Evaluation of hydrogen explosion hazards

1

EVALUATION OF HYDROGEN EXPLOSION HAZARDS:

PHENOMENOLOGY AND POTENTIAL FOR FLAME ACCELERATION AND DDT

Sergey DorofeevFM Global

Prepared for 4th

European Summer School on Hydrogen Safety Porticcio, Corsica, France, 7-16 September, 2009

2

Background

• Confined explosions

Internal loads

Pressure increase

• Unconfined explosions• Semi-confined

External loads

Blast waves

Confined and unconfined explosions

Enclosure or duct

Blast wave

PP

3

Background

•

H2

releases and transport of H2

- mixtures

represent significant safety problem

Tubes / ducts

–

Ventilation systems–

Exhaust pipes

Production facilities

Tunnels

•

Hydrogen: special attention because of high sensitivity to FA

Confined explosions

PP

4

Background

•

Slow subsonic flames –

mild hazards to confining structures

•

Fast flames (supersonic relative to a fixed observer) and detonations –

serious hazard

•

Possibility of FA to supersonic speeds limits implementation of mitigation techniques

explosion suppression

explosion venting

4 8 12t, s

0.00.40.81.2

0.6 0.8 1.0t, s

02468

10

0.2 0.210102030

P, bar

t, s

Detonation

Fast Flame

Slow Flame

Confined explosions -

hazards

5

Background

•

Release of hydrogen gas/liquid

•

Mixing with air and formation of “Vapor Cloud”

•

Ignition and flame propagation•

Generation of air blast wave

•

The problem is to evaluate blast parameters (P, I) = f(R) and blast effects

Unconfined explosions (VCE)

Blast wave

6

Background

•

Amplitudes of pressure waves generated by gaseous explosions depends on flame speed

•

There are solutions for P(R), I(R) as a function of flame speed

Vf

TNO multi-energy method (ME)

Baker-Strehlow-Tang (BST)

Kurchatov Institute (KI) method

•

The problem is to define flame speed

and explosion energy

Unconfined explosions (VCE) –

hazards

7

BackgroundP(R) for Various Flame Speeds

R* = R/(E/p0

)1/3

–

Sach’s

dimensionless distance

0.01

0.10

1.00

10.00

0.10 1.00 10.00R/(E/P0)1/3

(P-P

o)/P

o

gas detonationTNT400 m/s200 m/s100 m/s

8

Background

•

Explosions almost universally start by ignition of a flame

electrical spark

hot surface

•

Under certain conditions, flame can accelerate and undergo transition to detonation

•

Collectively this process is referred to as deflagration-to-detonation transition (DDT)

•

It is important to know critical conditions and resulting flame speeds → loads

Why FA and DDT?

9

Background

•

Significant advances made in understanding of FA and DDT

High resolution Schlieren

photography

Theoretical and advanced numerical studies

•

Basic mechanisms are well understood•

Yet there are limitations in predictive simulations of these complex phenomena

•

At present time, quantitative predictions typically rely on experiment based correlations

Understanding of FA and DDT

10

Background

•

This lecture presents a framework for estimating potential explosion hazards in hydrogen mixtures

