ARL-TR-7953 ● FEB 2017

US Army Research Laboratory

Considerations for Explosively Driven Conical 

Shock Tube Design: Computations and 

Experiments

by Joel B Stewart

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ARL-TR-7953 ● FEB 2017

US Army Research Laboratory

Considerations for Explosively Driven Conical 

Shock Tube Designs: Computations and 

Experiments

by Joel B Stewart 

Weapons and Materials Research Directorate, ARL

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4. TITLE AND SUBTITLE

Considerations for Explosively Driven Conical Shock Tube Design: 

Computations and Experiments 

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Joel B Stewart

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US Army Research Laboratory

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

This report covers computational and experimental work related to the development and design of explosively driven conical 

shock tubes. The first part of the report focuses on using Lawrence Livermore National Laboratory’s ALE3D shock physics 

code to replicate previous experimental results obtained from a 17° (full angle) shock tube. Next, a computational parameter 

study of various shock tube design choices, such as shock tube angle and explosive charge geometry, on the resulting air blast 

is detailed. Finally, experimental data using a new 10° shock tube along with some of the driver section design choices 

investigated in the computational parameter study is presented.

15. SUBJECT TERMS

shock tube, air blast, hydrocode, explosively driven shock tube, explosive

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Joel B Stewart

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Contents

List of Figures iv

List of Tables vii

Acknowledgments viii

1. Introduction 1

2. Computations vs Previous Experiments: 17° Conical Shock Tube 3

3. Shock Tube Parametric Computational Study 7

3.1 On the Influence of Driver Section and Charge Design: 10° Conical 

Shock Tube 8

3.2 On the Influence of Cone Angle 18

4. 10° Shock Tube: Computational and Experimental Results 20

4.1 Computational Predictions vs Experimental Results 22

4.2 Mitigation of Release Waves at the Exit Section 28

5. Conclusions 34

6. References 35

Appendix. 10° Shock Tube Pencil Gauge Data 36

List of Symbols, Abbreviations, and Acronyms 40

Distribution List 41
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iv

List of Figures

Fig. 1 Zoomed-in view of the ALE3D shock tube entry section geometry 

(the red material represents C4 and the gray represents the steel shock 

tube), which was used to replicate experimental data presented in 

Stewart and Pecora (2015).....................................................................4

Fig. 2 Comparison of computational vs experimental data on the axis of 

symmetry and at the exit (192 cm from the nearest surface of the C4 

explosive driver charge) of a 17° shock tube (a) overpressure and (b) 

impulse per unit area..............................................................................5

Fig. 3 Comparison of experimental vs computational data 15 cm off the axis 

of symmetry and at the exit (192 cm from the nearest surface of the 

C4 explosive driver charge) of a 17° shock tube (a) overpressure and 

(b) impulse per unit area ........................................................................6

Fig. 4 Schematic of shock tube driver section for reference with Table 1.....10

Fig. 5 Zoomed-in view of the ALE3D shock tube entry section geometry for 

the baseline shock tube design (the red material represents pentolite, 

the gray represents the steel shock tube, and the blue represents the 

air)........................................................................................................10

Fig. 6 Pressure loading measured 2.0 m downstream of the driver charge 

surface for the baseline design of the 10° shock tube driver section 

and 5-g driver charge compared with a Friedlander waveform obtained 

from CONWEP for a 544-g (1.2-lb) pentolite charge .........................11

Fig. 7 Influence of driver charge mass on the pressure profile of the 10° 

shock tube measured 2.0 m downstream of the driver charge surface 

(a) fixed aspect ratio (L/D = 1) and (b) fixed charge diameter (D = 

16.0 mm)..............................................................................................13

Fig. 8 Influence of a backing plate behind the 5-g driver charge on the 

pressure profile of the 10° shock tube measured 2.0 m downstream 

of the driver charge surface..................................................................14

Fig. 9 Influence of various modifications to the driver section and 5-g driver 

charge on the pressure profile of the 10° shock tube measured 2.0 m 

downstream of the driver charge surface .............................................15

Fig. 10 Pressure contours at 2 μs after detonation showing the detonation 

wave and shock reflections through the explosive driver charge (red 

boundary line) for the baseline case with no air gap between the driver 

charge and the steel walls (bottom half) and for the case with a 2-mm 

air gap (top half)...................................................................................16

Fig. 11 Influence of shock tube cone angle on the pressure profile measured 

2.0 m downstream of the driver charge surface...................................19

Fig. 12 Comparison of pressure contours at the approximate times when the 

primary blast wave has traveled 2.0 m inside the shock tube: (a) 10° 

cone (2.1 ms) and (b) 30° cone (1.5 ms)..............................................20
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v

Fig. 13 Shock tube basic engineering drawings (dimensions are in inches): 

(a) driver housing section, (b) 10° conical driver transition section, 

and (c) 10° conical body section including the cylindrical exit 

section ..................................................................................................22

Fig. 14 10° shock tube, without the cylindrical exit section ............................23

Fig. 15 Example shock tube driver section used in an experiment: (a) (from 

left to right) pentolite explosive charge, blue foam centering device, 

cylindrical driver housing section, and conical driver transition 

section prior to the experiment; (b) driver housing section and 

driver transition section postexperiment..............................................24

Fig. 16 Comparison of experimental vs computational data on the axis of 

symmetry and at the exit (2.16 m from the nearest surface of the 

pentolite explosive driver charge) of a 10° shock tube: 

(a) overpressure and (b) impulse per unit area.....................................26

Fig. 17 Comparison of experimental vs computational data 10 cm off the axis 

of symmetry and at the exit (2.16 m from the nearest surface of the 

pentolite explosive driver charge) of a 10° shock tube: 

(a) overpressure and (b) impulse per unit area.....................................27

Fig. 18 10° shock tube, with the cylindrical exit section attached ...................29

Fig. 19 Comparison of experimental data on the axis of symmetry and at the 

exit (2.16 m from the nearest surface of the 5-g pentolite explosive 

driver charge) of a 10° shock tube with an exit section vs a 

Friedlander waveform: (a) overpressure and (b) impulse per unit 

area.......................................................................................................30

Fig. 20 Comparison of experimental data 10 cm off the axis of symmetry and 

at the exit (2.16 m from the nearest surface of the 5-g pentolite 

explosive driver charge) of a 10° shock tube with an exit section vs a 

Friedlander waveform: (a) overpressure and (b) impulse per unit 

area.......................................................................................................31

Fig. 21 Shock tube experimental air blast data due to a 5-g pentolite charge at 

various locations compared with the Friedlander waveforms at 

corresponding locations for an 1814-g pentolite charge: (a) without 

an exit section and (b) with an exit section..........................................33

Fig. A-1 Experimental data from pencil gauges inserted 6 inches inside the 

shock tube’s conical exit (i.e., 2.00 m from the charge surface), with 

no cylindrical exit section. Data are shown from 2 experiments, both 

on and 102-mm off-axis.......................................................................37

Fig. A-2 Experimental data from pencil gauges inserted at the shock tube’s 

conical exit (i.e., 2.16 m from the charge surface), with no cylindrical 

exit section. Data are shown from 2 experiments, both on and 

102-mm off-axis...................................................................................37
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vi

Fig. A-3 Experimental data from pencil gauges inserted 6 inches outside the 

conical shock tube’s exit (i.e., 2.31 m from the charge surface), with 

no cylindrical exit section. Data are shown from 2 experiments, both 

on and 102-mm off-axis.......................................................................38

