Dynamics Of Shock Waves Research Articles

Design, Fabrication, and Commissioning of Transonic Linear Cascade for Micro-Shock Wave Analysis

Understanding shock wave behavior in supersonic flow environments is critical for optimizing the aerodynamic performance of turbomachinery components. This study introduces a novel transonic linear cascade design, focusing on advanced blade manufacturing and experimental validation. Blades were 3D-printed using Inconel 625, enabling tight control over the geometry and surface quality, which were verified through extensive dimensional accuracy assessments and surface finish quality checks using coordinate measuring machines (CMMs). Numerical simulations were performed using Ansys CFX with an implicit pressure-based solver and high-order numerical schemes to accurately model the shock wave phenomena. To validate the simulations, experimental tests were conducted using Schlieren visualization, ensuring high fidelity in capturing the shock wave dynamics. A custom-designed test rig was commissioned to replicate the specific requirements of the cascade, enabling stable and repeatable testing conditions. Experiments were conducted at three different inlet pressures (0.7-bar, 0.8-bar, and 0.9-bar gauges) at a constant temperature of 21 °C. Results indicated that the shock wave intensity and position are highly sensitive to the inlet pressure, with higher pressures producing more intense and extensive shock waves. While the numerical simulations aligned broadly with the experimental observations, discrepancies at finer flow scales suggest the need for the further refinement of the computational models to capture detailed flow phenomena accurately.

Magnetosonic shock waves in degenerate electron–positron–ion plasma with separated spin densities

This study investigates magnetosonic shock waves in a spin-polarized three-component quantum plasma using the quantum magnetic hydrodynamic model. We explore the influence of spin effects, specifically spin magnetization current and spin pressure, on shock wave behavior. Numerical analysis of the linear dispersion relation under varying parameters such as positron imbalance, spin polarization ratio, plasma beta, quantum diffraction, and magnetic diffusivity reveals differential impacts, with diffusion exerting significant influence on the plasma frequency. Our findings highlight the sensitivity discrepancy between the real and imaginary parts of the dispersion relation. Furthermore, nonlinear behavior of magnetosonic shock waves is examined via the Korteweg–de Vries–Burgers equation, showcasing transitions between oscillatory and monotonic wave patterns based on changes in dimensionless parameters. Notably, we observe the combined effects of spin-up and spin-down positrons with spin-up and spin-down electrons on shock wave dynamics, contributing to a deeper understanding of spin-plasma interactions with implications across various fields.

Experimental study on the evolution of shock waves in the near field of cylindrical charge explosion

Cylindrical charges are frequently used in blasting engineering and military operations, often detonated very close to target structures. Obtaining the characteristics of the flow field distribution in the near field of explosions through experimentation consistently poses challenges. These challenges constrain efforts to elucidate the evolutionary processes of explosive shock waves. Employing the explosive schlieren experimental system yields a clearer depiction of the near field flow than previous studies, thereby facilitating a more comprehensive understanding of the characteristics of cylindrical charge explosions. The overall flow field adopts a droplet shape, with the interface of the detonation products and the shock wave front forming continuous concave shapes. The detonation process in cylindrical charges can be conceptualized as the detonation wave propelling the detonation products at supersonic speeds. The formation of explosive shock waves can be elucidated through the dynamics of oblique shock waves generated by two-dimensional curved surfaces. This mechanism influences the relationship between the deflection angles of detonation products and the shock wave angles resulting from different detonation velocities. Theoretical calculations of shock wave positions align with experimental images. Significant variations in shock wave velocities at different positions within cylindrical charges are observed, identifying patterns of these variations. The research findings clarify the formation mechanisms of explosive shock waves in cylindrical charges and deepen the understanding of shock wave evolution in the near field.

Integrable approximations of dispersive shock waves of the granular chain

In the present work we revisit the shock wave dynamics in a granular chain with precompression. By approximating the model by an α-Fermi–Pasta–Ulam–Tsingou chain, we leverage the connection of the latter in the strain variable formulation to two separate integrable models, one continuum, namely the KdV equation, and one discrete, namely the Toda lattice. We bring to bear the Whitham modulation theory analysis of such integrable systems and the analytical approximation of their dispersive shock waves in order to provide, through the lens of the reductive connection to the granular crystal, an approximation to the shock wave of the granular problem. A detailed numerical comparison of the original granular chain and its approximate integrable-system-based dispersive shocks proves very favorable in a wide parametric range. The gradual deviations between (approximate) theory and numerical computation, as amplitude parameters of the solution increase are quantified and discussed.