•

Emphasis is placed on experimental correlations and analytical models

Basic physics

Simplified models

•

Accuracy within a factor of 2

Objective

11

Background

•

Few comments on basics of deflagrations and detonations

•

Description of FA and DDT •

FA and flame propagation regimes

FA in smooth tubes

FA in ducts with obstacles

Effects of initial/boundary conditions on FA

FA in unconfined clouds

•

Onset of detonations •

Summary of the framework

•

Concluding remarks

Outline

12

Deflagrations

•

Weak ignition results in LAMINAR FLAMES

•

Propagation mechanism: diffusion of temperature and species

•

Laminar burning velocity

•

Flame thickness

Laminar flames

srL cS

Fraction of reactants

Temperature

Reaction rate

Preheat zone,

Reaction zone, /

SL SL

Reactants Products

Tb

Tu

Y=1

Y=0

L

b

Lu

bb

ST

ST

)()(

13

Deflagrations

•

Laminar flames are intrinsically unstable

•

Hydrodynamic instability Landau-

Darrieus•

Thermal-diffusive instability

Le

= /DL

Le < 1 –

lean H2

flames

Flame instabilities

SL

SL

ReactantsProducts

t2 >t1t1

ReactantsProducts

t2 >t1t1DL

t1DL

t2 >t1

ReactantsProductsLe<1 Le>1

14

Deflagrations

•

Markstein: normal velocity of a curved flame, Sn

, may be expressed as in terms of flame stretch, = 2Sn

/Rf

Instabilities and flame stretch

LL

b

L

n

SMa

SL

SS

1 /bLMa

10% H2

/air

15

Deflagrations

•

Cellular flames in hydrogen mixtures

Cellular flames

Le

0.35 Le

1.0 Le

3.8

10%H2 in air 10%H2+5%O2+85%Ar 70%H2 in air

16

Deflagrations

•

Acoustic-flame instabilities •

Kelvin-Helmholtz (K-H) –

shear instability

•

Rayleigh-Taylor (R-T) •

Both K-H and R-T are triggered when flame is accelerated over an obstacle or through a vent

•

Powerful mechanisms for ducts with obstacles

More flame instabilities

17

DeflagrationsFlame instabilities

64 m3

18

Deflagrations

•

Laminar flames in initially quiescent mixture become turbulent

Development of flame instabilities

Growth of turbulence in the flame-generated flow

•

Preexisting turbulence

Turbulent flames

19

DeflagrationsFlame in turbulent flow

Reactants Products

20

Deflagrations

•

Flow instability results in the development of random oscillations superimposed on mean flow

•

r.m.s

velocity

•

Integral length and time scales LT

, T –

size and turnover time of the largest eddies

•

Kolmogorov

length and time scales: lK

, K – size

and turnover time of the smallest eddies

Viscous dissipation occurs at this scale

Scales of turbulence

uuu

0u

u

tu u

21

Deflagrations

•

ST

: propagation speed of turbulent reaction zone

•

n is uncertain

n ≈

1,

Le = (0.5-1) Kido et al.

Turbulent burning velocities

nLeL

SuF

SS T

LL

T ,,,,,'

ST

/SL

u′/SL

10

20

10 20 30

(ST

/SL

)max

= 10-20

quenching

nT

LL

T LeLSua

SS

6/12/1'

22

Detonations

•

1D detonation waves are unstable and transverse perturbations are formed

•

Spacing between transverse waves -

detonation cell size

-

is important parameter

•

The smaller is

the more reactive is the mixture

Structure of the front

Smoked foil after CH4

/air detonation

23

DDT Phenomenology

•

Early detonation studies (1900+) were in smooth tubes using weak ignition

Detonation wave produced at the end of the FA process

Flame run-up distance required to form detonation was considered mixture property

•

Chapman and Wheeler (1926) were the first to place obstacles in smooth tube to promote FA

•

Shchelkin

roughened tube by wire coil helix (1940)

Basic studies of DDT

24

DDT Phenomenology

•

Stroboscopic Schlieren

photographs by Urtiew

and Oppenheim (1966) –

a milestone in the study of

DDT phenomenon •

Photos showed initiation of detonation from local explosion within shock flame complex “explosion in the explosion”

•

Simulations of Elaine Oran and colleagues!

Explosion in the explosion

25

DDT PhenomenologyDetonation onset at flame front

26

DDT Phenomenology

•

Processes of DDT have been studied in smooth tubes

in channels with repeated obstacles

photochemical systems

hot turbulent jets

shock-flame interactions

other experimental situations

Studies of DDT

27

DDT Phenomenology

•

Following Lee & Moen (1980) and Shepherd & Lee (1991), DDT is divided into two phases:

1.

Creation of conditions for the onset of detonation by FA, vorticity

production, formation of jets, and

mixing of products and reactants; 2.

