Week 4.2 - Combustion Efficiency Calculation after Preheating

Aim:

1.To find the effect of preheating on AFT from changing temperature from 298K to 600K.

2. To find whether pre heating helps in saving the fuel and increases the combustion efficiency.

Recuperator and Regenerator:

A recuperator is a heat exchanger in which energy from a steady flow of hot combustion products,i.e flow gases is transferred to the air supplied to combustion process.

A regenerator also transfers energy from the gases to the incoming combustion air,here the energy storage medium,such as corrugated steel or ceramic matrix,is alternately heated by hot gases and cooled by air.

Combustion efficiency of recuperator:

We are going to write a code for energy balance for control volume,assumning both heat transferred to the system and heat loss are same ,with and without preheating.

`-Q= -Q_(load)-Q(loss)``=m(h_(Prod)-h_(react))`

=`(m_a +m_f)h_(Prod) - m_ah_a - m_fh_f`

A/F = `m_a/m_f`

So the above equation can be written as

-Q = `[(A/F+1)h_(Prod) - A/F.h_a-h_f]`

Fuel utilization energy is

`eta`= `Q/(m_f.LHV)`

So

`eta` = `[(A/F+1)h_(Prod) - A/F.h_a-h_f]`/(`LHV`)

To solve the above equation we need A/F

A/F = `(A/F)_(sToich)/phi`

We know that the stoichiometric ratio for combustion of methane in terms of mass is 17.19:1 and we assume the equivalence ratio is 1.

A/F = 17.19

Fuel saving = `1- (eta_(298)/eta_600)`

Case 1:

In this case we are changing the pre heating temperature from 298K to 600 K and find the AFT.

Step 1: We are defining all the preprocessors i.e Cantera ,numpy and matplotlibrary for the combustion and plot the results.

Step 2:We are defining a range for the pre heating temperature ,i.

Step 3: For loop is created in which all the AFT calculations are done using mole basis system and equilibrate the air and fuel for the combustion process.

Step 4:Plotting the results using matplotlibrary.

import cantera as ct 
import matplotlib.pyplot as plt
import numpy as np

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

i= np.linspace(298,600,100)

T_gas=[]

for t in i:
    React=ct.Quantity(gas)
    React.TPX=t,ct.one_atm,{'O2':1,'N2':3.76}
    React.moles =2

    Fuel = ct.Quantity(gas)
    Fuel.TPX = 298,ct.one_atm,'CH4:1'
    Fuel.moles =1

    M = React + Fuel

    M.equilibrate('HP','auto')
    T = M.T 
    T_gas.append(T)

print(T_gas)
plt.plot(i,T_gas)
plt.xlabel('Preheat temperature of inlet air in K')
plt.ylabel('AFT in K')
plt.title('Effect of combustion on preheated air')
plt.show()

As we can see the Adiabatic flame temperature increases with in crease in preheating temperature.

The Adiabatic flame temperature linearly increases with preheated air temperature.

Case 2: In this case we find the fuel saving with the increase in preheated temperature.

The combustion efficiency of recuperator is written above.

import cantera as ct 
import numpy as np 
import matplotlib.pyplot as plt
  

gas = ct.Solution('gri30.cti')
LHV_fuel = 50e6 
A_F= 17.1

T_ph=np.linspace(298,600,100)

Fuel= ct.Quantity(gas)
Fuel.TPX=298,ct.one_atm,'CH4:1'
Fuel.moles = 1 
h_fuel=Fuel.h
m_fuel=Fuel.mass

Prod = ct.Quantity(gas)
Prod.TPX = 1700,ct.one_atm,{'CO2':0.095,'H2O':0.1901,'N2':0.7148}
Prod.moles=10.92
h_Prod=Prod.h
m_Prod=Prod.mass

h_React=[]
Q=[]
efficiency=[]
F_S=[]
for i in range(0,len(T_ph)):
	React=ct.Quantity(gas)
	React.TPX=T_ph[i],ct.one_atm,{'O2':0.21,'N2':0.79}
	React.moles = 9.52
	h_React=React.h 
	m_React=React.mass
	

	


	Q = (m_React*h_React + m_fuel*h_fuel - m_Prod*h_Prod)/m_fuel
	eta= (Q*100)/LHV_fuel
	efficiency.append(eta)


	Fuel_saving = 1-(efficiency[0]/efficiency[i])
	FS=Fuel_saving*100
	F_S.append(FS)
	#print('Total fuel saving in % =',FS)

#print(T_ph,efficiency)
plt.plot(T_ph,efficiency)
plt.xlabel('Pre heating temperature of air')
plt.ylabel('combustion efficiency of recuperator %')
plt.grid('on')
plt.show()


plt.plot(T_ph,F_S)
plt.xlabel('Pre heating temperature of air')
plt.ylabel('Fuel Saving')
plt.show()

Step 1: We do the same as the above case,but we find the mass and enthalpy of air and fuel and the products.

Step 2: Put them in the for loop and calculate the heat produced by combustion in different pre hrating temperatures.

Step 3:Then we find the fuel saving and the efficiency of the recuperator using the derived formulas.

Step 4:Then we plot the results of the efficiency and the fuel saving percentage of the recuperator under different pre heating temperatures.

Results:

Preheating of inlet air vs Efficiency

Preheating of inlet air vs Fuel saving(%)

Conclusion:

From the above plots we can conclude that increase inlet air temperature will increase the combustion efficiency.

The percentage of fuel saving is found to be 23.93%,if we increase the inlet temperature to 600K.

It is wrong to fix the furnace exit temperature.Here we set the furnace exit temperature as 1700K for the simplicity.But there are many factors which dtermine th furnace exit temperature like the type of fuel,Gas species and intermediary reactions .