Course Summary:

After an introduction to shock waves, the four-day course continues with shock

matching and explosive technology. The formation and interaction of shock and

detonation waves are illustrated using computer movies generated by numerical

reactive hydrodynamic codes. Numerical methods for evaluating explosive and

propellant sensitivity to shock waves are described and applied to vulnerability

problems such as projectile impact and burning-to-detonation transitions. One-,

two- and three-dimensional hydrodynamic codes for modeling explosive and

propellant performance and vulnerability are described and typical applications

presented. Hands-on use of codes for evaluating explosive and propellant

performance is provided. We recommend that you bring your laptop to this

course.

Course Outline:

SHOCK WAVES

Fundamental Shock Wave Hydrodynamics

Shock Hugoniots

Shock Matching

Equation of State

Elastic-Plastic Flow

Phase Change

Oblique Shock Reflection

Regular and Mach Shock Reflection

SHOCK EQUATION OF STATE DATA BASES

Shock Hugoniot Data

Shock Wave Profile Data

Radiographic Data

Explosive Performance Data

Aquarium Data

Russian Shock and Explosive Data

PERFORMANCE OF EXPLOSIVES AND PROPELLANTS

Steady-State Explosives

Nonideal Explosives

Ammonium Salt-Explosive Mixtures

Ammonium Nitrate-Fuel Oil (ANFO) Mixtures

Metal Loaded Explosives

Nonsteady-State Detonations

Build-Up in Plane

Build-Up in Diverging Geometry and Converging Geometry

Chemistry of Build-Up

Propellant Performance

INITIATION OF DETONATION

Thermal Initiation

Explosive Hazard Calibration Tests

Shock Initiation of Homogeneous Explosives

Hydrodynamic Hot Spot Model

Shock Sensitivity and Effects of Composition

Particle Size and Temperature

THE FOREST FIRE MODEL

Failure Diameter

Corner Turning

Desensitization of Explosives by Preshocking

Projectile Initiation of Explosives

Burning to Detonation

MODELING HYDRODYNAMICS ON PERSONAL COMPUTERS

Numerical Solution of One-Dimensional and Two-Dimensional

Lagrangian Reactive Flow

Numerical Solution of Two-Dimensional and Three-Dimensional Eulerian

Reactive Flow

Numerical Solution of Explosive and Propellant Properties

DESIGN AND INTERPRETATION OF EXPERIMENTS

Plane-Wave Experiments

Explosions in Water

The Plate Dent Experiment

The Cylinder Test

Jet Penetration of Inerts and Explosives

Plane Wave Lens

Regular and Mach Reflection of Detonation Waves

Insensitive High Explosive Initiators

Colliding Detonations

Shaped Charge Jet Formation and Target Penetration

What You Will Learn:

What are Shock Waves and Detonation Waves?

What makes an Explosive Hazardous?

Where Shock Wave and Explosive Data is available.

How to model Explosive and Propellant Performance.

How to model Explosive Hazards and Vulnerability.

How to use the furnished explosive performance and hydrodynamic

computer codes.

The current state of explosive and propellant technology.

Instructor:

Charles L. Mader, Ph.D.,is a retired Fellow of the Los Alamos National

Laboratory and President of Mader Consulting Company. Dr. Mader authored

the monograph Numerical Modeling of Detonation, and also wrote four dynamic

material property data volumes published by the University of California Press.

His book and CD-ROM entitled Numerical Modeling of Explosives and

Propellants, Third Edition, published in 2008 by CRC Press will be the text for

the course. He is the author of Numerical Modeling of Water Waves, Second

Edition, published in 2004 by CRC Press. He is listed in Who's Who in America

and Who's Who in the World. He has consulted and guest lectured for public

and private organizations in several countries. The Mader Consulting Co. web

site is www.mccohi.com.

Explosives Technology & Modeling

Jan 25-28, 2010, Beltsville, MD

$1895 (8:30am- 4:30pm)4 day course

“Register 3 or More & Receive $100 each Off The Course Tuition.”

Course Materials:

Participants will receive a copy of Numerical Modeling of Explosives and

Propellants, Third Edition by Dr. Charles Mader, 2008 CRC Press. In addition,

participants will receive an updated CD-ROM.

Who Should Attend:

This course is suited for scientists, engineers, and managers interested in the

current state of explosive and propellant technology, and in the use of numerical

modeling to evaluate the performance and vulnerability of explosives and

propellants.

www.ATIcourses.com

Boost Your Skills with On-Site Courses Tailored to Your Needs The Applied Technology Institute specializes in training programs for technical professionals. Our courses keep you current in the state-of-the-art technology that is essential to keep your company on the cutting edge in today’s highly competitive marketplace. Since 1984, ATI has earned the trust of training departments nationwide, and has presented on-site training at the major Navy, Air Force and NASA centers, and for a large number of contractors. Our training increases effectiveness and productivity. Learn from the proven best. For a Free On-Site Quote Visit Us At: http://www.ATIcourses.com/free_onsite_quote.asp For Our Current Public Course Schedule Go To: http://www.ATIcourses.com/schedule.htm

chapter six

NOBEL and PRad

6.1 Fifty Year History

During the almost ten years since the last edition of this book was writtena technological revolution in numerical modeling occurred with the development ofthe NOBEL/SAGE/RAGE series of computer codes primarily by Michael Gittings ofSAIC/LANL.

Also during the last ten years an experimental technological revolution occurred withthe development of proton radiography (PRad)7 at LANL and its application to explosivesby John Zumbro6 and Eric Ferm10.

NOBEL modeling of PRad experimental studies will be described in this Chapterand PowerPoint presentations with computer movies of the studies are on the CD-ROM.The author was privileged to participate in this technological revolution at the end of hisprofessional career and to have worked with Gittings and Zumbro.

The 50 years of explosive technology and modeling described in this book have beendriven by the genius of many dedicated scientists and engineers

John M. Walsh created, in the 1950s, the experimental techniques that resulted in muchof the shock wave physics described in the Los Alamos Data Volumes. He then created, inthe 1960s, the Eulerian numerical modeling techniques described in Appendices E and D.Michael Gittings worked with Walsh and then proceeded, in the 1990s and 2000s, to createthe remarkable computer codes NOBEL/SAGE/RAGE that are described in this Chapter.The codes have resulted in a revolution of our ability to model not just explosives andweapon physics, but also the impact physics of projectiles and asteroids, and the generationand propagation of water waves and tsunamis by landslides and hydrovolcanic explosions.

Douglas Venable developed the X-Ray machine PHERMEX and applied it to manyproblems of shock and detonation wave physics in the 1960’s. In this chapter we will usethe NOBEL code to model some of his classic PHERMEX experimental observations ofMunroe jets. Most of our current understanding and modeling of detonation wave cornerturning depends upon the PHERMEX experiments of Venable.