Actual formation of detonation itself or the onset of detonation

Phases of DDT process

28

DDT Phenomenology

•


1.






29

FA in smooth tubes

•

Different from tubes with obstacles

•

Boundary layer plays an important role

•

Thickness

of b.l. at flame positions increases during FA

Mechanisms

Flame

Flame

Flame

V(x)

V(x)

V(x)SW

SW

Flame(t1) Flame(t2) Flame(t3)

b. l.

b. l.

b. l. (t1)

b. l. (t2)

b. l. (t3)

(t1) (t2)(t3)

(x)

30

FA in smooth tubesFlame shapes in smooth tubes

Shadow photos of Kuznetsov, et al.

Boundary layer

31

FA in smooth tubes

•

Substantial experimental data accumulated on XDDT

•

Ambiguous data on the effect of tube diameter and detonation cell size

•

Different mechanisms

Flame acceleration

Onset of detonation

Run-up distances in smooth tubes

V

X

Csp

DCJ

XS XDDT

32

FA in smooth tubes

•

We focus on run-up distances to supersonic flames in relatively smooth tubes

•

An approximate analytical model to be described, which is based on the following ideas

Relate flame shape / burning velocity evolution and the flame speed

Describe boundary layer thickness ahead of an accelerated flame

Run-up distances Xs

33

FA in smooth tubes

•

Mass balance

•

Burning velocity ST

•

Boundary layer thickness

•

Xs

: V+ST

= Csp

Xs

in smooth tubes

V

ST

+ V

D

X d

Boundary layer

m

T DDSDV

)1(

4

2

6/12/1'

T

LL

T LSu

SS

Kd

XC

ln1

KdD

CDX S

ln1

3/721

3/1

2)1(

m

L

sp

DSc

= /D:

Two unknown parameters: m and

34

FA in smooth tubes

•

Data with V(X)

Kuznetsov

et al., 1999, 2003, 2005

Lindstedt

and Michels

1989

•

BR: 0.002 –

0.1•

SL

: 0.6 –

11 m/s•

Csp

: 790 -1890 m/s

•

D: 0.015 –

0.5 m•

XS

/D: 10 -

80

Experimental data

35

FA in smooth tubes

•

= 2.1 m

= -0.18

•

Accuracy 25%

Correlation of model and experimental data

0

20

40

60

80

0 20 40 60 80XS/D experiment

XS /

D m

odel

H2/Air D=0.174m

H2/Air D=0.52m

H2/O2/Ar D=0.174m

H2/O2/He D=0.174m

H2/O2 D=0.105mH2/O2 D=0.015m

H2/O2 D=0.05m smooth

H2/O2 D=0.05m rough

C2H4/Air D=0.051m

model = test

36

FA in smooth tubes

•

XS

/D slightly decreases with D for given BR•

Large XS /D for C3

H8

and CH4

–

no data on XS

& XDDT

in smooth tubes

Run-up distances as a function of D

BR = 0.01

020406080

100120140160180200

0.01 0.1 1 10D, m

XS /

D m

odel

H2 BR<0.1C2H4 BR<0.1C3H8 BR<0.1CH4 BR<0.1

37

FA in smooth tubes

•

Only XS /D-data with initial turbulence for C3

H8

& CH4

•

Correlate with effective SL

: SLeff

= 2.5SL

Run-up distances in “turbulent mixtures”

0

20

40

60

80

100

120

0 20 40 60 80 100 120XS/D experiment

XS /

D m

odel

Bartknecht, H2, C3H8, CH4, D=0.2-0.4 m

model = test

38

FA in obstructed channels

•

Obstacles control FA:

Strong increase of flame surface

Fast development of highly turbulent flame

Flame evolution in channels with obstacles

105 ms

112

118.3

10% H2-air. Shadow photos of Matsukov, et al.

