Showing papers in "Shock Waves in 2013"

Numerical investigation of shock wave reflections near the head ends of rotating detonation engines

Abstract: The influence of various chamber geometries on shock wave reflections near the head end of rotating detonation engines was investigated. A hydrogen/air one-step chemical reaction model was used. The results demonstrated that the variation in flow field along the radial direction was not obvious when the chamber width was small, but became progressively more obvious as the chamber width increased. The thrust increased linearly, and the detonation height and the fuel-based gross specific impulse were almost constant as the chamber width increased. Near the head end, shock waves reflected repeatedly between the inner and outer walls. Both regular and Mach reflections were found near the head end. The length of the Mach stem increased as the chamber length increased. When the chamber width, chamber length and injection parameters were the same, the larger inner radius resulted in more shock wave reflections between the inner and outer walls. The greater the ratio of the chamber width to the inner radius, the weaker the shock wave reflection near the head end. The detonation height on the outer wall and the thrust, both increased correspondingly, while the specific impulse was almost constant as the inner radius of the chamber increased. The numerical shock wave reflection phenomena coincided qualitatively with the experimental results.

Dynamics of void collapse in shocked energetic materials: physics of void–void interactions

Abstract: This work presents the response of a porous energetic material subjected to severe transient loading conditions. The porosities, represented by voids, entirely change the response of an otherwise homogeneous material. The variations in terms of energy distribution and maximum temperature reached in the material in the presence of heterogeneities (voids) but in the absence of chemical reactions are studied. This study also accounts for void–void interactions to enhance the understanding of the localization of energy in the material. It is observed that relative position of voids can have important consequence on energy distribution as well as rise in temperature of the energetic material. The relative position of voids further influences the interaction of secondary shock waves generated during the collapse of one void with the downstream voids. This interaction can either enhance or diminish the strength of the shock depending on the location of downstream voids. This work also reveals that the findings from mutual void–void interactions can be used to study systems with multiple voids. This is shown by analyzing systems with 10–25 % void volume fraction. The effect of void–void interactions are connected to the overall response of a chemically inert porous material to imposed transient loads.

Numerical study of shock-wave mitigation through matrices of solid obstacles

Abstract: Shock-wave propagation through different arrays of solid obstacles and its attenuation are analyzed by means of numerical simulations. The two-dimensional compress- ible Navier-Stokes equations are solved using a fifth-order weighted essentially non-oscillatory scheme, in conjunction with an immersed-boundary method to treat the embedded solids within a cartesian grid. The present study focuses on the geometrical aspects of the solid obstacles, particularly at lower effective flow area, where the frictional forces are expected to be important. The main objective is to analyze the controlling mechanism for shock propagation and atten- uation in complex inhomogeneous and porous medium. Dif- ferent parameters are investigated such as the geometry of the obstacles, their orientation in space as well as the relaxation lengths between two consecutive columns. The study high- lights a number of interesting phenomena such as compress- ible vortices and shock-vortex interactions that are produced in the post-shock region. This also includes shock inter- actions, hydrodynamic instabilities and non-linear growth of the mixing. Ultimately, the Kelvin-Helmholtz instabil- ity invokes transition to a turbulent mixing region across the

Blast waves from cylindrical charges

Abstract: Comparisons of explosives are often carried out using TNT equivalency which is based on data for spherical charges, despite the fact that many explosive charges are not spherical in shape, but cylindrical. Previous work has shown that it is possible to predict the over pressure and impulse from the curved surface of cylindrical charges using simple empirical formulae for the case when the length-to-diameter (L/D) ratio is greater or equal to 2/1. In this paper, by examining data for all length-to-diameter ratios, it is shown that it is possible to predict the peak over pressure, P, for any length-to-diameter ratio from the curved side of a bare cylindrical charge of explosive using the equation $$P=K_PM(L/D)^{1/3}/R^3$$ , where M is the mass of explosive, R the distance from the charge and $$ K_P$$ is an explosive-dependent constant. Further out where the cylindrical blast wave ‘heals’ into a spherical one, the more complex equation $$P=C_1(Z^{\prime \prime })^{-3}+C_2(Z^{\prime \prime })^{-2}+C_3(Z^{\prime \prime })^{-1}$$ gives a better fit to experimental data, where $$ Z^{\prime \prime } = M^{1/3}(L/D)^{1/9}/D$$ and $$C_1,\, C_2 $$ and $$ C_3$$ are explosive-dependent constants. The impulse is found to be independent of the L/D ratio.