Bobby G. Craig refined explosively driven plate technology and discovered the time-dependent nature of the detonation wave. The experimental data he generated, in the 1960sand 1970s, furnished the basis of much of the detonation physics and modeling describedin this book.

307

308 chapter six: NOBEL and PRad

6.2 The NOBEL CODE

The Department of Energy’s Accelerated Strategic Computing Initiative (ASCI)program during 2000 to 2005 resulted in major advances in computing technology andin methods for improving the numerical resolution of compressible reactive hydrodynamiccalculations.

In this chapter the advanced ASCI computer codes, NOBEL/SAGE/RAGE, for mod-eling compressible fluid dynamics are described. The detonation physics described in Chap-ters 1 through 4 of this book has been included into the NOBEL code.

As described in reference 1 and Appendix D, the three-dimensional partial differentialequations for nonviscous, nonconducting, compressible fluid flow areThe Nomenclature

I internal energyP pressureUx velocity in x directionUy velocity in y directionUz velocity in z directionρ densityt time

∂ρ

∂t+ Ux

(∂ρ

∂x

)+ Uy

(∂ρ

∂y

)+ Uz

(∂ρ

∂z

)

= −ρ

(∂Ux

∂x+

∂Uy

∂y+

∂Uz

∂z

),

ρ

[∂Ux

∂t+ Ux

(∂Ux

∂x

)+ Uy

(∂Ux

∂y

)+ Uz

(∂Ux

∂z

)]= −∂P

∂x,

ρ

[∂Uy

∂t+ Ux

(∂Uy

∂x

)+ Uy

(∂Uy

∂y

)+ Uz

(∂Uy

∂z

)]= −∂P

∂y,

ρ

[∂Uz

∂t+ Ux

(∂Uz

∂x

)+ Uy

(∂Uz

∂y

)+ Uz

(∂Uz

∂z

)]= −∂P

∂z,

ρ

[∂I

∂t+ Ux

(∂I

∂x

)+ Uy

(∂I

∂y

)+ Uz

(∂I

∂z

)]

= −P

(∂Ux

∂x+

∂Uy

∂y+

∂Uz

∂z

).

6.2 The NOBEL Code 309

In NOBEL/SAGE/RAGE these equations are solved by a high-resolution Godunovdifferencing scheme using an adaptive grid technique described in references 2 and 3. Thesolution technique uses Continuous Adaptive Mesh Refinement (CAMR). The decision torefine the grid is made cell-by-cell continuously throughout the calculation. The computingis concentrated on the regions of the problem which require high resolution.

Refinement occurs when gradients in physical properties (density, pressure, tempera-ture, material constitution) exceed defined limits, down to a specified minimum cell sizefor each material. The mesh refinement is shown in Figure 6.1. With the computationalpower concentrated on the regions of the problem which require higher resolution, very largecomputational volumes and substantial differences in scale can be simulated at low cost.

The overhead associated with the CMAR technique is about 20% of the total runtime,which is small compared to the gains of using CMAR instead of a uniform mesh.

Figure 6.1 NOBEL adaptive mesh refinement allows isentropic refinement limited to a2:1 ratio. Adjacent cells may not differ by more than one level.

Much larger computational volumes, times and differences in scale can be simulatedthan is possible using previous Eulerian techniques such as those described in AppendicesC and D.

The original code is called SAGE. A later version with radiation is called RAGE.A recent version with the techniques for modeling reactive flow described in Chapters 1through 4 is called NOBEL and was used for modeling many problems in detonationphysics some of which are described later in this chapter.

The codes can describe one-dimensional slab or spherical geometry, two-dimensionalslab or cylindrical geometry, and three-dimensional Cartesian geometry.

Because modern supercomputing is currently done on clusters of machines containingmany identical processors, the parallel implementation of the code is very important. Forportability and scalability, the codes use the Message Passing Interface (MPI). Load levelingis accomplished through the use of an adaptive cell pointer list, in which newly createddaughter cells are placed immediately after the mother cells. Cells are redistributed amongprocessors at every time step, while keeping mothers and daughters together. If there area total of M cells and N processors, this technique gives nearly M/N cells per processor.As neighbor cell variables are needed, the MPI gather/scatter routines copy those neighborvariables into local scratch memory.

310 chapter six: NOBEL and PRad

The codes incorporate multiple material equations of state (analytical or SESAMEtabular). Every cell can in principle contain a mixture of all the materials in a problem as-suming that they are in pressure and temperature equilibrium. As described in Appendix C,pressure and temperature equilibrium is appropriate only for materials mixed molecularly.The assumption of temperature equilibrium is inappropriate for mixed cells with interfacesbetween different materials. The errors increase with increasing density differences. Whilethe mixture equations of state described in Appendix C would be more realistic, the problemis minimized by using fine numerical resolution at interfaces. The amount of mass in mixedcells is kept small resulting in small errors being introduced by the temperature equilibriumassumption.

The strength is treated using an elastic-plastic model identical to that described inAppendicies A, B and C.

A variety of boundary conditions is available, the most important being reflectiveboundary walls, reflective internal boundaries, and “freeze regions” which allow specificinflows and unrestricted outflows of material.

Very important for water cavity generation and collapse and the resulting water wavehistory is the capability to initialize gravity properly, which is included in the code. Forexample, this results in the initial density and initial pressure changing going from theatmosphere at 40 kilometers altitude down to the ocean surface. Likewise the water densityand pressure changes correctly with ocean depth.

As described in reference 1, it became possible to calculate water wave problems forminutes or even hours using compressible hydrodynamic models that require millions oftime steps for each second of flow. Only recently has it become possible to finely resolveinterfaces such as a water-air interface and follow the water wave with millimeter resolutionin a problem with 40 kilometers of air, 5 kilometers of water and tens of kilometers of oceancrust. Even more impressive is being able to finely resolve interfaces of detonation products,water and air including the thin water plumes and jets formed by explosions on the watersurface.

The codes have been used to model water waves generated from impact landslides,explosions, projectile impacts and asteroids as described in reference 1. Numerical modelingof water waves advanced so far so rapidly that it is clearly a technological revolution.

The NOBEL/SAGE/RAGE codes are intended for general applications without tuningof algorithms or parameters, and are portable enough to run on a wide variety of platforms,from desktop PC’s (Windows, Linux and Apple Macintosh) to the latest MMP and SMPsupercomputers. SAGE provided an early testbed for development of massive parallelismas part of the ASCI program and has been shown to scale well to thousands of proces-sors. Almost a decade of different supercomputers, the oldest being the ASCI Red systeminstalled at Sandia National Laboratory in 1996 and the BlueGene/L system, installed atLawrence Livermore National Laboratory in 2005, has resulted in a performance increase ofa factor of 20, resulting from both improvements in processor speeds and network speeds.The performance of these systems degrades by a factor of 2 for each thousand processors.The degradation results from the need for communication between logically neighboringprocessors as well as for the need for collective operations.

