Professional Development Short Course On:
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Explosives Technology & Modeling
Course Summary:
Jan 25-28, 2010, Beltsville, MD
After an introduction to shock waves, the four-day course continues with shock $1895 (8:30am- 4:30pm)
matching and explosive technology. The formation and interaction of shock and 4 day course
detonation waves are illustrated using computer movies generated by numerical “Register 3 or More & Receive $100 each Off The Course Tuition.”
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 Course Outline:
propellant performance and vulnerability are described and typical applications
presented. Hands-on use of codes for evaluating explosive and propellant SHOCK WAVES
performance is provided. We recommend that you bring your laptop to this Fundamental Shock Wave Hydrodynamics
course. Shock Hugoniots
Shock Matching
Equation of State
Elastic-Plastic Flow
Phase Change
Instructor: Oblique Shock Reflection
Regular and Mach Shock Reflection
Charles L. Mader, Ph.D.,is a retired Fellow of the Los Alamos National SHOCK EQUATION OF STATE DATA BASES
Laboratory and President of Mader Consulting Company. Dr. Mader authored Shock Hugoniot Data
the monograph Numerical Modeling of Detonation, and also wrote four dynamic Shock Wave Profile Data
material property data volumes published by the University of California Press. Radiographic Data
His book and CD-ROM entitled Numerical Modeling of Explosives and Explosive Performance Data
Propellants, Third Edition, published in 2008 by CRC Press will be the text for Aquarium Data
the course. He is the author of Numerical Modeling of Water Waves, Second Russian Shock and Explosive Data
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 PERFORMANCE OF EXPLOSIVES AND PROPELLANTS
and private organizations in several countries. The Mader Consulting Co. web Steady-State Explosives
site is www.mccohi.com. Nonideal Explosives
Ammonium Salt-Explosive Mixtures
Ammonium Nitrate-Fuel Oil (ANFO) Mixtures
Metal Loaded Explosives
Nonsteady-State Detonations
Who Should Attend: Build-Up in Plane
Build-Up in Diverging Geometry and Converging Geometry
Chemistry of Build-Up
This course is suited for scientists, engineers, and managers interested in the Propellant Performance
current state of explosive and propellant technology, and in the use of numerical
modeling to evaluate the performance and vulnerability of explosives and INITIATION OF DETONATION
propellants. Thermal Initiation
Explosive Hazard Calibration Tests
Shock Initiation of Homogeneous Explosives
Hydrodynamic Hot Spot Model
Course Materials: Shock Sensitivity and Effects of Composition
Particle Size and Temperature
THE FOREST FIRE MODEL
Participants will receive a copy of Numerical Modeling of Explosives and Failure Diameter
Propellants, Third Edition by Dr. Charles Mader, 2008 CRC Press. In addition, Corner Turning
participants will receive an updated CD-ROM. 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
What You Will Learn: Lagrangian Reactive Flow
Numerical Solution of Two-Dimensional and Three-Dimensional Eulerian
Reactive Flow
What are Shock Waves and Detonation Waves?
Numerical Solution of Explosive and Propellant Properties
What makes an Explosive Hazardous?
DESIGN AND INTERPRETATION OF EXPERIMENTS
Where Shock Wave and Explosive Data is available. Plane-Wave Experiments
How to model Explosive and Propellant Performance. Explosions in Water
The Plate Dent Experiment
How to model Explosive Hazards and Vulnerability. The Cylinder Test
Jet Penetration of Inerts and Explosives
How to use the furnished explosive performance and hydrodynamic
Plane Wave Lens
computer codes. Regular and Mach Reflection of Detonation Waves
Insensitive High Explosive Initiators
The current state of explosive and propellant technology. Colliding Detonations
Shaped Charge Jet Formation and Target Penetration

