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Challenge

Week 7 - Auto ignition using Cantera

JJagaveerapandiyan Selvaraj28 May 2021

study Methane (CH4) of Ignition delay at the various condition for 10 seconds

Given Data

Part 1

Case 1a

constant temperature T=1250 k

variable pressure varies from P= 1 to 5 bar

case 1b

constant pressure P=5 bar

variable Temperature varies from T=950 to 1450k

Part 2

case2a

constant Temperature T=500k

constant Pressure P=5 bar

case2b

constant Temperature T=1000k

constant Pressure P=5 bar

To Find

ignition delay time for 10 seconds

case 1

Auto Ignition time of Methane for a given condition with respect to time

case 2

molar concentrations H2O, O2, OH of given condition with respect to time

Solution

by using Cantera inbuilt combustion Data analysis are carried out at different condition by just adding input function data to Cantera to analyse the objective to solve the problem

Autoignition temperature

    • is the temperature at which a material spontaneously ignites in a normal atmosphere without an external source of ignition.
    • is the temperature required to supply the activation energy for combustion
    • is usually applied to combustible fuel mixtures
    • The ignition temperature of a substance is the least temperature at which the substance starts combustion

Auto Ignition time is the time when the temperature of the reactor is Initial Temperature plus 400K

`T_(AUTOIGNITION)=T_(INITIAL)+400K`

solving using Cantera & Python for the given condition

Python cantera code

"""
Ignition Delay analysis for various condition
 Auto Ignition Time for Methane under the following conditions for 10 secounds analysis

 Case1
case1 a
 Plot the variation of Auto Ignition time of Methane with a constant temperature of 1250K and pressure varying from 1 to 5 atm.
case1 b
 Plot the variation of Auto Ignition time of Methane with a constant pressure of 5 atm and temperature varying from 950K to 1450K.

Case2
molar concentrations of the given elements "H2O, O2, OH" with respect to the time
case2 a
When Temperature is 1000K and pressure 5 bar
case2 b
When Temperature is 500K and pressure 5 bar


Program by S.Jagaveerapandiyan
"""
import sys
import numpy as py
import cantera as ct
import numpy as np
import matplotlib.pyplot as plt

gas=ct.Solution('gri30.xml')
T=np.linspace(950,1450,51)
P=101325*(np.linspace(1,5,9))
t=np.linspace(0,10,10001)
species={'CH4':1,'O2':2,'N2':7.52}
Tm=[500,1000]
T_C=[]
def auto_ignition(T,P,spicies,t):
	gas.TPX=T,P,species
	r=ct.IdealGasReactor(gas)
	sim=ct.ReactorNet([r])
	states=ct.SolutionArray(gas,extra=['time_in_ms','t'])

	# creating Time loop
	for n in t:
		sim.advance(n)
		states.append(r.thermo.state, time_in_ms=n*1e3,t=n*1e-3)
	return states

#output
#time
#case 1a
T_in_T=[[0 for time in t] for temp in T]

#case 1b
P_in_T=[[0 for time in t] for press in P]

#case 2a,b
C_T=[[0 for time in t] for i in range(0,2)]

# storing variable with function of time 
time_fun_T=[]
time_fun_P=[]

# case 2 molar concentration
molefraction1=[[0 for time in t] for i in range(0,3)]
molefraction2=[[0 for time in t] for i in range(0,3)]

# Solution
# case 1a
print('Variable Pressure at maximum Autoignition Temperature')
for i in range(0,len(P)):
	states=auto_ignition(T[30],P[i],species,t)
	P_in_T[i]=states.T
	print(P[i]/101325,'bar''=',np.max(P_in_T),'k')
	# constraining auto ignition condition
	for n in range(0,len(states.T)):
		if states.T[n]>=states.T[0]+400:
			time_fun_P.append(states.time_in_ms[n])
			break

# plotting case 1a1
fig1,ax1=plt.subplots()

for i in range(0,len(P)):
	plt.plot(t,P_in_T[i],label=str(P[i]/101325)+'atm')


plt.xlabel('time [sec]',fontsize=13)
plt.ylabel('Temperature [K]',fontsize=13)
plt.title('Reaction Temperature with variable Pressure',fontsize=16,fontweight='bold')
plt.grid('both',linestyle='--',linewidth=0.5)
plt.legend(fontsize=13)
plt.savefig('case1_CT1.png')

