2840

University of Tsukuba

Title

Author(s),

Citation

Issue Date2013-03

Text versionauthor

URL http://hdl.handle.net/2241/118900

DOI

Right

Rotating Detonation EngineRDERDE

RDE

Multi-frame Short-time Open-shutter PhotographyMSOP

2

ir2

2

2

nD ChapmanJouguet CJD nD

CJn /DD ir 1 CJn /DD CJn /DD C2H4+3O22H2+O2 2C2H2+5O2+7Ar2 CJn /DD 1 ir ir

2

CJn /DD Yao and Stewart Sharpe

2

CJn /DD CJn DD 1 CJn DD

CJn DD

CJn DD

__________________________________________________________________________________________________________

i

1 1 1.1. 1

1.1.1. 1

1.1.2. 4

1.2. 6

1.2.1. 6

1.2.2. 7

1.2.3. 11

1.3. 14

1.3.1. 14

1.3.2. 17

2 18

2.1. 18

2.2. Multi-frame Short-time Open-shutter PhotographyMSOP 18

2.3. 22

2.4. 25

2.5. 26

2.5.1. 26

2.5.2. 27

2.5.3. 29

2.5.4. 32

2.6. 34

3 Dn/DCJ 35

3.1. 35

3.2. 35

3.3. 38

3.4. 41

3.5. 43

3.5.1. 43

__________________________________________________________________________________________________________

ii

3.5.2. 45

3.5.3. 48

3.5.4. 50

3.5.5. 51

3.5.6. Dn/DCJ 55 3.5.7. Dn/DCJ 59 3.5.8. 62

3.6. 66

3.6.1. Dn/DCJ 66 3.6.2. Dn/DCJ 68 3.6.3. 70

3.7. 75

4 1 76

4.1. 76

4.2. 76

4.3. 78

4.4. 80

4.5. 82

4.5.1. 82

4.5.2. 83

4.5.3. 84

4.6. 85

4.7. Dn/DCJ 88 4.8. Dn/DCJ 91 4.9. 95

4.9.1. 95

4.9.2. 100

4.9.3. Dn/DCJ 102 4.10. 105

5 106 5.1. 106

5.2. 109

__________________________________________________________________________________________________________

iii

111 113 123 A ChapmanJouguetCJ 128 B 131 C 136 D ChapmanJouguetCJ 142 E 148 F 151

__________________________________________________________________________________________________________

iv

1

1.1

ZND 2

1.2 4 1.3 vp 38) 5

1.4 7

1.5 PBX9502

62) 8

1.6 PBX9502

64) 8

1.7 12

1.8

12

1.9 92) 13

1.10 2 14

2

2.1 Short-time Open-shutter PhotographySOP 19

2.2 2 SOP 19

2.3 Multi-frame Short-time Open-shutter PhotographyMSOP 21

2.4 2MSOP 21

2.5 22

2.6 23

2.7 2 24

2.8 2

25

2.9 2

27

2.10 2

28

2.11 2

40i r mm 29 2.12 MSOP 40i r mm 31

__________________________________________________________________________________________________________

v

2.13 irMSOP 50.1 mm 33 3

3.1 2 2

37

3.2 2 37

3.3 2

39

3.4 2

C2H4+3O2 44

3.5 2

2H2+O2 44

3.6 2

2C2H2+5O2+7Ar 45

3.7 2

20i r mm2H2+O2 47 3.8 2

C2H4+3O2 48

3.9 2

2H2+O2 49

3.10 2

2C2H2+5O2+7Ar 49

3.11 2

20i r mm 70.0 mmC2H4+3O2 50 3.12 2

20i r mm 70.0 mm C2H4+3O2 51

3.13 2

20i r mm 70.0 mmC2H4+3O2 52 3.14 2

20i r mm 70.0 mmC2H4+3O2 53 3.15 2 33.100.1 i rr

20i r mm 70.0 mmC2H4+3O2 54

__________________________________________________________________________________________________________

vi

3.16 1 00.200.1 i rr 2 20.100.1 i rr CJn DD 20i r mm 70.0 mmC2H4+3O2 55 3.17 2

CJn DD C2H4+3O2 56 3.18 2

CJn DD 2H2+O2 57 3.19 2

CJn DD 2C2H2+5O2+7Ar 57 3.20 CJn DD 58 3.21 2

CJn DD 20i r mm 70.0 mmC2H4+3O2 60 3.22 2

CJn DD 40i r mm 56.1 mm2H2+O2 60 3.23 2

CJn DD 10i r mm 27.0 mm2C2H2+5O2+7Ar 61 3.24 Marker particle method 61

3.25 2

64

3.26 2

3.36i r C2H4+3O2 ir 65

3.27 2

5.27i r 20i r mm 65

3.28 2

01.3 mm 66 3.29 2

CJn DD 67 3.30 CJn DD

2 69

3.31 2

CJn DD 70

__________________________________________________________________________________________________________

vii

3.32

71

3.33 w 72

3.34 CJn DD 2

74

4

4.1 77 4.2 CJC 88 4.3 CJn DD

C2H4+3O2 90

4.4 CJn DD 2H2+O2 90

4.5 CJn DD 2C2H2+5O2+7Ar 91

4.6 CJn DD C2H4+3O2 93 4.7 CJn DD a~T

C2H4+3O2 94

4.8 CJn DD C C2H4+3O2 94 4.9 T~C2H4+3O2 96

4.10 ~C2H4+3O2 96 4.11 fr~a C2H4+3O2 97

4.12 n~u C2H4+3O2 97

4.13 p~C2H4+3O2 98

4.14 ~C2H4+3O2 98 4.15 YC2H4+3O2 99

4.16 M C2H4+3O2 99

4.17 CJn DD ~ ~ ~~ C2H4+3O2 101

4.18 CJn DD *Q M C2H4+3O2 102 4.19 CJn DD M

C2H4+3O2 104

__________________________________________________________________________________________________________

viii

A A.1 C2H4+3O2 129

A.2 2H2+O2 129

A.3 2C2H2+5O2+7Ar 130

B

B.1 Marker particle method 131

B.2 2

133

D

D.1 142

D.2 CJ

C2H4+3O2 144

ix

2

2.1 25

3 3.1 36

3.2 38

4

4.1 87

4.2 C2H4+3O2 92

__________________________________________________________________________________________________________

x

A

a

B

C ChapmanJouguet

c

D

D e

f f f1 ~ f5 6

G

g

h

K C.50

k

L

l

M

M

m 3.5

n

n

P

p

Q* 4.51

q

q* 4.49

R

R 2

r

s

T

T t

__________________________________________________________________________________________________________

xi

u

v

W

w

X

x

Y

y

Z

Z

D.25 ChapmanJouguet 4.48 4.47 D.24

__________________________________________________________________________________________________________

xii

a

asy

B

b

CJ ChapmanJouguet

CJp ChapmanJouguet

c

cr

D

eq

exp

f

fr

H

i 2

ig

im

ChapmanJouguet

in

ind

int

j

mt

n

nd

ng

o 2

out

overall

P

p

R

s

u

__________________________________________________________________________________________________________

xiii

v

vN von Neumann

w

0

1

2, 2, 2 1.3 22 2 3, 3, 3 1.3 33 3 +

0

m

~ 4.40

1

__________________________________________________________________________________________________________

1

1

1.1.

1.1.1.

5 ~ 7

1.1 1.1

1

1)

von NeumannvN

1.1

2)

1

__________________________________________________________________________________________________________

2

1) ChapmanJouguetCJCJ 1.1

Zeldovich3)von Neumann4) Dring5)ZND

CJ

CJ CJ

CJ CJ

CJ CJ

CJ

ZND 1

613)

Propagation direction

x

p, T, M,

Pressure, p

Temperature, T

Mach number, MM = 1

Front shock

Induction zone

CJ point

Induction length, lind

Reaction zone

Thermicity,


x

p, T, M,

Pressure, p

Temperature, T

Mach number, MM = 1

Front shock

Induction zone

CJ point

Induction length, lind

Reaction zone

Thermicity,

1.1

ZND

1

__________________________________________________________________________________________________________

3

ZND

1.2

1.2

1.2

3

1.2

CJ 1430)

CJ

CJ

CJ 1.8 CJ

0.6 31,32)

CJ

ZND CJ

2

1.2 3

1

__________________________________________________________________________________________________________

4

1.1.2.

Pulse

Detonation EnginePDE 3337)PDE

PDE PDE

1 PDE 1.3 vp

38)

Zeldovich39) Heiser and Pratt40) 1 Wu et al.41) 2

Wintenberger and Shepherd42)

D

Trajectory of triple point Cell width,

Incident shock (weak shock)

Transverse wave


Mach stem (strong shock)

Triple point

: Front shock: Forward edge of reaction zone

Micro explosion

Trajectory of triple point Cell width,

Incident shock (weak shock)

Transverse wave


Mach stem (strong shock)

Triple point

: Front shock: Forward edge of reaction zone

Micro explosion

1.2

1

__________________________________________________________________________________________________________

5

Humphrey cycleHBrayton cycle

B

Zeldovich39)PDE 1.3 1 PDE PDE

NvN

2CJ

32 13 132N1 PDE 1

1321 121 qhh outin inh outh q

inh

q outh 3h 3h 3 h 333 q333 sTh dd 1.3

222 sss 333 sss sTh dd h s 333 hhh D > H > B

p

v

1

2

von Neumann point

Hugoniot adiabatic curve

Frozen Hugoniot curve with fixed heat release

Isentropic process

CJ point

Rayleigh line

Detonation process

Constant-volume combustion process

Constant-pressure combustion process2'

3'3

2'', 3''

N

p

v

1

2

von Neumann point

Hugoniot adiabatic curve

Frozen Hugoniot curve with fixed heat release

Isentropic process

CJ point

Rayleigh line

Detonation process

Constant-volume combustion process

Constant-pressure combustion process2'

3'3

2'', 3''

N

1.3 vp 38)

1

__________________________________________________________________________________________________________

6

1.2.

