Week 4 - Combustion Efficiency Calculation after Preheating

Aim

To study the effect of preheating air on combustion of methane fuel and plot the variations in the adiabatic flame temperature and combustion efficiency using Cantera

1. Introduction

A recuperator is a counter-flow energy recovery heat exchanger device positioned within the air inlet and outlet systems. The exhaust gases from the combustion chamber are used to heat the inlet air. This preheating of the air inlet improves combustion of fuel inside the chamber which in turn improves the thermal efficiency of the system.

In this study, we study the combustion of methane fuel and study the effect of increasing preheating temperature of air on the adiabatic flame temperature. Using the plot we comment on the fuel saving nature of recuperators. The study also inspects the combustion efficiency or heat gain due to the preheating temperature. The study involves programming using Python and uses Cantera and matplotlib libraries to solve the equations.

2. Objective

The following are the objectives of the study:

• The effect of preheating on the adiabatic flame temperature by change pre-heating temperature from 298 to 600K
• Combustion efficiency as a function of pre-heating temperature for a fixed furnace exit temperature of 1700K

3. Effect of preheating temperature on adiabatic flame temperature

The combustion reaction of methane in constant pressure system is as follows:

CH₄ + 2(O₂ + 3.76 N₂) = CO₂ + 2H₂O + 7.52N₂

The program algorithm for calculating adiabatic flame temperature (AFT) is:

1. Import libraries cantera and matlibplot
2. Create an instance ‘gas’ of the Solution class and create instance method of Quantity()
3. Assign the initial conditions of fuel and air
4. Using for loop for variation in preheating temperature, calculate equilibrate condition for M, mixture of air and fuel, and plot the preheating vs AFT

The program code is as follows:

'''

Effect of preheating temperature on adiabatic flame temperature

Program written by Vignesh V

Reaction

CH4 + 2(O2 + 3.76 N2) = CO2 + 2H2O + 7.52N2 

'''
import matplotlib.pyplot as plt

import cantera as ct

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

#Assigning conditions for fuel

Fuel = ct.Quantity(gas)
Fuel.TPX = 298.15, ct.one_atm,{'CH4':1}
Fuel.moles=1


for T_p in range (298,600):
	Air = ct.Quantity(gas)
	Air.TPX = T_p, ct.one_atm,{'O2':1,'N2':3.76}
	
	Air.moles = 9.52

	M= Fuel + Air

	M.equilibrate('HP')
	plt.plot(Air.T,M.T,'*',color='blue')


plt.xlabel('Preheating temperature (in K) ')
plt.ylabel('Adiabatic Flame temperature (in K)')
plt.title('Effect of preheating temperature on AFT')
plt.show() 

It can be observed from the figure that with an increase in preheating temperature, the adiabatic flame temperature tends to increase. This can be explained by the increase in the temperature of air fuel mixture in the combustion chamber. Due to this, the enthalpy of reactants increase which in turn increases the enthalpy of products obtained after combustion process. Due to the rise in net enthalpy of the system, the adiabatic flame temperature is found to increase.

4 Preheating and fuel saving

It can be seen that that the AFT increases for the same amount of air fuel mixture into the system when preheated air is fed into the chamber. Considering a constant work output by the system, the amount of fuel required to produce the corresponding thermal output decreases with an increase in preheating temperature of air inlet. Thus, it can be said that a recuperator can be used to save fuel or reduce fuel consumption by the combustion system.

5. Effect of preheating on combustion efficiency

In this section, the combustion efficiency is determined for the variation in preheating temperature from 298 to 600 K and the results are plotted.

5.1 Formula for combustion efficiency

For a combustion reaction, the maximum heat output at STP conditions can be defined as

Q_{STP =} m_fuel x LHV

m_fuel, mass flow rate of fuel

LHV, lower heating value of fuel

For the given system equipped with a recuperator, the net heat output can be written as:

Q = H_reactants - H_products

Therefore, the combustion efficiency can be written as

η = Q/ Q_STP

η = (H_reactants - H_products) / (m_fuel x LHV)

5.2 Plot of combustion efficiency vs preheating temperature

The program algorithm for calculating adiabatic flame temperature (AFT) is:

1. Import libraries cantera and matlibplot
2. Create an instance ‘gas’ of the Solution class and create instance methods of Quantity()
3. Assign the initial conditions of fuel, air and products
4. Using for loop for variation in preheating temperature, calculate molar enthalpy using enthalpy_mole(). Using this, determine the heat output of the system
5. Calculate efficiency using the derived formula and plot for the varying preheating temperature

The program code is as follows:

'''

Effect of preheating temperature on combustion efficiency
Program written by Vignesh V

Reaction

CH4 + 2(O2 + 3.76 N2) = CO2 + 2H2O + 7.52N2 

'''

import cantera as ct 
import matplotlib.pyplot as plt 


LHV=50000000 #J

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

#Assigning conditions for fuel

Fuel = ct.Quantity(gas)
Fuel.TPX = 298.15, ct.one_atm,{'CH4':1}
Fuel.moles=1
h_fuel = Fuel.enthalpy_mole

Product = ct.Quantity(gas)
Product.TPX = 1700, ct.one_atm,{'CO2':1,'H2O':2,'N2':7.52}
Product.moles= 10.52
h_product= Product.enthalpy_mole

for T_p in range (298,600):
	Air = ct.Quantity(gas)
	Air.TPX = T_p, ct.one_atm,{'O2':1,'N2':3.76}
	Air.moles = 9.52
	h_air=Air.enthalpy_mole
	Q =Fuel.moles*h_fuel+Air.moles*h_air-Product.moles*h_product

	Efficiency = Q/(LHV*Fuel.mass)*100

	plt.plot(T_p,Efficiency,'*',color='red')

plt.xlabel('Preheating temperature')
plt.ylabel('Combustion in percentage %')
plt.title('Effect of preheating temperature on combustion efficiency')
plt.show()	

It can be observed that the combustion efficiency increases with an increase in preheating temperature, the result in line with the relationship established for AFT vs preheating temperature

5.2 Preheating and Furnace exit temperature

In the given study, we considered a constant furnace exit temperature of 1700 K. However, in practice, the preheating of air inlet would increase the temperature of exhaust gases continuously as the exhaust gases in turn heat the inlet air. This rise in furnace exit temperature would damage the recuperator system. Hence, there is a need to control the exit temperature justifying our assumption made in the study

6. Conclusion

It can be concluded from the given study that:

• Adiabatic flame temperature increases with an increase in preheating temperature of air inlet
• The combustion efficiency is found to increase with an increase in preheating temperature