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chapter six
NOBEL and PRad
6.1 Fifty Year History
During the almost ten years since the last edition of this book was written
a technological revolution in numerical modeling occurred with the development of
the NOBEL/SAGE/RAGE series of computer codes primarily by Michael Gittings of
SAIC/LANL.
Also during the last ten years an experimental technological revolution occurred with
the development of proton radiography (PRad)7 at LANL and its application to explosives
by John Zumbro6 and Eric Ferm10 .
NOBEL modeling of PRad experimental studies will be described in this Chapter
and 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 his
professional career and to have worked with Gittings and Zumbro.
The 50 years of explosive technology and modeling described in this book have been
driven by the genius of many dedicated scientists and engineers
John M. Walsh created, in the 1950s, the experimental techniques that resulted in much
of the shock wave physics described in the Los Alamos Data Volumes. He then created, in
the 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 create
the 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 and
weapon physics, but also the impact physics of projectiles and asteroids, and the generation
and propagation of water waves and tsunamis by landslides and hydrovolcanic explosions.
Douglas Venable developed the X-Ray machine PHERMEX and applied it to many
problems of shock and detonation wave physics in the 1960’s. In this chapter we will use
the NOBEL code to model some of his classic PHERMEX experimental observations of
Munroe jets. Most of our current understanding and modeling of detonation wave corner
turning 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 1960s
and 1970s, furnished the basis of much of the detonation physics and modeling described
in 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 and
in methods for improving the numerical resolution of compressible reactive hydrodynamic
calculations.
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 differential
equations for nonviscous, nonconducting, compressible fluid flow are
The Nomenclature
I internal energy
P pressure
Ux velocity in x direction
Uy velocity in y direction
Uz velocity in z direction
ρ density
t time
∂ρ ∂ρ ∂ρ ∂ρ
+ Ux + Uy + Uz
∂t ∂x ∂y ∂z
∂Ux ∂Uy ∂Uz
= −ρ + + ,
∂x ∂y ∂z
∂Ux ∂Ux ∂Ux ∂Ux ∂P
ρ + Ux + Uy + Uz =− ,
∂t ∂x ∂y ∂z ∂x
∂Uy ∂Uy ∂Uy ∂Uy ∂P
ρ + Ux + Uy + Uz =− ,
∂t ∂x ∂y ∂z ∂y
∂Uz ∂Uz ∂Uz ∂Uz ∂P
ρ + Ux + Uy + Uz =− ,
∂t ∂x ∂y ∂z ∂z
∂I ∂I ∂I ∂I
ρ + Ux + Uy + Uz
∂t ∂x ∂y ∂z
∂Ux ∂Uy ∂Uz
= −P + + .
∂x ∂y ∂z

6.2 The NOBEL Code 309
In NOBEL/SAGE/RAGE these equations are solved by a high-resolution Godunov
differencing scheme using an adaptive grid technique described in references 2 and 3. The
solution technique uses Continuous Adaptive Mesh Refinement (CAMR). The decision to
refine the grid is made cell-by-cell continuously throughout the calculation. The computing
is 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 size
for each material. The mesh refinement is shown in Figure 6.1. With the computational
power concentrated on the regions of the problem which require higher resolution, very large
computational 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 a
2:1 ratio. Adjacent cells may not differ by more than one level.
Much larger computational volumes, times and differences in scale can be simulated
than is possible using previous Eulerian techniques such as those described in Appendices
C 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 1
through 4 is called NOBEL and was used for modeling many problems in detonation
physics some of which are described later in this chapter.
The codes can describe one-dimensional slab or spherical geometry, two-dimensional
slab or cylindrical geometry, and three-dimensional Cartesian geometry.
Because modern supercomputing is currently done on clusters of machines containing
many identical processors, the parallel implementation of the code is very important. For
portability and scalability, the codes use the Message Passing Interface (MPI). Load leveling
is accomplished through the use of an adaptive cell pointer list, in which newly created
daughter cells are placed immediately after the mother cells. Cells are redistributed among
processors at every time step, while keeping mothers and daughters together. If there are
a 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 neighbor
variables into local scratch memory.

310 chapter six: NOBEL and PRad
The codes incorporate multiple material equations of state (analytical or SESAME
tabular). 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 interfaces
between different materials. The errors increase with increasing density differences. While
the mixture equations of state described in Appendix C would be more realistic, the problem
is minimized by using fine numerical resolution at interfaces. The amount of mass in mixed
cells is kept small resulting in small errors being introduced by the temperature equilibrium
assumption.
The strength is treated using an elastic-plastic model identical to that described in
Appendicies A, B and C.
A variety of boundary conditions is available, the most important being reflective
boundary walls, reflective internal boundaries, and “freeze regions” which allow specific
inflows and unrestricted outflows of material.
Very important for water cavity generation and collapse and the resulting water wave
history is the capability to initialize gravity properly, which is included in the code. For
example, this results in the initial density and initial pressure changing going from the
atmosphere at 40 kilometers altitude down to the ocean surface. Likewise the water density
and pressure changes correctly with ocean depth.
As described in reference 1, it became possible to calculate water wave problems for
minutes or even hours using compressible hydrodynamic models that require millions of
time steps for each second of flow. Only recently has it become possible to finely resolve
interfaces such as a water-air interface and follow the water wave with millimeter resolution
in a problem with 40 kilometers of air, 5 kilometers of water and tens of kilometers of ocean
crust. 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 water
surface.
The codes have been used to model water waves generated from impact landslides,
explosions, projectile impacts and asteroids as described in reference 1. Numerical modeling
of 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 tuning
of 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 SMP
supercomputers. SAGE provided an early testbed for development of massive parallelism
as 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 system
installed at Sandia National Laboratory in 1996 and the BlueGene/L system, installed at
Lawrence Livermore National Laboratory in 2005, has resulted in a performance increase of
a 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 neighboring
processors as well as for the need for collective operations.
Some of the remarkable advances in fluid physics using the SAGE code have been the
modeling of Richtmyer-Meshkov and shock induced instabilities described in references 4
and 5.