Blast wave mitigation by dry aqueous foams

Abstract: This paper presents results of experiments and numerical modeling on the mitigation of blast waves using dry aqueous foams. The multiphase formalism is used to model the dry aqueous foam as a dense non-equilibrium two-phase medium as well as its interaction with the high explosion detonation products. New experiments have been performed to study the mass scaling effects. The experimental as well as the numerical results, which are in good agreement, show that more than an order of magnitude reduction in the peak overpressure ratio can be achieved. The positive impulse reduction is less marked than the overpressures. The Hopkinson scaling is also found to hold particularly at larger scales for these two blast parameters. Furthermore, momentum and heat transfers, which have the main dominant role in the mitigation process, are shown to modify significantly the classical blast wave profile and thereafter to disperse the energy from the peak overpressure due to the induced relaxation zone. In addition, the velocity of the fireball, which acts as a piston on its environment, is smaller than in air. Moreover, the greater inertia of the liquid phase tends to project the aqueous foam far from the fireball. The created gap tempers the amplitude of the transmitted shock wave to the aqueous foam. As a consequence, this results in a lowering of blast wave parameters of the two-phase spherical decaying shock wave.

Experiments on the Richtmyer-Meshkov Instability with an Imposed, Random Initial Perturbation

Abstract: A vertical shock tube is used to perform experiments on the Richtmyer–Meshkov instability with a three-dimensional random initial perturbation. A membraneless flat interface is formed by opposed gas flows in which the light and heavy gases enter the shock tube from the top and from the bottom of the shock tube driven section. An air/SF $$_{6}$$ gas combination is used and a Mach number $$ M = 1.2$$ incident shock wave impulsively accelerates the interface. Initial perturbations on the interface are created by vertically oscillating the gas column within the shock tube to produce Faraday waves on the interface resulting in a short wavelength, three-dimensional perturbation. Planar Mie scattering is used to visualize the flow in which light from a laser sheet is scattered by smoke seeded in the air, and image sequences are captured using three high-speed video cameras. Measurements of the integral penetration depth prior to reshock show two growth behaviors, both having power law growth with growth exponents in the range found in previous experiments and simulations. Following reshock, all experiments show very consistent linear growth with a growth rate in good agreement with those found in previous studies.

The elastic–plastic behaviour of foam under shock loading

Abstract: An experimental investigation of the elastic–plastic nature of shock wave propagation in foams was undertaken. The study involved experimental blast wave and shock tube loading of three foams, two polyurethane open-cell foams and a low-density polyethylene closed-cell foam. Evidence of precursor waves was observed in all three foam samples under various compressive wave loadings. Experiments with an impermeable membrane are used to determine if the precursor wave in an open-cell foam is a result of gas filtration or an elastic response of the foam. The differences between quasi-static and shock compression of foams is discussed in terms of their compressive strain histories and the implications for the energy absorption capacity of foam in both loading scenarios. Through a comparison of shock tube and blast wave loading techniques, suggestions are made concerning the accurate measurements of the principal shock Hugoniot in foams.

Mach reflection in detonations propagating through a gas with a concentration gradient

Abstract: In accident scenarios where detonations can occur a concentration gradient constitutes a more realistic initial condition than a perfectly homogeneous mixture. In this paper, the influence of a concentration gradient on detonation front shape, detonation instabilities and pressure distribution is studied. First, a simple method to determine the front shape from a given fuel distribution is presented. It is based on Huygens’ principle and includes a correction to satisfy the boundary conditions on the enclosing walls. Next, the presented highly resolved Euler computations demonstrate the influence of a concentration gradient on detonation instabilities. In configurations with a strong concentration gradient, Mach reflection occurs and leads to an asymmetric pressure load on the enclosing geometry. In this case, the impulse on the wall is higher than in configurations with homogeneous fuel distribution, although the fuel content is much lower.

