Workshop 2012, UMC
December 4, Winc Aichi, Nagoya
Kazunari KUWAHARA, Takuya TADA, Osaka Institute of Technology Masahiro FURUTANI, Nagoya Institute of Technology
Yasuyuki SAKAI, Hiromistu ANDO, University of Fukui Workshop 2012, UMC
December 4, Winc Aichi, Nagoya
Kazunari KUWAHARA, Takuya TADA, Osaka Institute of Technology Masahiro FURUTANI, Nagoya Institute of Technology
Yasuyuki SAKAI, Hiromistu ANDO, University of Fukui
Chemical Kinetics Study on Ignition Process of Highly-Diluted Mixtures
- How to Activate Slow Ignition Process -
Chemical Kinetics Study on Ignition Process of Highly-Diluted Mixtures
- How to Activate Slow Ignition Process -
H
2O
2OH
HO
2CH
2O O
2H
2O
2HCO
H
2O CO
O
2Previous Studies Using Contribution Matrices
Thermal
Ignition: H+O
2+M=HO
2+M < H+O
2=OH+O
Fuel Series Chemistry
(RO
2Chemistry) LTO
Preparation
Time
Heat Release Rate
Thermal Ignition Preparation
LTO NTC
H
2O
2Chemistry
HO
2Chemistry
Hydrogen Oxygen System Chemistry
CO
2Chemistry: CO+OH=CO
2+H H
2O
2Loop
Fuel Fragment Chemistry HACA
Chemistry
H
2O
2Loop
H
2O
2Loop
Three Branches Controlling LTO Initiation and Termination
C
7H
16C
7H
15OO C
7H
14OOH HOOC
7H
14OO
OC
7H
13OOH C
7H
14cyO
R’COCH
2Aldehyde R’’’CO Alkene
R’’CHCO CH
2O
R’’’
OH
OH OH
OH
O
2OH CO
OH H
2O
OC
7H
13O OH
H
2O
H
2O Intermediates
Alkene R’
C
7H
15O
2(+M)
O
2(+M)
(+M)
OH
H
2O
2Loop Chemistry
H
2O
2OH
HO
2CH
2O
O
2H
2O
2HCO
H
2O
CO
O
2Main Loop
H
2O
2+ M Æ 2OH + M – 216 kJ OH + CH
2O Æ HCO + H
2O + 122 kJ HCO + O
2Æ HO
2+ CO + 138 kJ 2HO
2Æ H
2O
2+ O
2+168 kJ 2CH
2O + O
2Æ 2H
2O + 2CO + 473 kJ
Sub Reactions
H + O
2+ M Æ HO
2+ M + 202 kJ
H
2O
2+ OH Æ HO
2+ H
2O + 130 kJ
HO
2+ OH Æ H
2O + O
2+297 kJ
HO
2+ CH
2O Æ H
2O
2+ HCO – 7kJ
1. What is the final phase of ignition process of highly diluted mixtures like? Is it similar to the thermal ignition phase?
How is CO oxidized into CO
2at low temperatures?
2. Experimental data often show the two-stage main heat release in lean conditions.
Why the two-stage heat release takes place?
Motivations
Pressure [MPa]
τ
Pressure 2.5
2.0
1.5
1.0
0.5
0.0 25
0 P: 0.73 MPa
T: 626 K
Time after End of Compression [ms]
Ion Current
65
63 73
1 τ
3 Cool Flame
Appears
Blue Flame
Appears Hot Flame
Appears
τ2
Ion Current Density [nA/mm ]2
-25
70
What is KUCRS?
The pressure dependent rate constants of the O
2addition to R and R’OOH, and
the thermal decomposition of OR’’OOH have been introduced.
