Approximating a far-field blast environment in an advanced blast simulator for explosion resistance testing

Abstract

While the current state of blast-resistant design methods is based largely on empirical observations of actual explosive testing or numerical simulations, experimental testing remains the ultimate method for validating blast protection technologies. Field trials for performing systematic experimental studies are exceedingly expensive and inefficient. Conventional blast simulators (shock tubes) enable blast testing to be performed in a safe and controlled laboratory environment but are significantly deficient. The Australian National Facility of Physical Blast Simulation based on the ‘Advanced Blast Simulator’ concept was established to address the shortcomings of conventional blast simulators (shock tubes). The blast simulator at the National Facility of Physical Blast Simulation is a state-of-the-art design having a test section of 1.5 × 2.0 m with dual-mode driver able of operating with either compressed gas or gaseous detonation modes. The simulator is capable of a range of blast-test configurations such as full-reflection wall targets and diffraction model targets. This article aims to demonstrate the ability of the Advanced Blast Simulator in accurately generating a far-field blast environment suitable for high-precision and repeatable explosion testing of various building components. Blast pressure-time histories generated with the Advanced Blast Simulator are validated against equivalent TNT free-field curves reproduced with Conventional Weapons Effects Program. Numerical models based on Computational Fluid Dynamics were developed in ANSYS FLUENT to accurately characterise and visualise the internal flow environment of the National Facility of Physical Blast Simulation Advanced Blast Simulator. The Computational Fluid Dynamics model was also used to explain experimental observations and to determine density and dynamic pressure information for comparisons with free-field explosion conditions.

Keywords

Free-field blast simulation shock wave propagation shock tube blast loads ANSYS FLUENT CONWEP hemispherical explosion spherical explosion

Introduction

The past two decades has seen a significant increase in the number of terrorist attacks on embassies, commercial centres, government structures, industrial facilities and residential buildings. From a structural safety standpoint, these attacks have highlighted the vulnerability of existing civilian infrastructure to the dynamic effects of high pressure, short duration blast loading.

Civilian, government and military organisations have been addressing these vulnerabilities by developing new blast-resistant design guidelines and retrofit procedures to mitigate blast hazards (Bangash, 2009; DAHS CWE, 1998; DOE/TIC-11268, 1992; ESL-TR-87-57, 1989; Starossek, 2009; TM 5-855-1, 1986; UFC 3-340-02, 2008). Typically, the start to a design process of protective structures involves establishing the pressure-time loading from a given equivalent TNT explosive charge weight and standoff distance (Ngo et al., 2007; Remennikov, 2002; UFC 3-340-02, 2008). Empirical charts developed by Kingery and Bulmash (1984) reproduced in many design documents such as UFC 3-340-02 (2008) are commonly used to determine the incident and reflected overpressures and impulses of a spherical or hemispherical TNT explosion. These relations are automated in CONWEP (Conventional Weapons Effects Program) (Hyde, 1988) and together with Friedlander’s equation (Friedlander, 1946), pressure-time graphs can be reconstructed for the purpose of analysis and design of blast-resistant structures.

The empirical relationships of air-blast parameters by Kingery and Bulmash (1984) widely used today initially only consisted of relations for peak overpressure versus scaled distances of hemispherical TNT surface explosions from tests performed with 5-, 20- and 100-ton TNT charges when it was first compiled (Kingery and Pannill, 1964). Revisions to the original report were later made (Kingery, 1966) to describe more blast wave parameters to include shock front arrival time, incident peak overpressure and impulse, and positive phase duration. Final changes were made in 1984 (Kingery and Bulmash, 1984) to compile air-blast parameters for spherical and hemispherical TNT explosions based on data from numerous sources, corrected for calculations of kilogram mass of TNT at atmospheric pressure. A detailed historical account on developments leading to the final Kingery and Bulmash empirical relations can be found in Shin et al. (2014).

As an alternative method to using empirical relations of air-blast parameters to determine the pressure-time loading of an equivalent TNT explosive charge, Computational Fluid Dynamics (CFD) codes such as EUROPLEXUS (2019), LS-DYNA (LSTC, 2013), Autodyn (ANSYS Autodyn, 2016) and Air3D (Rose, 2006) are capable of predicting the output blast loadings by modelling detonation and solving Euler equations. Equations of States (EOS) like the Jones-Wilkins-Lee (JWL) (Lee et al., 1973), which itself is empirically derived, allows the expression of pressure as a function of internal energy and expansion of the high-explosive products. Extensive studies comparing CFD-generated results with CONWEP can be found in the body of literature (Anderson and Lu, 2016; Bogosian et al., 2002; Bouamoul and Nguyen-Dang, 2008; Fairlie, 1998; Fedorova et al., 2016; Schwer et al., 2014; Shin et al., 2014) with the general conclusion being that CONWEP tends to overpredict incident impulses as compared to CFD calculations.

With known uncertainties of empirical methods and CFD calculations along with the emergence of new construction materials and blast response, which may not be well characterised, the necessity of experimental studies cannot be overstated. Experimental test capabilities are the foundation for any research programme in blast vulnerability and remain the ultimate method for validating blast protection technologies.

Experimental blast testing capabilities generally fall into two categories: field trials and blast simulator facilities. For field trials, testing is commonly performed in a test arena with multiple targets set up at different distances around a single charge (Payne et al., 2016). Nevertheless, for systematic experimental studies of blast loading, damage and personal injury, field trials are exceedingly expensive and inefficient (e.g. depend on weather conditions). It could also be difficult to use large charges (e.g. greater than 500 kg) due to noise and safety restrictions (Bedon et al., 2014). Some examples of current testing standards for arena and shock tube blast testing of glazing and doors are given in Table 1.

Table 1.

Currently available blast testing standards.

