Week 7 - Auto ignition using Cantera

Objective: To write a code to calculate auto-ignition time for combustion of Methane under different operating conditions using cantera

Part 1:Plot Auto Ignition time of Methane with a constant temperature of 1250 K and pressure varying from 1 to 5 atm

Part 2: Plot Auto Ignition time of Methane with a constant pressure of 5 atm and temperature varying from 950 to 1450 K

Part 3: Rate of change of Molar concentrations of H2O, O2, OH with respect to time for a total simulation time of 10 seconds and for two conditions

• At P= 5 bar & T=1000 K
• At P= 5 bar & T=500 K

Part 1:

""""

CH4+2(O2+3.76N2)=CO2+2H2O+7.52N2

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

gas = ct.Solution('gri30.xml')
T_initial = 1250
Pressure = np.linspace(1,5,9)
Temp_at_diff_pressure = []
ignition_delay_time = []
n = 10000

for P in Pressure: 
	gas.TPX = T_initial,P*101325,{'CH4':1,'O2':2,'N2':7.52}
	autoignition_temp = 0
	autoignition_time = 0
	r = ct.IdealGasReactor(gas)
	sim = ct.ReactorNet([r])
	time = 0.0
	states = ct.SolutionArray(gas,extra = ['time_in_ms', 't'])

	for n in range(n):
		time += 1e-3
		sim.advance(time)
		states.append(r.thermo.state, time_in_ms = time*1e3, t = time)

	Temp_at_diff_pressure.append(states.T)

	for i in range(n):
		T_error = states.T[i] - T_initial - 400
		if T_error>0:
			autoignition_temp = states.T[i]
			autoignition_time = states.time_in_ms[i]

	ignition_delay_time.append(autoignition_time)

Temp_at_diff_pressure = np.array(Temp_at_diff_pressure)

for k in range (len(Pressure)):
	plt.figure(1)
	plt.plot(Temp_at_diff_pressure[k])
	plt.xlabel('number of time steps')
	plt.ylabel('Temperature')
	plt.title('Variation of auto ignition Temperature with pressure')
	plt.legend(['1 atm','1.5 atm','2 atm','2.5 atm','3 atm','3.5 atm','4 atm','4.5 atm','5 atm'])

plt.figure(2)
plt.plot(Pressure,ignition_delay_time,'k-*')
plt.xlabel('pressure')
plt.ylabel('Auto ignition time')
plt.title('Iginition delay vs pressure')
plt.show()

Results:

> Low pressure reactor => ignition delay is high

> High pressure reactor =>ignition delay is low.

> Max Flame temperature reached by the products is maximum for a high pressure reactor and low for a low pressure reactor

> Ign. delay is max for a low pressure reactor and minimum for a high pressure reactor.

> The high pressure enhances the auto-ignition and helps the fuel mixture burn faster reducing delay.

Part 2 :

""""

CH4+2(O2+3.76N2)=CO2+2H2O+7.52N2

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

gas = ct.Solution('gri30.xml')
Temperature = np.linspace(950,1450,11)
Pressure = 5
Temp_at_diff_temp = []
ignition_delay_time = []
n = 10000

for T in Temperature: 
	gas.TPX = T,Pressure*101325,{'CH4':1,'O2':2,'N2':7.52}
	autoignition_temp = 0
	autoignition_time = 0
	r = ct.IdealGasReactor(gas)
	sim = ct.ReactorNet([r])
	time = 0.0
	states = ct.SolutionArray(gas,extra = ['time_in_ms', 't'])

	for n in range(n):
		time += 1e-3
		sim.advance(time)
		states.append(r.thermo.state, time_in_ms = time*1e3, t = time)

	Temp_at_diff_temp.append(states.T)

	for i in range(n):
		T_error = states.T[i] - Tp - 400
		if T_error>0:
			autoignition_temp = states.T[i]
			autoignition_time = states.time_in_ms[i]

	ignition_delay_time.append(autoignition_time)

Temp_at_diff_temp = np.array(Temp_at_diff_temp)

for k in range (len(Temperature)):
	plt.figure(1)
	plt.plot(Temp_at_diff_temp[k])
	plt.xlabel('number of time steps')
	plt.ylabel('Temperature')
	plt.title('Variation of auto ignition Temperature with Temperature')
	plt.legend(['950','1000','1050','1100','1150','1200','1250','1300','1350','1400','1450'])

plt.figure(2)
plt.plot(Temperature,ignition_delay_time,'k-*')
plt.xlabel('Temperature')
plt.ylabel('Auto ignition time')
plt.title('Iginition delay vs Temperature')

plt.show()

Results:

> Higher initial temperature => auto-ignition delay time is the least

> Final temperature achieved after ignition is the highest for high initial temperature.

> Delay max for a low temperature reactor and minimum for a high temperature reactor.

> The high temperature enhances the auto-ignition and helps the fuel mixture burn faster.

Part 3:

""""

CH4+2(O2+3.76N2)=CO2+2H2O+7.52N2

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

gas = ct.Solution('gri30.xml')
T_initial = 500
Pressure = 5
n = 10000
molar_conc = []

gas.TPX = T_initial,Pressure*101325,{'CH4':1,'O2':2,'N2':7.52}
autoignition_temp = 0
autoignition_time = 0
r = ct.IdealGasReactor(gas)
sim = ct.ReactorNet([r])
time = 0.0
states = ct.SolutionArray(gas,extra = ['time_in_ms', 't'])

for n in range(n):
	time += 1e-3
	sim.advance(time)
	states.append(r.thermo.state, time_in_ms = time*1e3, t = time)
	
plt.subplot(3,1,1)
plt.title('Molar concentration vs Time')
plt.plot(states.t,states.X[:, gas.species_index('H2O')],'r')
plt.xlabel('time (s)')
plt.ylabel('H2O')

plt.subplot(3,1,2)
plt.plot(states.t,states.X[:, gas.species_index('O2')],'b')
plt.xlabel('time (s)')
plt.ylabel('O2')

plt.subplot(3,1,3)
plt.plot(states.t,states.X[:, gas.species_index('OH')],'g')
plt.xlabel('time (s)')
plt.ylabel('OH')

plt.show()

Results:

i ) Pressure: 5 atm; Temperature: 1000 K

ii) Pressure: 5 atm; Temperature: 500 K

Observation:

i) At, 5 atm and 1000 K, the auto-ignition occurs within a few miliseconds.

ii) For the second case, the auto-ignition does not occur.

iii) Hence, the initial temperature plays an important role in auto-igniting the fuel.