1.2.1.

1.4

2327,4347)

4856)

1621)

1.4

CJ Kudo et al.57)Maeda et

al.16) Pintgen and Shepherd44)

58)

1.2.2

1.4a

1.4b

52)

59)

CJ

52)

1.4c

1

__________________________________________________________________________________________________________

7

1.2.2.

CJ 60,61)

60)

62,63) 1.5

PBX9502PBX Plastic Bonded Explosive

62)

1.5

Projectile

(a)

(b)

(c)

ProjectileProjectile

(a)

(b)

(c)

1.4

1

__________________________________________________________________________________________________________

8

1.6 PBX9502

64) 1.5

1.6 PBX9502

64) 2

1.5

1.5 PBX9502

62)

1

__________________________________________________________________________________________________________

9

Eyring et al.65) Wood and Kirkwood66)

Bdzil and Stewart67,68)

ZND Wood and Kirkwood

2

3 1

Bdzil and Stewart Whitham

Geometrical Shock DynamicsGSD69) Detonation Shock DynamicsDSD70)

DSD

64,7173)DSD

7476)

70,74)

1.1.1

2 1

Menikoff et al.77)

1

77)

DSD

2

1

1

__________________________________________________________________________________________________________

10

53,64,7881)

1 1

53,7779)

Yao and Stewart80)

2 Sharpe81)

1 1

1.2.1

Maeda et al.16)

Maeda et al.

Maeda et al.

Kudo et al.57) C2H4+3O2

2

1

__________________________________________________________________________________________________________

11

2 in,D CJ CJD

8.0CJin, DD 8.06.0 CJin, DD 6.0CJin, DD 3 Kudo et al. 2

2

Thomas and Williams82) Edwards et al.83) 2C2H2+5O2Kudo et al.57) 2

59)

Thomas and Williams Edwards et al.Kudo et al. 2

2

2

Thomas and Williams

Edwards et al.

1.2.3. PDE

PDE

PDE

Rotating

Detonation EngineRDE8492)RDE 1.7

1.8 RDE

RDE PDE

4

RDE

1

1.9 RDE 92)

1

__________________________________________________________________________________________________________

12

20 92)

1.8

Burnt gasGaseous

detonation wave

Combustible gas injection

Contact surfaceShock wave

Combustible gas layer

Burnt gasGaseous

detonation wave

Combustible gas injection

Contact surfaceShock wave

Combustible gas layer

1.7

1

__________________________________________________________________________________________________________

13

RDE RDE

RDE

RDE

CJ 16,44,57)RDE

RDE

1.8 RDE

RDE

RDE

2 1.10 2

1.9 92)

1

__________________________________________________________________________________________________________

14

2

2

2

2

1.10

3.5.2

1.3.

1.3.1. 1.10 2

2 2

2 Kudo et

al.57)

3

Inner wall

Outer wall

Gaseous detonation wave

Initial pressure of combustible gas mixtureHigh Low

Shock waveReaction zone

Re-initiation (transverse

detonation wave)

Propagation of detonation waveSteady Unsteady


Shock wave

Reaction zone

Gaseous detonation waveInner radius

Inner radius of annular channelLarge Small

Inner wall

Outer wall


Initial pressure of combustible gas mixtureHigh LowInitial pressure of combustible gas mixtureHigh Low

Shock waveReaction zone

Re-initiation (transverse

detonation wave)

Propagation of detonation waveSteady UnsteadyPropagation of detonation waveSteady Unsteady


Shock wave

Reaction zone

Gaseous detonation waveInner radius

Inner radius of annular channelLarge SmallInner radius of annular channelLarge Small

1.10 2

1

__________________________________________________________________________________________________________

15

1 2

1.2.2 Kudo et al.57) 2

2

2

Thomas and Williams82) Edwards et al.83)2

2

RDE

RDE

2

RDE

2 2

1.2.2

62,63)

RDE

1

__________________________________________________________________________________________________________

16

RDE

3 1

1.2.2 ZND

1

2

Yao and Stewart80)

2 Sharpe81)

1 1

Yao and Stewart80) Sharpe81)

3

1 Multi-frame

Short-time Open-shutter PhotographyMSOP93)2

1

__________________________________________________________________________________________________________

17

2

2

3

2

1.3.2. 1 2 2

93) 3 2

94,95)

4

1 5

2

__________________________________________________________________________________________________________

18

2

2.1.

Multi-frame Short-time Open-shutter PhotographyMSOP93)

2

2

MSOP

2.2. Multi-frame Short-time Open-shutter PhotographyMSOP

2

Multi-frame Short-time Open-shutter Photography

MSOP93)MSOP Short-time Open-shutter PhotographySOP

2.1 SOP 2.1 2 expt

expt s expt

SOP

SOP expt

2.2 2 SOP

2 60 mm

20 mm 1 mm C2H4+3O2 30.8 kPa

expt 4 s 2.2 SOP

2

__________________________________________________________________________________________________________

19

Outer wall

Inner wall

Triple point trajectories

Strong luminescence by the shock wave reflected over the outer wall

Outer wall

Inner wall

Triple point trajectories

Strong luminescence by the shock wave reflected over the outer wall

2.2 2 SOP

2 60 mm 20 mm

1 mm C2H4+3O2

30.8 kPa 4 s

Detonation wave at t

Detonation wave at t+texp

Reflected shock waves at t+texp

Triple point trajectories recorded in texp(detonation cell structure)

Reflected shock waves at t

: Overexposure due tostrong luminescence by reflected shock waves

Inner wall

Outer wall


Detonation wave at t+texp

Reflected shock waves at t+texp

Triple point trajectories recorded in texp(detonation cell structure)

Reflected shock waves at t

: Overexposure due tostrong luminescence by reflected shock waves

Inner wall

Outer wall

2.1 Short-time Open-shutter PhotographySOP

2

__________________________________________________________________________________________________________

20

SOP

SOP SOP

1

Multi-frame Short-time Open-shutter

PhotographyMSOP 2.3 MSOP 2.3a

SOP intt expt intt

expt intt

SOP SOP 2.3

b1 MSOP MSOP

MSOP SOP m SOP

1m SOP SOP

MSOP

MSOP 2

MSOP MSOP

2.4 2 MSOP

2

20 mm 20 mm 1 mm C2H4+3O2 60.3 kPa expt 4 s 2.4 MSOP MSOP

2

__________________________________________________________________________________________________________

21

2.4 2 MSOP

2 20 mm 20 mm

1 mm C2H4+3O2

60.3 kPa 4 s

1st frame

2nd frame

3rd frame

Nth frame

tint

texp

tint tint tint

texp

texp

texp

Exposure

Exposure

Exposure

Exposure

1st frame

2nd frame

3rd frame

Nth frame

tint

texp

tint tint tint

texp

texp

texp

Exposure

Exposure

Exposure

Exposure

(a) SOP

1st frame 2nd frame 3rd frame Nth frame

+

Superimposed-photograph

+ + + =

1st frame 2nd frame 3rd frame Nth frame

+

Superimposed-photograph

+ + + =

(b) SOP MSOP

2.3 Multi-frame Short-time Open-shutter PhotographyMSOP

2

__________________________________________________________________________________________________________

22

2.3.

2.5

3 MSOP

3

Convex lens

Convex lens

Mirror

Concave mirror

Pinhole

Knife edge

Signal conditioner

Pulse generator

Observation chamber

Dump tank

Mixture tank

Light source

Rotary pump

Vacuum gauge

Pressure gauge

High-speed video camera

Ignition driver

Optical system

MSOP: w/o optical systemShadowgraph photography: w/ optical system (w/o knife edge)Schlieren photography: w/ optical system (w/ knife edge)Direct photography: w/o optical system

Convex lens

Convex lens

Mirror

Concave mirror

Pinhole

Knife edge

Signal conditioner

Pulse generator

Observation chamber

Dump tank

Mixture tank

Light source

Rotary pump

Vacuum gauge

Pressure gauge


Ignition driver

Optical system

Convex lens

Convex lens

Mirror

Concave mirror

Pinhole

Knife edge

Signal conditioner

Pulse generator

Observation chamber

Dump tank

Mixture tank

Light source

Rotary pump

Vacuum gauge

Pressure gauge


Ignition driver

Ignition driver

Optical system

MSOP: w/o optical systemShadowgraph photography: w/ optical system (w/o knife edge)Schlieren photography: w/ optical system (w/ knife edge)Direct photography: w/o optical system

2.5

2

__________________________________________________________________________________________________________

23

2.6 25.8 mm

20 mm x 16 mm 100 mm x 100 mm 2

12 m

CJ 2

2 40 mm

10 mm

(a) (b)

Spark plug Shchelkin spiral

Rectangular cross-section tube(20 mm x 16 mm)

Detonation tube ( 25.8 mm)

To dump tank

Housing

Diaphragm (12 m)

Curved channel(100 mm x 100 mm)

Curved section

Straight section

590 mm

60 mm

Pressure transducer

Detonation wave

(a) (b)




To dump tank

Housing

Diaphragm (12 m)


Curved section

Straight section

590 mm

60 mm

Pressure transducer

Detonation wave




To dump tank

Housing

Diaphragm (12 m)


Curved section

Straight section

590 mm

60 mm

Pressure transducer

Detonation wave

2.6

2

__________________________________________________________________________________________________________

24

2.7 2 2

ir or

2 5 ir 5 mm10 mm20 mm40 mm 60 mm

20 mm MSOP

1 mm

2.1 p T

CJ CJD CJ C2H4+3O2 T

p p A A.1 p CJD

CJ 2

CJD

2

Shimadzu HPV-2

4 s/frame MSOP 312 x 260 0.3 mm

Type 2 (ri = 10 mm, ro = 30 mm)

ri

50 mm

ro

O

Type 3 (ri = 20 mm, ro = 40 mm)

ri

50 mm

ro

O

Type 5 (ri = 60 mm, ro = 80 mm)

ri

10 mm

ro

O

ri

50 mm

ro

O

Type 1 (ri = 5 mm, ro = 25 mm)

