Development Of Shock Research Articles

Propagation of cylindrical converging shock wave in rotating ideal gas containing dust particles

In this article, the propagation of strong converging cylindrically symmetric shock waves in ideal dusty gas is studied using the Lie group technique while considering the effect of an axial magnetic field in a rotating gas atmosphere. The constant density in an undisturbed medium is assumed, whereas the magnetic field, the azimuthal, and axial components of fluid velocity are considered to be varying. The arbitrary constants appearing in the expressions for infinitesimals of the Local Lie group of transformations bring about three different cases of solutions, i.e., with power-law shock path, exponential-law shock path, and a particular case of power-law shock path. Numerical solutions are obtained in the cases of the power-law shock path. The self-similar solutions to the problem are obtained, and the effect of the Shock Cowling number, the mass concentration of solid dust particles, the relative specific heat, the ratio of the density of solid particles, and the ambient azimuthal velocity exponent on the shock evolution are depicted through graphs.

Shock waves characteristics and losses estimation of non-equilibrium condensation flow in nozzle and steam turbine cascade

The investigation of transonic non-equilibrium condensation is paramount due to its profound influence on the shock patterns and the distribution of losses. This study numerically investigates the shock wave morphology, evolution, and quantitative loss calculation under the influence of non-equilibrium condensation within the Moses-Stein nozzle and Dykas cascade. The results indicate that the vapor near the nozzle wall undergoes phase transition first and forms “X-shaped” condensation shock, which impervious to back pressure variations. Conversely, the “λ-shaped” aerodynamic shock moves towards the throat with increasing back pressure, triggering boundary layer separation. The entropy generation of “λ-shocks” accounts for over 98% and represents the primary source of shock losses. Strong pressure side shock induces shock wave-boundary layer interactions with the blade suction wall, resulting in reflected shocks. However, the latent heat released by non-equilibrium condensation mitigates this effect, increasing the total pressure loss coefficient by 0.188. The decrease in Mach number under high back pressure causes a notable increase in the trailing edge shock angle, with the wave foot shifting upstream. Notably, the proportion of shock losses attributed to the suction side of trailing edge exceeds 80%, significantly surpassing other regions, which progressively increases with rising back pressure. Therefore, it is crucial for cascade optimization. The findings can provide references for the optimization design of low-pressure steam turbine blade profiles. The results can serve as a guide for optimizing the blade profiles of low-pressure steam turbine.

Dust–ion–acoustic damped solitary waves and shocks in laboratory and Saturn's E-ring magnetized nonthermal dusty plasmas with anisotropic ion pressure and dust-charge fluctuation

We study the oblique propagation of weakly nonlinear dust–ion–acoustic (DIA) solitary waves (SWs) and shocks in collisional magnetized nonthermal dusty plasmas that are relevant in laboratory and space (Saturn's E-ring) environments. We consider plasmas to be composed of q-nonextensive hot electrons, thermal positive ions, and immobile negatively charged dust grains immersed in a static magnetic field and take into account the effects of ion creation (source), ion loss (sink), ion–neutral and ion–dust collisions, anisotropic ion pressure, and dust-charge fluctuations on the evolution of small-amplitude SWs and shocks. The ion–neutral collision enhancement equilibrium dust-charge number is self-consistently determined using Newton–Raphson method. We found that in laboratory dusty plasmas with adiabatic dust-charge variation [i.e., when the dust charging frequency (νch) is much higher than the dust–plasma oscillation frequency (ωpd)], the DIA solitary waves (DIASWs) get damped by the effects of the ion–dust and ion–neutral collisions, whereas the ion creation and ion loss lead to the amplification of solitary waves, and they appear as only compressive types with positive potential. On the other hand, in Saturn's E-ring plasmas, where the collisional and ion creation or ion loss effects are insignificant, the non-adiabaticity of dust-charge variation can give rise to the evolution of either damped DIASWs or DIA shocks, depending on the smallness of the ratios νch/ωpd or ωpd/νch, respectively. Furthermore, two critical values of the nonextensive parameter q exist, below (or above) which, the DIASWs and shocks can appear as rarefactive (or compressive) types. The characteristics of DIASWs and shocks are also analyzed numerically for parameters relevant to the laboratory and Saturn's E-ring plasmas.

