IX. Detonation Waves

8/3/2019 IX. Detonation Waves

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6/20/2007 Detonation 5

Chemical kinetics is initiated behind the shockwave

In connection with the problem of the process of the chemical

reaction in a detonation wave, the objections raised against theconceptions of Le Chatelier and Vieille of the 19th century with regardto the ignition of the gas by the shock wave are refuted. Ya. B.Zeldovich On the theory of the propagation of detonation in gaseoussystems JETP 1940

Ya. B. Zeldovich 1940

J. H. von Neumann 1942

W. Dring 1943

Detonation as a shock-initiated,

convected explosion of combined

chain-thermal nature


Wave Speed is Determined by Thermodynamics

CJ Hypothesis:

1. Wave travels at slowest possible speed consistent with themodynamics

2. Product velocity relative to wave is sonic (= sound speed)

Physical explanation:Expansion waves catch up to wave and slow it down until CJ state is reached.

6/20/2007 Detonation 7 6/20/2007 Detonation 8

Steady Reaction Zone

lawratekineticbygiven:

where

21

2

1

1

,,12

2

2

i

Ye

N

i i

i

i

i

ik

YP

c

dx

dYu

M

u

dx

dPu

M

u

dx

duu

Mdx

du

C2H4

CO2

H2O

CO

C2H4-3O2-9N2, 20kPa Warnatz

OH

H

O

Convection-reaction balance


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C2H4-3O2-9N2, 20kPa Warnatz

Characteristic thicknesses determined by energyrelease time and rate

Characteristic induction zone width

Characteristic energy release zone width

2ccdudP


Chemical Length and Time Scales

0.8 1 1.2 1.4

10-2

10-1

100

Normalized velocity, U/UCJ

InductionZonelength,cm

0 0.5 10

1000

2000

3000

0

0.01

0.02

0.03

0.04

0.05

OH

T

Distance, cm

Temperature,

K

OH

mole

fraction

2H2-O2-60%N2


Measuring Detonations

GDT

280mm diameter, 7.3m long

Velocity from time of arrival

Pressure from piezoelectric gaugesCell size from soot foils

Structure from schieren, shadowgraph, PLIF imaging


Propagating Pressure Wave


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Taylor-Zeldovich Expansion Wave

closedend

L

x

particle path

t

0

openend

2

1 - at rest

3

detonation

expansion fan

Stationary region


Multifront waves

150 x 150 mm

Schlieren OH emission


Laminar and Turbulent Detonations

scale:4mm

2H2-O2-85%Ar

Po=20kPa

C3H8-5O2-60%N2

Po=20kPa


Turbulent detonations?2H2+O2+2CO

0.0263 atm 2.7 km/s 0.3 atm 2 .2 km/s

Generalizations of available observations suggests that turbulence

is a common property of detonation waves. This leads to the

speculation that perhaps the limits of propagation of detonation arein part by the conditions required for generating and maintaining a

turbulent zone of combustion. D. R. White Turbulent Structure of

Gaseous Detonation PF 1961

Overdriven Near CJ


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Cellular Structure of Detonations

H2+O2+7Ar mixture

Self-propagating near CJ velocity


The sooted foil and cellular structure

C2H4-O2 75% Ar H2-O2 40% Ar C3H8-O2 C2H2-O2

Notice that because of its innate complexity, there is virtually no hope that

theoreticians will piece together an a prioritheory for detonation structure; they

must necessarily rely on detailed experimental observations. R. A. Strehlow

1970

Equilibrium Configurationtime average steady

B.V. Voytsekhovsky and V.V. Mitrofanov and M.Ye. Topchiyan "The

Structure of a Detonation Front in Gases 1966


Detonation Cell Widths

Cell width measurements

A sooted aluminum sheet

Soot foil:

1 < < 1000 mm, ~ A


Cell SizeMeasurements forCommon Fuels

Data from R. Knystautas,McGill university

CH4C4H10C3H8C2H6

H2C2H2

Fuel Smoke PressureFoil Oscillations

EQUIVALENCE RATIO

DETONATION

CEL

LSIZE

(cm)

0 1 2 3 4

100

50

20

10

5

2

1

0.5

0.2

C2H4


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Chemical structure of DetonationPLIF and Schlieren Images


How PLIF works

B12 : stimulated absorptiion

B21: stimulated emission

P2: predissociation

Q21: collisional quenching

A21: spontanious emission

Signal Intensity:

SF = C B12 N0 I

Quenching Q21 = f (T,background)

Absorption I = f (x)

Boltzmann fcator N0 = f (T)

Overlap integral = f (T,p,background)

A21

A21+ Q21 +P2

.

.


What PLIF Measures

Distance behind shock [cm]

N(OH)[mol/m

3

]

0 1 2 3 40

0.1

0.2

0.3

0.4N(OH) based on ZND calculation

calculated fluorescence based on ZND

experimental PLIF fluorescence

Compare predicted fluoresence

from ZND and PLIF models

with measured fluorescence

Experimental data obtained by

vertical averaging over

horizontal stripe

2H2+O2+85%Ar, 20kPa6/20/2007 Detonation 24

2H2-O2-12Ar,P1=20kPa

18x150mm test section

image height 60mm

Reference: J. Austin, F. PIntgen and J.E. Shepherd, Reaction

Zones in Highly Unstable Detonations, 30th Combustion

Symposium, Chicago, 2004.

image height 150mm

Narrow channel simultaneous PLIF-Schlieren


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Reaction zone structure

Normalized velocity (U/UCJ

)