39


•

Flame surface increase

Flame speed relative to fixed observer:

Vf

= SL

(Flame

area)/(Flow cross-section) > 10SL•

Turbulence generated in the flow ahead of the flame affect the burning velocity ST

Increase of burning velocity ST

/SL

up to about 10 to 20•

Total increase of flame speed relative to fixed observer: Vf

> 100SL

Two effects responsible for FA

40


Volume expansionFlow ahead of the flame

Turbulence + instabilitiesEnhanced combustion

More expansion

FA –

Feedback mechanism

41


•

Weak

FA results in slow unstable turbulent flame regimes

•

Strong

FA leads to fast flames propagating with supersonic speed relative to a fixed observer

Weak and strong FA

42

FA in obstructed channelsFlame structure –

weak

FA

43

FA in obstructed channelsFlame structure –

strong

FA

44

FA in obstructed channelsFlame speeds as a function of distance

H2-air BR=0.3

0 10 20 30 40 50 60 70x/D

0

400

800

1200

1600

2000

v, m

/s

520 mm10%H213%H2

80 mm10%H213%H2

174 mm10%H211%H212%H213%H215%H217.5%H2

H2

-air0 10 20 30 40 50 60 70

x/D

0

400

800

1200

1600

v, m

/s 520 mm10%H211%H2

80 mm10%H211%H213%H2

174 mm10%H211%H215%H225%H245%H2

Quasi-detonations

Fast flames

Slow flames

H2 - airBR = 0.6

45

FA in obstructed channelsCriteria for strong/weak FA

Effect of expansion ratio H2

-air at normal T, p

SLOW

FAST

2 3 4 5 6 7

0.0

0.5

1.0

1.5

2.0

v/c s

p

H2-air 174mmH2-air 174mmH2-air 520mmH2-air 520mmH2-O2-Ar 174mmH2-O2-Ar 174mmH2-O2-He 174mmH2-O2-He 174mmH2-O2-He 520mmH2-O2-N2 174mmH2-O2-N2 174mm

46

FA in obstructed channelsCriteria for strong/weak

FA

Effect of Markstein

number

-4 -2 0 2 4 6 8 10 12Mab

1

2

3

4

5

6

slow flameschoked flames and detonations

Increase of burning velocity with stretch

Decrease of burning velocity

with stretch

47

FA in obstructed channelsCriteria for strong/weak FAEffect of Zeldovich

number, β

2 3 4 5 6

1

2

3

4

5

6

Ma < 0slow flameschoked flames and detonations

3 4 5 6 7 8 9 10 11 12

1

2

3

4

5

6

7

8

9

Ma > 0slow flameschoked flames and detonations+- 8% deviation

H2 mixtures

CH - fuels

2

)(

b

uba

RTTTE

48

FA in obstructed channelsFlame –

high turbulence (u’/SL

)

Reactants Products

49


Quenching of the largest (=ALL) mixed eddies

:

16

)12/(

1

2/122

nn

n

Lee

n = 1

1

3

5

7

9

11

6 9 12 15

Le = 0.3Le = 1Le = 2

Only mixture properties

Criteria for strong/weak FA

3 4 5 6 7 8 9 10 11 12

1

2

3

4

5

6

7

8

9

Ma > 0slow flameschoked flames and detonations+- 8% deviation

H2 mixtures

CH - fuels

Experiment Theory

50


•

Flame shape is given by obstacle field

•

Burning velocity ST

is constant and equal to its max value ST

10SL

•

XS

is the distance where flame speed approaches Csp

•

XS

D for given mixture, BR, and initial T, p

Run-up distances Xs

X

R

Turbulent flame brush

ST

U

BRbBRa

cS

RX

sp

LS

11)1(10

Data:SL: 0.1–1.5 m/s

Csp

: 640–1900 m/s

51

Variations of Xs

•

XS

/D decreases with BR for given D•

FA is strongly promoted by obstructions

Run-up distances as a function of BR

D = 1 m

010203040

5060708090

0.01 0.1 1

BR

XS /

D m

odel

H2 BR<0.1C2H4 BR<0.1C3H8 BR<0.1CH4 BR<0.1H2 BR>0.3C2H4 BR>0.3C3H8 BR>0.3CH4 BR>0.3

Obstructed tube

BR>0.3Smooth

tube

52

Variations of Xs

•

XS

/D slightly decreases with D•

At sufficiently large d (so that BR>0.1) XS

/D drops

Run-up distances versus tube roughness, d

H2/air

0

10

20

30

40

50

60

70

0.01 0.1 1 10 100 1000 10000

d, mm

XS /

D m

odel

D=0.01m BR<0.1D=0.1m BR<0.1D=1m BR<0.1D=10m BR<0.1D=0.01m BR>0.3D=0.1m BR>0.3D=1m BR>0.3D=10m BR>0.3

53

Variations of Xs

•

Smooth tubes: XS

/D slightly decreases with D•

Obstructed tubes (BR>0.3): XS

/D independent of D

Run-up distances for various D

H2/air

0

10

20

30

40

50

60

70

0.01 0.1 1

BR

XS /

D m

odel


54

Variations of Xs

•

Decrease of the H2 from 30 to 12% leads to the increase of the run-up distances by a factor of 5

Effect of mixture composition

D = 0.1 m

0

50

100

150

200

250

300

0.01 0.1 1

BR

XS /

D m

odel

"30% H2, BR<0.1"20% H2, BR<0.115% H2, BR<0.112% H2, BR<0.130% H2, BR>0.320% H2, BR>0.315% H2, BR>0.312% H2, BR>0.3

55

Variations of Xs

•

Initial T and p affect SL

, Csp

, and •

Changes are specific to particular mixture

Effect of T and P on run-up distances

D = 0.1 m

0

510

1520

2530

3540

45

0.01 0.1 1

BR

XS /

D m

odel

298 K, 1 bar, BR<0.1353 K, 1 bar, BR<0.1353 K, 2 bar, BR<0.1498 K, 1 bar, BR<0.1298 K, 1 bar, BR>0.3353 K, 1 bar, BR>0.3353 K, 2 bar, BR>0.3498 K, 1 bar, BR>0.3

56


•

Pressure effect of a gas explosion essentially depends on the maximum flame speed

•

Congested and free clouds are of interest•

Flame speed increases due to:

Increase of the flame area in an obstacle field

Increase of the turbulent burning velocity during flame propagation

Flame speeds

R

fTf AA

SV

57

FA in unconfined cloudsModel for flame speeds•

Flame area –

flame folding due to obstacles

•

ST

–

Bradley’s correlation 3/12

2

)(341)1(

RxR

xySbaV Lf

ba

x

x

yRR

58

FA in unconfined cloudsFlame Speeds: Data•

Range of data used for evaluation of unknown parameters

1

10

100

1000

0.01 0.1 1 10 100Distance, m

Flam

e sp

eed,

m/s

x=45, y=4 mm H2x=33, y=4 mm H2x=31, y=4 mm H2x=18, y=1 mm H2x=12, y=1 mm H2x=10, y=1 mm H2x=9, y=0.65 mm H2x=7, y=0.65 mm H2x=6, y=0.65 mm H2x=39, y=5 cm C2H4x=22, y=5 cm C2H4no obstacles H2no obstacles C3H6Layer C3H8

59

FA in unconfined cloudsFlame Speeds: Model Calibration

1

10

100

1000

1 10 100 1000

Model flame speed, m/s

Exp.

flam

e sp

eed,

m/s

x=45, y=4 mm H2x=33, y=4 mm H2x=31, y=4 mm H2x=18, y=1 mm H2x=12, y=1 mm H2x=10, y=1 mm H2x=9, y=0.65 mm H2x=7, y=0.65 mm H2x=6, y=0.65 mm H2x=39, y=5 cm C2H4x=22, y=5 cm C2H4no obstacles H2no obstacles C3H6Layer C3H8 Layer C3H8Correlation

