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  • RECENT DEVELOPMENTS IN DETONATIONMODELING CONDENSED PHASE MEDIA

    Martin Braithwaite Imperial College, London UK

    40th UKELG Meeting 40th UKELG Meeting -- 25th Anniversary25th AnniversaryCardiff University 19th September 2007Cardiff University 19th September 2007

  • Gas Phase vs Condensed Phase Detonations

    simple thermodynamics

    cell structure can be measured

    role of turbulence

    no mass transfer control

    near CJ conditions

    supercritical fluids

    heterogeneity, hot spot control

    VOD < VODCJ

    limited characterization

    pronounced shock front curvature

  • Condensed Phase Detonations

    mining, quarrying, seismic applications

    demolition, tunneling

    safety eg FCMO, transport

    defence

    security & improvised devices

    EPSRC Condensed Phase Reactive Flow Networkhttp://www.dcmt.cranfield.ac.uk/dmas/cdc/condphase

  • Modeling of the Detonation (and Rarefaction) Processes for Commercial (Non-Ideal, heterogeneous) Explosives in Rock

    Simple Theoretical Approach

    Validation using AMR Finite Volume code

    Pressure History at Detonation Product RockInterface for Shock, Detonation (and Rarefaction)

  • Ammonium Nitrate Based Bulk Explosives ANFO, Emulsions

    Heterogeneous, gas sensitized

    Large critical diameter (detonation) & VOD < Ideal VOD

    Limited characterization studies for most explosives

    eg separate oil and oxidiser phasesporous prill, chemical gassing

    ex critical diameter > 30 mmsreaction zone (DDZ) > 10 mms

    Typically, unconfined VOD vs charge diameterDensity and thermodynamic parametersLimited Shock Front Curvature data (unconfined)Particle, droplet size distributions

  • Confinement RockCompression, crack propagation,fragmentationand muckpile formation

    Non-isotropic

    Variable properties strength, composition, density

    Acoustic velocity < VOD This study

  • Detonation

    Steady state , axisymmetric

    Homogeneous media

    Simple EoS, thermodynamics and rate law for boththe explosive, detonation products and confinement

    nb major aim of this work is to ascertain where fluid mechanicsapproximations in quasi-1-D theories are valid thereforenot a test for EoS or thermodynamics

    Detonation Velocity greater than sound speedof confining media

  • (i) Are the fluid dynamics in a quasi-one dimensional theory adequate to approximately describe the detonation process for central axis and product-confinement interface in the context of rock blasting ?

    (ii) What resolution is required in a finite volumecomputer simulation study such that the DDZpredictions are invariant with grid size ?

    (iii) Is some order of DSD theory as opposed toWood Kirkwood slightly divergent flow appropriateto the rock blasting problem ?

  • 0

    1

    2

    3

    4

    5

    6

    7

    0 0.02 0.04 0.06 0.08 0.1 0.12

    unconfined80% dry80% wetconf approxconf correct

    Plot of VOD (km/s) vs inverse diameter (1/mm)

  • Data Validation Preview Scaling

    WarningsDefaults

    DATA FILE

    BMS Vis.

    JointStats

    BMS

    Interface DLL

    BLO-UP

    JKSimBlast

    Hybrid StressBlast Model

    Vixen

  • Condensed Phase Detonations - Model

    Conservation relations (Euler equations)MassMomentumEnergy

    Thermodynamic EoS all phasesP, V, T, E relationsMixing rules (finite reaction zones)

    Rate Expression lumped

    Initial and Boundary Conditions

  • Cobra solution of 2Cobra solution of 2--D Reactive Euler EquationsD Reactive Euler Equations

    simplified rate expression

    same EoS explosive, detonation products and confinement

    open tube (rear boundary condition)

    run to steady state detonation

    Cobra Analysis of ANFO Rate Stick

    (all simplifications (rate and EoS) necessary to reduce run timesto > 2 weeks on Linux based PCs)

