Shock Wave Research Articles

Thermal ablation of soft tissue by a single shock wave sonication of discrete foci within the given volume

New protocols have been developed for shockwave irradiation of soft tissue volumes using trajectories uniformly filled within the given shape by discrete foci, while pulsed millisecond sonication immediately formed a single ablation. The influence of the initial peak power with the same time-average power, the interfocus distance and the geometry of the external contour of the trajectory on the shape, volume and ablation rate was analyzed. The most advantageous is the saturation mode using a trajectory with an interfocus step 1.5 times greater than the transverse size of a single lesion. To obtain volumes of thermal ablation on the order of cubic centimeters, layer-by-layer sonication protocols are proposed, which allow to 2.5 times greater thermal ablation rate compared with protocols used in clinical practice. The advantage of the proposed shockwave protocols is the possibility of obtaining localized and predictable thermal damage without accompanying MRI monitoring.

Locally linearized physics-informed neural networks for Riemann problems of hyperbolic conservation laws

In this work, we demonstrate that physics-informed neural networks (PINNs) tend to propagate predicted shock wave information bidirectionally in time, which does not align with the actual evolution direction of solutions to hyperbolic conservation laws. This mismatch results in instability and hinders the reduction of the loss of governing equations, as well as the initial condition loss by the deep neural network. In order to tackle this problem, we simplify the complexity of the problem by constructing equivalent linear transport equations in the region of shock wave generation. The speeds of these linearized waves are governed by the Rankine–Hugoniot relations of conservation laws. This approach is termed the Locally Linearized PINNs method. Specifically, an appropriate shock wave detector is initially designed to identify domains where shock waves occur. Near shock waves, the original nonlinear equations are transformed into their linearized forms, thereby modifying the residual terms of the partial differential equations. Additionally, an equilibrium factor is introduced in fluid compression regions to reduce prediction errors and stabilize the training of deep neural networks. Numerical examples illustrate that Locally Linearized PINNs effectively address the challenge of predicting global solutions in PINNs and significantly improve shock-capturing performance for hyperbolic conservation laws.

An improved efficient adaptive method for large-scale multi-explosives explosion simulations

Shock wave caused by a sudden release of high-energy, such as explosion and blast, usually affects a significant range of areas. The utilization of a uniform fine mesh to capture sharp shock wave and to obtain precise results is inefficient in terms of computational resource. This is particularly evident when large-scale fluid field simulations are conducted with significant differences in computational domain size. In this work, a variable-domain-size adaptive mesh enlargement (vAME) method is developed based on the proposed adaptive mesh enlargement (AME) method for modeling multi-explosives explosion problems. The vAME method reduces the division of numerous empty areas or unnecessary computational domains by adaptively suspending enlargement operation in one or two directions, rather than in all directions as in AME method. A series of numerical tests via AME and vAME with varying nonintegral enlargement ratios and different mesh numbers are simulated to verify the efficiency and order of accuracy. An estimate of speedup ratio is analyzed for further efficiency comparison. Several large-scale near-ground explosion experiments with single/multiple explosives are performed to analyze the shock wave superposition formed by the incident wave, reflected wave, and Mach wave. Additionally, the vAME method is employed to validate the accuracy, as well as to investigate the performance of the fluid field and shock wave propagation, considering explosive quantities ranging from 1 to 5 while maintaining a constant total mass. The results show a satisfactory correlation between the overpressure versus time curves for experiments and numerical simulations. The vAME method yields a competitive efficiency, increasing the computational speed to 3.0 and approximately 120,000 times in comparison to AME and the fully fine mesh method, respectively. It indicates that the vAME method reduces the computational cost with minimal impact on the results for such large-scale high-energy release problems with significant differences in computational domain size.