Theoretical development of a new surface heat flux calibration method for thin-film resistive temperature gauges and co-axial thermocouples

Abstract: This paper presents a theoretically developed and computationally demonstrated surface heat flux calibration method applicable to thin-film resistive temperature gauges and co-axial thermocouples. For this study, the physical situation of interest involves hypersonic shock-tunnel studies. For experiments instrumented with these gauges, constant thermophysical properties are assumed since small temperature variations normally occur in the short-duration run times. Extraction of the net surface heat flux is acquired by resolving a newly formulated first-kind Volterra integral equation that contains calibration data. The proposed calibration method is based on an inverse approach which contrasts system identification methods. Several key advantages to this approach are discussed and demonstrated in the context of these gauges. Advantages of the proposed approach include (a) only one unknown “regularization” parameter is required; (b) estimation of the optimal regularization parameter is systematically and theoretically developed and demonstrated through the energy residuals, (c) computational coding is minimal and computer run times are short, and (d) results indicate robustness, stability and accuracy in the methodology. This calibration formulation and its subsequent regularized numerical method do not explicitly require the thermal effusivity, $$\sqrt{\rho C k}$$ owing to its input–output based derivation.

Rapid compaction of granular material: characterizing two- and three-dimensional mesoscale simulations

Abstract: There have been a variety of numeric and experimental studies investigating the dynamic compaction behavior of heterogeneous materials, including loose dry granular materials. Mesoscale simulations have been used to determine averaged state variables such as particle velocity or stress, where multiple simulations are capable of mapping out a shock Hugoniot. Due to the computational expense of these simulations, most investigators have limited their approach to two-dimensional formulations. In this work we explore the differences between two- and three-dimensional simulations, as well as investigating the effect of stiction and sliding grain-on-grain contact laws on the dynamic compaction of loose dry granular materials. This work presents both averaged quantities as well as distributions of stress, velocity and temperature. The overarching results indicate that, with careful consideration, two- and three-dimensional simulations do result in similar averaged quantities, though differences in their distributions exist. These include differences in the extreme states achieved in the materials.

Laser ignition of hypersonic air–hydrogen flow

Abstract: An experimental investigation of the behaviour of laser-induced ignition in a hypersonic air–hydrogen flow is presented. A compression-ramp model with port-hole injection, fuelled with hydrogen gas, is used in the study. The experiments were conducted in the T-ADFA shock tunnel using a flow condition with a specific total enthalpy of 2.5 MJ/kg and a freestream velocity of 2 km/s. This study is the first comprehensive laser spark study in a hypersonic flow and demonstrates that laser-induced ignition at the fuel-injection site can be effective in terms of hydroxyl production. A semi-empirical method to estimate the conditions in the laser-heated gas kernel is presented in the paper. This method uses blast-wave theory together with an expansion-wave model to estimate the laser-heated gas conditions. The spatially averaged conditions found with this approach are matched to enthalpy curves generated using a standard chemical equilibrium code (NASA CEA). This allows us to account for differences that are introduced due to the idealised description of the blast wave, the isentropic expansion wave as well as thermochemical effects.

Background-oriented schlieren diagnostics for large-scale explosive testing

Abstract: Experimental measurements of shock wave propagation from explosions of C4 are presented. Each test is recorded with a high-speed digital video camera and the shock wave is visualized using background-oriented schlieren (BOS). Two different processing techniques for BOS analysis are presented: image subtraction and image correlation. The image subtraction technique is found to provide higher resolution for identifying the location of a shock wave propagating into still air. The image correlation technique is more appropriate for identifying shock reflections and multiple shock impacts in a region with complex flow patterns. The optical shock propagation measurements are used to predict the peak overpressure and overpressure duration at different locations and are compared to experimental pressure gage measurements. The overpressure predictions agree well with the pressure gage measurements and the overpressure duration prediction is within an order of magnitude of the experimental measurements. The BOS technique is shown to be an important tool for explosive research which can be simply incorporated into typical large-scale outdoor tests.