Blast Testing Standards	Application	Test Method
ISO 16934:2007 (2007). Glass in building – Explosion-resistant security glazing – Test and classification by shock tube loading.	Glass, windows	Shock Tube
EN 13541:2012 (2012). Glass in building – Security glazing – Testing and classification of resistance against explosion pressure.	Glass	Shock Tube
EN 13123-1:2001 (2001). Windows, Doors and Shutters – Explosion resistance; Requirements and classification – Part 1: Shock Tube.	Windows, doors and shutters	Shock Tube
EN 13124-1:2001 (2001). Windows, Doors and Shutters – Explosion resistance; Test Method – Part 1: Shock Tube.	Windows, doors and shutters	Shock Tube
ASTM F1642 / F1642M-17 (2017). Standard Test Method for Glazing and Glazing Systems Subject to Airblast Loadings.	Glass, windows	Shock Tube or Arena Test
ASTM F2927-12 (2012). Standard Test Method for Door Systems Subject to Airblast Loadings.	Doors	Shock Tube or Arena Test
GSA TS01-2003 (2003). Standard Test Method for Glazing and Window Systems Subject to Dynamic Overpressure Loadings.	Windows	Shock Tube or Arena Test
ISO 16933:2007 (2007). Glass in building – Explosion-resistant security glazing – Test and classification for arena air-blast loading.	Glass, Windows	Arena Test
EN 13123-2:2004 (2004). Windows, Doors and Shutters – Explosion resistance; Requirements and classification – Part 2: Range test.	Windows, doors and shutters	Arena Test
EN 13124-2:2004 (2004). Windows, Doors and Shutters – Explosion resistance – Test Method – Part 2: Range test.	Windows, doors and shutters	Arena Test

Since the invention of the shock tube by French engineer, Paul Vieille, to study combustion and detonation about 120 years ago (Vieille, 1899a, 1899b), shock tubes remain largely relevant today and have been integral for a variety of research such as experimentally simulating re-entry flows of space shuttles and supersonic aerodynamics (Gruszczynski and Rogers, 1965; Yu, 1999), studying the combustion processes in engines (AlAbbad et al., 2017), investigation of plasma physics (Fucks and Czech, 1965), blast injuries (Alay et al., 2018; Ning and Zhou, 2015), blast simulation (Aune et al., 2016; Richmond et al., 1966) and many others.

Shock tubes used for the purpose of simulating blast waves, are known as blast simulators. A blast simulator should ideally be able to replicate all the time-variant gas-dynamic conditions of a free-field explosion. Apart from overpressure, properties such as density and velocity are crucial, but are often incorrectly replicated by conventional blast simulators (shock tubes) (Uy et al., 2017). As emphasised by Ritzel (2007), a common but serious misconception by recent research assumes that a measured static overpressure profile from a simulator would imply that all other gas-dynamic conditions would also adhere to a free-field explosion scenario, which is not necessarily the case. Therefore, without careful consideration to the important characteristics of the generated flow, a blast simulator may potentially produce incorrect or deceptive shock wave conditions (Ritzel, 2007). In addition, flow problems (see Figure 1) occurring within the common design of blast simulators often leads to various flow anomalies such as transverse reflected waves, flow separation and jetting, and anomalous longitudinal waves (Uy et al., 2017).

Conventional blast simulators often employ a constant cylindrical driver with a sudden and abrupt expansion section leading up to the test section (Alay et al., 2018; Chandra et al., 2012; Dallriva et al., 2016; Lloyd et al., 2009; Stolz et al., 2016). In other cases, expanding circular drivers are connected directly and abruptly to a straight test section (Ritzel, 2007) or simply in a constant cross-section for the entire length of the blast simulator (Aune et al., 2016; Colombo et al., 2010). These configurations often lead to various problems in the generated flow as illustrated in Figure 1 as well as being unable to develop the distinct negative phase of a free-field explosion. Apart from that, other issues specific to compressed gas (CG) drivers include rapid cooling of the driver gas due to the sudden expansion, resulting in undesirable discontinuities forming between its interface with the driven air and wave anomalies (Ritzel and Parks, 2010). Also, for shock tubes with an open end, excessive outflow tends to occur and recompression shock moving upstream are developed which are completely contradictory to an explosive blast scenario (Ritzel and Parks, 2010; Stewart, 2018). It should also be noted that while static overpressure profiles resembling an explosive blast are possible to be generated at some locations within the test section for certain configurations of a conventional blast simulator, just as shown by Chandra et al. (2012), other gas-dynamic conditions particularly density and flow velocity would often still be incorrectly simulated which could lead to deceptive outcomes with respect to specimen loading and response (Uy et al., 2017).

Nevertheless, there are some conventional blast simulators fitted with ‘hex-divergent’ or expanding conical drivers operated with a compressed helium or air (DRDC Suffield facility) (Ritzel et al., 2011) or with an explosive charge (US Army Research Laboratory) (Stewart, 2018) attached to an expanding transition section capable of generating waveforms that resemble free-field explosions considerably well. However, with the latter successful only under very specific test section configurations but still with unresolved problems of reflected rarefactions coming from the open end.

The recently commissioned Australian National Facility for Physical Blast Simulation (NFPBS) (Remennikov et al., 2018) accommodates a state-of-the-art Advanced Blast Simulator (ABS), capable of recreating the wave characteristics of actual free-field explosive blast, overcoming the significant shortcomings of conventional blast simulators. This includes accurate replication of the entropy gradient and negative phase as well as other gas-dynamic conditions of a free-field explosion, which will be demonstrated in this article.

Description of the NFPBS ABS

The ABS design selected for the Australian NFPBS facility is based on the concept of intrinsically replicating the wave-dynamics of actual free-field explosive blast. The ABS concept was developed and patented by Ritzel and Parks (2015). A similar design idea was suggested several decades earlier by Cuthbertson (1967). Unfortunately, as explained by the Ritzel and Parks (2010), Cuthbertson’s concept had several significant issues that could not be resolved at that time such as non-uniform flow in the test section and therefore never went beyond the original prototype.

The ABS concept is governed by the principle that all blast waves which expand according to $x^{β}$ , where $x$ is the distance away from the point of detonation and $β$ is between 1 and 2 would resemble the far-field blast profiles which naturally include the exponential-like decay profile, negative phase and secondary shock (Ritzel and Parks, 2010; Uy et al., 2017). As depicted in Figure 2, all the important characteristics of blast waves are a direct consequence of blast propagation in a spherical geometry and can be assumed to be as spherically symmetric. This means that the physics of spherical blast decay with distance can be recreated in any solid angle taken from the flow field. Therefore, a shock tube with a constantly expanding area would be ideal for simulating blast conditions from an explosive charge.

The NFPBS ABS (Figure 3) was commissioned in mid-2018 (Remennikov et al., 2018) and is located within the Research and Testing Facility of the Faculty of Engineering and Information Sciences at the University of Wollongong. The NFPBS facility is unique within Australia and in the Southern Hemisphere as well as being one of only a few in the world, both in terms of its loading capacity and the size of specimens able to be tested.

This section briefly describes the different subassemblies and components which make up the blast simulator. An overview of these different sections is illustrated in a schematic in Figure 4.