Type 4 (ri = 40 mm, ro = 60 mm)

ri

30 mm

ro

O

Channel width: 20 mm

Channel depth: 1 mm

Type 2 (ri = 10 mm, ro = 30 mm)

ri

50 mm

ro

O

Type 2 (ri = 10 mm, ro = 30 mm)

ri

50 mm

ro

O

ri

50 mm

ro

O

Type 3 (ri = 20 mm, ro = 40 mm)

ri

50 mm

ro

O

Type 3 (ri = 20 mm, ro = 40 mm)

ri

50 mm

ro

O

ri

50 mm

ro

O

Type 5 (ri = 60 mm, ro = 80 mm)

ri

10 mm

ro

O

Type 5 (ri = 60 mm, ro = 80 mm)

ri

10 mm

ro

O

ri

10 mm

ro

O

ri

50 mm

ro

O


ri

50 mm

ro

O

ri

50 mm

ro

O


Type 4 (ri = 40 mm, ro = 60 mm)

ri

30 mm

ro

O

Type 4 (ri = 40 mm, ro = 60 mm)

ri

30 mm

ro

O

ri

30 mm

ro

O

Channel width: 20 mm

Channel depth: 1 mm

2.7 2

2

__________________________________________________________________________________________________________

25

2.1

Gas mixture p [kPa] T [K] [mm] CJD [m/s] C2H4+3O2 20.3 ~ 80.6 298 1 0.51 ~ 2.42 2121 ~ 2316

2.4.

2 2

2.8

2 2

i CJD

nD in,D

i iiin, rD i in,D CJin, DD Kudo et al.57)

1 stable mode: 8.0CJin, DD 2 critical mode: 8.0CJin, DD 6.0CJin, DD 3 unstable mode: 6.0CJin, DD

O Straight section

Curved section

Outer wall

inner wall

Detonation wave

Dn,i = rii

DCJ

ri i

Dn

O Straight section

Curved section

Outer wall

inner wall

Detonation wave

Dn,i = rii

DCJ

ri i

Dn

2.8 2

2

__________________________________________________________________________________________________________

26

2.5.

2.5.1. 2

2.9 2

CJD

NASA CEA96)

CJD

p 5%2

1 mm

2

A A.1 Nakayama et al. 93)

A A.1 p

2

__________________________________________________________________________________________________________

27

2.5.2. 2.10 ir ir 2 ir

2.10 .i constr .i constr 3 .i constr

.i constr

.i constr ir 1 32i r 21i r 2 3221 i r

10 20 30 40 50 60 70 80 900

500

1000

1500

2000

2500

3000

p- [kPa]

DC

J [m

/s]

: Theoretical (298.15 K): Experimental (ri = 5 mm): Experimental (ri = 10 mm): Experimental (ri = 20 mm): Experimental (ri = 40 mm): Experimental (ri = 60 mm)

2.9 2

2

__________________________________________________________________________________________________________

28

2.11 in,D ir 40 mm

in,D CJD CJin, DD

CJin, DD

CJin, DD

0.0 0.5 1.0 1.5 2.0 2.5 3.00

10

20

30

40

50

60

70

80

[mm]

r i [m

m]

: Stable, : Critical, : Unstable

Stablezone

Transitionzone

Unstablezone

ri/ = 32

ri/ = 21

0.0 0.5 1.0 1.5 2.0 2.5 3.00

10

20

30

40

50

60

70

80

[mm]

r i [m

m]


Stablezone

Transitionzone

Unstablezone

ri/ = 32

ri/ = 21

2.10 2

2

__________________________________________________________________________________________________________

29

2.5.3. 2.12 MSOP 2.12a 2.12b 2.12c 2.11 ir 40 mm

2

2.12a

2.11 CJin, DD

2

concave front focusingkinked front evolution wrinkled front

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

Dn,

i/DC

J [-]

i []

: = 1.10 mm (stable mode): = 1.48 mm (critical mode): = 2.36 mm (unstable mode)

2.11 2

40i r mm

2

__________________________________________________________________________________________________________

30

evolution 3

97)

2.12b2

2.11 CJin, DD

2.12c2

2

2.11 CJin, DD 0.4

2

2

__________________________________________________________________________________________________________

31

(a) = 1.10 mm

Stable mode

O

(c) = 2.36 mm

Unstable mode

O

(b) = 1.48 mm

Critical mode

O

(a) = 1.10 mm

Stable mode

O

Stable mode

OO

(c) = 2.36 mm

Unstable mode

O

Unstable mode

OO

(b) = 1.48 mm

Critical mode

O

Critical mode

OO

2.12 MSOP 40i r mm

2

__________________________________________________________________________________________________________

32

2.5.4. 2.13 ir MSOP 1.50 mm 2.13a 2.13b

2.13c~ 2.13e

2.13a 2

2.13b

2 2.13c~

2.13e 2

ir 2.13c~ 2.13e

2

2

2

2

1.2

2

__________________________________________________________________________________________________________

33

(a) ri = 60 mm

O

Stable mode = 1.51 mm

Critical mode

O

= 1.48 mm

(b) ri = 40 mm

O

Unstable mode = 1.54 mm

(c) ri = 20 mm

O


(d) ri = 10 mm

O


(e) ri = 5 mm

(a) ri = 60 mm

O


(a) ri = 60 mm

O


OO


Critical mode

O

= 1.48 mmCritical mode

OO

= 1.48 mm

(b) ri = 40 mm

O


OO


(c) ri = 20 mm

O


OO


(d) ri = 10 mm

O


OO


(e) ri = 5 mm 2.13 ir MSOP 50.1 mm

2

__________________________________________________________________________________________________________

34

2.6.

Multi-frame Short-time Open-shutter PhotographyMSOPMSOP 2

ir

2

2

3 Dn/DCJ

__________________________________________________________________________________________________________

35

3 Dn/DCJ

3.1.

2 MSOP

2 1 mm

MSOP 1 mm

2

2

2

or 2

3.2.

2.5 2.6

2.7 2

3 Dn/DCJ

__________________________________________________________________________________________________________

36

1 mm 16 mm

3.1 C2H4+3O2 2H2+O2

2C2H2+5O2+7Ar 3 2 T

p p A A.1~ A.3 p CJD CJ 2

2 2

Shimadzu HPV-2 2 s/frame C2H4+3O2 2C2H2+5O2+7Ar 2H2+O2

250 ns 312 x 260

0.3 mm

3.1

Gas mixture p [kPa] T [K] [mm] CJD [m/s] C2H4+3O2 20.4 ~ 100.9 298 6 0.40 ~ 2.41 2212 ~ 2387

2H2+O2 30.0 ~ 190.1 296 2 0.73 ~ 4.82 2680 ~ 2932 2C2H2+5O2+7Ar 15.0 ~ 150.1 294 2 0.23 ~ 3.00 1847 ~ 2033

2.5 2.6

2 2

2

3.1 2 2

2

2

3.2 2 20 mm

16 mm 50 mm 24

2

2.7

3 Dn/DCJ

__________________________________________________________________________________________________________

37

1 mm 16 mm

3.2 2C2H2+5O2+7Ar 2

T p

p 1 mm 4 A A.3 p CJD CJ

2

Channel depth: 16 mm

20 mm27.7 mm

R = 50 mm

2480 mm

Channel depth: 16 mm

20 mm27.7 mm

R = 50 mm

2480 mm

3.2 2

Transition region

Fully-developed region

Planar detonation wave

Converging detonation wave

(arc-like, negatively-curved)

R = 1/R

(a) 2

Outer wall

Inner wall

Negatively-curved detonation waveDetonation wave

(b) 2

Transition region





R = 1/R

Transition region





R = 1/R

(a) 2

Outer wall

Inner wall


Outer wall

Inner wall


(b) 2

3.1 2 2

3 Dn/DCJ

__________________________________________________________________________________________________________

38

2 2

2

Shimadzu HPV-2 1 s/frame 250 ns 312 x 260

0.1 mm

3.2

Gas mixture p [kPa] T [K] [mm] CJD [m/s] 2C2H2+5O2+7Ar 11.5 ~ 39.9 297 1 1.00 ~ 4.04 1828 ~ 1977

3.3.

2

3.3

3.3 2

r

2

rd td d

,P r rDnsin 3.1

dd1

sin1sintan

2

rr

3.2

nD

iin, rD 3.13.2

3 Dn/DCJ

__________________________________________________________________________________________________________

39

rDDr

r n

2n

2

dd 3.3

nD r3.3

r

r

r

rrDDr

i

dn

2n

2

i

3.4

2 nD

nD

nD

nD

9395)

mrrDDDD

iin,asyn,asyn,n 3.5

dr

Dndt

Straight section

Curved section

Outer wall

Inner wall

Initial line

Dndt

rj = 1 rj = 14 rj = 15

rdt

rj = 2 rj = 13


Detonation wave at t+dt(r+dr)dt

P

r

-di

dtri

rj = 0

rdDn,idt

O

dr

Dndt

Straight section

Curved section

Outer wall

Inner wall

Initial line

Dndt

rj = 1 rj = 14 rj = 15

rdt

rj = 2 rj = 13


Detonation wave at t+dt(r+dr)dt

P

r

-di

dtri

rj = 0

rdDn,idt

O

3.3 2

3 Dn/DCJ

__________________________________________________________________________________________________________

40

asyn,D m asyn,D r nD

3.53.43.5 nD r nD r in,D asyn,D

3.3

r r 15 asyn,D m

3.43.5 r r 94) asyn,D 0.005 CJD m 0.05 asyn,D

m CJD 2 asyn,D m ir

2 p r CJasyn, DD asyn,D m

asyn,D CJD

2 nD

nD nD in,D

1dd1

dd1 2

n

r

rr

rrD 3.6

3.63.3 nD 3.6 ddr r 2 ddr 93,94)

j1j2j1jj

2

2

j1jj d

d21

dd

rrrr 3.7

3.7 22 dd r 93,94)

22d

d 1jjj1j1jj

1jj

j1j

j1j

j2

2 rrrrr 3.8

3.73.8

3 Dn/DCJ

__________________________________________________________________________________________________________

41

ddr 22 dd r 3.43.5 r

23

22

2

222

dd

dd

dd2

rrrrrr 3.9

ddr 3.3 22 dd r 3.3 3.4

3.5

3.9

3.4.

