ABSTRACT 
 
 
 
 
Title of Thesis: COMPUTATIONAL FLUID DYNAMICS 
MODELING OF SHOCK TUBE GENERATED 
BLAST-INDUCED PRESSURE FIELDS ON 
THE HUMAN HEAD.   
  
 Rubbel Kumar 
Master of Science, 2018 
  
Thesis Directed By: Professor Elaine S. Oran, 
Department of Aerospace Engineering 
 
 
The increased use of explosives in military conflicts has been linked to an increase in the 
number of traumatic brain injuries (TBIs). Assessing the effectiveness of personal 
protective equipment to mitigate TBIs requires both the ability to replicate the pressure 
signatures caused by blast waves and an understanding of the interaction between blast 
waves and human bodies. Computational Fluid Dynamics (CFD) was used to understand 
the effect of varying different shock tube design parameters and to propose guidelines for 
selecting shock tube designs to accurately replicate blast wave pressure signatures 
representative of free-field explosive events. Additionally, a CFD model was developed to 
represent a shock tube built to mimic the primary overpressure magnitude and impulse 
loading on the human head surface as a result of free-field explosive events. This model 
  
was used to aid in the understanding of flow within the shock tube, characterize the applied 
pressure loading to a bare head form, augment experimental findings to fully understand 
the influence of headborne systems on pressure applied to the human head, and support the 
design of optimized laboratory test methodologies to represent a broad range of free-field 
blast events. 
  
  
 
 
 
 
 
 
 
 
 
 
 
COMPUTATIONAL FLUID DYNAMICS MODELING OF SHOCK TUBE 
GENERATED BLAST-INDUCED PRESSURE FIELDS ON THE HUMAN HEAD. 
 
 
 
By 
 
 
Rubbel Kumar 
 
 
 
 
 
Thesis submitted to the Faculty of the Graduate School of the  
University of Maryland, College Park, in partial fulfillment 
of the requirements for the degree of 
Master of Science 
2018 
 
 
 
 
 
 
 
 
 
 
Advisory Committee: 
Prof. Elaine S. Oran, Chair 
Dr. Alison B. Flatau 
Dr. David R. Mott 
Prof. Kenneth Yu 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
© Copyright by 
Rubbel Kumar 
2018 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
Acknowledgements 
I would like to start by thanking my advisor, Dr. Elaine Oran, for her guidance 
and support during my graduate research. I would also like to thank the other members 
of my thesis committee, Dr. Alison Flatau, Dr. David Mott, and Dr. Kenneth Yu for 
their feedback on my thesis and their flexibility with scheduling my thesis defense. 
A big thank you to my mentor, Dr. Ashish Nedungadi, for teaching me 
computational fluid dynamics, grid generation, bash scripting, and data visualization, 
and for getting me involved in the project that would ultimately become my thesis topic. 
Thank you to Roger Davis, Brad Marples, and Al Gronlund for your support and 
flexibility over these last four years as I completed my graduate degree part-time while 
working full time. Thank you to Katy Carneal for coordinating this work and all your 
feedback and support throughout the process. Also, thank you to Dr. Vanessa Alphonse 
for your help with finding prior research and John Clark for teaching me the 
experimental aspect of the program. A special thank you to Joan Murphy for your help 
navigating the public release process with tight deadlines. 
Thank you, Tom, Aileen, Matt, and the rest of the Department of Aerospace 
Engineering for always being so helpful and for creating a welcoming environment 
throughout my undergraduate and graduate studies at the University of Maryland. 
I would not be where I am today without the amazing support of my parents. 
Thank you, mom and dad, for sacrificing so much so that I could become a college 
graduate and pursue an advanced degree, and for teaching me to always work hard and 
ii 
 
 
 
do my best. And a very special thank you to Sylvie for all your support throughout the 
past four years of completing my graduate degree—I know it hasn’t always been easy! 
Finally, this material is based upon work supported by the United States Army 
Natick Soldier Research Development and Engineering Center.  
 
  
iii 
 
 
 
Table of Contents 
 
 
Acknowledgements ................................................................................................... ii 
Table of Contents ..................................................................................................... iv 
List of Tables .......................................................................................................... vii 
List of Figures ........................................................................................................ viii 
1. Introduction ....................................................................................................... 1 
1.1. Background and Motivation ....................................................................... 1 
1.1.1. Improvised Explosive Devices ........................................................... 1 
1.1.2. Blast Waves ....................................................................................... 1 
1.1.3. Free-field Testing ............................................................................... 3 
1.1.4. Shock Tube Testing ............................................................................ 5 
1.1.5. Blast Overpressure Simulation System ............................................... 9 
1.1.5.1. Geometry and Design ................................................................... 10 
1.1.5.2. Testing Procedure ......................................................................... 12 
1.1.5.3. Data Acquisition ........................................................................... 15 
1.2. Contributions of Thesis Research ............................................................. 15 
1.3. Overview of Thesis .................................................................................. 16 
2. Using Gas-Driven Shock Tubes to Produce Blast Wave Signatures.................. 18 
2.1. Introduction ............................................................................................. 18 
2.2. Materials and Methods ............................................................................. 18 
2.2.1. Shock Tube Geometry and Baseline Mesh Description ..................... 19 
2.2.2. CFD Solver and Settings .................................................................. 20 
iv 
 
 
 
2.2.3. Initial and Boundary Conditions ....................................................... 22 
2.2.4. Data Analysis and Post-Processing ................................................... 23 
2.3. CFD Pre-processing: Time, Mesh, and Turbulence Model Independence . 23 
2.4. Results ..................................................................................................... 25 
2.4.1. Burst Pressure Study ........................................................................ 25 
2.4.2. Driver Length Study ......................................................................... 27 
2.4.3. Driver Gas Study .............................................................................. 29 
2.5. Discussion................................................................................................ 36 
3. Assessment of Helmet Effectiveness against Blast Waves using Computational 
Fluid Dynamics Simulations of Gas-Driven Shock Tubes ........................................ 39 
3.1. Introduction ............................................................................................. 39 
3.2. Methodology ............................................................................................ 39 
3.2.1. Baseline Mesh Description ............................................................... 40 
3.2.2. CFD Solver and Settings .................................................................. 49 
3.2.3. Initial and Boundary Conditions ....................................................... 51 
3.2.4. Data Analysis and Post-processing ................................................... 52 
3.2.5. CFD Model Assumptions ................................................................. 54 
3.3. Results ..................................................................................................... 54 
3.3.1. Shock Formation .............................................................................. 54 
3.3.2. CFD Model Validation ..................................................................... 55 
3.3.2.1. Shock Tube Walls ........................................................................ 55 
3.3.2.2. Bare and Helmeted Head Form ..................................................... 58 
3.3.3. Additional CFD Results.................................................................... 61 
v 
 
 
 
3.3.3.1. Frontal Impact .............................................................................. 61 
3.3.3.2. Side Impact .................................................................................. 66 
3.3.3.3. Rear Impact .................................................................................. 69 
3.4. Discussion................................................................................................ 72 
4. Summary of Research .............................................................................. 74 
4.1.1. Using Gas-Driven Shock Tubes to Produce Blast Wave Signatures .. 74 
4.1.2. Assessment of Helmet Effectiveness against Blast Waves using 
Computational Fluid Dynamics Simulations of Gas-Driven Shock Tubes ........ 75 
4.2. Contributions to Modeling Blast Wave Exposures to the Human Head ..... 76 
4.3. Suggestions for Future Work .................................................................... 77 
5. References ............................................................................................... 79 
vi 
 
 
 
List of Tables 
Table 1 Initial Conditions .............................................................................................. 22	
Table 2 Initial Conditions .............................................................................................. 52	
  
vii 
 
 
 
List of Figures 
Figure 1.1: Friedlander wave profile with b = 1, P0 = 500 kPa, and td = 10 ms ................. 2	
Figure 1.2: Photograph of experimental set-up with two mannequins facing forward, 
toward the blast. Center pillar was a high explosive, which generated the blast wave once 
detonated. Testing was conducted by Naval Research Laboratory and Allen Vanguard 
[5]. .................................................................................................................................. 3	
Figure 1.3: Blast geometry modeled in CFD for frontal blast impacts [5] ......................... 4	
Figure 1.4: Pressure histories for front-facing blasts for four PPE configurations [6] ....... 5	
Figure 1.5: Simplified constant-area shock tube schematic .............................................. 6	
Figure 1.6: Representative photographs of the rat brains following exposure to different 
driving gases and at various peak overpressures. White arrows point to hematomas. [10] 7	
Figure 1.7: Simplified head, brain, and helmet interface model [14] ................................ 9	
Figure 1.8: Top-down and side views of BOSS. Two potential test-section locations 
shown. ........................................................................................................................... 11	
Figure 1.9: Current wall sensor port location in the BOSS (A = driver section, B = 
transition section, C = test section, R = right wall, L = left wall) .................................... 13	
Figure 1.10: Custom Pitot-static gauge mounted on the inertial frame ............................ 14	
Figure 2.1: (a) Shock tube baseline computational mesh with (b) zoomed-in view of 
interface between shock tube driven section and outside environment ........................... 20	
Figure 2.2: CFD schematic and probe locations ............................................................. 23	
viii 
 
 
 
Figure 2.3: Burst pressure study; (a) 1 meter and (b) 4.82 meters downstream of 
driver/driven intersection ............................................................................................... 26	
Figure 2.4: Driver Length Study; (a) 1 meter (b) 4.82 meters downstream of driver/driven 
intersection .................................................................................................................... 28	
Figure 2.5: 0.4572 meter driver section shock tube shock evaluation ............................. 29	
Figure 2.6: Driver gas study; (a) 1 meter and (b) 4.82 meters downstream of driver/driven 
intersection .................................................................................................................... 31	
Figure 2.7: Pressure flow contours for (a) Helium driving gas (b) Air driving gas .......... 33	
Figure 2.8: Air driving gas shock evolution ................................................................... 35	
Figure 3.1: Two-dimensional schematic of Blast Overpressure Simulator System.......... 40	
Figure 3.2: Failed diaphragm ......................................................................................... 41	
Figure 3.3: Diaphragm deformation study for (a) 588 kPa (b) 1295 kPa burst Pressure .. 42	
Figure 3.4: Helmeted head from (a) front view (b) side view (c) helmet padding 
underside view .............................................................................................................. 44	
Figure 3.5: Two-dimensional slice of GridPro-generated computational mesh of shock 
tube with spherical cut out in test section ....................................................................... 45	
Figure 3.6: Zoomed-in view of two-dimensional slice near driver/driven interface (curved 
grid lines model deformed diaphragm) .......................................................................... 46	
Figure 3.7: Zoomed-in view of two-dimensional slice showing spherical cut out ........... 47	
ix 
 
