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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.

We study the effects of non-parallel (diverging or converging) channel walls on flame propagation and acceleration in planar and cylindrical narrow channels, closed at the ignition end and open at the other, accounting for thermal expansion in both the zero Mach number and weakly compressible flow limits. For parallel channel walls, previous work has shown that thermal expansion induces an axial flow in the channel, which can significantly increase the propagation speed and acceleration of the flame. In this study, we consider examples of diverging/converging linear walls, although our asymptotic analysis is also valid for curved walls. The slope of the channel walls is chosen so that the magnitude of the thermal-expansion induced flow through the channel obtained for parallel walls is modified at leading-order, thereby influencing the leading-order flame propagation. For zero Mach number flows, the effect of the diverging/converging channel walls is moderate. However, for weakly compressible flows, the non-parallel walls directly affect the rate at which pressure diffuses through the channel, significantly inhibiting flame acceleration for diverging walls, whereas the flame acceleration process is enhanced for converging walls. We consider several values of the compressibility factor and channel wall slopes. We also show that the effect of a cylindrical channel geometry can act to significantly enhance flame acceleration relative to planar channels. The study reveals several new physical insights on how non-parallel channel walls can influence the ability of flames to accelerate by modifying the flow and pressure distribution induced by thermal expansion.

Detonation performance experiments and modeling are reported for the explosive PBX 9701, which is composed of 97% 3,3’-diamino-4,4’-azoxyfurazan (DAAF) and 3% vinylidene fluoride-chlorotrifluoroethylene copolymer (Kel-F 800) binder by weight. PBX 9701 is a newly developed reduced-sensitivity 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 fron curvature rate sticks and cylinder expansion test data. Prior shock initiation data is also reviewed. These data are used to develop programmed burn (PB) and reactive burn (RB) 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 equation of state (EOS) calibration process. It uses a PB hydrocode-based approach and development of a new methodology to improve the consistency between the PB and RB model calibrations and associated calculations. This link is achieved by populating the RB products EOS in direct reference to the PB release isentrope and Chapman-Jouguet state and in calibrating the timing components of each model using an equivalent procedure, all in order to facilitate comparison between the two modeling approaches. 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.

We examine, via multi-material simulation in a two-dimensional planar geometry, the effects on steady detonation propagation of the presence of a low-density intermediate layer between a condensed-phase high explosive (HE) and a high-density metallic confiner of finite thickness. Such elastomer intermediate layers are often added to eliminate air-gaps and the associated jetting effects that can arise due to machining imprecisions, or to prevent HE cracking due to environmental changes. Without an intermediate layer, the flow structure of a steady detonation/metal confiner interaction is well understood. In particular, there is no reflected wave passed into the HE due to the metal confinement. With the elastomer layer present, we find that, as the intermediate layer width increases, a complex wave interaction and communication path develops between the HE, intermediate, and metal layers. For thin intermediate layers, a shock-driven subsonic flow develops in the intermediate layer, passing information from the metal layer to the HE, with the detonation speed decreasing as the intermediate layer width increases. For wider intermediate layers, a Mach stem configuration develops in the intermediate layer, forcing a shock to be reflected into the HE. Simultaneously, a localized Prandtl-Meyer fan emerges from the intersection of the detonation shock with the HE-intermediate layer material interface. These HE structures are shown to have a substantial effect on the structure of the detonation driving zone. The Prandtl-Meyer fan becomes the dominant structure for critically large intermediate layer widths, wherein the presence of the metal layer does not affect the detonation propagation. We examine the detonation propagation speed and reaction and driving zone structure as a function of varying intermediate layer width. Two confinement metals are examined, along with two high explosive and three metal layer widths.

A surface evolution model is developed for the detonation propagation dynamics of the HMX-based conventional high explosive PBX 9501, which relates the normal surface speed Dn to its local surface curvature κ. Such surface evolution models are important for the understanding and modification of engineering design calculations for high explosive applications. We describe a series of unconfined PBX 9501 slab geometry experiments of varying thickness, and detail how the steady axial detonation speed and detonation front shape data are obtained. A merit-function based calibration process is then described that uses both the PBX 9501 thickness effect and front shape data to parametrize the D n − κ propagation law. The time-dependent PBX 9501 D n − κ surface evolution law is then applied to detonation wave propagation in two-dimensional circular arc geometries, systematically examining the effect of arc thickness, inner radius, relaxation dynamics to steady-state propagation and confinement.

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. In this study, 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.

