flame acceleration and ddt: a framework for … · flame acceleration and ddt: a framework for...

1

FLAME ACCELERATION AND DDT: A FRAMEWORK FOR ESTIMATING POTENTIAL

EXPLOSION HAZARDS IN HYDROGEN MIXTURES

Sergey DorofeevFM Global

Prepared for 3rd European Summer School on Hydrogen Safety Belfast, 21-30 July 2008

2

Background

• Confined explosionsInternal loadsPressure increase

• Unconfined explosions• Semi-confined

External loadsBlast 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 facilitiesTunnels

• 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

ΔP, 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 photographyTheoretical 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 physicsSimplified models

• Accuracy within a factor of 2

Objective

11

Background

• Few comments on basics of deflagrations and detonations

• Description of FA and DDT • Critical conditions for FA and onset of detonation

FA in smooth tubes FA in ducts with obstaclesEffects of initial/boundary conditions on FAFA in unconfined cloudsOnset 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 <<∝ τχ

Fraction of reactants

Temperature

Reaction rate

Preheat zone, δ

Reaction zone, δ/β

SL σSL

Reactants Products

Tb

Tu

Y=1

Y=0

L

b

Lu

bb

ST

ST

σχ

ρχρδ )()(

==

13

Deflagrations

• Laminar flames are intrinsically unstable

• Hydrodynamic instability Landau-Darrieus

• Thermal-diffusive instability

Le = χ/DL

Le < 1 – lean H2 flames

Flame instabilities

SL

σSL

ReactantsProducts

t2 >t1t1

ReactantsProducts

t2 >t1t1DL

χ

t1DL

χ

t2 >t1

ReactantsProductsLe<1 Le>1

14

Deflagrations

• Cellular flames in hydrogen mixtures

Cellular flames

Le ≈ 0.35 Le ≈ 1.0 Le ≈ 3.810%H2 in air 10%H2+5%O2+85%Ar 70%H2 in air

15

Deflagrations

• Acoustic-flame instabilities • Kelvin-Helmholtz (K-H) – shear instability• Rayleigh-Taylor (R-T)

Richtmyer-Meshkov (R-M) in compressible flows

• 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

16

DeflagrationsFlame instabilities

64 m3

17

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

18

DeflagrationsFlame in turbulent flow

Reactants Products

19

Deflagrations

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

• r.m.s velocity

• Integral length and time scales LT , τT – size and turnover time of the largest eddies

• Kolmogorov length and time scales: lK , τK – size and turnover time of the smallest eddies

Viscous dissipation occurs at this scale

Scales of turbulence

uuu ′+=

0≡′u

u

tu u′

20

Deflagrations

• ST : propagation speed of turbulent reaction zone

• n is uncertainn ≈ 1, Le = (0.5-1)Kido et al.

Turbulent burning velocities

⎟⎟⎠

⎞⎜⎜⎝

⎛= nLeL

SuF

SS T

LL

T ,,,,,' σβδ

ST/SL

u′/SL

10

20

10 20 30

(ST/SL)max = 10-20

quenching

nT

LL

T LeLSua

SS −⎟

⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

6/12/1'

δ

21

Detonations

• 1D detonation waves are unstable and transverse perturbations are formed

• Spacing between transverse waves - detonation cell size λ - is important parameter

• The smaller is λ the more reactive is the mixture

Structure of the front

Smoked foil after CH4/air detonation

22

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

23

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

24

DDT PhenomenologyDetonation onset at flame front

25

DDT Phenomenology

• Processes of DDT have been studied in smooth tubes

in channels with repeated obstaclesphotochemical systemshot turbulent jetsshock-flame interactionsother experimental situations

Since that time

26

DDT Phenomenology

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

1. Creation of conditions for the onset of detonationby 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

27

DDT Phenomenology





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FA in smooth tubes

• Different from tubes with obstacles

• Boundary layer plays an important role

• Thickness Δ 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)

Δ(t1) Δ(t2)Δ(t3)

Δ

Δ

Δ

Δ(x)

29

FA in smooth tubesFlame shapes in smooth tubes

Shadow photos of Kuznetsov, et al.