Some of the remarkable advances in fluid physics using the SAGE code have been themodeling of Richtmyer-Meshkov and shock induced instabilities described in references 4and 5.

6.3 Proton Radiography (PRad) 311

6.3 Proton Radiograph (PRad)

The Proton Radiography Program at LANL has developed a radiographic facility atthe Los Alamos Neutron Science Center (LANSCE). Multiple proton radiographic imagesof the same explosive experiment can be taken as described in references 6, 7 and 8. Thefacility provides a method of making multi-axis, multi-frame radiographs using the 800-MeV protons at LANSCE. It is analogous to taking an X-ray picture of an object, butusing protons instead of photons. A magnetic lens focuses the protons onto a detector totake a shadow radiograph.

Figure 6.2 Three ton explosive containment vessel (center) flanked by large electromagnetsthat focus the protons to produce sharp radiographs.

The PRad facility is shown in Figures 6.2 and 6.3. For PRad, 50 nanosecond wideproton beam pulses with approximately 109 protons per pulse are spaced in time at in-tervals predetermined by experimental requirements. Transmitted and scattered protonsare imaged by an electromagnetic lens system20 and recorded by cameras. This techniqueprovides multiframe radiographs across a 12 by 12 cm square field of view that spatially re-solves features to an accuracy of approximately 150 µm from samples with an areal densityof up to 60 g/cc. A permanent magnet magnifier lens is available that provides a factor of7 magnification to study small systems (such as explosive reaction zones) with an accuracyof 15 µm.

A number of PRad experiments on detonation physics have been performed. Theyinclude studies of a detonation front turning a corner as it propagates from a narrow cylin-der of high explosive into a wider one, rate sticks for measuring the velocity of the detonationfront and its curvature, colliding detonation fronts and failure cone experiments for deter-mining the radius at which a detonation fails to propagate. All of the experiments havebeen modeled using the NOBEL code.

A series of experiments has been performed with PRad to study how shocked metalsfail when a shock wave is reflected from a free metal surface and the resulting rarefactionwave puts the material in tension. Another series of experiments has been performed tostudy fragmentation. Some of the proton radiographs have been published in reference 8.

312 chapter six: NOBEL and PRad

11/10/04 4 P. D. Barnes, Jr., LLNL

Forming An Image With Magnetic LensesLANL LANSCE Line C

ObjectVessel

CameraSet 1

CameraSet 2

View looking into the proton radiography facility at LANSCE

ProtonBeam Lens 1 Lens 2

Figure 6.3 The Proton Radiographic Facility at LANCSE. The object vessel contains theexplosive experiment.

Figure 6.4 The Proton Radiography imaging system with gated CCD Cameras.

6.3 Proton Radiography (PRad) 313

Proton radiography’s potential would never have been realized if the blurring evident inearly proton radiographs had persisted. John Zumbro developed a lens design using a seriesof quadrupole electromagnets that preserves the angle that a proton makes with the opticalaxis of the lens so that the optical axis of the lens is proportional to the proton’s radialdistance from the axis. The Zumbro lenses can be used in series with minimal degradationof the images produced by later lenses and permit elemental identification.

The proton radiography imaging system is shown in Figure 6.4. The proton imagesare produced as protons transmitted through a dynamic experiment are focused on the 12by 12 cm tiled scintillator. The scintillator converts proton intensity to light intensity, andthe “turning” mirror reflects these light images to seven smaller mirrors, which reflect theimages to seven CCD cameras.

The CCD camera contains a 720x720 array of fast silicon photosensors and an inte-grated circuit, which turns the signals from the photosensors on and off to measure theincident light in as few as 100 nanoseconds. The camera is typically operated at an aper-ture time of 250 to 400 nanoseconds and the exposure time is determined by the durationof the proton pulse.

The large gray circular object in Figure 6.4 is the back of the turning mirror, beneathwhich are seven CCD cameras. These cameras store three frames each with the potentialto store at least 10 frames in the near term and possibly hundreds of frames eventually.The camera operates as fast as 4 million frames per second. An example of PRad multipleframes and the resulting movie is on the CD-ROM in the directory /NOBEL/CONE andPowerPoint program CONE.PPT.

The proton radiographic images are similar to PHERMEX images in that interpretationof the images is often difficult. Comparision of proton radiographs with computed densityor even the NOBEL “x-ray” density plots has large uncertainities. John Zumbro used adevelopmental version of the particle transport code Monte-Carlo-N-Particle (MCNP) tomodel the PRad proton beamline. The proton transport through the target and subsequentradiographs are simulated. The technique was used to generate Figure 6.9 and Figure 6.12.

Dr. John Zumbro Dr. Douglas Venable

314 chapter six: NOBEL and PRad

6.4 Colliding Diverging PBX-9502 Detonations

Introduction

A proton radiographic study of diverging and colliding PBX-9502 detonations andNOBEL modeling are described in reference 9 and in this section. TATB (Triamino-trinitrobenzene) explosives became important by the 1960’s because of their shock insensitivityto accidental initiation. Such explosives required large and powerful initiating systemswhich often resulted in large amounts of the explosive failing to detonate. These undeto-nated regions are described in Chapter 4. They were first qualitatively measured using thePHERMEX radiographic facility in planar experiments where the detonation propagation ofshock insensitive TATB based explosives X-0219 (90/10 TATB/Kel-F at 1.914 gm/cc) andPBX-9502 (95/5 TATB/Kel-F at 1.894 gm/cc) into a larger block of the explosive left largeregions of partially undecomposed explosive as the detonation wave tried to turn the corner.The corner turning PHERMEX radiographs for X-0219 are Shots 1795-97, 1936 1940, and1942 (Figure 4.17) and for PBX-9502 are Shots 1705, 1937, 1941 and 1943. The radiographsare available as part of the Los Alamos Series of Dynamic Material Properties on the CD-ROM. The observed undecomposed explosive formation for X-0219 was reproduced usingthe two-dimensional Lagrangian reactive hydrodynamic code, TDL, with the Forest Fireheterogeneous shock initiation rate model described in Chapter 4. The experimental resultswere also described using the two-dimensional Eulerian reactive hydrodynamic code, 2DEin Chapter 4.

PHERMEX radiographs are available for colliding planar detonations of CompositionB-3 (Shots 86, 87, 91, 92, 139, 140, 195, 196, and 273-277), of Cyclotol (Shots 203-206 and291), of Octol ( Shots 294-297) and of PBX-9404 (Shots 207-210, 292 and 1151). Theseshots were used to evaluate the equation of state of detonation products at pressures upto twice the C-J pressure of the explosives, such as the BKW equation of state which wasused to reproduce the radiographic results.