The Driver has a divergent wedge-shaped profile and can operate either in CG or gaseous detonation (GD) mode, depending on the requirement. Generally, CG mode produces shock waves with a more pronounced and adjustable negative phase with corresponding strong secondary shock, while GD mode produces much stronger blast simulations with weak negative phase. GD mode is capable of generating much higher shock levels than CG mode and has the operational advantage of not requiring the setup of a frangible diaphragm.

For this study, only the GD mode is investigated. In GD mode, the elevated pressure region within the Driver is instantaneously created by the detonation of combustible gas mixed with air and/or oxygen. Typical combustible gases include acetylene (C₂ H₂) and ethylene (C₂ H₄). The elevated pressure gas created from the detonation acts as a ‘piston’, rapidly compressing the ambient air at the interface of the high pressure/low pressure gas volumes creating a propagating shock wave. The characteristic ‘Friedlander’ blast wave shape is created by the expansion of the gas out of the divergent Driver and through the initial divergent Transition Section; once formed, the wave is smoothly re-converged into the Test Section.

The gas delivery system is designed to be operated from a safe distance, made possible by software-controlled solenoid valves. With flow rate and gas volume information from gas flow metres (GFM4 Dwyer Instruments, Inc), the software automatically controls solenoid valves to ensure a correct volume and gas ratio is filled into the Driver. In the event of an emergency, the explosive gas mix can be automatically and rapidly evacuated out of the lab by means of compressed air and a venturi pump.

Downstream of the divergent-area Driver Section, the connecting Transition Section continues to expand then smoothly and steadily re-converge the flow as a planar wave entering the constant cross-section geometry of the Test Section. The blast wave’s rate of expansion is smoothly reduced to zero by the time the blast wave arrives at the Test Section. The length of the Transition Section is set to provide sufficient run out for perturbations in the initial blast to dissipate before reaching the Test Section while minimising the rate of change of the wall curvature.

Unlike a conventional shock tube, a fully formed blast wave is generated from the Driver. Therefore, it is possible to locate targets at various distances from the first Transition Section as required for particular exposure levels similar to free-field blast where closer standoff gives stronger shock level with shorter duration. The NFPBS ABS is designed to be modular, that is, the Test Section is comprised of three segments which can be configured as required to increase or reduce the testing standoff distance (Figure 5). Figures 6 and 7 present the shock wave records generated with a 2.5 ft³ oxy-acetylene Driver along the length of the ABS and on the reflective wall target for the Short and Long ABS configurations, respectively. On each of the graphs, the waveforms which may appear as single traces are actually results of two identical tests superimposed, demonstrating exceptional repeatability of results. Details on the locations of the probes are given in Figure 11.

The Transition Section incorporates a set of louvers in the top panel venting for eliminating reflected shocks that propagate upstream from reflective targets which would otherwise be reflected again from the closed end of the Driver to propagate downstream and interfere with experiments (Figure 8). The louvers can also be used to reduce the blast wave duration for diffraction targets. The louvers can be selectively fixed shut by blocking-plate assemblies or allowed to open in a controlled manner by the force of the detonation. The extent and speed of venting is controlled by the adjustable mass of the louvers as well as recoil restraints if required.

The Test Section provides a constant 1.5 × 2.0 m cross-sectional area within the simulator for the placement of test targets. Diffraction targets such as scale-model structures are placed within the Test Section and reflective targets are mounted to the reaction frame of the Reaction Housing located at the end of the Test Section. The Test Section has instrumentation ports drilled through the walls, an observation window and an access hatch. Figure 9 presents shock wave records generated with a 2.5 ft³ oxy-acetylene Driver along the ABS for a diffractive test scenario. Just like Figures 6 and 7, this graph presents two identical tests superimposed.

For studies of loading and damage to diffraction targets set up in the Test Section, it is necessary to mitigate waves reflecting from the end of the Test Section once the primary blast wave has passed. Therefore, apart from serving as mounting surface for reflective targets such as walls or doors, the Reaction Housing at the end of the Test Section also serves as an ‘End-Wave Eliminator’ (EWE) and is configured with an internal shock diffuser having the form of a wedge with adjustable porosity (Figure 10). The porosity of the wedge is adjustable to allow for optimising its effectiveness in dissipating waves passing into the volume of the Reaction Housing which serves as a ‘dump tank’. The Reaction Housing has sufficient volume to dissipate the incoming shockwave as well as mitigate noise and gas efflux into the laboratory space.

Generation of far-field blast environment in an ABS

Calibration of blast wave parameters in an ABS

In order to demonstrate the capability of an ABS in approximating a far-field explosive environment, three different shock levels were tested. For the GD Driver mode, the shock strength is controlled by the initial volume of oxy-acetylene gas filled in the Driver. For both the diffractive and reflective test conditions, the role of standoff distance on the blast load experienced by the test specimen is also evaluated. Tables 2 and 3 summarise the test programme of this study.

Table 2.

Experimental programme for diffractive test condition.

Test ID	Initial setup
Test ID	Oxy-acetylene Driver volume (ft³)	Pressure sensor location in Test Section
D-2.5	2.5	8.85 m and 11.9 m from start of Driven Section
D-5.0	5.0
D-7.5	7.5

Table 3.

Experimental programme for reflective test condition.

Test ID	Initial setup
Test ID	Oxy-acetylene Driver volume (ft³)	ABS configuration
R-2.5-long	2.5	Long ABS
R-2.5-short	2.5	Short ABS
R-5.0-long	5.0	Long ABS
R-5.0-short	5.0	Short ABS
R-7.5-long	7.5	Long ABS
R-7.5-short	7.5	Short ABS

ABS: Advanced Blast Simulator.

Figure 11 presents a schematic of the locations of the pressure transducers for the different ABS configurations for this study. The pressure transducers (Endevco Model 8530C-100, 100 psi maximum pressure, 500 kHz resonant frequency) distributed along the length of the ABS at the side walls are employed to record pressure-time histories of shock wave at different locations of the ABS. Threaded Delrin adapters are employed to mount the pressure transducer flushed to the walls of the ABS as well as to minimise the transfer of wall vibrations to the transducers, following the best practices of Skotak et al. (2018). A high-speed data acquisition system (Synergy P Portable; Hi-Techniques, Inc.) was used to record data at a sampling rate of 500 kHz. Prior to the experiment, the data acquisition system is placed in a waiting mode where data are stored in high-speed buffer. Upon reaching the set pressure threshold, 10 s of data before and after the point of trigger are written to disk.

