detonation in gases - joseph shepherd

1

Detonation in Gases

Joseph E Shepherd

Aeronautics and Mechanical EngineeringCalifornia Institute of Technology

Pasadena, CA 91125 USA

Combustion SymposiumMcGill University August 2008

3

Marcelin Berthelot Paul Vielle

Ernest Mallard Henry Le Chatelier

1881

2006

4



C3H8+5O2 20 kPa

5



6

Donald Chapman Ehrile Jouguet

1889-1905

7


8


or

Sonic flow relative to wave

9

Yakov Zel’dovich John von Neumann Werner Döring

”ZND’’ 1940-43

Cold fuel/oxidizer mixture

shock

induction zone

products

Temperaturereactants

radicals

Energy release

products

Sonicplane

10

”ZND’’ 1940-43

P

v1

CJ

vN

11

”ZND’’ 1940-43

21

21

1

2

2

M

udxdPu

Mu

dxduu

Mdxdu

-

-=

-=

--

=

sr

s

srr

&

&

&

law rate kineticby given :

where,,1

2

i

Ye

N

i i

i

ii

ikYP

cσ

dxdYu

W

÷÷ø

ö¶¶W

=

W=

¹

å= r

r&srr &2ccdudP +±=

thermicity

12

”ZND’’ 1940-43

13

G. I. Taylor

X

particle path

t

0

2

1

3 Stationary region

14Bach et al 1969

18

Erpenbeck 1964, Lee and Stewart 1990, Short, Sharpe, Kasimov, Tumin, …

19

scale:4mm

2H2-O2-85%ArPo=20kPa

C3H8-5O2-60%N2Po=20kPa

20

• Cell width measurements

Soot foil:

l

21

Strehlow 1967 2H2+O2+7Ar

Gamezo et al 1999 E/RT = 7.4 DY/Dt = -A(1-y) exp(-E/RT)

22

2H2+O2+12Ar

2H2+O2+17Ar

H2+N2O+1.33N2

C3H8+5O2+9N2Austin 2003

23Pintgen et al 2003

24

[OH]ÑrPintgen 2000

2H2+O2+17Ar, 20kPa cellsize: 48 mmZND-calculated Induction-zone-length at CJ-state: 1.6 mm

26Austin 2003

29

2H2+O2+17Ar 2H2+O2+ 8 N2 H2+ N2O +3 N2

C2H4-3O2-10.5N2 C3H8-5O2-9N2 C3H8-5O2-9N2

31

Ng et al 2005

Eckett 2000

32Daimon & Matsuo 2008

P

1

CJ

V

f > 1

f = 1

33

ti – Induction Time

te – Energy Release Pulse Width

Stoichiometric H2-Air post-shock state for CJ detonation, pre-shock conditions: 1 atm, 300 K

Mechanism: GRI 3.0

q – Reduced Effective Activation Energy

ti/te

q = Ea/RT

34

02468

101214161820

0 2 4 6 8 10MCJ

Ea/R

T SNeutral stabilityboundaryC3H8-O2-N2

H2-O2-N2

H2-O2-AR

H2-N2O-N2

H2-N2O-O2-N2

H2-O2-CO2

C2H4-O2-N2

f=1

weakly unstable (low Ea/RTS)

highly unstable (high Ea/RTS)

stable

unstable

35Ng et al 2005

37

H2-O2 Chemistry: Explosion Limits

Lewis & von Elbe (1961)Extended Second Limit

H2O2 Enables Explosion

2

3

1

Classical Explosion Limits

HO2 Diffuses to Walls

Voevodesky & Soloukhin (1965)

2’

2

3

38

H2-O2 Chemistry: Two Pathways

• Chain-Branching Pathway

• Peroxide Straight-Chain Pathway

H + O2 ! OH + O R2(Rate Limiting Step)

O + H2 ! OH + H

OH + H2 ! H2O + H

H + O2 + M ! HO2 + M

HO2 + HO2 ! H2O2 + O2

H2O2 + M ! 2 OH + M R1(Rate Limiting Step)

39

Stoichiometric H2-Air

Rich H2-Air φ = 3.0

Lean H2-Air φ = 0.8

40


Competition

Stoichiometric H2-Air

Branching Pathway Dominant


Peroxide Pathway Dominant

Initial Conditions

T = 300 K, P = 0.7 atm

Browne, Liang, Shepherd 2005

41

Detonation limits?

H + O2 ! OH + O R1

H + O2 + M ! HO2 + M R2

r2/r1 = a

a=2

a=1

Cross-over Temperature Cannot Predict Limits

42Stoichiometric

C2H2-AirStoichiometric

C3H8-AirStoichiometric

C2H4-Air

Stoichiometric CH4-Air

Stoichiometric C2H6-Air

43

Ratio of Time Scales (τi/τe)

Stoichiometric H2-Air Stoichiometric C2H2-Air



44

Hydrocarbon Oxidation• Many Pathways

CO Oxidation• CO + O2 ! CO2 + O

• CO + OH ! CO2 + H

• CO + HO2 ! CO2 + OH

CH4 Oxidation• CH4 + X ! CH3 + XH

• CH3O + M ! H2CO + H + M

• H2CO + X ! HCO + XH

• HCO + M ! H + CO + MAdditional Pathways Can Bypass

Competition Effect

NO CROSS-OVER TEMPERATURE

46

Psuedo species: R (H2, O2), B (OH, H, O), C (HO2, H2O2), Pr(H2O)

