Combustion Efficiency Calculation after Preheating

Objective:

1. Plot the effect of preheating on the adiabatic flame temperature. Change pre-heating from 298 to 600K.
2. Write the formula for combustion efficiency
3. Plot the effect of preheating on combustion efficiency.
4. Plot the percentage of fuel-saving with air preheating

The fuel used in the furnace is methane. Stoichiometric equation of methane combustion is,

`CH_4+2(O_2+3.76N_2=> CO_2+2H_2O+7.52N_2`

Air and fuel are created as different objects of Quantity class so that the temperature of the air into the furnace can be changed individually. The adiabatic flame temperature of the mixture can be calculated using Cantera.

`m_(air)^(.)=`Mass flow rate of air

`m_(fuel)^(.)=`Mass flow rate of fuel

`m_(p rod)^(.)=`Mass flow rate of exhaust gas(products-For this case assume that the combustion products are CO2, H20, and N2

`h_(air)=` Enthalpy of air

`h_(fuel)=` Enthalpy of fuel

`h_(p rod)=` Enthalpy of products (Exhaust gas)

For calculating combustion efficiency energy balance equation of control volume shown in the figure above,

`m_(air)^.*h_(air)+m_(fuel)^.*h_(fuel)-Q-m_(pro d)^.*h_(pro d)=0`

`Q=m_(air)^.*h_(air)+m_(fuel)^.*h_(fuel)-m_(pro d)^.*h_(pro d)`

Combustion efficiency,

`eta=Q/(m_(fuel)^.*LHV)`

LHV= Lower heating value

Fuel-saving at preheat temperature T,

`savi ng=[1-(eta(298))/(eta(T))]`

Given,

The temperature of exhaust gas(products)=1700K

LHV of combustion of methane=50MJ/KG

Python code for the temperature of air vs AFT

"""
sample code to vary the temperature of air and oxidiser individualy
"""
import cantera as ct 
import matplotlib.pyplot as plt 
gas=ct.Solution('gri30.cti')
Final_temp=[]
Temp=[]
for T in range (298,600):
	#air
	A=ct.Quantity(gas)
	A.TPX=T,ct.one_atm,{'O2':0.21,'N2':0.79}
	A.moles=2/0.21
	#fuel
	B=ct.Quantity(gas)
	B.TPX=298.15,ct.one_atm,'CH4:1'
	B.moles=1


	M=A+B
	M.equilibrate('HP')
	Final_temp.append(M.T)
	Temp.append(T)
	
plt.plot(Temp,Final_temp)
plt.ylabel('Adiabatic flame temperature (K)')
plt.xlabel('Air preheat temperature (K)')
plt.show()	

Python code for efficiency vs air temperature

"""
sample code to vary the temperature of air and oxidiser individualy
"""
import cantera as ct 
import matplotlib.pyplot as plt 
gas=ct.Solution('gri30.cti')
Final_temp=[]
Temp=[]

#Products
C=ct.Quantity(gas)
C.TPX=1700,ct.one_atm,{'CO2':0.095,'H2O':0.190,'N2':0.714}
C.moles=10.52
Effi=[]

for T in range (298,600):
	#Air
	A=ct.Quantity(gas)
	A.TPX=T,ct.one_atm,{'O2':0.21,'N2':0.79}
	A.moles=9.52
	#Fuel
	B=ct.Quantity(gas)
	B.TPX=298.15,ct.one_atm,'CH4:1'
	B.moles=1
	#mixture
	M=A+B
	M.equilibrate('HP')
	Final_temp.append(M.T)
	Temp.append(T)
	m_air=A.mass
	m_fuel=B.mass
	m_prod=C.mass
	H_air=A.h
	H_fuel=B.h
	H_prod=C.h
	
	Q=m_air*H_air+m_fuel*H_fuel-(m_prod*H_prod)
	
	eff=(Q/(m_fuel*50e6))*100
	Effi.append(eff)
sav=[]	
for i in range(0,len(Effi)):
	savings=(1-(Effi[1]/Effi[i]))*100
	sav.append(savings)


plt.plot(Temp,Effi)
plt.plot(Temp,sav)
plt.legend(['Efficiency','Fuel saving'])
plt.xlabel('Air temperature(K)')
plt.ylabel('%')
plt.show()	

Result

Air preheat temperature vs adiabatic flame temperature

From the above plot, we can see that adiabatic flame temperature increases with an increase in air preheat temperature. The increase in adiabatic flame temperature is less than the change in preheat temperature.

Air preheat temperature vs efficiency/ fuel saving

From the above plot, we can see that Combustion efficiency increases with air temperature. So the same amount of energy can be generated with less amount of fuel. The percentage change in fuel-saving also increases with an increase in air preheating temperature.

As the exhaust gas temperature air preheating temperature also increases and this will increase the adiabatic flame temperature. Unless the exit temperature of the furnace is not fixed. Then it will lead to component failure. So the assumption is right.