Dynamic behavior and spatio-temporal mechanical characteristics of the individual cavitation bubble on hydraulic concrete wall

This study endeavors to delve into the dynamics and consequent mechanical responses induced by an individual cavitation bubble proximal to a concrete surface. Employing the laser-induced cavitation bubbles experimental method, the dynamic behavior of a cavitation bubble near horizontal smooth and locally defective concrete surfaces is systematically investigated. Using computational fluid dynamics (CFD) simulations, the impulsive pressure induced by bubble collapse within a specific surface range is quantitatively investigated. Our results reveal that the presence of local defects on the concrete surface activates gas nuclei within the defects upon bubble shock wave emission. Gas nuclei near the surface center penetrate the bubble, prolonging the bubble’s pulsation period and reducing microjet velocities. During bubble collapse, significant concentrated stresses due to microjets near the surface center may trigger instantaneous brittle failure of the concrete surface. Moreover, shock waves form high-pressure zones within a certain range of the surface. When the dimensionless distance γ ranges from 1.1 to 1.2, a superposition phenomenon of microjets and shock waves is observed, compared to individual effects, enhancing the impulse at central point below the bubble, prolonging the duration of pressure within the specific surface horizontal range, but simultaneously accelerating the pressure’s horizontal attenuation rate along the surface. Compared to the center pressure of the wall surface, the impulse of average pressure better reflects the surface’s pressure response.

Effect of pre-shock on the expanding fracture behavior of 1045 steel cylindrical shell under internal explosive loading

Explosively driven expansion fractures in metallic shells will be preceded by a compression shock wave, which inevitably changes the mechanical and microstructural state of the shell materials and thus affects their subsequent dynamic deformation and expansion fracture processes. To understand the influence of pre-shock pressure on the dynamic expansion fracture behavior of metallic shells, the incident shock waves with varying peak pressure were generated in a 1045 steel cylindrical shell by sweeping detonation wave loading. The pre-shock and subsequent expansion fracture processes were continuously diagnosed by combining a high-speed framing camera and the arrayed Photon Doppler Velocimetry (PDV) measurements to obtain the fracture strains at different axial positions (corresponding to different pre-shock pressures). The results clearly show that the pre-shock pressure during detonation loading has a significant effect on the expansion fracture properties of the 1045 steel cylinder; the fracture strain remarkably decreases with the increase of pre-shock pressure from ∼19 GPa to ∼20 GPa and then changes gently in the range of ∼20 GPa to ∼22 GPa. Metallurgical analyses reveal increased densities of microstructural defects, including dislocations and deformation twins, when a shock wave passes through, resulting in a reduced capacity for further defect storage in the shocked metals, ultimately leading to a decrease in the fracture strain during the subsequent expansion deformation process.

Non-inertial Computational Framework for Long-distance Shock-driven Object Dynamics

In the realm of dynamic separation problems, the motion of a body triggered by shock interactions is a common phenomenon. This is particularly important in terms of the safe separation of two-stage-to-orbit vehicles, where the motion must remain stable despite long-distance disturbances from shock waves. The flow field in these cases is complex, marked by interactions between hypersonic shock waves and a moving boundary. This leads to significant unsteady effects due to the body's translation and rotation over extended distances. Existing simulation techniques fall short in rapidly and accurately predicting the aerodynamic force and thermal properties for these problems, largely due to the overwhelming computational demands that result from oversize computational domains and the necessity of grid deformation. This paper presents a novel non-deforming grid method to address these challenges. The central concept is to anchor the reference frame to the moving object itself and to approach the problem from a non-inertial frame perspective. This accounts for the motion of the object solely via the inertial source term, circumventing the complexities of mesh manipulation typically required to link flow and motion equations. The moving shock boundary is designed to be closely compatible with selected shock-captured schemes, which reduces non-physical oscillations compared to the traditional method of direct assembly with theoretical shock relations. Other boundary conditions and the solution process are also refined to specifically target the unsteady, shock-dominated flow. These modifications significantly alleviate the computational burden. The effectiveness of the proposed method is demonstrated through several test cases. To showcase the method's practical application, a scenario is simulated wherein an ellipse is dislodged from a wedge by an incident shock wave, covering a long distance. These tests confirm the method's feasibility in aerospace engineering problems.

