Week 4.2 - Combustion Efficiency Calculation after Preheating

# PreHeat Temperature VS Adiabatic Flame Temperture

"""
The stoichiometric mixture of combustion of methene looks like the following

Ch4+2(O2+3.76N2)= Co2+2H2O+7.52N2

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

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

air = ct.Quantity(gas)
fuel = ct.Quantity(gas)

fuel.TPX = 298.15,ct.one_atm,'CH4:1'
fuel.moles = 1

#Preheating Temperature
preheat_T = []

# Adibatic Flame Temperature
Adiabatic_flame_temperature = []

for T in range(298,600):
		air.TPX = T,ct.one_atm,{'O2':0.21,'N2':0.79}
		air.moles = 9.52
		preheat_T.append(T)


		Mixture = fuel + air 
		Mixture.equilibrate('HP')


		Adiabatic_flame_temperature.append(Mixture.T)

print(Adiabatic_flame_temperature)
print(preheat_T)

plt.plot(preheat_T,Adiabatic_flame_temperature)
plt.title('preheat_T V/s Adiabatic_flame_temperature')
plt.xlabel('preheat_T(k) ', fontsize = 14)
plt.ylabel('Adiabatic_flame_temperature (K)',fontsize = 14)
plt.grid('on')
plt.show()

Aim

To Find the Combustion Efficiency of the Furnance with respect to Preheating.

Recuperator

Its is type of heat exchanger has separate flow paths for each fluid alongs their own passages and heat is transferred through the separating walls. Recuperators are used in power engineering, to increase the overall efficiency of thermodynamics cycles. For Example, in a gas turbine engine. The recuperator transfers some of the waste heat in the exhaust to the compressed air, thus preheating it before entering the combustion chamber. Many recuperators are designed as counter-flow heat exchangers.

Adiabatic Flame Temperature

The Final Temperature that is obtained after the fuel is completely burnt.

Case : 1 Effect of Pre-heating (Recuperator) on AFT

A Stoichiometric combustion of methene is analysed in the problem given by :-

CH4 + 2(O2 + 3.76N2) ---->CO2+ 2H2O+7.5N2

Method of this process is Quantiy class. These classes are composite representations of a substance which has thermodynamic, chemical kinetic,and taransport properties.

Pre-heating temperatures is varied 298 k to 600k and equilibrate method(constant enthalpy and pressure) is used to find AFT

OBSERVATIONS

It is clearly seen that AFT increase linearly with preheating temperature which is due to higher temperature of air entering the combustion chamber and hence the final temperature in the control volume chamber is higher which in turns leads to combustion efficiency through the use of less fuel. Preheating, therefore,helps to save fuel.

2. The effect of Preheating temperature on combustion efficiency:

Combustion efficiency is a defined the asb the ratio of heat released by the fuel to the heat input by the fuel. Hence by increasing on how greatly the fuel is being burned.

Q = Mass of air*Enthalpy of Air + Mass of Fuel*Enthpaly of Fuel - Mass of Product*Enthalpy of Product

or

Q = ma ha+mf hf - mp hp

with relation

mf+ ma = mp

Qsp = Q/mass of fuel

Efficiency = Qsp/LHV

where LHV is the lower heating value for which is given as 50MJ/kg

Here we used a Quantity class for generating and mixing our product reactants , we include the pre-heating temperature and the 1700 kelvin exhaust as per the problematic statement. Then, the combustion efficiency is calculated.

OBSERVATION

From 2nd image it can be clearly seen that as the preheat temperature increses, efficiency also increses. It is also important to note that the exit temperature of the furnace is kept as 1700k. it is important to control the exit tempearture since excessive high tempearture can damage the furnace.

It is very important to that the exit temperature from the furnace must be constant or in the other words a fixed value. The value depends on many factors including the material properties . It is a correct practice of fixing the exit temperature.