InductionLength(cm)

0.8 0.9 1 1.1 1.2 1.3 1.4

10-2

10-1

100

2 H2 + O2 + 17 Ar

Sharp rise in OH-concentration profile marks end of induction-zone

Induction zone length is stongly dependent on shock-velocity

keystone shapes features of lower reactance


Reaction zone structure

Sharp rise in OH-concentration profile marks end of induction-zone

Induction zone length is stongly dependent on shock-velocity

keystone shapes features of lower reactance

2H2+O2+17Ar,20kPa (Pintgen et al 2002)

20 mm


0

2

4

6

8

10

1214

16

18

20

0 2 4 6 8 10MCJ

Ea/RTS

Neutral stability

boundaryC3H8-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

Lee and Stewart

JFM 1990

Classification of Detonation Front Structure


2H2+O2+17Ar 2H2

+O2

+ 8 N2

H2+ N2O +3 N2

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


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Numerical Tools for Shocks andDetonation (CJ) Computations

NASA CeC code

STANJAN (in CHEMKIN)

Cantera Shock and detonation toolbox from

Caltech

GASEQ Computation not quite correct for

detonations

CHEETAH (export controlled) LLNL


Numerical Tools for Reaction ZoneStructure

Chemkin-based programs Reaction Design

ZND fortran program

Cantera-based programs Caltech shock and detonation toolbox

NASA,


Detonation Phenomena

Initiation by Blast Waves

Diffraction through tubes openingsand orifices

Limiting tube diameter

Deflagration-to-DetonationTransition


Initiation of Detonations

Direct initiation Requires a strong blast wave Fuel-oxygen mixtures

Exploding wire or

Electric discharge (spark) in air Fuel-air mixtures

High explosives Fuel-oxygen mixtures with DDT initiation

Deflagration-to-detonation transition Weak ignition source (glowplug or spark plug)


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Direct Initiation

What is the critical E needed to start a detonation?


Blast Wave Initiation

Subcritical, EEc


Plastic Bag

Containing C2H4-air

Inside View ShowingInstrumentation

Direct Initiation of Spherical Detonation


High-Explosive Detonating Cord Positioned on Bag Axis

Direct Initiation of Cylindrical Detonation


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LEGEND

0.0 1.0 2.0 3.0 4.0

EQUIVALENCE RATIO

100,000

10,000

1,000

100

10

1

0.1

0.01

INITIATIONENERGY(gramstetryl)

C2H4

H2

C2H2

C3H8

CH4

Spherical InitiationEnergy Data

Ec ~ 400UCJ2 3


Detonation Wave Diffraction

Detonation can fail, i.e., shock wave and

reaction zone decouple duringdiffraction

detonation

shocked reactants

shockproductsflowd


Detonation Diffraction Cases

Success Failure

Supercritical Critical Subcritical

Increasing cell size and reaction time


Tube Diameter = 1.83 m ; Bag Diameter = 3.66 m

Critical Tube Diameter Test


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Data from I.O Moen et al.

EQUIVALENCE RATIO

C

RITICALTUBEDIAMETERdc

(m)

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

5.0

2.0

1.0

0.5

0.2

0.1

PROPANE

ETHYLENE

HYDROGEN

ACETYLENE

NoGo

Critical TubeDiameter Data

Fuel-airdc~ 13

ordc~ 400


RS

Critical Radius for Reinitiation


Tube Initiation ConfigurationHigh-Explosive Initiation

Influence of Confinement on Propagation


Transmitted Air

Shock Wave

Detonation Wave

Bag Trajectory

(Contact Surface)

Still Frame from High-Speed Film


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Deflagration to DetonationTransition in gases

Flames and detonation propagation regimes Effect of confinement on flame propagation

Mechanisms of flame acceleration

Mechanisms involved in DDT

Pressure waves and structural response


Flames can become detonations!


Example: DDT in tubes

Obstacles or roughness is verysignificant


The path of DDT

DDT Process


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Flame passing an orifice


burned unburned

1. A smooth flame with laminar flow ahead

2. First wrinkling of flame and instability of upstream flow

3. Breakdown into turbulent flow and a corrugated flame

4. Production of pressure waves ahead of turbulent flame

5. Local explosion of vortical structure within the flame

6. Transition to detonation

DDT Process


Effect of FA on Pressure


Criteria For FA and DDT

Sufficient expansion ratio (>4)

Sufficiently high burning velocity Sufficient confinement

Need to reach choking regime

Sufficiently large volume L > 7large volumes Dorofeev)

d > obstructed tubes (Lee) d > 13diffraction


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Scaling of Detonation Onset


Effect of Expansion Ratio


References

1. A discussion of high explosive detonation from a practicingengineers perspective is given by: P. W. Cooper. ExplosivesEngineering. VCH, 1996.

2. More in-depth discussions are given in the compilation of: J. A.

Zukas and W.P. Walters, editors. Explosive Effects andApplications. High Pressure Shock Compression of CondensedMatter. Springer, 1995.

3. The classic reference on detonation is: Ya. B. Zeldovich and A. S.Kompaneets. Theory of Detonation. Academic Press, NY, 1960. Thisis an English translation of original Russian. Out of print and inmany ways out of date.

4. A more up to date theoretical treatment is given by: W. Fickettand W. C. Davis. Detonation. University of California Press,Berkeley, CA, 1979 Now available as a Dover paperback.

5. Gaseous detonations are discussed in most textbooks oncombustion.

IX. Detonation Waves

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