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. Smaller inner arc radii and lower activation energies increase the range of stable solutions.

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. 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.

We examine the evolution of cellular detonation patterns in a two-dimensional channel with yielding confinement on one side. It is shown that in a narrow channel of fixed width the number of cells first increase with decreasing level of confinement. Subsequently, with increasingly weaker confinement, the cells then grow in size and the total number of cells in the channel decreases. For sufficiently weak confinement, the flow becomes laminar with no detonation cells. We examine the relative importance of two fluid mechanisms underlying the observed evolution: global curvature of the detonation shock front due to induced flow divergence caused by the yielding confinement, and energy loss associated with transverse shock wave transmission to the confining material. In order to determine which effect is dominant, we compare two types of numerical calculations. One involves specialized calculations in which the explosive boundary, along which impermeable flow conditions are applied, is deflected through a range of specified angles upon detonation arrival. This set-up mimics the effect of yielding confinement in terms of induced flow divergence, but removes the transverse wave energy loss that would otherwise occur due to wave transmission into the confiner material. The second involves multi-material simulations which can account for transverse wave energy loss into the confining material. Shock polar theory is used to select confiner densities in the multi-material calculations that provide equivalent material interface deflection angles at the detonation shock to the angles imposed in the deflected solid wall calculations. We determine that the induced global curvature of the wave primarily drives both the evolution of the cellular pattern and eventual stabilization of the detonation front, characterized by laminar flow solutions. In wider channels, we show that the detonation front will likely remain unstable even for very weak confinement, as the mean curvature of the front only becomes significant near the edge of the explosive domain.

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.

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. 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.

An approach for the calibration of an advanced programmed burn (PB) model for detonation performance calculations in high explosive systems is detailed. Programmed burn methods split the detonation...

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. 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.

A series of detonation performance experiments are described for the plastic-bonded high explosive (HE) PBX 9012, nominally composed of 90% octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazine (HMX) and 10% polymeric binder vinylidene-hexafluoropropylene copolymer (Viton VTR-5883), by weight. The experiments provide information on the PBX 9012’s detonation propagation properties and metal pushing characteristics. Although this HE formulation has been in use for 50 years as a booster (compositionally similar to LX-07), our new data represent the first full detonation performance characterization for the HE (along with recently reported shock initiation experiments). Here, we compare the new PBX 9012 data with the well-studied PBX 9501 (95% HMX and 5% polymeric binder), establishing how the 5% difference in HMX content between the explosives is manifested in the performance measurements. A scaling argument based on the known energetic material content in a large selection of high HMX content formulations is also given to help explain the observed results. Finally, the accumulated PBX 9012 data is used to generate performance models using both programmed and reactive burn techniques, providing an additional avenue to compare PBX 9012 to the more energetic PBX 9501.

The dynamics of steady detonation propagation in a two-dimensional, high explosive circular arc geometry are examined computationally using a reactive flow model approach. The arc is surrounded by a low impedance material confiner on its inner surface, while its outer surface is surrounded either by the low impedance confiner or by a high impedance confiner. The angular speed of the detonation and properties of the steady detonation driving zone structure, i.e. the region between the detonation shock and sonic flow locus, are examined as a function of increasing arc thickness for a fixed inner arc radius. For low impedance material confinement on the inner and outer arc surfaces, the angular speed increases monotonically with increasing arc thickness, before limiting to a constant. The limiting behaviour is found to occur when the detonation driving zone detaches from the outer arc surface, leaving a region of supersonic flow on the outer surface. Consequently, the angular speed of the detonation becomes insensitive to further increases in the arc thickness. For high impedance material confinement on the outer arc surface, the observed flow structures are significantly more complex. As the arc thickness increases, we sequentially observe regions of negative shock curvature on the detonation front, reflected shock formation downstream of the reaction zone, and eventually Mach stem formation on the detonation front. Subsequently, a region of supersonic flow develops between the detonation driving zone and the Mach stem structure. For sufficiently wide arcs, the Mach stem structure disappears. For the high impedance material confinement, the angular speed of the detonation first increases with increasing arc thickness, reaches a maximum, decreases, and then limits to a constant for sufficiently large arc thickness. The limiting angular speed is the same as that found for the low impedance confiner on the outer arc surface.

