Curvature effect on stabilization of cellular detonations in channel, circular arc and spherical shell geometries
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Chiquete, Carlos (ORCID:0000000204675959)↗
Engineering topics
Short, Mark
Publications and source records attributed to Short, Mark.
Validation of a detonation product equation of state for an insensitive high explosive via slab geometry expansion tests
Slab expansion (SLABEX) tests are conducted to validate a process for calibrating the detonation products equation of state (EOS) of a high explosive (HE). The SLABEX tests use rectangular slabs of PBX 9502, a polymer-bonded HE formulation consisting of 95 wt.% 1,3,5-triamino-2,4,6-trinitrobenzene bound with Kel F-800, a co-polymer of chlorotrifluoroethylene and vinylidene-fluoride. Three PBX 9502 slab thicknesses are examined, each confined symmetrically by two rectangular copper (Cu) plates approximately one-tenth the thickness of the HE slab. For the duration of each experiment, the detonation flow along the central axis of the PBX 9502 slab remains two-dimensional. The lateral flow velocity component of the outer surfaces of the expanding Cu plates is measured, along with the steady axial detonation speed along the central axis of the SLABEX. Hydrodynamic simulations of the Cu plate expansion in the SLABEX geometry, driven by the energy stored in the detonation products by the detonation combustion event, are conducted using a Jones–Wilkins–Lee EOS for the detonation products. This EOS form was recently parameterized for PBX 9502 in the cylinder expansion test geometry using a newly developed calibration technique [Voelkel et al., Combust. Flame 246, 112373 (2022)]. Good agreement between the experiment and prediction is found in each SLABEX test, demonstrating that the detonation product EOS calibration technique produces EOSs that are predictive when applied to other geometries.
45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
Effect of lot microstructure variations on detonation performance of the triaminotrinitrobenzene (TATB)-Based insensitive high explosive PBX 9502
PBX 9502 is an important insensitive high explosive due to its combination of safety properties and detonation performance. It is a polymer-bonded formulation consisting of 95 wt.% 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) as the high explosive crystal, bound with Kel F-800 (FK-800), a co-polymer of chlorotrifluoroethylene and vinylidene-fluoride. Two different types are used, one known as virgin that uses only pristine manufactured TATB, and a second known as recycled that has 50 wt.% of its TATB reclaimed from machining scraps of previously pressed virgin PBX 9502. Recycled lots have a higher percentage of fine particles compared to virgin lots, due to the fracturing and damage sustained by TATB crystals during pressing. We examine the influence that this TATB microstructure difference between virgin and recycled PBX 9502 has on detonation performance properties. New rate-stick geometry diameter effect, detonation front shape and cylinder expansion test data are obtained for two previously uncharacterized virgin lots and one recycled lot of PBX 9502. This is combined with previously published data for one virgin and one recycled lot for evaluation purposes. Detonation shock dynamics model calibrations are conducted on each of the five lots to provide an assessment of the detonation timing characteristics of virgin versus recycled PBX 9502 lots. For two of the virgin lots, detonations propagate slower in the rate-stick geometry than those in the two recycled lots. However, the other virgin lot tested has propagation rates comparable to that of the recycled lots for larger diameter rate-sticks. The latter result, though, is shown to be geometry dependent and depends on the range of detonation curvatures accessed in different geometries. New copper-confined, cylinder expansion tests are conducted on each of the three virgin and two recycled lots to obtain detonation product Jones-Wilkins-Lee equations of state, enabling an assessment of the metal push capabilities for each of the five lots. We find that the metal push capabilities, characterized by the evolution of the heat of detonation with volume, are similar between the virgin and recycled lots. Thus, changes in microstructure between different PBX 9502 lots seemingly affect the rate of reaction, but not the overall energy content.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Experimental and modeling analysis of detonation in circular arcs of the conventional high explosive PBX 9501
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. Overall, 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.