 
 
Figure 3.8: Isometric view of spherical boundary shared between both meshes and 
Pointwise-meshed head-helmet geometry ...................................................................... 48	
Figure 3.9: Zoomed-in two-dimensional slice of merged mesh with GridPro-generated 
shock tube mesh and Pointwise-generated mesh around test article ................................ 49	
Figure 3.10: CFD probe location and experimental sensor placement on bare head form53	
Figure 3.11: Pressure contours and shock evolution ....................................................... 55	
Figure 3.12: CFD validation of pressure time-history for shock tube wall sensors for  (a) 
3.147m (b) 3.72m downstream of driver/driven interface ............................................... 57	
Figure 3.13: CFD validation of pressure-time history for bare head sensors ................... 59	
Figure 3.14: CFD validation of pressure-time history for helmeted head sensors ........... 60	
Figure 3.15: (a) Geometric gradients on average male face (b) Maximum overpressure for 
frontal impact ................................................................................................................ 63	
Figure 3.16: Additional CFD pressure time-history results for frontal impact................. 65	
Figure 3.17: Maximum pressures observed for a frontal impact for bare and helmeted 
head forms..................................................................................................................... 66	
Figure 3.18: Additional CFD pressure time-history results for side impact ..................... 68	
Figure 3.19: Maximum pressure observed for a side impact for bare and helmeted head 
form .............................................................................................................................. 69	
Figure 3.20: Additional CFD pressure time-history results for rear impact ..................... 71	
x 
 
 
 
Figure 3.21: Maximum pressure observed for a rear impact for bare and helmeted head 
form .............................................................................................................................. 72	
 
xi 
 
 
 
1. Introduction 
1.1. Background and Motivation 
1.1.1. Improvised Explosive Devices 
Detonation of improvised explosive devices (IEDs) is typically associated with 
shrapnel and fire, both of which lead to visible injuries. IEDs also produce blast waves that 
can lead to injuries that are superficially undetectable. The increased use of IEDs in military 
conflicts has now been associated with a major increase in the number of traumatic brain 
injuries (TBIs) [1]. The increased prevalence of this injury has led to a heightened need to 
investigate both the mechanisms by which the injury occurs and the need for personal 
protective equipment (PPE), such as helmet systems and goggles. 
1.1.2. Blast Waves 
To conduct these analyses effectively, it is important to develop well-characterized 
the blast overpressure signatures that represent relevant overpressure magnitudes and 
durations experienced by warfighters in theater, through either blast testing or laboratory-
based methods. The Friedlander shock profile is a good target waveform to replicate 
through laboratory-based methods because it is a theoretical approximation and neglects 
the effects of reverb, secondary shocks, ground bounce, and reflections. The Friedlander 
blast wave profile is described by the modified Friedlander equation shown below, where 
P is the pressure, P0 is the peak pressure, t is the time, td is the duration of the positive 
phase, and b is the exponential constant that controls the rate of decay [2]. 
1 
 
 
 
𝑃 = 𝑃 $1 − 𝑡
,-.
# )𝑡 * 𝑒
)./ 
(
Figure 1.1 shows a Friedlander profile obtained with a peak pressure, P0, of 500 
kPa, positive phase time-duration, td, of 10 seconds, and an exponential constant, b, of 1. 
A person subjected to this representative blast wave first experiences a sharp pressure rise 
due to the passage of the shock front, followed by an exponential decay, and finally a 
rarefaction wave [3]. The positive phase of the wave is the period between the initial 
pressure rise and the time the pressure first returns to ambient conditions, or the duration 
in which the pressure is positive. The positive phase is between 0 and 10 ms in Figure 1.1. 
Similarly, the negative phase of the wave is the period between when the pressure drops 
below the ambient conditions to the time the pressure once again returns to ambient 
conditions, or the duration in which the pressure is negative. The negative phase occurs 
after 10 ms in Figure 1.1. 
 
Figure 1.1: Friedlander wave profile with b = 1, P0 = 500 kPa, and td = 10 ms 
 
2 
 
 
 
Although the generation of a Friedlander profile provides experimentalists with a 
reasonable approximation of the blast-overpressures experienced in theater, additional 
complexities such as reverb, ground bounce, buildings, vehicles, and other people exist in 
the field that may be difficult to replicate experimentally. 
1.1.3. Free-field Testing 
Free-field testing refers to the field testing of mannequins outfitted with pressure 
gauges and exposed to simplistic blasts caused by explosive detonation some distance and 
angle away. Free-field testing may better replicate real-world scenarios and provide more 
representative overpressure data than laboratory methods. Organizations such as the Naval 
Research Laboratory (NRL), Allen Vanguard, and the Johns Hopkins University Applied 
Physics Laboratory (JHU/APL) often validate computational models and other 
experimental techniques against data obtained through free-field tests [4]. A photograph 
taken from the experimental setup of a free-field test conducted by NRL and Allen 
Vanguard is shown in Figure 1.2.  
 
Figure 1.2: Photograph of experimental set-up with two mannequins facing forward, 
toward the blast. Center pillar was a high explosive, which generated the blast wave once 
3 
 
 
 
detonated. Testing was conducted by Naval Research Laboratory and Allen Vanguard 
[5]. 
 
In addition to free-field testing, NRL has conducted computational fluid dynamics 
(CFD) studies modeling free-field tests and the blast’s impact on bare and protected head 
forms where different combinations of protection (e.g., helmets, goggles or visors, and 
mandible protection) were used  [5, 6]. Figure 1.3 is of a simple schematic showing the 
free-field test geometry modeled by NRL and Allen Vanguard. 
 
Figure 1.3: Blast geometry modeled in CFD for frontal blast impacts [5] 
 
A key finding of NRL’s research was that a particular type of protective equipment 
(e.g., visor) might decrease the overpressures at some locations, while simultaneously 
increasing the overpressures on separate regions of the head [6]. Figure 1.4 shows a 
summary of the pressure history results for front-facing blasts for four different PPE 
configurations [6].   
4 
 
 
 
 
Figure 1.4: Pressure histories for front-facing blasts for four PPE configurations [6] 
 
Unfortunately, free-field methods are costly, inherently limited in repeatability, and 
therefore not conducive to a large number of tests [7]. Laboratory test methods using shock 
tubes offer more controlled, repeatable, and less expensive platforms for assessing blast 
traumatic brain injuries (bTBI) and performance of PPE. Furthermore, previous research 
has shown specific shock tubes can generate blast signatures representative of free-field 
events [8]. 
1.1.4. Shock Tube Testing 
Although compression-driven shock tubes have been validated as a method of 
generating representative blast waves [8], blast waves produced by shock tubes depend on 
a number of design parameters, including the driving gas, the driver (breech) length, and 
the membrane burst pressure, which is the pressure at which the membrane separating the 
pressurized driver section from the driven section bursts [9]. A simplified schematic of a 
constant diameter shock tube is shown in Figure 1.5. The driver section, which is filled 
5 
 
 
 
with pressurized gas, is separated from the driven section by a membrane. Once the 
pressures in the driver section increase enough, the membrane will rupture and air will 
quickly escape into the driven section, forming a shock. The pressurized gas in the driver 
section is often referred to as the driving gas and the gas in the driven section as the driven 
gas. 
 
Figure 1.5: Simplified constant-area shock tube schematic 
 
Reneer et al. (2011) conducted experiments using a multi-mode shock tube and 
showed how the use of different driving gases affected the pressure signature and the 
injuries to a rat brain in the test section [10]. Figure 1.6 shows the different rat brains after 
being exposed to blast waves that resulted from different driving gases [10]. The vascular 
damage appears to be more pronounced for brains exposed to blast waves when the driving 
gas was compressed air instead of oxyhydrogen  [10]. 
6 
 
 
 
 
Figure 1.6: Representative photographs of the rat brains following exposure to different 
driving gases and at various peak overpressures. White arrows point to hematomas. [10] 
 
Sundaramurthy and Chandra (2014) also studied the impact of different driving 
gases on the shock profile generated by a shock tube and conducted additional parametric 
studies that varied the shock tube breech length and burst pressure [9]. They concluded that 
a compressed-gas shock tube can be used to simulate primary blast injury for blast-induced 
neurotrauma studies.  
Other researchers studied how flow properties differ inside and outside a shock tube 
to assess the validity of testing outside a shock tube, called “end-jet testing.” Chandra et 
al. (2012) studied the shock evolution within and outside shock tubes, concluding that the 
placement of a test article outside of the open end of a shock tube exposed the test article 
7 
 
 
 
to complex flow phenomena that were not representative of blast waves in the field [8]. 
Kuriakose et al. (2016) and Yu et al. (2014) also studied the effects of the test article’s 
placement and whether end-jet testing provided representative results [11, 12]. Kuriakose 
et al. (2016) agreed with Chandra’s conclusions, while Yu et al. (2014) concluded that end-
jet testing was acceptable under specific constraints [8, 11, 12]. Specifically, Yu et al. 
(2014)  concluded that testing inside is acceptable if the test article is placed at least 8-10 
shock tube diameters down the driven section, and testing outside is acceptable if the test 
article is placed within ½ a tube diameter from the exit [12].   
Shock tube testing has also been conducted with both surrogate bare and helmeted 
human head forms. The University of Nebraska-Lincoln (UNL) used conical shapes to 
model simplified head-helmet interfaces, such as the use of a cylindrical core to represent 
a head form, as shown in Figure 1.7 [13, 14].  
8 
 
 
 
 
Figure 1.7: Simplified head, brain, and helmet interface model [14] 
 