As described in Chapter 5, Travis used the image intensifier camera to examine thenature of the diverging detonation waves formed in PBX-9404, PBX-9502, and X0219 byhemispherical initiators. The geometries of the initiators were (A) a 0.635 cm radius hemi-sphere of PBX-9407 at 1.61 gm/cc surrounded by a 0.635 cm radius hemisphere of PBX-9404, (B) a 0.635 cm radius hemisphere of 1.7 gm/cc TATB surrounded by a 1.905 cm thickhemisphere of 1.8 gm/cc TATB or (C) a 1.6 cm radius hemisphere of X0351 at 1.89 gm/cc.The unreacted regions for PBX-9404 were too small to observe experimentally for initiatorsystem (A) while about 1/5 of the explosive PBX-9502 remained unreacted. The initiatorsystem (A) developed an unreacted region for X-0219 so large that the detonation failed inthe geometry studied. The larger detonator (B) resulted in smaller unreacted regions forPBX-9502 as did the higher pressure detonator (C).

The observed undecomposed explosive region formation and failure were reproducedusing the two-dimensional reactive Lagrangian hydrodynamic code, TDL, with the multiple-shock Forest Fire heterogeneous shock initiation rate model as described in Chapter 5.

6.4 Colliding Diverging PBX-9502 Detonations 315

Proton Radiography

Proton radiographic studies have been performed by Ferm et al.10 of the formationof unreacted regions by cylindrical PBX-9502 detonations as they propagated into largercylindrical blocks of PBX-9502. The regions persisted for more than 6 microseconds atdensities slightly higher than initial density. Parts of the unreacted regions show indicationof a slow reaction occurring. Attempts at modeling the cylinder edge break-out usingDetonation Shock Dynamics (DSD), implanted in the MESA code, were unsuccessful. Itwas concluded that the DSD model needs additional physics10.

Colliding Diverging PBX-9502 Detonations

Experimental and numerical studies of colliding planar detonations are available asare studies of the formation of unreacted regions in corner turning experiments and hemi-spherical initiator experiments for shock insensitive explosives such as PBX-9502. Whatremained to be determined was the interaction of colliding diverging detonations that alsoexhibit large regions of partially undecomposed explosives as the colliding detonation isformed.

The Proton radiographic shot PRAD0077 was designed to study the interaction ofcolliding diverging PBX-9502 detonations which exhibit unreacted region formation. Theshot consisted of a 50-mm by 50-mm cylinder of PBX-9502 initiated on the top and bottomat the axis by an SE-1 detonator and a 12.7-mm by 12.7-mm cylinder of 9407. The PBX-9502 was 95.0 wt.% TATB/ 5.0 wt.% Kel-F 800 at 1.890 gm/cc. Seven radiographs weretaken at times before and after the detonation collision.

The geometry of the system studied is shown in Figure 6.5.

Figure 6.5 The geometry of the PRAD077 Shot.

316 chapter six: NOBEL and PRad

The seven radiographs are shown in Figure 6.6 as dynamic to static ratios at intervalsof 0.358 microseconds.

.

Figure 6.6 The seven PRAD077 proton radiographs at intervals of 0.358 microsecondsincreasing from left to right and bottom to top.

The system results in a large dead or nonreactive zone as the detonation attempts toturn the corner. The detonation wave travels for over 10-mm before it starts to expand andturn the corner leaving more than half of the explosive unreacted.

The diverging detonations collide first along the center axis. The density of the result-ing shocked detonation products decays as the reflected shock travels back into the lowerdensity products. As the diverging detonation waves continue to collide, detonation regularreflections and then Mach stems develop at the interaction interfaces.

Modeling

The system was modeled using the one-dimensional SIN code with C-J Burn in planeand spherically diverging geometry and using the two-dimensional TDL code with C-J burnand multiple-shock Forest Fire. The HOM equation of state and Forest Fire rate constantsused were identical to those used to model the PHERMEX corner turning experiments inthe mid 1970’s and listed in Chapter 4.

The calculated pressure at the axis as a function of time is shown in Figure 6.7 for theSIN and TDL calculations.

6.4 Colliding Diverging PBX-9502 Detonations 317

Figure 6.7 The calculated pressure at the axis as a function of time for the one-dimensionalSIN code of a PBX-9501 diverging detonation and the two-dimensional TDL calculationwith multiple-shock Forest Fire shown in Figure 6.8.

The TDL calculated density and mass fraction of undecomposed explosive contours areshown in Figure 6.8 for the TDL calculation with the multiple-shock Forest Fire heteroge-neous shock initiation burn.

Figure 6.8 The two-dimensional density contours and mass fraction of undecomposedexplosive at 0.5 µsec intervals using the two-dimensional Lagrangian code TDL with multipleshock Forest Fire.

318 chapter six: NOBEL and PRad

Zumbro calculated the proton radiographic profile from the TDL density array of thediverging detonation wave just before collision shown in Figure 6.9

Figure 6.9 The calculated proton radiograph for the TDL densities just before the collisionof the PBX-9502 diverging detonation waves.

The system was also modeled with the AMR Eulerian reactive hydrodynamic codeNOBEL using Forest Fire. The calculated density contours and mass fraction of undecom-posed explosive at the same times as PRAD0077 (Figure 6.6) are shown in Figure 6.10 forthe NOBEL calculation with Forest Fire. The two-dimensional X-ray simulation for theNobel calculation is shown in Figure 6.11.

Figure 6.12 is a comparision of the NOBEL proton radiographic profile with the experi-mental radiograph just before detonation wave collision. Zumbro used the method describedon page 313 to generate the proton radiographic profile from the NOBEL calculated densityarray.

The NOBEL computer animations and PowerPoint are on the CD-ROM in/NOBEL/COLLID.

6.4 Colliding Diverging PBX-9502 Detonations 319

Figure 6.10 The two-dimensional density contours for the NOBEL calculation withmultiple-shock Forest Fire at the same times as the proton radiographs in Figure 6.6.

320 chapter six: NOBEL and PRad

Figure 6.10 (continued) The two-dimensional explosive decomposition contours for theNOBEL calculation with multiple-shock Forest Fire at the same times as the proton radio-graphs in Figure 6.6.

6.4 Colliding Diverging PBX-9502 Detonations 321

Figure 6.11 The two-dimensional X-ray simulation for the NOBEL calculation withmultiple-shock Forest Fire at the same times as the proton radiographs in Figure 6.6.