42 ENGINEERING↗
Detonation performance experiments and modeling for the DAAF-based high explosive PBX 9701
Detonation performance experiments and modeling are reported for the explosive PBX 9701, which is composed of 97% 3,3$\acute{-}$diamino-4,4$\acute{-}$azoxyfurazan (DAAF) and 3% vinylidene uoride-chlorotriuoroethylene copolymer (Kel-F 800) binder by weight. PBX 9701 is a newly-developed reducedsensitivity explosive with increased performance relative to the triaminotrinitrobenzene or TATB-based PBX 9502 while still retaining low sensitivity to mechanical insult. The first detonation performance measurements for this formulation are presented, including front-curvature ratesticks and cylinder expansion test data. Prior shock initiation data is also reviewed. These data are used to develop programmed burn and reactive flow calibrations for existing commonly-used performance models which allow engineering calculations with PBX 9701. The calibration process involves several enhancements relative to conventional approaches including the use of an analytical scaling correlation to speed the calibration process and development of a new methodology to improve the consistency between the programmed burn and reactive model calibration process and the resulting calculations. Overall, PBX 9701 is seen to exhibit improved performance relative to insensitive explosives, with a trinitrotoluene (TNT) equivalence of 1.24. The detonation performance properties are found to be well captured by existing models.
45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
Steady detonation propagation in thin channels with strong confinement
We examine asymptotically the dynamics of two-dimensional, steady detonation wave propagation and failure for a strongly confined high explosive (HE), in which the width of the explosive is small relative to the reaction zone length. An energy balance equation is derived, which shows how the longitudinal acceleration of subsonic flow behind the detonation shock is influenced both by chemical reaction and by the effects of HE boundary streamline deflection, specifically via the induced rate of change of mass flux through the detonation wave. The latter serves to either counteract or reinforce the acceleration of longitudinal flow, depending on the sign of the gradient of the boundary streamline deflection at the detonation shock. The analysis is valid for general equations of state and chemical reaction rates in the HE. The asymptotically derived form of the energy equation represents an eigenvalue problem for the determination of the steady detonation propagation speed, solved via a shooting method. We explore specific results for ideal and stiffened equations of state, along with a pressure-dependent reaction rate for which changes in the pressure exponent and reaction order are also studied. We consider the influences of both straight and curved HE boundary streamline shapes. The asymptotic analysis reveals significant physical insights into how detonation propagation and failure are affected by strong confinement.
42 ENGINEERING↗
Transients following the loss of detonation confinement
We present a theory for the evolution of a one-dimensional, steady-state detonation reaction zone to a two-dimensional reaction zone, when the explosive experiences a sudden loss of side-on confinement as a boundary of the explosive is impulsively withdrawn. Our focus is on condensed-phase explosives, which we describe as having a constant adiabatic gamma equation of state and an irreversible, state-independent reaction rate. We consider two detonation models: (i) the instantaneous reaction heat release Chapman–Jouguet (CJ)-limit and (ii) the spatially resolved reaction heat-release Zel’dovich–von Neumann–Döring (ZND) model, in the limit where only a small fraction of the energy release is resolved (the SRHR-limit). Two competing rarefaction waves are generated by this loss of confinement: (i) a smooth wave coming off the full length of the withdrawn boundary and (ii) a singular fan spreading out from the point where the detonation shock and the withdrawn boundary meet. For the CJ-limit, in all cases the singular rarefaction fan eventually dominates the competition to control the steady-state behaviour. For the SRHR-limit, the spatially resolved heat release moderates this competition. When the withdrawal speed is fast, the rarefaction fan dominates; when the withdrawal speed is slower, the smooth rarefaction eventually dominates, although the flow features a fan at early times. By examining the mathematical properties of the steady two-dimensional fan-based solution, we set down a mechanism for this transition in behaviours.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Detonation propagation for shock-driven, subsonic and supersonic confiner flow
In this work, we study the compressible flow dynamics of two-dimensional, steady detonation wave propagation in a high explosive (HE) confined by aluminium (Al) or stainless steel (SS), outside of which is an air layer. We examine how the thickness of the confinement affects the subsonic detonation driving zone structure (DDZ) and the detonation speed (D 0 ), demonstrating a strong dependence on whether the oblique shock-driven flow in the confiner is supersonic, as for SS, or subsonic, as for Al. A characteristic path analysis is used to examine the information flow from the material boundaries through the supersonic flow regions in both the HE and confiner that can impact the sonic surfaces bounding the subsonic flow regions. It is shown that the nature of gas-dynamic wave reflection off the SS–air or Al–air boundary can significantly influence the DDZ and D 0 .
