Spherical Blast Wave Research Articles

Analytical expressions for forces on structures due to spherical blast waves

The blast-resistant design of structures is becoming important due to the enhanced security requirements. The estimation of net forces and moments is essential to proportioning the design section of homogeneous structures such as blast-walls. The current design procedures consider the planar wave assumption, which is true when the structure is either small compared to the shock front or located very far from the explosion. Furthermore, due to the reflections of the shock waves, the structures experience reflected overpressure, which depends on the angle of incidence and incident overpressure of the shock wave front on the exposed structural surface. Under the planar wave assumption, the angle of incidence will always be normal, however, it will be significantly different from normal for spherical blast waves. Therefore, this study investigates the interaction of an unyielding straight structural surface with spherical blast waves and develops an exact solution for the blast pressures and net forces on the rigid surface. For direct design applications, the approximate closed-form approximations are also developed and compared with the exact solutions. The detailed discussions indicate that below a certain scaled distance, the planar wave solutions significantly overestimate the forces, and in those cases, the proposed closed-form approximations can be conveniently used. The applicability and limitations of the developed solution are illustrated through respective examples.

Analytical model for sound of explosives and firearms.

An analytical model is presented for approximate prediction of the waveform and the sound level spectrum of blast waves generated by explosives and firearms. The model is based on numerical results for spherical blast waves, with overpressures between 10 kPa and 100 MPa, and a nonlinear propagation theory for blast waves. The matching of the numerical results and the nonlinear propagation theory is investigated, and compared with results from the literature and results of calculations with a nonlinear propagation model. The analytical model presented here assumes a Friedlander waveform, from which formulas are derived for the 1/3-octave band spectrum of the sound exposure level. The formulas take into account the nonlinear effect of pulse broadening, and the corresponding frequency shift. For firearms, the muzzle blast levels vary in general with the emission direction, and the model takes into account an empirical directivity correction. Apart from the directivity correction, the model has no empirical parameters. The waveform and the spectrum follow directly from the explosion energy or the explosive charge mass. Model predictions are in good agreement with measurement results of explosives and firearms, with the explosive charge mass ranging from 0.4 g to 4 kg TNT.

A genuinely three-dimensional Riemann solver based on self-similar variables in curvilinear coordinates

A genuinely three-dimensional Riemann solver named MuSIC-3DC (Multidimensional, Self-similar, strongly-Interacting, Consistent, Three-dimensional, Curvilinear coordinates) in curvilinear coordinates is proposed to simulate three-dimensional complex engineering problems. Following Balsara's idea, a three-dimensional Riemann problem at each grid vertex is studied. In order to accurately capture contact discontinuities, the linear variations are assumed in the strongly-interacting zone. Also, the self-similar variables are adopted to simplify the derivation according to the self-similar evolution of the Riemann problem, and the strongly-interacting state could be determined by combining the contributions of all the two-dimensional Riemann problems at the surfaces bounded the strongly-interacting state. Besides, the one-dimensional Riemann problem at the center of each cell interface is solved by the one-dimensional HLLE scheme. After these, the numerical flux at each cell interface is obtained by assembling the three-dimensional fluxes at the vertices and the one-dimensional flux at the center of the cell interface. Several numerical test cases are simulated to validate the proposed solver. The spherical blast wave and three-dimensional Riemann problems indicate that the MuSIC-3DC scheme is capable of capturing three-dimensional self-similar flow structures accurately and suppressing the mesh imprinting phenomenon effectively. The transonic case demonstrates the MuSIC-3DC scheme's high resolution in capturing shock waves. In the hypersonic cases, the MuSIC-3DC scheme is more accurate in predicting stagnation and reattachment heating loads. Moreover, the MuSIC-3DC scheme is capable of obtaining more physical surface heating distribution by considering the information traveling both normal and transverse to the cell interfaces.

