Combustion Efficiency Calculation after Preheating

Objective: 

Part_1 - To know the effect of the range of inlet air preheating from 298K to 600K on the adiabatic flame temperature of Methane.

Part_2 - To know the effect of pre-heat temperature on combustion efficiency. 

Given: 

Device-  Recuperator (Constant pressure Heat exchanger)
Fuel- CH4
Programs used- Python and Cantera

Theory:

                                                                                                                   Recuperator & Regenerator

A Recuperator is a heat exchanger in which energy from a steady flow of hot combustion products i.e. flue gases, is transferred to the air supplied to the combustion process. A wide variety of recuperators are used in practice, many of which employ radiation heat transfer from the flue gases, as well as convection.

A Regenerator also transfers the energy from the flue gases to the incoming combustion air, but ib this case, an energy storage medium such as corrugated steel or ceramic matrix is alternatively heated by the hot gases and cooled by the air. 

A general flow diagram is shown below:
                                                                   

Combustion Efficiency of Recuperator:

We are going to write an energy balance for the control volume, assuming both the heat transferred to the load and the heat losses are the same, with and without preheating. 
Assuming steady flow, heat us transferred out of the control volume.

`-dotQ= -dotQ_"load"-dotQ_"loss"=dotm*(h_"prod"-h_"react")`

`-dotQ= (dotm_A+dotm_F)h_"prod"-dotm_F*h_F-dotm_A*h_A`

`A/F=dotm_A/dotm_F`

Above equation will be rewrite as,

`-dotQ=[(A/F+1)*h_"prod"-(A/F)*h_A-h_F]`

fuel utlization energy will be defined as,

`eta= dotQ/(dotm_F*LHV)`

Therefore,

`eta=[(A/F+1)*h_"prod"-(A/F)*h_A-h_F]/(LHV)`

Assuming equivalence ratio is 1.

`A/F=(A/F)_"stoich"/phi`

`A/F=17.1`

Fuel-saving defined as,

`"Fuel_Saving"= 1-(eta_298/eta_600)`

 

Solution:

PART-1: To know the effect of preheating inlet air temperature on adiabatic flame temperature. Assume fuel as METHANE (CH4)

Here, we are going to look at how adiabatic flame temperature is being effected by varying inlet air temperature ranging from 298 K to 600 K.

Python code:

STEP_1: At first we have imported all the necessary applications i.e. Cantera to perform chemical kinetics calculations, NumPy for numerical calculations, and matplotlib to visualize the results obtained by plotting the results.

STEP_2: Defined the range of preheating temperature in the variable "i" using 'linspace' command.

STEP_3: "For" loop created inside which for all the values of preheating inlet air temperature AFT calculation done by using a mole basis system. 

STEP_4: Printing and plotting the results we obtained.

"""
Program to know the effect of preheating air temperature on AFT on the combustion of methane using CANTERA.

By- GAURAV V. KHARWADE || Skill-Lync 2020

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


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

# To define the range of preheating inlet air temperature
i= np.linspace(298,600,100)

# To store the value of AFT
T_gas= []

# "For" loop to calculate AFT for all values of 'i'.
for t in i:

	# To define reactants
	React= ct.Quantity(gas)
	React.TPX= t,ct.one_atm,'O2:1,N2:3.76'
	React.moles= 2

	# To define fuel
	Fuel= ct.Quantity(gas)
	Fuel.TPX= 298,ct.one_atm,'CH4:1'

	M = React + Fuel

	M.equilibrate('HP',solver= '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 air preheat on adiabatic flame temperature for METHANE combustion (phi=1, Pressure= 1 atm)')
plt.show()

Result:

Observation:

1. An increase in inlet air temperature increases the adiabatic flame temperature of methane.
2. Adiabatic flame temperature varies linearly with air preheat temperature.
3. With an increase in inlet air temperature to 600 K adiabatic temperature increases to 1302.84 K which is 245.63 K higher than that inlet air temperature of 298 K.

 

PART-2: To plot the effect of pre-heat temperature on combustion efficiency.

Here, we are utilizing the waste heat of flue gases to increase the temperature of the inlet air and how this preheating of inlet temperature affects the combustion efficiency of methane is visualized. 

Assumptions made here are, equivalence ratio is 1, LHV of methane is 50 MJ, A/F ratio is 17.1.

Python Code:

"""
Program to know the effect of preheating air inlet temperature on combustion efficiency
Assuming fuel is METHANE (CH4)
Heat loss:
Q = (ma + mf)*h_prod - mf*h_fuel -ma*h_air
A/F = mass of air / mass of fuel
Q = -(((A_f + 1) * h_prod) - (A_f * h_React[g]) - h_fuel)
LHV= 50 Mj
A/F= 17.1 assuming phi=1

By- GAURAV V. KHARWADE || Skill-Lync 2020

"""

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


gas= ct.Solution('gri30.cti')
LHV_fuel= 50e6
A_f= 17.121

# To define the range of inlet temperature from 298 to 600
i= np.linspace(298,600,100)


# To get the enthalpy of fuel
Fuel= ct.Quantity(gas)
Fuel.TPX= 298,ct.one_atm,'CH4:1'
h_fuel = Fuel.enthalpy_mass
Fuel.moles= 1

# To get the enthalpy of products
Prod= ct.Quantity(gas)
Prod.TPX= 1700,ct.one_atm,'CO2:1,H2O:2,N2:7.52'
h_prod = Prod.enthalpy_mass
Prod.moles= 1

# To get the enthalpy of reactants at a varying inlet temperature
h_React = []

for j in i:

	React= ct.Quantity(gas)
	React.TPX= j,ct.one_atm,'O2:1,N2:3.76'
	React.moles= 2
	h_React.append(React.enthalpy_mass)

Q= []
eta= [] # To get the array of combustion efficiency 

# To get the combustion efficiency for different range of inlet air preheat temperature.
for g in range(len(i)):

	Q = -(((A_f + 1) * h_prod) - (A_f * h_React[g]) - h_fuel)
	eta.append(Q*100/LHV_fuel)


# To find out the fuel saving in percentage by sending the high temperature air
Fuel_saving= 1-(eta[0]/eta[99])
FS= Fuel_saving*100
print('Total fuel saving in % =',FS)

print(i,eta)
plt.plot(i,eta)
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')
plt.show()

 

Results:

Observations:

1. From the plot above, we can say an increase in inlet air temperature will increase the combustion efficiency linearly.
2. We also know that nitric oxide emissions also be effected, since peak temperature will increase as a result of the preheating of inlet air.
3. The percentage of fuel-saving is found out as 23.93% if we increase the inlet air temperature to 600 K.

As we can see, an increase in preheating inlet air temperature increases the adiabatic flame temperature which in turn all the available quantity of fuel to participate in the combustion process hence increase in peak temperature improves the combustion efficiency of fuel. Since we are considering equivalence ratio of 1 so stoichiometric combustion will relaese more heat energy which will definitely increase the peak temperature and fuel utilization efficiency.

For the sake of simplicity, we have taken the product temperature of 1700 K which wrong because there are various factors such as the type of fuel, flue gas species or composition, combustion reaction, intermediary species on which exhaust gas temperature depends.

In this way, we have completed the study of the effect of preheating inlet air on combustion efficiency and the adiabatic flame temperature of methane using constant pressure heat exchanger application ie. Recuperator for preheating purpose.