Fig. A-4 Experimental data from pencil gauges inserted at the shock tube’s 

conical exit (i.e., 2.16 m from the charge surface), when a cylindrical 

exit section is used. Data are shown from 2 experiments, both on and 

102-mm off-axis...................................................................................38

Fig. A-5 Experimental data from pencil gauges inserted 6 inches outside the 

conical shock tube’s exit (i.e., 2.31 m from the charge surface), when 

a cylindrical exit section is used. Data are shown from 2 experiments, 

both on and 102 mm off-axis...............................................................39
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vii

List of Tables

Table 1 Computational test matrix for 10° shock tube study..............................9

Table 2 Peak pressures (gauge) in 10° shock tube study ..................................17

Table 3 Computational test matrix for shock tube cone angle study................18
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viii

Acknowledgments

I would like to acknowledge Ms Rachel Ehlers for initiating this research into 

explosively driven shock tubes and facilitating the various programs covered under 

this report. Drs Scott Kukuck and Barrie Homan made themselves available for 

technical discussions during all phases of this work, and I appreciate their insight 

and feedback. Mr Stephen Schraml provided a technical review for this report, and 

his feedback greatly improved its quality. For the experiments involving the 10°

shock tube, I would like to acknowledge Mr Paul Duvall and Mr Benjamin 

Showalter as the test directors; Mr James Racine, Mr Rick Rapposelli, Mr Larry 

Stevenson, and Mr Charles Wilhelm for range setup and execution; Dr Brian Roos 

and Ms Dawnn Megonnell for coordination and fabrication of explosive charges; 

Mr James Gyolai and Mr Bobby Hall at the US Army Research Laboratory (ARL)

machine shop for fabricating the shock tube driver sections; Mr Robert Bruce for 

coordination and Mr David Weyand for press-braking the shock tube body section 

and fabricating the steel part of the shock tube stand at the ARL weld shop; and Mr 

Gerard Chaney at the ARL wood shop for fabricating the foam centering devices 

and the wooden stand. 
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1. Introduction

Shock tubes have been used for more than a century to provide a controlled, 

repeatable environment to investigate shock waves travelling through various 

media and the interaction of these shock waves with other structures (Henshall 

1957). Shock tubes generally fall into one of the following categories: 1) gas-driven

shock tubes, where high-pressure gases combined with a burst disc result in a shock 

wave; or 2) explosively driven shock tubes, where an explosive charge generates 

the shock wave. The challenges associated with operating the different types of 

shock tubes and accurately producing the particular waveforms of interest have 

been listed elsewhere (e.g., Courtney et al. 2012), but a limited list of advantages 

and disadvantages for explosively driven shock tubes specifically is as follows:

Advantages:

 Expensive diagnostic equipment can be shielded from violent detonative 

events.

 Researchers can study near-field (i.e., prior to shock separation from 

explosive product gases into air) as well as mid-field (the region where 

product gases, in addition to the air shock, contribute to the loading) and 

far-field (the region where only the air shock contributes to the loading) 

effects.

 Researchers can investigate nonideal explosive effects (e.g., late-time 

burning).

Disadvantages:

 Explosive handling is a safety risk requiring specialized facilities and 

personnel.

 The explosively driven flow field must transition through the near and midfields, even for projects that are only interested in far-field effects. 

Stewart and Pecora (2015) investigated the use of a conical shock tube (1.933 m 

long with a 17° full cone angle) with an explosive driver charge to approximate the 

free-field shock moving through air (commonly referred to as air blast) due to a 

large (relative to the explosive driver charge) explosive detonation. The work 

documented in this report seeks to build upon the previous work by looking in more 

detail at various modifications to the explosive driver charge, the driver section 

(i.e., the portion of the tube that confines the explosive charge and transitions to the 

body section), and the shock tube’s body section (i.e., the portion of the shock tube 
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2

designed to confine the air blast). Specifically, the influence of these modifications 

on the air blast downstream of the shock tube’s driver section will be investigated. 

All pressures listed in this report are overpressures, and all reported impulses are 

obtained by integrating these overpressures over time (i.e., impulse per unit area).

Pressure time histories due to air blast have a distinct shape. Friedlander (1946) 

suggested an equation to describe the shock profile that agrees well with 

experimental data after the air blast separates from the explosive product gases. 

When dealing with large peak overpressures (above 1 atm), Dewey (2010) 

recommends the following modified form of the Friedlander waveform:

  











  



t

t

P t P e

t

S 1



, (1)

where 

P

is the time-dependent overpressure at the gauge location, 

PS

is the peak 

overpressure, 

t

is the time after the air blast arrival, 



t

is the positive phase 

duration, and 



is a fitting parameter (the original Friedlander equation may be 

recovered by setting 

  1 t

). 

The Friedlander waveform is an idealized representation of a free-field air blast, 

without any influence of shock reflections (either from the ground or from shock 

tube surfaces). Since the shock tube is a tool designed to approximate the free-field 

air blast, it is instructive to compare the shock tube data back to a Friedlander 

waveform. Therefore, in some of the plots contained in this report, shock tube 

experimental and computational data are compared against the modified 

Friedlander waveform of Eq. 1. For the comparison,

PS

and distance from the 

charge to the gauge location are obtained from the experiment or computation while 

the corresponding values of 



t

and 



are obtained from ConWep (Hyde 1988). 

The air blast time of arrival, 

0

t

, is adjusted to line up with the data being compared 

against (typically, 0

t

needs to be adjusted on the order of 10% to line up with the 

shock tube data).

The Lawrence Livermore National Laboratory shock physics code ALE3D 

(Nichols 2014) was used for all computations shown in this report. All 

computations were performed in 2-D axisymmetry with 0.5 mm per square 

computational zone. This mesh resolution resulted in problem sizes ranging from 

approximately 10 to 30 million elements, with the shock tube problem requiring 

increasingly larger computational domains as the shock tube angle is increased. The 

arbitrary Lagrangian-Eulerian (ALE) formulation was used in all calculations to 

weight the mesh toward the steel shock tube walls as well as toward the shock front 

by assigning a higher weight to the artificial viscosity in the air. 
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When dealing with finite element codes, it is good practice to conduct a mesh 

resolution study to ensure that the metric of interest (e.g., peak pressure at a certain 

location) has adequately converged for the mesh resolution being employed (i.e., 

the solution should be mesh independent). Unfortunately, such a study was not 

feasible for this work. The combination of thin shock tube walls (on the order of 

millimeters), small charge size (on the order of centimeters), long shock tube length 

(on the order of meters), and prolonged event duration (on the order of 

milliseconds) makes this problem challenging from a computational standpoint. 

Because of these challenges and the absence of a mesh resolution study, no claim 

is being made that the solutions presented in this report are fully resolved; the peak 

pressures and impulses would almost certainly increase if higher-density 

computational meshes could be afforded. However, the computational goal of this 

work was to use ALE3D as an iterative design tool for obtaining qualitative trends 

and yielding more informed design decisions. Roughly speaking, this goal 

translated into the general rule of being able to run a single computation with a 

specific shock tube design within 24 h on 1000 processors. 

This report is organized as follows: Section 2 focuses on computationally 

reproducing experimental results from Stewart and Pecora’s 17° shock tube. Next, 

Section 3.1 details a computational study investigating various modifications to the 

explosive driver charge and inert driver section for a 10° conical shock tube. 