UNL also conducted more detailed computational and experimental studies on the 
effect of blast waves on surrogate head forms [15, 16]. The University Carlos III of Madrid, 
National University of Singapore, and University of Melbourne conducted a joint 
computational study to understand the effect of helmet systems on human head responses 
under blast loading [17]. Similar to NRL, they used different combinations of PPE to 
understand how each combination influenced the head’s response. 
1.1.5. Blast Overpressure Simulation System 
For a number of years, personnel at JHU/APL have conducted studies to improve 
their ability to replicate blast wave scenarios that cause injuries [4]. They used both shock 
tubes and free-field testing to characterize shocks generated by IEDs and assess the 
9 
 
 
 
overpressures on surrogate head forms with and without PPE. Ultimately, JHU/APL built 
the Blast Overpressure Simulator System (BOSS) to improve their capability for laboratory 
testing.1  Chapter 3 describes the development of a CFD model of the BOSS and its 
validation against experimental data obtained from the BOSS. 
1.1.5.1. Geometry and Design 
The geometrical and operational basis for the JHU/APL blast simulator was an 
existing Advanced Blast Simulator (ABS) with a 0.6096m x 0.6096m cross-sectional test 
area developed for use in small animal studies [18]. Key attributes of the original ABS 
system design preserved in the BOSS included the driver and transition sections with 
expanding cross-sectional area, which were found to be critical in replicating the wave 
dynamics of an expanding spherical blast including the negative phase and secondary 
shock [18]. The ABS design creates a fully-developed planar pressure exposure on test 
articles located at the test stations and an End-Wave Eliminator (EWE) following the test 
section that uses optimized venting to prevent unwanted reflection and rarefaction waves 
from the end affecting test conditions as well as mitigating noise and shock-flow efflux 
into the laboratory space [18]. Top-down and side views of the BOSS are shown in Figure 
1.8. 
                                               
 
 
1 Experimental work was conducted by Joseph R. Andrist, Darrell A. Zinn, and John A. Clark at JHU/APL. 
The following information about the BOSS was provided by John A. Clark. 
10 
 
 
 
 
Figure 1.8: Top-down and side views of BOSS. Two potential test-section locations shown. 
 
The BOSS is operated using compressed bottled gas that is rapidly filled into the 
driver section. The driver section can be filled with either mixed air or helium gas 
depending on the desired downstream pressure signature during system operation. Tests 
have been conducted using standard mixed air or Helium as the driving gas. Ambient air 
was always used as the driven gas.  
During system operation, the diaphragm membrane materials are clamped at the 
junction of the driver and driven sections. The diaphragm-clamping frame was outfitted 
with six book bolts used to hold the two sections together while six 20-ton hydraulic rams 
evenly applied pressure to clamp the diaphragm during testing. The rupture characteristics 
of the diaphragm materials directly influence the waves created by the laboratory blast 
simulator system; therefore, it is important to get clean, complete, and consistent ruptures 
to produce repeatable data with minimal artifacts in the pressure-time histories. The mode 
of material failure (e.g., brittle vs elastic, rupture speed, failure patterns and direction) all 
influence the validity, duration, and repeatability of the waveforms. 
11 
 
 
 
The transition section provides a gradual, sigmoidal-shaped transition from the 
relatively narrow exit of the driver section (0.2286m width) to the full-width test section 
(0.9144m width) over the length of 3.048m. The expanding shape of this section ensures 
that a fully developed planar overpressure shock front is formed downstream of the 
diaphragm after the membrane bursts. 
Two locations in the blast simulator system were selected to install test fixtures and 
instrumentation to support full helmeted head and neck evaluation. These locations have 
sufficiently large cross sectional areas and planar flow profiles to allow the idealized 
pressure signatures formed in the transition section to arrive at the test apparatus with a 
planar exposure and minimal artifacts. 
1.1.5.2. Testing Procedure 
The system requires two individuals to operate. Test articles and desired 
instrumentation are prepared and placed in the appropriate test location within the system 
as the first step. Next, membrane materials are carefully loaded between the diaphragm 
clamping frame and downstream ambient sections to ensure there are no creases of the 
material, and pre-clamping is achieved by manually tightening the book bolts. Once this is 
achieved, the hydraulic rams are used to apply an evenly distributed clamping pressure 
until the diaphragm is held in place with approximately 140 klbf of force. For safety 
purposes, both manual and computer controlled valves are used to fill the driver section 
with gas at a constant rate until the membrane bursts. Custom-built LabVIEW software 
allows the operator to monitor and control the supply and driver pressures while remotely 
initiating the test sequence.   
12 
 
 
 
A number of sensors are used during testing with the BOSS. These sensors were 
chosen for their high resonance frequency, high response rate, and their appropriate 
pressure sensing range and form factor. The wall gauges are mounted flush with the inner 
surface of the BOSS walls. Pitot-static gauges are mounted on the inertial frame at the test 
locations and are used to measure pressure in the center of the tube. 
The BOSS is currently outfitted with a total of 15 sensor ports on the top and side 
walls to measure the pressure flow characteristics during operation. This includes one port 
in the driver section, three ports in the top wall of the transition section, one port on the 
right side of the transition section, and five ports each on the top and side walls of the test 
section, respectively. The current ports contain pressure sensors (Model HKS-375-100SG, 
Kulite Semiconductor Products, Inc., Leonia, NJ, USA), but can be modified to remove 
instrumentation or be replaced with clear windows for high-speed video at these locations. 
These sensor ports can be seen in top-down and side views of the BOSS apparatus in Figure 
1.9.  
 
Figure 1.9: Current wall sensor port location in the BOSS (A = driver section, B = 
transition section, C = test section, R = right wall, L = left wall) 
13 
 
 
 
 
In addition to the wall pressure data, pressure can be characterized in the center of 
the system via a modified Pitot-static probe fixture containing forward and rearward facing 
pressure gauges to capture total (forward-facing) and static (rearward-facing) overpressure, 
and a disc gauge to capture static overpressure. This Pitot-static gauge was designed and 
fabricated for use within the BOSS (Figure 1.10). This consists of three pressure sensors 
(Model 113A36, PCB Piezotronics, Depew, NY, USA). Two of the pressure sensors are 
mounted with the sensing surfaces perpendicular to the flow, one facing forward and the 
other facing rearward. The third pressure sensor measurement surface is oriented parallel 
to the flow; a plastic disc with a flat surface ensures zero flow velocity at this location. The 
original disc was fabricated out of aluminum but allowed vibration noise to be picked up 
by the pressure gauge, switching to a rapid-prototyped plastic disc alleviated the issue. This 
Pitot-static gauge is mounted within the flow field of the BOSS as shown in Figure 1.10, 
and measures stagnation and static overpressure in the center of the tube. The potential 
locations of this gauge are the two test stations shown in Figure 1.8. 
 
Figure 1.10: Custom Pitot-static gauge mounted on the inertial frame 
14 
 
 
 
1.1.5.3. Data Acquisition 
All data were recorded at 500 ksps using a high-rate data acquisition system (Model 
801, DEWETRON GmbH, Grambach, Austria). High-speed video2 was taken at a frame 
rate of 20-25 kfps. Short videos were saved at the full frame rate to observe the arrival of 
the shock front and its progression around the headform. Longer videos were saved at a 
decimated frame rate to observe the headform kinematics.  
1.2. Contributions of Thesis Research 
The first objective of this research was to demonstrate the ability to use CFD to 
accurately predict the overpressures inside a shock tube. Then, CFD was used to 
corroborate the results of other researchers by reaffirming the ability to use shock tubes to 
generate pressure signatures that are representative of blast waves. However, this work 
focused on the evolution of the blast wave as it traveled down the shock tube for all shock 
tube designs that were studied instead of assuming a single test section location as was 
done for previous work. Parametric studies were performed with CFD to characterize the 
primary overpressure blast environment created from a variety of laboratory shock tube 
designs and understand the effects of varying the membrane burst pressure, driver length, 
and driving gas. The results from these analyses are provided in this thesis and can be used 
to inform future shock tube design and experiments to ensure the generated pressures are 
representative of blast waves. 
                                               
 
 
2 Video taken by Phantom V1611, high-speed camera from Vision Research, Inc., Wayne, NJ, USA 
15 
 
 
 
Additionally, a CFD model was developed to facilitate assessing the effectiveness 
of PPE. As part of the modeling process, a new bulging diaphragm model was developed 
to improve agreement of CFD-based pressure signatures with experimental measurements. 
Then, CFD was used to characterize the overpressures on bare and helmeted head forms 
for frontal, side, and rear impacts and assess the effectiveness of helmets for reduction of 
overpressures on the human head. CFD allows for computation of the overpressures 
throughout the shock tube and across the entire head form, whereas experimental studies 
provide results at only finite locations.  
1.3. Overview of Thesis 
This thesis is organized into four chapters. The first portion of this thesis relates to 
the characterization of shock tubes and the assessment of their ability to replicate free-field 
blast wave signatures. The second portion of the thesis focuses on validating a 
computational fluid dynamics model of a blast wave simulator and a head form test article 
against experimental data. The remainder of the thesis examines the effect of a nominal 
helmet geometry on overpressures on various portions of the head under different blast 
loading conditions.  
Chapter 1: Introduction. This chapter presents an overview of the background and 
motivation for studying blast wave pressure signatures and shock tubes as a means of 
generating them. It provides necessary background on prior research on shock tubes and 
the effect of PPE on the human head. It also covers the objectives of the present research.  
Chapter 2: Using Gas-Driven Shock Tubes to Produce Blast Wave Signatures. This 
chapter describes the characterization of constant-diameter shock tubes as key design 
parameters are changed, including membrane burst pressure, driver length, and driving gas. 
16 
 
 
 
It establishes the validity of using gas-driven shock tubes to produce blast wave signatures, 
forming the baseline for the remainder of the research. 
Chapter 3: Assessment of Helmet Effectiveness against Blast Waves using 
Computational Fluid Dynamics Simulations of Gas-Driven Shock Tubes. This chapter 
establishes the validity of a CFD model of a custom blast wave simulator system by 
comparing pressure signatures at key locations in the shock tube to measured experimental 
data. Overpressures measured at select locations on bare and helmeted head forms serving 
as test articles are also compared between the CFD simulations and experimental data. 
Once the CFD simulations are validated, the remainder of this chapter assesses the effect 
of a nominal helmet on predicted head form overpressures under different impact 
orientations: frontal impact, side impact, and rear impact.  
Chapter 4: Conclusions. A summary of observations and key findings from the 
previous chapters are provided. Contributions of this work and suggestions for future work 
are also discussed. 
17 
 