Numerical investigation on transonic flutter characteristics of an airfoil with split drag rudder

In this paper, a series of flutter simulations are carried out to investigate the effects of split drag rudder (SDR) on the transonic flutter characteristic of rigid NACA 64A010. A structural dynamic model addressing two-degree-of-freedom pitch-plunge aeroelastic oscillations was coupled with the unsteady Reynolds-averaged Navier-Stokes equations to perform flutter simulation. Meanwhile, the influence mechanism of SDR on flutter boundary is explained through aerodynamic work and the correlated shock wave location. The results show that the SDR delays the shock wave shifting downstream, and the Mach number corresponding to reaching freeze region increases as the split angle increases. Therefore, the peak value of aerodynamic moment coefficient amplitude and the sharp ascent process of phase occurs at higher Mach number, which leads to the delay in the occurrence of the transonic dip. Besides, before the transonic dip of airfoil without SDR occurs, the aerodynamic moment phase of airfoil with the SDR decreases slowly due to the decrease in the speed of shock wave moving downstream. This results in an increased flutter speed when employing the SDR before the transonic dip of airfoil without SDR occurs. Meanwhile, the effects of asymmetric split angles on the transonic flutter characteristics are also investigated. Before the transonic dip of airfoil without SDR occurs, the flutter characteristic is dominated by the smaller split angle.

X-ray phase-contrast imaging of strong shocks on OMEGA EP.

The ongoing improvement in laser technology and target fabrication is opening new possibilities for diagnostic development. An example is x-ray phase-contrast imaging (XPCI), which serves as an advanced x-ray imaging diagnostic in laser-driven experiments. In this work, we present the results of the XPCI platform that was developed at the OMEGA EP Laser-Facility to study multi-Mbar single and double shocks produced using a kilojoule laser driver. Two-dimensional radiation-hydrodynamic simulations agree well with the shock progression and the spherical curvature of the shock fronts. It is demonstrated that XPCI is an excellent method to determine with high accuracy the front position of a trailing shock wave propagating through an expanding CH plasma that was heated by a precursor Mbar shock wave. The interaction between the rarefaction wave and the shock wave results in a clear signature in the radiograph that is well reproduced by radiation-hydrodynamic simulations.

Simultaneous X-Ray and Optical Polarization Observations of the Blazar Mrk 421

We present near-simultaneous X-ray and optical polarization measurements in the high synchrotron peaked (HSP) blazar Mrk 421. The X-ray polarimetric observations were carried out using Imaging X-ray Polarimetry Explorer (IXPE) on 2023 December 6. During IXPE observations, we also carried out optical polarimetric observations using 104 cm Sampurnanand telescope at Nainital and multiband optical imaging observations using 2 m Himalayan Chandra Telescope at Hanle. From model-independent analysis of IXPE data, we detected X-ray polarization with degree of polarization (ΠX) of 8.5% ± 0.5% and an electric vector position angle (ΨX) of 10.°6 ± 1.°7 in the 2−8 keV band. From optical polarimetry on 2023 December 6, in B, V, and R bands, we found values of Π B = 4.27% ± 0.32%, Π V = 3.57% ± 0.31%, and Π R = 3.13% ± 0.25%. The value of Π B is greater than that observed at longer optical wavelengths, with the degree of polarization suggesting an energy-dependent trend, gradually decreasing from higher to lower energies. This is consistent with that seen in other HSP blazars and favors a stratified emission region encompassing a shock front. The emission happening in the vicinity of the shock front will be more polarized due to the ordered magnetic field resulting from shock compression. The X-ray emission, involving high-energy electrons, originates closer to the shock front than the optical emission. The difference in the spatial extension could plausibly account for the observed variation in polarization between X-ray and optical wavelengths. This hypothesis is further supported by the broadband spectral energy distribution modeling of the X-ray and optical data.

On space–time diversity in shock train self-excited oscillation mode during wide-range evolution in a scramjet isolator