The fluid mechanics of the interaction between a porous material confiner and a steady propagating high explosive (HE) detonation in a two-dimensional slab geometry is investigated through analytical oblique wave polar analysis and multi-material numerical simulation. Two HE models are considered, broadly representing the properties of either a high- or low-detonation-speed HE, which permits studies of detonation propagating at speeds faster or slower than the confiner sound speed. The HE detonation is responsible for driving the compaction front in the confiner, while, in turn, the high material density generated in the confiner as a result of the compaction process can provide a strong confinement effect on the HE detonation structure. Polar solutions that describe the local flow interaction of the oblique HE detonation shock and equilibrium state behind an oblique compaction wave with rapid compaction relaxation rates are studied for varying initial solid volume fractions of the porous confiner. Multi-material numerical simulations are conducted to study the effect of detonation wave driven compaction in the porous confiner on both the detonation propagation speed and detonation driving zone structure. We perform a parametric study to establish how detonation confinement is influenced both by the initial solid volume fraction of the porous confiner and by the time scale of the dynamic compaction relaxation process relative to the detonation reaction time scale, for both the high- and low-detonation-speed HE models. The compaction relaxation time scale is found to have a significant influence on the confinement dynamics, with slower compaction relaxation time scales resulting in more strongly confined detonations and increased detonation speeds. The dynamics of detonation confinement by porous materials when the detonation is propagating either faster or slower than the confiner sound speed is found to be significantly different from that with solid material confiners.

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–Doring (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.

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 , 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 .

People from diverse backgrounds enrich the rural, regional, and remote communities where they relocate and settle. Research about rural diversity tends to focus on demographics (age, gender, country of origin) while ignoring personal narratives of integration, for example, engagements with religious institutions (such as the local Christian church). This article presents the research themes from an investigation using co-operative inquiry into rural diversity and the Anglican Church, with specific reference to the Australian experience. It is a cross-disciplinary dialogic exchange between social workers and theologians. Positive narratives about connection, welcome, participation, and belonging are shared.

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.

Dynamic compression experiments have proven useful for decades in examining material response at high pressures and providing equation-of-state and other information on numerous phenomena including phase transitions, strength, and kinetics.

Experiments were conducted to characterize the detonation phase-velocity dependence on charge thickness for two-dimensional detonation in condensed-phase explosive slabs of PBX 9501, PBX 9502 and ANFO. In combination with previous diameter-effect measurements from a cylindrical rate-stick geometry, these data permit examination of the relative scaling of detonation phase velocity between axisymmetric and two-dimensional detonation. We find that the ratio of cylinder radius ($R$) to slab thickness ($T$) at each detonation phase velocity ($D_{0}$) is such that$R(D_{0})/T(D_{0}). The variation in the$R(D_{0})/T(D_{0})$scaling is investigated with two detonation shock dynamics (DSD) models: a lower-order model relates the normal detonation velocity to local shock curvature, while a higher-order model includes the effect of front acceleration and transverse flow. The experimentally observed$R(D_{0})/T(D_{0})$(${) scaling behaviour for PBX 9501 and PBX 9502 is captured by the lower-order DSD theory, revealing that the variation in the scale factor is due to a difference in the slab and axisymmetric components of the curvature along the shock in the cylindrical geometry. The higher-order DSD theory is required to capture the observed$R(D_{0})/T(D_{0})$(${) scaling behaviour for ANFO. An asymptotic analysis of the lower-order DSD formulation describes the geometric scaling of the detonation phase velocity between the cylinder and slab geometries as the detonation phase velocity approaches the Chapman–Jouguet value.

The results of 14 tests examining the behavior of aluminum (Al) confiners driven by non-ideal ANFO detonation in a cylinder test configuration are presented. In each test, the measured detonation phase velocity is slower than the aluminum sound speed. Thus, in the detonation reference frame, the flow in the Al is both shockless and subsonic. The tests involve: 3-in. inner diameter (ID) cylinders with Al wall thicknesses of 1/4, 3/8, 1/2, 1 and 2 in.; a 4-in. ID cylinder with a 1/2-in. Al wall thickness; and 6-in. ID cylinders with Al wall thicknesses of 1/2, 1 and 2 in. The ANFO detonation velocity is seen to increase with increasing wall thickness for both the 3- and 6-in. ID tests, with no limiting velocity reached for the wall thicknesses used. The motion of the outer Al wall due to precursor elastic waves in the Al running ahead of the detonation is also measured at various axial locations along the cylinders. It is found that the magnitude of the outer wall motion due to the precursor elastic waves is small, while the associated wall motion is unsteady and decays in amplitude as the elastic disturbances move further ahead of the detonation front. The variations in the expansion history of the main outer wall motion of the cylinders are presented for increasing wall thickness at fixed ID, and for increasing cylinder inner diameter at a fixed wall thickness. Finally, we also explore the existence of a geometric similarity scaling of the wall expansion history for three geometrically scaled tests (3- and 6-in. ID cylinders with 1/4- and 1/2-in. walls, 3- and 6-in. ID cylinders with 1/2- and 1-in. walls and 3- and 6-in. ID cylinders with 1- and 2-in. walls respectively). We find that the wall velocity histories for each of the three scaled tests, when plotted directly against time relative to start of main motion of the wall, are similar over a certain range of wall velocities without any geometric based rescaling in time. The range of wall velocities where the overlap occurs increases as the ratio of the wall thickness to inner diameter decreases. This is in contrast to ideal high explosives, where the outer wall velocity histories are only similar when the geometric scale factor (in this case a factor of 2) is applied to the wall velocity motion.