6.3 Proton Radiography (PRad) 311
6.3 Proton Radiograph (PRad)
The Proton Radiography Program at LANL has developed a radiographic facility at
the Los Alamos Neutron Science Center (LANSCE). Multiple proton radiographic images
of the same explosive experiment can be taken as described in references 6, 7 and 8. The
facility 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, but
using protons instead of photons. A magnetic lens focuses the protons onto a detector to
take a shadow radiograph.
Figure 6.2 Three ton explosive containment vessel (center) flanked by large electromagnets
that focus the protons to produce sharp radiographs.
The PRad facility is shown in Figures 6.2 and 6.3. For PRad, 50 nanosecond wide
proton beam pulses with approximately 109 protons per pulse are spaced in time at in-
tervals predetermined by experimental requirements. Transmitted and scattered protons
are imaged by an electromagnetic lens system20 and recorded by cameras. This technique
provides 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 density
of up to 60 g/cc. A permanent magnet magnifier lens is available that provides a factor of
7 magnification to study small systems (such as explosive reaction zones) with an accuracy
of 15 µm.
A number of PRad experiments on detonation physics have been performed. They
include 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 detonation
front 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 have
been modeled using the NOBEL code.
A series of experiments has been performed with PRad to study how shocked metals
fail when a shock wave is reflected from a free metal surface and the resulting rarefaction
wave puts the material in tension. Another series of experiments has been performed to
study fragmentation. Some of the proton radiographs have been published in reference 8.