2

nD nD 93)

2

ir

2

rr p T CJD CJD

nD irr CJD 4

CJi1n ,,, DrrfD 3.10 ir r ir irr 2 ir irr

2

3.10

3 Dn/DCJ

__________________________________________________________________________________________________________

42

i

i2

CJ

n ,rrrf

DD

3.11 in,D ir 3.43.11

r

r

r

r

r

r

rrr

rrfrrrf

rr

rrD

DDD

rr

rrDDr

i

i

i

d11,,

d11

d

21

2

i

i2

2

i

ii2

2

i

21

2

CJ

n

2

CJ

in,2

i

n

2n

2

i

3.12

3.12 2f ir

3.9 3.12 ddr 22 dd r ir irr r3.12

ddr 22 dd r 3.93.9 ir irr r

rrrrf 1,i

i3 3.13

3.13

i

i4

1

i

1i

i

i3

i

i3 ,,, r

rrfrrr

rrrf

rrrrf

3.14

3.14 irr 3.11

,i

5CJ

n rfDD 3.15

3.15

CJn DD ir CJn DD ir 3 nD CJn DD ir 3 nD

3 Dn/DCJ

__________________________________________________________________________________________________________

43

1.2.2

nD 62,63)3.15 CJn DD ir CJn DD

nD ir CJn DD CJn DD ir CJn DD CJD 2

3.5.

3.5.1. 2

3.4 ~ 3.6 CJD

NASA CEA96) CJD

2 16 mm

3 Dn/DCJ

__________________________________________________________________________________________________________

44

20 40 60 80 100 120 140 160 180 2000

500

1000

1500

2000

2500

3000

3500

p- [kPa]

DC

J [m

/s]


3.5 2

2H2+O2

10 20 30 40 50 60 70 80 90 100 1100

500

1000

1500

2000

2500

3000

p- [kPa]

DC

J [m

/s]


3.4 2

C2H4+3O2

3 Dn/DCJ

__________________________________________________________________________________________________________

45

3.5.2. 3.7 2

4 s ir 20 mm 2H2+O2 2.4

3.7a 2

2.12a MSOP

3.7b

2.12b

MSOP

0 20 40 60 80 100 120 140 1600

500

1000

1500

2000

2500

p- [kPa]

DC

J [m

/s]


3.6 2

2C2H2+5O2+7Ar

3 Dn/DCJ

__________________________________________________________________________________________________________

46

3.7c 2

2.12c MSOP

3 Dn/DCJ

__________________________________________________________________________________________________________

47

(c)

(b)

(a)

O

= 0.73 mm

O

= 1.56 mm

Unburnt gas pockets

O

= 4.09 mm

Transverse detonation wave

Re-initiation

(c)

(b)

(a)

O

= 0.73 mm

OOO

= 0.73 mm

O

= 1.56 mm

Unburnt gas pockets

OOO

= 1.56 mm

Unburnt gas pockets

O

= 4.09 mm


Re-initiation

OOO

= 4.09 mm


Re-initiation

3.7 2

20i r mm2H2+O2

3 Dn/DCJ

__________________________________________________________________________________________________________

48

3.5.3. 3.8 ~ 3.10 ir 2.5.2 2.10 .i constr C2H4+3O2 23i r 2H2+O2 22i r 2C2H2+5O2+7Ar 24i r C2H4+3O2 13i r 2H2+O2 14i r 2C2H2+5O2+7Ar 13i r ir 2 2313 i r

23i r 3.5.8

0.0 0.5 1.0 1.5 2.0 2.5 3.00

10

20

30

40

50

60

70

80

ri/ = 23

[mm]

r i [m

m]


ri/ = 14

Stablezone

Unstablezone

Transitionzone

0.0 0.5 1.0 1.5 2.0 2.5 3.00

10

20

30

40

50

60

70

80

ri/ = 23

[mm]

r i [m

m]


ri/ = 14

Stablezone

Unstablezone

Transitionzone

3.8 2

C2H4+3O2

3 Dn/DCJ

__________________________________________________________________________________________________________

49

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50

10

20

30

40

50

60

70

80

Transitionzone

[mm]

r i [m

m]

ri/ = 24: Stable, : Critical, : Unstable

ri/ = 14Stablezone

Unstablezone

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50

10

20

30

40

50

60

70

80

Transitionzone

[mm]

r i [m

m]


ri/ = 14Stablezone

Unstablezone

3.10 2

2C2H2+5O2+7Ar

0 1 2 3 4 50

10

20

30

40

50

60

70

80

[mm]

r i [m

m]


ri/ = 13Stablezone

Unstablezone

Transitionzone

0 1 2 3 4 50

10

20

30

40

50

60

70

80

[mm]

r i [m

m]


ri/ = 13Stablezone

Unstablezone

Transitionzone

3.9 2

2H2+O2

3 Dn/DCJ

__________________________________________________________________________________________________________

50

3.5.4. 3.11 2 ir 20 mm 0.70 mm C2H4+3O2 r r ir2

or 2

3.12 2

3.11 r ir

2 i

-35-30-25-20-15-10-501.0

1.2

1.4

1.6

1.8

2.0

-i []

r/r i

[-]

Outer wall

Inner wall

ri = 20 mm, = 0.70 mm: i = 10.7: i = 34.5: i = 57.7: i = 80.9: i = 103.7: i = 127.1: i = 150.0: i = 173.0

3.11 2

20i r mm 70.0 mmC2H4+3O2

3 Dn/DCJ

__________________________________________________________________________________________________________

51

3.3 2

3.11 3.12

3.5.5. 3.11 3.12 2

3.4

3.4

3.5

3.13 2

3.43.5

3.11 r r ir 3.12 in,D iin, rD

1.0 1.2 1.4 1.6 1.8 2.00.0

0.5

1.0

1.5

r/ri [-]

[1

05 ra

d/s]

ri = 20 mm, = 0.70 mm: Experimental (i = 115.1): Experimental (i = 127.1): Experimental (i = 138.8): Average (= 1.0231105 rad/s)

Inner wall Outer wall

3.12 2 20i r mm 70.0 mmC2H4+3O2

3 Dn/DCJ

__________________________________________________________________________________________________________

52

asyn,D m CJasyn, 980.0 DD 10.8m 3.13 asyn,D m2

3.43.5

3.14 2

nD 3.11

nD

nD r CJD ir 3.6

3.13 3.5 nD 2 3.14 asyn,D m

2

nD 3.53.5

nD 3.53.4

-35-30-25-20-15-10-501.0

1.2

1.4

1.6

1.8

2.0

r/r i

[-]

-i []

ri = 20 mm, = 0.70 mm: Experimental (i = 115.1): Experimental (i = 127.1): Experimental (i = 138.8): Fitting

(Dn,i = 0.87235DCJ, Dn,asy = 0.980DCJ, m = 8.10, = 1.0231105 rad/s)

Outer wall

Inner wall

3.13 2 20i r mm 70.0 mmC2H4+3O2

3 Dn/DCJ

__________________________________________________________________________________________________________

53

3.43.52 nD

3.9 nD 3.133.43.5 2

3.15 2 3.43.5

3.13

1 3.13

2 3.13 5 3.3 5j 33.100.1 i rr 2 CJasyn, 995.0 DD 50.7m 12

2 33.100.1 i rr 2 3.16

1.0 1.2 1.4 1.6 1.8 2.00.80

0.85

0.90

0.95

1.00

1.05

r/ri [-]

ri = 20 mm, = 0.70 mm: Experimental (i = 115.1): Experimental (i = 127.1): Experimental (i = 138.8): Fitting

(Dn,i = 0.87235DCJ, Dn,asy = 0.980DCJ, m = 8.10)

Dn/D

CJ [

-]

Inner wall Outer wall

3.14 2

20i r mm 70.0 mmC2H4+3O2

3 Dn/DCJ

__________________________________________________________________________________________________________

54

12 nD nD CJD 1 CJn DD 00.200.1 i rr 2 CJn DD21 20.100.1 i rr 3.16 CJn DD

CJn DD 0.05 0.003

CJn DD

CJn DD

-7-6-5-4-3-2-101.0

1.1

1.2

1.3

1.4

r/r i

[-]

-i []

ri = 20 mm, = 0.70 mm: Experimental (i = 115.1): Experimental (i = 127.1): Experimental (i = 138.8): Fitting (1)


: Fitting (2)(Dn,i = 0.87235DCJ, Dn,asy = 0.995DCJ, m = 7.50, = 1.0231105 rad/s)

Inner wall

3.15 2 33.100.1 i rr

20i r mm 70.0 mmC2H4+3O2

3 Dn/DCJ

__________________________________________________________________________________________________________

55

3.5.6. Dn/DCJ 3.17 ~ 3.19 CJn DD 3.8 ~ 3.10 ir

CJn DD C2H4+3O2 10 2H2+O2 9 2C2H2+5O2+7Ar 13 CJn DD

CJn DD ir 2 p ir 1 CJn DD 3.15 CJn DD ir CJn DD ir nD 62,63)

nD p CJn DD

0.00 0.02 0.04 0.06 0.08 0.10 0.120.6

0.7

0.8

0.9

1.0

[-]