The evolution of the normal detonation shock velocity (Dn) with local shock curvature (κ) is experimentally and numerically examined along entire evolving fronts of a weakly unstable cellular detonation cycle with the intention of extending the understanding of cellular evolution dynamics. As expected, a single velocity–curvature relation is not recovered due to the unsteady evolution of the cell. However, geometric features of the Dn–κ evolution during a cell cycle reveal some new details of the mechanisms driving cellular detonation. On the cell centerline, the local shock velocity and curvature monotonically decrease throughout the cellular cycle. Off centerline, a larger range of wavefront curvature was exhibited in expanding cells as compared to shrinking ones, indicating that most curvature variation in a detonation cell occurs near the Mach stem. In normal shock velocity–curvature space, the cell dynamics can be mapped to three features that are characteristic of (feature 1) a detonation with a spatially short reaction zone, (feature 2) a transitional regime of shock and reaction zone decoupling, and (feature 3) a diffracting inert blast wave. New, growing cells predominately exhibited features 1 and 2, while decaying cells only exhibited feature 3. The portions of all profiles with normal velocities below the Chapman–Jouguet velocity were characteristic of inert blast propagation, indicating the possibility that exceeding this velocity may be a necessary condition for the existence of shock and reaction zone coupling. In this inert blast regime, Dn and κ vary spatially across the wave front so each segment is not geometrically cylindrical, but when accumulated, the Dn–κ data map out a straight line, indicating elements of self-similar flow for each stage in the cell cycle.

Ammonium nitrate mixed with aluminum powder forms a non-ideal explosive often referred to as ammonal. Non-ideal detonation can result in significant energy release behind the detonation sonic surface that does not contribute to the detonation velocity, but may affect the expansion energy of the product gases. In this work, we use scaled cylinder expansion tests to characterize the product energy variation with scale for ammonal. The results of two cylinder tests with 50.8-mm and 72.6-mm inner diameters are compared to prior data at other scales. We find that cylinder wall velocity increases with increasing charge diameter and also with increasing charge length.

Cyclotol is a melt-castable high explosive composed of RDX and TNT, and typically a small amount of HMX. The term Cyclotol may apply to other mixtures of these components, but for the present work, experiments were conducted using Cyclotol containing 80 wt% RDX and HMX and 20 wt% TNT (we will refer to mixtures of RDX and TNT using the notation RDX%/TNT%). In the current effort, we report detonation velocity measurements at several diameters for unconfined rate sticks. The results are compared to prior diameter-effect data for Cyclotol 77/23, and a density-corrected Eyring-form fit for all available rate-stick data is reported.

Detonations in explosive mixtures of ammonium-nitrate-fuel-oil (ANFO) confined by aluminum allow for transport of detonation energy ahead of the detonation front due to the aluminum sound-speed exceeding the detonation velocity. The net effect of this energy transport on the detonation is unclear. It could enhance the detonation by precompressing the explosive near the wall. Alternatively, it could decrease the explosive performance by crushing porosity required for initiation by shock compression or destroying confinement ahead of the detonation. At present, these phenomena are not well understood. But with slowly detonating, non-ideal high explosive (NIHE) systems becoming increasing prevalent, proper understanding and prediction of the performance of these metal-confined NIHE systems is desirable. Experiments are discussed that measured the effect of ANFO detonation energy transported upstream of the front by a 76-mm-inner-diameter aluminum confining tube. Detonation velocity, detonation front-shape, and aluminum response are recorded as a function of confiner wall thickness and length. Detonation shape profiles display little curvature near the confining surface, which is attributed to energy transported upstream modifying the flow. Average detonation velocities were seen to increase with increasing confiner thickness, while wavefront curvature decreased due to the stiffer, subsonic confinement. Significant radial sidewall tube motion was observed immediately ahead of the detonation. Axial motion was also detected, which interfered with the front-shape measurements in some cases. It was concluded that the confiner was able to transport energy ahead of the detonation and that this transport has a definite effect on the detonation by modifying its characteristic shape.