322 chapter six: NOBEL and PRad

Figure 6.12 The NOBEL calculated PRAD077 proton radiograph on the right and theproton radiograph from Figure 6.6 on the left after the diverging PBX-9502 detonation waveturned the corner and just before the detonation waves collided.

The calculated peak detonation pressure achieved by the colliding diverging detonationwas 500 kb with a density of 3.125 gm/cc which is about the same as that achieved byone-dimensional spherically diverging 9502 detonations but less than the calculated one-dimensional plane 9502 peak colliding detonation pressure of 650 kb and density of 3.4gm/cc.

The calculated detonation wave travels for over 10-mm before it starts to expand andturn the corner, leaving more than half of the explosive unreacted. The resulting divergingdetonation is more curved than a one-dimensional spherical diverging detonation and hasa steeper slope behind the detonation front. This results in the colliding pressure decayingfaster than one-dimensional colliding spherical diverging pressures decay.

Conclusions

The interaction of colliding diverging detonations that also exhibit large regions ofpartially undecomposed explosives as the colliding detonation is formed has been experi-mentally radiographed using the Proton Radiographic Facility. Numerical modeling usingLagrangian and Eulerian reactive hydrodynamic codes and the Forest Fire heterogeneousshock initiation rate model gave results that reproduced the radiographs.

Many important features of detonation physics are exhibited by this study of diverging,colliding PBX-9502 detonations which exhibit significant additional curvature as they fail toturn corners promptly. New detonation models must be able to reproduce the complicatedphysics illustrated by proton radiograph PRAD0077.

Explosively Generated Water Cavities 323

6.5 Explosively Generated Water Cavities

Introduction

In the mid 1960’s, B. G. Craig11 at the Los Alamos National Laboratory performedexperiments designed to characterize the formation of water waves from explosives detonatednear the water surface. He reported observing the formation of ejecta water jets above andjets or “roots” below the expanding gas cavity. This was unexpected and a scientific mysterywhich remained unsolved until it was finally modeled using the NOBEL code in Decemberof 2002.

In the early 1980’s, the hypervelocity impact (1.25 to 6 kilometers/sec) of projectilesinto water was studied at the University of Arizona by Gault and Sonett12. They observedquite different behavior of the water cavity as it expanded when the atmospheric pressurewas reduced from one to a tenth atmosphere. Above about a third of an atmosphere, a jetof water formed above the expanding cavity and a jet or “root” emerged below the bottomof the cavity.

In the mid 1980’s, similar results were observed by Kedrinskii13 at the Institute ofHydrodynamics in Novosibirsk, Russia, who created cavities in water by sending largeelectrical currents through small lengths of small diameter Gold wires (bridge wires) causingthe Gold to vaporize. The “exploding bridge wire” is a common method used to initiatepropagating detonation in explosives. He observed water ejecta jets and roots forming fornormal atmospheric pressure and not for reduced pressures.

Thus the earlier Craig observations were not caused by some unique feature of gen-eration of the cavity by an explosion. The process of cavity generation by projectiles orexplosives in the ocean surface and the resulting complicated fluid flows has been an im-portant unsolved problem for over 50 years. The prediction of water waves generated bylarge-yield explosions and asteroid impacts has been based on extrapolation of empirical cor-relations of small-yield experimental data or numerical modeling assuming incompressibleflow, which does not reproduce the above experimental observations.

The NOBEL code has been used to model the experimental geometries of Sonett andof Craig. The experimental observations were reproduced as the atmospheric pressure wasvaried as described in reference 14.

Projectile and Exploding Bridge Wire Generated Cavities

In the early 1980’s, experiments were being performed at the University of Arizonato simulate asteroid impacts in the ocean. The hypervelocity impact (1.25 to 6 kilome-ters/sec) of various solid spherical projectiles (Pyrex or Aluminum) with water was per-formed by Gault and Sonett12. Their observations were similar to those previously observedby Craig11. While the water cavity was expanding, an ejecta jet was formed at the axisabove the water plume and a jet or “root” emerged along the axis below the cavity. Thewater cavity appeared to close and descend into deeper water.

To improve the photographic resolution and reduce the light from the air shock, Sonettrepeated his impact experiments under reduced atmospheric pressure. Much to everyone’ssurprise, when the pressure was reduced from one to a tenth atmosphere, the ejecta jet andthe root did not occur and the water cavity expanded and collapsed upward toward thesurface. This was what had been expected to occur in both the earlier Craig experimentsand the projectile impacts at one atmosphere pressure.

324 chapter six: NOBEL and PRad

It became evident that the atmospheric pressure and the pressure differences insideand outside the water plume above the water surface were the cause of the formation of thejet, the root, the cavity closure and descent into deeper water.

Figure 6.13 shows the Gault and Sonett12 results for a 0.25 cm diameter aluminumprojectile moving at 1.8 kilometers/sec impacting water at one atmosphere (760 mm), andat 16 mm air pressure. A water stem and jet occurs at one atmosphere and not at lowpressure.

Figure 6.14 shows the Gault and Sonett results for a 0.635 cm diameter aluminumprojectile moving at 2.5 kilometers/sec impacting water at one atmosphere (760 mm) anda 0.3175 cm diameter Pyrex projectile moving at 2.32 kilometers/sec impacting water at 16mm air pressure. A water stem and jet occurs at one atmosphere and not at low pressure.

Professor Kedrinskii13 at the Russian Institute for Hydrodynamics was also studyingthe generation of water cavities from exploding bridge wires. He was observing the formationof ejecta jets and roots as the water cavity expanded similar to those observed by Craigusing explosives and by Gault and Sonett using projectiles. After we showed him theeffect of reduced atmospheric pressure, he proceeded to repeat his exploding bridge wireexperiments under reduced pressure. He observed that the jets and roots did not form whenthe atmospheric pressure was reduced to 0.2 atmosphere.

Figure 6.15 shows the Kedrinskii results for an exploding bridge wire in water at oneatmosphere and at 0.2 atmosphere air pressure.

Compressible Navier-Stokes Modeling

The projectile impact and explosive generated water cavity were modeled with therecently developed full Navier-Stokes AMR (Adaptive Mesh Refinement) Eulerian com-pressible hydrodynamic code NOBEL described earlier. The continuous adaptive meshrefinement permits the following of shocks and contact discontinuities with a very fine gridwhile using a coarse grid in smooth flow regions. It can resolve the water plume and thepressure gradients across the water plume and follow the generation of the water ejecta jetand root.

Figure 6.16 shows the calculated density profiles for a 0.25 cm diameter aluminumprojectile moving at 2.0 kilometers/sec impacting water at five atmosphere air pressure.The water plume collapses at the axis creating a jet moving upward and downward. The jetpasses down through the cavity, penetrating the bottom of the cavity at the axis formingthe stem. The flow results in the cavity descending down into the water.