An overview of ion-acoustic solitary and shock waves in a magnetized nonthermal plasma: influence of trapped positrons and electrons

A magnetized nonthermal electron–positron-ion (e-p-i) plasma is considered to study the propagation properties of ion-acoustic solitary and shock waves in the presence of trapped positrons and electrons for the first time. The Schamel-κ (kappa) distribution function that describes plasma nonthermality and particle trapping is assumed to consider electrons and positrons. The diffusive effect of ion plasma fluid, which is responsible for shock dynamics, is taken into account. A nonlinear Schamel-Korteweg–de Vries-Burgers’ (SKdVB) equation is derived by employing the reductive perturbation approach, and the solitary and shock wave solutions of the SKdVB equation have also been derived for different limiting cases. It is found that only positive potential nonlinear structures (for both solitary and shock waves) are formed in the proposed plasma system. The condition for stable solitons in the absence of dissipation is analyzed, and the nature of arbitrary amplitude solitary waves (obtained via the Sagdeev potential approach) is discussed. It is found through theoretical and numerical investigation that different plasma compositional parameters (such as the trapping effect of electrons (β e ) and positrons (β p ), the obliquity effect (θ), electron-to-ion number density ratio (µ e ), the magnetic field effect (via Ω) and the viscous effect (via η)) have a significant influence on the dynamics of ion-acoustic solitary and shock waves. The theoretical and numerical investigations in this study may be helpful in describing the nature of localized structures in different plasma contexts, e.g. space and astrophysical plasmas and experimental plasmas where electron–positron-ion plasmas exist.

Impact of Sudden Expansion Structure Length on Shock Wave Dynamics and Autoignition in High-Pressure Hydrogen Releases

This study investigates the effects of expansion structure length on shock wave behavior, specifically focusing on pressure dynamics, and subsequent autoignition in high-pressure hydrogen systems. Using configurations EPT1 and EPT2, along with a direct pipe (SP1) as a control, we analyze how different expansion lengths influence pressure profiles, shock wave attenuation, and ignition phenomena.

Delayed Detached-Eddy Simulations of Rough-Wall Turbulent Reactive Flows in a Supersonic Combustor

Reactive delayed detached-eddy simulations (DDESs) of hydrogen injection into a confined transverse supersonic flow of vitiated air are conducted. The corresponding conditions were studied in the LAPCAT-II combustor, which—due to thermal coating—exhibits non-negligible wall roughness. Its effects are taken into account with the equivalent sand-grain roughness model, and, to the best of the authors’ knowledge, it is the first time that this modeling framework is considered within the DDES framework to simulate turbulent reactive flows. Two operating conditions are considered, which differ in the value of the momentum ratio between the hydrogen and vitiated air inlet streams, thus leading to two distinct values of the operating equivalence ratio (ER). For its smallest value, smooth combustion is subject to a preliminary thermal runaway period, while for its largest value, combustion is more strongly intertwined with shock wave dynamics and boundary-layer separation. Since it features large subsonic regions, which are characteristic of situations close to thermal choking, the latter is referred to as the sudden or partially choked combustion mode. Computational results are assessed through comparisons with available experimental data for both operating conditions. The main mechanism through which wall roughness alters the combustion development lies in the reduction of the effective cross-sectional area that is induced by boundary-layer thickening. For the largest ER value, DDES conducted with the sand-grain roughness model does recover the partially choked combustion mode, while smooth wall (i.e., standard) DDES does not.

Coupled models for propagation of explosive shock waves in cylindrical and spherical geometries

The propagation of shock waves in different geometries is crucial in engineering and scientific applications. A comprehensive model is developed to elucidate the hydrodynamic growth and decay of shock waves in cylindrical and spherical geometries by using the strong shock wave assumption. This model takes into consideration the conservation equations governing mass, momentum, and energy, thereby allowing for an accurate description of the coupled behavior between the piston and shock wave propagation. In contrast to the localized analysis employed in previous self-similar methods, this model incorporates the finite sound wave velocity to introduce the concept of retarded pressure on the piston surface. Consequently, the proposed model offers a multitude of advantages by providing a complete set of dynamic information concerning the trajectories, velocities, and accelerations of both the piston and shock wave. Furthermore, an asymptotic analytical solution is derived to describe the decay of shock waves in cylindrical and spherical geometries. To validate the theoretical analysis and illustrate the propagation characteristics of shock waves in these specific geometries, thorough comparisons are conducted. These findings contribute to the advancement of our understanding of shock wave dynamics in various physical systems, particularly in the field of plasma physics.