For recording reflected shock wave pressure profiles, a calibration wall (Figure 12) with pressure transducers mounted in an array was employed. In addition to reflected shock profiles, the planarity of the shock front can be deduced by comparing the arrival times, peak pressures and positive impulse between the pressure transducers.

Figure 13(a) illustrates a typical pressure history recorded from a pressure transducer. It can be observed that significant perturbations (i.e. pressure oscillations) are present along the record coupled with a large overshoot which represents an exaggerated peak overpressure. These issues are common with blast measurements and have been widely documented with various mitigative methods available (Kinney, 1968; Skotak et al., 2018).

This study overcomes these measurement problems by curve fitting the pressure records with the Friedlander equation (Friedlander, 1946) as represented in equation (1). The graphing software DPlot (Hydesoft Computing, LCC, n.d.) was used to determine a best fit solution by iteratively resolving the decay coefficient, $α$ and peak overpressure of the experimental data, as depicted in Figure 13(b).

The positive phase duration, $t_{d}$ , is the intersection point of the Friedlander fitted curve and ambient pressure, see Figure 13(c)

P (t) = P_{m a x} [1 - \frac{t - t_{a}}{t_{d}}] e^{- α \frac{t - t_{a}}{t_{d}}}

(1)

where $P_{m a x}$ is the peak overpressure, $t_{a}$ is the time of arrival, $t_{d}$ is the positive phase duration and $α$ is the dimensionless decay coefficient.

The positive impulse of the incident or reflected pressures is the area under the pressure-time curve as represented in equation (2)

\int_{t_{a}}^{t_{a} + t_{d}} P (t) d t

(2)

Generation of incident overpressure and impulses in an ABS

This section introduces the capabilities of the ABS in approximating a far-field blast environment for the diffractive shock wave condition. The strength of the shock wave generated by NFPBS ABS is controlled by the initial filled volume of oxy-acetylene in the Driver for the GD mode. While this study presents results for only three levels of shock strengths, in practice, the ranges could be much lower or higher depending on the test requirement.

Table 4 presents the shock wave conditions generated along the ABS Test Section and associated equivalent TNT charge mass and standoff distance. The ABS experimental shock wave records were fitted with Friedlander curves to determine the peak pressure and impulse as illustrated earlier in Figure 13. The free-air (spherical) and surface (hemispherical) burst parameters are then found by relating the experimental peak pressure and positive impulse values determined with the Friedlander curves with the Kingery and Bulmash (1984) relations reproduced in Figures 2 –7 and 2 -15 of UFC 3-340-02 (2008). The ABS-generated diffractive shock wave conditions are estimated to approximate a free-field explosion of up to 936 kg at 28 m (or approximately 1000 kg at 29 m) and 474 kg at 26 m (or approximately 500 kg at 27 m) for a spherical and hemispherical TNT, respectively, with a 7.5 ft³ oxy-acetylene Driver.

Table 4.

Diffractive shock wave conditions along the Test Section for a GD Driver.

Initial condition	Probe location^a	Friedlander curve^b		Spherical TNT			Hemispherical TNT
Oxy-acetylene volume (ft³)	Probe location^a	P_{i, max} (kPa)	i_i+ (kPa ms)	W (kg)	R (m)	Z (m/kg^1/3)	W (kg)	R (m)	Z (m/kg^1/3)
2.5	x = 8.85 m	48.0	255	130	19.8	3.91	67.2	19.1	4.71
2.5	x = 11.9 m	47.6	266	149	20.8	3.93	76.9	20.1	4.73
5.0	x = 8.85 m	80.6	501	491	23.8	3.01	248	22.4	3.57
5.0	x = 11.9 m	73.6	514	595	26.5	3.15	303	25.1	3.74
7.5	x = 8.85 m	104	666	818	24.8	2.65	419	23.5	3.15
7.5	x = 11.9 m	90.2	654	936	27.8	2.84	474	26.3	3.38

GD: gaseous detonation.

Distance from start of Driven Section.

Experimental data curve fitted with Friedlander curve.

Figures 14 to 16 compare the ABS experimental shock wave records, Friedlander curves and the approximate free-field curves generated in CONWEP (Hyde, 1988) for the diffractive shock wave condition.

It can be observed that the waveforms generated with the ABS replicate a far-field TNT explosion, with an instantaneous rise to peak incident pressure followed by an exponential decay to ambient pressure is found to occur and match the equivalent TNT free-field curves generated with CONWEP. It should be noted that while a period of negative phase was recorded with the ABS experimental measurements, the Friedlander curve employed to curve-fit the ABS experimental data and to generate the free-field curves in CONWEP simplifies the true loading history and ignores this.

The results reveal that the combination of initial oxy-acetylene in the Driver and ABS standoff distance (i.e. location of test specimen from the point of detonation) allows for the generated waveform to be adjusted to suit the test requirement.

Generation of reflective overpressure and impulses in an ABS

This section presents the reflective far-field shock conditions generated with the ABS using the calibration wall. Table 5 presents the shock wave conditions recorded at the centre of the calibration wall and the fitted Friedlander curves in comparison with equivalent TNT explosions, determined with the same method as detailed in the ‘Generation of incident overpressure and impulses in an ABS’ section. The ABS-generated reflective shock wave conditions are found to represent a free-field explosion of up to 891 kg at 29 m (or approximately 1000 kg at 31 m) and 441 kg at 27 m (or approximately 500 kg at 30 m) for a spherical and hemispherical TNT, respectively.

Table 5.

Reflective shock wave conditions at different standoff distances for a GD Driver.

Initial condition	ABS configuration	Friedlander curve^a		Spherical TNT			Hemispherical TNT
Oxy-acetylene volume (ft³)	ABS configuration	P_{r, max} (kPa)	i_r+ (kPa ms)	W (kg)	R (m)	Z (m/kg^1/3)	W (kg)	R (m)	Z (m/kg^1/3)
2.5	Short ABS	127	607	150	19.8	3.72	71.3	18.5	4.45
2.5	Long ABS	95.5	582	188	24.3	4.25	106	24.2	5.12
5.0	Short ABS	224	1265	604	24.8	2.94	299	23.3	3.49
5.0	Long ABS	167	1118	630	28.3	3.31	310	26.7	3.94
7.5	Short ABS	327	1506	594	21.3	2.54	302	20.2	3.01
7.5	Long ABS	210	1396	891	29.0	3.01	441	27.2	3.58

GD: gaseous detonation; ABS: Advanced Blast Simulator.

Experimental data curve fitted with Friedlander curve.