60


•

KI method (published in 1996)•

Dimensionless P*

and I*

are functions of flame

speed, Vf

, and R*

Link to blast parameters

),min( *2

*1

* PPP ),min( *2

*1

* III 3*2*3/4**

1 )/(0033.0)/(062.0)/(34.0 RRRP 968.0**

1 )/(0353.0 RI

))/(14.0/83.0(1 2**20

2*

2 RRcV

P f

))/(0025.0)/(04.0/06.0(14.011 3*2**

00

*2 RRR

cV

cV

I ff

61

FA in unconfined cloudsP(R) for Various Flame Speeds

R* = R/(E/p0

)1/3

–

Sach’s

dimensionless distance

0.01

0.10

1.00

10.00

0.10 1.00 10.00R/(E/P0)1/3

(P-P

o)/P

o

gas detonationTNT400 m/s200 m/s100 m/s

62


•

MERGE data –

heavy congestion and IST data –

unconfined H2

/air (R=10m)

Validation -

example

1

10

100

1000

1 10 100 1000Experimental P, kPa

Mod

el P

, kPa

CH4 MERGE

C3H8 MERGE

H2 ICT R=10munconfined

63


•

Stoichiometric mixtures and medium congestion y/x

= 0.33 and x = 1 m

Flame speeds -examples

0

50

100

150

200

250

300

350

400

0 5 10 15Distance, m

Flam

e sp

eed,

m/s

H2

C2H4

C3H8

CH4

64


•

Variable concentration•

Maximum concentration in the center,

Cmax

•

‘Worst case’: maximum flame speed parameter < >=<(-1)SL

>, averaged between UFL and LFL•

Properties of ‘worst case’:

Flame speed is a fraction of max,

Energy is a fraction of total chemical energy

Nonuniform

cloud –

‘worst case’

LFL

Cmax

UFL

65


•

‘Worst case’

clouds and medium congestion y/x

= 0.33 and x = 1 m

Flame speeds -

examples

0

50

100

150

200

250

300

350

400

1 10 100 1,000 10,000 100,000m, kg

Flam

e sp

eed,

m/s

H2

C2H4

C3H8

CH4

66


•

Total amount of H2

near the source is limited by buoyancy

•

Maximum mass of H2

near release can be estimated as

Engineering correlation for release rate

Release time t* is time for

buoyant displacement of

cloud with CLFL

=0.04 to be equal to size of cloud with C=CLFL

.

High pressure releases of H2

vvrd PAKCm 2'

5/35/1

2 2'*

gCmt

cloud

cloudair

HLFL

67


•

Estimate of maximum mass of H2

near the sourceHigh pressure releases of H2

0.001

0.01

0.1

1

10

100

1000

10000

0 200 400 600 800P, bar

m, k

g d = 1 mmd = 10 mmd = 100 mm

Release orifice

d

>10mm and high P are necessary for H2

clouds with m >10 kg and flame speeds > 80 –

100 m/s

68

DDT Phenomenology

•


1.






69

Onset of detonations

•

The key is to create conditions of localized explosion somewhere in the mixture

•

Two types of detonation onset phenomena:1.

Detonation initiation from shock reflection or focusing

2.

Onset of detonation caused by instabilities and mixing processes•

instabilities near the flame front

•

explosion of a quenched pocket of mixture •

P and T fluctuations in the flow and boundary layer

•

…

Types of detonation onset phenomena

70


•

Onset of detonation resulting from Mach reflection of lead shock of fast deflagration

Shock induced detonation initiation

71


•

Onset of detonation triggered by interactions of pressure waves, flame, and boundary layer

Onset of detonation caused by instabilities

Boundary layer

Flame front

72


•

Seemingly unrelated phenomena may be controlled by a single underlying mechanism

Shock Wave Amplification by Coherent Energy Release (SWACER)

Underlying mechanism

X

Induction time

Sequential ignition

Dsp

= (di

/dX)-1

Zeldovich

et al. theory 1970Lee et al. experiments and SWACER concept 1978

73

Onset of Detonations

1.