 
 
2. Using Gas-Driven Shock Tubes to Produce Blast Wave 
Signatures 
2.1. Introduction 
The objective of the work described in this chapter is to use computational fluid 
dynamics (CFD) simulations to show whether or not shock tubes can be used to generate 
pressure signatures that are representative of blast waves. Parametric studies were 
performed to characterize the primary overpressure blast environment created from a 
variety of laboratory shock tube designs. Studies were conducted to understand the effects 
of varying the membrane burst pressure, driver length, and driving gas. Conducting CFD 
simulations is less expensive, faster, and therefore better suited for the parametric studies 
than building an array of modular shock tubes to conduct laboratory experiments. The 
results from these analyses can be used to inform shock tube design and experiments to 
ensure the generated pressures are representative of blast waves. 
2.2. Materials and Methods 
The shock tube in this study consists of a high-pressure region (the driver section), 
separated by a diaphragm from a low-pressure region (the driven section). Depending on 
the application, the driver section may be at a different temperature and filled with a 
different gas than the driven section. When the diaphragm ruptures, a normal shock travels 
into the driven section and an expansion wave travels into the driver section [19]. For the 
current study, a constant-diameter shock tube was modeled with a driver that was allowed 
18 
 
 
 
to vent to the atmosphere (farfield). No test article was modeled so shock tube conditions 
were considered unobstructed. 
2.2.1. Shock Tube Geometry and Baseline Mesh Description 
The shock tube geometry for these studies was a 0.1524 meter constant-diameter 
shock tube with a 0.1524 meter long driver section and a 4.87 meter long driven section. 
The computational mesh was generated in 2D using the commercial mesh generation 
software, Pointwise3. Pointwise can be used to create structured, unstructured, overset, and 
hybrid meshes. In this case, Pointwise was used to create a mesh with only quad elements. 
The mesh was created such that the bottom edge was a symmetry plane and the overall 
geometry was defined as 2D axisymmetric to model a circular cross section for the shock 
tube. Figure 2.1a shows the overall mesh of the shock tube, and Figure 2.1b shows a 
detailed view of the end of the driven section (highlighted in beige) with a small gap 
modeled between the shock tube wall (highlighted in red) and outside environment. This 
gap was modeled to give the shock tube wall a finite thickness while still allowing the 
exiting flow to turn the corner. A grid resolution study was conducted using the baseline 
mesh shown in Figure 2.1, a coarser mesh, and a finer mesh to ensure the results were grid 
independent.  
                                               
 
 
3 The software Pointwise and more information about it is available at www.pointwise.com  
19 
 
 
 
 
Figure 2.1: (a) Shock tube baseline computational mesh with (b) zoomed-in view of 
interface between shock tube driven section and outside environment 
 
2.2.2. CFD Solver and Settings 
CFD++4 (version 15.1.1.u6), a commercial CFD solver developed by Metacomp 
Technologies Incorporated, was used for all the simulations described in the following 
studies. CFD++ is a versatile and generalized code that can solve the one, two, or three-
dimensional, steady or unsteady, incompressible or compressible Reynolds-Averaged 
Navier Stokes (RANS) equations. The code’s ability to include multiple species of gases 
was utilized for some of the parametric studies performed as part of this analysis. The code 
also has the ability to solve the Euler equations that describe inviscid flows. The code uses 
                                               
 
 
4 The software CFD++ and more information about it and about Metacomp Technologies Incorporated can 
be found at www.metacomptech.com 
20 
 
 
 
a finite volume formulation, a total variation diminishing scheme for spatial discretization, 
an implicit time-stepping algorithm for time discretization, and a modified Roe’s Riemann 
solver for updating cell averages in time [20].  
For the work described in this report, all simulations were set up to solve the two-
dimensional (2-D) axisymmetric, unsteady, compressible fluid equations. For each time-
step and grid cell, the code solves four 2-D conservation equations: mass, x-momentum, y-
momentum, and energy. One or more additional equations are solved when a turbulence 
model is used and no additional equations are solved when the flow is modeled as inviscid. 
When solving for flows with multiple species, additional N-1 equations are 
required, where N is the number of species. The study described in 2.4.3 was conducted to 
understand the effect of the driver gas on the pressures. At most, two species (air and 
helium) were modeled as one driver gas mixture, so one additional equation was solved for 
those simulations. 
The flow through a shock tube is unsteady. The implicit (backward Euler), dual 
time-stepping algorithm was used to advance the solution from one physical time-step to 
another. At each global iteration (or time-step) the dual time-stepping algorithm iteratively 
solves the governing equations for a predefined number of inner iterations or until a 
predefined convergence criterion is satisfied. For simulating unsteady flows, the selection 
of the physical time-step is critical and depends on the velocities in the flow and the size 
of the smallest grid cell. If the time-step chosen is too large, the flow solution could become 
unstable and unphysical. If the time-step is too small, then the overall simulation (wall-
clock) time can become very large. These issues are exacerbated when dealing with 
complex flows because of the need to have computational grids with many computational 
21 
 
 
 
cells. A time-step study (not described here for brevity) was conducted for each candidate 
grid. Most cases were conducted to achieve at least 15 milliseconds of flow time. The inner 
iterations were set to 20 to achieve a convergence of two orders of magnitude. Early in the 
simulations, the code required 15-20 inner iterations to reach convergence; however, after 
the initial high-gradient transient flow decays, only 6-7 inner iterations were required for 
convergence. 
2.2.3. Initial and Boundary Conditions 
Each CFD simulation requires initial conditions (ICs) and boundary conditions 
(BCs). Here, the driver section was initialized with the driver gas at a given pressure (burst 
pressure) of 689.476, 1034.214, or 1378.951 kPa. The remaining ICs are shown in Table 
1. 
Table 1 Initial Conditions 
Region Absolute Pressure Temperature XYZ Velocity 
(Pa) (Kelvin) (m/s) 
Driver Burst Pressure 295  (0,0,0) 
Driven 101325 295 (0,0,0) 
Farfield 101325 295 (0,0,0) 
 
 At all solid surfaces (shock tube walls), boundaries were assumed isothermal. At 
the farfield boundaries, characteristic inflow/outflow conditions were applied with pressure 
and temperature set at 101325 Pa and 295 K, respectively. Most simulations were 
conducted assuming a symmetry in the Z = 0 plane. For these simulations, a symmetry BC 
was applied, where the normal (to the symmetry) component of velocity is zero. The 
symmetry BC acts as an inviscid wall BC, where only tangential flow is allowed. All 
22 
 
 
 
simulations were conducted using a 0.1524 meter long driver section, a gauge burst 
pressure of 1034.214 kPa, and Helium driver gas unless otherwise noted. 
2.2.4. Data Analysis and Post-Processing 
Selected locations, shown in Figure 2.2, along the shock tube centerline and the top 
wall were used to probe the flow. Data at these locations were taken at every time-step in 
order to find the pressure history at each probe location, and the maximum pressure at each 
location was calculated. The time at which this peak pressure occurs, tpmax, was also 
recorded. Flow-field contours of the symmetry plane were saved every 100 time-steps.  
 
Figure 2.2: CFD schematic and probe locations 
 
2.3. CFD Pre-processing: Time, Mesh, and Turbulence Model 
Independence 
Mesh and time resolution studies were conducted to ensure that all results were 
mesh and time independent. An under-resolved mesh would artificially dissipate the shock, 
and a time-step that is too large could reduce the stability of the simulations leading to 
spurious oscillations, particularly near discontinuities such as shocks (Gibbs phenomena) 
23 
 
 
 
[21, 22, 23]. Similarly, a mesh that was too coarse would be unable to resolve the shock, 
and a mesh that was too fine would increase the simulation’s runtime significantly. Because 
the flow along the shock tube centerline was of more interest than the flow near the wall 
where the effects of viscosity are more significant, the inviscid equations were solved and 
the mesh resolution was only varied within the tube and in the axial direction. After mesh-
independence and time-independence studies were completed, a turbulence-model study 
was also conducted to ensure viscosity did not significantly change the results. The driver 
section was initialized with helium (He) for these studies. Pressure traces were compared 
for each simulation at two separate probe locations: 1 meter and 4.82 meters downstream 
from the driver/driven intersection. These two locations were chosen to compare the effect 
of design parameters on both the initial shock formation and the shock decay with distance. 
The studies found that regardless of the computational mesh used, the time of 
arrival for the shock and maximum peak pressures remain within two percent for each of 
the simulations. A mesh containing approximately 94,000 computational cells was grid and 
time-step independent when using a time-step of 1 µs. The turbulence models did not 
significantly impact these results. The impact to shock arrival time is less than 1% and the 
effect on peak pressure is less than 5%. Therefore, the remainder of the simulations were 
conducted assuming an inviscid flow field to reduce the average simulation runtime. On 
average, simulations took three hours to run.  
24 
 
 
 
2.4. Results 
2.4.1. Burst Pressure Study 
In a laboratory experiment, a burst pressure study is one that tests the effect of the 
choice of the membrane on the pressure history. Different types of membranes burst at 
different pressures and, thus, the relation between the burst pressure and test-section peak 
pressure is observed. For our studies, it is necessary to understand the effect of membrane 
burst pressure on the positive phase duration of the wave. If the positive phase duration 
increases with the peak pressure, the overall impulse may increase significantly compared 
to a situation where the peak pressure increased and the positive phase duration did not. 
The results of the burst pressure study, shown in Figure 2.3, show that the peak 
pressure increased as the membrane burst pressure increased, but the recovery percentage, 
𝑃0123⁄𝑃4567., decreased as the burst pressure increased. Furthermore, the rate of decay as 
the wave travels downstream is higher as the burst pressure increases. Finally, the higher 
burst pressures do increase the positive phase duration of the wave, suggesting that the 
impulse will be greatly increased. 
25 
 
 
 
 
Figure 2.3: Burst pressure study; (a) 1 meter and (b) 4.82 meters downstream of 
driver/driven intersection 
26 
 
 
 