Figures 17 to 19 compare the ABS experimental shock wave records recorded from the middle of the calibration wall, Friedlander curves and the approximate free-field curves generated in CONWEP (Hyde, 1988) for the reflective shock wave condition. Just as observed previously with the diffractive scenario, the TNT free-field pressure histories generated with CONWEP validates the recorded waveforms on the calibration wall.

The reflective results show that the shape of the waveform (i.e. peak reflected pressure and reflected impulse) can be controlled by adjusting the initial oxy-acetylene volume in the Driver and length of the ABS (i.e. distance of reflective target from point of detonation) depending on the test requirement.

Shock wave planarity in a far-field explosion

In a far-field explosion, the travelling shock front can be assumed to be a plane wave. Figure 20 taken from UFC 3-340-02 (2008) demonstrates this. This premise allows for the application of a uniform pressure distribution when testing plane structural elements.

As part of the experimental programme for the reflective test condition as outlined earlier in Table 3, the planarity of the generated shock front in the ABS as a function of shock strength and ABS standoff distance configuration was determined. An array of pressure transducers was mounted on a 1-in-thick reflective calibration wall.

Figures 21 and 22 illustrate the shock wave planarity for the Short and Long ABS configurations, looking in the direction of the oncoming wave. Shock wave planarity was deduced from the difference in time of arrival, peak pressure and positive impulse at different points on the target relative to the middle of the wall.

For the Short ABS configuration (Figure 21), it can be observed that the shock wave was vertically slanted with the bottom of the reflective wall experiencing the shock wave the quickest and slowest at the top. While the variations of reflected peak pressures recorded on the reflective wall vary between −8% and 22% (i.e. 117 to 155 kPa) compared to the middle of the wall (i.e. 128 kPa), the overall shape of the waveform recorded around the wall remains similar and as a consequence, the variation of positive impulse around the wall is insignificant, with a maximum deviation of −2% (i.e. 610 kPa ms) from the middle (i.e. 622 kPa ms). The maximum impulse was recorded in the middle of the wall.

In comparison with the Long ABS configuration (Figure 22), the shock wave was given time to properly develop within the straight Test Section. As a consequence, the planarity of the shock wave recorded at the calibration wall improved dramatically. In terms of time of arrival, differences recorded around the calibration wall were negligible. From the loading perspective, consistency along the reflective wall was excellent with a recorded difference for peak reflected pressure to be between −3.6% to 3.6% (i.e. 95 to 102 kPa) from the middle (i.e. 99 kPa) and maximum difference of −1% (i.e. 578 kPa ms) for reflected impulse from the middle (i.e. 584 kPa ms). Just like the Short ABS configuration, the maximum impulse was recorded in the middle of the reflective calibration wall.

‘Virtual’ far-field blast environment

Numerical flow simulations were performed in the commercial CFD solver, ANSYS FLUENT, employing the simulation techniques and best practices of Lamnaouer et al. (2010). Actual experimental data collected during ABS lab tests are used to validate the numerical model of the ABS.

The two-dimensional (2D) computer model is represented in space and time with the control volume approach and is discretised in structured, hexahedral elements. Adaptive mesh refinement is employed to automatically refine the grid at locations of steep gradients of density (Figure 24).

The pressure-based solver is used together with PISO pressure-velocity coupling method. The PISO algorithm is highly recommended for all transient flow calculations (ANSYS FLUENT, 2006b). The flow is defined as viscous and ideal gas law is used for the calculation of density.

For simplicity, the walls of the ABS are numerically defined to be frictionless and to have negligible shear. Convective terms are spatially discretised with the Second Order Upwind scheme where it was found to perform best based on the comparative test performed by Lamnaouer et al. (2010). The gauge locations defined follows the exact placements of the pressure transducers of the experimental setup as presented in Figure 11.

The shear-stress transport (SST) k-ω viscous model selected for this flow problem had been noted for its accuracy and reliability for a wider range of flows such including adverse pressure gradient flows, air foils and transonic shock waves, compared to other variants (ANSYS FLUENT, 2006a). Moreover, this particular viscous model has been successfully used in the past in other shock wave CFD simulations (Groethe et al., 2007; Zhang and Kim, 2015).

Prior to starting the calculation, the Driver is completely filled with oxy-acetylene (5:2) combustible gas mixture, while ambient air is defined in the Driven Section. A spark ignition is introduced at the start of the Driver Section, initiating a shock wave which propagates towards the Driven Section (Figure 23). The spark model in ANSYS FLUENT is based on the one-dimensional analysis performed by Lipatnikov and Chomiak (2002). The strength of the shock wave is controlled by the initial spark size. The selected viscous model (k-ω model) calculates of the turbulent flame speed and length scales as well as eddy-dissipation which is used to compute the mixing rate of the different materials in the model (i.e. O₂, C₂ H₂, CO₂ and H₂O). Table 6 summarises the inputs used in the CFD model.

Table 6.

Summary of inputs used in the CFD model for GD Driver mode.

Parameter		Input
Initial Driver pressure		101.325 kPa^a
Initial Driven pressure		101.325 kPa^a
Initial Driver temperature		293.15 K
Initial Driven temperature		293.15 K
Driver gas		Oxy-acetylene initially^b (ideal gas)^c
Driven gas		Air initially^b (ideal gas)^c
Initial spark size	2.5 ft³ oxy-acetylene	8.0 cm
	5.0 ft³ oxy-acetylene	12.5 cm
	7.5 ft³ oxy-acetylene	14.5 cm
Spark duration		0.001 s
Flame speed model		Turbulent length^d
Mass fraction of O₂ in Driven Section		0.23^e
Mass fraction of O₂ in Driver Section		0.75^e
Mass fraction of C₂ H₂ in Driver Section		0.25^e
Amount of explosive gas filled		100% of Driver^f

CFD: Computational Fluid Dynamics; GD: gaseous detonation.

Absolute pressure is shown.

Post-detonation, the chemical reaction of oxy-acetylene is calculated by the solver and is converted to respective quantities of oxygen, acetylene, carbon dioxide and water.

Ideal gas law remains valid for Mach numbers, M_s < 3.

In the turbulent length model, the turbulent flame speed is calculated based on either the laminar flame speed or the turbulent flame speed evaluated at the turbulent length scale of the spark radius, whichever is greater.

Mass fractions were calculated based on ratios of the product of volumetric fraction and molar mass.

The amount of explosive gas filled in driver is assumed to be always 100%. The strength of shock is instead numerically controlled by the initial spark size.