R+O
2(+M)=ROO(+M)
R’OOH+O
2(+M)=O
2R’OOH(+M)
OR’’OOH(+M)=OR’’O(+M)
0.8 1 1.2 1.41000 / T0 (1/K)
0.9 1.1 1.3
Ignition Delay (s)
10-1
10-5 10-3 10-2
10-4
1.5 n-C7H16(Computation) iso-C8H18(Computation) n-C7H16(Experiment) iso-C8H18(Experiment)
φ = 1, p0 = 4 MPa φ = 1, p0 = 4 MPa
0.8 1 1.2 1.4
1000 / T0 (1/K)
0.9 1.1 1.3
Ignition Delay (s)
10-1
10-5 10-3 10-2
10-4
1.5 n-C7H16(Computation) iso-C8H18(Computation) n-C7H16(Experiment) iso-C8H18(Experiment)
0.8 1 1.2 1.4
1000 / T0 (1/K)
0.9 1.1 1.3
Ignition Delay (s)
10-1
10-5 10-3 10-2
10-4
1.5 n-C7H16(Computation) iso-C8H18(Computation) n-C7H16(Experiment) iso-C8H18(Experiment) n-C7H16(Computation) iso-C8H18(Computation) n-C7H16(Experiment) iso-C8H18(Experiment)
φ = 1, p0 = 4 MPa φ = 1, p0 = 4 MPa
Computational Conditions
Kinetics Scheme Detailed n-C
7H
16Model Generated by KUCRS
Solver CHEMKIN-PRO
Reactor
0 Dimensional Adiabatic Closed Constant-Volume Mixtures n-C
7H
16, O
2and N
2Base Values of
Initial Concentrations
n-C
7H
16: 3.04 mol/m
3O
2: 66.8 mol/m
3N
2: 251 mol/m
3Equivalent to Those in n-C
7H
16/Air Mixture at φ : 0.5, T
0: 759 K and p
0: 2.027 MPa
Initial Temperature T
0669, 759, 849, 1029 K Initial Fuel Changed by 1/1, 1/2, 1/4
Initial N
2Changed by 1/1, 2/1, 4/1
600 700 800
Initial Temperature (K)
1000 1100 1200 900
10-1
10-4 10-3 10-2
Ignition Delay (s)
1. Effect of Dilution on Ignition Process
2. Two-Stage Main Heat Release of Highly-Diluted Mixtures 3. CO Chemistry of Highly-Diluted Mixtures
4. Ignition Process with High Initial Temperature
5. How to Activate Slow Ignition Process
Histories of Temperature and Overall Heat Release Rate
Time (ms) 0
2200 1800 1400 1000 600
1600 1400 1200 800 600 1000
1200 1000 800 600
2300 1900 1500 1100 700
1700 1500 1300 900 700 1100
1300 1100 900 700
0 0
4 8 12 8 16 24 60 120 180
0 1 2 3 0 4 8 12 0 20 40 60
0 300 600
0 4 8
0 0.3 0.6
0 400 800
0 4 8
0 0.7 1.4
Time (ms) Time (ms)
Time (ms) Time (ms) Time (ms)
Temperature (K)
Temperature (K) T0: 669 K
T0: 759 K
N2: 2/1 Fuel: 1/2
N2: 2/1 Fuel: 1/2
N2: 4/1 Fuel: 1/4
N2: 4/1 Fuel: 1/4 x5
x5
HRR (kJ/(cm3
·
s))HRR (kJ/(cm3
·
s)) 0.9Base Values 2.1 Base Values
T0: 669 K
T0: 759 K
T0: 669 K
T0: 759 K
Histories of Temperature and Overall Heat Release Rate
Time (ms) 0
2400 2000 1600 1200 800
1800 1600 1400 1000 800 1200
1400 1200 1000 800
2600 2200 1800 1400 1000
2000 1800 1600 1200 1000 1400
1600 1400 1200 1000
0 0
1 2 3 3 6 9 10 20 30
0 0.4 0.8 0 0.6 1.2 1.8 0 2 4 6
0 600 1200
0 9 18
0 1.2 2.4
0 1000 2000
0 60 120
0 4 8
Time (ms) Time (ms)
Time (ms) Time (ms) Time (ms)
Temperature (K) HRR (kJ/(cm3
·