Spherical combustion clouds in explosions

Abstract: This study explores the properties of spherical combustion clouds in explosions. Two cases are investigated: (1) detonation of a TNT charge and combustion of its detonation products with air, and (2) shock dispersion of aluminum powder and its combustion with air. The evolution of the blast wave and ensuing combustion cloud dynamics are studied via numerical simulations with our adaptive mesh refinement combustion code. The code solves the multi-phase conservation laws for a dilute heterogeneous continuum as formulated by Nigmatulin. Single-phase combustion (e.g., TNT with air) is modeled in the fast-chemistry limit. Two-phase combustion (e.g., Al powder with air) uses an induction time model based on Arrhenius fits to Boiko’s shock tube data, along with an ignition temperature criterion based on fits to Gurevich’s data, and an ignition probability model that accounts for multi-particle effects on cloud ignition. Equations of state are based on polynomial fits to thermodynamic calculations with the Cheetah code, assuming frozen reactants and equilibrium products. Adaptive mesh refinement is used to resolve thin reaction zones and capture the energy-bearing scales of turbulence on the computational mesh (ILES approach). Taking advantage of the symmetry of the problem, azimuthal averaging was used to extract the mean and rms fluctuations from the numerical solution, including: thermodynamic profiles, kinematic profiles, and reaction-zone profiles across the combustion cloud. Fuel consumption was limited to $$\sim $$ 60–70 %, due to the limited amount of air a spherical combustion cloud can entrain before the turbulent velocity field decays away. Turbulent kinetic energy spectra of the solution were found to have both rotational and dilatational components, due to compressibility effects. The dilatational component was typically about 1 % of the rotational component; both seemed to preserve their spectra as they decayed. Kinetic energy of the blast wave decayed due to the pressure field. Turbulent kinetic energy of the combustion cloud decayed due to enstrophy $$\overline{\omega ^{2}} $$ and dilatation $$\overline{\Delta ^{2}} $$ .

Macro-mechanical modelling of blast wave mitigation in foams. Part I: review of available experiments and models

Abstract: Multiphase flows, which involve compressible or incompressible fluids with linear or nonlinear dynamics, are found in all areas of technology at all length scales and flow regimes. In this contribution, we discuss application of aqueous-foam barriers against blast wave impact. The first experiments demonstrating this behaviour were conducted in the early 1980s in free-field tests. Based on structural requirements, various foams with different blast energy contents were tested with the aim of characterizing the time history of the blast pressure reduction. A number of consistent methodologies for calculating this pressure reduction in foam are based on the effective gas flow model. For estimating the uncertainties of these methodologies, we briefly demonstrate their comparison with existing experimental data. Thereafter, we present various modifications of modelling approaches and their comparison with new results of blast wave experiments.

Formation of particle jetting in a cylindrical shock tube

Abstract: A dense, solid particle flow is numerically studied at a mesoscale level for a cylindrical shock tube problem. The shock tube consists of a central high pressure gas driver section and an annular solid powder bed with air in void regions as a driven section with its far end adjacent to ambient air. Simulations are conducted to explore the fundamental phenomena, causing clustering of particles and formation of coherent particle jet structures in such a dense solid flow. The influence of a range of parameters is investigated, including driver pressure, particle morphology, particle distribution and powder bed configuration. The results indicate that the physical mechanism responsible for this phenomenon is twofold: the driver gas jet flow induced by the shock wave as it passes through the initial gaps between the particles in the innermost layer of the powder bed, and the chaining of solid particles by inelastic collision. The particle jet forming time is determined as the time when the motion of the outermost particle layer of the powder bed is first detected. The maximum number of particle jets is bounded by the total number of particles in the innermost layer of the powder bed. The number of particle jets is mainly a function of the number of particles in the innermost layer and the mass ratio of the powder bed to the gas in the driver section, or the ratio of powder bed mass (in dimensionless form) to the pressure ratio between the driver and driven sections.

