Converging Shock Waves Research Articles

On the focusing effect and interfacial evolution of incident shock waves impinging on double-layer nested heavy gas bubbles

A detailed numerical study about the planar incident shock wave impinging on heavy bubbles with different components and nested structures was conducted. Results show that the shock wave convergence occurs when the incident shock wave impinging on the pure SF6 bubble or CO2-SF6 nested bubbles, which triggers the shock wave focusing and obtains a high transient pressure. Changing the nested position and radius of the SF6 bubble in CO2-SF6 nested bubbles will change the interactional time and relative position of waves to affect the shock wave focusing time and peak pressure. Specifically, the shock wave focusing effect is enhanced, and the peak pressure is increased when the inner bubble is drifted downstream, high density, and larger sized. Thus, the later the shock wave focusing occurs, the higher the transient maximum pressure. The shock wave focusing process of double-layer nested bubbles is presented as follows: the new small shock wave (SS) formed by the intersection between the incident transmitted shock wave and the transmitted shock wave and another new shock wave formed by the collision of diffracted transmitted shock waves move in opposite directions to squeeze the undisturbed region and finally produce a high instantaneous pressure, where SS plays a major role in shock wave focusing. Further, the greater the intensity and velocity of focusing shock waves, the stronger the focusing effect and the higher the transient pressure.

Study on load characteristics and structural impact response propagation law of cabin internal explosion

Aiming at the problem that the distribution of explosion load in the cabin and the propagation law of structural impact response was unclear, this paper established the numerical calculation model of explosion in a closed cabin by ALE (Arbitrary Lagrangian Eulerian) method. There was an apparent convergence of shock waves at the cabin's corners, and the pressure relief hole's area and its position significantly affected the peak of quasi-static pressure. The peak acceleration of the deck structure decreased exponentially as the distance from the location of charge increased. Peak acceleration decreased by approximately 50% for each bulkhead crossing. There was a “paper window effect” during the cabin interior explosion on the whole ship. It meant there was a limit to the value for the energy generated by the explosion to be transmitted along the frame structure. When the charge was 150 kg, it reached the limit of the energy transferred by the structure in this paper. The response of the distant structure did not change significantly with the increase in the charge quality. The research revealed the impact response propagation mechanism in the structure and provided a reference for designing protective structures.

Kinks on elliptical convergent shock waves in hypersonic flow

Kinks commonly appear on the convergent shock surface when an internal conical flow deviates from the axisymmetric state. In this paper, the formation mechanisms of kinks on internal conical shocks (ICSs) generated by elliptical ring wedges with typical entry aspect ratios ( $AR{\rm s}$ ) in a Mach 6 flow are revealed using a theoretical method, in which the spatial evolution of the three-dimensional elliptical ICS is converted into a temporal evolution of a two-dimensional elliptical moving shock (EMS) using the hypersonic equivalence principle. To simultaneously track the shock front of the EMS and the disturbances propagating along it, a front-disturbance tracking method (FDTM) based on geometrical shock dynamics is proposed. It is found that the shock–compression disturbances from the same family initially near the major axis catch up with the disturbance initially emitted from the major axis to form kinks on the EMS. The equivalent kink formation positions predicted by the FDTM always lag behind the real kink formation positions on the elliptical ICS because the applicability of the hypersonic equivalence principle decays as the shock strengthens along the incoming flow direction. The accuracy of the equivalent kink formation positions predicted by the FDTM gradually declines with the reduction in $AR$ , but it can be significantly improved for all $AR{\rm s}$ after a modification of the equivalent relationship using the shock angle in the major plane of the elliptical ICS, which provides a new way to solve the kinks on the elliptical ICS.

Self-excited converging shock structure in a complex plasma medium.

We report the study of a self-excited converging shock structure observed in a complex plasma medium. A high-density dust cloud of melamine formaldehyde particles is created and horizontally confined by a circular ring in a dc glow discharge plasma at a particular discharge voltage and pressure. Later, as the discharge voltage is increased, a circular density crest is spontaneously generated around the outer boundary of the dust cloud. This nonlinear density structure is seen to propagate inward towards the center of the dust cloud. The properties of the excited structure are analyzed and found to follow the characteristics of a converging shock structure. A three-dimensional molecular dynamics simulation has also been performed in which a stable dust cloud is formed and levitated by the balance of forces due to gravity and an external electric field mimicking the cathode sheath electric field in the experiment. Particles are also horizontally confined by an external electric field, representing the sheath electric field of the circular ring present in the experiment. A circular shock structure has been excited by applying an external perturbation in the horizontal electric field around the outer boundary of the dust cloud. The characteristic properties of the shock are analyzed in the simulation and qualitatively compared with the experimental findings. This paper is not only of fundamental interest but has many implications concerning the study of converging shock waves excited in other media for various potential applications.