The shock train self-excited oscillation can induce combustor instabilities and reduce engine margin. In a dual-mode scramjet, the shock train undergoes a complete evolution process, exhibiting structural changes closely tied to this inherent unsteadiness. This study aims to elucidate the space–time diversity in shock train self-excited oscillation mode and the underlying mechanisms during wide-range evolution. The experimental investigations were conducted at Ma = 1.95, capturing the complete evolution of the shock train. The results indicate the evolution can be categorized into three regimes based on structural characteristics. In regime I, the shock region gradually forms, followed by the occurrence of the mixing region in regime II. Regime III corresponds to inlet unstart. In regime II, isolator outlet pressure fluctuations exhibit higher frequency and lower amplitude compared to regime I, while the shock motion demonstrates lower frequency and higher amplitude. The shock train behaves in a large-scale, low-frequency (1.53 times the duct height, 10 Hz) unsteady motion in regime II, posing a potential threat to engine operation. Coherence and phase analysis reveal the disturbance source originates downstream. Proper orthogonal decomposition modal analysis shows two oscillation modes: low-frequency components correspond to shock motion, and high-frequency components correspond to pressure fluctuations across the entire pseudoshock. The propagating of downstream disturbance differs between the two regimes. In regime I, the shock train exhibits rigid-body motion synchronously. In regime II, the relative motion between each shock wave and the cumulative effect of pressure disturbance lead to frequency decay upstream, amplifying the shock train motion.

Damage power enhancement of fuel air explosive with typical metal hydrides additions

To study the damage power enhancement of fuel air explosive (FAE) with metal hydrides, the effects of metal hydrides (TiH2, MgH2, ZrH2) powders on shock wave and thermal damage of pure propylene oxide (PO) were explored using a 20 L spherical explosion test system combined with colorimetric thermometry technology. The experimental results showed that compared with the base metal powders, the explosion overpressures, maximum pressure rise rates and maximum average temperatures of the solid-liquid mixed fuel with the metal hydrides (TiH2, MgH2, ZrH2) powders increased by 11.04 %, 22.61 %, 4.80 % and 26.68 %, 38.18 %, 13.91 % as well as 6.85 %, 8.57 %, 1.34 %, respectively. Furthermore, the effects of metal hydride powders on the cloud explosion fuel were better than those of Al powders, and MgH2 powders had the most significant effects on the damage power enhancement of pure PO. Metal hydride powders as high-energy additives could improve the energy release characteristics of FAE.

Multiple shock and acceleration processes of high-velocity flyers driven by the HEAVEN-I laser facility

The experiments of high-velocity flyer acceleration were performed on the HEAVEN-I KrF laser facility with a long-pulse duration (∼ 28 ns). Double-layered flyers consisting of polystyrene and aluminum films can be accelerated to more than 10 km/s measured by VISAR. The polystyrene layer is used as the ablative material, insulation layer, and shock wave regulator. Multiple shock and acceleration processes were observed by adjusting the thickness of the polystyrene layer. We simulated and analyzed the multiple shock processes driven by the long laser pulses and square pressure pulses. The results indicate that the reverberation processes can be induced by the alternating shock and rarefaction waves due to the wave–interface interactions. The reverberations in the Al layer can modulate the pressure evolution and the fine structure of flyer acceleration history. Similar processes in the polystyrene layer can lead to a secondary or multiple shock loading process when the driving pulse duration is several times longer than the shock round trip time in the double-layered flyer. Multiple accelerations can effectively enhance the final velocities in the experimental and simulation results. However, multiple accelerations involve more complex shock loading and unloading processes, and flyers are more prone to breakup compared with single acceleration.

Enhancing aviation safety: Multifunctional graphene nanostructured foams for lightweight fire suppression materials

Fuel tank fires and explosions are the primary causes of military and civilian aircraft losses and have been a major concern for the aviation and defense industries. Passive protection systems with explosion-suppression materials generate a protected environment within fuel tanks before ignition can occur and help prevent catastrophic failures. To minimize these concerns, open-cell reticulated polyurethane foams are extensively used in passive protection systems. However, fire- and explosion-related incidents are still taking place and need to be urgently addressed for aviation safety. This study investigates the effects of graphene nanostructured foams for redesigning the next-generation lightweight fire-retardant materials in aviation. Graphene foams have a unique open-cell morphology with three dimensional (3D) continuous and interconnected network structures and hollow features, which can be suitable for aircraft and defense applications. In this study, mechanical and thermal characterizations tests were conducted on graphene nanostructured foams for a better evaluation. Mechanical loading-unloading studies highlighted their outstanding mechanical energy-absorption capabilities against external loads. The thermogravimetric analysis revealed that the graphene foams provided excellent thermal properties against fire and high-temperature degradation. It was also confirmed that graphene foams uniquely manifested self-extinguishing characteristics during burning tests without catching fire or dripping for secondary fire formations. According to the tube explosion experiments, the graphene foams kept their appearance and strength after blast impacts and elevated explosion temperatures and shock waves. As a result, the proposed multifunctional graphene micro- and nanofoams offer significant potential for the next-generation fire- and explosion-suppression materials in various critical industries, such as aircraft, defense, space, drone, energy, and automotive.

