Week 4.2 - Combustion Efficiency Calculation after Preheating

Aim --> Combustion Efficiency Calculation after Preheating.

--> A furnace is used to burn Methane and Air Mixture. A recuperator is connected to this furnace to recover some energy.

1. What is the effect of preheating on the adiabatic flame temperature?
   1. Change pre-heating from 298 to 600K
   2. Explain your results
2. Does preheating help with fuel saving? If yes, how does combustion efficiency go up as a function of pre-heating temperature? Assume that the furnace exit temperature is 1700K (For this case assume that the combustion products are CO2, H20, and N2).
   1. Write the formula for combustion efficiency
   2. Plot the effect of pre-heat temperature on combustion efficiency
   3. Is it right or wrong to assume a fixed furnace exit temperature? Explain your answer.

NOTE: You will use Cantera for these calculations. Assume the LHV of combustion of Methane as 50 MJ/KG.

--> Following is the python code for the effect of preheating on the adiabatic flame temperature.

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

n2=100
#phi = ny.linspace(0.1,2.0,n1) # Equivalence ratio
T_ph=ny.linspace(298.15,600,n2) # Pre-Heating Temperature from the recuiperator
LHV=50000 # Lower-heating-value of methane KJ/KG
T_aft=ny.ones(n2)

gas=ct.Solution('gri30.xml')
fuel=ct.Quantity(gas)
fuel.TPX=298.15,ct.one_atm,{'CH4':1}
fuel.moles=1

for i in range(len(T_ph)):
   oxidiser=ct.Quantity(gas)
   oxidiser.TPX=T_ph[i],ct.one_atm,{'N2':0.79,'O2':0.21}
   oxidiser.moles=9.52
   Mixture=fuel+oxidiser
   Mixture.equilibrate('HP','auto')
   T_aft[i]=Mixture.T

plt.plot(T_ph,T_aft)
plt.xlabel('Air Pre-Heating Temperature')
plt.ylabel('Adiabatic Flame Temperature')
plt.grid('on')
plt.show()

From the above plot, we can see that with the increase in the air preheating temperature the Adiabatic flame temperature (AFT) also increases (almost in a linear fashion).

--> Following is the python code for the effect of preheating on the combustion efficiency.

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

n2=100
phi = 1 # Equivalence ratio
T_ph=ny.linspace(298.15,600,n2) # Pre-Heating Temperature from the recuiperator
LHV=50000 # Lower-heating-value of methane KJ/KG
# for phi=1[STOICHIOMETRIC]  ///// CH4 + 2 [ O2 + 3.76 N2 ] ----->  CO2 + 2 H2O + 7.52 N2
gas=ct.Solution('gri30.xml')
eff=ny.ones(n2)
for i in range(len(T_ph)):
	air=ct.Quantity(gas)
	air.TPX=T_ph[i],ct.one_atm,{'N2':0.79,'O2':0.21}
	air.moles=9.52
	m_air=air.mass
	h_air=air.enthalpy_mass

	fuel=ct.Quantity(gas)
	fuel.TPX=298.15,ct.one_atm,{'CH4':1}
	fuel.moles=1
	m_fuel=fuel.mass
	h_fuel=fuel.enthalpy_mass

	product=ct.Quantity(gas)
	product.TPX=1700,ct.one_atm,{'CO2':0.095,'H2O':0.190,'N2':0.714}
	product.moles=10.52
	m_product=product.mass
	h_product=product.enthalpy_mass
	A_F=m_air/m_fuel
	Q=A_F*h_air + h_fuel - (A_F+1)*h_product
	eff[i]=Q/(m_fuel*LHV*100)

plt.plot(T_ph,eff)
plt.xlabel('Air Pre-Heating Temperature')
plt.ylabel('efficiency of Combustion')
plt.grid('on')
plt.show()

--> Yes, with preheating we are saving fuel. The above plot shows us how the efficiency of combustion is a function of Air pre-heating temperature.

--> Formula for Combustion Efficiency:--

--> In the exhaust we have taken 1700 K constant temperature. This is due to multiple reasons, one is to make sure that the material can withstand the temperature. Also, the exhaust Temperature has to be lower than AFT as some amount of Enthalpy is lost in doing Useful Work (Turbine work or Qu etc.) so we take a value of 1700 K.