# plotting case 1a2
fig2,ax2=plt.subplots()

plt.plot(P/101325,time_fun_P,'r','-*')
plt.xlabel('Pressure [atm]',fontsize=13)
plt.ylabel('Ignition delay [ms]',fontsize=13)
plt.title('Ignition delay with variable Temperature',fontsize=16,fontweight='bold')
ax2.yaxis.set_major_locator(plt.MaxNLocator(10))
plt.yticks(rotation = 0)
plt.grid('both',linestyle='--',linewidth=0.5)
plt.legend(fontsize=13)
plt.savefig('case1_CT2.png')
# Solution
# case 1b
print('Variable initial Temperature to maximum Autoignition Temperature')
for i in range(0,len(T)):
	states=auto_ignition(T[i],P[-1],species,t)
	T_in_T[i]=states.T
	print(T[i],'k','=',np.max(T_in_T),'k')
	for n in range(0,len(states.T)):
		if states.T[n]>=states.T[0]+400:
			time_fun_T.append(states.time_in_ms[n])
			break

# plotting case 1b1
fig3,ax3=plt.subplots()
for i in range(0,len(P)):
	plt.plot(t,T_in_T[i],label=str(T[i])+'K')
	
plt.xlabel('time [sec]',fontsize=13)
plt.ylabel('Temperature [K]',fontsize=13)
plt.title('Reaction Temperature with variable initial Temperature',fontsize=16,fontweight='bold')
plt.grid('both',linestyle='--',linewidth=0.5)
plt.legend(fontsize=13)
plt.savefig('case1b1_CT1.png')

# plotting case 1a2
fig4,ax4=plt.subplots()

plt.plot(T,time_fun_T,'r','-*')
plt.xlabel('Temperature [k]',fontsize=13)
plt.ylabel('Ignition delay [ms]',fontsize=13)
plt.title('Ignition delay with variable Temperature',fontsize=16,fontweight='bold')
plt.grid('both',linestyle='--',linewidth=0.5)
plt.legend(fontsize=13)
plt.savefig('case1a2_ig.png')
plt.xlim([T[0],T[-1]])
ax4.yaxis.set_major_locator(plt.MaxNLocator(10))
plt.yticks(rotation = 10)
plt.savefig('case1a2_CP2.png')

print(np.max(time_fun_T))
#case 2a
states=auto_ignition(Tm[0],P[-1],species,t)
molefraction1[0]=states.X[:,states.species_index('H2O')]
molefraction1[1]=states.X[:,states.species_index('O2')]
molefraction1[2]=states.X[:,states.species_index('OH')]
C_T[0]=states.T

#plotting case2a
fig5,ax5=plt.subplots(3)
ax5[0].plot(t,molefraction1[0],'r')
ax5[1].plot(t,molefraction1[1],'r')
ax5[2].plot(t,molefraction1[2],'r')
plt.suptitle('Mole Fractions for reaction at 500 k & 5 bar')
ax5[0].set_ylabel('$X_{H_2O}$',fontsize=13)
ax5[1].set_ylabel('$X_{O_2}$',fontsize=13)
ax5[2].set_ylabel('$X_{OH}$',fontsize=13)
ax5[2].set_xlabel('Time [sec]',fontsize=13)
ax5[0].grid('both',linestyle='--',linewidth=0.5)
ax5[1].grid('both',linestyle='--',linewidth=0.5)
ax5[2].grid('both',linestyle='--',linewidth=0.5)
plt.savefig('case2a1_x.png')

# printing maximum concentration of species
print('maximum concentration of species 500k 5bar')
print('H_2O=',np.max(molefraction1[0]))
print('O_2=',np.max(molefraction1[1]))
print('OH=',np.max(molefraction1[2]))

# printing minimum concentration of species
print('maximum concentration of species 500k 5bar')
print('H_2O=',np.min(molefraction1[0]))
print('O_2=',np.max(molefraction1[1]))
print('OH=',np.max(molefraction1[2]))
#case 2b
states=auto_ignition(Tm[-1],P[-1],species,t)
molefraction2[0]=states.X[:,states.species_index('H2O')]
molefraction2[1]=states.X[:,states.species_index('O2')]
molefraction2[2]=states.X[:,states.species_index('OH')]
C_T[1]=states.T


#plotting case2b
fig6,ax6=plt.subplots(3)
ax6[0].plot(t,molefraction2[0],'r')
ax6[1].plot(t,molefraction2[1],'r')
ax6[2].plot(t,molefraction2[2],'r')
plt.suptitle('Mole Fractions for reaction at 1000 k & 5 bar')
ax6[0].set_ylabel('$X_{H_2O}$',fontsize=13)
ax6[1].set_ylabel('$X_{O_2}$',fontsize=13)
ax6[2].set_ylabel('$X_{OH}$',fontsize=13)
ax6[2].set_xlabel('Time [sec]',fontsize=13)
ax6[0].grid('both',linestyle='--',linewidth=0.5)
ax6[1].grid('both',linestyle='--',linewidth=0.5)
ax6[2].grid('both',linestyle='--',linewidth=0.5)
plt.savefig('case2b1_x.png')

# printing maximum concentration of species
print('maximum concentration of species 1000k 5bar')
print('H_2O=',np.max(molefraction2[0]))
print('O_2=',np.max(molefraction2[1]))
print('OH=',np.max(molefraction2[2]))