Nonlinear Perturbations and Weak Shock Waves in Isentropic Atmospheres

Acoustic perturbations to stellar envelopes can lead to the formation of weak shock waves via nonlinear wave steepening. Close to the stellar surface, the weak shock wave increases in strength and can potentially lead to the expulsion of part of the stellar envelope. While accurate analytic solutions to the fluid equations exist in the limits of low-amplitude waves or strong shocks, connecting these phases generally requires simulations. We address this problem using the fact that the plane-parallel Euler equations, in the presence of a constant gravitational field, admit exact Riemann invariants when the flow is isentropic. We obtain exact solutions for acoustic perturbations and show that after they steepen into shock waves, Whitham’s approximation can be used to solve for the shock’s dynamics in the weak to moderately strong regimes, using a simple ordinary differential equation. Numerical simulations show that our analytic shock approximation is accurate up to moderate (∼few–15) Mach numbers, where the accuracy increases with the adiabatic index.

Mechanism investigation of stability enhancement by slot on a transonic compressor

Abstract As aircraft engine blades develop towards high loads and low aspect ratios, the flow conditions in the tip region of transonic compressor rotors become more complex. The interaction between shock waves and boundary layers tends to induce fluid separation, thereby reducing the stable operating range of the rotor. To enhance the stability margin of the rotor, this study employs numerical simulation techniques to design jet slots on the rotor 37. Research results show that, without compromising the performance of the rotor, the slotted rotor can effectively enhance the stability margin of the rotor at both design and off-design speeds, with increases of 60.9% and 47.9% in surge margins compared to the prototype.

Fluid-Structure Interactions of a Fin over a Compliant Panel in Supersonic Flow

The fluid-structure interactions of a blunt fin mounted over a compliant panel in Mach 2 flow were investigated. The test geometry consisted of a thin, flexible panel fixed on all edges with a blunt fin with a hemispherically rounded leading edge mounted in a manner that the leading edge of the fin overhung the panel. The blunt fin was also pivoted to several angles of attack with respect to the oncoming flow. This allowed for the study of the dynamic system created by the interactions between the compliant panel and the blunt fin geometries. Both rigid and compliant panel models were used in order to provide a comparison between the flow with and without the dynamics of the compliant panel. High-speed schlieren and surface oil flow visualizations showed that the time-averaged flow remained almost entirely unchanged between the rigid and compliant panels. The instantaneous flow fields, however, showed a highly dynamic system where the compliant panel induced oscillatory shock waves that were both stationary and freely moving. Simultaneous high-speed schlieren visualization and stereo digital-image correlation showed a strong linkage between the motion of the shock waves and the deformation of the panel. This was demonstrated through frequency analysis and modal decomposition of the panel deformation and shock motions.

High-order discontinuous Galerkin method with immersed boundary treatment for compressible flows on parallel adaptive Cartesian grids

Adaptive mesh refinement (AMR) technology and high-order methods are important means to improve the quality of simulation results and have been hotspots in the computational fluid dynamics community. In this paper, high-order discontinuous Galerkin (DG) and direct DG (DDG) finite element methods are developed based on a parallel adaptive Cartesian grid to simulate compressible flow. On the one hand, a high-order multi-resolution weighted essentially nonoscillatory limiter is proposed for DG and DDG methods. This limiter can enhance the stability of DG/DDG methods for compressible flows dominated by shock waves. It is also compact, making it suitable for the implementation of AMR with frequent refinement/coarsening. On the other hand, a coupling method of DG and immersed boundary method is proposed to simulate flow around objects. Due to the compactness of DG, the physical quantities of image points can be directly obtained through the DG/DDG polynomial of the corresponding cells. It avoids the wide interpolation stencil of traditional IBM and makes it more suitable for the parallel adaptive Cartesian grid framework in this paper. Finally, the performance of the proposed method is verified through typical two- and three-dimensional cases. The results indicate that the method proposed in this paper has low numerical dissipation in smooth areas and can effectively handle compressible flow dominated by discontinuities. Moreover, for transonic flow over a sphere, the error of results between the proposed method and direct numerical simulation is within 1%, fully validating the accuracy of the method presented in this paper.