Section 3.2 continues the parametric study by considering the influence of cone 

angle on the downstream air blast profile. Finally, experimental results for a 10°

conical shock tube with a specific driver charge and driver section geometry are 

presented in Section 4 and compared against computational results; Section 4.2 

investigates preliminary work on alleviating release waves at the shock tube exit 

section (where test items would typically be placed). 

2. Computations vs Previous Experiments: 17° Conical Shock 

Tube

Prior to conducting a computational study on geometries for which no experimental 

data exist, an attempt was made to ensure that the experimental data presented in 

Stewart and Pecora (2015) could be replicated computationally with reasonable 

accuracy. The shock tube in that article used a 14.5-g cylindrical Composition C4 

(C4) driver charge, 28.2 mm in diameter and 15.2 mm long, placed with its rear 

surface flush with the entry of a 17° conical steel driver section. All cone angles 

listed in this report refer to the full angle of the conical section. The minimum 

diameter at the entry of the driver section was 32.0 mm, with a 101.6-mm outer 

diameter, and both ends of the shock tube were open to the air. Figure 1 shows a 

schematic of the geometry used to perform the computations; these computations 
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neglected both the blue foam centering device for the explosive charge and the 

Teledyne RISI RP-83 detonator. The driver section shown in Fig. 1 consists of a 

steel cylinder with a conical interior, which houses the C4 driver charge (red) and 

transitions after 233.2 mm to the constant 4.8-mm-thick steel body section. For 

computational purposes, a Jones-Wilkes-Lee (JWL) model was used to describe the 

C4 product gases (an initial density of 1.52 g/cm3 was assumed, consistent with the 

experimental estimate), and detonation was described using programmed burn with 

point initiation at the center of the back surface. Air was described using a tabular 

equation of state (EOS), and the steel was modeled as 4340 steel using a SteinbergGuinan rate-independent strength model with a Mie-Grüneisen EOS. 

Fig. 1 Zoomed-in view of the ALE3D shock tube entry section geometry (the red material 

represents C4 and the gray represents the steel shock tube), which was used to replicate 

experimental data presented in Stewart and Pecora (2015)

A comparison of the computational results with experimental results, taken from 

shot 7 of Stewart and Pecora (2015), is shown in Figs. 2 and 3 along with a modified 

Friedlander waveform taken from ConWep and corresponding to the free-field 

detonation of an 861.8-g (1.9-lb) sphere of C4 at the specified gauge distance from 

the charge. The shock tube loading profiles undershoot the Friedlander waveform 

once release waves from the shock tube exit arrive at the gauge locations. All data 

are taken at the exit of the 1.933-m-long shock tube (i.e., 1.918 m from the closest 

surface of the C4 charge), where the inner diameter of the shock tube is 

0.61 m. Figure 2 shows results on the axis (also referred to as the centerline, or 

“CL” in the plots), and Fig. 3 shows results 0.15 m off-axis (referred to as “OA” in 

the plots).
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Fig. 2 Comparison of computational vs experimental data on the axis of symmetry and at 

the exit (192 cm from the nearest surface of the C4 explosive driver charge) of a 17° shock 

tube (a) overpressure and (b) impulse per unit area

(a)

(b)

-10.0

0.0

10.0

20.0

30.0

40.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 Gauge Pressure [psi]

Time [ms]

exp - exit (CL)

ALE3D - exit (CL)

Friedlander (1.9 lb C4)

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 Impulse per Unit Area [psi*ms]

Time [ms]

exp - exit (CL)

ALE3D - exit (CL)

Friedlander (1.9 lb C4)
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Fig. 3 Comparison of experimental vs computational data 15 cm off the axis of symmetry 

and at the exit (192 cm from the nearest surface of the C4 explosive driver charge) of a 17°

shock tube (a) overpressure and (b) impulse per unit area

(a)

(b)

-10.0

0.0

10.0

20.0

30.0

40.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 Gauge Pressure [psi]

Time [ms]

exp - exit (OA)

ALE3D - exit (OA)

Friedlander (1.9 lb C4)

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 Impulse per Unit Area [psi*ms]

Time [ms]

exp - exit (OA)

ALE3D - exit (OA)

Friedlander (1.9 lb C4)
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The ALE3D computational results shown in Figs. 2 and 3 do a reasonable job of 

replicating the experimental data in terms of the peak pressure, time of arrival, and 

impulse (per unit area). The arrival of release waves from the shock tube exit, 

resulting in a pronounced negative pressure phase, is captured in the ALE3D 

calculation (the Friedlander waveform does not exhibit this behavior since release 

waves due to exiting the shock tube would not be present in a free-field detonation). 

The computational pressure profile on the axis yields a complex shock structure not 

seen in either the on-axis experimental results or the off-axis results (see Figs. 2a 

and 3a). This noisy on-axis computational result is consistent with experience, 

increases with mesh refinement, and is believed to arise from numerical difficulties 

due to the axisymmetric treatment (e.g., elements along the axis contain very little 

mass/volume, especially as the mesh is refined, and the mass inside a single element 

increases substantially as one progresses radially away from the axis). The on-axis 

computational impulse overshoots the experimental result while the off-axis 

impulse undershoots the experiment (see Figs. 2b and 3b). In general, the ALE3D 

computational results were deemed to qualitatively replicate the experimental data 

sufficiently well to warrant proceeding with the parametric study.

3. Shock Tube Parametric Computational Study

The ALE3D computational approach discussed in the previous sections was shown 

to replicate the main features of the experimental data when using a 17° conical 

shock tube along with a C4 driver charge. This same computational approach is 

used in the current section to investigate the influence that various shock tube 

design choices have on the resultant loading profile downstream of the explosive 

charge. All explosive charges used in the work presented in this and all subsequent 

sections are 50/50 pentolite (modeled using a JWL EOS with programmed burn) as 

opposed to the C4 used in Section 2. This change was made because of

experimental considerations related to the work presented in Section 4 (pentolite is 

castable and should lead to increased repeatability compared to the putty-like C4). 

The explosive charge, as in the previous section, has the detonation initiated at a 

point located at the center of the back surface. The initial density of the pentolite is 

taken to be 1.56 g/cm3for the computational study presented in this section. For the 

rest of this report, the driver section of the shock tube is often referred to as 2

separate sections: 1) the piece housing the explosive charge, which is denoted as 

the driver housing section, and 2) the part connecting the driver housing section 

with the body section of the shock tube, which is denoted as the driver transition 

section. 
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For all computations in this section, a conical body section 2.5 m long with 

4.8-mm-thick steel walls is used. In all cases, the exterior geometry of the driver 

section is a cylinder with diameter 3.5 times that of the explosive charge (for the 

special case of the conical frustum in Section 3.1, “diameter” refers to the smallest 

diameter). The interior geometry of the driver housing section corresponds to that 

of the explosive charge (i.e., cylindrical in all but the frustum case) before 

immediately transitions to a conical geometry in the driver transition section for 

mating with the body section of the shock tube. The length of the driver transition 

section is always taken to be 2 times the charge diameter, and the body section of 

the shock tube is always 2.5 m long. All computational data in this section are 

computed at a fixed gauge 2.0 m downstream of the nearest charge surface and offaxis (mainly due to the noise generated on-axis as seen in the previous section). The 

radial position of the gauges used in this subsection is located halfway between the 

axis of symmetry and the shock tube wall (i.e., the exact radial location of the 

gauges depends on the shock tube angle). The length of the tube is taken to extend 

well beyond the gauge location so that release waves from the exit do not 

complicate the analysis. 