54 ENVIRONMENTAL SCIENCES↗
Multiscale Approach to Shock to Detonation Transition in Energetic Materials
In this study we present a multiscale approach for coupling the dynamics of void collapse at the microscale to simulations at the mesoscale. We solve the reactive Euler equations, with the energy equation augmented by a power deposition term. The reaction rate at the mesoscale is modelled using a pressure–dependent power law. The deposition term is based on previous simulations of void collapse, modelled at the mesoscale as hot–spots. The equation of state was previously calibrated for PBX 9501. The run–to–detonation distance is calculated as part of the numerical solution procedure. Results for 1–D, 2–D homogeneous, and 2–D heterogeneous medium are presented, and show good agreement to experimental data.
42 ENGINEERING↗
Characteristic path analysis of confinement influence on steady two-dimensional detonation propagation
Steady detonation in multi-dimensional flow is controlled by the chemical energy release that occurs in a subsonic elliptic flow region known as the detonation driving zone (DDZ). It is the region encompassing the detonation shock and sonic flow locus (in the frame of the detonation shock). A detonation that is strongly confined by material surrounding the explosive has the shock and sonic locus separated at the material interface. Information about the material boundary is traditionally believed to influence the DDZ structure via the subsonic flow on the boundary ahead of the sonic locus. A detonation that is weakly confined has the detonation shock and sonic locus intersecting at the material boundary. The sonic nature of the flow at the intersection point on the boundary is believed to isolate the DDZ structure from the material properties of the confinement. We examine the paths of characteristics propagating information about the confinement through the supersonic hyperbolic flow region that exists beyond the sonic locus, and determine whether these paths may impinge on the sonic locus and consequently influence the DDZ structure. Our configuration consists of a solid wall boundary deflected through a specified angle on detonation shock arrival, so that the streamline turning angle of the wall at the explosive edge is unambiguously defined. By varying the wall deflection angle from small through large values, we can systematically capture the evolution of the DDZ structure and the characteristic flow regions that influence its structure for strongly to weakly confined detonations. In all strong and weak confinement cases examined, we find that a subset of characteristics from the supersonic flow regions always impinge on the sonic locus. Limiting characteristics are identified that define the boundary between characteristics that impinge on the sonic surface and those that propagate information downstream of the sonic surface. In combination with an oblique-shock polar analysis, we show that the effects on the DDZ of characteristic impingement can be significant.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Propagation of a stable gaseous detonation in a circular arc configuration
Here, we examine numerically the effect that detonation wavefront curvature has on gaseous detonation cellular structure in a circular arc geometry with rigid walls. For the model considered, a planar detonation is weakly unstable. The detonation curvature is induced by diffraction and flow divergence as the wave sweeps around the arc. We examine the effect of arc thickness, inner arc radius and activation energy on the cellular pattern. A combination of pseudo-Schlieren, pseudo-soot foil records and detonation shock and sonic flow loci are used to explore the observed detonation structures. We find that for sufficiently wide arcs, the detonation wavefront curvature renders the detonation hydrodynamically stable, i.e. laminar flow with no cells. The stable configuration consists of a broadly curved wave originating from the inner arc surface, which is typically connected to the outer arc boundary by a stable Mach stem. The stable detonation is driven by a small region of subsonic flow attached to the inner arc surface, outside of which the flow is supersonic. The initiation dynamics of a stable propagating wave case are explored. The evolution dynamics between an unstable (cellular) and stable arc thickness are also examined. Finally, smaller inner arc radii and lower activation energies increase the range of stable solutions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Calibration of the Pseudo-Reaction-Zone Model for Detonation Wave Propagation using a Finite-Volume Based Shock-Fit Approach
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Chiquete, Carlos↗
