Week 4 - Combustion Efficiency Calculation after Preheating

1) Effect of preheating on the adiabatic flame temperature

The effect of preheating air on Adiabatic Flame Tempreature (AFT) of CH4 was calculated. The Quantity class method of Cantera was used to created a Mixture Methane/Air to determine the AFT.

Combustion efficiency is a measurement of how well the fuel burned is being utilized in the combustion process. We used air temerature from 298 to 600K. From the graph we conclude that, AFT increses linearly with increasing air temperature. This means that, a larger amount of useful heat is available for a given amount of fuel, that implies that for a desired amount of usuful heat or work, the amount of fuel required is lesser. Hence, preheating air helps with fuel saving.

"""
Effect of preheating air on AFT.Methane

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

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

#CH4 + 2(O2 + 3.76N2) = CO2 + 2H20 + 7.52N2

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

#Air
air = ct.Quantity(gas)
T_min = 289 #K
T_max = 600 #K
 
plot_interval = 5 #if its divited in 5 shows the point

for T_preheating in range(T_min,T_max):
	air.TPX= T_preheating,ct.one_atm,{'O2':0.21,'N2':0.79}
	air.moles =(2*3.76)/0.79

	M=fuel+air
	M.equilibrate('HP','auto')
	
	if T_preheating%plot_interval is 0:
		plt.plot(T_preheating,M.T,'.',color = 'grey')

plt.grid()
plt.title('Effect of preheating air on AFT-CH4')
plt.xlabel('Preheating air temperature [K]')
plt.ylabel('Adiabatic Flame Temperature [K]')
plt.show()

The following output has been obtained from the program:

• Adiabatic Flame Temperature is when no heat is lost to the surroundings. At constant pressure heat generated from the combustion process alone is going to increase the enthalpy and we get high temperatures in our chambers.
• When the incoming cold air is allowed to mix with the heat from the flue gases that leaves through the exhaust. This happens in the recuperator device.
• From the plot we see that as the temperature within the recuperator(T_preheat) increases the value of the Adiabatic Flame Temperature increases as well.
• So we can conclude that as a result of preheating we can achieve high temperatures during combustion process. As a result more fuel can be saved.

2. Does preheating help with fuel saving? If yes, how does combustion efficiency go up as a function of pre-heating temperature ?

Any heat input to the system is positive and any heat that leaves the system is negative.

The heat release that happens because of combustion is calculated using the following formula :

Qloss = (Mreactants * Hreactants) - (Mproducts * Hproducts)

The combustion efficiency is calculated using the formula :

ηcomb = [Heat Loss that happens when the reaction takes place / (LHV * M fuel)] * 100 %

When we are not preheating the amount of heat energy we are going to get is called as the LHV(Lower Heating Value) with the help of which we can calculate the efficiencies.

The following input is written in the form of the code as shown below:

"""
PROGRAM TO VISUALIZE THE EFFECT OF PREHEATING ON THE COMBUSTION EFFICIENCY AND FUEL SAVINGS 
"""

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

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

# Product Mixture 
products = ct.Quantity(gas)
products.TPX = 1700, ct.one_atm, { 'CO2': 0.0951, 'H2O':0.1901, 'N2':0.7148 } #Providing a particular temperature for the products
products.moles = 10.52

#Mass of products
m_p = products.mass
print('Product Mass =',m_p)

#Enthalpy of products
h_p = products.h
print('Product Enthalpy =',h_p)

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

#Mass of fuel 
m_f = fuel.mass
print('Fuel Mass =',m_f)

#Enthalpy of fuel 
h_f = fuel.h
print('Fuel Enthalpy =',h_f)

#Range of Preheating Temperature

T_preheat = np.linspace(298,600,8)

#Assumed Lower Heating Value of Methane Fuel
LHV = 50e6 #J/Kg  

# Oxidizer Mixture
oxidizer = ct.Quantity(gas)

oxidizer.TPX = 298.15, ct.one_atm, {'O2':0.21, 'N2':0.79}
oxidizer.moles = 9.52
m_o = oxidizer.mass
h_o = oxidizer.h

Q_out = (m_f*h_f) + (m_o*h_o) -(m_p*h_p) #The heat lost to the surroundings when the reaction happens 
η_comb_standard = (Q_out/(LHV*m_f)) * 100 #Combustion Efficiency without Preheating
print("Standard Combusiton Efficiency", η_comb_standard)

for i in range(len(T_preheat)):
	#Mass of oxidizer
	oxidizer.TPX = T_preheat[i], ct.one_atm, {'O2':0.21, 'N2':0.79}
	oxidizer.moles = 9.52
	m_o = oxidizer.mass
	print('Oxidizer Mass =', m_o)
	h_o = oxidizer.h
	print('Oxidizer Enthalpy =', h_o)
	Q_out = (m_f*h_f) + (m_o*h_o) -(m_p*h_p)
	print('Heat Released =', Q_out)
	Q_specific = Q_out/m_f
	print('Specific Heat =', Q_specific)
	η_comb = (Q_out/(LHV*m_f)) * 100 #Combustion Efficiency with Preheating 
	print('Combustion Efficiency', η_comb)
	plt.plot(T_preheat[i], η_comb, 'o', color = 'green')
	fuel_savings = ((η_comb/η_comb_standard)-1)* 100 #Formula which helps in estimating the amount of fuel 
	plt.plot(T_preheat[i], fuel_savings, 'd', color = 'orange')
plt.xlabel('Preheated Temperature [T_preheat]')
plt.ylabel('Percentage %')
plt.title('Effect of Preheating on the Combustion Efficiency and Fuel Savings' )
plt.legend(['Combustion Efficiency', 'Fuel Savings'])
plt.grid('on')
plt.show()

The output we get from our program is shown below:

• As indicated in the diagram above there is an efficiency increase of upto 13% as a result of preheating in the mixture as indicated in the plot for a range of temperatures.
• The plot for the fuel savings is indicated by a linear curve. More the preheated temperature more will be the fuel savings. We see in the graph for the temperature as high as 600 K there seems to be a 30% rise in fuel savings as well.
• When we take a look at our code with respect to the product side we have assumed a particular exit temperature i.e. 1700K. Based on intuition it is safe to assume a fixed exit temperature for our products. If the temperature further increases there is steep increase in the fuel saving but there will be a decrease in the combustion efficiency.
• When the exit temperature goes beyond a certain value there will be cracks or fractures on the exit surface of the furnace. So it is safe to assume a fixed value for the exit temperature