Experimental and modeling analysis of detonation in circular arcs of the conventional high explosive PBX 9501

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Abstract

We examine the diffraction dynamics of a two-dimensional (2D) detonation in a circular arc of the conventional HMX-based, high performance, solid explosive PBX 9501, for which the detonation reaction zone length scale is estimated to be of the order of 100–150 µm. In this configuration, a steady propagating detonation will develop, sweeping around the arc with constant angular speed. We report on results from three PBX 9501 arc experiments, exploring the variation in linear speed on the inner and outer arc surfaces for the steady wave along with the structure of the curved detonation front, as a function of varying inner surface radius and arc thickness. Comparisons of the properties of the motion of the steady wave for each arc configuration are then made with a spatially-distributed PBX 9501 reactive burn model, calibrated to detonation performance properties in a 2D planar slab geometry. We show that geometry-induced curvature of the detonation near the inner arc surface has a significant effect on the detonation motion even for conventional high explosives. We also examine the detonation driving zone structure for each arc case, and thus the subsonic regions of the flow that determine the influence of the arc geometry on the detonation propagation. In addition, streamline paths and reaction progress isolines are calculated. We conclude that a common approximation for modeling conventional high explosive detonation, wherein the shock-normal detonation speed is assumed equal to the Chapman–Jouguet speed, can lead to significant errors in describing the speed at which the detonation propagates.

Introduction

Geometry-induced diffraction of a detonation in a condensed-phase high explosive (HE) affects the detonation propagation dynamics due to the resulting modification of the structure of the finite-length detonation reaction zone. An ideal geometry to examine the primary effects of diffraction is the two-dimensional (2D) circular arc [1], [2], [3], shown schematically in Fig. 1. In particular, after relaxing from an initiation transient, a steady detonation sweeping around the arc with constant angular speed will develop in the circular arc configuration. The energy release within the subsonic detonation-driving-zone (or DDZ), i.e. the region bounded by the non-planar detonation shock and sonic flow locus (relative to the frame of the steady rotating shock), controls the propagation properties of the detonation [4]. The circular arc configuration is also important in gaseous explosive systems to the understanding of the diffraction mechanics of detonation propagating in a rotating detonation engine [5], [6], [7].

A number of physical insights on the dynamics of a steadily propagating, diffracting detonation in a 2D circular arc of HE have recently been uncovered in [1], [2]. For example, the authors found that for a fixed inner arc surface radius, and beyond a critical arc thickness, the angular speed of the detonation limits to a constant, independent of either further increases in the arc thickness or changes in the type of confinement on the outer arc surface. This is a result of the subsonic DDZ flow region detaching from the outer arc surface, with supersonic flow now surrounding the DDZ. Also, the authors of [1], [2] found that a small radial layer of the arc attached to the inner arc surface played a disproportionate role in controlling the angular speed of the detonation propagation. In this layer, there is a strong influence of both the detonation curvature and the material confinement properties on the inner arc surface.

In addition to the theory-based studies [1], [2], Short et al. [3] describe an experiment in a circular section of the insensitive high explosive (IHE) PBX 9502 (95 wt.% TATB (2,4,6-triamino-1,3,5-trinitrobenzene)/5 wt.% Kel-F 800 poly(chlorotrifluoroethylene-co-vinylidene fluoride)), designed to measure the structure and speed of a 2D steady detonation in a circular arc geometry. The arc section had an inner radius of Ri=64.98 mm, an outer radius of Re=89.97 mm and was 200 mm wide to ensure that the hydrodynamic flow along the centerline of the arc remained two-dimensional during the course of the experiment (Fig. 2). Associated reactive burn modeling showed that the sonic flow locus of the DDZ largely lies at the end of, or within, the fast reaction stage of the PBX 9502 detonation [3] for the 64.98 x 89.97 mm arc, with the largest area section of the DDZ lying close to the inner arc surface.

A number of other experiments with either the circular arc section or rib geometry in TATB-based (insensitive) explosive formulations have also been conducted [8], [9], [10], although all had arc section widths smaller than both the inner and outer arc circumferential distances. Two-dimensional reactive burn simulations of the arc configurations in [8], [9], [10] have been conducted by Tarver and Chidester [11] and Ioannou et al. [12]. To date, the diffraction dynamics of a 2D steady detonation in a circular arc configuration of a conventional high explosive (CHE) have not been examined. Given the extensive use of CHEs in precision munition applications, it is important to demonstrate that we can accurately simulate and understand CHE detonation dynamics in geometries other than simplified 2D planar slabs or 2D axisymmetric cylinders [13]. This is the purpose of the current study.