Numerical investigation of the interaction between a converging shock wave and an offset cylindrical bubble containing different gases

A numerical study investigating the interaction process between a converging shock wave and a gas bubble placed at an offset location is presented. As a first step, for proofing the reliability of the used numerical scheme, a simulation of relevant available experimental findings of Hosseini and Takayama [“Richtmyer–Meshkov instability induced by cylindrical shock wave loading of cylindrical gaseous inhomogeneities,” AIAA Paper No. 2000-2464, 2000] and Hosseini and Takayama [“Study of a converging shock wave interaction with a gaseous interfaces in an eccentric arrangement,” in Japanese Symposium on Shock Waves, 2000] is conducted; the tested gases were helium (He) and sulfur hexafluoride (SF6). The converging shock wave had a Mach number of 1.18 prior to its impact on the 50 mm diameter gas bubble. Achieving good agreement with the experimental findings ensures the reliability of the applied numerical scheme. After the converging shock wave impacted the gas bubble, different shock waves are created. These shock waves propagate differently than those observed in the case of planar shock wave impacting a cylindrical gas bubble or that of a converging shock wave where the gas bubble is located at the center. Furthermore, once the converging shock wave converged, a diverging shock wave expands and again impacts the remaining gas bubble, thus creating more complex shock wave patterns. The gas contained inside the bubble has an effect on the location of the converging shock wave focus point. In the case of the heavy gas SF6, the focus point is near the center of the converging shock wave, but in the case of light gas He, it is offset from the converging shock wave focus point and outside of the initial location of the He bubble. The new results from the current numerical simulation include more detailed results for both bubbles, which were not reported in Hosseini and Takayama [“Richtmyer–Meshkov instability induced by cylindrical shock wave loading of cylindrical gaseous inhomogeneities,” AIAA Paper No. 2000-2464, 2000] and Hosseini and Takayama [“Study of a converging shock wave interaction with a gaseous interfaces in an eccentric arrangement,” in Japanese Symposium on Shock Waves, 2000]. In addition, a shock wave focusing of the transmitted shock wave inside the SF6 bubble is observed. This later creates a secondary diverging shock wave. Higher pressure is achieved in the SF6 case.

Formation of microbands in copper under loading by spherically converging shock waves

Formation of microbands in copper under loading by spherically converging shock waves

Convergent Richtmyer–Meshkov instability on two-dimensional dual-mode interfaces

We report the first shock-tube experiments on two-dimensional dual-mode air–SF $_6$ interfaces with different initial spectra subjected to a convergent shock wave. The convergent shock tube is specially designed with a tail opening to highlight the Bell–Plesset (BP) and mode-coupling effects on amplitude development of fundamental mode (FM). The results show that the BP effect promotes the occurrence of mode coupling, and the feedback of high-order modes to the FM also arises earlier in convergent geometry than that in its planar counterpart. Relatively, the amplitude growth of the FM with a higher mode number is inhibited by the feedback, and saturates earlier. The FM with a lower mode number is affected more heavily by the BP effect, and finally dominates the flow. A new model is proposed to well predict the amplitude growths of the FM and high-order modes in convergent geometry. In particular, for FM that reaches its saturation amplitude, the post-saturation relation is introduced in the model to achieve a better prediction.

Hydrodynamic instabilities of a dual-mode air–SF6 interface induced by a cylindrically convergent shock

