Week 4.2 - Combustion Efficiency Calculation after Preheating

Aim: - To analyse the effect of recuperator on a furnace burning Methane-Air mixture Using Cantera.

Objective: -

1. To study the effect of preheating on Adiabatic Flame temperature.
2. To analyse the effect of preheating on fuel saving by finding Combustion efficiency.

Theory: -

Recuperator –

A recuperator is a special purpose counter-flow energy recovery heat exchanger positioned within the supply and exhaust air streams. They are used to extract heat from the exhaust and use it to preheat air entering the combustion system.

Combustion of Methane –

CH4 + 2(O2+3.76N2) --> CO2 + 2H2O + 7.52N2

1 mole of methane interacts with 9.52 moles (2 + 2*3.76 moles) of air during combustion to produce carbon Di-oxide and other by products with energy.

The energy released after the combustion can be calculated using the formula given below:

`Q=m_a*h_a+m_f*h_f-(m_a+m_f )*h_p`

were,

`m_a , m_f` = mass of air and fuel respectively

`h_a , h_f and h_p` = Enthalpy of air, fuel and product respectively.

Combustion efficiency can be calculated using following formula –

`eff=Q/(m_f*LHV)`

were LHV is lower heating value of methane (= 50 MJ/kg)

Steps –

1. A gas object is created in Cantera after importing necessary files to Python.
2. An instance of gas objects is created as fuel and its temperature, pressure and Mole fraction are set.
3. Temperature range are set for pre heating. If products are included for efficiency calculation its instance is created and proper values are entered.
4. An instance of gas objects is created as air and its pressure and Mole fraction are set, whilst temperature is entered in loop for the range created.
5. Proper equations are applied as for AFT the mixture is equilibrated as in Cantera and for efficiency energy balance is done and calculated using proper formulae.
6. The variables are plotted as required.

case 1: To plot Pre-heat temperature VS AFT

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

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

T_pre = np.linspace(298,600,20)

fuel = ct.Quantity(gas)
fuel.TPX = 298.15,ct.one_atm,'CH4:1546'
fuel.moles = 1

air = ct.Quantity(gas)

for temp in T_pre:
	air.TPX = temp,ct.one_atm,{'O2': 0.21, 'N2': 0.79}
	air.moles = 9.52
	M = air + fuel
	M.equilibrate('HP')
	plt.plot(temp,M.T,'*',color='blue')

plt.title('Effect of preheating on the Adiabatic Flame Temperature(AFT) of $CH_4$')
plt.xlabel('Preheating Temperature (K)')
plt.ylabel('Adiabatic flame Temperature (K)')
plt.grid(True)
plt.show()

Result: -

Conclusion: -

As pre- heat temperature is raised for air by using Recuperator, the enthalpy of inlet air increases. Hence it raises the Adiabatic Flame Temperature. Therefore, increasing the Inlet temperature increases the AFT as shown from the above plot.

Case 2: To plot pre-heat temperature Vs Combustion Efficiency

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

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

T_pre = np.linspace(298,600,20)
LHV = 50E6

# Methane Fuel 
fuel = ct.Quantity(gas)
fuel.TPX = 298.15,ct.one_atm,'CH4:1546'
fuel.moles = 1
mass_fuel = fuel.mass

# Combustion products
product = ct.Quantity(gas)
product.TPX = 1700,ct.one_atm,{'CO2': 0.095, "H2O": 0.19 ,'N2': 0.715}
product.moles = 10.52
mass_product = product.mass

# Air for mixing
air = ct.Quantity(gas)
for temp in T_pre:
	air.TPX = temp,ct.one_atm,{'O2': 0.21, 'N2': 0.79}
	air.moles = 9.52
	mass_air = air.mass

	Q = mass_air*air.h + mass_fuel*fuel.h - mass_product*product.h 

	eff = Q/(mass_fuel*LHV)

	plt.plot(temp,eff,'*',color='red')

plt.title('Effect of preheating on the Combustion efficiency of $CH_4$')
plt.xlabel('Preheating Temperature (K)')
plt.ylabel('Efficiency')
plt.grid(True)
plt.show()

Result: -

Conclusion: -

As Pre-heating temperature increases the Combustion efficiency increases, because the energy is extracted from exhaust which otherwise gone to waste.Using Recuperator saves the fuel as efficiency goes up and from efficiency formulae it is inversely proportion to mass of fuel keeping energy generated same.

Comment on Exit temperature of the exhaust: –

The exit temperature of exhaust should be maintained constant and within the permissible limit, As it keeps on increasing for each combustion cycle and after a certain limit it can increase the temperature of the air-fuel mixture and proper combustion can be affected causing lower efficiency.

it can also lead to mechanical damage due to overheat. Hence it is necessary to limit and maintain Exit temperature when using Recuperator.