3.1 On the Influence of Driver Section and Charge Design: 

10° Conical Shock Tube

The influence of various driver section (e.g., geometry and material) and explosive 

charge (e.g., geometry and size) modifications on the downstream loading profile 

is investigated in the following paragraphs. Table 1 lists the computational test 

matrix used for this investigation, and Fig. 4 depicts a schematic for reference. A 

10° cone angle is used for all computations in this subsection. As an example, 

Fig. 5 shows a zoomed-in view of the ALE3D geometry used for the baseline 

design, with the design parameters defined in Table 1 for the various iterations.
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Table 1 Computational test matrix for 10° shock tube study

Configuration

Driver 

section 

material

Backing 

material

Air gap 

(mm)

Charge 

geometry Charge L/D 

Charge 

diameter 

(mm)

Charge 

mass 

(g)

Baseline

4340 steel

Air

None

Cylinder

1.0

16.0 5.0

50% mass 

(L/D = 1) 12.7

2.5

50% mass 

(L/D = 0.5) 0.5 16.0

150% mass 

(L/D = 1) 1.0 18.3

7.5

150% mass 

(L/D = 1.5) 1.5 16.0

200% mass 

(L/D = 1) 1.0 20.1

10.0

200% mass 

(L/D = 2)

2.0

16.0

L/D = 2 12.7

5.0

Frustum 10° conical 

frustum 1.25a

16.0

Air gap 2.0

Cylinder 1.0

Steel back 32 mm 

4340 steel

Al back None 32 mm 

7075 Al

Al driver 7075 Al Air

a Measured with respect to the smallest diameter (reported as “charge diameter”)
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Fig. 4 Schematic of shock tube driver section for reference with Table 1

Fig. 5 Zoomed-in view of the ALE3D shock tube entry section geometry for the baseline 

shock tube design (the red material represents pentolite, the gray represents the steel shock 

tube, and the blue represents the air)

chg Backing 

material

air gap 2D

D

L

3.5D 10 

Driver section material
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Figure 6 presents the ALE3D pressure profile for the baseline driver section design 

with a 5-g driver charge (see Table 1) obtained 2.0 m downstream of the nearest 

charge surface and halfway between the axis and shock tube wall (approximately 

93 mm off-axis for this baseline design). Also included in the figure is the modified 

Friedlander waveform for a 544-g (1.2-lb) pentolite charge obtained from ConWep 

(as mentioned in the Introduction, the Friedlander parameters were obtained by 

inputting ALE3D’s peak pressure and distance from the charge to the gauge into 

ConWep). Notice that the shock tube waveform appears to diverge from the 

Friedlander around 3.2 ms; this divergence is not due to release waves from the exit 

of the tube since the shock has only just arrived at the exit, another 0.5 m 

downstream from the point at which the data is gathered, around 3.2 ms. In general, 

the loading profile of this baseline case provides a good approximation of a 

Friedlander waveform. 

Fig. 6 Pressure loading measured 2.0 m downstream of the driver charge surface for the 

baseline design of the 10° shock tube driver section and 5-g driver charge compared with a 

Friedlander waveform obtained from CONWEP for a 544-g (1.2-lb) pentolite charge

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

1.50 2.00 2.50 3.00 3.50 4.00 Gauge Pressure [psi]

Time [ms]

Baseline

Modified Friedlander (1.2 lb Pentolite)
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12

Figure 7 shows the resultant air blast as a function of shock tube driver explosive 

mass. For each mass (other than the baseline), 2 configurations are shown: 

Fig. 7a shows the aspect ratio being held constant (L/D = 1) while the diameter and 

length are modified, whereas Fig. 7b shows the diameter being held constant 

(D = 16.0 mm) while the charge length is modified. Either configuration results in 

similar peak pressures relative to the baseline case; however, a comparison of 

Fig. 7a and Fig. 7b indicates that the longer charges (L/D > 1) do a worse job of 

approximating a Friedlander waveform. For the controlled aspect ratio pressure 

profiles of Fig. 7a, the peak pressures appear to be increasing at approximately half 

the rate of the mass (i.e., doubling the mass yields a roughly 50% increase in peak 

pressure). In general, Fig. 7 indicates that a shock tube with a fixed conical angle 

is sufficiently flexible to produce a range of loading profiles approximating a 

Friedlander waveform simply by increasing the explosive mass. 
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13

Fig. 7 Influence of driver charge mass on the pressure profile of the 10° shock tube 

measured 2.0 m downstream of the driver charge surface (a) fixed aspect ratio (L/D = 1) and 

(b) fixed charge diameter (D = 16.0 mm)

(a)

(b)

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

1.50 2.00 2.50 3.00 3.50 4.00 Gauge Pressure [psi]

Time [ms]

Baseline (L/D=1)

50% baseline mass (L/D=1)

150% baseline mass (L/D=1)

200% baseline mass (L/D=1)

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

1.50 2.00 2.50 3.00 3.50 4.00 Gauge Pressure [psi]

Time [ms]

Baseline (L/D=1)

50% baseline mass (L/D=0.5)

150% baseline mass (L/D=1.5)

200% baseline mass (L/D=2.0)
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14

The influence of placing a backing material behind the driver charge is investigated 

in Fig. 8. In this case, a 32-mm-thick disc of either 4340 steel or 7075 aluminum 

(Al) is placed directly behind the explosive charge (see Fig. 4) to minimize energy 

losses due to product gases escaping out the back of the shock tube; the diameters 

of these backing discs are the same as the outer diameter of the driver section (i.e., 

3.5 times the explosive charge diameter). Figure 8 shows that the pressure peak 

measured at the gauge location 2.0 m downstream from the charge surface is 

increased substantially (nearly 70% for the steel backing) relative to the baseline 

case where the product gases freely escape. The Al backing material results in a 

slightly lower peak pressure relative to using a steel backing material. The shock 

structure does appear to be significantly noisier when using either Al or steel as a 

backing material, and the loading profile deviates somewhat from a smooth 

Friedlander waveform. In fact, the shock profiles when using a backing material 

other than air (Fig. 8) look qualitatively similar to the shock profiles from having 

long charges (e.g., the L/D > 1 cases in Fig. 7b). One possibility for this similarity 

is that both designs mitigate the influence of release waves from behind—in the 

first case due to the relatively high shock impedance backing material and, in the 

second case, due to the detonation through a relatively longer, narrow channel—

and, for similar reasons, generate more secondary shocks in the driver section 

relative to the baseline case that are then propagated forward down the shock tube 

body section.

Fig. 8 Influence of a backing plate behind the 5-g driver charge on the pressure profile of 

the 10° shock tube measured 2.0 m downstream of the driver charge surface

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

1.50 2.00 2.50 3.00 3.50 4.00 Gauge Pressure [psi]

Time [ms]

Baseline (L/D=1)

Steel back

Al back
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15

Finally, a number of other modifications, all using a 5-g explosive charge, were 

investigated and are presented in Fig. 9. Using a frustum geometry for the driver 

charge (and coincident driver section) instead of the more easily manufactured 

conical geometry increased the peak pressures by 6%. Introducing an air gap 

between the explosive and driver section walls also resulted in higher pressures 

(5.0% higher peak) relative to the baseline. Increasing the charge’s L/D from 1 to 

2 resulted in a more than 15% decrease in peak pressure relative to the baseline 

design, while changing the driver section’s material from steel to Al decreased the 

peak pressure by 23.5%. Fabricating the entire shock tube out of Al results in 

practically the same downstream pressure profile (not shown here) as simply 

making the driver section Al; this result implies, as might be expected, that the body 

section primarily serves to propagate the shock waves downstream and does not 

contribute notably to the downstream pressure profile.