The influence of thermal expansion on the dynamics of thick to moderately thick premixed flames (flame thickness less than or comparable to the channel height) for a variable-density flow in a narrow, rectangular channel is explored. The study is conducted within the framework of the zero-Mach-number, variable-density Navier–Stokes equations. Both adiabatic and non-adiabatic channel walls are considered. A small Péclet number asymptotic solution is developed for steady, variable-density flame propagation in the narrow channel. The dynamics of channel flames are also examined numerically for O(1) Péclet numbers in configurations which include flame propagation in a semi-closed channel from the closed to the open end of the channel, flame propagation in a semi-closed channel towards the closed end of the channel and flame propagation in an open channel in which a Poiseuille flow (flame assisting or flame opposing) is imposed at the channel inlet. Comparisons of the finite-Péclet-number dynamics are made with the behaviour of the small-Péclet-number solutions. We also compare how thermal expansion modifies the flow dynamics from those determined by a constant-density model. The small-Péclet-number variable-density solution for a flame propagating in a circular pipe is given in the Appendix.

This paper presents a simplified reactive multi-gas model for the numerical simulation of detonation waves. The mathematical model is formulated based on a thermodynamically consistent and fully conservative formulation, and is extended to model reactive flow by considering the reactant and product gases as two constituents of the system and modelling the conversion between these by a simple one-step reaction mechanism. This simplified model allows simulations using more appropriate chemico-thermodynamic properties of the combustible mixture and yields close Chapman–Jouguet detonation parameters from detailed chemistry. The governing equations are approximated using a high-resolution finite volume centred scheme in an adaptive mesh refinement code, permitting high-resolution simulations to be performed at flow regions of interest. The algorithm is tested and validated by comparing results to predictions of the one-dimensional linear stability analysis of the steady detonation and through the study of the evolution of two-dimensional cellular detonation waves in gaseous hydrogen-based mixtures.

BACKGROUND AND OBJECTIVE To determine the prophylactic and therapeutic value of a single subthreshold 810-nanometer laser treatment in patients with high risk drusen as a manifestation of dry age-related macular degeneration in both eyes. PATIENTS AND METHODS The Prophylactic Treatment of Age-related Macular Degeneration study enrolled 1,278 eyes of 639 participants who were 50 years or older with at least 5 drusen 63 µm or more in diameter in each eye. Treatment consisted of the placement of an annular grid of 48 extrafoveal, subthreshold 810-nm diode laser applications centered at but sparing the foveola in one eye of each participant, with the fellow eye serving as a control. Development of choroidal neovascularization and change in best-corrected visual acuity were compared between treated and untreated eyes. RESULTS Subthreshold laser treatment did not decrease the incidence of choroidal neovascularization in treated versus untreated eyes. A modest visual acuity benefit in treated eyes was found at 24 months (1.5 letter difference; P = .04) and in the treated eyes of participants with a baseline visual acuity between 20/32 and 20/63 (4.0 letter difference; P = .0034). However, this treatment effect was not sustained at 3 years. CONCLUSION A single subthreshold 810-nanometer laser treatment to eyes of participants with bilateral high risk drusen is not an effective prophylactic strategy against choroidal neovascularization. [Ophthalmic Surg Lasers Imaging 2009;40:530-538.] AUTHORS From the UPMC Eye Center (TRF, PMB), University of Pittsburgh, Pittsburgh, Pennsylvania; the Shiley Eye Center (WRF), University of California–San Diego, La Jolla, California; and the W. K. Kellogg Eye Center (DCM), University of Michigan, Ann Arbor, Michigan. Accepted for publication December 19, 2008. Supported by Iridex Corporation, Mountain View, California, and the sources listed under the individual center descriptions found at the end of the article; the Eye and Ear Foundation of Pittsburgh, Pittsburgh, Pennsylvania; Research to Prevent Blindness, Inc., New York, New York; and unrestricted funds from several participating centers. Presented in part at the annual meeting of the American Academy of Ophthalmology, October 15-18, 2005, Chicago, Illinois, and the annual meeting of the Association for Research in Vision and Ophthalmology, April 30-May 4, 2006, Ft. Lauderdale, Florida. The authors thank photographic readers Cheryl Hiner, Columbia, MD, Rosemary J. Brothers, Madison, WI, and Linda Huang, MD, and Maria Palaiou, MS, Pittsburgh, PA; the Data and Safety Monitoring Committee voting members Donald J. D’Amico, MD, Mark W. Johnson, MD, J. Richard Landis, PhD, and nonvoting ex-officio member, Dr. Musch; and Giorgio Dorin for his contribution to the manuscript. The authors have no financial or proprietary interest in the materials presented herein. Address correspondence to Thomas R. Friberg, MS, MD, UPMC Eye Center, 203 Lothrop Street, Suite 824, Pittsburgh, PA 15213. doi: 10.3928/15428877-20091030-01