s))Temperature (K) HRR (kJ/(cm3
·
s))T0: 849 K
T0: 1029 K
N2: 2/1 Fuel: 1/2
N2: 2/1 Fuel: 1/2
N2: 4/1 Fuel: 1/4
N2: 4/1 Fuel: 1/4 x5
x5
3.6
Base Values 12 Base Values
T0: 849 K
T0: 1029 K
T0: 849 K
T0: 1029 K
Histories of Temperature and Overall Heat Release Rate
Time (ms) 6
1800 1400 1000 600
0 0
9 12 15 2 4 6 2 4 6
Time (ms) Time (ms)
Temperature (K)
T0: 669 K T0: 759 K T0: 849 K
N2: 1.6/1 N2: 1.7/1 N2: 1.8/1
2000 1600 1400 1200 1000
0 0.4 0.8 0
3 6
Time (ms) Temperature (K)
T0: 1029 K
HRR (J/(cm3
·
s)) 010 20
0 5 10
0 4 8 1700
1500 1300 900 700 1100
1800 1400 1000 800 1600 1200
HRR (kJ/(cm3
·
s))N2: 1.9/1 N2: 2.0/1 N2: 2.1/1
N2: 2.2/1 N2: 2.3/1 N2: 2.4/1
12
1800
N2: 2.2/1 9 N2: 2.3/1 N2: 2.4/1
1. Effect of Dilution on Ignition Process
2. Two-Stage Main Heat Release of Highly-Diluted Mixtures
3. CO Chemistry of Highly-Diluted Mixtures
4. Ignition Process with High Initial Temperature
5. How to Activate Slow Ignition Process
700 900 1100
Temperature during Process (K)
1300 1500 1700 1900 2100 2300 101
10-4 10-3 10-2 10-1 100 106
101 102 103 104 105
HRR (J/(cm3
·
s))Reaction Rate (mol/(cm3·
s))Overall
Fuel Series Reactions H2O2 Loop Reactions H+O2+M=HO2+M
HCCO+O2=HCO+CO2 HO2+OH=O2+H2O CO+OH=CO2+H
n-C7H16+OH=C7H15+H2O H2O2(+M)=OH+OH(+M) H+O2+M=HO2+M
H+O2=OH+O CO+OH=CO2+H O+H2O=OH+OH CO+HO2=CO2+OH T0: 759 K
Base Values
Heat Release Rates and Reaction Rates with T
0: 759 K
Heat Release Rates and Reaction Rates with T
0: 759 K
700 900 1100
Temperature during Process (K) 1300 1500 1700
10-1
10-6 10-5 10-4 10-3 10-2 105
100 101 102 103 104
HRR (J/(cm3
·
s))Reaction Rate (mol/(cm3·
s))Overall
Fuel Series Reactions H2O2 Loop Reactions H+O2+M=HO2+M
HCCO+O2=HCO+CO2 HO2+OH=O2+H2O CO+OH=CO2+H
n-C7H16+OH=C7H15+H2O H2O2(+M)=OH+OH(+M) H+O2+M=HO2+M
H+O2=OH+O CO+OH=CO2+H O+H2O=OH+OH CO+HO2=CO2+OH T0: 759 K, N2: 2/1 T0: 759 K
N2: 4/1
700 900 1100 1300 10-1
10-6 10-5 10-4 10-3 10-2 105
100 101 102 103 104
Fuel, CH
2O and H
2O
2Concentrations with T
0: 759 K
700 900 1100
Temperature during Process (K) 1300 1500 1700 106
101 103 104 105
Overall Heat Release Rate (J/(cm3
·
s))0 0.4 0.8 0 1.2
1 2 3
0 0.6 1.2 1.8
[H 2O 2] x10-6 (mol/cm3 ) [CH 2O] x10-6 (mol/cm3 )
[n-C 7H 16] (mol/cm3 )
700 900 1100
Temperature during Process (K) 1300 1500 1700 102
HRR
n-C7H16
CH2O
H2O2 Base Values N2: 2/1
N2: 4/1
T0 = 759 K Base Values N2: 2/1
N2: 4/1
1. Effect of Dilution on Ignition Process
2. Two-Stage Main Heat Release of Highly-Diluted Mixtures 3. CO Chemistry of Highly-Diluted Mixtures
4. Ignition Process with High Initial Temperature
5. How to Activate Slow Ignition Process
700 900 1100