Figure 6.17 shows the calculated density profiles for a 0.25 cm diameter aluminumprojectile moving at 2.0 kilometers/sec impacting water at one atmosphere air pressure.

Figure 6.18 shows the calculated density profiles for a 0.25 cm diameter aluminumprojectile moving at 2.0 kilometers/sec impacting water at 0.1 atmosphere air pressure. Thetip of the water plume continues to expand in contrast to what is observed at atmosphericpressures higher than 200 mm.

6.5 Explosively Generated Water Cavities 325

760 mm AIR PRESSURE

16 mm AIR PRESSURE

Figure 6.13 The Gault and Sonett experimental results for a 0.250 cm diameter aluminumprojectile moving at 1.8 kilometers/sec impacting water.

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760 mm AIR PRESSURE

16 mm AIR PRESSURE

Figure 6.14 The Gault and Sonett experimental results for a 0.635 cm diameter aluminumprojectile moving at 2.5 kilometers/sec at 760 mm air pressure. A 0.3175 cm diameter Pyrexprojectile moving at 2.32 kilometers/sec in 16 mm of air is shown in the bottom frame.

6.5 Explosively Generated Water Cavities 327

760 mm AIR PRESSURE

150 mm AIR PRESSURE

Figure 6.15 The Kedrinskii results for an exploding bridge wire in water at 760 mm and150 mm air pressure.

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.00 s .005 s

.01 s .015 s

.03 s .07 s

Figure 6.16 The density profiles for a 0.25 cm diameter Aluminum projectile moving at2.0 kilometers/sec impacting water at 5 atmosphere air pressure. The times are 0, 5, 10, 15,30, and 70 milliseconds. The graphs are 100 cm wide by 120 cm tall, with 50 cm of water.

6.5 Explosively Generated Water Cavities 329

.000 s .025 s

.075 s .125 s

Figure 6.17 The density profiles for a 0.25 cm diameter Aluminum projectile moving at2.0 kilometers/sec impacting water at 1 atmosphere air pressure. The times are 0, 25, 75,and 125 milliseconds. The graphs are 100 cm wide and 120 cm tall, with 50 cm of waterand 70 cm air.

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.00 s .005 s

.02 s .05 s

Figure 6.18 The density profiles for a 0.25 cm diameter Aluminum projectile moving at2.0 kilometers/sec impacting water at 76 mm (0.1 atmosphere) air pressure. The times are0, 5, 20, and 50 milliseconds. The graphs are 80 cm wide by 100 cm tall with 40 cm ofwater and 60 cm air.

6.5 Explosively Generated Water Cavities 331

Explosive Generated Cavities

In reference 15, detailed one-dimensional compressible hydrodynamic modeling is de-scribed for explosives detonated in deep water. Agreement was obtained with the exper-imentally observed explosive cavity maximum radius and the period of the oscillation. Itwas concluded that the detonation product equation of state over the required range of 1megabar to 0.01 atmosphere was adequate for accurately determining the energy partitionbetween detonation products and the water. It was also concluded that the equations ofstate for water and detonation products were sufficiently accurate that they could be re-liably used in multidimensional studies of water cavity formation and the resulting waterwave generation in the region of the “upper critical depth”.

The “upper critical depth” is the experimentally observed location of an explosivecharge relative to the initial water surface that results in the maximum water wave height.It occurs when the explosive charge is approximately two-thirds submerged. The observedwave height at the upper critical depth is twice that observed for completely submergedexplosive charges at the “lower critical depth.” If the waves formed are shallow water wavescapable of forming tsunamis, then the upper critical depth phenomenon would be importantin evaluating the magnitude of a tsunami event from other than tectonic events.

The water wave amplitude as a function of the depth the explosive is immersed in wateris shown in Figure 6.19. The scaled amplitude is AR/W and the scaled depth is D/Wwhere A is maximum wave amplitude at a distance R from the explosive charge of weightW . The “upper critical depth” is at the first wave height maximum which occurs when anexplosive charge is located at the water surface. The second smaller increase in wave heightis at the “lower critical depth” which is about half the upper critical height but results inlonger wave length water waves. Data are included for explosives with weights of 0.017 to175 kilograms. The Craig11 experimental results are shown with a large x.

Figure 6.19 The scaled wave height as a function of scaled explosive charge depth. The“upper critical depth” is the explosive charge depth when the maximum wave height occurswhich is approximately two-thirds submerged. The second smaller increase in wave heightis the “lower critical depth.”

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During the study of the upper critical depth phenomenon in the 1960’s evidence ofcomplicated and unexpected fluid flows during water cavity formation was generated by B.G. Craig and described in references 1, 11 and 15.

A sphere of explosive consisting of a 0.635 cm radius XTX 8003 (80/20 PETN/SiliconBinder at 1.5 g/cc) explosive and a 0.635 cm radius PBX-9404 (94/6 HMX/binder at 1.84g/cc) explosive was detonated at its center. The sphere was submerged at various depthsin water. PHERMEX16 radiographs and photographs were taken with framing and moviecameras. The radiographs are shown in Figure 6.20.

The cavity, water ejecta and water surface profiles shown in the PHERMEX radiogra-phy in Figure 6.20 were closely approximated by the compressible hydrodynamic modelingdescribed in reference 15 using the 2DE code and in Figure 6.21 using the NOBEL code.

15.8µs 26.3µs

61.3µs

Figure 6.20 Dynamic radiographs of a 2.54 cm diameter PBX-9404 explosive sphere det-onated at its center and half submerged in water at 1 atmosphere air pressure. The timesare 15.8, 26.3 and 61.3 microseconds. The sketch shows the prominent features of theradiographs with the water shock dashed.

6.5 Explosively Generated Water Cavities 333

15µs 26µs

60µs

Figure 6.21 NOBEL density profiles for a 2.54 cm diameter PBX-9404 explosive spheredetonated at its center and half submerged in water at 1 atmosphere air pressure. Thetimes are 15.0, 26.0 and 60.0 microseconds for comparision with the radiographs in Figure6.20. The width is 16 cm and the height is 24 cm, of which 16 cm is water.

At later times, while the water cavity was expanding, the upper ejecta plume collapsedand converged on the axis generating an upward water ejecta jet on the axis above the waterplume and a downward water jet which generated a root on the axis below the bottom ofthe cavity. These results were not anticipated and neither was the observation that thewater cavity proceeded to close at its top and descend down into deeper water.

At first it was assumed that there was something unique about the explosive sourcethat was resulting in these remarkable observations. The reactive compressible hydrody-namic numerical models available were unable to reproduce the experimental observationsor suggest any possible physical mechanisms unique to explosives.