312 chapter six: NOBEL and PRad
Forming An Image With Magnetic Lenses
LANL LANSCE Line C
Proton Object Camera Camera
Lens 1 Lens 2
Beam Vessel Set 1 Set 2
View looking into the proton radiography facility at LANSCE
11/10/04 4 P. D. Barnes, Jr., LLNL
Figure 6.3 The Proton Radiographic Facility at LANCSE. The object vessel contains the
explosive 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 in
early proton radiographs had persisted. John Zumbro developed a lens design using a series
of quadrupole electromagnets that preserves the angle that a proton makes with the optical
axis of the lens so that the optical axis of the lens is proportional to the proton’s radial
distance from the axis. The Zumbro lenses can be used in series with minimal degradation
of the images produced by later lenses and permit elemental identification.
The proton radiography imaging system is shown in Figure 6.4. The proton images
are produced as protons transmitted through a dynamic experiment are focused on the 12
by 12 cm tiled scintillator. The scintillator converts proton intensity to light intensity, and
the “turning” mirror reflects these light images to seven smaller mirrors, which reflect the
images 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 the
incident 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 duration
of the proton pulse.
The large gray circular object in Figure 6.4 is the back of the turning mirror, beneath
which are seven CCD cameras. These cameras store three frames each with the potential
to 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 multiple
frames and the resulting movie is on the CD-ROM in the directory /NOBEL/CONE and
PowerPoint program CONE.PPT.
The proton radiographic images are similar to PHERMEX images in that interpretation
of the images is often difficult. Comparision of proton radiographs with computed density
or even the NOBEL “x-ray” density plots has large uncertainities. John Zumbro used a
developmental version of the particle transport code Monte-Carlo-N-Particle (MCNP) to
model the PRad proton beamline. The proton transport through the target and subsequent
radiographs 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 and
NOBEL modeling are described in reference 9 and in this section. TATB (Triamino-trinitro
benzene) explosives became important by the 1960’s because of their shock insensitivity
to accidental initiation. Such explosives required large and powerful initiating systems
which 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 the
PHERMEX radiographic facility in planar experiments where the detonation propagation of
shock insensitive TATB based explosives X-0219 (90/10 TATB/Kel-F at 1.914 gm/cc) and
PBX-9502 (95/5 TATB/Kel-F at 1.894 gm/cc) into a larger block of the explosive left large
regions 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, and
1942 (Figure 4.17) and for PBX-9502 are Shots 1705, 1937, 1941 and 1943. The radiographs
are 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 using
the two-dimensional Lagrangian reactive hydrodynamic code, TDL, with the Forest Fire
heterogeneous shock initiation rate model described in Chapter 4. The experimental results
were also described using the two-dimensional Eulerian reactive hydrodynamic code, 2DE
in Chapter 4.
PHERMEX radiographs are available for colliding planar detonations of Composition
B-3 (Shots 86, 87, 91, 92, 139, 140, 195, 196, and 273-277), of Cyclotol (Shots 203-206 and
291), of Octol ( Shots 294-297) and of PBX-9404 (Shots 207-210, 292 and 1151). These
shots were used to evaluate the equation of state of detonation products at pressures up
to twice the C-J pressure of the explosives, such as the BKW equation of state which was
used to reproduce the radiographic results.
As described in Chapter 5, Travis used the image intensifier camera to examine the
nature of the diverging detonation waves formed in PBX-9404, PBX-9502, and X0219 by
hemispherical 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 thick
hemisphere 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 initiator
system (A) while about 1/5 of the explosive PBX-9502 remained unreacted. The initiator
system (A) developed an unreacted region for X-0219 so large that the detonation failed in
the geometry studied. The larger detonator (B) resulted in smaller unreacted regions for
PBX-9502 as did the higher pressure detonator (C).
The observed undecomposed explosive region formation and failure were reproduced
using 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 formation
of unreacted regions by cylindrical PBX-9502 detonations as they propagated into larger
cylindrical blocks of PBX-9502. The regions persisted for more than 6 microseconds at
densities slightly higher than initial density. Parts of the unreacted regions show indication
of a slow reaction occurring. Attempts at modeling the cylinder edge break-out using
Detonation Shock Dynamics (DSD), implanted in the MESA code, were unsuccessful. It
was concluded that the DSD model needs additional physics10 .
Colliding Diverging PBX-9502 Detonations
Experimental and numerical studies of colliding planar detonations are available as
are studies of the formation of unreacted regions in corner turning experiments and hemi-
spherical initiator experiments for shock insensitive explosives such as PBX-9502. What
remained to be determined was the interaction of colliding diverging detonations that also
exhibit large regions of partially undecomposed explosives as the colliding detonation is
formed.
The Proton radiographic shot PRAD0077 was designed to study the interaction of
colliding diverging PBX-9502 detonations which exhibit unreacted region formation. The
shot consisted of a 50-mm by 50-mm cylinder of PBX-9502 initiated on the top and bottom
at 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 were
taken 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 intervals
of 0.358 microseconds.
.
Figure 6.6 The seven PRAD077 proton radiographs at intervals of 0.358 microseconds
increasing from left to right and bottom to top.
The system results in a large dead or nonreactive zone as the detonation attempts to
turn the corner. The detonation wave travels for over 10-mm before it starts to expand and
turn 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 lower
density products. As the diverging detonation waves continue to collide, detonation regular
reflections 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 plane
and spherically diverging geometry and using the two-dimensional TDL code with C-J burn
and multiple-shock Forest Fire. The HOM equation of state and Forest Fire rate constants
used were identical to those used to model the PHERMEX corner turning experiments in
the 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 the
SIN 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-dimensional
SIN code of a PBX-9501 diverging detonation and the two-dimensional TDL calculation
with multiple-shock Forest Fire shown in Figure 6.8.
The TDL calculated density and mass fraction of undecomposed explosive contours are
shown 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 undecomposed
explosive at 0.5 µsec intervals using the two-dimensional Lagrangian code TDL with multiple
shock Forest Fire.