As mentioned earlier, the numerical model takes advantage of the dynamic mesh adaption that is available in ANSYS FLUENT. The mesh is configured to dynamically refine and coarsen every five time steps according to the normalised gradient of the pressure and density of the fluid. This algorithm ensures that higher cell concentrations are automatically allocated to areas only with high flow gradients. This ensures that shock and contact discontinuities are properly and efficiently captured without needlessly requiring an extremely fine mesh for the entire domain. Figure 24 demonstrates this with pressure contours at t = 5 ms.

A mesh convergence study was performed with two different base mesh resolutions at 30600 and 108420 elements, with dynamic mesh adaption algorithm switched on. The impact of mesh resolution was evaluated with the generated solutions for pressure and density along the length of the ABS and with the recorded pressure histories at the locations of the pressure transducers, P1 (x = 4 m), P2 (x = 8.85 m) and P3 (x = 11.9 m). The outcome proves that as long as that the dynamic mesh adaption is enabled to refine the mesh at areas of high flow gradients, the generated solutions are generally independent of the base grid size. Therefore, for efficiency and for minimising computational expense, this study employs the grid with 30600 elements.

For direct comparison with experimental results and model validation, three probes at 4.0 m (P1), 8.85 m (P2), 11.9 m (P3) from the start of Driven Section were defined to collect pressure-time histories of flow properties such as static overpressure, dynamic pressure and density. The locations of these probes defined are based on the exact locations used experimentally as described in Figure 11(a).

Figure 25 compares CFD generated shock wave records with experimental results. It can be observed that the numerical model was able to predict the overall shape of the waveform reasonably well, in particular, with the time of arrival at the probe locations. The peak overpressures and impulses calculated by the CFD model at the probes are also found to closely match the experimental data as shown in Figure 26.

As a diffractive target could in practice be mounted anywhere within the ABS, the CFD model was used to calculate shock wave conditions along the ABS at 1-m intervals. The relationship between peak overpressure and positive impulse in comparison with experimental data along the length of the ABS is shown in Figure 26.

In these graphs, peak pressures are shown to be at their highest levels at the start of the Driven Section and rapidly reduce along the curved Transition Section and eventually stabilising in the straight Test Section (i.e. x ⩾ 8.4 m), implying the gradient of the diverging and re-converging geometry of the ABS influences the rate of decay of the peak pressure. Positive phase durations progressively increase with standoff distance which leads to a gradual rise in positive impulse with ABS standoff distance.

The CFD model was also used to capture the shock wave propagation along the ABS. Figure 27 presents the reflective test scenario for a 2.5 ft³ oxy-acetylene Driver. It can be observed that the incident shock front initially travels with a prominent curvature.

At t = 20 ms, the incident shock wave approaches the end of the curved Transition Section and towards the start of the straight Test Section. For testing full-reflection wall targets with the Short ABS configuration, the reflective test specimen would be mounted at this location. At this position, the shock wave appears to be in a backwards lean and is confirmed with experimental measurements in Figure 21. This wave would eventually flatten into a reasonably planar wave (one-dimensional wave) as it travels along the straight Test Section.

At t = 35 ms, the shock wave can be seen moving towards the opposite direction after reflecting off the reflective wall target. The reflected wave will continue propagating towards the left and right multiple times until dissipating completely. This behaviour subjects the test specimen with repeated loadings which is undesirable and unrealistic. With the use of Transition Section louvers shown earlier in Figure 8, the vents would flip-open sometime after the incident wave passes the location, allowing for reflected waves coming from the wall target to evacuate the ABS into the atmosphere.

Table 7 compares the peak incident pressure and the corresponding peak dynamic pressure and density values derived with the CFD model versus free-field conditions taken from Figure 2–3 in UFC 3-340-02 (2008). Together with the experimental pressure history profiles presented earlier in the ‘Generation of far-field blast environment in an ABS’ section, which includes the exponential-like decay profile and negative phase, these results demonstrate that the ABS is able to closely reproduce gas-dynamic conditions of a free-field explosion.

Table 7.

Comparison between peak incident overpressure, peak dynamic pressure and density of air behind the shock front for a free-field explosion with the conditions generated within the ABS Test Section.

Initial condition	Probe location^a	Peak incident overpressure (kPa)		Peak dynamic pressure (kPa)		Density (kg/m³)
Oxy-acetylene volume (ft³)	Probe location^a	ABS (CFD)	Free-field^b	ABS (CFD)	Free-field^b	ABS (CFD)	Free-field^b
2.5	x = 8.85 m	45.9		7.03	7.14	1.56	1.76
2.5	x = 11.9 m	40.8		5.55	5.72	1.53	1.70
5.0	x = 8.85 m	86.0		23.4	23.4	2.27	2.17
5.0	x = 11.9 m	75.7		18.3	18.5	1.78	2.07
7.5	x = 8.85 m	111		37.8	37.6	2.01	2.39
7.5	x = 11.9 m	97.4		29.4	29.5	1.92	2.27

ABS: Advanced Blast Simulator; CFD: Computational Fluid Dynamics.

Distance from start of Driven Section.

Values determined from Figure 2–3 in UFC 3-340-02 (2008) based on given peak incident pressure.

Concluding remarks

The current state of blast-resistant assessment and design methods is based largely on empirical observations of actual explosive testing or with numerical simulations. However, experimental testing remains the ultimate method for validating blast protection technologies.

Field trials for performing systematic experimental testing are exceedingly expensive and inefficient. Blast simulators enable blast testing to be performed in a safe and controlled laboratory environment.

This article describes the advanced blast simulator (ABS) at the Australian National Facility for Physical Blast Simulation (NFPBS) and the experimental programme to ascertain its capabilities to simulate the distinctive shock wave profiles produced by free-field explosions. Detailed measurements have been performed to validate incident and reflected blast wave profiles as well as the planarity of the shock wave generated by the ABS. The key findings of this article can be summarised as follows:

The ABS was found to produce highly repeatable results for both diffractive and reflective test conditions.

Shock wave records generated by the ABS were found to closely replicate the pressure history curves of free-field TNT explosions generated with CONWEP.

The generated shock wave records showed that diffractive and reflective conditions representative of free-field explosions of up to 1000 kg and 500 kg for a spherical and hemispherical TNT, respectively, are achievable with the ABS.

The ABS was shown to generate realistic and accurate free-field blast environments which included the accurate replication of the entropy gradient and negative phase.

It was demonstrated that the shape of the free-field profiles (i.e. peak reflected pressure and reflected impulse) can be controlled by adjusting the initial oxy-acetylene volume in the Driver and standoff distance of the target to suit the test requirement.