Dn/D

CJ [

-]

ri = 20 mm, = 0.70 mm: Fitting (1)



)00.200.1( i rr

)20.100.1( i rr

0.00 0.02 0.04 0.06 0.08 0.10 0.120.6

0.7

0.8

0.9

1.0

[-]

Dn/D

CJ [

-]

ri = 20 mm, = 0.70 mm: Fitting (1)



)00.200.1( i rr

)20.100.1( i rr

3.16 1 00.200.1 i rr 2 20.100.1 i rr CJn DD 20i r mm

70.0 mmC2H4+3O2

3 Dn/DCJ

__________________________________________________________________________________________________________

56

0 1CJn DD CJn DD 0 1CJn DD 3.43.5 asyn,D CJD

3.17 ~ 3.19 CJn DD 0 1CJn DD 3.43.5 0

CJn DD 3.5 0 CJn DD

0 1CJn DD CJn DD 3.5

0.00 0.02 0.04 0.06 0.08 0.10 0.120.6

0.7

0.8

0.9

1.0

[-]

Dn/D

CJ [

-]

: ri = 10 mm, = 0.40 mm: ri = 20 mm, = 0.40 mm: ri = 20 mm, = 0.59 mm: ri = 20 mm, = 0.87 mm: ri = 40 mm, = 0.40 mm: ri = 40 mm, = 0.86 mm: ri = 40 mm, = 1.51 mm: ri = 60 mm, = 0.40 mm: ri = 60 mm, = 1.11 mm: ri = 60 mm, = 2.07 mm

3.17 2

CJn DD C2H4+3O2

3 Dn/DCJ

__________________________________________________________________________________________________________

57

0.00 0.02 0.04 0.06 0.08 0.10 0.120.6

0.7

0.8

0.9

1.0

[-]

Dn/D

CJ [

-] : ri = 5 mm, = 0.23 mm: ri = 10 mm, = 0.23 mm: ri = 10 mm, = 0.36 mm: ri = 10 mm, = 0.46 mm: ri = 20 mm, = 0.23 mm: ri = 20 mm, = 0.53 mm: ri = 20 mm, = 0.90 mm: ri = 40 mm, = 0.23 mm: ri = 40 mm, = 0.78 mm: ri = 40 mm, = 1.55 mm: ri = 60 mm, = 0.23 mm: ri = 60 mm, = 1.38 mm: ri = 60 mm, = 2.16 mm

3.19 2

CJn DD 2C2H2+5O2+7Ar

0.00 0.02 0.04 0.06 0.08 0.10 0.120.6

0.7

0.8

0.9

1.0

[-]

Dn/D

CJ [

-]

: ri = 20 mm, = 0.73 mm: ri = 20 mm, = 0.82 mm: ri = 20 mm, = 0.93 mm: ri = 40 mm, = 0.73 mm: ri = 40 mm, = 1.27 mm: ri = 40 mm, = 1.76 mm: ri = 60 mm, = 0.74 mm: ri = 60 mm, = 1.56 mm: ri = 60 mm, = 2.37 mm

3.18 2

CJn DD 2H2+O2

3 Dn/DCJ

__________________________________________________________________________________________________________

58

3.20 CJn DD 3.17 ~ 3.19 CJn DD CJn DD CJn DD CJn DD CJn DD

332210CJn aaaa DD 0000.1a0 3017.1a1 089.16a 2 67.169a3 3.20 CJn DD 0 1CJn DD

0 1CJn DD 8.0CJin, DD CJn DD 11614.000000.0 0.18.0 CJn DD

0.00 0.02 0.04 0.06 0.08 0.10 0.120.6

0.7

0.8

0.9

1.0

[-]

Dn/D

CJ [

-]

: C2H4+3O2: 2H2+O2: 2C2H2+5O2+7Ar: Fitting (overall)

Dn/DCJ = aj()j (j = 0~3)a0 = 1.0000, a1 = -1.3017a2 = 16.089, a3 = -169.67

3.20 CJn DD

3 Dn/DCJ

__________________________________________________________________________________________________________

59

3.5.7. Dn/DCJ 3.21 ~ 3.23 2 CJn DD 3.21 ir 20 mm 0.70 mm C2H4+3O2 3.22 ir 40 mm 1.56 mm 2H2+O2 3.23 ir 10 mm 0.27 mm 2C2H2+5O2+7Ar marker particle method98)

Marker particle method 3.24

1 2

2

B

2 s 4 s 3.21 ~ 3.23 CJn DD

CJn DD 2 ir p CJn DD CJn DD

CJn DD

CJn DD 1 1.2.2

3.21 ~ 3.23 2 CJn DD

p 11614.000000.0 0.18.0 CJn DD

CJn DD

3 Dn/DCJ

__________________________________________________________________________________________________________

60

Photograph: schlieren photography (t = 2 s): Front shock reconstructed with overall Dn/DCJ- relation (t = 4 s)



3.22 2

CJn DD 40i r mm 56.1 mm2H2+O2

Photograph: shadowgraph photography (t = 2 s): Front shock reconstructed with overall Dn/DCJ- relation (t = 4 s)



3.21 2

CJn DD 20i r mm 70.0 mmC2H4+3O2

3 Dn/DCJ

__________________________________________________________________________________________________________

61

Wave front at t

Wave front at t+t

: node

Wave front at t

Wave front at t+t

: node: node

3.24 Marker particle method




3.23 2

CJn DD 10i r mm 27.0 mm 2C2H2+5O2+7Ar

3 Dn/DCJ

__________________________________________________________________________________________________________

62

3.5.8. 3.21 ~ 3.23 CJn DD CJn DD x y t irx iry iCJ rtD

3.25 2

ir 2350 108 3 CJn DD 3.25a

3.25b CJn DD

1 2

or

CJn DD

3.14 3.25 CJn DD

2

3.11 3.12 3.25 CJn DD irr CJn DD io rr 2 3.25 ir CJn DD 1 0

ir

3.25 CJn DD ir ir 2 ir ir ir CJn DD 2

3 Dn/DCJ

__________________________________________________________________________________________________________

63

ir 3.26 3.27 r r ir 3.26

ir 36.3 C2H4+3O2 ir 20 mm40 mm 60 mm 3 3.27 ir 27.5 ir 20 mm

CJn DD ir ir 2

3 Dn/DCJ

__________________________________________________________________________________________________________

64

: Constant Dn/DCJ line : Front shock reconstructed with

overall Dn/DCJ- relation ( = 1)

(b) Dn/DCJ

(a)

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-] [-

]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

0.0000

0.0104

0.0207

0.0414

0.0518

0.0725

0.0829

0.0932

0.1036

0.0622

0.0311

0.8270

0.8443

0.8616

0.8962

0.9135

0.9481

0.9654

0.9827

1.0000

0.9308

0.8789

0.0000

0.0104

0.0207

0.0414

0.0518

0.0725

0.0829

0.0932

0.1036

0.0622

0.0311

0.8270

0.8443

0.8616

0.8962

0.9135

0.9481

0.9654

0.9827

1.0000

0.9308

0.8789

0.0000

0.0104

0.0207

0.0414

0.0518

0.0725

0.0829

0.0932

0.1036

0.0622

0.0311

0.8270

0.8443

0.8616

0.8962

0.9135

0.9481

0.9654

0.9827

1.0000

0.9308

0.8789

: Constant line : Front shock reconstructed with


= 0

= 2

= 4 =

6

= 8

= 10

(i) ri/ = 23

= 0.0104

= 0.0104

= 0

= 2

= 4 =

6

= 8

= 10

(i) ri/ = 23

Dn/DCJ = 0.9827

Dn/DCJ = 0.9654

= 0

= 2

= 4 =

6

= 8

= 0

= 2

= 4 =

6

= 8

(iii) ri/ = 108 (iii) ri/ = 108

= 0

= 2

= 4 =

6

= 8

= 10

= 0

= 2

= 4 =

6

= 8

= 10

= 0.0104

= 0.0104(ii) ri/ = 50 (ii) ri/ = 50

Dn/DCJ = 0.9827

Dn/DCJ = 0.9654

: Constant Dn/DCJ line : Front shock reconstructed with

overall Dn/DCJ- relation ( = 1): Constant Dn/DCJ line : Front shock reconstructed with


(b) Dn/DCJ

(a)

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-] [

-]-5 -4 -3 -2 -1 0 1 2 3 4 5

-5-4-3-2-1012345

[-] [

-]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345

[-]

[-]