Conditions for localized autoignition should be created

2.

Gradient of induction time should provide coupling of chemistry and gasdynamics

to

create explosion wave3.

This wave should survive propagating thorough gradient of induction time and adjust itself to the chemical length scale of ambient mixture

Requirementst

X

Reaction length

Spontaneous flame Shock

wave

Compression wave

Reaction front

Sensitized mixture

Unperturbed mixture

•

1 and 2 require sufficiently high flame speed (~csp

)•

3 requires sufficiently large size of sensitized region (~10)

74

Onset of D in smooth tubes

•

Flame should reach a speed of about csp

See FA correlations

•

Min. scale requirement related to the tube size

Tube diameter should be greater than the detonation cell width D

> (Peraldi

et al.)

Kogarko

& Zeldovich, and Lindstedt

et al., argued

that D

> / should be used

Most conservative D

> / preferable for

applications

Necessary conditions

75

Onset of D in smooth tubes

•

Stoichiometric H2

-air, roughness=0.1mm, =10mm

DDT possible with D=10 cm at X > Xs ≈

4.5 m

Onset of D impossible with D < 3mm (D

> /)

Example

H2/air

0

10

20

30

40

50

60

70

0.01 0.1 1 10 100 1000 10000

d, mm

XS /

D m

odel


76

Onset of D in channels with obstacles

•

Flame should reach a speed of about csp

•

Scale requirement related to tube size

Size of unobstructed passage d/ > 1

d/ increases with decrease of obstacle spacing and with increase of BR

Variations of critical d/ can be quite large, from 0.8 to 5.1 for BR from 0.3 to 0.6

Necessary conditions: d/

77


•

Scale requirement related to possible macroscopic size of the sensitized mixture or characteristic mixture size L

For a channel or room with obstacles the characteristic size L

is given by

Necessary conditions: L/

HdSHL/1

2/)(

L

dSH

78


•

L/>7 correlation for predicting DO is applicable over wide range of scales

L/-criterion

2 3 5 2 3 5100 1000 10000Geometrical size L, mm

2

3

5

2

3

5

1

10

100

L/

d2

d2g3

s1

s1

s1

s1

s1

s1

t3

t3

t3

a1

a1a1a1

a1

a1

a1

a1

a1

a1a1

a1

a1

a1

a1

a1a1

f1

f3

r2

r2

r5

r5

r5

r5

r5r5

r5

r5r5

r6

r6

v2

b1b1

b1

b2

b2

b2b2

b4b4

b4

b4

b4

b5b5

b6b6

b6

b6

m3m3 m4m4m4 m5

d3

g1

g1g6

g6

g6

g7

g7

g7

g8

g8

g9

r1s2

s2

s2

r3

r4r4r4r4

r4

r4

r4r4

r7

v1

riri

d1

d1

t4

d2d2

g3

s1

a1a1

a1

a1

a1

a1

a1

a1

a1

a1

a1

a1a1a1a1

f1

f3

r2r2

r5

r5

r6v2

b1b1

b2

b2

b3b3

b4

b5b5b6b6

m3

m3m3

m4

m4m4 m5

m1m2

m6

m6m6

m7

m7m7

m8m8m8

g1g1

g1

g7

g7

g8

g8

r1r3r4

r4

r4r4

r4

r4

r4

r4

r7

r7v1

riri

ri

ri

No DDT, BR<0.5

No DDT, BR>0.5

& rooms

DDT, BR<0.5

DDT, BR>0.5

& rooms

L = 7

accuracy limits

79


•

Stoichiometric H2

-air, =10 mm

DDT possible with D=10 cm, BR=0.3 at X > Xs ≈

0.4m

Onset of D impossible with D = 1cm, BR = 0.6 (L<7)