In the following, we examine the CHE PBX 9501 (95 wt.% HMX explosive crystals bonded with a binder mixture of 2.5 wt.% Estane and a 2.5 wt.% eutectic mixture of bis(2,2-dinitropropyl)acetal and bis(2,2-dinitropropyl)formal (BDNPA/BDNPF)). PBX 9501 has detonation performance properties that are characteristic of most types of CHEs [13]. The total PBX 9501 detonation reaction zone length is on the order of 100–150 µm, compared to the more complex structure of the IHE PBX 9502 detonation, having a fast reaction layer of size  ≈  100–150 µm followed by a slower reaction depletion layer of length  ≈  1–1.5 mm [3]. Figure 3 shows a comparison of the experimentally determined, steady axial detonation propagation speeds for PBX 9501 and PBX 9502 in 2D planar geometries (slabs) as a function of 1/T, where T is the slab thickness [13]. The detonation speeds of PBX 9502 decrease significantly more rapidly with decreasing T than for PBX 9501. Primarily, the flow divergence effects associated with a shock curvature of a given size will more significantly affect the longer reaction zone structure of a PBX 9502 detonation. In particular, the reaction progress along the DDZ sonic flow surface will be smaller than that for a PBX 9501 detonation. The failure thickness for a PBX 9502 detonation is significantly larger than for PBX 9501, in the region 3.5 < T < 3.75 mm for PBX 9502, and smaller than T=0.8 mm for PBX 9501 [13]. A comparison of the detonation shock shapes for the same slab geometry thicknesses (4 and 8 mm) are shown in Fig. 4, revealing some significant features. While the PBX 9501 detonations are flatter in the center of the charges than for the equivalent PBX 9502 detonations, significantly larger shock curvatures exist near the charge edges for PBX 9501. The near-edge curvature variation is significant since, as noted above, a detonation in a circular arc configuration is largely controlled by the shock curvature variation in a layer near the inner arc surface [1], [2], [3].

In the current study, three experiments are described examining the variation in speed and shock shape of the steady rotating detonation as a function of varying inner arc surface radius and arc thickness. The arc results are then used to validate a new PBX 9501 reactive burn model, calibrated via the slab geometry detonation properties in Figs. 3 and 4. Physical insights about the effects of the circular arc geometry on the PBX 9501 detonation reaction zone structure and speed are explored through the reactive burn model. This includes an examination of the DDZ structures to determine the subsonic flow region in each of the arcs influencing the detonation propagation.

Section snippets

PBX 9501 circular arc section experiments

Three different PBX 9501 arc section experiments were conducted with dimensions as follows (see Fig. 1, Fig. 2 and 5): for arc 1, 65.35 mm (Ri) x 67.35 mm (Re) x 200 mm (width); for arc 2, 65.47 mm (Ri) x 69.97 mm (Re) x 200 mm (width); and for arc 3, 100.35 mm (Ri) x 120.35 mm (Re) x 200 mm (width). The angular extent of each of the arcs was  ≈ 3π/4 radians. The density of arcs 1 and 3 was 1.841 g/cm3, while arc 2 was 1.840 g/cm3. Polycarbonate (PC) supports of 9.2 mm nominal thickness were

PBX 9501 reactive burn modeling

Reactive burn modeling allows the structure of both the detonation driving zone and reaction zone in the PBX 9501 arc configuration to be explored. Using a newly calibrated reactive burn model for PBX 9501, we now describe computational simulations of detonation in the three circular arcs with inner and outer radii given in Section 2, with each of the arcs extending the angular region 0 ≤ θ ≤ 3π/2 in polar coordinates (r, θ). The PBX 9501 is surrounded by a low-density elastomer. This is a

Summary

We have described three experiments on 2D steady detonation of the high performance, HMX-based conventional high explosive (CHE) PBX 9501 in a circular arc geometry, measuring linear propagation speeds on the inner and outer arc surfaces, along with the detonation shock front shape. We have used this data to validate a MWSD reactive burn model, previously calibrated to 2D planar slab geometry data, and demonstrated very good agreement. Using the MWSD model, an extensive study of the detonation

Declaration of Competing Interest

None.

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