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.00 s .025 s

.075 s .275 s

Figure 6.22 The density profiles for a 2.54 cm diameter PBX-9404 explosive sphere det-onated at its center and half submerged in water at 1 atmosphere air pressure. The timesare 0, 25, 75, and 275 milliseconds. The graphs are 100 cm wide and 120 cm tall, with 50cm of water and 70 cm of air.

6.5 Explosively Generated Water Cavities 335

As described previously, the different behavior of the water cavity as it expanded whenthe atmospheric pressure was reduced from one atmosphere to less than a third of anatmosphere is independent of the method used to generate the cavity, such as an explodingbridge wire or a hypervelocity projectile impact.

These remarkable experimental observations resisted all modeling attempts for over 25years. The numerical simulations could not describe the thin water ejecta plumes formedabove the cavity or the interaction with the atmosphere on the outside of the ejecta plumeand the pressure inside the expanding cavity and plume.

Figure 6.22 shows the calculated water profiles for a 0.25 cm diameter PBX-9404 explo-sive sphere detonated at its center half submerged in water at one atmosphere air pressure.

All the projectile, exploding bridge wire and explosive experimental observations werereproduced as the atmospheric pressure was varied. At sufficiently high atmospheric pres-sure, the difference between the pressure outside the ejecta plume and the decreasing pres-sure inside the water plume and cavity as it expanded, resulted in the ejecta plume converg-ing and colliding at the axis. A jet of water formed and proceeded above and back into thebubble cavity along the axis. The jet proceedes back through the bubble cavity penetratingthe bottom of the cavity and formed the root observed experimentally. The complicatedcavity collapse and resulting descent into deeper water was also numerically modeled.Explosive Generated Water Wave

Craig11 measured the wave amplitude as a function of time for the first few seconds ata distance of 4 meters from a 2.54 cm diameter PBX-9404 explosive sphere initiated at itscenter in 3 meters of water. He included mass markers in the water. Mass markers located1 meter below the water surface and markers located 0.5 meter below the surface and 1meter from the explosive showed no appreciable movement compared with those locatednearer the surface or explosive charge. These results showed that the wave formed was nota shallow water wave.

The experimental and calculated wave parameters are summarized in Table 6.1. Theparameters are given after 4 meters of travel from the center of the explosive charge. Thewave parameters for the Airy wave were calculated using the WAVE code described inreference 1 for a depth of 3 meters and the experimentally observed wave length. Sincethe group velocity is almost exactly half the wave velocity, the Airy wave is a deep waterwave. The shallow water results are from reference 1. A small wave from the initial cavityformation is followed by a larger negative and then a positive wave resulting from the cavitycollapse. Only the second wave parameters are given in the table.

TABLE 6.1

Calculated and Experimental Wave Parameters

Airy Shallow NOBELExperimental Wave Water

Wave Velocity (m/sec) 2.50±0.2 2.41 5.42 2.50±0.10Amplitude (cm) 0.8 1.0 10.1 0.6Wave Length (m) 3.75 3.75(input) 1.0 3.75Period (sec) 1.5 1.55 0.18 1.5±0.1Group Velocity (m/sec) 1.21

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The wave gauge was close to the edge of the water tank, which resulted in reflectedwaves which perturbed the subsequent wave measurements. Since the wave gauge waslocated close (0.69 meter) to the side of the tank, the reflections from the first small waveperturbed the second wave, which probably explains the larger than calculated amplitude,as the calculated wave was unperturbed by any boundary.

Conclusions

In the late 1960’s and early 1970’s, B. G. Craig at the Los Alamos National Laboratoryreported observing the formation of ejecta jets and roots from cavities generated by smallspherical explosives detonated near the water surface while the gas cavity was expanding.

The hypervelocity impact (1.25 to 6 kilometers/sec) of projectiles into water was studiedat the University of Arizona in the early 1980’s by Gault and Sonett. They observed quitedifferent behavior of the water cavity as it expanded when the atmospheric pressure wasreduced from one to a tenth atmosphere. Above about a third of an atmosphere, a jet ofwater formed above the expanding cavity and a root developed below the bottom of thebubble cavity. They did not occur for atmospheric pressures below a third of an atmosphere.

Similar results were observed in the middle 1980’s by Kedrinskii at the Institute ofHydrodynamics in Novosibirsk, Russia when the water cavity was generated by explodingbridge wires, with jets and roots forming for normal atmospheric pressure and not forreduced pressures.

The NOBEL code has been used to model the experimental geometries of Sonett andof Craig. The experimental observations were reproduced as the atmospheric pressure wasvaried.

When the atmospheric pressure was increased, the difference between the pressureoutside the ejecta plume above the water cavity and the decreasing pressure inside the waterplume and cavity as it expanded resulted in the ejecta plume converging and colliding atthe axis forming a jet of water proceeding above and back into the bubble cavity alongthe axis. The jet proceeding back through the bubble cavity penetrated the bottom of thecavity and formed the root observed experimentally. The complicated cavity collapse wasnumerically modeled.

A PowerPoint presentation with Craig’s and Sonett’s experimental movies and com-puter animations is available on the CD-ROM in the /NOBEL/CAVITY directory.

Bobby G. Craig

6.6 Munroe Jets 337

6.6 Munroe Jets

Munroe jets are formed by the oblique interaction of detonation products from twoexplosive charges separated by an air gap. The jet consists of a high velocity jet of lowdensity precursor gases and particles that travel faster than the primary jet which is a highpressure regular shock reflection.

The Los Alamos PHERMEX Data Volumes contain 40 radiographs taken by DouglasVenable in the 1960’s of Munroe jets generated by Composition B explosive charges sepa-rated by 0.5 to 8 cm of air. In several of the experiments the Munroe jets interacted withthin Tantalum foils and with aluminum plates. The complete list of the Munroe jet shotsis on pages 23-24 of reference 15 and the Los Alamos Data Volumes are on the CD-ROM.

PHERMEX Experiments

The geometry of the PHERMEX Munroe jet experiments is shown in Figure 6.23. TheMunroe jet was formed by the interaction of the detonation products from two CompositionB-3 explosive charges separated by an air gap 1 cm wide. The charges are initiated by 2.54cm of Composition B-3 initiated by a P-081 lens.

Figure 6.23 Experimental geometry for studying Munroe jets.

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The dynamic PHERMEX radiograph for Shot 248 with a 1 cm wide gap after thedetonations had run 5.08 cm is shown in Figure 6.24 and for Shot 283 after the detonationshad run 10 cm in Figure 6.25. Figure 6.26 shows the NOBEL calculated density profiles.

Figure 6.24 Dynamic PHERMEX radiograph for Shot 248 after the Composition B-3detonations had run 5.08 cm along a 1 cm wide air gap.