Shock-tube experiments are performed on the convergent Richtmyer–Meshkov (RM) instability of a multimode interface. The temporal growth of each Fourier mode perturbation is measured. The hydrodynamic instabilities, including the RM instability and the additional Rayleigh–Taylor (RT) effect, imposed by the convergent shock wave on the dual-mode interface, are investigated. The mode-coupling effect on the convergent RM instability coupled with the RT effect is quantified. It is evident that the amplitude growths of all first-order modes and second-order harmonics and their couplings depend on the variance of the interface radius, and are influenced by the mode-coupling from the very beginning. It is confirmed that the mode-coupling mechanism is closely related to the initial spectrum, including azimuthal wavenumbers, relative phases and initial amplitudes of the constituent modes. Different from the conclusion in previous studies on the convergent single-mode RM instability that the additional RT effect always suppresses the perturbation growth, the mode-coupling might result in the additional RT effect promoting the instability of the constituent Fourier mode. By considering the geometry convergence, the mode-coupling effect and other physical mechanisms, second-order nonlinear solutions are established to predict the RM instability and the additional RT effect in the cylindrical geometry, reasonably quantifying the amplitude growths of each mode, harmonic and coupling. The nonlinear solutions are further validated by simulations considering various initial spectra. Last, the temporal evolutions of the mixed mass and normalized mixed mass of a shocked multimode interface are calculated numerically to quantify the mixing of two fluids in the cylindrical geometry.

Radially symmetric non-isentropic Euler flows: Continuous blowup with positive pressure

We establish the existence of radial self-similar Euler flows in which a continuous incoming wave generates a blowup of primary (undifferentiated) flow variables. A key point is that the solutions have a strictly positive pressure field, in contrast to Guderley's classic construction of converging shock waves. In Guderley's solutions, a converging shock invades a quiescent region at zero pressure (due to vanishing temperature), and the velocity and pressure in its immediate wake become unbounded at the time of collapse. It is reasonable that the lack of upstream counter-pressure is conducive to large speeds, with concomitant large amplitudes. Based on Guderley's original solutions, it is therefore unclear if it is the zero-pressure region that is responsible for blowup. The same applies to self-similar Euler flows describing radial cavity flow. Our results demonstrate that the geometric mechanism of wave focusing is sufficiently strong on its own to drive unbounded growth. We propagate the solution beyond blowup and observe numerically that there are two distinct possibilities depending on the incoming flow: either an expanding spherical shock wave is generated, or the flow propagates in a continuous manner. Focusing on the former case, we show that the resulting flows define global admissible weak solutions to the full, multi-d compressible Euler system. These solutions have the unusual property that the flow is isentropic in each of the two regions separated by the shock.

Corner Convergence Effect of Enclosed Blast Shock Wave and High-Pressure Range

An explosion inside a cabin will converge at the corners to form high-pressure areas, significantly impacting the destruction of a bulkhead structure. This paper investigates shock wave convergence characteristics at the corners when the explosive detonates at the center of the cabin, based on a combination of the wall reflection law for shock waves and a numerical simulation method. The parameter K represents the aspect ratio of the cabin structure. This study shows that when 1 ≤ K ≤ 1.19, the high pressure at the corner is caused by the superposition of Mach waves along both wall surfaces. However, for the initial shock wave, when 1.2 < K ≤ 2, the high pressure is caused by the superposition of Mach waves along the longer wall surface and regular reflected waves on the shorter wall surface; when 2 < K, the cause are Mach waves along the longer wall surface and the corresponding positive reflection on the shorter wall surface. The influence of K on the range for the high-pressure region at the corner is also analyzed, the functional relationship between the range of the high-pressure area and K is given, and the universality is verified.

Development of an x-ray radiography platform to study laser-direct-drive energy coupling at the National Ignition Facility.

A platform has been developed to study laser-direct-drive energy coupling at the National Ignition Facility (NIF) using a plastic sphere target irradiated in a polar-direct-drive geometry to launch a spherically converging shock wave. To diagnose this system evolution, eight NIF laser beams are directed onto a curved Cu foil to generate Heα line emission at a photon energy of 8.4keV. These x rays are collected by a 100-ps gated x-ray imager in the opposing port to produce temporally gated radiographs. The platform is capable of acquiring images during and after the laser drive launches the shock wave. A backlighter profile is fit to the radiographs, and the resulting transmission images are Abel inverted to infer radial density profiles of the shock front and to track its temporal evolution. The measurements provide experimental shock trajectories and radial density profiles that are compared to 2D radiation-hydrodynamic simulations using cross-beam energy transfer and nonlocal heat-transport models.