The dynamics of non-premixed edge-flames, including the generation of cellular structures, in an unsteady, symmetric counterflow are examined for positive rates of strain. A one-step reaction is assumed, ν Y F + ν X O → ν p P , in which the oxidizer Lewis number is 1. For a variety of Damkohler numbers, we examine the edge-flame evolution for two values of the fuel Lewis number Le Y , 0.3 and 1, and two values of the initial mixture fraction γ, 0.36 and 1, representing fuel lean and stoichiometric supply conditions. For Le Y = 0.3 and γ = 0.36 , unsteady forcing can convert non-cellular edge-flames into ones containing various characteristics of near- or sub-limit cellular structures, including drifting, splitting and stationary flame strings. The transition regimes between the different edge-flame structures are examined as a function of the amplitude and frequency of the strain rate variations in the unsteady counterflow and also as a function of the instantaneous and equivalent strain rate functions. For Le Y = 0.3 and γ = 1 , while no cellular edge-flames can be generated for steady counterflows, we show that cellular structures can be observed in the presence of unsteady forcing. For Le Y = 1 and γ = 1 , it is shown that unsteady forcing can significantly modify the mean propagation speeds of both ignition and failure waves. Finally, the quenching boundaries of two-dimensional edge-flames induced by the unsteady counterflow are examined for Le Y = 0.3 , γ = 0.36 and Le Y = 1 , γ = 1 .

Shock-induced ignition is considered for a three-step chain-branching mechanism at large activation energies. The nature of the ignition process depends critically on the magnitude of the initial post-shock temperature relative to the chain-branching cross-over temperature. For the limits examined, the induction region is preceded by an exponentially weak initiation zone that provides relevant initial conditions for the induction phase. When the initial post-shock temperature is sufficiently close to the chain-branching temperature, ignition is characterized by logarithmic singular behaviors in the pressure and temperature perturbations and the structure has some similarities with the one-step chemistry problem. However, for larger initial post-shock temperatures, the logarithmic singularities are replaced by linear temporal growth. Suitable non-linear Clarke equations are deduced for both of these cases and numerical solutions are presented.

We examine, via two-dimensional numerical simulation of a model system, some unsteady transient ignition scenarios and sustained oscillatory combustion modes that can occur in a single-pass, conductive channel, premixed microburner. These issues are relevant to the problem of ignition, evolution to stable combustion and the operational modes of microcombustors. First, we describe an unsteady ignition sequence that may occur when a single-pass microburner with initially cold walls has its exit walls heated and maintained at a fixed temperature. In particular, we demonstrate that as the heat from the exit walls propagates down the microburner walls, a reaction wave is driven rapidly down the channel towards the inlet via a sequence of oscillatory ignition and quenching transients. This scenario has been observed experimentally during the ignition of a single-pass microburner. Secondly, we show how an initial axial wall temperature gradient can lead to a variety of sustained combustion modes within the chann...