Boundary layer

30

FA in smooth tubes

• Substantial experimental data accumulated on XDDT

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

• Different mechanismsFlame accelerationOnset of detonation

Run-up distances in smooth tubes

V

X

Csp

DCJ

XS XDDT

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FA in smooth tubes

• We focus on run-up distances to supersonic flamesin 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 speedDescribe boundary layer thickness ahead of an accelerated flame

Run-up distances Xs

32

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 Δ d

Boundary layer

m

T DDSDV ⎟

⎠⎞

⎜⎝⎛ Δ

−Δ= )1(4

2

σπαπ

6/12/1'

⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛=

δϕ T

LL

T LSu

SS

Kd

XC +⎟⎠⎞

⎜⎝⎛ Δ

=Δ

ln1κ

⎥⎦

⎤⎢⎣

⎡+⎟

⎠⎞

⎜⎝⎛= KdD

CDX S γ

κγ ln1

3/721

3/1

2)1(

+

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

−=

m

L

sp

DSc δ

σβγ

γ = Δ/D:

Two unknown parameters: m and β

33

FA in smooth tubes

• Data with V(X)Kuznetsov et al., 1999, 2003, 2005Lindstedt 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

34

FA in smooth tubes

• β = 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

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FA in smooth tubes

• XS/D slightly decreases with D for given BR• Large XS /D for C3H8 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

36

FA in smooth tubes

• Only XS /D-data with initial turbulence for C3H8 & 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

37

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.

38


• Flame surface increaseFlame speed relative to fixed observer:Vf = SLσ(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

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Volume expansionFlow ahead of the flame

Turbulence + instabilitiesEnhanced combustion

More expansion

FA – Feedback mechanism

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• 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

41

FA in obstructed channelsFlame structure – weak FA

42

FA in obstructed channelsFlame structure – strong FA

43

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

44

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 7σ

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

45

FA in obstructed channelsCriteria for strong/weak FAEffect of Markstein number

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

1

2

3

4

5

6

σ

slow flameschoked flames and detonations

Increase of burning velocity with stretch

Decrease of burning velocity with stretch

46

FA in obstructed channelsCriteria for strong/weak FAEffect of Zeldovich number, β

2 3 4 5 6β

1

2

3

4

5

6

σ

Ma < 0slow flameschoked flames and detonations

3 4 5 6 7 8 9 10 11 12β

1

2

3

4

5

6

7

8

9

σ

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

H2 mixtures

CH - fuels

2

)(

b

uba

RTTTE −

=β

47

FA in obstructed channelsFlame – high turbulence (u’/SL)

Reactants Products

48


Quenching of the largest (=ALL) mixed eddies :

16

)12/(

1

2/122

=Γ−

+

−

κββσ β

nn

n

Lee

n = 1

1

3

5

7

9

11

6 9 12 15β

σ

Le = 0.3Le = 1Le = 2

Only mixture properties

Criteria for strong/weak FA

3 4 5 6 7 8 9 10 11 12β

1

2

3

4

5

6

7

8

9

σ

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

H2 mixtures

CH - fuels

Experiment Theory

49


• 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

Ω

Turbulent flame brush

ST

U

BRbBRa

cS

RX

sp

LS

⋅+−

≈−

11)1(10 σ

Data:SL: 0.1–1.5 m/sCsp: 640–1900 m/s

50

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

51

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

52

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


53

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

54

Variations of Xs

• Initial T and p affect SL, Csp, and σ• 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

55

FA in unconfined clouds

• 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 σ=

56

FA in unconfined cloudsModel for flame speeds• Flame area – flame folding due to obstacles

• ST – Bradley’s correlation 3/12

2

)(341)1( ⎟

⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛+−=

δσσσσ α

α RxR

xySbaV Lf

ba

∼σx

x

yRR

57

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

58

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

59


• 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 −−

=σ

σ

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

00

*2 RRR

cV

cV

I ff −+⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

−=

σσ

σσ

60

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

61


• 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

62


• 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

63


• Variable concentration• Maximum concentration in the center, Cmax

• ‘Worst case’: maximum flame speed parameter <γ >=<σ(σ-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

64


• ‘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

65


• 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 ρ2'=

5/35/1

2 2'*

−

⎟⎟⎠

⎞⎜⎜⎝

⎛ −⎟⎟⎠

⎞⎜⎜⎝

⎛=

gCmt

cloud

cloudair

HLFL ρρρ

ρξ

66


• 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

67

DDT Phenomenology





68

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 focusing2. 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

69


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

Shock induced detonation initiation

70


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

Onset of detonation caused by instabilities

Boundary layer

Flame front

71


• Seemingly unrelated phenomena may be controlled by a single underlying mechanism