Detonation diffraction in a circular arc geometry of the insensitive high explosive PBX 9502
We describe the details of an unconfined insensitive high explosive (PBX 9502) circular arc section experiment, in which, after a transient period, a detonation sweeps around the arc with constant angular speed. The arc section is sufficiently wide that the flow along the centerline of the arc section remains two-dimensional. Data includes time-of-arrival diagnostics of the detonation along the centerline inner and outer arc surfaces, which is used to obtain the angular speed of the steadily rotating detonation. We also obtain the lead shock shape of the detonation as it sweeps around the arc. Reactive burn model simulations of the PBX 9502 arc experiment are then conducted to establish the structure of the detonation driving zone, i.e. the region enclosed between the detonation shock and flow sonic locus (in the frame of the steady rotating detonation). It is only the energy released in this zone which determines the speed at which the steady detonation sweeps around the arc. We show that the sonic flow locus of the detonation driving zone largely lies at the end of, or within, the fast reaction stage of the PBX 9502 detonation, with the largest section of the detonation driving zone lying close to the inner arc surface. In conclusion, we also demonstrate that the reactive burn model provides a good prediction of both the angular speed of the detonation wave and the curved detonation front shape.
42 ENGINEERING↗
An intrinsic velocity–curvature–acceleration relationship for weakly unstable gaseous detonations
The shock motion of calculated weakly unstable cellular detonation was analyzed using concepts from velocity-curvature theory to develop new insight into the underlying physical mechanisms driving the cellular instability. The cellular cycle was shown to follow a surface in a three-dimensional coordinate system composed of the local shock velocity, curvature, and acceleration. Wavelets of the detonation shock were found to follow a velocity-curvature trajectory that was characteristic of an initially reactive wave that decays in time to a decoupled blast wave. Near the Mach stem, these trajectories were only modulated by the strength of the Mach stem at the time the wavelet was generated, indicating that the small reaction zone present in this region is the dominant factor driving the flow. Away from the Mach stem, all wavelet trajectories collapsed to a common curve in velocity-curvature space that was consistent with motion of a decaying blast wave. For the mixture studied, the apparent adherence of shock motion to a unique surface in velocity-curvature-acceleration space indicates the possible existence of an intrinsic mixture-specific relationship for cellular gaseous detonation. In conclusion, this relationship and analysis methodology also provides a mechanism for quantification of the shock velocity and shape fluctuations present in cellular detonation, which may provide utility for modeling detonation engineering applications such as rotating detonation engine design.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
High Explosive Detonation–Confiner Interactions
The primary purpose of a detonation in a high explosive (HE) is to provide the energy to drive a surrounding confiner, typically for mining or munitions applications. The details of the interaction between an HE detonation and its confinement are essential to achieving the objectives of the explosive device. For the high pressures induced by detonation loading, both the solid HE and confiner materials will flow. The structure and speed of a propagating detonation, and ultimately the pressures generated in the reaction zone to drive the confiner, depend on the induced flow both within the confiner and along the HE–confiner material interface. The detonation–confiner interactions are heavily influenced by the material properties and, in some cases, the thickness of the confiner. This review discusses the use of oblique shock polar analysis as a means of characterizing the possible range of detonation–confiner interactions. Computations that reveal the fluid mechanics of HE detonation–confiner interactions for finite reaction-zone length detonations are discussed and compared with the polar analysis. Furthermore this includes cases of supersonic confiner flow; subsonic, shock-driven confiner flow; subsonic, but shockless confiner flow; and sonic flow at the intersection of the detonation shock and confiner material interface. We also summarize recent developments, including the effects of geometry and porous material confinement, on detonation–confiner interactions.