Procedure :

By using Fuel.TPX, Products.TPX ,we provide the initial conditions of the fuel and the products

products.TPX = 1700,ct.one_atm,{'CO2':0.096,'H2O':0.19,'N2':0.714} #Products are CO2,H20,N2

Fuel.TPX = 298.15,ct.one_atm,'CH4:1' #Fuel is methane

which stands for the temperature of the air at the inlet is 298k, the pressure of air is 1 atm and X stands for the mole fraction of O2 and N2 in the air which is provided as a dictionary. Oxygen and Nitrogen in the air at 21% and 79% by molar percentage,respectively.

Until now we have just defined the mole fraction of air being used, Now we determine the number of moles of air involved in the stoichiometric equation by using a variable fuel and products .moles thorugh the Quantity class.

Number of moles of Oxygen in Air = 2

Number of moles of Nitrogen in Air = 2*3.76 = 7.52

Total number of Moles of Air = 9.52 (i.e 2+7.52)

Now to define A.moles we can put it as 9.52 or 2/0.21 or 2/0.79 .

In the above to determine the total number of moles following formula is used.

total no. of moles = moles of individual compound/mole fraction of individual compound

A.moles = 9.52 or 2/ 0.21 or 7.52/0.79

If we do not define the total number of moles of the compound (i.e A.moles) , cantera by default assumes the number of moles per gram or (K-mol/kg) of compound which leads to wrong results. For example,

Mass of 1 mole of O2 = 31.9988 gm

Mass of 1 mole of O2 = 28.01348 gm

Number of moles in 1gm of O2 = 1/31.9988 = 0.03125117191

Number of moles in 1gm of N2 = 1/28.01348 = 0.0356971011

Number of moles in 1gm of air = 0.21*0.03125117191 + 0.79*0.0356971011 = 0.03476345518

Similary for Ch4

Mass of 1 mole of ch4 = 16.04 gm

Number of moles of 1 gm of ch4 = 0.0623441397

So after these all plot the 2 figures for AFT v/s Efficiency and AFT v/s combustion

 #PreHeat Temperature v/s Combustion efficiency
 # PreHeat Temperature v/s Fuel Saving

"""
The stoichiometric mixture of combustion of methene looks like the following

Ch4+2(O2+3.76N2)= Co2+2H2O+7.52N2

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

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


Fuel = ct.Quantity(gas)
Air = ct.Quantity(gas)
products = ct.Quantity(gas)

#Methane has 1 mole
Fuel.TPX = 298.15,ct.one_atm,'CH4:1'
Fuel.moles = 1

#products
products.TPX = 1700,ct.one_atm,{'CO2':0.096,'H2O':0.19,'N2':0.714}
products.moles = 10.52


#Preheating Temperature
preheat_T = [] 

#Combustion efficiency with respect to varing preheat Tempwarture
Efficiency = []

#Fuel Saving
Fuel_saving = []


for T in range(298,600):
		Air.TPX = T,ct.one_atm,{'O2':0.21,'N2':0.79}
		Air.moles = 9.52
		Air_Fuel = Air.mass/Fuel.mass

		LHV = 50*10^6
		heat = Fuel.enthalpy_mass + Air_Fuel*Air.enthalpy_mass - (1+ Air_Fuel)*products.enthalpy_mass
		Eff = (heat/LHV)*100
		Efficiency.append(Eff)
		preheat_T.append(T)

		if (T == 298):
			Eff_no_preheat = Eff 
		saved_Fuel = (1 - (Eff_no_preheat/Eff))*100
		Fuel_saving.append(saved_Fuel)


plt.figure(1)
plt.plot(preheat_T,Efficiency,'-r')
plt.title('preheat_T v/s Efficiency')
plt.xlabel('Preheating')
plt.ylabel('Efficiency')
plt.grid()
plt.show()


plt.figure(2)
plt.plot(preheat_T,Fuel_saving,'-g')
plt.title('preheat_T v/s Fuel_saving')
plt.xlabel('Preheating')
plt.ylabel('Fuel_saving')
plt.grid()
plt.show()