)
fuel = ct.Quantity(gas)

fuel.TPX = 298.15,ct.one_atm,{'CH4':1}
fuel.moles = 1

#Preheating Temperature
preheat_T =[]

#Adiabatic Flame Temperature
Adiabatic_flame_temperature = []


for T in range(298,601):
	air.TPX = T,ct.one_atm,{'O2':0.21,'N2':0.79}
	air.moles = 9.52
	preheat_T.append(T)

	Mixture = fuel + air
	Mixture.equilibrate('HP')

	Adiabatic_flame_temperature.append(Mixture.T)

print(Adiabatic_flame_temperature)
print(preheat_T)

plt.plot(preheat_T,Adiabatic_flame_temperature)
plt.title('PreHeating Vs Adiabatic_flame_temperature')
plt.xlabel('preheat_T(K)', fontsize = 14)
plt.ylabel('Adiabatic_flame_temperature (K)',fontsize = 14)
plt.grid(True)
plt.show()

When looking at the Plot we can the AFT increasing linearly with respect to the Preheating Temperature of the air. This means the varing the temperature of the Air getting heated increases the AFT.When the Air temperature decreases the Adiabatic flame temperature is also decreased meaning the air temperature is cold.

Case: 2

#Preheat Temperature vs Combsution Efficiency
#Preheat Temperature vs Fuel Saving

""""
The stoichiometric mixture of combustion of methane looks like the following :-

CH4 + 2(O2+3.76N2)  -> CO2 + 2H2O + 7.52N2

"""

import cantera as ct 
import matplotlib.pyplot as plt 


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

Air = ct.Quantity(gas)
Fuel = ct.Quantity(gas)
Product = ct.Quantity(gas)

#Air has 9.52 moles
Air.TPX = 298.15,ct.one_atm,{'O2':0.21,'N2':0.79}
Air.moles = 9.52
mass_Air = Air.mass
H_Air = Air.enthalpy_mass

#Methane has 1 moles
Fuel.TPX = 298.15,ct.one_atm,{'CH4': 1}
Fuel.moles = 1
mass_Fuel  = Fuel.mass
H_Fuel= Fuel.enthalpy_mass
#Methane Lower Heating Value
LHV = 50e6

#The Total number of moles in the product is 10.52 which is calculatd from the Stiochiometric Mixture.
Product.TPX = 1700,ct.one_atm,{'CO2':1/10.52,'H2O':2/10.52,'N2':7.52/10.52}
Product.moles= 10.52
mass_Product = Product.mass
H_Product = Product.enthalpy_mass

M_Air_Fuel= mass_Air/mass_Fuel

#Combustion Efficiency at STP 
eff_stp = (M_Air_Fuel*H_Air + H_Fuel - (M_Air_Fuel+1)*H_Product )/(LHV)
print("Combustion Effciency at STP=",eff_stp)

#PreHeat Temperature
preheat_T = []

#Combustion Efficiency with respect to varing Preheat Temperature
Efficiency = []

#Fuel Saving 
Fuel_saving = []

for T in range(298,601):
	Air.TPX = T,ct.one_atm,{'O2':0.21,'N2':0.79}
	Air.moles = 9.52
	mass_Air = Air.mass
	H_Air = Air.enthalpy_mass
	M_Air_Fuel = mass_Air/mass_Fuel

	eff = (M_Air_Fuel*H_Air + H_Fuel - (M_Air_Fuel+1)*H_Product )/(LHV)
	Fuel_savings = abs(1- (eff_stp/eff))

	preheat_T.append(T) 
	Fuel_saving.append(Fuel_savings)
	Efficiency.append(eff)

print("Combustion Effciency at varied PreHeating Conditions =",Efficiency)
print("PreHeating Temperatures(K) =",preheat_T)
plt.plot(preheat_T,Efficiency)
plt.plot(preheat_T,Fuel_saving,color= 'orange')
plt.xlabel('PreHeating')
plt.ylabel('Efficiency')
plt.legend(['Combustion Efficiency','Fuel Saving'])
plt.title('Combustion Efficiency with PreHeating',size = 20)
plt.grid(True)

print("Fuel Saved=",Fuel_saving)

plt.show()

When looking at the plot we can see the combustion efficiency is increased with Temperature and also there is saving in fuel. Initially the fuel saving is neglible amount but as the Air temperature is increased the fuel saving is also increased.

At 298.15 K the Fuel saved is 0.00015312320481752906 kg but at the temperature 608 K the fuel saved is 0.23923117747906109 kg giving as 199.74% increase in fuel saving with respect to the preheating temperature

Similarly for the Combustion Efficiency at 298K is 0.33873306622138993 and combustion efficiency at 608 K is 0.44531916146543044 giving as 27.188% increase in combustion efficiency.

• Yes, Preheating helps the fuel saving and it increses the combustion efficiency of the furnance. As the temperature of the air increases the combustion efficiency is also increased propostionally with respect to the preheating temperature assigned to the air.
• Combustion Efficiency

Combustion Efficiency `eta = ((A/F)*H_(air) + H_(fuel) - (A/F + 1) * H_(pro duct) )/ (LHV)`

where

A/F= Mass of Air/ Mass of Fuel

H_air = Air Enthalpy

H_fuel = Fuel Enthalpy

H_product = Product Enthalpy

LHV = Lower Heating Value of Fuel

• Fuel Saving

`Fuel Savi ng = 1- (eta_(STP)/ eta_(PreheatTemperature))`

• The Exit temperature depends upon the Product temperature of the reaction which is necessary for the recuperator to preheat the air. If the Exist temperature of the high then the preheating of the air will be faster which will help in increasing the thermal efficiency or the combustion efficiency which in turn helps in saving the fuel.This means that the Exist Temperature is directly propotional to the Preheat Temperature of the air.

Conclusion

From this we can see that preheating helps in increasing the Combustion Efficiency of the Furance and also there is increase in Fuel Saving.