Shock Wave Amplification by Coherent Energy Release (SWACER)

Underlying mechanism

τ

X

Induction time

Sequential ignition

Dsp = (dτi/dX)-1

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

72

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 wave

3. 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 (~10λ)

73

Onset of D in smooth tubes

• Flame should reach a speed of about cspSee FA correlations

• Min. scale requirement related to the tube sizeTube diameter should be greater than the detonation cell width D > λ (Peraldi et al.)Kogarko & Zeldovich, and Lindstedt et al., argued that D > λ/π should be usedMost conservative D > λ/π preferable for applications

Necessary conditions

74

Onset of D in smooth tubes

• Stoichiometric H2-air, roughness=0.1mm, λ=10mmDDT possible with D=10 cm at X > Xs ≈ 4.5 mOnset of D impossible with D < 3mm (D > λ/π)

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


75

Onset of D in channels with obstacles

• Flame should reach a speed of about csp

• Scale requirement related to tube sizeSize of unobstructed passage d/λ > 1d/λ increases with decrease of obstacle spacing and with increase of BR Variations of critical d/λ can be quite large, from 0.8 to 5.1 for BR from 0.3 to 0.6

Necessary conditions: d/λ

76


• 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/λ

HdSHL/1

2/)(−+

=

L

dSH

77


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

L/λ-criterion

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

2

3

5

2

3

5

1

10

100

L/ λ

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 = 7λ

λ accuracy limits

78


• Stoichiometric H2-air, λ=10 mmDDT possible with D=10 cm, BR=0.3 at X > Xs ≈ 0.4mOnset of D impossible with D = 1cm, BR = 0.6 (L<7λ)

Example

H2/air

0

10

20

30

40

50

60

70

0.01 0.1 1

BR

XS /

D m

odel


79

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 700±200 m/sWith stoichiometric H2-air DDT observed in cloud containing 4 g of H2

Congested areas

80


• No convincing observations of DO under truly unconfined conditions

Turbulent jet initiationSensitive 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

81


• Shchelkin 22% C2H2 +78%O2 in 420mm rubber sphere – DO at 50 mm

Nearly unconfined DDT

82


• Critical conditions: Djet ≥ (14-24)λ

Turbulent jet initiation

Mixture

Hot jet

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

83

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 (δ)

3. If strong FA is possible (σ > σ*, D > 102δ), 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

84

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 λ

D ≥ λ/π, where D is the internal diameter of a smooth tube d ≥ λ, where d is the transverse dimension of the unobstructed passage in a channel with obstaclesL ≥ 7λ, where L is a more general characteristic size defined for rooms or channels Djet ≥ (14-24)λ , where Djet refers to the exit diameter of the jet

Detonation is possible

85

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

86

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 dataLaminar burning velocity and flame thicknessEffect 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

87

Questions?

88

Deflagrations

• Laminar burning velocity

• Zeldovich number

• Flame thickness

Laminar flames – one step reaction

rnbn

nLTLeSτβ

χσ 11

)(21++Γ=

2

)(

b

uba

RTTTE −

=β

L

b

Lu

bb

ST

ST

σχ

ρχρδ )()(

==LS

νδ =

89

Deflagrations

• Markstein suggested that normal velocity of a curved flame, Sn, may be expressed as in terms of flame stretch, α = 2Sn/Rf

Instabilities and flame stretch

αδα

LL

b

L

n

SMa

SL

SS

==−1

δ/bLMa =

90

Deflagrations

• Stretch may be created by both flame curvature (αc) and strain rate (αs)

• Flames with negative Ma, such as lean H2-air mixtures, are known to be extremely unstable

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

Markstein number

⎟⎟⎠

⎞⎜⎜⎝

⎛ +−⋅

−−

+−

= ∫−1

0

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

1

σσ

σβσ

σσ dx

xxLeMab

ssccnL MaMaSS δαδα +=−

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/δ

LT = δ

lK = δ

Laminar flamelets

Thick flames

Well stirred reactor

FA in given geometry

92

Detonations

• 1D model

Chapman Jouguet Detonation

QUu3

P1ρ1

P3ρ3

Shock waveReaction zone

P/P1

ρ1/ρ

1

1

J

V

P1

C

EquilibriumHugoniot

Rayleigh Line2

ShockHugoniot

13 )1(2 aQDCJ >>+≅ γ

flame acceleration and ddt: a framework for … · flame acceleration and ddt: a framework for...

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