Week 4 - Combustion Efficiency Calculation after Preheating

Aim

1. To Find Adiabatic Temperature when reactant of air heated from range 298 to 600k with 41 number of divisions which was given by recuperator using the class method in Cantera
2. Product exit 1700k temperature with preheater of air effect of combustion efficiency with LHV=50MJ/KG.

Combustion Analysis of methane Using Cantera

`C_xH_y+a(O2+3.76N2)=xCO2+(y/2)H2O+3.76aN2`

`a=x+y/4`

for solving in cantera

CH4

`a=1+4/4=2`

Reactant side (fuel=CH4:1),(air=O2:2,N2:7.52)

`(A/F)_(STOICHIOMETRIC)=(m_(air)/m_(fuel))_(STOICHIOMETRIC)=(4.76*a)/1 (MW)_(Air)/(MW)_(Fuel)=4.76*2=9.52`

air is heated from a range of 298 to 600 k with 41 number of division using a recuperator

1. Effect of preheating on the adiabatic flame temperature

Python code

"""
effect of preheating on the adiabatic flame temperature at stiochiometric condition

Project by
JagaveeraPandiyan.S
"""

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

# CH4+ air(2O2+7.52N2)= CO2+2H2O+7.52N2

T_min=298
T_max=600
T_atm=298.15
T_pre=np.linspace(T_min,T_max,41)
gas = ct.Solution('gri30.cti')
air= ct.Quantity(gas)
#CH4+Air(2O2+7.52N2)=CO2+2H2O+7.52N2
fuel=ct.Quantity(gas)
fuel.TPX= 298.15,ct.one_atm,'CH4:1'
fuel.moles=1
T_AFT=[]

for T_p in T_pre:

	air.TPX= T_p,ct.one_atm,{'O2':0.21, 'N2':0.79} 
	air.moles=9.52 # m_air/m_fuel=4.76a/1
	M=air+fuel
	M.equilibrate('HP')
	T_AFT.append(M.T)
T_I_AFT=np.max(T_AFT)-np.min(T_AFT)
plt.plot(T_pre,T_AFT, '*',color='dodgerblue')
plt.title('Effect of Preheater')
plt.xlabel('Air temperature')
plt.ylabel('AFT')
plt.grid()
plt.savefig('Preheater_AFT')
plt.show()

print('Minimum Preheater temperature obtain at 298k')
print('minimum_AFT=',min(T_AFT))
print('Due to linear increase in temperature maximum temperature obtain at 600k')
print('maximum_AFT=',max(T_AFT))
print("Due to increase in Preheater temperature change in Temperature=",T_I_AFT,'K')
print('which is =',(T_I_AFT/np.min(T_AFT))*100,'%')

Graph

Observation

when air inlet temperature increases (298 to 600 k) there is a linear increase in temperature

air at 600k maximum AFT=2346.6093

air at 298k minimum AFT=2346.609

Due to an increase in temperature, there is an increasing inefficiency.

B.Preheated & combustion exit temperature 1700k

Product

mole fraction=species/total_species

Co2 mole fraction=1/10.56=0.094

H2O mole fraction=2/10.56=0.189

N2 mole fration=7.52/10.56=0.7159

Total mole=10.56

Efficiency Of combustion

constant volume with stiochiometry condition

`dotQ=mcp(T_(Product)-T_(Reactant))=mh_(Product)-mh_(Reactant)`

`dotQ=(dotm_(Air)+dotm_(fuel))*h_(Product)-dotm_(fuel)h_(fuel)-dotm_(air)h_(air)`

`eta=dotQ/(dotm_fLHV)`

Fuel Utilization Efficiency as

`eta=((A/F)*h_(air)+h_(fuel)-((A/F)+1)*h_(Product))/(LHV)`

Python code

"""
combustion efficiency of methane with Preheater

Project by 
Jagaveerapandiyan.S
"""
import math
import matplotlib.pyplot as plt
import numpy as np
import cantera as ct

T_min=298
T_max=600
T_atm=298.15
T_pre=np.linspace(T_min,T_max,41)
gas = ct.Solution('gri30.cti')
air= ct.Quantity(gas)
#CH4+Air(2O2+7.52N2)=CO2+2H2O+7.52N2
fuel=ct.Quantity(gas)
fuel.TPX= 298.15,ct.one_atm,'CH4:1'
fuel.moles=1
T_AFT=[]
LHV=50*pow(10,6)
# Product mole=CH4+O2+N2 (1+2+7.56)
Product=ct.Quantity(gas)
Product.TPX=1700,ct.one_atm,{'CO2':0.094,'H2O':0.189,'N2':0.7159}
Product.mole=10.56
efficiency=[]
for T_p in T_pre:

	air.TPX= T_p,ct.one_atm,{'O2':0.21, 'N2':0.79} 
	air.moles=9.52 # m_air/m_fuel=4.76a/1
	M=air+fuel
	M.equilibrate('HP')
	A_F=air.mass/fuel.mass
	h_f=fuel.enthalpy_mass
	h_a=air.enthalpy_mass
	h_p=Product.enthalpy_mass
	Q=(A_F*h_a)+h_f-((A_F+1)*h_p)
	eff=Q/LHV
	efficiency.append(eff)
saving=1-((np.min(efficiency))/(np.max(efficiency)))

plt.plot(T_pre,efficiency,'o',color='fuchsia')
plt.grid()
plt.title('combustion efficiency with preheater')
plt.xlabel('Preheater Temperature')
plt.ylabel('efficiency')
plt.savefig('Preheater_efficiency')
plt.show()

print("AT 298K")
print("minimum efficiency =",np.min(efficiency))
print("AT 600K")
print("maximum efficiency =",np.max(efficiency))
print("saving of fuel=",saving*100)

Graph

Observation

preheated inlet air condition the efficiency of combustion increases linearly range from

AT 298K
minimum efficiency = 0.3315
AT 600K
maximum efficiency = 0.438

Conclusion

• above observation when there is an increase in air temperature there is increase in Adiabatic Flame Temperature this means heat energy for given fuel it reduces Fuel conception=24.32%.Due to Prehreating AFT increases to 122.26k which is 5.49 %.
• Preheater helps in Fuel-saving improve energy Utilization or increase Flame Temperature.
• Due to high Temperature, there is nox formation that affects environment & engine parts to avoid it we can use exit Temperature in combustion so Exhause gas recirculation can use( fixed exit temperature) So EGR is used in an automobile engine.