Temperature during Process (K)
1300 1500 1700 1900 2100 2300 101
10-4 10-3 10-2 10-1 100 106
101 102 103 104 105
HRR (J/(cm3
·
s))Reaction Rate (mol/(cm3·
s))Overall
Fuel Series Reactions H2O2 Loop Reactions H+O2+M=HO2+M
HCCO+O2=HCO+CO2 HO2+OH=O2+H2O CO+OH=CO2+H
n-C7H16+OH=C7H15+H2O H2O2(+M)=OH+OH(+M) H+O2+M=HO2+M
H+O2=OH+O CO+OH=CO2+H O+H2O=OH+OH CO+HO2=CO2+OH Thermal
Ignition Point T0: 759 K
Base Values
Heat Release Rates and Reaction Rates with T
0: 759 K
Heat Release Rates and Reaction Rates with T
0: 759 K
700 900 1100
Temperature during Process (K) 1300 1500 1700
10-1
10-6 10-5 10-4 10-3 10-2 105
100 101 102 103 104
HRR (J/(cm3
·
s))Reaction Rate (mol/(cm3·
s))Overall
Fuel Series Reactions H2O2 Loop Reactions H+O2+M=HO2+M
HCCO+O2=HCO+CO2 HO2+OH=O2+H2O CO+OH=CO2+H
n-C7H16+OH=C7H15+H2O H2O2(+M)=OH+OH(+M) H+O2+M=HO2+M
H+O2=OH+O CO+OH=CO2+H O+H2O=OH+OH CO+HO2=CO2+OH T0: 759 K, N2: 2/1 T0: 759 K
N2: 4/1
700 900 1100 1300 10-1
10-6 10-5 10-4 10-3 10-2 105
100 101 102 103 104
1. Effect of Dilution on Ignition Process
2. Two-Stage Main Heat Release of Highly-Diluted Mixtures 3. CO Chemistry of Highly-Diluted Mixtures
4. Ignition Process with High Initial Temperature
5. How to Activate Slow Ignition Process
1000 1200 1400
Temperature during Process (K)
1600 1800 2000 2200 2400 2600 101
10-4 10-3 10-2 10-1 100 107
102 103 104 105 106
HRR (J/(cm3
·
s))Reaction Rate (mol/(cm3·
s))Overall
Fuel Series Reactions H2O2 Loop Reactions H+O2+M=HO2+M
HCCO+O2=HCO+CO2 HO2+OH=O2+H2O CO+OH=CO2+H
n-C7H16+OH=C7H15+H2O H2O2(+M)=OH+OH(+M) H+O2+M=HO2+M
H+O2=OH+O CO+OH=CO2+H O+H2O=OH+OH CO+HO2=CO2+OH Thermal
Ignition Point T0: 1029 K
Base Values
Heat Release Rates and Reaction Rates with T
0: 1029 K
1000 1200 1400
Temperature during Process (K) 1600 1800 2000
100
10-5 10-4 10-3 10-2 10-1 106
101 102 103 104 105
HRR (J/(cm3
·
s))Reaction Rate (mol/(cm3·
s))Overall
Fuel Series Reactions H2O2 Loop Reactions H+O2+M=HO2+M
HCCO+O2=HCO+CO2 HO2+OH=O2+H2O CO+OH=CO2+H
n-C7H16+OH=C7H15+H2O H2O2(+M)=OH+OH(+M) H+O2+M=HO2+M
H+O2=OH+O CO+OH=CO2+H O+H2O=OH+OH CO+HO2=CO2+OH T0: 1029 K, N2: 2/1 T0: 1029 K
N2: 4/1
1000 1200 1400 1600 100
10-5 10-4 10-3 10-2 10-1 106
101 102 103 104 105
Heat Release Rates and Reaction Rates with T
0: 1029 K
Fuel, CH
2O and H
2O
2Concentrations with T
0: 1029 K
1000 1200 1400
Temperature during Process (K) 1800 107
102 104 105 106
Overall Heat Release Rate (J/(cm3
·
s))0 0.3 0.6 0 0.9
1 2 3
0 0.06 0.12 0.18
[H 2O 2] x10-6 (mol/cm3 ) [CH 2O] x10-6 (mol/cm3 )
[n-C 7H 16] (mol/cm3 )
1000 1200 1400
Temperature during Process (K) 1800 103
T0 = 1029 K Base Values N2: 2/1