Fig. 9 Influence of various modifications to the driver section and 5-g driver charge on the 

pressure profile of the 10° shock tube measured 2.0 m downstream of the driver charge surface

One seemingly counterintuitive observation from Fig. 9 is that the introduction of 

an air gap between the explosive charge and the radial wall of the driver section 

yields an increase in the downstream pressure relative to the baseline design, which 

has the explosive charge in contact with the wall. The reasoning for this 

phenomenon is as follows. The primary blast wave generated when the driver 

section is in contact with the detonating charge will indeed be slightly stronger than 

the primary blast wave generated when there is an air gap between the detonating 

charge and the radial driver section walls; this difference in the primary shock wave 

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

2.00 2.50 3.00 3.50 4.00 Gauge Pressure [psi]

Time [ms]

Frustum

Air gap (2 mm)

Baseline (D=16 mm)

Charge L/D=2 (D=13 mm)

Al driver
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16

strength is to be expected because of release waves at the explosive-air interface 

when an air gap is present. However, there are also reflected shock waves that are 

generated behind the detonation wave, some of which combine downstream with 

the primary blast wave generated from the detonation front, and it is this combined 

shock wave that is measured downstream. 

When the driver section wall is in contact with the detonating charge, reflected 

shock waves are generated at the wall-explosive interface (and transmitted back 

through the product gases) from the velocity component of the curved detonation 

wave that is normal to the radial wall; much of these reflections get lost out the 

open end of the shock tube into the surrounding air. In contrast, when an air gap is 

introduced between the explosive charge and the wall of the driver section, release 

waves decrease the pressures at the explosive’s radial surface, as would be 

expected, but the impact of the expanding product gases with the wall generates a 

reflected shock wave back through the explosive products (see the top half of 

Fig. 10), which then gets transmitted downstream and eventually combines with the 

primary air blast. The shock waves reflected back into the product gases when an 

air gap is present are moving toward the axis and down the shock tube because of

the direction of the expanding gases when they impact and, therefore, fewer of these 

shock waves are lost out of the open end of the shock tube. In either case, the 

secondary shock reflection (and subsequent reflections off the axis and shock tube 

wall) gets transmitted into the air downstream and eventually combines with the 

primary air blast because of the detonation wave. 

Fig. 10 Pressure contours at 2 μs after detonation showing the detonation wave and shock 

reflections through the explosive driver charge (red boundary line) for the baseline case with 

no air gap between the driver charge and the steel walls (bottom half) and for the case with a 

2-mm air gap (top half)
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17

Table 2 lists the peak overpressures for all cases investigated in this subsection (see 

also Table 1) and the percent difference of these peak pressures relative to the 

baseline. Using a steel backing disc in the driver section resulted in the highest peak 

pressure relative to the baseline (higher even than doubling the explosive mass),

whereas using an Al driver or halving the explosive mass resulted in the lowest 

peak pressures. 

Table 2 Peak pressures (gauge) in 10° shock tube study

Configuration

Charge

mass 

(g)

Peak 

overpressure 

@ 2 m (psi)

% diff from 

baseline

Baseline 5.0 21.92 0.0

50% mass 

(L/D = 1)

2.5

12.77 –41.7

50% mass 

(L/D = 0.5) 13.33 –39.2

150% mass 

(L/D = 1)

7.5

27.29 24.5

150% mass 

(L/D = 1.5) 27.02 23.3

200% mass 

(L/D = 1)

10.0

32.85 49.9

200% mass 

(L/D = 2.0) 36.14 64.9

L/D = 2

5.0

18.54 –15.4

Frustum 23.23 6.0

Air gap 23.02 5.0

Steel back 36.72 67.6

Al back 33.27 51.8

Al driver 16.76 –23.5
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18

3.2 On the Influence of Cone Angle

Section 3.1 focuses on the influence of various modifications to a 10° conical shock 

tube. In this subsection the influence of cone angle will be investigated. The 

baseline design from the previous subsection will be used in this section as well: in 

other words, a cylindrical explosive charge, L/D = 1, no air gap, a steel driver 

section, and no backing material. Table 3 provides a computational test matrix for 

the ALE3D calculations performed in this subsection.

Table 3 Computational test matrix for shock tube cone angle study

Cone angle 

(°)

Ideal 

performance 

factor

Estimated 

performance 

factora

Shock tube 

driver charge 

(g)

10 526 109 5

20 132 27 20

30 59 12 45

40 33 6.8 80

50 21 4.4 123

a Assuming 20.7% efficiency based on comparing 10° ALE3D 

calculations with CONWEP.

A shock tube’s performance factor is defined as the equivalent free-field mass 

divided by the shock tube’s explosive mass. The equivalent free-field mass is the 

explosive mass that, when detonated in the free-field, is necessary to achieve 

similar pressures and impulses at the gauge or test location to those measured in the 

shock tube. This equivalent mass can be determined using free-field experiments 

or estimated using computational tools; in this report, the equivalent mass is 

estimated using ConWep. The ideal performance factor, 

PFI

, for a conical shock 

tube is found as in Stewart and Pecora (2015) from the following equation: 

 

2

1 cos

2

 

PFI , (2)

where 



is the full cone angle (for example,= 10° in Fig. 4). 

The efficiency of the shock tube is defined as the actual performance factor divided 

by the ideal performance factor from Eq. 2. In this section, an estimate of the actual 

performance factor is found by considering the 5-g charge in the 10° shock tube 

and comparing the pressure load at 2.0 m with an equivalent free-field air blast from 

ConWep. In the case of the baseline 10° shock tube design, this procedure results 

in an estimate of 20.7% efficiency. If it is assumed (without justification) that the 

shock tube efficiency is constant with cone angle, then the estimated performance 

factors shown in Table 3 are arrived at, and the masses of the shock tube explosive 
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19

charges required to approximate the air blast from a 544-g (1.2-lb) free-field 

pentolite charge can be determined.

Figure 11 shows the air blast profile 2.0 m downstream for the baseline 10° shock 

tube presented in the previous subsection (see, for example, Fig. 6) along with 

results from the different cone angles of Table 3. All waveforms are taken at radial 

locations off the axis of symmetry and halfway between the axis and the shock tube 

wall (i.e., the gauge’s axial location is always 2.0 m downstream, but the radial 

location depends on the cone angle). The waveforms of both the 10° and 

20° conical shock tubes do a reasonable job of approximating a Friedlander 

waveform; however, the shock tubes with cone angles of 30° and above indicate 

multiple strong shocks in the flow field (see also Fig. 12), which is not desirable if 

the goal is to approximate the Friedlander waveform seen in free-field air blast 

experiments. Unfortunately, these trailing shocks behind the primary air blast show 

up in the flow field regardless of modifications to the driver section or driver charge 

(i.e., making modifications similar to what was investigated in the previous 

subsection as well as using a planar detonation instead of a point detonation). This 

presence of strong secondary shocks downstream and the general nonuniformity of 

the flow field shown in Fig. 12b, regardless of driver section/charge design, indicate 

that when increasing the cone angle, there may be a critical angle at which the flow 

cannot stay attached to the shock tube walls. 