0.0000

0.0104

0.0207

0.0414

0.0518

0.0725

0.0829

0.0932

0.1036

0.0622

0.0311

0.0000

0.0104

0.0207

0.0414

0.0518

0.0725

0.0829

0.0932

0.1036

0.0622

0.0311

0.8270

0.8443

0.8616

0.8962

0.9135

0.9481

0.9654

0.9827

1.0000

0.9308

0.8789

0.8270

0.8443

0.8616

0.8962

0.9135

0.9481

0.9654

0.9827

1.0000

0.9308

0.8789

0.0000

0.0104

0.0207

0.0414

0.0518

0.0725

0.0829

0.0932

0.1036

0.0622

0.0311

0.0000

0.0104

0.0207

0.0414

0.0518

0.0725

0.0829

0.0932

0.1036

0.0622

0.0311

0.8270

0.8443

0.8616

0.8962

0.9135

0.9481

0.9654

0.9827

1.0000

0.9308

0.8789

0.8270

0.8443

0.8616

0.8962

0.9135

0.9481

0.9654

0.9827

1.0000

0.9308

0.8789

0.0000

0.0104

0.0207

0.0414

0.0518

0.0725

0.0829

0.0932

0.1036

0.0622

0.0311

0.0000

0.0104

0.0207

0.0414

0.0518

0.0725

0.0829

0.0932

0.1036

0.0622

0.0311

0.8270

0.8443

0.8616

0.8962

0.9135

0.9481

0.9654

0.9827

1.0000

0.9308

0.8789

0.8270

0.8443

0.8616

0.8962

0.9135

0.9481

0.9654

0.9827

1.0000

0.9308

0.8789

: Constant line : Front shock reconstructed with

overall Dn/DCJ- relation ( = 1): Constant line : Front shock reconstructed with


= 0

= 2

= 4 =

6

= 8

= 10

(i) ri/ = 23

= 0.0104

= 0.0104

= 0

= 2

= 4 =

6

= 8

= 10

(i) ri/ = 23

Dn/DCJ = 0.9827

Dn/DCJ = 0.9654

= 0

= 2

= 4 =

6

= 8

= 0

= 2

= 4 =

6

= 8

(iii) ri/ = 108 (iii) ri/ = 108

= 0

= 2

= 4 =

6

= 8

= 10

= 0

= 2

= 4 =

6

= 8

= 10

= 0.0104

= 0.0104(ii) ri/ = 50 (ii) ri/ = 50

Dn/DCJ = 0.9827

Dn/DCJ = 0.9654

3.25 2

3 Dn/DCJ

__________________________________________________________________________________________________________

65

-35-30-25-20-15-10-501.0

1.2

1.4

1.6

1.8

2.0

-i []

r/ri [

-]

Outer wall

Experimental: C2H4+3O2: 2H2+O2: 2C2H2+5O2+7Ar

Reconstructed: Overall Dn/DCJ- relationInner wall

3.27 2

5.27i r 20i r mm

-35-30-25-20-15-10-501.0

1.2

1.4

1.6

1.8

2.0

-i []

r/ri [

-]

Outer wall

Experimental: ri = 20 mm: ri = 40 mm: ri = 60 mm

Reconstructed: Overall Dn/DCJ- relationInner wall

3.26 2

3.36i r C2H4+3O2 ir

3 Dn/DCJ

__________________________________________________________________________________________________________

66

3.6.

3.6.1. Dn/DCJ 2

CJD 3.6

3.28 2

3.01 mm R1 ~ R3 17.5 mm 2

CJn DD

3.29 2 CJn DD CJn DD CJn DD CJn DD 3.19 CJn DD p 1 CJn DD 1CJn DD

CJ

R1

R1 = 17.5 mmR2 = 17.4 mmR3 = 17.5 mm Transition region


R3R2R1

R1 = 17.5 mmR2 = 17.4 mmR3 = 17.5 mm Transition region


R3R2

3.28 2 01.3 mm

3 Dn/DCJ

__________________________________________________________________________________________________________

67

CJ 3.29 CJn DD CJn DD

CJn DD

CJn DD CJn DD

CJn DD 3.29

CJn DD 332210CJn aaaa DD 00000.1a0 41858.0a1 25821.0a 2 13027.0a3 CJn DD 0 1CJn DD CJn DD 0.07.0 2042.10000.1 CJn DD

-0.80 -0.60 -0.40 -0.20 0.00 0.200.80

0.90

1.00

1.10

1.20

1.30

[-]

: FittingDn/DCJ = aj()j (j = 0~3)a0 = 1.00000, a1 = -0.41858a2 = -0.25821, a3 = -0.13027

Dn/D

CJ [

-]

Interpolation limit ofDn/DCJ- relation (negative)

: = 4.02 mm: = 3.01 mm: = 2.00 mm: = 1.00 mm

Positive

Negative

3.29 2

CJn DD

3 Dn/DCJ

__________________________________________________________________________________________________________

68

3.6.2. Dn/DCJ 3.30 2

CJn DD 2 marker particle

method98) 2

B

1 s 2 s 2

2

2

3.30 2

CJn DD

CJn DD

CJn DD

3 Dn/DCJ

__________________________________________________________________________________________________________

69

CJn DD CJn DD 2 3.31 2 CJn DD

3 cm CJn DD

CJn DD CJn DD 0 0 CJn DD

99) 2C2H2+5O2

CJn DD

(a) = 4.00 mm(), 4.03 mm()

(b) = 3.01 mm(), 3.01 mm()

(c) = 2.00 mm(), 2.00 mm()

(d) = 1.00 mm(), 1.00 mm()

Photograph: direct photography (t = 1 s): Front shock reconstructed with Dn/DCJ- relation (t = 2 s)

(a) = 4.00 mm(), 4.03 mm()

(b) = 3.01 mm(), 3.01 mm()

(c) = 2.00 mm(), 2.00 mm()

(d) = 1.00 mm(), 1.00 mm()



3.30 CJn DD 2

3 Dn/DCJ

__________________________________________________________________________________________________________

70

3.6.3. 2 CJn DD

CJn DD 2

2

3.32 3.32 sM

w

w

w w

Dn/DCJ= 1.08

Dn/DCJ= 1.07

1.191.20

1.181.171.161.151.141.131.121.111.101.091.081.071.061.051.041.031.021.011.00

(a) = 4.00 mm (b) = 3.00 mm (c) = 2.00 mm (d) = 1.00 mm

Dn/DCJ= 1.06

Dn/DCJ= 1.05

Dn/DCJ= 1.04

Dn/DCJ= 1.07

Dn/DCJ= 1.06

Dn/DCJ= 1.05

Dn/DCJ= 1.08

Dn/DCJ= 1.07

1.191.20

1.181.171.161.151.141.131.121.111.101.091.081.071.061.051.041.031.021.011.00

1.191.20

1.181.171.161.151.141.131.121.111.101.091.081.071.061.051.041.031.021.011.00

(a) = 4.00 mm (b) = 3.00 mm (c) = 2.00 mm (d) = 1.00 mm

Dn/DCJ= 1.06

Dn/DCJ= 1.05

Dn/DCJ= 1.04

Dn/DCJ= 1.07

Dn/DCJ= 1.06

Dn/DCJ= 1.05

3.31 2 CJn DD

3 Dn/DCJ

__________________________________________________________________________________________________________

71

3.33 w DW RS MS

Vasilev et al. 100) 3.33 2 w von Neumann condition 101) 3.32 w von Neumann condition 3.32 w w 3.33 Skews and Kleine 102) CJn DD 1

1 CJn DD

CJn DD 3.33 2C2H2+5O2+7Ar 9.23w CJn DD

9.23w CJn DD

O

Ms


ww

ro

Outer wall (concave)

Msw

Simplified geometric relationship between the planar detonation wave and the outer wall with fixed wO

Ms


ww

ro

Outer wall (concave)

Msw

Simplified geometric relationship between the planar detonation wave and the outer wall with fixed w

3.32

3 Dn/DCJ

__________________________________________________________________________________________________________

72

3.34 2 CJn DD marker particle method98) 2

B 2

3.34c 3.34d CJn DD 3.34a 3.34b 1CJn DD

1 s 0.07.0 2042.10000.1 CJn DD 3.34 CJn DD 2 or p

2

1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

70

80

90

Ms [-]

w [

]

Sonic condition

Detachment criterion(2-shock theory)

von Neumann condition(3-shock theory)

No reflection

Machreflection

Regularreflection

MCJ = 6.3125

w = 23.9

1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

70

80

90

Ms [-]

w [

]

Sonic condition



No reflection

Machreflection

Regularreflection

MCJ = 6.3125

w = 23.9

DW

DW

DW

RS

RSMS

1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

70

80

90

Ms [-]

w [

]

Sonic condition



No reflection

Machreflection

Regularreflection

MCJ = 6.3125

w = 23.9

1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

70

80

90

Ms [-]

w [

]

Sonic condition



No reflection

Machreflection

Regularreflection

MCJ = 6.3125

w = 23.9

DW

DW

DW

RS

RSMS

3.33 w

3 Dn/DCJ

__________________________________________________________________________________________________________

73

0.07.0 2042.10000.1 CJn DD CJn DD

CJn DD

3 Dn/DCJ

__________________________________________________________________________________________________________

74

Head of expansion wave

w = 23.9 w = 23.9


w = 23.9

w = 23.9

(a) ro = 30 mm, = 4.01 mm


(b) ro = 30 mm, = 1.00 mm

(c) ro = 40 mm, = 1.00 mm (d) ro = 80 mm, = 1.00 mm


w = 23.9


w = 23.9 w = 23.9


w = 23.9


w = 23.9w = 23.9

w = 23.9w = 23.9

(a) ro = 30 mm, = 4.01 mm



(b) ro = 30 mm, = 1.00 mm

(c) ro = 40 mm, = 1.00 mm (d) ro = 80 mm, = 1.00 mm 3.34 CJn DD

2

3 Dn/DCJ

__________________________________________________________________________________________________________

75

3.7.

C2H4+3O22H2+O2 2C2H2+5O2+7Ar 3 2

2 2313 i r

23i r 2

CJn DD CJn DD ir 2 p

ir 1 CJn DD CJn DD

CJn DD 1 ir CJn /DD 1 ir ir ir 2

2C2H2+5O2+7Ar CJn DD CJn DD

CJn DD

4

__________________________________________________________________________________________________________

76

4

1

4.1.

3 CJn DD ir

Yao and Stewart80)

2 Sharpe81)

1 1


2

CJn DD 3 CJn DD

4.2.