A computational investigation of shock wave train in diverse duct geometries using machine learning-adopted k-ω turbulence model

This research paper presents a thorough examination of shock wave train phenomena in various duct structures, utilizing a machine learning-optimized k-ω model. The focus of the study is to apply machine learning techniques to adapt the constant coefficients of the k-ω turbulence model, improving its accuracy and computational efficiency in capturing the dynamics of shock waves. An important aspect of this investigation is the impact of diverging sections within the duct, specifically how changes in the divergence angle, while maintaining a constant ratio of the exit area to the throat area, affect compressible flow parameters, shock wave positions, and other related characteristics of shock trains. The study systematically explores these effects and provides fresh insights into the behavior of shock wave trains under different divergence conditions. In a departure from the usual practices in supersonic research, this study compares the phenomena of shock wave trains in rectangular and circular duct geometries. The findings contribute valuable data and analyses to a field that has traditionally focused on rectangular configurations. The results indicate that the shape of the duct has a significant influence on the shock wave train, emphasizing the importance of considering geometric diversity in the study of supersonic flows and shock wave phenomena. This research sets the stage for further investigations into the interaction between duct geometry, shock wave propagation, and the dynamics of compressible flows.

Hybrid Approach for Multiscale and Multimodal Time-Resolved Diagnosis of Ultrafast Processes in Materials via Tailored Synchronization of Laser and X-ray Sources at MHz Repetition Rates

The synchronization of laser and X-ray sources is essential for time-resolved measurements in the study of ultrafast processes, including photo-induced piezo-effects, shock wave generation, and phase transitions. On the one hand, optical diagnostics (by synchronization of two laser sources) provides information about changes in vibration frequencies, shock wave dynamics, and linear and nonlinear refractive index behavior. On the other hand, optical pump–X-ray probe diagnostics provide an opportunity to directly reveal lattice dynamics. To integrate two approaches into a unified whole, one needs to create a robust method for the synchronization of two systems with different repetition rates up to the MHz range. In this paper, we propose a universal approach utilizing a field-programmable gate array (FPGA) to achieve precise synchronization between different MHz sources such as various lasers and synchrotron X-ray sources. This synchronization method offers numerous advantages, such as high flexibility, fast response, and low jitter. Experimental results demonstrate the successful synchronization of two different MHz systems with a temporal resolution of 250 ps. This enables ultrafast measurements with a sub-nanosecond resolution, facilitating the uncovering of complex dynamics in ultrafast processes.

Parsec-scale evolution of the gigahertz-peaked spectrum quasar PKS 0858 − 279

ABSTRACT We conducted multi-epoch, multifrequency parsec-scale studies on the gigahertz-peaked spectrum quasar PKS 0858 − 279 with the Very Long Baseline Array (VLBA). Our observations on 2005 November 26 elucidated a weak core, characterized by an inverted spectrum, and a distinctly bent jet that exhibited a notable bright feature in its Stokes I emission. Through comprehensive analysis of polarization and spectral data, we inferred the formation of a shock wave within this feature, stemming from interactions with a dense cloud in the ambient medium. In this paper, Very Long Baseline Interferometry-Gaia astrometry further reinforces the core identification. With a deep analysis of six additional VLBA epochs spanning from 2007 to 2018, we observed that while the quasar’s parsec-scale structure remained largely consistent, there were discernible flux density changes. These variations strongly imply the recurrent ejection of plasma into the jet. Complementing our VLBA data, RATAN-600 observations of the integrated spectra suggested an interaction between standing and travelling shock waves in 2005. Moreover, our multi-epoch polarization analysis revealed a drastic drop in rotation measure values from 6000 to 1000 rad m−2 within a single year, attributable to diminishing magnetic fields and particle density in an external cloud. This change is likely instigated by a shock in the cloud, triggered by the cloud’s interaction with the jet, subsequently prompting its expansion. Notably, we also observed a significant change in the magnetic field direction of the jet, from being perpendicular post its observed bend to being perpendicular prior to the bend – an alteration possibly induced by the dynamics of shock waves.