2.4.2. Driver Length Study 
A study was conducted to examine the effect of different driver lengths on the shock 
evolution. Pressure traces were compared for this study at two separate probe locations: 1 
meter and 4.82 meters downstream from the driver/driven intersection. These two pressure 
traces allow us to compare the shocks at those specific locations as the driver length is 
varied. Additionally, the evolution of the shock between these two locations can be 
compared. 
 Figure 2.4 shows that longer drivers can result in the formation of a flat-top wave. 
Some driven length is needed before the pressure signature generated by the shock tube 
with a 0.4572 meter driver is representative of a Friedlander wave. However, the 
overpressures generated 4.82 meters downstream by this shock tube are significantly 
higher than those generated by shock tubes with smaller driver lengths. Additionally, the 
positive phase duration is also longer, which would result in greater impulses on the test 
article. 
Figure 2.5 shows the evolution of the primary shock as it travels down the shock 
tube for a 0.4572 meter driver. At 1 meter downstream from the driver/driven intersection, 
there is clearly a flat-top wave. The position history shows that the shock strength quickly 
dissipates between the 1.53 and 2.99 meter locations, but the wave is now more 
representative of a Friedlander wave by the 2.99 meter location. By the time the shock is 
4.82 meters downstream, the resulting pressure signature is once again no longer 
representative of a Friedlander wave. This study shows that there is a critical area in which 
the test article should be placed such that the impacting wave exhibits the desired blast 
profile. 
27 
 
 
 
 
Figure 2.4: Driver Length Study; (a) 1 meter (b) 4.82 meters downstream of driver/driven 
intersection 
28 
 
 
 
 
 
Figure 2.5: 0.4572 meter driver section shock tube shock evaluation 
 
2.4.3. Driver Gas Study 
The final study conducted as part of this work was to look at the effect of using air, 
helium, or an equal parts mixture as the driver gas. The driver gas is an important facet of 
the experimental setup because IEDs and explosives may release other gases, which may 
alter the shock properties. In a laboratory setting, it may be less desirable to use explosive 
nitroanimes, including RDX, due to licensing requirements and the need for specialized 
equipment for storage and transport [10]. Because one objective of this work is to help 
29 
 
 
 
inform future experiments, air, helium, and an equal-parts mixture, all of which are more 
likely to be experimentally used, were studied for this analysis. Pressure traces were 
compared for each simulation at two separate probe locations: 1 meter and 4.82 meters 
downstream from the driver/driven intersection. These pressure traces also show how the 
generated shock profile changes, how the shock evolution/decay changes, and how 
characteristics such as peak pressure and positive-phase duration are altered. 
30 
 
 
 
 
Figure 2.6: Driver gas study; (a) 1 meter and (b) 4.82 meters downstream of driver/driven 
intersection 
31 
 
 
 
From Figure 2.6a, the simulations show that the shock arrival time is the earliest 
for a helium driver gas and the latest for an air driver gas. This is unsurprising considering 
that the molecular weight of helium is less than air and it also corresponds to the strength 
of the shock. Figure 2.6b shows that the order in which the shocks arrive changes such that 
the shock from a mixture arrives first and the shocks from the air and helium driver gases 
arrive nearly at the same time. This can be attributed to changes in the shock strength. The 
shock due to the air driver gas remains the strongest and thus the fastest, enabling that 
shock to “catch-up” to the other shocks. While both the helium and air-helium mixture 
produce shock profiles similar to the Friedlander profile, the air driver gas creates a flat-
top profile instead.  
32 
 
 
 
 
Figure	2.7:	Pressure	flow	contours	for	(a)	Helium	driving	gas	(b)	Air	driving	gas	
33 
 
 
 
Figure 2.7a shows a pressure contour for the helium simulation, and Figure 2.7b 
shows a pressure contour for the air simulation. These flow contours corroborate the 
pressure signatures observed: the shock for the helium simulation has travelled farther and 
the thickness of the highest-pressure level is smaller corresponding to the immediate decay 
in the pressure signature, whereas the air simulation has a thicker region of high pressure 
which corresponds to the flat-top wave.  
If the test section is far away from the start of the driver section, then the results in 
Figure 2.6b may be more important. From this plot, one can see that the simulations for 
each gas resulted in similarly shaped pressure signatures sufficiently downstream of the 
driver/driven intersection. Each pressure signature features a short and linear decay 
between the initial pressure rise and exponential decay, meaning none of them match the 
desired blast wave profile. 
34 
 
 
 
 
Figure 2.8: Air driving gas shock evolution 
 
Figure 2.8 shows that the blast profile generated by air can generate the desired 
profile, but it occurs farther downstream than the point where the desired profile is 
generated when the driver gas is helium. The region in which the desired shock profile is 
generated is small and, thus, the test section placement would need to be optimized for the 
conditions of the test. If helium or a mixture are used instead, researchers would likely have 
more freedom in test section placement. However, both the helium and air-helium mixture 
show a significant decrease in max pressure with distance relative to the air mixture. 
35 
 
 
 
2.5. Discussion 
The purpose of this chapter was to provide design guidelines for shock tubes such 
that they can be used to generate blast waves. Parametric studies were conducted using 
CFD to characterize the primary overpressure blast environment created by a variety of 
laboratory shock tube designs. CFD was used to characterize changes in the flow that 
resulted from varying specific design features, such as: burst pressure, driver length, and 
driver gas. These studies demonstrated that a shock tube can be used to generate the desired 
Friedlander-shaped blast profile under two conditions. The test section must be placed far 
enough from the driver/driven interface that there is no flat-top wave profile. In addition, 
the test section must be placed far enough from the shock tube exit such that the complex 
flow phenomena near the shock tube exit do not influence the blast profile. The exact 
distances that the test section should be placed away from the driver/driven interface and 
shock tube exit depend on other design parameters such as shock tube length and driving 
gas. 
Experimentalists using shock tubes for this work will have two major goals – to 
generate both a Friedlander-shaped blast profile and a sufficiently high peak pressure in 
the test section to correlate the results of free-field testing for a corresponding amount of 
explosive. The studies showed that the use of air as the driver gas results in a flat-top blast 
profile that briefly changes into a Friedlander-shaped blast profile farther downstream. The 
differences in the peak pressure and impulses between flat-top and Friedlander-shaped 
blast profiles would depend on the exact wave and the time duration of the flat-top portion 
of the profile, but these differences could lead to incorrect assessments about how injuries 
occur in the field. Selecting helium as the driver gas immediately results in a Friedlander-
36 
 
 
 
shaped blast profile. This is desirable if the test section can be placed close to the 
driver/driven interface. If the test section has to be placed farther away for other 
requirements, the use of helium may be detrimental to peak pressure requirements because 
helium has a higher rate of decay in peak pressure as the wave travels downstream than air. 
An optimized air-helium mixture for the driver gas may provide both a Friedlander shock 
profile and required peak pressures in the test section. Experimentalists may be able to 
meet peak pressure requirements with helium as the driver gas by selecting a diaphragm 
material that will not burst until higher pressures. As the pressure in the driver section 
increases prior to burst, the resulting peak pressures in the driven section will also increase. 
If this option is utilized, the sublinear relationship between burst pressure and the resultant 
peak pressure of the wave is important to keep in mind.  
A key finding of the driver length study was that an increase in driver length can 
lead to a flat-top wave profile farther downstream the shock tube, even with a helium 
driving gas. Thus, the test section should be placed sufficiently far away to ensure that the 
test article is impacted by a shock exhibiting the appropriate pressure decay. The placement 
of the test section is further complicated by the change in the pressure signature, deviating 
from the Friedlander profile, as the shock travels downstream. Pre-test predictions using 
CFD may be used to determine the ideal location for the placement of a test article such 
that it is impacted by a shock that also provides the desired blast profile and peak pressure. 
Each study showed that the peak pressure of the shock decreased as it traveled downstream. 
These two results should drive an experimentalist to minimize the driver length such that 
the acoustic waves can quickly coalesce and form the strong shock before losses reduce 
the peak pressure below the requirement for a given test. 
37 
 
 
 
In conclusion, the studies demonstrated that shock tubes are a viable method of 
generating Friedlander-shaped blast profiles. However, careful attention must be paid to 
the shock tube and experimental design to ensure this profile is achieved while meeting 
minimum peak pressure requirements in a test section. CFD can be used to help design the 
shock tube and provide pre-test predictions to verify that all requirements will be met. 
38 
 
 
 
3. Assessment of Helmet Effectiveness against Blast Waves using 
Computational Fluid Dynamics Simulations of Gas-Driven 
Shock Tubes 
3.1. Introduction 
The primary objective of the work described here was to use computational fluid 
dynamics (CFD) simulations, validated against experimental data from laboratory testing, 
to perform a comprehensive study of shock tube flow and its impact on a head form inside 
the test section. Simulations were conducted to compare the overpressures experienced by 
bare and helmeted head forms in front, side, and rear orientations. The author hopes that 
these results will be used to inform future helmet design for blast wave protection. 
3.2. Methodology 
The shock tube in this study consists of a high-pressure region (the driver section), 
separated by a diaphragm from a low-pressure region (the driven section). The diaphragm 
is made of multiple sheets of acetate and polyester screen material. The sheets of acetate 
vary in thickness depending on the desired burst pressure and the polyester is used to 
reinforce the acetate. Depending on the application, the driver section is at a different 
temperature and is filled with a different gas than the driven section. Once the driver section 
is sufficiently pressurized causing the diaphragm to rupture, a normal shock travels into 
the driven section, and an expansion wave travels into the driver section. Researchers at 
JHU/APL built a shock tube—the Blast Overpressure Simulator System (BOSS)—with a 
0.9144m x 0.9144m cross-sectional test-section area. This shock tube was based on a 
39 
 
 
 
design specifically made to generate pressure signatures similar to those produced by blast 
waves [18]. Additional information on this shock tube was provided in 1.1.5. The shock 
tube geometry was modeled using CFD meshing software and the three-dimensional (3-D) 
unsteady, and compressible equations were solved using CFD software. Additional details 
on the solver are provided in Section 3.2.2. CFD simulations were conducted for models 
with unobstructed shock tube conditions, as well as models of a bare or helmeted head 
form inside the test section. 
3.2.1. Baseline Mesh Description 
The BOSS was used as the nominal geometry for this computational effort. A 2D 
schematic of a top-down view of the shock tube is shown in Figure 3.1.  
 