# printing minimum concentration of species
print('maximum concentration of species 1000k 5bar')
print('H_2O=',np.min(molefraction2[0]))
print('O_2=',np.max(molefraction2[1]))
print('OH=',np.max(molefraction2[2]))

#Auto ignition plotting
print('maximum temperature at 5 bar,1000k')
fig7,ax7=plt.subplots()
for i in range(0,2):
	plt.plot(t,C_T[i],label=str(Tm[i])+'K')
	print(np.max(C_T[i]))
plt.xlabel('Time [sec]',fontsize=13)
plt.ylabel('Temperature [K]',fontsize=13)
plt.title('Reaction Temperature with variable initial Temperature')
plt.grid('both',linestyle='--',linewidth=0.5)
plt.legend(fontsize=10)
plt.savefig('ig.png')

plt.show()

Result

case1 a

The reaction of temperature at variable Pressure time Vs Temperature

Detail View

Maximum Temperature with respect to Pressure

the above graph for maximum temperature with the function of initial Pressure given below

Points Pressure(bar) Temperature (K)
1 1 2843.425961
2 1.5 2870.43795
3 2 2903.912127
4 2.5 2912.895224
5 3 2923.149813
6 3.5 2935.044279
7 4 2945.332147
8 4.5 2954.493342
9 5 2979.948726

case1 a

Ignition Delay VS Pressure with various Temperature

case 1 b

Temperature Vs Time at variable Initial Temperature

Detail view

maximum Ignition Temperature with the function of Initial Temperature

the above graph for maximum temperature with the function of initial temperature given below

Points Initial Temperature (K) Ignition Temperature (K)
1 950 2864.395148
2 960 2867.846787
3 970 2869.870487
4 980 2872.357707
5 990 2874.53726
6 1000 2891.64114
7 1010 2891.64114
8 1020 2899.887006
9 1030 2899.887006
10 1040 2899.887006
11 1050 2899.887006
12 1060 2901.211085
13 1070 2901.8416
14 1080 2905.324338
15 1090 2910.487157
16 1100 2928.608197
17 1110 2928.608197
18 1120 2928.608197
19 1130 2928.608197
20 1140 2928.608197
21 1150 2928.608197
22 1160 2932.198126
23 1170 2955.271056
24 1180 2955.271056
25 1190 2955.271056
26 1200 2955.271056
27 1210 2955.271056
28 1220 2955.271056
29 1230 2955.271056
30 1240 2959.414182
31 1250 2959.414182
32 1260 2959.414182
33 1270 2959.414182
34 1280 2959.414182
35 1290 2959.414182
36 1300 2959.414182
37 1310 2982.305284
38 1320 2985.601769
39 1330 2997.743691
40 1340 2997.743691
41 1350 2997.743691
42 1360 2997.743691
43 1370 3002.050005
44 1380 3005.324502
45 1390 3027.888725
46 1400 3027.888725
47 1410 3027.888725
48 1420 3027.888725
49 1430 3027.888725
50 1440 3027.888725
51 1450 3027.888725

Gradual increases in ignition time with initial time shown above

Case 1b

Temperature Vs Ignition Delay with variable initial Temperature

Case2 a

The molar concentration OF H2O, O2, OH varies Vs time with constant Pressure 5 Bar & Constant initial Temperature of 500K

Case2 a

The molar concentration OF H2O, O2, OH varies Vs time with constant Pressure 5 Bar & Constant initial Temperature of 1000K

Variable Initial Temperature VS Time

case1a

Frome absorbed in the graph

At 5bar=2979.948726 k ignition temperature which is faster in time than all Pressure

so when pressure is a function of time if is increases ignition delay time decreases

`Ppropto(1/T_(IGNITION DELAY))`

case1b

Frome absorbed in the graph

At From 1380k the ignition delay is constant at lesser time which is maximum 3027.88k after that it become constant

`T_(INITIAL)propto(1/T_(IGNITION DELAY))`

case2a

molar Fraction for different species

maximum concentration of species
H_2O= 1.58442590583662e-16
O_2= 0.19011406844106465
OH= 2.655661879743359e-23
maximum concentration of species
H_2O= 0.0
O_2= 0.19011406844106465
OH= 2.655661879743359e-23

case2b

maximum concentration of species
H_2O= 0.16567020336733546
O_2= 0.19011406844106465
OH= 0.013952869738833114
maximum concentration of species
H_2O= 0.0
O_2= 0.19011406844106465
OH= 0.013952869738833114

from the absoube from graph Maximum Ignition Temperature for 1000K 5bar is 2891.641 k

Source

https://www.engineeringtoolbox.com/flash-point-autoignition-temperature-kindling-hydrocarbons-alkane-alkene-d_1941.html

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