45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
Interaction of a Condensed-Phase Explosive Detonation with a Compliant Boundary: The Impulsively Withdrawn Wall
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Bdzil, John Bohdan↗
Theory of Mach reflection of detonation at glancing incidence
In this paper, we present a theory for Mach reflection of a detonation undergoing glancing incidence reflection off of a rigid wall. Our focus is on condensed-phase explosives, which we describe with a constant adiabatic gamma equation of state and an irreversible and either state-independent or weakly state-dependent reaction rate. We consider two detonation models: (1) the instantaneous reaction heat-release Chapman–Jouguet (CJ) limit and (2) the spatially resolved reaction heat-release Zeldovich–von Neumann–D$\ddot{Ø}$ring (ZND) limit, where here we only consider that a small fraction of the detonation energy release is spatially resolved (the SRHR limit). We observe a three-shock reflection in the CJ limit case, with a Mach shock that is curved. In addition, we develop an analytical expression for the triple-point track angle as a function of the angle of incidence. For the SRHR model, we observe a smooth lead shock, akin to von Neumann reflection, with no reflected shock in the reaction zone. Only at larger angles of incidence is a three-shock Mach reflection observed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Steady detonation propagation in a circular arc: a Detonation Shock Dynamics model
We study the physics of steady detonation wave propagation in a two-dimensional circular arc via a Detonation Shock Dynamics (DSD) surface evolution model. The dependence of the surface angular speed and surface spatial structure on the inner arc radius ( $R_{i}$ ), the arc thickness ( $R_{e}-R_{i}$ , where $R_{e}$ is the outer arc radius) and the degree of confinement on the inner and outer arc is examined. We first analyse the results for a linear $D_{n}$ – $\unicode[STIX]{x1D705}$ model, in which the normal surface velocity $D_{n}=D_{CJ}(1-B\unicode[STIX]{x1D705})$ , where $D_{CJ}$ is the planar Chapman–Jouguet velocity, $\unicode[STIX]{x1D705}$ is the total surface curvature and $B$ is a length scale representative of a reaction zone thickness. An asymptotic analysis assuming the ratio $B/R_{i}\ll 1$ is conducted for this model and reveals a complex surface structure as a function of the radial variation from the inner to the outer arc. For sufficiently thin arcs, where $(R_{e}-R_{i})/R_{i}=O(B/R_{i})$ , the angular speed of the surface depends on the inner arc radius, the arc thickness and the inner and outer arc confinement. For thicker arcs, where $(R_{e}-R_{i})/R_{i}=O(1)$ , the angular speed does not depend on the outer arc radius or the outer arc confinement to the order calculated. It is found that the leading-order angular speed depends only on $D_{CJ}$ and $R_{i}$ , and corresponds to a Huygens limit (zero curvature) propagation model where $D_{n}=D_{CJ}$ , assuming a constant angular speed and perfect confinement on the inner arc surface. Having the normal surface speed depend on curvature requires the insertion of a boundary layer structure near the inner arc surface. This is driven by an increase in the magnitude of the surface wave curvature as the inner arc surface is approached that is needed to meet the confinement condition on the inner arc surface. For weak inner arc confinement, the surface wave spatial variation with the radial coordinate is described by a triple-deck structure. The first-order correction to the angular speed brings in a dependence on the surface curvature through the parameter $B$ , while the influence of the inner arc confinement on the angular velocity only appears in the second-order correction. For stronger inner arc confinement, the surface wave structure is described by a two-layer solution, where the effect of the confinement on the angular speed is promoted to the first-order correction. We also compare the steady-state arc solution for a PBX 9502 DSD model to an experimental two-dimensional arc geometry validation test.
Short, Mark↗