A CFD model of the ABS was developed to reveal the flow environment within the blast simulator. The CFD model is validated with the experimental test data.

Shock wave propagation was visualised with the CFD model, allowing for an understanding on how shock wave evolves as it travels along the ABS and elucidating shock wave planarity differences between the Short and Long ABS configurations measured experimentally.

Density and dynamic pressure behind the shock front provided by the CFD model closely match corresponding free-field values given in UFC 3-340-02 (2008), validating the ability of the ABS to generate accurate gas-dynamic conditions of a free-field explosion.

Footnotes

Acknowledgements

The authors would like to thank the technical staff at the structural laboratory of the University of Wollongong, in particular, Mr Alan Grant and Mr Cameron Nielson for their invaluable support. Contributions of Mr Steve Parks, Mr Andy Riegel and Mr Danny Boppe of ORA Inc. (USA) towards the developmental work and fabrication of the ABS are greatly acknowledged. The authors also wish to thank Mr Anxiu Liu and Associate Professor Ting Ren of the University of Wollongong for valuable discussions in relation to modelling gas detonation in ANSYS FLUENT.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This work was funded partially by the Australian Government through the Australian Research Council’s Linkage Infrastructure, Equipment and Facilities (LIEF) funding scheme [LE130100133].

ORCID iDs

Edward Chern Jinn Gan

Alex Remennikov

References

AlAbbad

Javed

Khaled

, et al. (2017) Ignition delay time measurements of primary reference fuel blends. Combustion and Flame 178: 205–216.

Alay

Skotak

Misistia

, et al. (2018) Dynamic loads on human and animal surrogates at different test locations in compressed-gas-driven shock tubes. Shock Waves 28: 51–62.

Anderson

(2016) Modelling of blast overpressure and particle flow velocity from a composition B spherical bare charge. In: International symposium on military aspects of blast and shock (MABS 24), Halifax, NS, Canada, 18–23 September.

ANSYS Autodyn (2016) Autodyn user’s manual, release 17.1.

ANSYS FLUENT (2006a) 12.5.2 shear-stress transport (SST) k-ω model.

ANSYS FLUENT (2006b) 25.9.1 choosing the pressure-velocity coupling method.

ASTM F2927-12 (2012) Standard test method for door systems subject to airblast loadings.

ASTM F1642/F1642M-17 (2017) Standard test method for glazing and glazing systems subject to airblast loadings.

Aune

Fagerholt

Langseth

, et al. (2016) A shock tube facility to generate blast loading on structures. International Journal of Protective Structures 7: 340–366.

10.

Bangash

MYH

(2009) Shock, impact and explosion. Berlin, Germany: Springer.

11.

Bedon

Kevin

van Doormaal

, et al. (2014) A comparison of existing standards for testing blast resistant glazing and windows. European Commission, Joint Research Centre, Institute for the Protection and Security of the Citizen.

12.

Bogosian

Ferritto

Shi

(2002) Measuring uncertainty and conservatism in simplified blast models. In: 30th explosives safety seminar, Atlanta, GA, 13–15 August.

13.

Bouamoul

Nguyen-Dang

(2008) High Explosive Simulation Using Arbitrary Lagrangian-Eulerian Formulation. Ottawa, ON, Canada: Defence R&D Canada – Calcartier.

14.

Chandra

Ganpule

Kleinschmit

, et al. (2012) Evolution of blast wave profiles in simulated air blasts: experiment and computational modeling. Shock Waves 22: 403–415.

15.

Colombo

di Prisco

Martinelli

(2010) A new shock tube facility for tunnel safety. Experimental Mechanics 51: 1143–1154.

16.

Cuthbertson

(1967) A description and predicted performance of a conical shock tube nuclear-blast simulator. In: Military aspects of blast and shock (MABS 1), Alberta, Canada, 18–21 July.

17.

DAHS CWE (1998) Technical Manual – Design and Analysis of Hardened Structures to Conventional Weapons Effects. Washington, DC: US Army Corps of Engineers.

18.

Dallriva

Johnson

O’Daniel

, et al. (2016) Blast Load Simulator Experiments for Computational Model Validation – Report 1. Vicksburg, MS: Engineer Research and Development Center (ERDC), US Army Corps of Engineers (USACE).

19.

DOE/TIC-11268 (1992) A Manual for the Prediction of Blast and Fragment Loadings on Structures. Washington, DC: US Department of Energy.

20.

EN 13123-1:2001 (2001) Windows, doors and shutters – explosion resistance; requirements and classification – part 1: shock tube.

21.

EN 13124-1:2001 (2001) Windows, doors and shutters – explosion resistance; test method – part 1: shock tube.

22.

EN 13123-2:2004 (2004) Windows, doors and shutters – explosion resistance; requirements and classification – part 2: range test.

23.

EN 13124-2:2004 (2004) Windows, doors and shutters – explosion resistance – test method – part 2: range test.

24.

EN 13541:2012 (2012) Glass in building – security glazing – testing and classification of resistance against explosion pressure.

25.

ESL-TR-87-57 (1989) Protective Construction Design Manual. Tyndall Air Force Base, FL: US Air Force Engineering and Services Center.

26.

EUROPLEXUS (2019) EUROPLEXUS – A Computer Program for the Finite Element Simulation of Fluid-Structure Systems under Transient Dynamic Loading – User’s Manual. Ispra: European Commission, Joint Research Centre.

27.

Fairlie

(1998) The numerical simulation of high explosives using AUTODYN-2D & 3D. In: Explo ’98, institute of explosive engineers 4th biannual symposium, UK, September.

28.

Fedorova

Valger

Fedorov

(2016) Simulation of blast action on civil structures using ANSYS autodyn. In: International conference on the methods of aerophysical research (ICMAR 2016), Perm, 27 June–3 July.

29.

Friedlander

(1946) The diffraction of sound pulses I. Diffraction by a semi-infinite plane. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 186: 322–344.

30.

Fucks

Czech

(1965) Plasma motion and shock waves in theta-pinch operated shock tubes. Physics of Fluids 8: 204–205.

31.

Groethe

Merilo

Colton

, et al. (2007) Large-scale hydrogen deflagrations and detonations. International Journal of Hydrogen Energy 32: 2125–2133.

32.

Gruszczynski

Rogers

(1965) Shock tube instrumentation techniques for study of hypervelocity entry problems. IEEE Transactions on Aerospace and Electronic Systems 1: 43–56.

33.