Energy quantification framework for underwater explosive loading into PVC foam cladded composite plates

This paper presents a novel approach for analyzing the effects of near-field underwater blast loading on composite marine structures. The operational requirements of these structures often expose them to blast or shock loading, which can lead to significant damage. The study focuses on the propagation of spherical blast waves and the subsequent secondary bubble collapse pulse that affects the structure under near-field underwater blast loading events. An analytical framework is developed to calculate the blast energies and structural energies during this complex loading event. The study further investigates the effect of applying a sacrificial cladding made of low-density closed-cell foam to the loading face of a composite panel. Experiments were conducted in a specialized facility to characterize the explosive-driven blast-loading and the subsequent interaction between the shock pressure front and the structure. Dynamic pressure measurements and high-speed imaging were utilized to capture the behavior of the composite panel under these extreme conditions. 3D digital image correlation was employed to analyze strain and deformation of the composite panel, while high-speed side view cameras captured the fluid-structure interaction during the blast and bubble collapse loading event. The results strongly indicate that the collapse of the explosion bubble is the dominant failure source in near-field underwater blast loadings. The analytical quantification of energy further corroborates the significant damaging effects of bubble collapse due to the buildup of after-flow energies during the bubble collapse duration. Furthermore, the inclusion of low-impedance elastic-plastic PVC foam cladding is shown to significantly mitigate the effect of blast loading on the composite structure.

Self-Similar-Structure–Based All-Speed Genuinely Two-Dimensional Riemann Solver

In this study, the low-speed asymptotic analysis of the Multidimensional, Self-Similar, Strongly Interacting, Consistent with the Second-Order Moment (MuSIC2) scheme in the low-speed limit is conducted. Based on such analysis, a controlling function is employed to control the numerical dissipation in the momentum equations at low speeds, and the All-Speed MuSIC2 (AMuSIC2) scheme is proposed in curvilinear coordinates. Systematic numerical tests are illustrated. The one-dimensional cases show that the AMuSIC2 scheme is capable of accurately capturing one-dimensional shocks, expansion waves, and contact discontinuities. The two-dimensional odd–even decoupling case indicates that the AMuSIC2 scheme is robust against the unphysical shock anomaly in capturing strong shocks. The spherical blast wave case indicates that the AMuSIC2 scheme improves the traditional one-dimensional Riemann solvers’ mesh imprinting phenomenon as the MuSIC2 scheme. The two-dimensional inviscid flow over the NACA0012 airfoil case and the low-speed Gresho vortex case suggest that the AMuSIC2 scheme improves the MuSCI2 scheme’s accuracy at low speeds remarkably. The turbulent flow over the flat plate case and the turbulent flow past the NACA4412 airfoil case also suggest that the AMuSIC2 scheme has a much higher level of accuracy at low speeds than its counterpart.

Decay behavior and internal interactions of regularly reflected spherical blast waves

Blast wave reflection is a critical area in military and infrastructure defense, converging shock dynamics, and colliding blast waves. While irregular blast reflections have garnered remarkable attention, research on regularly reflected (RR) blast waves remains comparatively limited. This study presents a detailed literature on shortcomings of post-reflection quantities of RR blast waves and aims to bridge this gap by extensively analyzing RR behaviors of spherical blast waves against a planar surface in air via numerical methods. With 31 scenarios involving a 1 kg charge and scaled distances from 0.5 to 4.0 m/kg1/3, comprehensive field data on parameters including pressure, density, and velocity were gathered using a fan-like gauge array. A dedicated program for tracking the RR shock front was developed, enabling precise trajectory detection and detailed quantitative analyses of RR wave decay. First, accurate empirical trajectory equations for RR waves were formulated along its normal axis. Second, spatial decay analysis was conducted, revealing consistent decay rates for each RR field parameter under 1 m/kg1/3 and diminishing decay rates beyond this threshold. Third, parameter profiles preceding RR shock fronts at various post-reflection distances were examined, while discrepancies and complexities against generalized profiles were uncovered. Qualitatively, this study identified four internal interactions within the reflection phenomenon, categorized by scaled distance ranges, and elucidated the secondary wave's impact on RR wave propagation. The comprehensive quantitative and qualitative findings in this work offer profound insights into blast wave dynamics, addressing several gaps on RR blast wave behaviors and laying a foundation for understanding more complex blast reflection phenomena crucial in various domains.

