Week 4.2 - Combustion Efficiency Calculation after Preheating
AIM:
- To find the effect of preheating on the adiabatic flame temperature.
- To plot the effect of preheat temperature on combustion efficiency.
THEORY:
A recuperator is a special purpose counter flow energy recovery heat exchanger positioned within the supply and exhaust air streams of an air handling system, or in the ehaust gases of an industrial process, in order to recover the waste heat. Generally, they are used to extract heat from the exhaust and use it to preheat air entering the combustion system.
EFFECT OF PREHEATING ON AFT:
- The stoichiometric combustion of methane is analysed in this problem which is given by
CH4 + 2(O2 + 3.76N2) = CO2 + 2H2O + 7.52N2
- The inlet air is assumed to be preheated from temperatures 298k to 600k.
- We apply different temperature using quantity class to fuel and air and then mix them at last.
- This mixture is then combusted using a equilibrate method for constant enthalpy and pressure and the plots are obtained.
CODING APPROACH:
- First step is to import cantera and matplotlib modules to do plotting.
- The gas object is created and the solution class is defined for gri30.cti.
- Then the quantity class of air and fuel object i.e, O2 and CH4.
- The for loop is used to calculate preheating temperature from 298k to 600k.
- Then the temperature, pressure and mole fraction is defined for air object.
- The equilibrate function is used to get the solution.
- Then the plotting is done between preheating temperature vs the adiabatic flame temperature.
CODE:
"""
code to study the effect of preheating on Adiabatic flame temperature
"""
import cantera as ct
import matplotlib.pyplot as plt
#methane combustion equation : CH4 + 2(O2 + 3.76N2) = CO2 + 2H2O + 7.52N2
gas = ct.Solution('gri30.cti')
#sefining fuel
Fuel = ct.Quantity(gas)
Fuel.TPX = 298.15,ct.one_atm,'CH4:1'
Fuel.moles = 1
#preheat temperature
Tmin = 298
Tmax = 600
#defining air constituents
Air = ct.Quantity(gas)
for T in range(Tmin,Tmax):
Air.TPX = T,ct.one_atm,{'O2':0.21,'N2':0.79}
Air.moles = 9.52
#the following step is used to apply the right molar balance
M = Fuel + Air
M.equilibrate('HP','auto')
#plotting
if (T%10==0):
plt.plot(T,M.T,'.',color='red')
plt.xlabel('pre-heating temperature [k]')
plt.ylabel('Adiabatic Flame Temperature [k]')
plt.title('Effect of Pre-heating on AFT')
plt.grid()
plt.show()RESULT:
From the plot as we can see that AFT increases linearly with preheating temperature of air entering the combustion chamber and hence the final temperature is high.
EFFECT OF PREHEATING ON CYCLE EFFICIENCY AND FUEL SAVING:
- The heat released from the reaction or exhaust temperature is at 1700k and these adjustment is done in order to understand the effect of preheating on fuel saving.
- Combustion efficiency is defined as the ratio of heat released by the fuel to the heat input by the fuel.
- The total energy from the combustion reaction is given below
- The combustion efficiency is calculated using the below formula
- The lower heat value of methane is taken as 50MJ/KG
-
- The fuel saving is calculated using the below equation.
CODING APPROACH:
- First step is to import cantera and matplotlib modules to do plotting.
- The gas object is created and the solution class is defined for gri30.cti.
- Then the quantity class of air and fuel object i.e, O2 and CH4.
- The for loop is used to calculate preheating temperature from 298k to 600k.
- Then the temperature, pressure and mole fraction is defined for air object.
- The efficiency is calculated.
- Then the plotting is done between preheating temperature vs combustion efficiency and fuel saving.
CODE:
"""
Study of effect of Preheating through Recuperator on Combustion Efficiency
Reaction: CH4+2(O2+3.76N2) => CO2+2H2O+7.52N2
"""
import cantera as ct
import matplotlib.pyplot as plt
gas = ct.Solution('gri30.cti')
"""
Calculating moles
Product moles = n_total = 1+2+7.52 = 10.52
n_CO2 = 1/n_total = 0.096 ; n_H2O = 2/n_total = 0.1901 ; n_N2 = 7.52/n_total = 0.7148
"""
# Creating fuel and air quantities reacting in the chamber
fuel = ct.Quantity(gas)
fuel.TPX = 298.15, ct.one_atm,'CH4:1'
fuel.moles = 1
mixture_fuel = fuel.mass
#Creating products formed during the combustion process
prod = ct.Quantity(gas)
prod.TPX = 1700, ct.one_atm,{'CO2':0.095,'H2O':0.1901, 'N2':0.7148}
prod.moles = 10.52
mixture_prod = prod.mass
T_min = 298
T_max = 600
LHV = 50e6
eff = []
fuel_saving = []
T_ph = []
for T in range(T_min,T_max):
Air = ct.Quantity(gas)
Air.TPX = T,ct.one_atm,{'O2':0.21,'N2':0.79}
Air.moles = 9.52
mixture_Air = Air.mass
h_air = Air.enthalpy_mass
h_fuel = fuel.enthalpy_mass
h_prod = prod.enthalpy_mass
Q = mixture_Air*h_air+mixture_fuel*h_fuel-mixture_prod*h_prod
Qsp = Q/mixture_fuel #sp = specific work
Eff = (Qsp/LHV )
if T==298:
eff_0=Eff
secured_fuel = 100*(1-(eff_0/Eff))
fuel_saving.append(secured_fuel)
T_ph.append(T)
eff.append(Eff)
#plotting
if (T%10==0):
plt.figure(1)
plt.plot(T,Eff,'.',color='red')
plt.xlabel('Pre Heat Temperature(K)')
plt.ylabel('Combustion Efficiency')
plt.title('Effect of Pre Heating on Combustion Efficiency')
plt.grid()
plt.figure(2)
plt.plot(T_ph,fuel_saving,color='green')
plt.xlabel('Pre-Heat temperature(K)')
plt.ylabel('Percentage Fuel Saved')
plt.title('Fuel Saving with Pre Heating')
plt.grid()
plt.show()RESULT:
From the graph we can see that combustion efficiency increases with increase in preheating temperature. The preheater helps in combustion to take place effectively thus increasing the efficiency.
From this graph we can conclude that fuel savings increases with combustion efficiency which is calculated below,
Fuel saving = 1- (efficiency with no preheat/efficiency with preheat)
At no preheat,
At 298k, efficiency is 0.33 and
At 600k, efficiency is 0.44
Hence fuel saving = 1-(0.33/0.44) = 0.23% which is the value after preheating.
CONCLUSION:
- AFT increases linearly with increase in preheating temperature.
- As preheat temperature increases the combustion efficiency also increases.
- The amount of fuel saved increases with increases in preheat temperature.