318 chapter six: NOBEL and PRad
Zumbro calculated the proton radiographic profile from the TDL density array of the
diverging detonation wave just before collision shown in Figure 6.9
Figure 6.9 The calculated proton radiograph for the TDL densities just before the collision
of the PBX-9502 diverging detonation waves.
The system was also modeled with the AMR Eulerian reactive hydrodynamic code
NOBEL 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 for
the NOBEL calculation with Forest Fire. The two-dimensional X-ray simulation for the
Nobel 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 described
on page 313 to generate the proton radiographic profile from the NOBEL calculated density
array.
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 with
multiple-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 the
NOBEL 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 with
multiple-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 the
proton radiograph from Figure 6.6 on the left after the diverging PBX-9502 detonation wave
turned the corner and just before the detonation waves collided.
The calculated peak detonation pressure achieved by the colliding diverging detonation
was 500 kb with a density of 3.125 gm/cc which is about the same as that achieved by
one-dimensional spherically diverging 9502 detonations but less than the calculated one-
dimensional plane 9502 peak colliding detonation pressure of 650 kb and density of 3.4
gm/cc.
The calculated detonation wave travels for over 10-mm before it starts to expand and
turn the corner, leaving more than half of the explosive unreacted. The resulting diverging
detonation is more curved than a one-dimensional spherical diverging detonation and has
a steeper slope behind the detonation front. This results in the colliding pressure decaying
faster than one-dimensional colliding spherical diverging pressures decay.
Conclusions
The interaction of colliding diverging detonations that also exhibit large regions of
partially undecomposed explosives as the colliding detonation is formed has been experi-
mentally radiographed using the Proton Radiographic Facility. Numerical modeling using
Lagrangian and Eulerian reactive hydrodynamic codes and the Forest Fire heterogeneous
shock 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 to
turn corners promptly. New detonation models must be able to reproduce the complicated
physics 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 performed
experiments designed to characterize the formation of water waves from explosives detonated
near the water surface. He reported observing the formation of ejecta water jets above and
jets or “roots” below the expanding gas cavity. This was unexpected and a scientific mystery
which remained unsolved until it was finally modeled using the NOBEL code in December
of 2002.
In the early 1980’s, the hypervelocity impact (1.25 to 6 kilometers/sec) of projectiles
into water was studied at the University of Arizona by Gault and Sonett12 . They observed
quite different behavior of the water cavity as it expanded when the atmospheric pressure
was reduced from one to a tenth atmosphere. Above about a third of an atmosphere, a jet
of water formed above the expanding cavity and a jet or “root” emerged below the bottom
of the cavity.
In the mid 1980’s, similar results were observed by Kedrinskii13 at the Institute of
Hydrodynamics in Novosibirsk, Russia, who created cavities in water by sending large
electrical currents through small lengths of small diameter Gold wires (bridge wires) causing
the Gold to vaporize. The “exploding bridge wire” is a common method used to initiate
propagating detonation in explosives. He observed water ejecta jets and roots forming for
normal 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 or
explosives 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 by
large-yield explosions and asteroid impacts has been based on extrapolation of empirical cor-
relations of small-yield experimental data or numerical modeling assuming incompressible
flow, which does not reproduce the above experimental observations.
The NOBEL code has been used to model the experimental geometries of Sonett and
of Craig. The experimental observations were reproduced as the atmospheric pressure was
varied 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 Arizona
to 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 observed
by Craig11 . While the water cavity was expanding, an ejecta jet was formed at the axis
above the water plume and a jet or “root” emerged along the axis below the cavity. The
water cavity appeared to close and descend into deeper water.
To improve the photographic resolution and reduce the light from the air shock, Sonett
repeated his impact experiments under reduced atmospheric pressure. Much to everyone’s
surprise, when the pressure was reduced from one to a tenth atmosphere, the ejecta jet and
the root did not occur and the water cavity expanded and collapsed upward toward the
surface. This was what had been expected to occur in both the earlier Craig experiments
and the projectile impacts at one atmosphere pressure.