Photographic investigation into the mechanism of combustion in irregular detonation waves

Abstract: Irregular detonations are supersonic combustion waves in which the inherent multi-dimensional structure is highly variable. In such waves, it is questionable whether auto-ignition induced by shock compression is the only combustion mechanism present. Through the use of high-speed schlieren and self-emitted light photography, the velocity of the different components of detonation waves in a $${\text{ CH}}_4+2\text{ O}_2$$ mixture is analyzed. The observed burn-out of unreacted pockets is hypothesized to be due to turbulent combustion.

Flow visualization of supersonic laminar flow over a backward-facing step via NPLS

Abstract: An experimental study on a supersonic laminar flow over a backward-facing step of 5 mm height was undertaken in a low-noise indraft wind tunnel. To investigate the fine structures of Ma = 3.0 and 3.8 laminar flow over a backward-facing step, nanotracer planar laser scattering was adopted for flow visualization. Flow structures, including supersonic laminar boundary layer, separation, reattachment, redeveloping turbulent boundary layer, expansion wave fan and reattachment shock, were revealed in the transient flow fields. In the Ma = 3.0 BFS (backward-facing step) flow, by measuring four typical regions, it could be found that the emergence of weak shock waves was related to the K–H (Kelvin–Helmholtz) vortex which appeared in the free shear layer and that the convergence of these waves into a reattachment shock was distinct. Based on large numbers of measurements, the structure of time-averaging flow field could be gained. Reattachment occurred at the location downstream from the step, about 7–7.5 h distance. After reattachment, the recovery boundary layer developed into turbulence quickly and its thickness increased at an angle of 4.6°. At the location of X = 14h, the redeveloping boundary layer was about ten times thicker than its original thickness, but it still had not changed into fully developed turbulence. However, in the Ma = 3.8 flow, the emergence of weak shock waves could be seen seldom, due to the decrease of expansion. The reattachment point was thought to be near X = 15h according to the averaging result. The reattachment shock was not legible, which meant the expansion and compression effects were not intensive.

Three-dimensional cellular structure of detonations in suspensions of aluminium particles

Abstract: Recently, we have used scarce available data on the detonation cell size in suspensions of aluminium particles in air and oxygen to adjust the kinetic parameters of our two-phase model of detonations in these mixtures. The calculated detonation cell width was derived by means of two-dimensional (2D) unsteady simulations using an assumption of cylindrical symmetry of the flow in the tube. However, in reality, the detonation cells are three-dimensional (3D). In this work, we have applied the same detonation model which is based on the continuous mechanics of two-phase flows, for 3D numerical simulations of cellular detonation structures in aluminium particle suspensions in oxygen. Reasonable agreement on the detonation cell width was obtained with the aforementioned 2D results. The range of tube diameters where detonations in $$\text{ Al/O}_2$$ mixture at a given particle size and concentration would propagate in the spinning mode has been estimated (these results make a complement to our previous analysis of spinning detonations in Al/air mixtures). Coupling these results with the dependencies of detonation cell size on the mean particle diameter is of great interest for the understanding of fundamental mechanisms of detonation propagation in solid particle suspensions in gas and can help to better guide the experimental studies of detonations in aluminium suspensions. It is shown that the part of detonation wave energy used for transverse kinetic energy of both gas and particles is quite small, which explains why the propagation velocity of spinning and multi-headed detonations reasonably agrees with the ideal CJ values.

Micro-blast Waves Using Detonation Transmission Tubing

Abstract: Micro-blast waves emerging from the open end of a detonation transmission tube were experimentally visualized in this study. A commercially available detonation transmission tube was used (Nonel tube, M/s Dyno Nobel, Sweden), which is a small diameter tube coated with a thin layer of explosive mixture (HMX \(+\) traces of Al) on its inner side. The typical explosive loading for this tube is of the order of 18 mg/m of tube length. The blast wave was visualized using a high speed digital camera (frame rate 1 MHz) to acquire time-resolved schlieren images of the resulting flow field. The visualization studies were complemented by computational fluid dynamic simulations. An analysis of the schlieren images showed that although the blast wave appears to be spherical, it propagates faster along the tube axis than along a direction perpendicular to the tube axis. Additionally, CFD analysis revealed the presence of a barrel shock and Mach disc, showing structures that are typical of an underexpanded jet. A theory in use for centered large–scale explosions of intermediate strength \((10\, < \Delta {p}/{p}_0 \lesssim \, 0.02)\) gave good agreement with the blast trajectory along the tube axis. The energy of these micro-blast waves was found to be \(1.25 \pm 0.94\) J and the average TNT equivalent was found to be \(0.3\). The repeatability in generating these micro-blast waves using the Nonel tube was very good \((\pm 2~\%)\) and this opens up the possibility of using this device for studying some of the phenomena associated with muzzle blasts in the near future.