Modeling Competing RadicalsHydrogen Chemistry

Shepherd PAA 86Model Chemistry

MMBB

BC

MCMBR

BBR

BR

K

K

K

K

K

2Pr)5(

2)4(

)3(

2)2(

)1(

5

4

3

2

1

+®++

®

+®++

®+

®

ïî

ïí

ì

+«++«++«+

HOHHOHHOHHОOOHOH

22

2

2

MHOMOH +«++ 22

HHOOH +®+ 222

îíì

+«++®+MOHMOHOOHHOHO

222

22222

MOHMOHH +«++ 2

Initiation

Branchingpathway

Peroxidepathway

Termination

Dold & Kapila CF 91, Short & Quirk 97 JFM

Browne, Liang, Shepherd 2005

47

Case1Ucj=1785 m/s q=4.3U=0.85Ucj q=7.2

Case2 Ucj=1390 m/s q=10U=0.85Ucj q=29

Effective Activation Energy q

Extended second limitr3 =1.5r2

2H2+O2+17Arq~5

48

Case 1 Case 2Ucj D=0.029 mm Di/De=0.9

85%Ucj D=0.16 mm Di/De =1.5Ucj D=0.64 mm Di/De=1.3

85%Ucj D=275 mm Di/De =33

YB is much larger than YC YB is comparable with YC

Case 2ZND Structures

49

Case 1 regular structure

Case 2 irregular structure

Unburned

Unburned

YB (OH)

YB (OH)

Species “B” (OH, H, or O)

50

Case 1 regular structure


Case 1

Case 2

Inaba & Matsuo 2001

reactingtransversedetonation

Gamezo et.al 2000

51

1 1

123

2 2

33

Case 1 Case 2

CJ

CJ

UUU

123.0==

d

CJU068.0=d

CJU087.0=d

CJ

CJ

UUU

123.0==

d

CJU132.0=d

CJU116.0=d

Fluctuations in Shock Velocity

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• Mean velocity for both cases• Most likely velocity for both,

lower for irregular mixture

• Regular mixture: 0.8 UCJ~1.35 UCJ

• Irregular mixture: 0.7 UCJ~1.5 UCJ

CJUU =

CJUU <

•`Regular mixture:

- most likely

• Irregular mixture

- most likely

- faster decay rate!

tCJU

dtdU 08.0»-

tCJU

dtdU 2.0»-

Case 1

Case 2

Case 1

Case 2

PDF – Velocity, Acceleration

53

123

CJD=D 993.1

CJD= 247.1d

CJD=D 728.1

CJD= 697.0d

CJD=D 732.1

CJD= 963.0d

Case 1

CJD=D 961.0

CJD= 084.0d

CJD=D 9637.0

CJD= 1592.0d

CJD=D 0746.1

CJD= 1137.0d

Case 2Fluctuations in Reaction Length

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• Regular mixture • Most likely

• Irregular mixture

CJD>D

CJD>D

CJDDD ~~

• Regular mixture slower acceleration• Irregular mixture faster acceleration

Case 1

Case 2

PDF – Reaction thickness

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Probability of D of Case 1

regular mixture • steady (F(U)) and unsteady (D) reaction thickness is highly correlated; • quasi-steady reaction zone.

irregular mixture • steady (F(U)) and unsteady (D) reaction thickness is less correlated;• unsteady reaction zone

)(UF=D

quasi-steady unsteady

Probability of D of Case 2

)(UF=D

Influence of Unsteadiness

56

Critical shock decay rate

Eckett, Quick, Shepherd JFM 2000

( ) ( ) ( ) ( )tP

tuu

dtdUuuUu

xRj

RTEZQkM

DtDTCM a

P ¶¶

+¶¶

-+--

+÷øö

çèæ -

--=-r

g 1exp111 222

tgg

S

acd

d RTEt

dtdU

Ut 116 11

, +-

==

57

.Quenching td < td,c.

Eckett et al 1999

Coupling, td > td,c.

58

Joint Probability of U & D of case 1 Joint Probability U & D of case 2

regular mixture steady relation of U and D is close to the most likely unsteady solution.

irregular mixture large difference between steady and unsteady relation.

Joint PDF (D, U)

59

• Irregular structure larger ratio between max D and min Dchallenge for experimental measurements and computations

Case 1 regular

structure


Fluctuations in spatial scales

61

Propagation limit in small tubes

62

Quenching in porous tubes

Radulescu and Lee Comb Flame 2002

63Radelescu et al 2005, Radelescu, Law, Sharpe 2005

E/RT = 11

CH4+2O2

Formation of unburned “pockets”

64

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

00.20.40.60.81

heat release fraction before sonic surface

U/U C

J

Diffusive burning?

65

CH4-air

66from N. Peters (2000) Turbulent Combustion

67

Warm reactants

Hot products

2H2–O2–5.6N2C3H8–5O2–9N2

Massa, Austin, Jackson 2007

[OH]

68

Stoichiometric hydrogen-oxygen mixture at an initial pressure of 20 kPa

7.4 mm

77 mm 500 nm l/L = 74,000

Large range of spatial & temporal scales

69N. Tsuboi & A. K. Hayashi 2007

71

Needs

• Scientific studies of turbulence– Experiments with quantitative data on

statistics of flow field– Statistical analysis of high-fidelity numerical

simulations• Engineering models of turbulent fronts

– Subgrid scale models for quantitative prediction and analysis

72

Thank You!• Past students and postdoctoral scholars, particularly

– Joanna Austin– Florian Pintgen– Rita Liang

• Financial and Institutional support– California Institute of Technology– US DOE– US NRC– ONR– GE Global Research– Sandia, Los Alamos, and Lawrence Livermore National

Laboratories

detonation in gases - joseph shepherd

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