Fig. 11 Influence of shock tube cone angle on the pressure profile measured 2.0 m 

downstream of the driver charge surface

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

1.0 1.5 2.0 2.5 3.0 3.5 4.0 Gauge Pressure [psi]

Time [ms]

10 degrees (5 g)

20 degrees (20 g)

30 degrees (45 g)

40 degrees (80 g)

50 degrees (123 g)
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20

Fig. 12 Comparison of pressure contours at the approximate times when the primary blast 

wave has traveled 2.0 m inside the shock tube: (a) 10° cone (2.1 ms) and (b) 30° cone (1.5 ms)

4. 10° Shock Tube: Computational and Experimental Results

This section documents the resulting air blast from a 10° conical shock tube, which 

uses a driver section design that blends various features (e.g., air gap, steel back, 

L/D = 2) investigated in Section 3.1. This driver section was fabricated prior to 

completing the computational study presented in Section 3.1 and is likely not an 

ideal design; however, the experimental series provides data for comparison with 

the computational trends discussed in the previous section. The current section is 

(a)

(b)
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21

structured as follows. Section 4.1 presents a comparison of ALE3D computational 

data with experimental data obtained using PCB Piezotronics 50-psi blast pencil 

gauges placed at various locations downstream of the explosive charge and either 

on the axis of the shock tube or 101.6 mm (4 inches) off axis. Section 4.2 then 

investigates the use of a cylindrical exit section to alleviate the release wave 

interaction with the blast wave at the exit of the cylindrical shock tube body section. 

Only selected experiments will be presented in the current section. Data from 

additional experiments can be found in the Appendix. 

Basic engineering drawings for the shock tube used to collect the experimental data 

in this section are shown in Fig. 13. The shock tube is fabricated from mild steel 

throughout. The driver section has a 19.05-mm-thick steel disc backing the 5-g 

pentolite charge, which is separated from the steel walls (both back and radial) by 

a 2.54-mm-thick foam centering device. A 7.62-mm hole is drilled through both the 

steel back and the foam centering device to allow for insertion of the RISI RP-80 

detonator. The outer diameter of the driver section is 63.5 mm, and the inner 

diameter at the smallest end is 17.78 mm. The explosive charge used throughout is 

12.7 mm in diameter and 25.4 mm long. The driver transition section (Fig. 13b) 

extends 25.4 mm beyond the surface of the charge, which sits flush with the end of 

the driver housing section. The body section of the tube (Fig. 13c) is 4.76 mm thick 

and comprises seven 304.8-mm-long conical sections; the inner diameter at the exit 

of the shock tube (i.e., at the end of the seventh conical section) is 395.6 mm. Some 

of the experiments include a 609.6-mm-long cylindrical exit section to alleviate 

release waves at the exit of the conical section. In all figures, “exit” denotes the exit 

of the shock tube’s body section (i.e., 2.16 m downstream from the nearest surface 

of the 5-g explosive charge), regardless of whether an exit section is attached.
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22

Fig. 13 Shock tube basic engineering drawings (dimensions are in inches): (a) driver housing 

section, (b) 10° conical driver transition section, and (c) 10° conical body section including the 

cylindrical exit section

4.1 Computational Predictions vs Experimental Results

The first set of experiments were conducted without the cylindrical exit section, as 

shown in Fig. 14. The shock tube was placed on top of a steel frame that was 

attached to a 152.4-mm (6-ft)-tall wooden stand. This stand was designed to avoid 

the influence of shock waves reflecting off the ground and interacting with the air 

blast. 

(a) (b)

(c)
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23

Fig. 14 10° shock tube, without the cylindrical exit section

The shock tube’s driver section is shown in Fig. 15. Figure 15a shows the 5-g 

pentolite charge (white cylinder), foam centering device (light blue), cylindrical 

portion that houses the explosive charge inside the centering device (see also Fig. 

13a), and the conical transition section (see also Fig. 13b) that mates up with the 

conical body section of the shock tube prior to conducting one of the experiments. 

Figure 15b shows the driver section after an experiment has been conducted, 

indicating some minor deformation of the steel adjacent to the detonated explosive. 

A new driver section (both the cylindrical and transition portions) was used for each 

experiment conducted in this series. 
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24

Fig. 15 Example shock tube driver section used in an experiment: (a) (from left to right) 

pentolite explosive charge, blue foam centering device, cylindrical driver housing section, and 

conical driver transition section prior to the experiment; (b) driver housing section and driver 

transition section postexperiment

(a)

(b)
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25

The blast profiles from 2 separate experiments where the pencil gauges are placed 

at the exit of the shock tube’s conical body section are shown in Figs. 16 and 17.

Pencil gauges were placed both on-axis (denoted “CL” in Fig. 16) as well as 

101.6 mm (4 inches) off-axis (denoted “OA” in Fig. 17). Figures 16a and 17a show 

a comparison between the pressure time histories of the experimental data with both 

ALE3D computational data (the pentolite density is taken to be 1.69 g/cm3, 

consistent with experimental estimates) and a Friedlander waveform. For these 

shock tube experiments, the pressure peak and initial decay of the air blast are 

described well by the Friedlander waveform corresponding to a 1814-g (4-lb) 

sphere of pentolite. This result translates to a performance factor (i.e., actual charge 

mass/effective charge mass) of roughly 360 compared to the performance factor of 

60 obtained with the earlier 17° shock tube (see Section 2). Figures 16b and 17b 

show the corresponding impulse per unit area obtained by integrating the pressure 

profile over time. A few things are evident from Figs. 16 and 17:

 The experimental peak overpressures and impulses are significantly higher 

than those obtained using ALE3D, and the agreement is notably worse than 

that obtained using the air-backed driver section in the 17° tube (see Figs. 2 

and 3).

 The experimental pressure profiles indicate a far less uniform shock front 

and overall structure relative to either the ALE3D predictions or the earlier 

17° shock tube results shown in Figs. 2 and 3. 

 The experimental data do a reasonable job of reproducing a Friedlander 

waveform, especially in terms of the impulses, until release waves arrive (at 

approximately 2.5 ms), at which point the pressures and impulses rapidly 

decay relative to the Friedlander waveform. 
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26

(a)

(b)

Fig. 16 Comparison of experimental vs computational data on the axis of symmetry and at 

the exit (2.16 m from the nearest surface of the pentolite explosive driver charge) of a 10°

shock tube: (a) overpressure and (b) impulse per unit area

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 Gauge Pressure [psi]

Time [ms]

exp - exit (CL)

exp2 - exit (CL)

Friedlander (4.0 lb Pentolite)

ALE3D - exit (CL)

0.0

5.0

10.0

15.0

20.0

25.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 Impulse per Unit Area [psi*ms]

Time [ms]

exp - exit (CL)

exp2 - exit (CL)

Friedlander (4.0 lb Pentolite)

ALE3D - exit (CL)
Approved for public release; distribution is unlimited.