4.1

Menikoff et al. 77)

ZND

Yao and Stewart80)

induction zoneIZreaction zone

RZ 2 Whitham ray tube theory69)

1

4

__________________________________________________________________________________________________________

77

4.1 n igl

mtl igl mtl indl

A AnA dd indl 1ind l

IZ RZ 2 ZND CJ CJind,l

CJ CJind,l CJind,Cl C 28) CJn DD CJD CJ 0 NASA CEA96) CJ

CJn DD 2 CJind,CJn lDD CJind,Cl

CJind,CJn lDD CJn DD

Induction zone (IZ)

Reaction zone (RZ)

n

Ray tubeThermicity

Reaction progress

lig

lmt

Front shockPropagation

direction

CJ point

0

Analysis domain (IZ+RZ)

Onset point of ignition

Reaction progressor

Thermicity

Max. thermicity

Reaction progress at CJ point

Induction length: lind = lig+lmtCell width: = Clind,CJCurvature: = (dA/dn)/A

C: ConstantA: Cross-section area of ray tube

lind

Induction zone (IZ)

Reaction zone (RZ)

n

Ray tubeThermicity

Reaction progress

lig

lmt

Front shockPropagation

direction

CJ point

0

Analysis domain (IZ+RZ)

Onset point of ignition

Reaction progressor

Thermicity

Max. thermicity

Reaction progress at CJ point

Induction length: lind = lig+lmtCell width: = Clind,CJCurvature: = (dA/dn)/A

C: ConstantA: Cross-section area of ray tube

lind

4.1

4

__________________________________________________________________________________________________________

78

4.3.

1

1

64)

0nnn

uDnu

t 4.1

01nnnn

np

nuu

tuD

4.2

0n2n

n

ut

pneu

te

4.3

wnYu

tY

n 4.4

Yqpe 1 4.5 RTp 4.6

t nu nD peY

0Y 1Y w q RT

80)

80,81)

N21N21 PPPRRR R : , P : 1

1

4

__________________________________________________________________________________________________________

79

RTqKYY

TTZw exp1exp a1 4.7

Z aT K4.7 C

4.74.7 aT

aT

4.7 1 4.7 2 K g 1)

YYRTKRTqg

1lnln 4.8

0 CJCJ 1,81,103) CJ CJ 4.8 0g 1) K CJ CJ

CJpeq,CJpeq,

CJpeq, exp1

RTq

YY

K 4.9

eq CJp CJ

eq,CJp CJ CJ

CJpeq,Y

CJ D CJ 2 CJpeq,

2CJpn, au 1,81,103) CJpeq,a CJ CJ

CJ CJ CJpfr,a

1)

4

__________________________________________________________________________________________________________

80

CJpeq,CJpeq,2

2CJpfr,

2

2

2CJpfr,

2CJpfr,

2CJpfr,

2CJpeq,

1111

1

1

YYaq

aqa

aa

4.10

fra T

RTpa 2fr 4.11

CJpfr,a 4.11 CJpeq,T CJpfr,a q

q 4.5.2 CJpeq,Y CJpeq,T

4.9 K

4.4.

IZ RZ

4.1~ 4.4 1 t 4.1

~ 4.4

0d

dnn

n uDnu 4.12

0dd1

dd n

n np

nuu 4.13

0dd

dd

2 np

ne

4.14

wnYu

dd

n 4.15

4.5 Ypee ,,

nY

Ye

np

pe

ne

ne

dd

dd

dd

dd

4.16

4.164.14

0dd

dd

dd

2

nY

pe

Ye

np

npeep

4.17 fra

4

__________________________________________________________________________________________________________

81

peepa

2

2fr 4.18

1)4.184.17

0dd

dd

dd2

fr

nY

pe

Ye

np

na 4.19

4.124.134.154.19

2n

2fr

nn2fr

n

1

dd

ua

uDawpe

Ye

nu

4.20

4.5

qYe 4.21

1

11

p

e 4.22

4.214.224.20

2

nn2fr

2n

2fr

nn2frn

1

11

dd

M

uDwaq

uauDaqw

nu

4.23

M 2fr2n

2 auM 4.23 1

IZ RZ 80,81)

4.134.14

02d

d 2n

upen 4.24

4.244.5

021dd 2n

Yq

upn

4.25

.212n constYqup

4.26 4.26

4.26

2n2n

21

121DpYqup

4.27 4.27 pa 2fr

4

__________________________________________________________________________________________________________

82

YquDpa

21

2n

2n2

fr 4.28

4.28 1 IZ RZ

4.5.

4.5.1. ZND IZ RZ 2 igl

0w CJ 0w CJ

104) 1ind l 1 t 1 CJ

T igt

TT

TT

qZRt a

a

21

ig exp1 4.29

4.29 E

ltnu

l

ig

0n

d1 4.30

ln ln 4.29 igt 4.30 l igl

4.30 0n igln nu T 0w 0Y p nD 4.234.28 0n nu 4.12 0n

4

__________________________________________________________________________________________________________

83

1

21 2n

nn,

D

pDu 4.31

n,

n

uD 4.32

105)+T4.11

4.28

4.5.2. CJ 0 CJn DD 4.124.13 CJn Du 4.33 2CJ

2n Dpup 4.34

4.334.34 p CJD fra CJn2CJ

CJ

n2fr DuDpD

upa

4.35

nu w

aq

2fr

1 4.36

58) CJ CJmt,l 4.23 0

mtn,

ig,n

mtn,

ig,n

n

a1

2n

2fr

n

2n

2fr

CJmt,

d

exp1exp1

d1

u

u

u

u

u

RTqKYY

TTZq

ua

uqwual

4.37

CJ ZND

CJ CJig,l

4.30

TT

TT

qZRu

utl aa

21n,

n,,igCJig, exp1 4.38

CJ CJind,l CJig,l CJmt,l

4

__________________________________________________________________________________________________________

84

mtn,

i,n

n

a1

2n

2fr

a

a

21n,

CJind,

d

exp1exp1

exp1

u

u g

u

RTqKYY

TTZq

ua

TT

TT

qZRu

l

4.39

p CJD 4.394.35 ign,u mtn,u ind,CJl CJ

0n CJig,ln 1 0w 0Y n,n uu TT

n,ign, uu n,u 4.31 4.324.33 T 4.114.354.39 CJig,ln nu T4.234.35 0 CJig,ln nu n,ign,n uuu nu 4.114.334.35 T CJ D CJ

2CJpeq,

2CJpn, au 1,81,103) p CJpeq,Y

0 CJn DD 4.104.284.35 q NewtonRaphson 106)q4.104.284.35 2 CJpeq,a

CJpfr,a CJpfr,a 4.3 K

4.5.3. l tu pT e

CJ

1

CJind,

~DZl

lll

1~ Ztt

CJ

~Duu

~ 2CJ

~Dpp

2CJ

~DRTT 2

CJ

~Dee 4.40

~4.40 ~ 1 p~

2CJ

2CJ

1~MD

pp

4.41

4

__________________________________________________________________________________________________________

85

CJM CJ CJ 1

4.39

mtn,

ig,n

~

~

n

a1

2n

2fr

a

a

21n,

~d

~~

exp1~~

exp~~1

~~

~~

exp~~

~~1

~

u

u

u

TqKYY

TTq

ua

TT

TT

qu

4.42

4.6.

p CJD CJM R nD 0n p T 4.12~ 4.15 aT q CJpeq,Y Z K 4.12~ 4.15 0n CJ pT4.12~ 4.15 0n igln 0w igln CJ 0w

4.54.64.114.28

1 CJ

nD nD

0 CJ D CJ 81,103)4.12~ 4.15 2 CJpfr,

2CJpn, au 4.23 0

4.23 0 81,103)

CJ

4.23 CJ CJ nD

shooting method107) nD nD

4

__________________________________________________________________________________________________________

86

nD 4.12~ 4.154 108)

CJ 0 CJ 4.3 2 CJpeq,

2CJpn, au eqfr aa CJ

1,81,103) 0 CJ CJ 2 CJpeq,

2CJpn, au 0 CJ

CJ CJ CJ

0CJ D 0 0n D 81,103)Sharpe

0 0n D CJ 81) 0n D Sharpe 0 0 0CJ D CJ 81) Sharpe

0CJ D CJ 0 CJ CJ 2 CJpfr,2 CJpn, au 0 CJ 0CJ D 0 CJ 2 CJpfr,

2CJpn, au CJ

0CJ D 0n D 0CJ D

0CJ D 0.3% 1) 0n D 0CJ D CJ

nD 3 C2H4+3O22H2+O2 2C2H2+5O2+7Ar 4.1

T 298.15 K 4.40

C p 0.1 MPa

CJM CEA96) CJD CJM CEA96) CJpeq,Y overallCJ qq CJq CJ CJ

0.1 MPa298.15 K CJ

2 Thompson109) CJq CJ CJ

4

__________________________________________________________________________________________________________

87

CEA96) overallq

22242 2COO2H3OHC 4.43 O2HO2H 222 4.44 7Ar4COO2H7Ar5OH2C 22222 4.45 0.1 MPa298.15 K 110)C CJind,l A A.1~ A.3 p CJind,l T 298.15

K CJ ZND CJind,Cl 28)C p C2H4+3O2

Konnov mechanism111)2H2+O2 2C2H2+5O2+7Ar GRI-Mech 3.0112) 4.2

CJ p C 4.2 p

3.1 C p

C a~T

Schultz and Shepherd 104) a~T

F p 1 A A.1~ A.3 p 4.1 K 4.3 q~ 4.5.2 4.5.3

4.1

Gas mixture CJM a~T q~ CJpeq,Y K C C2H4+3O2 7.2528 1.3402 0.74480 1.3113 0.45481 1.1893 199.12 2.1270 12.860

2H2+O2 5.2743 1.4016 0.95076 0.91776 0.51881 3.7329 31.134 2.0242 26.986

2C2H2+5O2+7Ar 6.3125 1.4409 0.74701 0.98095 0.44256 0.89014 57.110 2.1173 10.225

4.1 ~~n D 4.40 nD CJD CJind,l

~~n D CJind,CJn lDD nD CJn DD CJind,CJn lDD 4.2 CJind,Cl CJind,CJn lDD CJn DD

4

__________________________________________________________________________________________________________

88

4.7. Dn/DCJ 4.3 ~ 4.5 CJn DD

4.3 ~ 4.5 3.17 ~ 3.19

4.1 1 1


1 1 p 1 CJn DD 1 1 p CJn DD 1 CJn DD

CJn DD crCJn DD cr cr CJn DD 4.3 ~ 4.5 CJn DD p 1

0 50 100 150 2000

5

10

15

20

25

30

35

40

p- [kPa]