N2: 4/1
1600
1600 HRR
n-C7H16
CH2O
H2O2 Base Values N2: 2/1
N2: 4/1
Fuel, CH
2O and H
2O
2Concentrations with T
0: 759 K
700 900 1100
Temperature during Process (K) 1300 1500 1700 106
101 103 104 105
Overall Heat Release Rate (J/(cm3
·
s))0 0.4 0.8 0 1.2
1 2 3
0 0.6 1.2 1.8
[H 2O 2] x10-6 (mol/cm3 ) [CH 2O] x10-6 (mol/cm3 )
[n-C 7H 16] (mol/cm3 )
700 900 1100
Temperature during Process (K) 1300 1500 1700 102
HRR
n-C7H16
CH2O
H2O2 T0 = 759 K
Base Values N2: 2/1
N2: 4/1
Base Values N2: 2/1
N2: 4/1
Contribution Ratios to H
2O
2Formation and Removal
1000 1100 1200
Temperature during Process (K)
1300 1500
10-3 10-2 10-1 100
Contribution Ratio to H 2O 2Formation (%)
1400
700 900 1100
Temperature during Process (K) 1300 1500 10-4
10-3 10-2 10-1
100 60 20 0
Contribution Ratio to H 2O 2Removal (%)Overall H 2O 2Formation or Removal Rate (mol/(cm3
·
s))T0: 759 K T0: 1029 K
40 80
100 60 20 0 40 80
0 40 80 100 60 20 0
40 80 100 60 20 H2O2 Formation
H2O2 Removal
HO2+n-C7H16=H2O2+C7H15 HO2+CH2O=H2O2+HCO
H2O2(+M)=OH+OH(+M) H2O2+OH=HO2+H2O
H2O2 Formation H2O2 Removal
H2O2(+M)=OH+OH(+M) H2O2+OH=HO2+H2O HO2+HO2=H2O2+O2
HO2+n-C7H16=H2O2+C7H15 HO2+CH2O=H2O2+HCO HO2+HO2=H2O2+O2
Contribution Ratios to HO
2Removal
1000 1100 1200
Temperature during Process (K)
1300 1500
10-3 10-2 10-1 100
Contribution Ratio to HO 2Removal (%) 1400
700 900 1100
Temperature during Process (K) 1300 1500 10-4
10-3 10-2 10-1
Overall H 2O 2Formation or Removal Rate (mol/(cm3
·
s))T0: 759 K T0: 1029 K
80 40 20 0
60 80
60 20 0
40 H2O2 Formation H2O2 Removal
HO2+n-C7H16=H2O2+C7H15 HO2+CH2O=H2O2+HCO HO2+OH=O2+H2O
H2O2 Formation H2O2 Removal
HO2+HO2=H2O2+O2
HO2+n-C7H16=H2O2+C7H15 HO2+CH2O=H2O2+HCO HO2+OH=O2+H2O
HO2+HO2=H2O2+O2
1000 1100 1200 1300 1400 1500
700 900 1100 1300 1500
Sum of Others Sum of Others
1. When a mixture is highly diluted, an ignition process with LTO indicates two peaks of the heat release in the thermal ignition preparation phase.
The mechanism of the two-stage heat release is;
2. When the fuel is consumed in the early stage of the thermal ignition preparation phase, n-C
7H
16+HO
2=C
7H
15+H
2O
2is
reduced, and H
2O
2+OH=HO
2+H
2O and HO
2+OH=O
2+H
2O are enhanced.
Which decreases the efficiency of the H
2O
2regeneration loop, and H
2O
2is consumed in the middle stage of the thermal
ignition preparation phase.
3. In the ignition process of highly-diluted mixtures, the rate of H+O
2=OH+O cannot overtake the rate of H+O
2+M=HO
2+M.
CO+OH=CO
2+H proceeds slowly with H+O
2+M=HO
2+M,
not with the branching chain reaction, in the final stage of the ignition process.