27

(a)

(b)

Fig. 17 Comparison of experimental vs computational data 10 cm off the axis of symmetry 

and at the exit (2.16 m from the nearest surface of the pentolite explosive driver charge) of a 

10° shock tube: (a) overpressure and (b) impulse per unit area

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 Gauge Pressure [psi]

Time [ms]

exp - exit (OA)

exp2 - exit (OA)

Friedlander (4.0 lb Pentolite)

ALE3D - exit (OA)

0.0

5.0

10.0

15.0

20.0

25.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 Impulse per Unit Area [psi*ms]

Time [ms]

exp - exit (OA)

exp2 - exit (OA)

Friedlander (4.0 lb Pentolite)

ALE3D - exit (OA)
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28

One possible explanation for the first 2 observations listed previously (i.e., that the 

10° shock tube experimental data and ALE3D computational data agree much less 

than in the previous 17° shock tube results summarized in Section 2) is that the 

pentolite JWL model is simply less accurate compared to the C4 JWL model used 

previously (there are no cylinder expansion data for the pentolite at the assumed 

density of 1.69 g/cm3). Additionally, as mentioned in Section 3.1, the steel backing 

material results in a shock being reflected back into the compressed product gases, 

and this re-shock of the product gases may be difficult for the JWL model to 

accurately capture. This re-shock issue is an especially plausible culprit since the 

50% TNT in pentolite is known to behave non-ideally (i.e., there could be 

secondary reactions occurring in the experiments due to re-shocks—reactions that 

the model is not calibrated to capture). A third potential explanation for the first 2 

observations is that the under-resolved mesh being used in this study (see the 

discussion in the Introduction) provides a worse approximation of the 10° shock 

tube’s performance relative to the 17° case. A degraded approximation could be 

due to, for example, either the relatively fewer elements across the radius of the

explosive charge (a 5-g charge was used for the 10° tube compared to a 14.5-g 

charge in the 17° case) or the increased influence of the shock tube walls in the 

smaller angle case.

4.2 Mitigation of Release Waves at the Exit Section

One observation from the shock tube experimental data in Figs. 16 and 17 relative 

to the Friedlander waveform is that release waves arriving radially from the shock 

tube exit have a significant influence on the shock tube blast profile (these release 

waves were also evident in the earlier shock tube work presented in Figs. 2 and 3). 

This release wave interaction prevents the shock tube blast profile from providing 

a reasonable approximation of an air blast resulting from a free-field detonation 

once the release waves interact with it. There are 2 obvious ways to alleviate the 

influence of the release waves: 1) insert the test item far enough up the shock tube 

that the release waves do not arrive to influence the experiment during the time 

period of interest, or 2) extend the shock tube. 

In this subsection, the second approach is taken by attaching a 609.6-mm (2-ft) 

cylindrical exit section to the conical shock tube (see Fig. 18). Ideally, the geometry 

of the exit section would be a rectangular prism so that windows could be 

straightforwardly inserted for optical diagnostics. However, this cylindrical 

geometry is a first step toward developing a test section that both alleviates the 

influence of release waves and allows for easier integration of diagnostics. 
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29

Fig. 18 10° shock tube, with the cylindrical exit section attached

Figures 19 and 20 show the experimental data on- and off-axis, respectively, when 

using the cylindrical exit section compared with the same Friedlander waveform 

from Section 4.1 (i.e., due to an 1814-g pentolite free-field detonation). It is evident

when comparing the blast profiles with the cylindrical exit section in Figs. 19 and 

20 with the profiles shown in Figs. 16 and 17 without an exit section that the 

prevention of release waves leads to better agreement with the Friedlander freefield air blast. Unfortunately, the blast profiles when using a cylindrical exit section 

result in greater impulses relative to the Friedlander waveform and impulses that 

continue to increase beyond the time where the Friedlander has peaked. Both of 

these features are likely due to the fact that the air blast is being constrained by a 

constant rather than a diverging geometry once it leaves the shock tube’s conical 

body section and enters into the cylindrical exit section.
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30

Fig. 19 Comparison of experimental data on the axis of symmetry and at the exit (2.16 m 

from the nearest surface of the 5-g pentolite explosive driver charge) of a 10° shock tube with 

an exit section vs a Friedlander waveform: (a) overpressure and (b) impulse per unit area

(a)

(b)

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 Gauge Pressure [psi]

Time [ms]

exp - exit w/ exit section (CL)

exp2 - exit w/ exit section (CL)

Friedlander (4.0 lb Pentolite)

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 Impulse per Unit Area [psi*ms]

Time [ms]

exp - exit w/ exit section (CL)

exp2 - exit w/ exit section (CL)

Friedlander (4.0 lb Pentolite)
Approved for public release; distribution is unlimited.

31

Fig. 20 Comparison of experimental data 10 cm off the axis of symmetry and at the exit (2.16 

m from the nearest surface of the 5-g pentolite explosive driver charge) of a 10° shock tube 

with an exit section vs a Friedlander waveform: (a) overpressure and (b) impulse per unit area

(a)

(b)

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 Gauge Pressure [psi]

Time [ms]

exp - exit w/ exit section (OA)

exp2 - exit w/ exit section (OA)

Friedlander (4.0 lb Pentolite)

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 Impulse per Unit Area [psi*ms]

Time [ms]

exp - exit w/ exit section (OA)

exp2 - exit w/ exit section (OA)

Friedlander (4.0 lb Pentolite)
Approved for public release; distribution is unlimited.

32

Figure 21 shows shock tube experimental data using the 5-g pentolite driver charge 

versus the Friedlander waveform due to an 1814-g pentolite free-field detonation 

for the configuration with no exit section (Fig. 21a) and using an exit section 

(Fig. 21b). Obviously, the exit section alleviates the influence of release waves. 

When using the exit section, there appears to be a secondary shock reflected into 

the exit section (see, for example, the outside curves in Fig. 21b around 2.3 ms). 

This secondary shock is likely due to a reflection off the cylindrical steel walls 

when the slope changes from the conical section to the cylindrical section. It is 

possible that this shock reflection could be mitigated by using a material with a 

lower shock impedance than the steel being used in this work. In general, the use 

of an exit section shows promise for alleviating the release wave interactions with 

the air blast exiting the conical body section of the shock tube.
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33

Fig. 21 Shock tube experimental air blast data due to a 5-g pentolite charge at various 

locations compared with the Friedlander waveforms at corresponding locations for an 1814-g 

pentolite charge: (a) without an exit section and (b) with an exit section

(a)

(b)

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 Gauge Pressure [psi]

Time [ms]

Friedlander (4.0 lb Pentolite)

exp - 6" inside (CL)

exp - 6" inside (OA)

exp2 - exit (CL)

exp2 - exit (OA)

exp - 6" outside (CL)

exp - 6" outside (OA)

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 Gauge Pressure [psi]

Time [ms]

Friedlander (4.0 lb Pentolite)

exp2 - exit w/ exit section (CL)

exp2 - exit w/ exit section (OA)

exp - 6" outside w/ exit section (CL)

exp - 6" outside w/ exit section (OA)
Approved for public release; distribution is unlimited.

34

5. Conclusions

This report has detailed both computational and experimental work focused on the 

design of explosively driven conical shock tubes. Earlier experimental work done 

by the author using a 17° shock tube was compared with ALE3D computational 

data to demonstrate the ability of the computations to capture the main features of 

interest (e.g., the pressure loading profiles and impulse per unit area). This 

computational approach was then used to conduct a parametric study on various 

shock tube design parameters, such as cone angle and explosive driver geometry. 