GSA TS01-2003 (2003) Standard test method for glazing and window systems subject to dynamic overpressure loadings.

34.

Hyde

(1988) User’s Guide for Microcomputer Programs CONWEP and FUNPRO – Applications of TM 5-855-1. Vicksburg, MS: Fundamentals of Protection Design for Conventional Weapons.

35.

Hydesoft Computing, LLC (n.d.) Dplot: Graph Software for Scientists and Engineers. Available at: http://www.dplot.com

36.

ISO 16933:2007 (2007) Glass in building – explosion-resistant security glazing – test and classification for arena air-blast loading.

37.

ISO 16934:2007 (2007) Glass in building – explosion-resistant security glazing – test and classification by shock tube loading.

38.

Kingery

(1966) Air Blast Parameters Versus Distance for Hemispherical TNT Surface Bursts. Aberdeen Proving Ground, MD: Ballistic Research Laboratories.

39.

Kingery

Bulmash

(1984) Air Blast Parameters from TNT Spherical Air Burst and Hemispherical Surface Burst. Aberdeen Proving Ground, MD: Ballistic Research Laboratories.

40.

Kingery

Pannill

(1964) Peak Overpressure vs Scaled Distance for TNT Surface Bursts (Hemispherical Charges). Aberdeen Proving Ground, MD: Ballistic Research Laboratories.

41.

Kinney

(1968) Engineering Elements of Explosions. Monterey, CA: Naval Postgraduate School.

42.

Lamnaouer

Kassab

Divo

(2010) Time-accurate simulation of shock propagation and reflection in an axi-symmetric shock tube. In: 48th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, Orlando, FL, 4–7 January.

43.

Lee

Finger

Collins

(1973) JWL Equation of State Coefficients for High Explosives. Livermore, CA: University of California.

44.

Lipatnikov

Chomiak

(2002) Turbulent flame speed and thickness: phenomenology, evaluation, and application in multi-dimensional simulations. Progress in Energy and Combustion Science 28: 1–74.

45.

Livermore Software Technology Corporation (LSTC) (2013) LS-DYNA Keyword User’s Manual Ver.R7.0. Livermore, CA: LSTC.

46.

Lloyd

Saatcioglu

Nistor

, et al. (2009) New shock tube testing facilities for simulated blast loading of structural and non-structural components. In: 2nd international workshop on performance, protection & strengthening of structures under extreme loading, Hayama, Japan, 19–21 August.

47.

Ngo

Mendis

Gupta

, et al. (2007) Blast loading and blast effects on structures – an overview. Electronic Journal of Structural Engineering 7: 76–91.

48.

Ning

Y-L

Zhou

Y-G

(2015) Shock tubes and blast injury modeling. Chinese Journal of Traumatology 18: 187–193.

49.

Payne

Williams

Worfolk

, et al. (2016) Large-scale explosive arena trials – is your target being loaded correctly? Explosives Engineering: 10–16.

50.

Remennikov

Parks

Ritzel

, et al. (2018) Commissioning of the Australian National Facility for physical blast simulation. In: International symposium on military aspects of blast and shock (MABS 25), The Hague, 23–28 September.

51.

Remennikov

(2002) Blast resistant consulting: a new challenge for structural engineers. Australian of Structural Engineering 4: 121–134.

52.

Richmond

Gaylord

Damon

, et al. (1966) DASA-AEC-Lovelace Foundation, Blast-Simulation Facility. Albuquerque, NM: Lovelace Foundation for Medical Education and Research.

53.

Ritzel

(2007) Upgrade of the DRDC Suffield Blast Tube Facility. Suffield, AB, Canada: Defence Research and Development Canada.

54.

Ritzel

Parks

(2015) Shock Tube Apparatus for Blast Wave Simulation. Andover, MA: ORA, Inc.

55.

Ritzel

Parks

(2010) Blast simulation using shock-tube technology. In: International symposium on military aspects of blast and shock (MABS 21), Jerusalem, Israel, 3–8 October.

56.

Ritzel

Parks

Roseveare

, et al. (2011) Experimental blast simulation for injury studies. In: NATO HFM 207, Halifax, NS, Canada, 3–5 October.

57.

Rose

(2006) A Computational Tool for Airblast Calculations – Air3d Version 9 Users’ Guide. Cranfield: Cranfield University.

58.

Schwer

Netherton

Stewart

(2014) Comparisons of University of Newcastle free air blast data with CONWEP and LS-DYNA simulations. In: International symposium on military aspects of blast and shock (MABS 23), Oxford, 7–12 September.

59.

Shin

Whittaker

Aref

, et al. (2014) Air-Blast Effects on Civil Structures. Buffalo, NY: University at Buffalo, State University of New York.

60.

Skotak

Alay

Chandra

(2018) On the accurate determination of shock wave time-pressure profile in the experimental models of blast-induced neurotrauma. Frontiers in Neurology 9: 52.

61.

Starossek

(2009) Progressive Collapse of Structures. London: Thomas Telford Limited.

62.

Stewart

(2018) Approximating a free-field blast environment in the test section of an explosively driven conical shock tube. Shock Waves 29: 355–360.

63.

Stolz

Millon

Klomfass

(2016) Analysis of the resistance of structural components to explosive loading by shock-tube tests and SDOF models. Chemical Engineering Transactions 48: 151–156.

64.

TM 5-855-1 (1986) Fundamentals of Protective Design for Conventional Weapons. Washington, DC: US Department of the Army.

65.

UFC 3-340-02 (2008) Structures to Resist the Effects of Accidental Explosions, Unified Facilities Criteria (UFC). Manual Number 3-340-02 (This manual supersedes US ARMY TM5-1300). Washington DC: US Department of Defense.

66.

Remennikov

Ritzel

, et al. (2017) Development of the Australian National facility for physical blast simulation. In: 12th international conference on shock & impact loads on structures, Singapore, 15–16 June.

67.

Vieille

(1899a) Etude sur les roles des discontinuites dans les phenomenes de propagation. Mémoire des Poudres et Saltpêtres 10: 117–260.

68.

Vieille

(1899b) Sur les discontinuites produites par la de’tente brusque de gas comprimes. Comptes Rendus de l’Aca- demie des Sciences de Paris 129: 1228–1230.

69.

(1999) Oxyhydrogen combustion and detonation driven shock tube. Acta Mechanica Sinica 15: 97–107.

70.

Zhang

Kim

(2015) Numerical simulation of shock wave and contact surface propagation in micro shock tubes. Journal of Mechanical Science and Technology 29: 1689–1696.