324 chapter six: NOBEL and PRad
It became evident that the atmospheric pressure and the pressure differences inside
and outside the water plume above the water surface were the cause of the formation of the
jet, 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 aluminum
projectile moving at 1.8 kilometers/sec impacting water at one atmosphere (760 mm), and
at 16 mm air pressure. A water stem and jet occurs at one atmosphere and not at low
pressure.
Figure 6.14 shows the Gault and Sonett results for a 0.635 cm diameter aluminum
projectile moving at 2.5 kilometers/sec impacting water at one atmosphere (760 mm) and
a 0.3175 cm diameter Pyrex projectile moving at 2.32 kilometers/sec impacting water at 16
mm 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 studying
the generation of water cavities from exploding bridge wires. He was observing the formation
of ejecta jets and roots as the water cavity expanded similar to those observed by Craig
using explosives and by Gault and Sonett using projectiles. After we showed him the
effect of reduced atmospheric pressure, he proceeded to repeat his exploding bridge wire
experiments under reduced pressure. He observed that the jets and roots did not form when
the atmospheric pressure was reduced to 0.2 atmosphere.
Figure 6.15 shows the Kedrinskii results for an exploding bridge wire in water at one
atmosphere and at 0.2 atmosphere air pressure.
Compressible Navier-Stokes Modeling
The projectile impact and explosive generated water cavity were modeled with the
recently developed full Navier-Stokes AMR (Adaptive Mesh Refinement) Eulerian com-
pressible hydrodynamic code NOBEL described earlier. The continuous adaptive mesh
refinement permits the following of shocks and contact discontinuities with a very fine grid
while using a coarse grid in smooth flow regions. It can resolve the water plume and the
pressure gradients across the water plume and follow the generation of the water ejecta jet
and root.
Figure 6.16 shows the calculated density profiles for a 0.25 cm diameter aluminum
projectile 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 jet
passes down through the cavity, penetrating the bottom of the cavity at the axis forming
the 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 aluminum
projectile 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 aluminum
projectile moving at 2.0 kilometers/sec impacting water at 0.1 atmosphere air pressure. The
tip of the water plume continues to expand in contrast to what is observed at atmospheric
pressures 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 aluminum
projectile moving at 1.8 kilometers/sec impacting water.

326 chapter six: NOBEL and PRad
760 mm AIR PRESSURE
16 mm AIR PRESSURE
Figure 6.14 The Gault and Sonett experimental results for a 0.635 cm diameter aluminum
projectile moving at 2.5 kilometers/sec at 760 mm air pressure. A 0.3175 cm diameter Pyrex
projectile 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 and
150 mm air pressure.

328 chapter six: NOBEL and PRad
.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 at
2.0 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 at
2.0 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 water
and 70 cm air.

330 chapter six: NOBEL and PRad
.00 s .005 s
.02 s .05 s
Figure 6.18 The density profiles for a 0.25 cm diameter Aluminum projectile moving at
2.0 kilometers/sec impacting water at 76 mm (0.1 atmosphere) air pressure. The times are
0, 5, 20, and 50 milliseconds. The graphs are 80 cm wide by 100 cm tall with 40 cm of
water 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. It
was concluded that the detonation product equation of state over the required range of 1
megabar to 0.01 atmosphere was adequate for accurately determining the energy partition
between detonation products and the water. It was also concluded that the equations of
state 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 water
wave generation in the region of the “upper critical depth”.
The “upper critical depth” is the experimentally observed location of an explosive
charge 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 observed
wave height at the upper critical depth is twice that observed for completely submerged
explosive charges at the “lower critical depth.” If the waves formed are shallow water waves
capable of forming tsunamis, then the upper critical depth phenomenon would be important
in 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 water
is shown in Figure 6.19. The scaled amplitude is AR/W and the scaled depth is D/W
where A is maximum wave amplitude at a distance R from the explosive charge of weight
W . The “upper critical depth” is at the first wave height maximum which occurs when an
explosive charge is located at the water surface. The second smaller increase in wave height
is at the “lower critical depth” which is about half the upper critical height but results in
longer wave length water waves. Data are included for explosives with weights of 0.017 to
175 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 occurs
which is approximately two-thirds submerged. The second smaller increase in wave height
is the “lower critical depth.”

332 chapter six: NOBEL and PRad
During the study of the upper critical depth phenomenon in the 1960’s evidence of
complicated 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/Silicon
Binder at 1.5 g/cc) explosive and a 0.635 cm radius PBX-9404 (94/6 HMX/binder at 1.84
g/cc) explosive was detonated at its center. The sphere was submerged at various depths
in water. PHERMEX16 radiographs and photographs were taken with framing and movie
cameras. 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 modeling
described 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 times
are 15.8, 26.3 and 61.3 microseconds. The sketch shows the prominent features of the
radiographs 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 sphere
detonated at its center and half submerged in water at 1 atmosphere air pressure. The
times are 15.0, 26.0 and 60.0 microseconds for comparision with the radiographs in Figure
6.20. 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 collapsed
and converged on the axis generating an upward water ejecta jet on the axis above the water
plume and a downward water jet which generated a root on the axis below the bottom of
the cavity. These results were not anticipated and neither was the observation that the
water 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 source
that was resulting in these remarkable observations. The reactive compressible hydrody-
namic numerical models available were unable to reproduce the experimental observations
or suggest any possible physical mechanisms unique to explosives.