On the mechanism of ionization of atoms at compression of a substance by front of the converging shock wave

Purpose. To study changes in the microstructure of metals after exposure to high-energy plasma jets formed by the cumulation of gas-dynamic flows in a conical target. To estimate the expected state of matter in a strong shock wave compression, taking into account the change in volumetric energy density at the moment of transformation of a solid body plasma into nuclear matter. Methodology. The technique of laser initiation of a profiled front of detonation waves in explosive charges and the corresponding profile of shock waves in materials, methods and techniques for measuring the dynamic parameters of shock-compressed substances are used. Findings. An experimental study on the physicochemical state of a substance that has been processed with extremely high pressures and temperatures during compression by converging shock waves in conical targets has been carried out. Scientific results of physical and mathematical modelling of converging shock waves are analysed. Originality. For the first time, the formation of symmetric plasma jets during gas compression in conical targets has been experimentally observed. For the first time, metallo-physical studies on the microstructure of cast iron and steel have been carried out. These studies were made after the action of high-energy dense plasma jets with a temperature of (2.52.8) × 106K and a pressure 1.12 × 1012 arising from the collision of the jet with a barrier. Iron-55 and copper-64 isotopes were found in the cast iron microstructure near the surface formed by the action of the plasma jet. The main components of the plasma jet were gaseous oxygen, nitrogen, argon, and atomic iron, copper and gold. The fact of formation of isotopes is the result of nuclear reactions. One of the main conditions for the implementation of such reactions is a dense high-temperature plasma. It is assumed that under the action of a strong shock wave in a conical target, in addition to the synthesis reaction, other nuclear reactions with heavy elements can be realized. The ideas about the expected state of matter in a compression shock wave are presented, taking into account the change in the volumetric energy density at the moment of transformation of a solid body plasma into nuclear matter. Practical value. The proposed technique for conducting experimental studies on a shock-compressed substance under the action of extreme temperatures and pressures in conical targets using laser initiation of chemical explosives is of practical importance. The idea of the expected state of matter in the shock wave is also important.

Preparation of bulk nano-aluminum materials from nanopowder using explosive consolidation

To optimize powder explosive consolidation technology, an improved explosive consolidation device capable of relieving pressure was designed. Bulk nano-aluminum materials achieving more than 98% of standard density were successfully fabricated by explosive consolidation. The effect of different detonation velocities on the properties of the consolidated aluminum was investigated by varying the ratio of the ammonium nitrate explosive (AN-TNT) and wood flour to adjust the detonation velocity. The results revealed that the production of “Mach holes” (defects produced by excess energy in a converging shock wave) can be reduced by decreasing the detonation velocity. At a detonation velocity of 2158 m/s, bulk aluminum with high density, high hardness, high strength, and uniform microstructure without any Mach holes and with a grain size of about 80 nm can be achieved. The hardness of explosively consolidated aluminum was four times that of aluminum prepared by general industrial technology, and its compressive strength double that of industrially prepared aluminum.

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.

Unbalanced distribution of electric current in underwater electrical wire array explosion

The uniformity of electric current distribution in a wire array and its unstable behavior during the process of underwater electrical explosion have been investigated. Two exploding wires in parallel were used in the experiments and the current waveforms flowing through each wire were obtained using two self-integrating coils. Significant differences in the current waveforms of the two wires were observed near the melting point, which was attributed to the non-simultaneity of heating and phase transition. Unbalanced current distribution caused by the deviations of wire dimensions was analyzed based on a magneto-hydrodynamic model, and the simulation results show that thermodynamic state difference between two wires is present throughout the entire electrical explosion process. It is also found that the initial stored energy of pulse generator will affect the thermodynamic state evolution of exploding wires, resulting in different behaviors of current distribution after the explosion time. The slightly different heating rate caused by unbalanced current distribution in a wire array can break the symmetry of converging shock waves and lower the pressure peak in the vicinity of implosion axis, which was discussed based on the two-dimensional hydrodynamic simulations.

Evolution mechanism of double-layer heavy gas column interface with sinusoidal disturbance induced by convergent shock wave