Summaries
1. Effect of Dilution on Ignition Process
2. Two-Stage Main Heat Release of Highly-Diluted Mixtures 3. CO Chemistry of Highly-Diluted Mixtures
4. Ignition Process with High Initial Temperature
5. How to Activate Slow Ignition Process
T0: 759 K, Fuel: 1/2
Temperature Increase by 100 K
Activation by Temperature Increase in Ignition Process
0 4 8
Time (ms)
12 16 0 0.6 1.2
Time (ms)
1.8 2.4
1700 1500 1300 900 700 1100
Temperature (K)
2000 1800 1600 1200 1000 1400
0 6 3
Heat Release Rate (kJ/(cm3
·
s)) 90 80 40 120 T0: 1029 K, Fuel: 1/2
Temperature Increase by 100 K
Heat Release Rates and Reaction Rates with T
0: 759 K
700 900 1100
Temperature during Process (K) 1300 1500 700
10-1
10-6 10-5 10-4 10-3 10-2 104
10-1 100 101 102 103
HHR (J/(cm3
·
s))Reaction Rate (mol/(cm3·
s))T0: 759 K, Fuel: 2/1
900 1100 1300 1500 10-1
10-6 10-5 10-4 10-3 10-2 104
10-1 100 101 102
103 Overall
Fuel Series Reactions H2O2 Loop Reactions H+O2+M=HO2+M
HCCO+O2=HCO+CO2 HO2+OH=O2+H2O CO+OH=CO2+H
n-C7H16+OH=C7H15+H2O H2O2(+M)=OH+OH(+M) H+O2+M=HO2+M
H+O2=OH+O CO+OH=CO2+H O+H2O=OH+OH CO+HO2=CO2+OH
1700 1700
Temperature Increase by 100 K
Heat Release Rates and Reaction Rates with T
0: 759 K
700 900 1100
Temperature during Process (K) 1300 1500 700
10-1
10-6 10-5 10-4 10-3 10-2 104
10-1 100 101 102 103
HHR (J/(cm3
·
s))Reaction Rate (mol/(cm3·
s))T0: 759 K, Fuel: 2/1
900 1100 1300 1500 10-1
10-6 10-5 10-4 10-3 10-2 104
10-1 100 101 102
103 Overall
Fuel Series Reactions H2O2 Loop Reactions H+O2+M=HO2+M
HCCO+O2=HCO+CO2 HO2+OH=O2+H2O CO+OH=CO2+H
n-C7H16+OH=C7H15+H2O H2O2(+M)=OH+OH(+M) H+O2+M=HO2+M
H+O2=OH+O CO+OH=CO2+H O+H2O=OH+OH CO+HO2=CO2+OH
1700 1700
Temperature Increase by 100 K
Activation by OH and H Addition in Ignition Process
0 4 8
Time (ms)
12 16 0 4 8
Time (ms)
12 16
1700 1500 1300 900 700 1100
Temperature (K)
1700 1500 1300 900 700 1100
0 6 3
Heat Release Rate (kJ/(cm3
·
s)) 90 6 3 9 T0: 759 K, Fuel: 1/2
Temperature Increase by 100 K
T0: 759 K, Fuel: 1/2
OH Addition by 5000 ppm + H Addition by 5000 ppm
Heat Release Rates and Reaction Rates with T
0: 759 K
700 900 1100
Temperature during Process (K) 1300 1500 700
10-1
10-6 10-5 10-4 10-3 10-2 105
100 101 102 103 104
HHR (J/(cm3
·
s))Reaction Rate (mol/(cm3·
s))T0: 759 K, Fuel: 2/1
900 1100 1300 1500 10-1
10-6 10-5 10-4 10-3 10-2 105
100 101 102 103
104 Overall
Fuel Series Reactions H2O2 Loop Reactions H+O2+M=HO2+M
HCCO+O2=HCO+CO2 HO2+OH=O2+H2O CO+OH=CO2+H
n-C7H16+OH=C7H15+H2O H2O2(+M)=OH+OH(+M) H+O2+M=HO2+M
H+O2=OH+O CO+OH=CO2+H O+H2O=OH+OH CO+HO2=CO2+OH
1700 1700
OH and H Addition
Heat Release Rates and Reaction Rates with T
0: 759 K
700 900 1100
Temperature during Process (K) 1300 1500 700
10-1
10-6 10-5 10-4 10-3 10-2 105
100 101 102 103 104
HHR (J/(cm3
·
s))Reaction Rate (mol/(cm3·
s))T0: 759 K, Fuel: 2/1
900 1100 1300 1500 10-1
10-6 10-5 10-4 10-3 10-2 105
100 101 102 103
104 Overall
Fuel Series Reactions H2O2 Loop Reactions H+O2+M=HO2+M
HCCO+O2=HCO+CO2 HO2+OH=O2+H2O CO+OH=CO2+H
n-C7H16+OH=C7H15+H2O H2O2(+M)=OH+OH(+M) H+O2+M=HO2+M
H+O2=OH+O CO+OH=CO2+H O+H2O=OH+OH CO+HO2=CO2+OH
1700 1700
OH and H Addition