334 chapter six: NOBEL and PRad
.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 times
are 0, 25, 75, and 275 milliseconds. The graphs are 100 cm wide and 120 cm tall, with 50
cm 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 when
the atmospheric pressure was reduced from one atmosphere to less than a third of an
atmosphere is independent of the method used to generate the cavity, such as an exploding
bridge wire or a hypervelocity projectile impact.
These remarkable experimental observations resisted all modeling attempts for over 25
years. The numerical simulations could not describe the thin water ejecta plumes formed
above the cavity or the interaction with the atmosphere on the outside of the ejecta plume
and 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 were
reproduced 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 the
bubble cavity along the axis. The jet proceedes back through the bubble cavity penetrating
the bottom of the cavity and formed the root observed experimentally. The complicated
cavity 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 at
a distance of 4 meters from a 2.54 cm diameter PBX-9404 explosive sphere initiated at its
center in 3 meters of water. He included mass markers in the water. Mass markers located
1 meter below the water surface and markers located 0.5 meter below the surface and 1
meter from the explosive showed no appreciable movement compared with those located
nearer the surface or explosive charge. These results showed that the wave formed was not
a shallow water wave.
The experimental and calculated wave parameters are summarized in Table 6.1. The
parameters are given after 4 meters of travel from the center of the explosive charge. The
wave parameters for the Airy wave were calculated using the WAVE code described in
reference 1 for a depth of 3 meters and the experimentally observed wave length. Since
the group velocity is almost exactly half the wave velocity, the Airy wave is a deep water
wave. The shallow water results are from reference 1. A small wave from the initial cavity
formation is followed by a larger negative and then a positive wave resulting from the cavity
collapse. Only the second wave parameters are given in the table.
TABLE 6.1
Calculated and Experimental Wave Parameters
Airy Shallow NOBEL
Experimental Wave Water
Wave Velocity (m/sec) 2.50±0.2 2.41 5.42 2.50±0.10
Amplitude (cm) 0.8 1.0 10.1 0.6
Wave Length (m) 3.75 3.75(input) 1.0 3.75
Period (sec) 1.5 1.55 0.18 1.5±0.1
Group Velocity (m/sec) 1.21

336 chapter six: NOBEL and PRad
The wave gauge was close to the edge of the water tank, which resulted in reflected
waves which perturbed the subsequent wave measurements. Since the wave gauge was
located close (0.69 meter) to the side of the tank, the reflections from the first small wave
perturbed 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 Laboratory
reported observing the formation of ejecta jets and roots from cavities generated by small
spherical 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 studied
at the University of Arizona in the early 1980’s by Gault and Sonett. They observed quite
different behavior of the water cavity as it expanded when the atmospheric pressure was
reduced from one to a tenth atmosphere. Above about a third of an atmosphere, a jet of
water formed above the expanding cavity and a root developed below the bottom of the
bubble 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 of
Hydrodynamics in Novosibirsk, Russia when the water cavity was generated by exploding
bridge wires, with jets and roots forming for normal atmospheric pressure and not for
reduced pressures.
The NOBEL code has been used to model the experimental geometries of Sonett and
of Craig. The experimental observations were reproduced as the atmospheric pressure was
varied.
When the atmospheric pressure was increased, the difference between the pressure
outside the ejecta plume above the water cavity and the decreasing pressure inside the water
plume and cavity as it expanded resulted in the ejecta plume converging and colliding at
the axis forming a jet of water proceeding above and back into the bubble cavity along
the axis. The jet proceeding back through the bubble cavity penetrated the bottom of the
cavity and formed the root observed experimentally. The complicated cavity collapse was
numerically 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 two
explosive charges separated by an air gap. The jet consists of a high velocity jet of low
density precursor gases and particles that travel faster than the primary jet which is a high
pressure regular shock reflection.
The Los Alamos PHERMEX Data Volumes contain 40 radiographs taken by Douglas
Venable 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 with
thin Tantalum foils and with aluminum plates. The complete list of the Munroe jet shots
is 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. The
Munroe jet was formed by the interaction of the detonation products from two Composition
B-3 explosive charges separated by an air gap 1 cm wide. The charges are initiated by 2.54
cm of Composition B-3 initiated by a P-081 lens.
Figure 6.23 Experimental geometry for studying Munroe jets.