On some conditions for detonation initiation downstream of a perforated plate

Abstract: An experimental study is presented of the influence of detonation wave parameters and detonation product composition upstream of a perforated plate on the onset of detonation downstream. Experiments were performed in detonation tube 106 mm in diameter, separated into two sections by a perforated plate combined with a diaphragm. The tube was equipped with pressure sensors and a semi-cylindrical smoked foil. Hydrogen–air mixtures with different hydrogen concentrations were used upstream and downstream of the perforated plate. It is shown for mixtures containing 25 and 34 % of hydrogen in air that the onset of detonation downstream depends on detonation parameters upstream of the perforated plate. An increase in the initial pressure upstream of the plate leads to detonation initiation immediately downstream. The variation of mixture composition upstream of a perforated plate does not affect on detonation initiation downstream under the present experimental conditions.

Model predictions of higher-order normal alkane ignition from dilute shock-tube experiments

Abstract: Shock-induced oxidation of two higher-order linear alkanes was measured using a heated shock tube facility. Experimental overlap in stoichiometric ignition delay times obtained under dilute (99 % Ar) conditions near atmospheric pressure was observed in the temperature-dependent ignition trends of n-nonane (n-C9H20) and n-undecane (n-C11H24). Despite the overlap, model predictions of ignition using two different detailed chemical kinetics mechanisms show discrepancies relative to both the measured data as well as to one another. The present study therefore focuses on the differences observed in the modeled, high-temperature ignition delay times of higher-order n-alkanes, which are generally regarded to have identical ignition behavior for carbon numbers above C7. Comparisons are drawn using experimental data from the present study and from recent work by the authors relative to two existing chemical kinetics mechanisms. Time histories from the shock-tube OH* measurements are also compared to the model predictions; a double-peaked structure observed in the data shows that the time response of the detector electronics is crucial for properly capturing the first, incipient peak near time zero. Calculations using the two mechanisms were carried out at the dilution level employed in the shock-tube experiments for lean \({({\rm {\phi}} = 0.5)}\), stoichiometric, and rich \({({\rm {\phi}} = 2.0)}\) equivalence ratios, 1230–1620 K, and for both 1.5 and 10 atm. In general, the models show differing trends relative to both measured data and to one another, indicating that agreement among chemical kinetics models for higher-order n-alkanes is not consistent. For example, under certain conditions, one mechanism predicts the ignition delay times to be virtually identical between the n-nonane and n-undecane fuels (in fact, also for all alkanes between at least C8 and C12), which is in agreement with the experiment, while the other mechanism predicts the larger fuels to ignite progressively more slowly.

Numerical simulation of shock–vortex interaction in Schardin’s problem

Abstract: Shock diffraction over a two-dimensional wedge and subsequent shock–vortex interaction have been numerically simulated using the AUSM\(+\) scheme. After the passage of the incident shock over the wedge, the generated tip vortex interacts with a reflected shock. The resulting shock pattern has been captured well. It matches the existing experimental and numerical results reported in the literature. We solve the Navier–Stokes equations using high accuracy schemes and extend the existing results by focussing on the Kelvin–Helmholtz instability generated vortices which follow a spiral path to the vortex core and on their way interact with shock waves embedded within the vortex. Vortex detection algorithms have been used to visualize the spiral structure of the initial vortex and its final breakdown into a turbulent state. Plotting the dilatation field we notice a new source of diverging acoustic waves and a lambda shock at the wedge tip.