Numerical investigation of the underwater explosion of a cylindrical explosive with the Eulerian finite-element method

The shock wave and bubble dynamics of an underwater explosion are significant in various fields. When the charge is non-spherical, the detonation process will remarkably affect the shock wave formation and the subsequent bubble motion. In this work, the underwater explosion of a cylindrical explosive is investigated numerically with the Eulerian finite-element method combined with the programed burn model treating the detonation process. The present model is validated by comparing the simulated results with the experimental ones. Then, several cases with different slenderness of the explosive charge in various buoyancy environments are simulated and analyzed. The results demonstrate a notable variation of the shock wave in different directions. The shock wave will reach the highest pressure peak and shortest pulse width at a certain angle determined by the ratio between the speeds of the detonation wave and the shock wave. Furthermore, the non-spherical initial expansion of the bubble casts a significant influence on the subsequent bubble evolution. Three typical jet morphologies are identified with different combinations of buoyancy parameter and oblateness ratios of the bubble, featured by a slightly oblique upward jet penetrating the bubble, a laminar jet that failed to penetrate the bubble continuously, and a pair of opposite horizontal jets penetrating the bubble. Meanwhile, the horizontal jets that happen under a weak buoyancy environment will reduce the upward migration.

Pressure dynamics of an internal shock wave emission inside a water droplet and potential cavitation

Shock reflected by a spherical interface is involved in shock-droplet interaction. Here, we investigate the pressure dynamics of an internal spherical shock wave and the potential cavitation inside a spherical water droplet. We conduct hydrodynamic simulation and employ the linear geometrical acoustics approximation to analyze the negative pressure and the wavefront at different intervals d between the source point of the shock and the droplet surface. Studies indicate that the negative pressure at a very large d is primarily attributed to the focusing effect of the droplet surface, whereas the collision of the reflected waves contributes to negative pressure at a small d. The caustic, which is the locus of the cusps (singular points) on the shock wavefront is determined by the parametric equations. Notably, the caustic also has singular points owing to the off-axis reflection. Finally, we evaluate the cavitation inside the droplet. Cavitation occurs on the opposite side of the droplet and moves away from the surface with d increasing, which agrees with previous experimental results. Additionally, we demonstrate that cavitation can occur with less damage to the droplet compared to a planar shock impact on a water droplet.

Relaxation method for Mie–Grüneisen type equations of state

Mie–Grüneisen type equations of state (EOS) are widely used to describe the thermodynamics of solids, liquids, and gases in a variety of physics problems, including shock wave dynamics in condensed materials and the thermodynamic behavior of dense gases generated by detonation waves. The Jones–Wilkins–Lee (JWL), Cochran–Chan, and original Mie–Grüneisen EOSs are relevant examples. However, these EOSs present several major difficulties. First, their range of validity is limited because these EOSs are fitted to a reference curve and tolerate only small deviations from that curve. The second difficulty lies in the complexity of the mathematical formulations, affecting the efficiency of pressure relaxation solvers. These two difficulties give rise to a third. Under extreme flow conditions, computational failures are quite common. Methods for “extending” the equations of state are often used to continue the computations. For example, below a certain arbitrary density, the JWL EOS is sometimes extended to the ideal-gas EOS. A fundamentally new method is presented in this work. It consists of using the much simpler Noble–Abel-stiffened-gas EOS as a predictor, to close the corresponding flow model. A thermodynamic relaxation step follows the prediction step. The solution is projected onto the target EOS, in this case the Mie–Grüneisen EOS, with the help of additional transport equations. Therefore, the flow model is an extended version, much more efficient for numerical resolution. This method solves the three problems above by extending the validity domain of the thermodynamic formulation, making the relaxation solvers much faster, and dramatically increasing the robustness of computations.

Reactive Flow Dynamics of Low-Frequency Instability in a Scramjet Combustor

This study numerically investigated the combustion instability and characteristics of a laboratory-scale gaseous hydrogen-fueled scramjet combustor. For this purpose, a numerical simulation with an improved detached eddy simulation and a detailed hydrogen/oxygen reaction mechanism was performed. The numerical framework used high-resolution schemes with high-order accuracy to ensure high resolution and fidelity. A total of five fuel injection pressures were considered to characterize the combustion instability as a function of the equivalence ratio. A sampling time of up to 100 ms was considered to sufficiently accumulate several cycles of low-frequency combustion instability dynamics with a period in the order of 100 Hz. Numerical results revealed the repetitive formation/dissipation dynamics of the upstream-traveling shock wave, and it acts as a key factor of combustion instability. The period and derived principal frequency of these upstream-traveling shock waves is several ms. The frequency analysis showed that the instability frequency increased in the low-frequency range as the combustion mode transitioned from the cavity shear-layer to the jet-wake type. This characteristic was derived from the transition in combustion mode at the same equivalence ratio. Therefore, it suggests that the instability frequency shifting is governed by the combustion mode rather than the equivalence ratio. These comprehensive numerical results demonstrated not only the effect of the equivalence ratio but also the important role of the combustion mode on the low-frequency combustion instability.

