Week 4.2 - Combustion Efficiency Calculation after Preheating

Aim:

1. To know the effect of the range of inlet air preheating from 298K to 600K on the adiabatic flame temperature of Methane.
2. To know the effect of pre-heat temperature on combustion efficiency assuming the furnace exit temmperature is 1700K.

Theory:

Recuperator:-

The energy from a steady flow of hot combustion products, such as flue gases, is transferred to the air supplied to the combustion process in a recuperator, which is a heat exchanger.
Recuperators come in a vast variety, and many of them utilise convection and radiation heat transfer from exhaust gases.

An energy storage medium like corrugated steel or ceramic matrix is alternately heated by the hot gases and cooled by the air in a regenerator, which also transmits energy from the flue gases to the incoming combustion air.

Schematic diagram of a recuperator can be seen in figure(1):

Figure 1: Schematic of furnace with air preheated by recuperation.

To find fuel saved as a result of preheating the air, we write energy balance for control volume

`-dot(Q)=-dot(Q)underset(load) ()- dot(Q)underset(loss)()=dot(m)*(hunderset(pro) ()-hunderset(react) ())`

`-dot(Q)=(dot(m)underset(A) ()+dot(m)underset(F) ())hunderset(P) ()-(dot(m)underset(F) ())hunderset(F) () -(dot(m)underset(A) ())hunderset(A) ()`

Fuel utilization efficiency can be written as:

`eta=-dot(Q)/(dot(m)underset(F)()*LHV)`

Therefore,

`eta=(((A/F)+ 1)*hunderset(P) ()-(A/F)hunderset(A) () -hunderset(F) ())/(dot(m)underset(F)()*LHV)`

We know that

`A/F=((A/F)underset(s)())/phi`

here `phi=1`

`A/F=17.1`

Fuel saving percentage=`((etaunderset(600)()-etaunderset(298)())/(etaunderset(600)()))*100`

Code:

#Karan Dholkaria
import cantera as ct
import matplotlib.pyplot as plt
import numpy as np
import math

# PART 1
l=10 # INTERVALS
t1=298 # Initial temparture
t2=600 # Final temperature
t=np.linspace(t1,t2,l) #Temperature array
gas=ct.Solution('gri30.xml')
air=ct.Quantity(gas)
T=np.zeros(l)
fuel=ct.Quantity(gas)
fuel.TPX=298,ct.one_atm,'CH4:1'
fuel.moles=1

for i in range(l):
	air.TPX=t[i],ct.one_atm,'O2:1,N2:3.76'
	air.moles=2

	M=air+fuel
	M.equilibrate('HP','auto')
	T[i]=M.T

print(T)
plt.figure(1)
plt.plot(t,T,marker='o')
plt.xlabel('Preheat temperature of inlet air in Kelvin')
plt.ylabel('Aadiabatic Flame Temperature in K')
plt.title('Effect of Preheated air on Aadiabatic Flame Temperature for Methane ')
plt.grid('on',linestyle='--')
plt.show()

# PART 2
lhv= 50e6 #Lower heating value
A_f= 17.121 # Air fuel ratio
f= ct.Quantity(gas) # fuel
f.TPX= 298,ct.one_atm,'CH4:1'
h_f = f.enthalpy_mass
f.moles= 1
# To get the enthalpy of products
p= ct.Quantity(gas) #product
p.TPX= 1700,ct.one_atm,'CO2:1,H2O:2,N2:7.52'
h_p = p.enthalpy_mass
p.moles= 1
# To get the enthalpy of reactants at a varying inlet temperature
h_a = np.zeros(l)
Q= np.zeros(l)
eta= np.zeros(l) # To get the array of combustion efficiency
for i in range(l):
	a= ct.Quantity(gas)
	a.TPX= t[i],ct.one_atm,'O2:1,N2:3.76'
	a.moles= 2
	h_a[i]=a.enthalpy_mass

Q = -(((A_f + 1) * h_p) - (A_f * h_a) - h_f)
eta=(Q*100/lhv) # To get the combustion efficiency.
FS= (1-(eta[0]/eta))*100 # To find out the fuel saving
print('Total fuel saving in % =',FS[-1])

plt.figure(2)
plt.plot(t,eta,marker='o')
plt.xlabel('Pre_heat Temperature of air')
plt.ylabel('Combustion Efficiency of Recuperator (%) ')
plt.title('Effect of Pre_heat temperature on Combustion efficiency')
plt.grid('on',linestyle='--')
plt.show()

plt.figure(3)
plt.plot(t,FS,marker='o')
plt.xlabel('Pre_heat Temperature of air')
plt.ylabel('Fuel Saving')
plt.title('Effect of air pre-heating on fuel saving')
plt.grid('on',linestyle='--')
plt.show()

Results:

Figure 2:Effect of preheated air on Adiabatic flame temperature for methane.

Figure 3: Effect of preheat temperature on combustion efficiency.

Figure 4: Effect of air preheating on fuel saving.

Conclusion:

1. In figure 2, it can be seen that as we increase preheating temperature of inlet air, adiabatic flame temperature increases linearly.
2. In figure 3, it can be seen that as we increase preheating temperature of inlet air, combustion efficiency of the recuperator increases linearly.
3. In figure 4, it can be seen that as we increase preheating temperature of inlet air, fuel saving increases. The fuel saving is found to be 23.93477% at 600K.
4. It is wrong to assume that the furnace exit temperature is constant because there will be presence of different product gas species at different composition, presence of intermediary species and heat losses won't be same on which exhaust gas temperature would depend .