Large Eddy simulation of turbulent hydrogen-fuelled supersonic combustion in an air cross-flow

Abstract: The main aim of this article is to provide a theoretical understanding of the physics of supersonic mixing and combustion. Research in advanced air-breathing propulsion systems able to push vehicles well beyond $$M=4$$ is of interest around the world. In a scramjet, the air stream flow captured by the inlet is decelerated but still maintains supersonic conditions. As the residence time is very short $$(\sim \!\!\mathrm{1ms})$$ , the study of an efficient mixing and combustion is a key issue in the ongoing research on compressible flows. Due to experimental difficulties in measuring complex high-speed unsteady flowfields, the most convenient way to understand unsteady features of supersonic mixing and combustion is to use computational fluid dynamics. This work investigates supersonic combustion physics in the Hyshot II combustion chamber within the Large Eddy simulation framework. The resolution of this turbulent compressible reacting flow requires: (1) highly accurate non-dissipative numerical schemes to properly simulate strong gradients near shock waves and turbulent structures away from these discontinuities; (2) proper modelling of the small subgrid scales for supersonic combustion, including effects from compressibility on mixing and combustion; (3) highly detailed kinetic mechanisms (the Warnatz scheme including 9 species and 38 reactions is adopted) accounting for the formation and recombination of radicals to properly predict flame anchoring. Numerical results reveal the complex topology of the flow under investigation. The importance of baroclinic and dilatational effects on mixing and flame anchoring is evidenced. Moreover, their effects on turbulence-scale generation and the scaling law are analysed.

Early time spectroscopic measurements during high-explosive detonation breakout into air

Abstract: Explosive breakout of PBX-9407 into air is examined using time-resolved optical spectroscopy over a period of several microseconds. Emission is monitored over the 250–700 nm range, and several atomic and molecular species are observed including atomic calcium, and copper, as well as OH and CN. Several lines and bands remain unidentified. Fits to Ca and OH spectra suggest that early time temperatures exceed 13,000 K behind the air shock and that temperature decay is fairly rapid over the first $$10\,\upmu \mathrm{s}$$ . Considering the proposed shock structure of the blast wave, it is likely that these temperatures are confined to a narrow region behind the blast wave, but nevertheless generate emission signatures that dominate the spectra at early times.

Effect of wall conditions on DDT in hydrogen–oxygen mixtures

Abstract: Detonation in ducts is usually studied assuming adiabatic walls because of the high kinetic energy due to the incoming flow being supersonic. In the present work, numerical simulations of deflagration-to-detonation transition (DDT) using a detailed chemical reaction model are performed under adiabatic and isothermal boundary conditions in a tube with no-slip walls. The results show a local explosion driving DDT, which occurs near the tube wall in the case of an adiabatic wall, but close to the flame front in the case of an isothermal wall. Furthermore, to examine the effects of a turbulent boundary layer, a simulation using the Baldwin–Lomax turbulence model is carried out. In the case of the isothermal wall, there is again a local explosion near the tube wall, which leads to detonation. In summary, the present study confirms that the boundary conditions affect the transition to detonation and that the boundary layer is a key component of DDT.

Numerical models for afterburning of TNT detonation products in air

Abstract: Afterburning occurs when fuel-rich explosive detonation products react with oxygen in the surrounding atmosphere. This energy release can further contribute to the air blast, resulting in a more severe explosion hazard particularly in confined scenarios. The primary objective of this study was to investigate the influence of the products equation of state (EOS) on the prediction of the efficiency of trinitrotoluene (TNT) afterburning and the times of arrival of reverberating shock waves in a closed chamber. A new EOS is proposed, denoted the Afterburning (AB) EOS. This EOS employs the JWL EOS in the high pressure regime, transitioning to a Variable-Gamma (VG) EOS at lower pressures. Simulations of three TNT charges suspended in a \(26\,\hbox {m}^3\) explosion chamber were performed. When compared to numerical results using existing methods, it was determined that the Afterburning EOS delays the shock arrival times giving better agreement with the experimental measurements in the early to mid time. In the late time, the Afterburning EOS roughly halved the error between the experimental measurements and results obtained using existing methods. Use of the Afterburning EOS for products with the Variable-Gamma EOS for the surrounding air further significantly improved results, both in the transient solution and the quasi-static pressure. This final combination of EOS and mixture model is recommended for future studies involving afterburning explosives, particularly those in partial and full confinement.