Figure 3.1: Two-dimensional schematic of Blast Overpressure Simulator System 
 
As shown in Figure 3.1, the End-Wave Eliminator was not modeled to reduce the 
complexity of the mesh. Instead, the mesh’s axial spacing was rapidly increased after the 
test section to artificially diffuse the shock and prevent a reflection off the rear wall of the 
shock tube from influencing the test section. The diffusor section behind the test section is 
40 
 
 
 
longer than what is depicted in the figure. Experimental pressure sensors along the top wall 
are depicted by colored cubes, while sensors along the side walls are depicted by black 
cubes.  
Although it is easier to model an instantaneous and complete diaphragm rupture, 
non-metal diaphragms may deform prior to rupture and may not fully rupture. Active 
research on this topic includes both the numerical analysis of non-ideal diaphragm rupture 
in expansion tubes [24] and experimentation with instantaneous diaphragm rupture 
techniques such as laser beam irradiation [24, 25]. An image of a diaphragm that both 
bulged and failed to rupture during testing at the JHU/APL BOSS facility is shown in 
Figure 3.2. Diaphragm deformation prior to rupture was modeled through spherical 
deformation of the driver section where the radius could be changed to model different 
levels of bulging. A small computational study was conducted to determine what bulging 
levels in the CFD model led to results that best matched experimental data. 
 
Figure 3.2: Failed diaphragm 
 
41 
 
 
 
a)
b)
 
Figure 3.3: Diaphragm deformation study for (a) 588 kPa (b) 1295 kPa burst Pressure 
42 
 
 
 
Figure 3.3 shows the comparison of experimental runs to computational simulation 
results for various levels of deformation modeled. The burst pressures in the CFD 
simulations were set to match the burst pressures for the corresponding experimental runs. 
The plots suggest that 0.0762 meters of deformation results in a pressure trace that best 
matches the experimental data. It is also worth noting that there is secondary spike in the 
experimental data that was taken at a gauge burst pressure of 1295 kPa. It is believed that 
the secondary spike was caused by an acoustic wave that coalesced with the primary shock 
front later than expected due to non-ideal diaphragm rupture. Although the peak pressure 
is lower than the predicted peak pressure for a 0.0762 meter deformation, the two curves 
show good agreement after the secondary spike in the experimental data. Furthermore, due 
to the simplicity of the model and variability in the experiment, an exact match was not 
expected. 
43 
 
 
 
a)
b)
c)
 
Figure 3.4: Helmeted head from (a) front view (b) side view (c) helmet padding 
underside view 
44 
 
 
 
Figure 3.4 shows images of the head form and helmet geometries that were modeled 
for this study. The underside of the helmet is also shown, with some of the padding that 
makes contact with the head. 
A hybrid meshing technique was employed to increase the flexibility of the mesh. 
GridPro5, an automatic multiblock structured grid generation tool, was used to create a 
fully structured grid of the shock tube interior with a spherical cut-out in the test section, 
as shown in Figure 3.5. This figure also depicts the stretching of the grid spacing used to 
dissipate the shock after the test section in the simulations.  
 
Figure 3.5: Two-dimensional slice of GridPro-generated computational mesh of shock 
tube with spherical cut out in test section 
 
Figure 3.6 shows a zoomed in view of the mesh near the driver/driven interface and 
the curved grid lines that model diaphragm deformation. 
                                               
 
 
5 The software GridPro and more information about it and about Program Development Company can be 
found at http://www.gridpro.com/  
45 
 
 
 
 
Figure 3.6: Zoomed-in view of two-dimensional slice near driver/driven interface (curved 
grid lines model deformed diaphragm) 
 
Figure 3.7 shows a zoomed in view of the 2D slice and spherical cut out in the 
structured GridPro mesh. The boundary of this cut out was extracted from GridPro, brought 
into Pointwise6, and used as the outer boundary for the mesh around the test article. 
                                               
 
 
6 The software Pointwise and more information about it is available at www.pointwise.com  
46 
 
 
 
 
Figure 3.7: Zoomed-in view of two-dimensional slice showing spherical cut out 
 
Pointwise can be used to create structured, unstructured, overset, and hybrid 
meshes. For this study, Pointwise was used to create an unstructured grid between the test 
article geometry and the aforementioned spherical outer boundary. Pointwise’s T-Rex 
feature, which utilizes anisotropic tetrahedral extrusion to create hexahedra off walls and 
tetrahedral cells farther away, was used to generate the mesh around the test articles. Figure 
3.8 shows the boundaries for one of the generated grids, where the test article was a 
helmeted head form. 
47 
 
 
 
 
Figure 3.8: Isometric view of spherical boundary shared between both meshes and 
Pointwise-meshed head-helmet geometry 
 
This approach allowed for the test article to be swappable (i.e., only the 
unstructured Pointwise mesh would need to be regenerated to conduct simulations with 
different test articles), while keeping the spherical boundary the same. Additionally, the 
spherical mesh could be rotated to study the impact of test article orientation with respect 
to the incoming shock wave, while maintaining point-to-point connectivity at the spherical 
boundary. The two separate meshes were then combined in Pointwise, as shown in the 
zoomed in view in Figure 3.9. 
48 
 
 
 
 
Figure 3.9: Zoomed-in two-dimensional slice of merged mesh with GridPro-generated 
shock tube mesh and Pointwise-generated mesh around test article 
 
3.2.2. CFD Solver and Settings 
CFD++ (version 15.1.1.u6), a commercial CFD solver developed by Metacomp 
Technologies Incorporated, was used for all the simulations described in the following 
studies. CFD++ is a versatile and generalized code that can solve the one, two, or three-
dimensional, steady or unsteady, incompressible or compressible Reynolds-Averaged 
Navier Stokes (RANS) equations for viscous flows. The code uses a finite volume 
formulation, a total variation diminishing scheme for spatial discretization, an implicit 
49 
 
 
 
time-stepping algorithm for time discretization, and a modified Roe’s Riemann solver for 
updating cell averages in time [20]. 
For the work described in this report, all simulations were set up to solve the three-
dimensional (3-D) unsteady, and compressible equations. For each time-step and grid cell, 
the code solves the five 3-D conservation equations: mass, x-momentum, y-momentum, z-
momentum, and energy. Two additional equations are solved for the realizable k-e 
turbulence model, which is recommended by Metacomp Technologies Incorporated for 
internal flows. A turbulence model study (not shown for brevity) found insignificant 
differences between the pressure signatures generated from simulations with different 
turbulence models, but did find that including some turbulence changed the resulting 
solution.  
When solving flows that involve multiple species, an additional N-1 equations are 
required, where N is the number of species. For this work, pressurized air was modeled in 
the driver section to match the experimental set up. Since only one gas species was modeled 
for the entire simulation, no additional equations needed to be modeled. It should be noted 
that Reener et al. found significant differences in the pressure signatures based on the driver 
gas [10]. Not only did Reneer et al. find that different driver gases affected the pressure 
signature’s match with the Friedlander wave, but they also found that the injury to the brain 
differed significantly for different driver gases [10].  
The flow through a shock tube is fundamentally unsteady. The implicit (backward 
Euler), dual time-stepping algorithm was used to advance the solution from one physical 
time-step to another. At each global iteration (or time-step) the dual time-stepping 
algorithm iteratively solves the governing equations for some pre-defined number of inner 
50 
 
 
 
iterations or until a predefined convergence is satisfied. In simulating unsteady flows, the 
selection of the physical time-step is critical and is highly dependent on the velocities in 
the flow and the size of the smallest grid cell. If the time-step is chosen to be too high, the 
flow solution is unphysical and could become unstable. If the chosen time-step is too low, 
then the overall simulation (wall-clock) time can become very large. These issues are 
exacerbated when dealing with complex flows because of the need to have large grids. For 
this work, the time-step was set to 1 microsecond, based on time-step independence study. 
Mesh resolution was based on a mesh independence study to ensure adequate 
accuracy of the shock propagation. Both of these results were important because an under-
resolved mesh would create artificial dissipation of the shock, while a time-step that is too 
large could make reduce the stability of the simulations leading to spurious oscillations, 
particularly near discontinuities such as shocks (Gibbs phenomena) [21, 22, 23]. Most 
cases were run to achieve at least 15 milliseconds of flow time. The maximum number of 
inner iterations was set to 30 to achieve a convergence of two orders of magnitude. Early 
in the simulations, the code required 15 to 30 inner iterations to reach convergence. When 
the shock arrived near the test article and the flow became more transient again, 15 to 30 
inner iterations were required to reach convergence. However, for the majority of the 
simulation where the problem was a simple 1-D propagation of the shock, only 6 to 8 inner 
iterations were required for convergence. 
3.2.3. Initial and Boundary Conditions 
Each CFD simulation requires initial conditions (ICs) and boundary conditions 
(BCs). Here, the driver section was initialized with the driver gas at a given gauge burst 
pressure of 1295.85 kPa. The remaining ICs are shown in Table 2. 
51 
 
 
 
Table 2 Initial Conditions 
Region Absolute Pressure Temperature XYZ Velocity 
(Pa) (Kelvin) (m/s) 
Driver Burst Pressure 295  (0,0,0) 
Driven 101325 295 (0,0,0) 
Farfield 101325 295 (0,0,0) 
 
At all solid surfaces (shock tube walls, head form, and helmet), boundaries were 
modeled as adiabatic walls. 
3.2.4. Data Analysis and Post-processing 
The focus of this work was to study the interaction between a blast wave and bare 
and helmeted head forms in different orientations. Several points along the shock tube top 
and side walls were probed. These locations corresponded with pressure sensor locations 
on the JHU/APL shock tube, which are depicted in the 2D schematic shown in Figure 3.1. 
Similarly, specific points corresponding to experimental sensor locations were probed for 
both the bare and helmeted head forms. The locations of these probes are shown in Figure 
3.10. The X, Y, Z coordinates of each probe location were provided to the CFD code and 
the corresponding pressures at each time-step were recorded to a file as the simulations 
were running. The data was recorded at every time-step. Additionally, the flow-field 
contours of a slice along the centerline were saved every 25 time-steps. 
52 
 
 
 
 
 
Figure 3.10: CFD probe location and experimental sensor placement on bare head form 
53 
 
 
 