The propagation characteristics of a detonation wave in uniformly premixed gases within a semi-confined channel

Based on the OpenFOAM platform, a numerical study was conducted to investigate the propagation characteristics of a detonation wave in uniformly premixed gases within a semi-confined channel, specifically examining the changes in wave's structure and analyzing the detonation reinitiation-extinguishment process. The results indicate that, due to the weak confinement, the detonation wave experiences lateral expansion, with transverse waves on the detonation wave front penetrating into the inert gas and forming segmented protrusions on the oblique shock wave. During the propagation process, the number of transverse waves decreases gradually, and the reflected waves formed by the interaction between transverse waves and the inert gas are weak, collectively leading to a gradual decay in the strength of the detonation wave and a reduction in the frequency of pressure oscillation on the detonation wave front. Furthermore, when transverse waves interact with the inert gas and undergo Mach reflection, the reflected waves would detach the inert gas and form new transverse waves promoted by upward-moving old transverse waves and disturbances on the flame front, thereby extending the duration distance of the detonation wave. Subsequently, after the detonation wave decouples, a transverse wave reflected from the inert gas interface interacts with the lower wall, triggering local detonation reinitiation, which generates a higher-intensity longitudinal wave that couples with the leading shock wave, temporarily restoring the detonation wave and forming lateral detonation in the decoupled region. However, the detonation wave will ultimately extinguish due to the attenuation of transverse waves' intensity and decreasing number of these waves.

Numerical simulation of jet interaction flow field of complex configuration based on hybrid grid method

Abstract The supersonic/hypersonic jet interaction flow field includes many fluid phenomena such as shock waves, separation and reattachment of the boundary layer, expansion wave, Mach disk, shear layer, and so on. The complexity of the jet interaction flow field makes it difficult to simulate accurately, and the structured grid method is generally used in engineering applications. However, the structured grid has many shortcomings when dealing with complex configurations, and the traditional hybrid grid method has the problem of insufficient accuracy. In the paper, a structured/unstructured grid algorithmic coupling numerical simulation method is developed. Firstly, the feasibility and accuracy of this method are verified by numerical simulation of the jet interference flow field of cone-cylinder-skirt shape, along with a comparison with the results of the experiment and structural method. Then, the jet interference flow fields of the rudders and the grid fins configuration are simulated to show the efficiency of the method, and the accuracy is further verified. The results show that the hybrid numerical simulation method can save grid generation time and grid quantity to a certain extent when compared with the structural, showing higher accuracy, which provides an accurate and efficient solution to jet interaction problems with complex configurations.

Damage features and mechanism of prestressed hollow square piles subjected to non-contact underwater explosion

Critical hydraulic structures are increasingly vulnerable to underwater explosion attacks, with the supporting piles being prime targets for terrorist activities. This study investigates the damage effects and mechanisms of prestressed concrete hollow square (PCHS) piles under non-contact underwater explosions. A series of underwater explosion experiments was conducted on four PCHS piles. The dynamic response of PCHS piles throughout the underwater explosion process was simulated using a coupled fluid-solid numerical model. The mechanisms of dynamic damage to the PCHS piles were elucidated through an integrated analysis of both experimental and numerical results. The research indicates that the damage characteristics of PCHS piles include longitudinal and oblique cracks on the lateral surfaces, transverse cracks on the rear side, and localized fragmentation of concrete. Three primary damage modes have been identified: bending failure(L¯c= 0.59 m/kg1/3), combined bending-shear failure(L¯c= 0.36 m/kg1/3), and punching failure(L¯c= 0.24 m/kg1/3). The local and global responses induced by shock waves are the primary causes of structural damage. Furthermore, as the stand-off distance decreases, the impact of explosive bubbles increases the magnitude of the overall response. A comparative analysis also examined the impact of prestress and axial load on the damage behavior of hollow square piles.