Material effects on dynamics in triple-nozzle gas-puff Z pinches.

The gas-puff Z pinch has a long history with myriad applications as an efficient neutron or x-ray source. Its simplicity as a load configuration makes it suitable for studying fundamental plasma physics phenomena such as instabilities and energy transport. For example, the implosion of cylindrical shells onto a fusion fuel are inherently susceptible to instability growth on their external surfaces; if such instabilities are unmitigated, then the consequences in terms of degraded performance can be substantial. Similarly, mitigating heat transport from a hot fuel to its colder surrounding container can make fusion conditions more easily achievable. Here we have conducted a systematic study of triple-nozzle (outer liner, inner liner, fuel) gas puffs using two-dimensional (2D) magnetohydrodynamic simulations to investigate the effect of load material on the relevant dynamics. Analogous to past studies on spherical blast waves and converging shock waves, a trend emerges linking increased radiative cooling, lower adiabatic index, and increased magneto-Rayleigh-Taylor instability growth. Notably, our results suggest that, for the present configuration, Ar radiates less than both Ne and Kr during the early stages of the implosion while mass is being swept up and perturbations begin to seed instability growth. Consequently, pinches with Ar on the outer surface exhibit more stable 2D behavior. Here we also present a parameter scan of thermonuclear neutron yield, Y, as a function of peak current, I_{pk} and dopant concentration with Ne or Ar, depending on the inner liner material. Above 6 MA, our results suggest Y∝I_{pk}^{5} and even substantial mixing (10% by volume) of Ne into the fuel does not drastically reduce yield, suggesting an Ar/Ne/fuel configuration may reliably achieve DD thermonuclear yields of 10^{13}-10^{14}/cm in the 10-20 MA range.

CFD analysis of large-scale hydrogen detonation and blast wave overpressure in partially confined spaces

The effect of confinement on the magnitude of overpressure due to a gaseous detonation of a hydrogen-air mixture was studied with the aid of numerical simulations. A simplified combustion reaction kinetic model applied along with computational fluid dynamics (CFD) allowed for the numerical simulation of large-scale detonations of hydrogen-air mixtures. The model was validated against experimental data reported in the literature for the case of a large-scale (300 m3) surface (unconfined space) detonation of a hydrogen-air mixture and the results of a hydrogen-air (confined space) detonation test performed in a 263 m3 tunnel facility. The predicted overpressure and detonation velocity was in agreement with the measurements in both unconfined and confined detonation cases. To verify the effect of confinement on the magnitude of the blast wave overpressure due to detonation of a combustible gas cloud, a series of CFD simulations of hydrogen detonations followed by propagation of a non-reactive blast wave in various geometries were carried out. The results were compared with the correlation applicable for unconfined detonations, which was also found to be applicable for partially confined detonations after the transformation of the distance from explosion centre to spherical blast wave equivalent radius.

Propagation of spherical weak blast waves over rough periodic surfaces

Propagation of spherical weak blast waves over rough periodic surfaces

Study of particle lifting mechanisms in an electrostatic discharge plasma

Although particle-laden electrostatic discharges are widely used in research as well as in industrial applications, the mechanisms of particle lifting for a particle initially at rest in such highly unsteady flows are not well understood. A multiphase plasma flow is modeled by solving the continuum conservation equations and particles as discrete entities in a Lagrangian approach. The gas phase solver is used to study the generation of shock waves and the high temperature plasma kernel. A one-way coupling approach between the two phases is used and various Lagrangian sub-models are developed to study the particle phase evolution in the system. Comparison with shock tube measurements where a planar shock wave perpendicular to the shock tube wall interacts with particles residing on the wall showed that the predominant mechanism of particle lifting is the Saffman force generated on particles due to velocity gradients in the gas boundary layer. A second configuration with an overhead spherical blast wave generated by an electrostatic discharge (ESD) interacting with a polydisperse distribution of spherical particles placed at three wall-electrode distances was considered. The predicted particle lifting heights and velocities are found to compare well with measurements in an ESD configuration initiated by the dielectric breakdown of ambient air.