The study was conducted to investigate the influence of these parameters on the air 

blast 2.0 m downstream of the explosive charge and to determine shock tube driver 

modification options that might be used to tailor the air blast arriving downstream 

at a test location. Experimental data from a 10° shock tube utilizing various features 

from the computational parametric study was presented and compared with ALE3D 

predictions. This same shock tube was also employed with a newly designed exit 

section to successfully alleviate the influence of release waves on the measured air 

blast. 

The 10° shock tube resulted in a much higher performance factor than the earlier 

17° shock tube (roughly 360 instead of the earlier 60, as calculated using modified 

Friedlander curves taken from ConWep). However, 2 issues arose out of the 

experimental work with the 10° conical shock tube: 1) the experimental data were 

much noisier using the 10° shock tube than the data collected using the previous 

17° shock tube, and 2) the ALE3D computational approach provided a much worse 

comparison to the 10° shock tube experimental data than it did to the earlier 17°

shock tube experimental data. Both issues can potentially be explained by the 

presence of the steel back used in the 10° shock tube compared with the open back 

used in the 17° shock tube. The steel back results in an increase in reflected shock 

waves being transmitted into the compressed product gases that eventually 

propagate downstream. These secondary shock waves could result in the noisy 

signals observed when using the 10° tube relative to the 17° tube. It is also possible 

that the reflected shock waves promote secondary reactions in the pentolite 

(pentolite is 50% PETN and 50% TNT, the latter of which is known to behave in a 

nonideal manner)—reactions that are not captured by the simple JWL model being 

employed in the calculations. 

One option that will be investigated in the future is the use of a driver section 

without a steel backing disc in the 10° shock tube to see if 1) the pressure loading 

profiles become less noisy relative to the experimental data presented here and 2) 

if the inability of the ALE3D computational data to replicate the experimental 

results is due to problems associated with shock reflections off the steel back plate. 
Approved for public release; distribution is unlimited.

35

6. References

Courtney AC. Andrusiv LP, Courtney MW. Oxy-acetylene driven laboratory scale 

shock tubes for studying blast wave effects. Review of Scientific Instruments.

2012;83(4):045111.

Dewey JM. The shape of the blast wave: studies of the Friedlander equation. 

Proceedings of the 21st International Symposium on Military Aspects of Blast 

and Shock; 2010; Jerusalem, Israel.

Freidlander FG. The diffraction of sound pulses. I. Diffraction by a semi-infinite 

plate. Proc Roy Soc Lond A. 1946;186;322–344.

Henshall BD. On some aspects of the use of shock tubes in aerodynamic research. 

London (UK): Aeronautical Research Council Reports and Memoranda, Her 

Majesty’s Stationary Office; 1957. R & M No. 3044.

Hyde DW. Microcomputer programs CONWEP and FUNPRO, applications of 

TM 5-855-1, fundamentals of protective design for conventional weapons 

(user's guide). Vicksburg (MS): Army Corps of Engineer Waterways

Experiment Station Structures Lab; 1988. Report No.: WES/IR/SL-88-1.

Nichols AL III. An arbitrary Lagrange/Eulerian 2D and 3D code system. Ver.

4.24.x. Livermore (CA): Lawrence Livermore National Laboratories; 2014

Sep. Report No.: LLNL-SM-662355; Vols. 1 and 2.

Stewart JB, Pecora C. Explosively-driven air blast in a conical shock tube. Review 

of Scientific Instruments. 2015;86(3):035108.
Approved for public release; distribution is unlimited.

36

Appendix. 10° Shock Tube Pencil Gauge Data
Approved for public release; distribution is unlimited.

37

Fig. A-1 Experimental data from pencil gauges inserted 6 inches inside the shock tube’s 

conical exit (i.e., 2.00 m from the charge surface), with no cylindrical exit section. Data are 

shown from 2 experiments, both on and 102-mm off-axis.

Fig. A-2 Experimental data from pencil gauges inserted at the shock tube’s conical exit (i.e., 

2.16 m from the charge surface), with no cylindrical exit section. Data are shown from 2 

experiments, both on and 102-mm off-axis.

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Gauge Pressure [psi]

Time [ms]

exp - 6" inside (CL)

exp - 6" inside (OA)

exp2 - 6" inside (CL)

exp2 - 6" inside (OA)

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Gauge Pressure [psi]

Time [ms]

exp - exit (CL)

exp - exit (OA)

exp2 - exit (CL)

exp2 - exit (OA)
Approved for public release; distribution is unlimited.

38

Fig. A-3 Experimental data from pencil gauges inserted 6 inches outside the conical shock 

tube’s exit (i.e., 2.31 m from the charge surface), with no cylindrical exit section. Data are 

shown from 2 experiments, both on and 102-mm off-axis.

Fig. A-4 Experimental data from pencil gauges inserted at the shock tube’s conical exit (i.e., 

2.16 m from the charge surface), when a cylindrical exit section is used. Data are shown from 

2 experiments, both on and 102-mm off-axis.

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Gauge Pressure [psi]

Time [ms]

exp - 6" outside (CL)

exp - 6" outside (OA)

exp2 - 6" outside (CL)

exp2 - 6" outside (OA)

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Gauge Pressure [psi]

Time [ms]

exp - exit w/ exit section (CL)

exp - exit w/ exit section (OA)

exp2 - exit w/ exit section (CL)

exp2 - exit w/ exit section (OA)
Approved for public release; distribution is unlimited.

39

Fig. A-5 Experimental data from pencil gauges inserted 6 inches outside the conical shock 

tube’s exit (i.e., 2.31 m from the charge surface), when a cylindrical exit section is used. Data 

are shown from 2 experiments, both on and 102 mm off-axis.

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Gauge Pressure [psi]

Time [ms]

exp - 6" from exit w/ exit section (CL)

exp - 6" from exit w/ exit section (OA)

exp2 - 6" from exit w/ exit section (CL)

exp2 - 6" from exit w/ exit section (OA)
Approved for public release; distribution is unlimited.

40

List of Symbols, Abbreviations, and Acronyms

Al aluminum

ALE arbitrary Lagrangian-Eulerian

C4 Composition C4

EOS equation of state

JWL Jones-Wilkes-Lee

TNT trinitrotoluene
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41

1 DEFENSE TECHNICAL

(PDF) INFORMATION CTR

DTIC OCA

2 DIRECTOR

(PDF) US ARMY RESEARCH LAB

RDRL CIO L

IMAL HRA MAIL & RECORDS

MGMT

1 GOVT PRINTG OFC

(PDF) A MALHOTRA

33 DIR USARL

(PDF) RDRL WMP

S SCHOENFELD

RDRL WMP A

S BILYK

RDRL WMP B

C HOPPEL

A DILEONARDI

T WEERASOORIYA

RDRL WMP C

T BJERKE

R BECKER

RDRL WMP D

J RUNYEON

R DONEY

S SCHRAML 

RDRL WMP E 

P SWOBODA

RDRL WMP F

N GNIAZDOWSKI

C CUMMINS

RDRL WMP G

R EHLERS

P DUVALL

B HOMAN

S KUKUCK

R BANTON

J BOYD

D KOOKER

C PECORA

B SHOWALTER

R SPINK

J STARKENBERG

RDRL WML C

S AUBERT

D MEGONNELL

B ROOS

G SUTHERLAND

RDRL WMM D

D HASH

G CHANEY

B HALL

J GYOLAI

D WEYAND
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42

INTENTIONALLY LEFT BLANK.