Injection Process of Pickup Ion Acceleration at an Oblique Heliospheric Termination Shock

The injection process of pickup ion acceleration at a heliospheric termination shock is investigated. Using two-dimensional fully kinetic particle-in-cell simulation, accelerated pickup ions are self-consistently reproduced by tracking long time evolution of shocks with an unprecedentedly large system size in the shock normal direction. Reflected pickup ions drive upstream large-amplitude waves through resonant instabilities. Convection of the large-amplitude waves causes shock surface reformation and alters the downstream electromagnetic structure. A part of pickup ions are accelerated to tens of upstream flow energy in the timescale of ∼100 times inverse ion gyrofrequency. The initial acceleration occurs through the shock surfing acceleration (SSA) mechanism followed by the shock drift acceleration mechanism. Large electrostatic potential accompanied by the upstream waves enables the SSA to occur.

Prognostic performance of the SCAI shock classification at admission and during ICU treatment: A retrospective, observational cohort study

BackgroundCardiogenic shock (CS) is characterized by high mortality and requires accurate prognostic tools to predict outcomes and guide treatment. The Society for Cardiovascular Angiography and Interventions (SCAI) shock classification indicates shock severity and can be used for outcome prediction. ObjectiveHere, we compare the prognostic performance of SCAI shock classification determined on admission and during intensive care unit (ICU) stay. MethodsWe included all patients with CS or conditions associated with developing CS based on ICD codes. SCAI shock stages were determined on admission and during the first 5 days of ICU stay. Receiver operating curves were used to compare the prognostic performance of SCAI stages on admission, SCAI stages during ICU stay and CS evolution (absent, resolved, persistent and new onset) for in-hospital mortality. ResultsBetween 01/2018 and 06/2022, 1303 patients were identified and 862 patients were included. On admission, 50.6 % patients had SCAI shock stage A, 3.9 % SCAI shock stage B, 17.7 % SCAI shock stage C, 7.0 % SCAI shock stage D and 20.8 % SCAI shock stage E. Shock stage distribution changed dynamically during ICU stay. Compared to SCAI stage on admission (AUC 0.80; 95 % CI 0.77–0.83), highest achieved SCAI stage during ICU (AUC 0.86, 95 % CI 0.83–0.89, p < 0.0001) and shock evolution (AUC 0.87, 95 % CI 0.85–0.90, p < 0.0001) yielded better prognostic performance. ConclusionsSCAI shock stages changed dynamically during ICU stay, and prognostic performance can be improved by considering highest achieved SCAI shock stage as well as the evolution of CS compared to SCAI shock stage on admission.

Shock wave formation in radiative plasmas.

The temporal evolution of weak shocks in radiative media is theoretically investigated in this work. The structure of radiative shocks has traditionally been studied in a stationary framework. Their systematic classification is complex because layers of optically thick and thin regions alternate to form a radiatively driven precursor and a temperature-relaxation layer, between which the hydrodynamic shock is embedded. In this work we analyze the formation of weak shocks when two radiative plasmas with different pressures are put in contact. Applying a reductive perturbative method yields a Burgers-type equationthat governs the temporal evolution of the perturbed variables including the radiation field. The conditions upon which optically thick and thin solutions exist have been derived and expressed as a function of the shock strength and Boltzmann number. Below a certain Boltzmann number threshold, weak shocks always become optically thick asymptotically in time, while thin solutions appear as transitory structures. The existence of an optically thin regime is related to the presence of an overdense layer in the compressed material. Scaling laws for the characteristic formation time and shock width are provided for each regime. The theoretical analysis is supported by FLASH simulations, and a comprehensive test case has been designed to benchmark radiative hydrodynamic codes.

