Week 4 - Combustion Efficiency Calculation after Preheating

Effect of preheating on the adiabatic flame temperature

Introduction: In this challenge a mixture of methane-air fuel burned in a furnace connected to a recuperator for recovery of some energy.

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

Recuperator: A recuperator is a special purpose counter-flow energy recovery heat exchanger positioned within the supply and exhaust air streams of an air handling system, or in the exhaust gases of an industrial process, in order to recover the waste heat.

Objective-1: Determining the effect of preheating on the adiabatic flame temperature by varying the preheating of the gas from 298 to 600 kelvin using cantera library for the combustion.

• Quantity class is used to vary the temperature of intake air.
• Air consists of 21% of oxygen and 79% nitrogen.
• Molar mass of the air is 9.52
• Fuel taken is methane of 1 mole.

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

#Here we are writing individual code for Air and Fuel using quantity class from cantera library.

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

# no of moles of air taken for one mole of fuel.

fuel = ct.Quantity(gas)
fuel.TPX = 298.15,101325,{'CH4':1} 
fuel.moles = 1

air = ct.Quantity(gas)
T_ph = np.linspace(298,600,20) #preheating temeperature
AFT=[]
for i in range(0,len(T_ph)):
	air.TPX = T_ph[i],101325,{'O2':0.21,'N2':0.79}
	air.moles = 9.52 
	
	M = fuel + air
	M.equilibrate('HP','auto')
	AFT.append(M.T)

plt.plot(T_ph,AFT,'*',color='red',label='Cantera')
plt.xlabel('Preheating temperature')
plt.ylabel('Adiabatic flame temperature (K)')
plt.grid('on')
plt.legend(fontsize = 12)
plt.title('Preheating temperature vs AFT of Methane-Air combustion')
plt.show()

From the above graph, preheating of the intake air results in the increase of the adiabtic flame temperature linearly, which means more heat is available to be utilized as work which eventually results in the increase of efficency of combustion.

Objective-2: Effect of preheating on the combustion efficiency. we are considering a stochiometric reaction of methane fuel

Combustion efficiency(n) : The amount of heat utilized to do work to the maximum possible heat generated.

n = Q/mf.LHV

Q = heat utilized by the system

Q = ma.ha + mf.hf - mp.hp

m = mass

h = enthalpy

a = air

f = fuel

p = products

products = CO2, H20, and N2

LHV = 50000 kJ/kg

mole fraction of CO2 = 1/10.52 = 0.095

mole fraction of H2O = 2/10.52 = 0.1901

mole fraction of N2 = 7.52/10.52 = 0.7148

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

#Here we are writing individual code for Air and Fuel using quantity class from cantera library.

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

LHV = 50000000 #J/Kg

fuel = ct.Quantity(gas)
fuel.TPX = 298.15,101325,{'CH4':1} 
fuel.moles = 1

products = ct.Quantity(gas)
products.TPX = 1700,101325,{'CO2':0.095,'H2O':0.1901,'N2':0.7148}
products.moles = 10.92

T_ph = np.linspace(298,600,20) #preheating temeperature
eff = []
fuel_sav = []
for i in range(0,len(T_ph)):
	
	air = ct.Quantity(gas)
	air.TPX = T_ph[i],101325,{'O2':0.21,'N2':0.79}
	air.moles = 9.52 
	
	Q = (air.mass*air.h + fuel.mass*fuel.h - products.mass*products.h)/fuel.mass

	n = (Q/LHV)*100
	eff.append(n)

	#fuel saving
	fs = 1 - (eff[0]/eff[i])
	
	fuel_sav.append(fs)


plt.plot(T_ph,eff,'*',color='red')
plt.xlabel('Preheating temperature(k)')
plt.ylabel('combustion efficiency (%)')
plt.grid('on')
plt.legend(fontsize = 12)
plt.title('Preheating temperature vs combustion efficiency of Methane-Air combustion')
plt.show()

plt.plot(T_ph,fuel_sav,'*',color='red')
plt.xlabel('Preheating temperature(k)')
plt.ylabel('fuel saved')
plt.grid('on')
plt.legend(fontsize = 12)
plt.title('Preheating temperature vs fuel saved')
plt.show()
	

Combustion efficiency of the engine increased linearly with respect to the increase in preheating temperature. Since there is more amount of heat available to utilize for work for same amount of fuel, efficiency has increased.

The amount of fuel that is saved increased with respect to fuel consumed at standard temperature = 298 to a range of preheating temperatures till 600k. This is due to presence of heat in the intake mixture which lead to need of less fuel requirement to produce the desired output.

Assuming the exit temperature or maintaining the exit temperature at 1700k is a productive step towards the life and effective performance of the recuperator. In the real world senerios, exit temperature depends of the products, enthalpies,reaction and combustion rates.