Shock waves in semi-infinite photonic lattices

We investigate the existence, stability and propagation dynamics of shock waves existing in defocusing saturable media modulated by a semi-infinite photonic lattice. Such surface waves consist of modulationally stable pedestals in bulk media and decaying oscillatory tails in semi-infinite photonic lattices. Due to Bragg-type reflection, they are strongly localized at the edge of the optical lattice. The kink steepness, pedestal height and localization degree can be controlled by propagation constant, saturable degree and lattice depth. Two types of kinks, i.e., “out-of-phase” and two branches of “in-phase” shock waves are revealed. Out-of-phase shock waves are stable in a substantial part of their existence domain. While the lower-branch in-phase waves with low energy flow are stable in almost their whole existence domain, the higher-branch in-phase waves are completely unstable. We thus show the first example of stable in-phase shock waves in nonlinear optics. Our findings provide new insight into the dynamics of semi-localized nonlinear surface shock waves or kink solitons.

Molecular Simulations of Liquid Jet Explosions and Shock Waves Induced by X-Ray Free-Electron Lasers.

X-ray free-electron lasers (XFELs) produce x-ray pulses with high brilliance and short pulse duration. These properties enable structural investigations of biomolecular nanocrystals, and they allow one to resolve the dynamics of biomolecules down to the femtosecond timescale. Liquid jets are widely used to deliver samples into the XFEL beam. The impact of the x-ray pulse leads to vaporization and explosion of the liquid jet, while the expanding gas triggers the formation of shock wave trains traveling along the jet, which may affect biomolecular samples before they have been probed. Here, we used molecular dynamics simulations to reveal the structural dynamics of shock waves after an x-ray impact. Analysis of the density and temperature in the jet revealed shock waves that form close to the explosion center, travel along the jet with supersonic velocities, and decay exponentially with an attenuation length proportional to the jet diameter. A trailing shock wave formed after the first shock wave, similar to the shock wave trains in experiments. High shock wave velocities in our simulations are compatible with the phenomenon of "fast sound," as emerging at large sound frequencies. Although using purely classical models in the simulations, the resulting explosion geometry and shock wave dynamics closely resemble experimental findings, and they highlight the importance of atomistic details for modeling shock wave attenuation.

Numerical and experimental investigations on the jet and shock wave dynamics during the cavitation bubble collapsing near spherical particles based on OpenFOAM

The interaction between cavitation bubbles and particles is essential for the operational performance many kinds of fluid machineries. In the present paper, jet dynamics and shock waves induced by the cavitation bubble collapsing near two spherical particles are numerically investigated based on OpenFOAM. The numerical scheme is validated by the experimental data obtained based on our high-speed camera cavitation system. Our results reveal that bubble split induced by annular jet is the primary feature during bubble collapsing with four typical cases defined. For the jet formation, the localized high pressure produced at the bubble split point is the main reason and the split point also serves as the source of the shock waves shown by the numerical schlieren. Furthermore, the nondimensional bubble-particle distance is the most paramount parameter influencing the jet phenomenon (e.g. jet velocity).

Single-shot ultrafast dual-view imaging of shock waves in parallel laser processing

Single-shot ultrafast optical imaging has revealed various non-repetitive processes, but it has conventionally provided only single-view measurements. Here, we demonstrate a single-shot ultrafast dual-view imaging technique by monitoring shock waves in laser processing of glass using single or parallelized excitation pulses. We visualize the spatiotemporal evolution of shock waves in air at 0.5 Gfps with five frames in both top and side views, indicating the velocity anisotropy and interaction of shock waves. Our technique can contribute to a comprehensive understanding not only of shock wave dynamics but also of other spatially complex ultrafast phenomena including laser-induced plasma and electrical discharge.

Traveling discontinuity at the quantum butterfly front

We formulate a kinetic theory of quantum information scrambling in the context of a paradigmatic model of interacting electrons in the vicinity of a superconducting phase transition. We carefully derive a set of coupled partial differential equations that effectively govern the dynamics of information spreading in generic dimensions. Their solutions show that scrambling propagates at the maximal speed set by the Fermi velocity. At early times, we find exponential growth at a rate set by the inelastic scattering. At late times, we find that scrambling is governed by shock-wave dynamics with traveling waves exhibiting a discontinuity at the boundary of the light cone. Notably, we find perfectly causal dynamics where the solutions do not spill outside of the light cone.