ANALYSIS OF THE BIFURCATING DUCT OF AN INLET PARTICLE SEPARATOR IN TRANSONIC FLOW CONDITIONS

Abstract To increase the reliability of turboprop and turboshaft engines in extreme operating conditions, filtering protections such as Inlet Particle Separators (IPS) can be installed at the intake. The flow inside an IPS is highly 3D and unsteady, with fluctuations especially pronounced when transonic conditions are reached. In this paper, we aim at providing the transonic analysis of an industrial IPS designed for aerodynamic lab testing. As a first step, we define the threshold beyond which sonic conditions are reached in the boundary cross sections of the IPS by means of a 1D semi-empirical model. Second, we select a critical configuration, and we perform CFD simulations to analyze the locations and evolution of the transonic flow inside the IPS. Different models are presented, i.e. steady and unsteady Reynolds-Averaged Navier-Stokes, Detached Eddy Simulation and Large Eddy Simulation, characterized by three levels of resolution. The results show the evolution of some transonic shocks: the steady-state model is only providing information on averaged quantities, while the time-resolved simulations offer a more precise overview in the time domain. The analysis in the frequency domain reveals the frequencies of the transonic fluctuations. Finally, we discuss three alternative designs to effectively improve the operating range and mitigate the risks related to the transonic instabilities, comparing the differences in separation efficiency with respect to the baseline case. The results prove that the optimal design choice is given by the trade-off between operating range, pressure losses and separation efficiency.

Shocks, clouds, and atomic outflows in active galactic nuclei hosting relativistic jets

Context. A number of observations have revealed atomic and/or molecular lines in active galaxies hosting jets and outflows. Line widths indicate outward motions of hundreds to a few thousands of kilometers per second. They appear to be associated with the presence of radio emission in Gigahert-peaked spectrum (GPS) and/or compact steep spectrum (CSS) sources, with linear sizes of ≤10 kpc. Numerical simulations have shown that the bow shocks triggered by relativistic jets in their host galaxies drive ionization and turbulence in the interstellar medium (ISM). However, the presence of atomic lines requires rapid recombination of ionized gas, which appears challenging to explain from the physical conditions revealed thus far based on numerical simulations of powerful jets. Aims. The aim of this paper is to provide a global framework to explain the presence of lines in terms of jet and shock evolution and to fix the parameter space where the atomic and molecular outflows might occur. Methods. This parameter space is inspired by numerical simulations and basic analytical models of jet evolution as a background. Results. Our results show that a plausible general explanation involves momentum transfer and heating to the interstellar medium gas by jet triggered shocks within the inner kiloparsecs. The presence of post-shock atomic gas is possible in the case of shocks interacting with dense clouds that remain relatively stable after the shock passage. Conclusions. According to our results, current numerical simulations cannot reproduce the physical conditions to explain the presence of atomic and molecular outflows in young radio sources. However, I show that these outflows might occur in low-power jets at all scales and I predict a trend towards powerful jets showing lines at CSS scales, when clouds have cooled to recombination temperatures.

Correlation of Coronal Mass Ejection Shock Temperature with Solar Energetic Particle Intensity

Solar energetic particle (SEP) events have been observed by the Parker Solar Probe (PSP) spacecraft since its launch in 2018. These events include sources from solar flares and coronal mass ejections (CMEs). The IS⊙IS instrument suite on board PSP is measuring ions over energies from ∼ 20 keV nucleon−1 to 200 MeV nucleon−1 and electrons from ∼ 20 keV to 6 MeV. Previous studies sought to group CME characteristics based on their plasma conditions and arrived at general descriptions with large statistical errors, leaving open questions on how to properly group CMEs based solely on their plasma conditions. To help resolve these open questions, the plasma properties of CMEs have been examined in relation to SEPs. Here, we reexamine one plasma property, the solar wind proton temperature, and compare it to the proton SEP intensity in a region immediately downstream of a CME-driven shock for seven CMEs observed at radial distances within 1 au. We find a statistically strong correlation between proton SEP intensity and bulk proton temperature, indicating a clear relationship between SEPs and the conditions in the solar wind. Furthermore, we propose that an indirect coupling of SEP intensity to the level of turbulence and the amount of energy dissipation that results is mainly responsible for the observed correlation between SEP intensity and proton temperature. These results are key to understanding the interaction of SEPs with the bulk solar wind in CME-driven shocks and will improve our ability to model the interplay of shock evolution and particle acceleration.