Figure 6.25 Dynamic PHERMEX radiograph for Shot 283 after the Composition B-3detonations had run 10 cm along a 1 cm wide air gap.

6.6 Munroe Jets 339

Figure 6.26 NOBEL calculated density profiles when the Composition B-3 detonationshad run 5 and 10 cm along a 1 cm wide air gap.

Figure 6.27 is the dynamic PHERMEX radiograph for Shot 343. The gap is 2 cm wideand the detonations have run 10.1 cm. A 0.0254-mm-thick Tantalum foil across the top ofthe gap has been deformed considerably by the precursor gases and particles which travelfaster than either the detonation waves or the regular reflection.

Figure 6.27 Dynamic PHERMEX radiograph for Shot 343 after the Composition B-3detonations had run 100 mm along a 20 mm wide air gap. A 0.0254-mm-thick tantalumfoil has been deformed by the precursor particles and gases.

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In the PHERMEX experiments, when the detonation arrives at the bottom of the gap,the detonation products expand against the air and a high velocity of precursor gases travelahead of the detonation wave in the explosive. The expanding detonation products fromthe explosive collide and result in a high pressure regular shock reflection. The interactionwith a metal plate consists of first the interaction of the precursor gases and then the highpressure regular shock reflection arrives to further damage the metal plate.

The PHERMEX radiographs are shown for Shot 345 with a 2 cm wide gap and a 2.54cm thick Dural plate on top. The static radiograph is shown in Figure 6.28 and after theDural Plate was shocked in Figure 6.29.

Figure 6.28 Static PHERMEX radiograph for Shot 345.

Figure 6.29 Dynamic PHERMEX radiograph for Shot 345 after the Composition B-3detonations had shocked the 2.54 cm thick Dural plate.

6.6 Munroe Jets 341

Figure 6.30 The NOBEL density profile for Shot 345 after the Composition B-3 detonationshad shocked the 2.54 cm thick Dural plate.

The PHERMEX radiographs are shown for Shot 344 with a 2 cm wide gap and a0.625 cm thick Dural plate on top with a 2.54 cm long plug extending 1.915 cm betweenthe Composition B-3 charges. The static radiograph is shown in Figure 6.31 and after theDural Plate was shocked in Figure 6.32.

Figure 6.31 Static PHERMEX radiograph for Shot 344.

Figure 6.32 Dynamic PHERMEX radiograph for Shot 344 after the Composition B-3detonations had shocked the 2.54 cm thick Dural plate.

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Figure 6.33 The NOBEL X-Ray density profile for Shot 344 after the Composition B-3detonations had shocked the 0.625 cm thick Dural plate and the 2.54 cm long plug.

The PHERMEX radiographs show the formation of Munroe jets by the oblique inter-action of the detonation product fronts of the two explosive charges separated by an airgap. The jet consists of a high velocity jet of precursor gases and particles that travel fasterthan the primary jet which is a high pressure regular shock reflection. The Munroe jetis more energetic than the explosive detonation wave and can result in significantly moredeformation of metal plates.

Explosive interfaces or defects such as cracks will result in Munroe jets which can causesignificant damage to adjacent metals. The Munroe jets formed by etchings on explosivesurfaces can result in remarkable sketches such as the metal plate image of Alfred Nobelmade during his lifetime shown in Figure 6.34. The NOBEL code described in this chapteruses the Nobel image as its symbol.

Figure 6.34 The metal etching of Alfred Nobel generated by Munroe jets created bysketches on the explosive surface in contact with a metal plate.

6.6 Munroe Jets 343

Davis and Hill16 have performed an extensive test series studying the damage to steelwitness plates by a detonation running in PBX-9502 with small gaps.

Figure 6.35 A scale drawing of the experimental geometry.

Figure 6.36 The witness plate and a cross section across the trench left in the steel plateby the Munroe jet created by a 0.1 cm gap between two PBX-9502 charges.

The experimental study examined the damage on metal plates resulting from small gapsin explosive charges. The 2-inch square by 1-inch thick PBX-9502 blocks were placed on a1-inch by 4-inch diameter 304 steel witness plate. The blocks were separated by Plexiglasshims to form an air gap of 1 mm thickness. The PBX-9502 blocks were initiated from thetop by an SE-1 detonator and a 1/4 inch thick PBX-9501 booster.

The thin air gap results in significant additional damage to the steel witness plate inthe region near the gap. A 1/2 mm gap produces an effect essentially the same as the 1mm case. As the gap width is decreased from 1/2 mm, the amount of damage decreasesuntil at 1/32 mm the damage is just a score line. The 1 mm air gaps were placed at variousangles to the detonation. The damage at 0 and 10 degree experiments gave about the samedamage, while 20 and more degree gaps resulted in very little damage.

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The plate dent experiments are so difficult to understand or model that reference 16did not consider Munroe jets as a mechanism for the formation of the dents or connect theresults of the experiments with the PHERMEX Munroe jet data base. Such experimentsare similar to attempting to do biology from road kill.

Until the development of the NOBEL code, it was not possible to numerically modelsmall gaps with the resolution needed. The NOBEL initial geometry and the plate dent areshown in Figure 6.37.

Figure 6.37 The NOBEL initial geometry and the resulting plate dent.

In the plate dent experiments the diverging PBX-9501 detonation interacts with the 1/4inch long Plexiglas shim and initiates the PBX-9502. The shocked Plexiglas shim developsa surface spall layer which moves down the gap faster than the PBX-9502 detonation wave.The expanding detonation products from the explosive collide and a high pressure regularreflection proceeds down the gap compressing the gas ahead of it which drives the spalledshim layer. The shim and precursor gases dent the metal plate followed by the high pressureregular reflection of the detonation products.

The resulting dent profiles for the NOBEL calculation and the experiment are shownin Figure 6.38.

Figure 6.38 The NOBEL witness plate profile and the experimental dent.

6.6 Munroe Jets 345

As the angle of the gap relative to the detonation wave is increased, the high velocityprecursor gases interact with the sides of the gap and the regular reflection interactionbecomes weaker.

The PHERMEX and the plate dent experiments were modeled using the AMR reactivehydrodynamic code NOBEL. In the PHERMEX experiments, when the detonation arrivesat the bottom of the gap, the detonation products expand against the air resulting in highvelocity precursor gases traveling ahead of the explosive detonation wave. The expand-ing detonation products from the explosive collide at the axis of the gap and result in ahigh pressure regular shock reflection. The interaction with a metal plate consists of firstthe interaction of the precursor gases and then the high pressure regular shock reflectionarrives to further damage the plate. A PowerPoint presentation of the Munroe jet studywith NOBEL computer movies is available on the CD-ROM at the /NOBEL/MUNROEdirectory.

Michael Gittings

John M. Walsh