3.2.5. CFD Model Assumptions 
CFD modeling assumptions related to diaphragm deformation and modeling of an 
idealized membrane rupture were discussed in Section 3.2.1. Additionally, the CFD model 
assumes that the test article is composed of rigid, non-moving walls when modeling a test 
article in the shock tube. In reality, the interface connecting the head forms to the bottom 
wall of the shock tube is flexible and allows for movement of the head form. It is expected 
that the motion will likely increase the rate of decay in overpressures, particularly for the 
forward-facing side of the head.  
Although the head and helmet are separate entities in reality and in laboratory 
experiments, the CFD models them as a single entity. Thus, the helmet’s position relative 
to the head form is fixed and no movement or compression occurs in the CFD simulations. 
The current CFD model is not able to simulate kinematics and resulting changes in 
overpressures. Additionally, the pads that make contact with the head form are also 
modeled as rigid and without any porosity in the CFD model. These modeling assumptions 
may reduce how quickly pressure underneath the helmet can dissipate and increase the 
overall pressures and pressure spikes caused by reflection underneath the helmet. 
3.3. Results 
3.3.1. Shock Formation 
A key advantage of using the BOSS is that it ensures the generation of a planar 
shock front. Therefore, a CFD simulation was conducted with an empty test section to 
study the shock evolution along the length of the shock tube. Figure 3.11 displays pressure 
contours as the shock travels downstream the shock tube. At time zero, the region of high 
54 
 
 
 
pressure is extremely curved due to diaphragm deformation, but the pressure contours 
clearly depict how the shock straightens out as the wave travels downstream in the test 
section. 
 
Figure 3.11: Pressure contours and shock evolution 
 
3.3.2. CFD Model Validation 
3.3.2.1. Shock Tube Walls 
Prior to analyzing the CFD-predicted overpressures on the bare and helmeted head 
forms, it was important to validate the CFD results relative to the available experimental 
data. Although the CFD model only has a limited capability to accurately model the 
55 
 
 
 
diaphragm rupture, it should be able to accurately predict the pressure signature some 
distance downstream. The CFD and experimental data were first compared 3.147 meters 
downstream of the driver/driven interface, near the end of the transition section, as shown 
in Figure 3.12. Both sets of results were shifted in time (x-axis) such that the shock arrival 
was at time zero. From these results, it is evident that both the experimental peak pressure 
and positive phase duration predicted by the CFD simulations are within 20% of the 
experimental results, despite noise in the experimental sensors. Furthermore, the data were 
once again compared at the start of the test section, 3.72 meters downstream of the 
driver/driven interface. The same shift in time that was applied to the earlier comparison 
was applied once again. Both the experimental and CFD results show that the shock travels 
the 0.576 meter distance between the two sensor locations in about 1.2 milliseconds. 
Furthermore, the peak pressure predicted by the CFD simulations match the experimental 
peak pressure at this location within 5% and the positive phase duration prediction is still 
within 20% of experimental results. 
56 
 
 
 
a)
b)
 
Figure 3.12: CFD validation of pressure time-history for shock tube wall sensors for  
(a) 3.147m (b) 3.72m downstream of driver/driven interface 
57 
 
 
 
3.3.2.2. Bare and Helmeted Head Form 
Experimental data for the pressure sensors on the head forms were only available 
with the head forms oriented to face the oncoming shock. Due to noise in the experimental 
data and concerns about the filtering process, both raw and filtered experimental data were 
compared to the CFD results. For brevity, comparisons are shown and analyzed for only 
the forehead, right eye, and side right sensors. 
Figure 3.13 shows the comparison of experimental and computational data for the 
bare head data. Once again, the CFD predictions for peak pressure continue to be within 
20% of the raw experimental data and predictions for the positive phase duration lie within 
20% of the filtered experimental data. Furthermore, the computational data shows good 
agreement with the filtered data traces and mostly lies within the scatter of the raw data. 
The CFD data consistently predicts both lower peak pressures and lower rates of decay 
than observed in the experiment. Given the agreement between CFD and experimental data 
in the flow immediately prior to the test article, it is possible that the peak pressures are 
being under-predicted due to a lack of sufficient mesh resolution on the head form and 
immediately near the head form. As mentioned in Section 3.2.5, the CFD model does not 
simulate any head motion, which is likely contributing to the lower rates of decay in 
overpressure. 
58 
 
 
 
 
Figure 3.13: CFD validation of pressure-time history for bare head sensors 
59 
 
 
 
 
Figure 3.14: CFD validation of pressure-time history for helmeted head sensors 
60 
 
 
 
Figure 3.14 shows a similar comparison for the helmeted head data. The majority 
of the pressure-time history trends show good agreement, suggesting that the CFD models 
predict these flows well. The shock arrival time and positive-phase time duration are in 
good agreement between the CFD model and experimental data. However, the agreement 
between experimental and CFD data is worse than the agreement shown for the bare head 
form data. The CFD-predicted shock arrival time is slightly earlier than the experimental 
data suggests and the peak pressure differences are larger. The peak pressure at the side 
right location is the second local maximum in the CFD data set, which is also captured in 
the filtered experimental data. However, the magnitude of these pressure peaks is higher in 
the CFD data. Furthermore, although the trends are different for the side right location as 
the experimental data shows a constant decay and the CFD shows an oscillating decay, the 
rate of decay appears to be similar. 
3.3.3. Additional CFD Results 
Additional results and analyses performed using only CFD results are shown in this 
section. Experimental data was unavailable for side and rear impact conditions. 
3.3.3.1. Frontal Impact 
Figure 3.16 shows CFD predictions of the pressure-time history at both previously 
shown and additional locations around the bare and helmeted head forms for a frontal 
impact. Unsurprisingly, as the location of the probe moves away from the front of the face, 
the peak pressure decreases. This is most noticeable at the right ear, side right, and nape 
locations. The highest peak pressures are observed at the right eye location for both the 
CFD data shown in Figure 3.16 and experimental data shown in Figure 3.13 and Figure 
61 
 
 
 
3.14. This peak pressure observation holds for both the bare and helmeted head form. The 
same trend was observed in free-field testing by NRL researchers, who showed that a face 
shield (e.g., goggles) was needed to reduce the overpressures around the eyes [6]. An 
explanation for why the highest overpressures are observed at the eyes is the natural 
geometric gradients contained within an average human face. The eye cavity serves as a 
geometric valley where flow can stagnate, greatly increasing the pressure, as shown in 
Figure 3.15a. When comparing Figure 3.15a, which shows the geometric gradients on the 
average male face, with Figure 3.15b, which shows a contour of the maximum pressures 
observed at any time during the CFD simulation at each discrete mesh point on the face, it 
is evident that many of the pressure contour lines align fairly well with many of the 
geometric lines.  
62 
 
 
 
 
Figure 3.15: (a) Geometric gradients on average male face (b) Maximum overpressure for 
frontal impact 
63 
 
 
 
The lowest peak pressure observed is at the side right location and not the nape. 
This is likely due to an intersection of waves meeting together at the back of the head form 
and increasing the overpressures near the nape, which were originally bifurcated at the 
front of the head form. A second explanation for higher pressures at the nape when the 
head form is helmeted is the occurrence of reflections from the helmet onto the rear of the 
head. Similar phenomena were observed by NRL when testing a head form protected by a 
helmet liner [6]. 
Figure 3.16 also shows that, for this particular PPE geometry, peak pressures were 
reduced at the right ear and side right locations. However, although the initial peak 
pressures were reduced, interactions and reflections under the helmet caused secondary 
peaks and potentially higher overall impulses. In some cases, such as the location of the 
nape, the peak pressure actually increases and there are also additional oscillations from 
reflections under the helmet further increasing the overall impulse. It should be noted that 
the NRL researchers also observed similar effects; however, the exact locations of these 
interactions varied due to differences in their PPE geometry [6].  
64 
 
 
 
 
Figure 3.16: Additional CFD pressure time-history results for frontal impact 
65 
 
 
 
Figure 3.17 shows the maximum pressure observed at each point along the head 
and neck surface at any point during the blast wave’s impact. It is evident from this image 
that regardless of the helmet, the eyes still experience the highest pressures. Furthermore, 
the existence of a helmet creates pressure hotspots in areas where the flow reflects off the 
helmet’s pads and back onto the head.  
 
Figure 3.17: Maximum pressures observed for a frontal impact for bare and helmeted 
head forms 
3.3.3.2. Side Impact 
Figure 3.18 shows CFD predictions of the pressure-time history at both previously 
shown and additional locations around the bare and helmeted head forms for a side impact 
occurring at 90 degrees from a face-on impact. The test article was turned such that the 
right side of the face was impacted by the shock first and the left side of the face was 
66 
 
 
 
somewhat protected. There is a significant decrease in peak pressure for both eyes and the 
forehead relative to the frontal impact scenario. The helmeted head form has lower peak 
pressures at the right ear location compared to when it is unprotected. The peak pressures 
at the side left location is higher for a protected head form, which is likely due to reflections 
between the head and helmet. However, overall pressure magnitudes for locations where 
the face is exposed are not significantly impacted.  
For a protected head form, there are additional oscillations in the data at the side 
left and side right locations, which are also likely due to reflections. These reflections and 
secondary pressure peaks will likely increase the total impulse experienced at these 
locations. Figure 3.19 shows the maximum peak pressures across the head form and shows 
how a helmet reduces the maximum pressures near the ear, but also increases the maximum 
pressures near some of the pad locations. 
67 
 
 
 
 
Figure 3.18: Additional CFD pressure time-history results for side impact 
68 
 
 
 
 
Figure 3.19: Maximum pressure observed for a side impact for bare and helmeted head 
form 
 
3.3.3.3. Rear Impact 
Figure 3.20 shows CFD predictions of the pressure-time history at both previously 
shown and additional locations around the bare and helmeted head forms for a rear impact. 
The peak pressures are significantly reduced at the locations being studied when the impact 
is to the back of the head. This result is expected because the back of the head is shaped in 
a manner which will tend to direct flow around itself rather than into a valley, as was 
observed with the eye sockets. Once again, the helmet clearly protects some areas of the 
head, evidenced by decreased peak pressures at the nape location. Similar to other impact 
orientations, the side right location (and side left location) experiences secondary pressure 
peaks, likely due to reflections between the head form and helmet. 
69 
 