Upstream Plasma Waves and Downstream Magnetic Reconnection at a Reforming Quasi-parallel Shock

With the help of a two-dimensional particle-in-cell simulation model, we investigate the long-time evolution (near 100Ωi0−1 , where Ω i0 is the ion gyrofrequency in the upstream) of a quasi-parallel shock. Some of the upstream ions are reflected by the shock front, and their interactions with the incident ions excite low-frequency magnetosonic waves in the upstream. Detailed analyses have shown that the dominant wave mode is caused by the resonant ion–ion beam instability, and the wavelength can reach tens of ion inertial lengths. Although these plasma waves are directed toward the upstream in the upstream plasma frame, they are brought by the incident plasma flow toward the shock front, and their amplitude is enhanced during the approaching. The interaction of the upstream plasma waves with the shock leads to the cyclic reformation of the shock front, and the reformation period is slightly larger than 10 Ωi0−1 . When crossing the shock front, these large-amplitude plasma waves are compressed and evolve into current sheets in the transition region of the shock. At last, magnetic reconnection occurs in these current sheets, accompanying the generation of magnetic islands. Simultaneously, there still exist plasma waves of another kind, with the wavelength of several ion inertial lengths in the ramp of the shock, which are excited by the nonresonant ion–ion beam instability. The current sheets in the transition region are distorted and broken into several segments when the plasma waves of this kind are transmitted into the downstream, where magnetic reconnection and the generated islands have a much smaller size. No obvious ion flow can be observed around some X-lines produced in the magnetic reconnection, and this implies that electron-only reconnection may occur.

Evolution of characteristic shocks in two-phase modified Chaplygin flow consisting of source term

This manuscript presents a system of partial differential equations (PDEs) governed by the isentropic two-phase flow model with modified Chaplygin equation of state consisting of a non-constant source term in one-dimension. Lie symmetry analysis is employed to reduce the governing system into an equivalent system of ordinary differential equations (ODEs). The patterns of flow variables and the effects of source term parameters are investigated graphically. Further, the transport equation for the evolution of characteristic shocks is derived and solved numerically using an exact solution of the system under consideration. Also, the effects of inclination of flow and acceleration due to gravity on the behavior of the characteristic shock are analyzed.

Derivation of shock front evolution with rarefaction wave and its verification in dusty plasma simulations

The evolution of unsupported shocks is theoretically investigated using the method of characteristics. It is found that the location and the speed of the generated non-uniform shock (NUS) front vary with the propagation time and the initial compression strength. The relationship between the NUS front location and the propagation time is asymptotically parabolic, while the speed of the NUS front decreases gradually with the propagation time. These analytical derivations are verified using computer simulations of unsupported shocks in 2D dusty plasmas performed here. The transition of the NUS front speed found previously [Sun et al., Phys. Plasmas 28, 103703 (2021)] using data fitting with the simulation data is re-investigated and further confirmed with the theoretical derivation of the NUS front in the current investigation.

Application of higher-order FV-WENO scheme to the interaction between shock wave and bubble

The high-order finite volume-WENO (Weighted Essentially Non-Oscillatory) scheme combines the finite volume method with the WENO method, allowing for high-order accuracy and accurate simulation of complex physical phenomena. It has advantages in handling shock waves and bubble interactions. The idea of this method is to discretize the physical equations into a set of conservation equations and use the WENO method to calculate the numerical fluxes on each finite volume cell. This approach is effective in dealing with problems such as shock wave propagation, bubble deformation, and evolution. In fluid dynamics simulation and research, the high-order FV-WENO scheme has significant application prospects. It can provide accurate numerical solutions and simulate complex physical phenomena, making it widely applicable in scientific research and engineering. In this study, we simulated the interactions between shock waves and single or double bubbles, obtaining the complete process of bubble collapse with clear bubble interfaces and strong program stability.

On the treatment of phenomenological turbulent effects in one-dimensional simulations of core-collapse supernovae

ABSTRACT We have developed a phenomenological turbulent model with one-dimensional (1D) simulation based on Reynolds decomposition. Using this method, we have systematically studied models with different effects of compression, mixing length parameters, and diffusion coefficient of internal energy, turbulence energy, and electron fraction. With employed turbulent effects, supernova explosion can be achieved in 1D geometry, which can mimic the evolution of shock in the 3D simulations. We found that enhancement of turbulent energy by compression affects the early shock evolution. The diffusion coefficients of internal energy and turbulent energy also affect the explodability. The smaller diffusion makes the shock revival faster. Our comparison between the two reveals that the diffusion coefficients of internal energy has a greater impact. These simulations would help understand the role of turbulence in core-collapse supernovae.