WENO interpolation for Lagrangian particles in highly compressible flow regimes

Lagrangian particles can be used either to analyze different complex flows, as massless tracers, or to model multiphase flows, as particles with mass. As particles can have arbitrary positions within the computational domain, interpolation of different flow quantities from the Eulerian grid is essential. Low-order centered interpolation schemes generally do not provide a sufficient level of accuracy for many flow configurations of interest. Thus, typically, high-order centered interpolation schemes are utilized. The current study demonstrates that for highly compressible non-reacting and reacting flow regimes, in which discontinuities in the flow field, e.g., shock waves arise, centered interpolation schemes tend to smear the shock and high order schemes also produce numerical oscillations. It is shown that this problem can be remedied by using Weighted-Essentially-Non-Oscillatory (WENO) interpolation schemes. Extensive numerical tests are performed in order to demonstrate this, comparing the performance of WENO-3 and WENO-5 interpolation schemes with a variety of centered interpolation schemes. The first test case involves specially designed steady state two-dimensional vortex flows. For a smooth flow, WENO schemes provide comparable accuracy to other high-order centered schemes. For flow fields with discontinuities, WENO-3 and WENO-5 interpolation schemes can decrease the interpolation error by more than two and three orders of magnitude, respectively, in comparison with centered schemes. Solution accuracy is further studied with a normal shock wave test. It is demonstrated that centered schemes tend to smear the shock, whereas, WENO schemes capture it in a much sharper manner. Moreover, high-order centered schemes tend to oscillate in the vicinity of the discontinuity leading to non-physical results, such as negative absolute pressure values. The same trends are retained for an unsteady three-dimensional spherical blast wave, where the shock is smeared across several grid cells, which is typical for shock-capturing flow solvers. Finally, the benefits of WENO schemes for the Lagrangian-particle tracking analysis of highly compressible reactive flows are explored by comparing various Lagrangian particle trajectories and joint probability density functions (PDFs) for a two-dimensional cellular detonation. The results indicate that high-order centered schemes lead to unphysical results, whereas WENO schemes can provide high-order interpolation that is free of severe numerical oscillations and non-physical artifacts, which is critical for the proper analysis of the flow.

ALMA, ATCA, and Spitzer Observations of the Luminous Extragalactic Supernova SN 1978K

Abstract Only three extragalactic supernovae have been detected at late times at millimeter wavelengths: SN 1987A, SN 1978K, and SN 1996cr. SN 1978K is a remarkably luminous Type IIn supernova that remains bright at all wavelengths 40 years after its explosion. Here, we present Atacama Large Millimeter/submillimeter Array (ALMA) observations taken in 2016 using Bands 3, 4, 6, and 7 that show a steepening in the spectrum. An absorbed single power-law model broadly fits all of the radio and millimeter observations, but would require significant chromatic variability. Alternatively, a broken power law fits the radio-millimeter spectrum; this can be explained using an ultra-relativistic spherical blast wave in a wind scaling with a cooling break, as in a gamma-ray burst afterglow. Using updated Australia Telescope Compact Array light curves, we show that the non-thermal radio continuum continues to decay as t −1.53; in the fireball model, this independently defines the power-law indices found in the radio-millimeter spectrum. Supernovae such as SN 1978K might be important contributors to the universal dust budget: only SN 1978K was detected in a search for warm dust in supernovae in the transitional phase (age 10–100 yr). Using Spitzer Space Telescope observations, we show that at least some of this dust emission has been decaying rapidly as t −2.45 over the past decade, suggesting it is being destroyed. Depending on the modeling of the synchrotron emission, the ALMA observations suggest there may be emission from a cold dust component.