 
 
The nape location’s sensor is near the data acquisition junction box, which makes 
this head form geometry less realistic. A future analysis should be done without the 
junction box modeled in order to understand whether this trends continue to hold. This 
CFD model included the junction box to best match the experimental geometry. 
Figure 3.21 shows the maximum pressures on the head form. It is evident that most 
of the pressures are occurring in the cusp formed by the back of the head and the junction 
box. An analysis without the junction box would be needed to understand what the 
maximum pressure distribution would be for a real human head. 
70 
 
 
 
 
Figure 3.20: Additional CFD pressure time-history results for rear impact 
71 
 
 
 
	
 
Figure 3.21: Maximum pressure observed for a rear impact for bare and helmeted head 
form 
3.4. Discussion 
The purpose of this paper was to use CFD simulations of bare and helmeted head 
models inside the JHU/APL BOSS to understand the impact of a nominal helmet design 
for different blast-impact orientations. Data from the CFD simulations were compared 
directly to experimental data from the shock tube experiments to validate the CFD process. 
General trends were compared to conclusions made by NRL through free-field tests of 
unprotected and protected head forms in different orientations.  
A key finding of this work is that CFD models can accurately model the flow inside 
of a shock tube and the overpressures on the complex test article within it. Experimental 
and CFD data were found to agree within 20% for peak pressures and positive phase time 
72 
 
 
 
duration at many of the studied locations representing a majority of the head form. This 
validation allows the use of future CFD simulations to gather data over the entire head 
surface instead of relying on select probe locations. For example, the total impulse to the 
head could be calculated from the CFD data to understand the impact of protective 
equipment in one metric. 
From comparing the bare and helmeted head form data, it is clear that the helmet 
did not reduce the peak pressures at all locations, nor does it decrease the impulse at all 
locations. However, the helmet did reduce the peak pressure at many locations, depending 
on the blast-impact orientation. These trends are consistent with those observed in the study 
conducted by NRL when using free-field tests. Furthermore, the helmet does not negatively 
impact any exposed locations due to extraneous reflections. It is evident that both the side 
left and side right locations are affected by multiple reflections caused by the helmet, likely 
increasing total impulse at those locations. 
Overall, the highest overpressures were observed at the eyes for a frontal impact 
with or without the helmet. This result can be explained by the natural geometric contours 
of the human face. This result also suggests that PPE such as goggles or visors may be 
beneficial. Future work should include a study of some key metrics such as total impulse 
on the head form for different combinations of PPE. Although NRL has already provided 
data on different combinations of PPE, the data were limited to pressure-time traces at 
specific locations. Additionally, the CFD model for this study should be used without the 
data acquisition junction box to improve the realism of the results in that area.  
73 
 
 
 
4. Summary of Research 
CFD simulations were used to characterize the flow inside shock tubes and 
corroborate previous research that showed shock tubes can be used to replicate free-field 
blast waves. Then, CFD was used to study of the flow inside a custom shock tube built at 
JHU/APL. The CFD model was validated against available experimental data taken from 
shock tube wall pressure sensors and pressure sensors on test articles within the shock tube. 
The validated CFD model was then used to study the impact of helmets on head 
overpressures for different blast-impact orientations. The key results of this research are 
described below.  
4.1.1. Using Gas-Driven Shock Tubes to Produce Blast Wave Signatures 
In the first study, a CFD model of a constant area shock tube was created. 
Computational studies were performed to characterize the primary overpressure blast 
environment created by the shock tube design as the membrane burst pressure 
(implemented through a higher initial pressure in the driver section), driver length, and 
driving gas were parametrically varied. Prior research results, such as the production of 
flat-top waves with the use of air as a driving gas, were corroborated. A key finding of 
these studies was the confirmation of previous work showing that shock tubes can be used 
to generate blast waves. However, the studies also demonstrated that a pressure signature 
representative of a blast wave only existed for a short period of time and at a particular 
location within the shock tube. The location at which this pressure signature occurred 
varied with shock tube design parameters. The change in the pressure-time history was 
shown as a function of location for various CFD simulations to highlight how a certain 
74 
 
 
 
setup could result in a blast wave that varied significantly depending on the test section 
location. 
4.1.2. Assessment of Helmet Effectiveness against Blast Waves using 
Computational Fluid Dynamics Simulations of Gas-Driven Shock 
Tubes 
In this study, a CFD model of the BOSS, a custom shock tube built at JHU/APL 
with a test-section cross-sectional area large enough to test head forms without wall 
interference effects, was created. The BOSS was specifically chosen due to the availability 
of experimental data of pressures along the shock tube walls and on test articles. The CFD 
model was first validated against pressure data along the shock tube walls from laboratory 
testing. Initial agreement between the CFD model and experimental data was improved 
through the implementation of a custom diaphragm rupture model. The diaphragm of the 
shock tube was modeled as a hemispherical curve by implementing a boundary condition 
along it. This model effectively increased the driver section’s volume, which increased the 
peak pressure downstream the shock tube. Next, the CFD model was validated against 
pressure data measured by sensors on both bare and helmeted head forms. General 
agreement for pressures along the head form was worse than agreement for data measured 
on the shock tube wall, but peak pressure and positive phase durations were within 20% of 
the corresponding experimental data.  
Once the CFD model was validated, a comprehensive study of shock tube flow and 
its impact on a head form inside the test section was performed. CFD simulations 
corroborated experimental data, which showed that the helmet did not always decrease 
75 
 
 
 
overpressures at all locations. An effect known as “underwash” causes pressure in certain 
areas to increase because the gas is able to flow between the helmet and head, ultimately 
reflecting off pads under the helmet and onto the head. Simulations were conducted to 
show the effect of varying the impact orientation between the front, side, and rear. It was 
found that the highest overpressures on the head were at the eye sockets when the head 
directly faced the incoming blast wave. The helmet did not influence the pressures near the 
eyes, suggesting that goggles would be needed if the overpressures near the eyes could 
cause injury. Overall, impacts to the side or rear of the head resulted in higher overpressures 
for some locations along the head and lower overpressures elsewhere. The effects of the 
helmet were similar – overpressures were reduced in some areas while the total impulse 
was increased in some areas due to reflections. 
4.2. Contributions to Modeling Blast Wave Exposures to the Human Head 
The first contribution of this research was to corroborate that shock tubes can be 
used to replicate free-field blast waves by examining results from prior experimental 
research and demonstrating the feasibility and reliability of using shock tubes to replicate 
free-field blast waves. Prior research typically focused on a single location for the test 
section, whereas this work focused on the evolution of the blast wave as it traveled down 
the shock tube for all shock tube designs that were studied. The CFD simulations conducted 
as part of this thesis verified the experimental results, showcased the ability of CFD to 
accurately predict the shock tube physics in both time and space, and highlighted the 
sensitivity of the blast wave to test section location. As a result, this work enables 
researchers to use CFD to check the influence of a shock tube or experimental apparatus 
change prior to finalizing any major changes and conducting experiments. Furthermore, 
76 
 
 
 
the results shown in this thesis highlight the need to look at the evolution of the blast as it 
travels downstream. The blast may not generate the desired pressure signature at one test 
section location, but it may generate a desired signature elsewhere. 
The second contribution of this research was the development of a CFD model for 
a custom shock tube design. This work advances current knowledge through the 
development of a technique to model the diaphragm rupture to improve agreement between 
CFD and experimental data. Furthermore, grid and time independence studies were 
conducted to ensure good accuracy from the CFD model. Both wave speed and shock 
reflections were captured in the CFD model with sufficient accuracy relative to the 
experimental data. This CFD model enables researchers to rapidly run simulations to assess 
different protective equipment designs on test articles and quickly vary conditions to test 
different blast impact orientations. CFD predictions of shock tube designs and 
overpressures on head forms allow researchers to quickly and more thoroughly assess the 
impact of new concepts prior to collecting more time-consuming experimental data. 
Prior experimental research using free-field testing found that some PPE lower the 
pressure experienced on parts of the head, while simultaneously increasing the pressure on 
experienced at other locations. This research also found that the same type of trends 
occurred when a CFD model of a shock tube was used to predict the overpressures on the 
modeled head form with a different helmet than was used in the previous research.   
4.3. Suggestions for Future Work 
This thesis focused on the use of CFD simulations that modeled the head forms as 
rigid bodies. Helmeted head forms were also modeled as single rigid bodies. Thus, the 
motions of the head forms and the helmets relative to the head forms were not modeled. 
77 
 
 
 
The overpressures predicted by the CFD simulations described in this research were then 
input into separate simulations that modeled head form dynamics, resulting in a decoupled 
approach. Coupling the head form motion with the CFD simulations such that the pressure 
informed the motion and the motion informed future pressures would be worthwhile future 
work.  
Additionally, the CFD simulations were set up such that the helmet and the padding 
underneath the helmet were both set to wall boundary conditions with no porosity. In 
reality, the padding is likely to compress and deform as the head and helmet are impacted 
by the blast wave. Additionally, some of the gas will likely pass through the helmet and its 
padding instead of completely reflecting off of them. Modeling porosity may be a simple 
way to reduce and more accurately predict the magnitude of the overpressures caused by 
reflections from the helmet. A sensitivity study that compared computational results for 
different levels of porosity to experimental data could result in improved predictive 
capability when using CFD.  
Finally, assessment of other forms of PPE, such as goggles and mandible protection 
would be beneficial. Understanding how various forms of PPE and their different designs 
impact the resulting overpressures could assist researchers with improve the design of PPE 
for the warfighter. CFD could be used to understand the reasons why certain PPE increases 
overpressures for specific regions of the head. This understanding could then influence 
alterations to the design of that PPE. 
Finally, much of this research focused on larger diameter blast simulators, but not 
all research centers have the luxury of having systems with these larger diameters. Some 
prior research efforts have begun to characterize the effects of testing outside the end of a 
78 
 
 
 
shock tube, called end-jet testing, and if the resulting blast wave is valid. However, 
researchers have drawn conflicting conclusions and most research efforts have focused on 
single shock tube designs. Fully characterizing when it is acceptable to conduct end-jet 
testing through a parametric study would be extremely valuable future work to enable 
laboratory and shock tube testing of test articles larger than the test sections.  
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