Based on Navier-Stokes equations, combining the fifth-order weighted essentially non-oscillatory scheme with the adaptive structured grid refinement technique, the interactions between converging shock and annular SF<sub>6</sub> layers with different initial perturbation amplitudes and thickness are numerically investigated. The evolution mechanism of shock structure and interface are revealed in detail, and the variations of the circulation, mixing rate and turbulent kinetic energy are quantitatively analyzed. The dynamic mode decomposition method is used to analyze the dynamic characteristics of the vorticity. The results show that in the case with large initial perturbation amplitude, the transmitted shock wave forms Mach reflection structures both inside and outside of the inner interface of SF<sub>6</sub> layer, and multiple shock focusing phenomena occur in the center. After the transmitted shock wave penetrates the outer interface, the circulation increases faster, and the “spike” and “bubble” structure on inner interface develop faster, so that the amplitude of the inner and outer interfaces and the gas mixing rate increase. As for the case with larger thickness of the gas layer, the phase of the transmitted shock wave changes inside the layer, which forms “bubble” at the crest of the inner interface and “spike” at the trough. When the thickness of the gas layer decreases, the crest of the inner interface does not move inside after being impacted, and “spike” and “bubble” are generated in the late stage. The dynamic modes show that the main structure of vorticity and the exchange of positive and negative vorticity on the main structure are determined by the modes with weak growth and low frequency, but the modes with weak growth and high frequency determine rapid exchange of positive and negative vorticity at the interface in the cases with weak coupling effect.

Limitation in velocity of converging shock wave

The commonly applied self-similar solution of the problem of the converging shock wave (shock) evolution with constant compression of the medium behind the shock front results in an unlimited increase in the medium velocity in the vicinity of the implosion. In this paper, the convergence of cylindrical shocks in water is analyzed using the mass conservation law, when the water compression behind the shock front is a variable. The model predicts a finite range of radii, which depends on the adiabatic index of water and where the increase in pressure exceeds the sum of the change in the kinetic and internal energy densities behind the shock front. In this range of radii, only the finite increase in the shock and water flow velocities is realized.

Intensification of non-uniformity in convergent near-conical hypersonic flow

The inevitable formation of a Mach disk at the central axis of a convergent conical shock wave may suffer from fundamental changes when the flow deviates from the axisymmetric condition. In this paper, the behaviours of near-conical shocks, which are generated by a circular ring wedge of $10^{\circ }$ at typical angles of attack (AoAs), are investigated at a free stream Mach number of 6 in a shock tunnel. To reveal the characteristics and mechanism of the flow, numerical analyses are carried out under the same conditions. The results indicate that when the flow deviates from axial symmetry, the circumferential non-uniformity is remarkably intensified as the shock converges downstream. The converging centre shifts against the inclination of the incoming flow and moves to the leeward side. For a sufficiently small AoA, the formation of a Mach disk remains similar to that in the axisymmetric case, although the Mach disk shrinks in size and is slightly flattened. As the circumferential non-uniformity of the shock increases at an AoA of approximately $3^{\circ }$ , a pair of kinks separate the shock surface into two discontinuous segments with the stronger shock segment on the windward side and the weaker shock segment on the leeward side. When the AoA increases further, the shrinkage of the Mach disk continuously occurs, and the Mach disk is eventually replaced by a regular reflection. The discontinuity of a convergent shock with flattening on the separated shock segments and the insufficient strength increase during the subsequent convergence are responsible for the appearance of regular reflection.

Linear analysis of Rayleigh-Taylor instability in viscoelastic materials.

Rayleigh-Taylor instability (RTI) has become a powerful tool for determining the mechanical properties of materials under extreme conditions. In this paper, we first present the exact and approximate linear dispersion relations for RTI in viscoelastic materials based on the Maxwell and Kelvin-Voigt models. The approximate dispersion relation produces good predictions of growth rates in comparison with the exact one. The motion of the interface in Maxwell flow is mainly controlled by viscosity and elasticity dominates this behavior in Kelvin-Voigt flow. Since elasticity plays a distinct role from viscosity, cutoff wavelengths arise only in Kelvin-Voigt flow. The variation of the maximum growth rates and their corresponding wave numbers are also carefully studied. For both types of materials, viscosity suppresses the growth of instability, while elasticity speeds it up. This is at odds with the well-known understanding that elasticity suppresses hydrodynamic instabilities. The dependence of the maximum growth rate on slab thickness is also investigated for RTI in both types of flow, since the metal slab as a pusher has been extensively employed in high-energy-density physics. The model presented here allows study of more realistic situations by considering convergent effects and shock wave interactions, for the traditional potential flow theory is not suitable. To summary, it is able to provide guidances for future experimental designs for studies of materials under high strain and high strain rate conditions, as well as allow us to study RTI theoretically in more complicated conditions.

Calculation of Small Deformations of a Radially Convergent Shock Wave Inside a Cavitation Bubble

Calculation of Small Deformations of a Radially Convergent Shock Wave Inside a Cavitation Bubble