338 chapter six: NOBEL and PRad
The dynamic PHERMEX radiograph for Shot 248 with a 1 cm wide gap after the
detonations had run 5.08 cm is shown in Figure 6.24 and for Shot 283 after the detonations
had 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-3
detonations 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-3
detonations 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 detonations
had 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 wide
and the detonations have run 10.1 cm. A 0.0254-mm-thick Tantalum foil across the top of
the gap has been deformed considerably by the precursor gases and particles which travel
faster than either the detonation waves or the regular reflection.
Figure 6.27 Dynamic PHERMEX radiograph for Shot 343 after the Composition B-3
detonations had run 100 mm along a 20 mm wide air gap. A 0.0254-mm-thick tantalum
foil has been deformed by the precursor particles and gases.

340 chapter six: NOBEL and PRad
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 travel
ahead of the detonation wave in the explosive. The expanding detonation products from
the explosive collide and result in a high pressure regular shock reflection. The interaction
with a metal plate consists of first the interaction of the precursor gases and then the high
pressure 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 2.54
cm thick Dural plate on top. The static radiograph is shown in Figure 6.28 and after the
Dural 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-3
detonations 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 detonations
had shocked the 2.54 cm thick Dural plate.
The PHERMEX radiographs are shown for Shot 344 with a 2 cm wide gap and a
0.625 cm thick Dural plate on top with a 2.54 cm long plug extending 1.915 cm between
the Composition B-3 charges. The static radiograph is shown in Figure 6.31 and after the
Dural 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-3
detonations had shocked the 2.54 cm thick Dural plate.

342 chapter six: NOBEL and PRad
Figure 6.33 The NOBEL X-Ray density profile for Shot 344 after the Composition B-3
detonations 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 air
gap. The jet consists of a high velocity jet of precursor gases and particles that travel faster
than the primary jet which is a high pressure regular shock reflection. The Munroe jet
is more energetic than the explosive detonation wave and can result in significantly more
deformation of metal plates.
Explosive interfaces or defects such as cracks will result in Munroe jets which can cause
significant damage to adjacent metals. The Munroe jets formed by etchings on explosive
surfaces can result in remarkable sketches such as the metal plate image of Alfred Nobel
made during his lifetime shown in Figure 6.34. The NOBEL code described in this chapter
uses the Nobel image as its symbol.
Figure 6.34 The metal etching of Alfred Nobel generated by Munroe jets created by
sketches 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 steel
witness 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 plate
by 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 gaps
in explosive charges. The 2-inch square by 1-inch thick PBX-9502 blocks were placed on a
1-inch by 4-inch diameter 304 steel witness plate. The blocks were separated by Plexiglas
shims to form an air gap of 1 mm thickness. The PBX-9502 blocks were initiated from the
top 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 in
the region near the gap. A 1/2 mm gap produces an effect essentially the same as the 1
mm case. As the gap width is decreased from 1/2 mm, the amount of damage decreases
until at 1/32 mm the damage is just a score line. The 1 mm air gaps were placed at various
angles to the detonation. The damage at 0 and 10 degree experiments gave about the same
damage, while 20 and more degree gaps resulted in very little damage.

344 chapter six: NOBEL and PRad
The plate dent experiments are so difficult to understand or model that reference 16
did not consider Munroe jets as a mechanism for the formation of the dents or connect the
results of the experiments with the PHERMEX Munroe jet data base. Such experiments
are similar to attempting to do biology from road kill.
Until the development of the NOBEL code, it was not possible to numerically model
small gaps with the resolution needed. The NOBEL initial geometry and the plate dent are
shown 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 1/4
inch long Plexiglas shim and initiates the PBX-9502. The shocked Plexiglas shim develops
a 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 regular
reflection proceeds down the gap compressing the gas ahead of it which drives the spalled
shim layer. The shim and precursor gases dent the metal plate followed by the high pressure
regular reflection of the detonation products.
The resulting dent profiles for the NOBEL calculation and the experiment are shown
in 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 velocity
precursor gases interact with the sides of the gap and the regular reflection interaction
becomes weaker.
The PHERMEX and the plate dent experiments were modeled using the AMR reactive
hydrodynamic code NOBEL. In the PHERMEX experiments, when the detonation arrives
at the bottom of the gap, the detonation products expand against the air resulting in high
velocity 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 a
high pressure regular shock reflection. The interaction with a metal plate consists of first
the interaction of the precursor gases and then the high pressure regular shock reflection
arrives to further damage the plate. A PowerPoint presentation of the Munroe jet study
with NOBEL computer movies is available on the CD-ROM at the /NOBEL/MUNROE
directory.
Michael Gittings
John M. Walsh

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