Combustion Efficiency Calculation after Preheating   (Cantera, Skill Lync, Easy)

Aim:

To calculate the effect of preheating the inlet air on AFT, cycle efficiency and fuel savings.

Introduction:

The products of combustion, having high temperature, expand in turbines and cool down to certain temperature. The efficiency of turbine never reaches 100%, so after expansion there is some amount of work or heat that can be extracted from these product gases. This heat is used for heating fresh air before entering the combustion chamber. A heat exchanger or recuperator is used for this purpose. The diagram given below shows schematic diagram for the cycle. [Ref 1]

Theory:

When preheated air is used for combustion instead of normal air, with same amount of fuel, the internal energy entering chamber is higher than in normal case. This increased energy is expected to raise the inside temperature. The exhaust temperature would increase and cause problems with turbines and recuperator which would lead to inlet air temperature being hotter than before.

This would lead to heat accumulation in the combustion chamber. To overcome this, it is recommended that the heat output of the reaction be same even after the preheating. This balancing would give a constant temperature of exhaust gas. In this report, the exhaust temperature is assumed constant as 1700 K. This approach of keeping exhaust temperature constant is valid due to above reasons and is also mentioned in chapter 2 of [Ref 1]. The report consists of 2 parts: Effect of preheating on AFT and Effect of preheating on cycle efficiency and fuel savings.

1) Effect of preheating on AFT:

The balanced reaction of combustion of methane is:

It contains air having 21 % oxygen and 79 % nitrogen on mole fraction basis. The total moles of air required are 9.52. It has 2 moles of oxygen and 7.52 moles of nitrogen. The inlet air is assumed to be preheated from temperatures 298K to 600K. In this code, we apply different temperatures using ‘Quantity’ class to fuel and air and then mix them using ‘+’. This mixture is then combusted using ‘equilibrate’ function, for constant pressure condition and appropriate temperatures are saved to plot a graph. The code is more generalized to accept different values of equivalence ratio.

2) Effect of preheating on cycle efficiency and fuel savings:

As mentioned before, the heat released from reaction (or exhaust temperature) is to be kept constant while using preheating. So, for calculating the values of efficiency, we would first need to know the amount of heat that has to be kept constant:

This heat value is kept constant by lowering the mass flow rate of fuel and accordingly lowering the mass flow rate of air, to maintain the air-fuel ratio. In this case, the heat loss due to conduction to outer atmosphere is neglected, i.e. the system is assumed to be adiabatic.

The combustion efficiency can be represented using:

Also, fuel savings is calculated using:

Code:

1) Effect of preheating on AFT:

import cantera as ct
import matplotlib.pyplot as plt

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

phi = 1

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

T_min = 298 #K
T_max = 600 #K

T_AFT = []
T_Pre = []

for temp_a in range(T_min, T_max + 1):
	
	A_ir = ct.Quantity(gas)
	A_ir.TPX = temp_a, ct.one_atm, {'O2':0.21, 'N2':0.79}
	A_ir.moles = 9.52/phi

	Mix_ture = A_ir + F_uel
	Mix_ture.equilibrate('HP','auto')

	T_AFT.append(Mix_ture.T)
	T_Pre.append(temp_a)

print('The AFT for ' + str(temp_a) + 'K of preheated air temperature is ' + str(Mix_ture.T) + ' K')
plt.plot(T_Pre, T_AFT, color = 'red')
plt.title("Effect of Preheating of Air on AFT")
plt.xlabel("Preheated Air Temperature (K)")
plt.ylabel("Adiabatic Flame Temperature (K)")
plt.grid(which = 'major')
plt.minorticks_on()
plt.grid(which = 'minor', alpha = 0.2)
plt.show()

2) Effect of preheating on efficiency and fuel savings:

import cantera as ct
import matplotlib.pyplot as plt

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

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

#finding mole fractions of species
n_moles = 10.52 # sum of moles on products side
x_co2 = 1/n_moles
x_h2o = 2/n_moles
x_n2 = 7.52/n_moles

# To find mass and enthalpy of fuel
Fuel = ct.Quantity(gas)
Fuel.TPX = 298.15, ct.one_atm, {'CH4': 1}
Fuel.moles = 1
fuel_m = Fuel.mass
fuel_h = Fuel.enthalpy_mass

# To find enthalpy of exhaust gases
Exhaust = ct.Quantity(gas)
Exhaust.TPX = 1700, ct.one_atm, {'CO2': x_co2, 'H2O': x_h2o, 'N2': x_n2}
Exhaust.moles = n_moles
exhaust_h = Exhaust.enthalpy_mass

T_min = 298 #K
T_max = 600 #K
LHV = 50e6 # J/kg # Lower heating value

T_Pre = []
effi_ciency = []
fuel_save = []

for temp_a in range (T_min, T_max + 1):

	# to find mass and enthalpy of air
	Air = ct.Quantity(gas)
	Air.TPX = temp_a, ct.one_atm, {'O2': 0.21, 'N2': 0.79}
	Air.moles = 9.52
	air_m = Air.mass
	air_h = Air.enthalpy_mass

	AF = air_m/fuel_m # Air fuel ratio

	Q_spec = fuel_h + (AF * air_h) - ((1 + AF) * exhaust_h)
	effi_ciency.append((Q_spec/LHV)*100)

	if (temp_a == 298):
		Q_298 = Q_spec

	fuel_save.append((1 - Q_298/Q_spec) * 100)
	T_Pre.append(temp_a)

print("Efficiency without preheating (T = 298 K) = ", round(effi_ciency[0],4), '%')
print("Efficiency after preheating (T = 600 K) = ", round(effi_ciency[len(effi_ciency)-1],4), '%')
print("Fuel Savings after preheating (T = 600 K) = ", round(fuel_save[len(fuel_save)-1],4), '%')

plt.figure(1)
plt.plot(T_Pre, effi_ciency, color = 'red')
plt.title("Effect of Preheating of Air on Efficiency")
plt.xlabel("Preheated Air Temperature (K)")
plt.ylabel("Efficiency (%)")
plt.grid(which='major')
plt.minorticks_on()
plt.grid(which='minor', alpha=0.2)

plt.figure(2)
plt.plot(T_Pre, fuel_save, color = 'red')
plt.title("Effect of Preheating of Air on fuel savings")
plt.xlabel("Preheated Air Temperature (K)")
plt.ylabel("Fuel Savings (%)")
plt.grid(which='major')
plt.minorticks_on()
plt.grid(which='minor', alpha=0.2)
plt.show()

Results:

1) Case 1: Effect of preheating on temperature:

The effect of preheating is clearly visible in the graph. As the temperature of preheated inlet air increased by 300K, the AFT increased by 120K. This temperature increase is due to the continous accumulation of heat inside the chamber, as explained before.

2) Case 2: Effect of preheating on efficiency and fuel savings:

By preheating the inlet air using energy of exhaust gases, we reducing the heat lost from exhaust gases. Since we have considered a constant heat input to chamber or constant exhaust temperature, the work extracted remains constant and the fuel used to generate this heat gets reduced. This leads to higher efficiency of the combustion cycle.

As stated above, the fuel is saved when preheating using exhaust gas is done. This fact is confirmed from plot above which says that upto 23.9% fuel can be saved by preheating inlet air upto 600K.

The difference in the values can be seen in this image. The efficiency increases from 33.8 % to 44.5 % and upto 23.9% fuel is saved by preheating.

Conclusion:

The effect of preheating of air on AFT, Efficiency and fuel savings is seen.

References:

1) "An Introduction of Combustion" by Stephen Turns.