  • Cobra Analysis ApproachCobra Analysis ApproachANFO Rate StickANFO Rate Stick

    simple pseudo-polytropic EoS explosive, products and confinement

    simplified rate expression

    ( ) ( )2

    0 1 2 20 0

    1 :1

    Pe Q

    = + = + +

    ( )32

    ref

    1 1PwP

    =

  • 0.523.252.934.73.2

    0.213.673.019.31.6

    0.153.883.0518.70.8

    0.124.113.1037.30.4

    0.094.243.1274.50.2

    0.054.323.131490.1

    LambdashkPshockGPa

    VOD(km/s)

    Points/lDDZ(mm)

    Effect of grid spacing/ no of points in DDZ on predicted VOD, shock pressure and extent of reaction at the shock front

  • Cobra Analysis Comparison Cobra Analysis Comparison -- ANFO Rate StickANFO Rate Stick

    0.8736100H0.7462100G0.6480.0013 - air100F0.9018100E0.8294100D0.8370.8200C0.7780.8150B0.6520.8100A

    D/DCJConfinementDensity g/ccDiameter (mm)Case

  • Blue shockRed sonic locusGreen - contact

    100 mm 0.8 g/cc

    150 mm 0.8 g/cc

    200 mm 0.8 g/cc

    100 mm 4 g/cc

    100 mm 8 g/cc

  • 100 mm 0.8 g/cc

    150 mm 0.8 g/cc

    200 mm 0.8 g/cc

    100 mm 4.0 g/cc

    100 mm 8.0 g/cc

  • 100 mm ANFO charge in 2 g/cc confinement Pressure profile

  • 100 mm ANFO charge in 2 g/cc confinement - Density Profile

  • 100 mm ANFO charge in 2 g/cc confinement Radial Velocity Profile

  • 100 mm ANFO charge in 2 g/cc confinement Reaction Extent Profile

  • Quasi- 1-D Analysis for General EoS and Rate Law

    Shock

    Reaction Zone

    n

    is normal direction to shockn

    is tangential direction to shock

    & are fluid velocities normal and perpendicular to shocknu u

  • Steady Euler Equations in curvilinear coordinates

    ( )( )

    ( ) ( )

    2

    terms1

    1 terms

    terms

    terms

    where terms involve derivatives and : Reaction rate and EoS, are given by

    W=W ,P, & , , . and

    n nnn

    nn

    nn

    n

    u Du un n nKu Pun n

    e Pn n

    uu Wn

    u

    e e P D

    + + = +

    +

    = +

    =

    = +

    = are the local total curvature and normal component of detonation speed. , and correspond to pressure, density and extent of reaction respectively.

    P

  • Quasi-1-D approximation

    radial derivative and velocity terms are assumed negligible

    remaining partial derivatives become full

    Dn normal velocity becomes VOD

    Analogous to WK central stream-tube but without unknown divergence term

  • Q1D Equations in curvilinear coordinates final

    ( )

    2

    2 2

    2 200

    0

    22

    ( )(1 )

    ( )(1 )

    1 1, ,2 2

    /

    /

    n n n

    n

    n

    n n n

    n

    n

    n

    n n

    u u DWu nd

    dn c uu u DW

    du ndn c ud Wdn u

    PPe P u e D

    P e ecP

    e eP

    +

    + =

    +

    + =

    =

    + + = + +

    = =

  • 3

    3.4

    3.8

    4.2

    4.6

    0 100 200 300 400 500 600 700

    D (k

    m/s)

    Rshk (mm)Axial Detonation velocity vs axial radius of curvature,

    Q1D predictions are given as a solid line and the data from COBRA runs as circles

  • 2.5

    3

    3.5

    4

    4.5

    5

    0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

    Dn

    (km

    /s)

    (1/mm)kkkkkkkkkkkkkkkkkk

    nD

    Normal Detonation Speed vs curvature (ex COBRA) for a range of charge diameter and confinement densitycf Q1D theory (dotted line)

  • Conclusions

    High resolution AMR simulations required ~ 0.1 mm

    Reasonable to good agreement Q1D and COBRAfor central axis

    Disadvantage of Wood Kirkwood unknown axial divergence parameter

    DSD for non-ideal explosives in heavy confinement eg rock ?

    Limited impact of DDZ directly on rock

  • Acknowledgements

    SponsorsAEL, De Beers, Debswana, Dyno Nobel, Placer Dome,Codelco, Rio Tinto, Anglo Chile, Sandvik Tamrock.

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