C [

-]2H2+O2 (average: 26.986)

2C2H2+5O2+7Ar (average: 10.225)

C2H4+3O2 (average: 12.860)

4.2 CJ C

4

__________________________________________________________________________________________________________

89

CJn DD CJn DD 1

CJn DD CJn DD 1 crCJn DD 0.83 ~ 0.86

crCJn DD Radulescu and Lee

113,114)

113,114)Radulescu and Lee

CJD

CJn DD 0.80 ~ 0.86 crCJn DD CJn DD 1 Radulescu and Lee 2 3 8.0CJin, DD crCJn DD

CJn DD 1

4.9.3

C2H4+3O2 2H2+O2 CJn DD 1 1 2C2H2+5O2+7Ar 1 CJn DD 1 1 CJn DD CJn DD 1 2

CJn DD

1

CJn DD

4

__________________________________________________________________________________________________________

90

0.00 0.05 0.10 0.15 0.20 0.25 0.300.6

0.7

0.8

0.9

1.0

(= C ) [-]

Dn/D

CJ (

= D

n) [-

]

: Experimental (9 cases of ri/): Model ( = 2.0242): Model ( = 1.0000)

(Dn/DCJ)cr= 0.86344

()cr= 0.16429

~

~

0.29333

0.85857

4.4 CJn DD

2H2+O2

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140.6

0.7

0.8

0.9

1.0

(= C ) [-]

Dn/D

CJ (

= D

n) [-

]


0.85682

()cr= 0.080327

~

~

0.14237

(Dn/DCJ)cr= 0.86548

4.3 CJn DD C2H4+3O2

4

__________________________________________________________________________________________________________

91

4.8. Dn/DCJ CJn DD 1

4.1 CJn DD 1 4.1 a~T C 4.1

CJn DD a~T C

C2H4+3O2 4.1 C2H4+3O2 a~T C10% CJn DD 4.2 a~T C 1 CJM a~T q~ K CJM

a

~T

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140.6

0.7

0.8

0.9

1.0

(= C ) [-]

Dn/D

CJ (

= D

n) [-

]


()cr= 0.049173

~

~

0.13109

(Dn/DCJ)cr = 0.83290 ( = 2.1173)

0.83268( = 1.0000)

4.5 CJn DD

2C2H2+5O2+7Ar

4

__________________________________________________________________________________________________________

92

CCC CJind,l C

C

4.2 C2H4+3O2

CJM a~T q~ CJpeq,Y K C Baseline 7.2528 1.3402 0.74480 1.3113 0.45481 1.1893 199.12 2.1270 12.860

1.1 7.2528 1.4742 0.67709 0.88619 0.45481 0.22649 39.015 2.1270 12.8609.0 7.2528 1.2062 0.82755 2.3094 0.45481 3.9447 9302.2 2.1270 12.860

a~1.1 T 7.2528 1.3402 0.81928 1.3113 0.45481 1.4601 199.12 2.1270 12.860

a~9.0 T 7.2528 1.3402 0.67032 1.3113 0.45481 0.44295 199.12 2.1270 12.860

C1.1 7.2528 1.3402 0.74480 1.3113 0.45481 1.1893 199.12 2.1270 14.147

C9.0 7.2528 1.3402 0.74480 1.3113 0.45481 1.1893 199.12 2.1270 11.574

4.6 ~ 4.8 CJn DD a~T C CJ 1.2 4.6 0.9 CJn DD 1 CJn DD 1 1 4.7 4.8 CJn DD a

~T C

1 a~T

CJn DD 1 1 0.5 ~ 2.0 115,116)

C CJn DD 1 1

CJn DD

4

__________________________________________________________________________________________________________

93

CJn DD

0.00 0.02 0.04 0.06 0.08 0.10 0.120.6

0.7

0.8

0.9

1.0

(= C ) [-]

Dn/D

CJ (

= D

n) [-

]

0.91025

()cr= 0.043275

: (baseline): 1.1: 0.9

(Dn/DCJ)cr= 0.81767

0.85682

0.080327

0.068855

~

~

4.6 CJn DD C2H4+3O2

4

__________________________________________________________________________________________________________

94

0.00 0.02 0.04 0.06 0.08 0.10 0.120.6

0.7

0.8

0.9

1.0

(= C ) [-]

Dn/D

CJ (

= D

n) [-

]

()cr= 0.088359

: C (baseline): 1.1C: 0.9C

(Dn/DCJ)cr= 0.85682

0.080327

0.072294

~

~

4.8 CJn DD C C2H4+3O2

0.00 0.02 0.04 0.06 0.08 0.10 0.120.6

0.7

0.8

0.9

1.0

(= C ) [-]

Dn/D

CJ (

= D

n) [-

](Dn/DCJ)cr= 0.87122

()cr= 0.084519

: Ta (baseline): 1.1Ta: 0.9Ta

0.856820.83972

0.0803270.073568

~~~

~

~

4.7 CJn DD a

~T C2H4+3O2

4

__________________________________________________________________________________________________________

95

4.9.

4.9.1. C2H4+3O2 1 T~ ~ fr~a n~u p~ ~ YM 4.9 ~ 4.16 0 cr 026776.0 4 n~ 0~ n 0~ n 1~ n CJind,l CJn DD 4.9 T~ cr 4.10 ~ ~ T~ 4.11 fr

~a 4.12 ~ 4.14 p~ ~ 4.15 CJ Y CJpY T~

4.9 T~ CJ 4.16 CJ CJ

CJ CJ

CJ

CJ CJ 10 Vasilev et al. 117,118) CJ CJ

CJ

4.10 CJ 0~ CJ

4

__________________________________________________________________________________________________________

96

0.1 0.5 1.0 5.0 10.0 50.00.00

0.05

0.10

0.15

0.20

0.25

0.30

-n [-]

T [-

]

~

: = 0.000000, Dn/DCJ = 1.00000: = 0.026776, Dn/DCJ = 0.97202: = 0.053551, Dn/DCJ = 0.93907: = 0.080327, Dn/DCJ = 0.85682

~

4.9 T~ C2H4+3O2

0.1 0.5 1.0 5.0 10.0 50.0

0.00

0.05

0.10

0.15

-n [-]

[-]

~


~

4.10 ~ C2H4+3O2

4

__________________________________________________________________________________________________________

97

0.1 0.5 1.0 5.0 10.0 50.00.2

0.3

0.4

0.5

0.6

0.7

0.8

-n [-]

a fr [

-]

~


~

4.11 fr~a C2H4+3O2

0.1 0.5 1.0 5.0 10.0 50.00.0

0.2

0.4

0.6

0.8

-n [-]

-un [

-]

~


~

4.12 n~u C2H4+3O2

4

__________________________________________________________________________________________________________

98

0.1 0.5 1.0 5.0 10.0 50.00.0

0.2

0.4

0.6

0.8

1.0

-n [-]

p [-

]

~


~

4.13 p~ C2H4+3O2

0.1 0.5 1.0 5.0 10.0 50.00.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

-n [-]

[-]

~


~

4.14 ~ C2H4+3O2

4

__________________________________________________________________________________________________________

99

0.1 0.5 1.0 5.0 10.0 50.00.0

0.2

0.4

0.6

0.8

1.0

-n [-]

Y [-

]

~


4.15 YC2H4+3O2

0.1 0.5 1.0 5.0 10.0 50.00.0

0.2

0.4

0.6

0.8

1.0

-n [-]

M [-

]

~


4.16 M C2H4+3O2

4

__________________________________________________________________________________________________________

100

4.9.2. CJn DD 1 CJn DD

p 1 CJn DD

4.284.23

2

fr

nn2

2fr

2

12

1211

dd

Ma

uDMwaqM

nM

4.46

2fr

2fr

2

12

11

Ma

waqM

4.47

2fr nn2

1212

MauDM

4.48

nM4.46 nM dd

C2H4+3O2 CJn DD 1 ~ ~ ~~ 4.17 0~ M

CJ

0w 0~ 0~~ M CJ

0~ 0~~ M

M

M 4.16

4

__________________________________________________________________________________________________________

101

*q

RTqq* 4.49

*q q~

qMq ~2CJ* 4.50

*q CJM *q

*Q

** YqQ 4.51 CJ

*CJp

*CJp qYQ C2H4+3O2 CJn DD 1

C2H4+3O2 CJn DD 85682.0crCJn DD 6.2144 C2H4+3O2

CJ CJ CJ 440.30* imCJp, Q 48.345*CJp Q im

0.1 0.5 1.0 5.0 10.0 50.0-0.10

-0.05

0.00

0.05

0.10

0.15

-n [-]

, ,

+

[-]

~

~~

~~

: : : +

~~~ ~

CJ pointOnset of ignition

4.17 CJn DD ~ ~ ~~ C2H4+3O2

4

__________________________________________________________________________________________________________

102

CJ

4.18 C2H4+3O2 CJn DD *Q M

440.30* imCJp, Q M 0.6 M 1M

905.17* Q *q

*q CJ

4.9.3. Dn/DCJ 4.3 ~ 4.5 CJn DD C2H4+3O2 CJn DD 1

CJn DD 4.19a cr 0.1% crCJn DD 0.1% 4 4.19bM

0.1 0.5 1.0 5.0 10.0 50.00

10

20

30

40

50

60

70

0.0

0.2

0.4

0.6

0.8

1.0

-n [-]~

Q* [

-] Q*

MQ*CJp

Q*CJp,im

: Q*: M

M [-

]CJ point

4.18 CJn DD *Q M C2H4+3O2

4

______________________________________

2840

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