Attenuation of Shock Waves in Bubbly Media

Experiments on the attenuation of spherical shock waves were carried out in a vessel and a shock tube filled with a two-phase gas babble–water mixture with a gas volume fraction of β = 2.3–26%. The attenuation of the spherical blast wave generated by a charge directly into a two-phase medium proved to be more effective than in the case of using bubble screens. Experiments have shown that, at β = 2.3%, the intensity of spherical shock waves decreases 20-fold, whereas at β = 26%, by a factor of 40–50. A bubble layer enhances the dynamic effect on the barrier for extended waves and weakens it in the case of short-pulse disturbances. The degree of attenuation or amplification of the blast wave depends on the thickness of the layer, pulse duration, and volume fraction of bubbles.

Asymptotic scaling laws and semi-similarity solutions for a finite-source spherical blast wave

A spherical blast wave generated by a sudden release of a sphere of compressed gas is an important model problem to understand blast phenomena such as volcanic eruptions and explosive detonations. The resulting explosion flow physics, such as the instability at the gas contact discontinuity and the interaction between the shock wave and the gas contact, are dictated by the initial pressure and sound-speed ratios between the compressed gas and the ambience. Since the initial pressure and sound-speed ratios vary over a wide range in practical applications, it is of interest to investigate the scaling laws and similarity solutions for the spherical symmetric explosion flow. In the present study, numerical simulation of a spherical blast wave is performed. A long-term length scale that incorporates the initial charge radius and the initial pressure ratio is introduced. The trajectories of the main shock normalized by the long-term length scale for a wide range of parameters collapse after a short transition time, indicating an asymptotic similarity solution exists for the far field in the long term. With the assistance of this similarity solution, the full evolution of the main shock can be obtained semi-analytically. For near-field features, i.e. the gas contact and the secondary shock wave, only semi-similarity solutions are observed, which depend on the initial sound-speed ratio but not the initial pressure ratio. The gas contact and the secondary shock share the same scaling relations. Asymptotic analysis is performed to obtain the short-term dynamics of the gas contact, including the gas contact acceleration and the Atwood number, which are the key parameters determining the Rayleigh–Taylor instability development at the gas contact. The asymptotic contact radius as$t\rightarrow \infty$is also obtained, which is found to be well represented by the long-term length scale and thus only depends on the initial pressure ratio. A simple model of an oscillating bubble is employed to explain the scaling relation of the asymptotic gas contact radius.

Simulation and scaling analysis of a spherical particle-laden blast wave

A spherical particle-laden blast wave, generated by a sudden release of a sphere of compressed gas–particle mixture, is investigated by numerical simulation. The present problem is a multiphase extension of the classic finite-source spherical blast-wave problem. The gas–particle flow can be fully determined by the initial radius of the spherical mixture and the properties of gas and particles. In many applications, the key dimensionless parameters, such as the initial pressure and density ratios between the compressed gas and the ambient air, can vary over a wide range. Parametric studies are thus performed to investigate the effects of these parameters on the characteristic time and spatial scales of the particle-laden blast wave, such as the maximum radius the contact discontinuity can reach and the time when the particle front crosses the contact discontinuity. A scaling analysis is conducted to establish a scaling relation between the characteristic scales and the controlling parameters. A length scale that incorporates the initial pressure ratio is proposed, which is able to approximately collapse the simulation results for the gas flow for a wide range of initial pressure ratios. This indicates that an approximate similarity solution for a spherical blast wave exists, which is independent of the initial pressure ratio. The approximate scaling is also valid for the particle front if the particles are small and closely follow the surrounding gas.