High Energy Concentration by Symmetric Shock Focusing

Abstract: High-energy concentrations in gas are achieved experimentally in a specially constructed shock tube facility at KTH Mechanics. The high-energy concentration is manifested by a formation of a hot, light-emitting gas core. Experimental, numerical and theoretical investigations show that the shape of the imploding shock is of pivotal importance for the final energy concentration. Cylindrical shocks are unstable. Symmetric polygonal shocks are shown to be dynamically stable and are produced by various methods, e.g. thin wing profiles placed radially in the test section. Such symmetric polygonal shocks are able to produce extremely high energy levels at the focal point. Spectral data from 60 nanosecond short intervals of 8 microsecond light pulse give temperatures in the range of 6,000 K.

Parametric study of double cellular detonation structure

Abstract: A parametric numerical study is performed of a detonation cellular structure in a model gaseous explosive mixture whose decomposition occurs in two successive exothermic reaction steps with markedly different characteristic times. Kinetic and energetic parameters of both reactions are varied in a wide range in the case of one-dimensional steady and two-dimensional (2D) quasi-steady self-supported detonations. The range of governing parameters of both exothermic steps is defined where a “marked” double cellular structure exists. It is shown that the two-level cellular structure is completely governed by the kinetic parameters and the local overdrive ratio of the detonation front propagating inside large cells. Furthermore, since it is quite cumbersome to use detailed chemical kinetics in unsteady 2D case, the proposed work should help to identify the mixtures and the domain of their equivalence ratio where double detonation structure could be observed.

A comparison between constant volume induction times and results from spatially resolved simulation of ignition behind reflected shocks: implications for shock tube experiments

Abstract: The induction time measured in shock tube experiments is typically converted into kinetic data assuming that the reaction takes place in a constant volume process, thus neglecting spatial gradients. The actual process of shock ignition is, however, both time- and space-dependent; ignition takes place at a well-defined location, and subsequently a front travels, which may couple with the pressure wave that it created and forms a detonation wave behind the shock that reflects off the wall. To assess how different the actual processes are compared with the constant volume assumption, a numerical study was performed using a simplified three step chain-branching kinetic scheme. To overcome the difficulties that arise when simulating shock-induced ignition due to the initial absence of a domain filled with shocked reactive mixture, the problem is solved in a transformed frame of reference. Furthermore, initial conditions are derived from short-time asymptotics, which resolves the initial singularity. The induction times obtained using the full unsteady formulation with those of the homogeneous explosion are compared for various values of the heat release. Results for the spatially dependent formulation show that the evolution of the post-shock flow is complex, and that it leads to a gradient in induction times, after the passage of the reflected shock. For all cases simulated, thermal explosion initially occurs very close to the wall, and the corresponding induction time is found to be larger than that predicted under the constant volume assumption. As the measurement is made further away however, the actual time interval between passage of the reflected shock, and the specified pressure increase denoting ignition, decreases to a value close to zero, corresponding to that obtained along a Rayleigh line matching that of a steady ZND process (assuming a long enough tube). In situations where the constant volume assumption is expected to be weak, more accurate kinetic data will be obtained using a spatially resolved computation such as the one used in the current comparison.

Non-uniqueness of solutions in asymptotically self-similar shock reflections

Abstract: The present study addresses the self-similar problem of unsteady shock reflection on an inclined wedge. The start-up conditions are studied by modifying the wedge corner and allowing for a finite radius of curvature. It is found that the type of shock reflection observed far from the corner, namely regular or Mach reflection, depends intimately on the start-up condition, as the flow “remembers” how it was started. Substantial differences were found. For example, the type of shock reflection for an incident shock Mach number $$M=6.6$$ and an isentropic exponent $$\gamma =1.2$$ changes from regular to Mach reflection between $$44^\circ $$ and $$45^\circ $$ when a straight wedge tip is used, while the transition for an initially curved wedge occurs between $$57^\circ $$ and $$58^\circ $$ .