Example

H2/air

0

10

20

30

40

50

60

70

0.01 0.1 1

BR

XS /

D m

odel


80

Onset of D in unconfined mixtures

•

There are several observations of onset of detonations

DO was observed as soon as flame speed reached a value of about 700200

m/s

With stoichiometric H2-air DDT observed in cloud containing 4 g of H2

Congested areas

81


•

No convincing observations of DO under truly unconfined conditions

Turbulent jet initiation

Sensitive mixtures in envelopes •

Shchelkin

22% C2H2 +78%O2

in 420mm rubber

sphere –

DO at 50 mm•

Gostintsev

et al. no transition, same mixture,

rubber sphere 600mm

No obstructions

82


•

Shchelkin

22% C2H2 +78%O2

in 420mm rubber sphere –

DO at 50 mm

Nearly unconfined DDT

83


•

Critical conditions: Djet

(14-24)

Turbulent jet initiation

Mixture

Hot jet

215 m3Detonation of H2-air initiated by hot turbulent jet of combustion products

84

Summary

1.

In order for FA to be strong, a sufficiently large expansion ratio σ

= ρu

/ρb

> σ* is necessary •

σ* depends on the mixture composition and initial T and P

2.

Even if σ

> σ*, tube diameter should be > 102 laminar flame thickness ()

3.

If strong

FA is possible (σ

> σ*, D > 102), a sufficiently large run-up distance Xs

is necessary for actual development of supersonic combustion regimes

Evaluation of potential for FA and DDT

Vflame

= f(R) ≤

Csp

85

Summary

4.

If supersonic regime is developed, detonation may only occur if the size of a duct or mixture volume is sufficiently large compared to

D

/, where D

is the internal diameter of a

smooth tube

d

, where d

is the transverse dimension of the

unobstructed passage in a channel with obstacles

L

7, where L

is a more general characteristic

size defined for rooms or channels

Djet

(14-24) , where Djet

refers to the exit diameter of the jet

Detonation is possible

86

Concluding Remarks 1

•

There are many spatial and temporal physical scales involved in FA and detonation

•

These scales are given by chemistry, turbulence, and confinement

•

The interplay of these scales control major

features and thresholds,

Onset of instabilities & flame structure,

Onset & structure of detonations•

Wide range of the scales makes it difficult to resolve all the phenomena from first principles

•

However, it is the comparison of scales that give us a way to approach practical problems

87

Concluding Remarks 2

•

Critical conditions for strong FA and the onset of detonation are formulated as necessary criteria

•

Uncertainties are related to

Critical values of mixture expansion ratio,

Detonation cell size data

Laminar burning velocity and flame thickness

Effect of the Lewis number

Issues in respect to changes of thermodynamic state of unburned mixture during FA, which can change the critical conditions for DDT

•

All should be taken into account in practical applications

88

Questions?

89

Deflagrations

•

Laminar burning velocity

•

Zeldovich

number

•

Flame thickness

Laminar flames –

one step reaction

rnbn

nLTLeS

11

)(21

2

)(

b

uba

RTTTE

L

b

Lu

bb

ST

ST

)()(

LS

90

Deflagrations

•

Stretch may be created by both flame curvature (c

) and strain rate (s

) •

Flames with negative Ma, such as lean H2

-air mixtures, are known to be extremely unstable

•

For >> 1, parameter (Le – 1) defines the value and the sign of Ma

Markstein

number

1

0

1)1()1(2)1(ln

1

dx

xxLeMab

ssccnL MaMaSS

91

DeflagrationsTurbulent combustion regimes

Borghi

diagram

PLIF images of flame structure for various regimes –

U-Munich

u'/SL

1 10 100 1000

1

10

100

LT /

LT

=

lK

=

Laminar flamelets

Thick flames

Well stirred reactor

FA in given geometry

92

Detonations

•

1D model

Chapman Jouguet Detonation

QUu3

P11

P33

Shock waveReaction zone

P/P1

/

1

1

J

V

P1

C

Equilibrium

Hugoniot

Rayleigh Line2

Shock

Hugoniot

13 )1(2 aQDCJ

Documents

Evaluation of hydrogen explosion hazards