Experimental and numerical investigation of v-shape plates subjected to blast loadings

This paper presents the experimental and numerical investigation of angled shape metal plates response when subjected to an air blast loading. V shaped plates were fabricated at angles of 90o, 120o and 150o respectively. The charge weight of 1 kg (PE4) was used to create a spherical blast wave at several standoff configurations. The experimental results were then compared with the numerical simulation model computed using LSDYNA3D.

Experimental and numerical investigation on blast wave propagation in soil structure

This paper presents a study on blast wave propagation in a soil structure when subjected to a surface air blast loading. The experimental work utilized the use of plastic explosive of 1 kg weight (PE4) in order to create a spherical blast wave at a fixed standoff distance. The experimental results were then compared with the numerical simulation model computed using LSDYNA3D. Although the computed simulation and experimental results showed large difference in terms of values, but both results provide a similar trend in terms of blast peak overpressure.

Astrophysical fluid dynamics

These lecture notes and example problems are based on a course given at the University of Cambridge in Part III of the Mathematical Tripos. Fluid dynamics is involved in a very wide range of astrophysical phenomena, such as the formation and internal dynamics of stars and giant planets, the workings of jets and accretion discs around stars and black holes and the dynamics of the expanding Universe. Effects that can be important in astrophysical fluids include compressibility, self-gravitation and the dynamical influence of the magnetic field that is ‘frozen in’ to a highly conducting plasma. The basic models introduced and applied in this course are Newtonian gas dynamics and magnetohydrodynamics (MHD) for an ideal compressible fluid. The mathematical structure of the governing equations and the associated conservation laws are explored in some detail because of their importance for both analytical and numerical methods of solution, as well as for physical interpretation. Linear and nonlinear waves, including shocks and other discontinuities, are discussed. The spherical blast wave resulting from a supernova, and involving a strong shock, is a classic problem that can be solved analytically. Steady solutions with spherical or axial symmetry reveal the physics of winds and jets from stars and discs. The linearized equations determine the oscillation modes of astrophysical bodies, as well as their stability and their response to tidal forcing.

Spherical explosion with a central energy source

Abstract We present a novel semi-analytic solution that describes the propagation of a spherical blast wave driven by a central energy source. The initial density profile has a power-law function of the distance from the center and the energy is injected only into the central region at a rate given by a power-law function of time. This solution is composed of three regions separated by the contact surface and the shock front. The innermost region is assumed to be uniform and the outside of the contact surface includes the shocked matter described by self-similar solutions. We analytically derive the applicable range of parameters of this solution from requirements needed to satisfy the boundary conditions. We perform numerical simulations for flows with various values of parameters, some of which reside out of the thus-derived applicable range, and compare the results with the semi-analytic solutions.

SELF-SIMILAR ULTRARELATIVISTIC JETTED BLAST WAVE

Following a suggestion that a directed relativistic explosion may have a universal intermediate asymptotic, we derive a self-similar solution for an ultra-relativistic jetted blast wave. The solution involves three distinct regions: an approximately paraboloid head where the Lorentz factor $\gamma$ exceeds $\sim1/2$ of its maximal, nose value; a geometrically self-similar, expanding envelope slightly narrower than a paraboloid; and an axial core in which the (cylindrically, henceforth) radial flow $u$ converges inward towards the axis. Most ($\sim 80\%$) of the energy lies well beyond the leading, head region. Here, a radial cross section shows a maximal $\gamma$ (separating the core and the envelope), a sign reversal in $u$, and a minimal $\gamma$, at respectively $\sim 1/6$, $\sim1/4$, and $\sim3/4$ of the shock radius. The solution is apparently unique, and approximately agrees with previous simulations, of different initial conditions, that resolved the head. This suggests that unlike a spherical relativistic blast wave, our solution is an attractor, and may thus describe directed blast waves such as in the external shock phase of a $\gamma$-ray burst.