The stability of travelling wave Chapman–Jouguet and moderately overdriven detonations of Zeldovich–von Neumann–Döring type is formulated for a general system that incorporates the idealized gas and condensed-phase (liquid or solid) detonation models. The general model consists of a two-component mixture with a one-step irreversible reaction between reactant and product. The reaction rate has both temperature and pressure sensitivities and has a variable reaction order. The idealized condensed-phase model assumes a pressure-sensitive reaction rate, a constant-γ caloric equation of state for an ideal fluid, with the isentropic derivative γ=3, and invokes the strong shock limit. A linear stability analysis of the steady, planar, ZND detonation wave for the general model is conducted using a normal-mode approach. An asymptotic analysis of the eigenmode structure at the end of the reaction zone is conducted, and spatial boundedness (closure) conditions formally derived, whose precise form depends on the magnitude of the detonation overdrive and reaction order. A scaling analysis of the transonic flow region for Chapman–Jouguet detonations is also studied to illustrate the validity of the linearization for Chapman–Jouguet detonations. Neutral stability boundaries are calculated for the idealized condensed-phase model for one- and two-dimensional perturbations. Comparisons of the growth rates and frequencies predicted by the normal-mode analysis for an unstable detonation are made with a numerical solution of the reactive Euler equations. The numerical calculations are conducted using a new, high-order algorithm that employs a shock-fitting strategy, an approach that has significant advantages over standard shock-capturing methods for calculating unstable detonations. For the idealized condensed-phase model, nonlinear numerical solutions are also obtained to study the long-time behaviour of one- and two-dimensional unstable Chapman–Jouguet ZND waves.

Many current models of condensed-phase explosives employ reaction rate law models where the form of the rate has a power-law dependence on pressure (i.e. proportional to pn where n is an adjustable parameter). Here, shock-induced ignition is investigated using a simple model of this form. In particular, the solutions are contrasted with those from Arrhenius rate law models as studied previously. A large n asymptotic analysis is first performed, which shows that in this limit the evolution begins with an induction stage, followed by a sequence of pressure runaways, resulting in a forward propagating, decelerating, shockless supersonic reaction wave (a weak detonation). The theory predicts secondary shock and super-detonation formation once the weak detonation reaches the Chapman–Jouguet speed. However, it is found that secondary shock formation does not occur until the weak detonation has reached a point close to the initiating shock, whereas for Arrhenius rate laws the shock forms closer to the piston. Numerical simulations are then conducted for O(1) values of n, and it is shown that the idealized condensed-phase model can qualitatively describe a wide range of experimentally observed behaviours, from growth mainly at the shock, to smooth growth of a pressure pulse behind the shock, to cases where a secondary shock and possibly a super-detonation form. The numerics are used to reveal the different evolutionary mechanisms for each of these cases. However, the evolution is found to be sensitive to n, with the whole range of behaviours covered by varying n from about 3 to 5. The simulations also confirm the predictions of the theory that pressure-dependent rate laws are unable to describe homogeneous explosive scenarios where a super-detonation forms very close to the point of initial runaway.

A general normal-mode linear stability formulation of steady planar detonation waves is presented that is valid both for an arbitrary equation of state and for multi-step, multi-species chemical kinetics. The general formulation can be used for many purposes, including an examination of gaseous detonation stability with complex reaction kinetics in which the individual reacting species have variable thermochemical properties. In the present paper, we consider two cases that could not be obtained by previous one-step chemistry, polytropic gas formulations: the first concerns the effect of a difference in heat capacities between product and fuel species, as well as a possible mole change, in a single-step irreversible reaction. The second examines the effects of exothermic or endothermic heat release/absorption in the chain-initiation stage of a model three-step reaction.

We examine the structure of confined, laminar methane–oxygen diffusion flames in an alumina microburner with a sub-millimetre dimension. To minimize termination of gas-phase combustion via surface radical quenching, the reactor walls are chemically treated and annealed. We show, through chemiluminescent images, that gas-phase methane–oxygen diffusion flames exist in the microburner without the need for catalytic reaction. However, their structure differs from the continuous laminar diffusion flame profiles that we would expect in a similar burner configuration on a macroscopic scale. Instead, we observe a sequence of isolated reaction zones structures (flame cells) that form along the length of the microburner combustion channel aligned in the direction of the gas flow. This form of cellular diffusion flame instability appears to be unique to wall-confined combustion in microscale devices. The number of flame cells observed depends on the inlet gas velocities and initial mixture strengths.

We provide the first theoretical demonstration of the existence of quasi-one-dimensional, quasi-steady, self-sustaining convergent detonation waves. These occur in systems where, in the planar wave, the rate of heat release by chemical reaction reaches a maximum at a point of incomplete reaction. The case examined in the present paper is that for a two-step sequential reaction, with the second stage endothermic. We construct detonation velocity against curvature relationships for converging waves, and compare these theoretical curves with direct numerical simulations of imploding detonations in cylindrical and spherical geometries. We also comment on the one-dimensional stability of imploding and diverging detonation fronts governed by the two-step model.

We examine the cellular instabilities of laminar non-premixed diffusion flames that arise in a polycrystalline alumina microburner with a channel wall gap of dimension 0.75 mm. Changes in the flame structure are observed as a function of the fuel type (H 2 , CH 4 , and C 3 H 8 ) and diluent. The oxidizer is O 2 /inert. In contrast to previous observations on laminar diffusion flame instabilities, the current instabilities occur in the direction of flow above the splitter plate, and only occur for the heavier fuel types. They are not observed in a H 2 –O 2 mixture, which will only support a continuous laminar flame inside our burner, regardless of the initial mixture strength and whether or not the flame is in near-quenching conditions. The only exception is when helium is added to the H 2 –O 2 mixture, raising the effective Lewis numbers of both components.

We examine edge-flames in the context of symmetric counterflows of fresh mixture, and examine their dynamics when the rate of strain is varied periodically in time. For a Lewis number of 1, extinction boundaries and zero (in the mean) edge propagation speed boundaries are constructed in the forcing amplitude—Damkohler number plane. Forcing can turn advancing edges into retreating edges. For a Lewis number of 0.3, the fundamental distinction is between flames that display cellular structures and flames that do not. Forcing can convert a non-cellular flame into one with cells; and it can strongly affect the dynamics of cellular structures that exist in the absence of forcing.

The process of planar detonation ignition, induced by a constant-velocity piston or equivalently by a shock reflected from a stationary wall, is investigated using high-resolution one-dimensional numerical simulations. The standard one-step model with Arrhenius kinetics, which models thermally sensitive explosives, is employed. Emphasis is on comparing and contrasting the results of the finite activation temperature simulations with high activation temperature asymptotic predictions and previous simulations. During the induction phase, it is shown that the asymptotic results give qualitatively good predictions. However, for parameters representative of gaseous explosives, subsequent to thermal runaway at the piston and the formation of a reaction wave, the high activation temperature asymptotic theory is qualitatively incorrect for moderately high activation temperatures. It is shown that the results are very sensitive to the value of the activation temperature, especially the distance from the piston at which a secondary shock forms and the degree of unsteadiness in the reaction wave which moves away from the piston. The dependence of the ignition evolution on the other parameters (initial shock Mach number, heat of reaction and polytropic index) is also investigated. It is shown that qualitative predictions regarding the dependence of the ignition evolution on each of the parameters can be elucidated from finite activation temperature homogeneous explosion calculations together with the high activation temperature asymptotic shock ignition results. It is found that for sufficiently strong initiating shocks the ignition evolution is qualitatively different from cases studied previously in that no secondary shock forms. For a high polytropic index, corresponding to a simple equation of state model for condensed phase explosives, the results are in much better qualitative agreement with the asymptotic theory.

Until recently, the concept of combustion within a confined space defined by a microburner was thought to be impossible. Extensive literature dating back to Davy's seminal work in 1817 has discussed how thermal and chemical quenching set a minimum size below which no flame can exist. In this report, though, it is shown that microcombustion is possible if the wall composition and structure are carefully controlled. It is suggested that there are three keys to obtaining microcombustion: (1) the walls of the microburner need to be fabricated from materials that do not quench radicals so that the gas-phase combustion reactions can occur unimpeded; (2) the device needs to be insulated well enough that the net heat generation is sufficient to keep the reacting mixture hot enough to sustain significant combustion; and (3) the flow pattern in the burner needs to be such that the temperature is low enough not to melt the walls, yet the flame fills the entire space. Using this design strategy, devices burning methane–air and propane–air mixtures in a 750-μm slot were designed and optimized to achieve high conversion. These results show that microcombustion is possible with consideration of microscale engineering challenges and fitting combustor design. © 2004 American Institute of Chemical Engineers AIChE J, 50: 3206–3214, 2004

We examine the structure and oscillatory instability of low Peclet number, non-premixed edge-flames in a fixed rectangular channel, closed at one end, with constant side-wall mass injection, one su...

We have described, for the first time, a fully coupled low Mach number numerical algorithm which can be used to investigate the combustion of composite propellants. The code uses a body fitted grid along the moving interface by means of a mapping technique. Specifically, the surface is assumed to be single valued, thus allowing the use of a mapping function that effectively maps the propagating corrugated surface into a stationary flat surface. The transformed connection conditions are then applied along the stationary flat surface, allowing second-order one-sided derivatives to be used. This has proven to be a very robust and efficient way to treat the surface and the connection conditions. Numerical tests are performed and the scheme is shown to be second-order accurate in the spatial directions as well as in time. Selected results are presented for heterogeneous propellants.