Kinetic simulations comparing quasi-parallel and quasi-perpendicular piston-driven collisionless shock dynamics in magnetized laboratory plasmas

Magnetized collisionless shocks are common in astrophysical systems, and scaled versions can be created in laboratory experiments by utilizing laser-driven piston plasmas to create these shocks in a magnetized background plasma. A key parameter for these experiments is the angle θB between the shock propagation direction and the background magnetic field. We performed quasi-1D piston-driven shock simulations to explore shock formation, evolution, and key observables relevant to laboratory experiments for a range of shock angles between θB=90° to θB=30°. Our results show that the spatial and temporal scales of shock formation for all angles considered are similar when expressed in terms of the perpendicular component of the magnetic field. In a steady state, ion and electron temperatures become more isotropic, and the electron-to-ion temperature ratio is higher for smaller θB. At θB=30°, ion heating parallel to the magnetic field becomes dominant, associated with more ions being reflected at one discontinuity and subsequently trapped by the next discontinuity due to shock reformation.

Relativistic spherical shocks in expanding media

ABSTRACT We investigate the propagation of spherically symmetric shocks in relativistic homologously expanding media with density distributions following a power-law profile in their Lorentz factor. That is, $\rho _{_{\rm {ej}}} \propto t^{-3}\gamma _{_{\rm {ej}}}(r,t)^{-\alpha }$, where $\rho _{_{\rm {ej}}}$ is the medium proper density, $\gamma _{_{\rm {ej}}}$ is its Lorentz factor, α &amp;gt; 0 is constant, and t, r are the time and radius from the centre. We find that the shocks behaviour can be characterized by their proper velocity, $U^{\prime }=\Gamma _s^{\prime }\beta _s^{\prime }$, where $\Gamma _s^{\prime }$ is the shock Lorentz factor as measured in the immediate upstream frame and $\beta _s^{\prime }$ is the corresponding three velocity. While generally, we do not expect the shock evolution to be self-similar, for every α &amp;gt; 0 we find a critical value $U^{\prime }_c$ for which a self-similar solution with constant U′ exists. We then use numerical simulations to investigate the behaviour of general shocks. We find that shocks with $U^{\prime }\gt U^{\prime }_c$ have a monotonously growing U′, while those with $U^{\prime }\lt U^{\prime }_c$ have a decreasing U′ and will eventually die out. Finally, we present an analytic approximation, based on our numerical results, for the evolution of general shocks in the regime where U′ is ultrarelativistic.

The Maximum Energy of Shock-accelerated Cosmic Rays

Identifying the accelerators of Galactic cosmic ray (CR) protons with energies up to a few PeV (1015 eV) remains a theoretical and observational challenge. Supernova remnants (SNRs) represent strong candidates because they provide sufficient energetics to reproduce the CR flux observed at Earth. However, it remains unclear whether they can accelerate particles to PeV energies, particularly after the very early stages of their evolution. This uncertainty has prompted searches for other source classes and necessitates comprehensive theoretical modeling of the maximum proton energy, , accelerated by an arbitrary shock. While analytic estimates of have been put forward in the literature, they do not fully account for the complex interplay between particle acceleration, magnetic field amplification, and shock evolution. This paper uses a multizone, semianalytic model of particle acceleration based on kinetic simulations to place constraints on for a wide range of astrophysical shocks. In particular, we develop relationships between , shock velocity, size, and ambient medium. We find that SNRs can only accelerate PeV particles under a select set of circumstances, namely, if the shock velocity exceeds ∼104 km s−1 and escaping particles drive magnetic field amplification. However, older and slower SNRs may still produce observational signatures of PeV particles due to populations accelerated when the shock was younger. Our results serve as a reference for modelers seeking to quickly produce a self-consistent estimate of the maximum energy accelerated by an arbitrary astrophysical shock. 1 1 Presented as a thesis to the Department of Astronomy and Astrophysics, The University of Chicago, in partial fulfillment of the requirements for a Ph.D. degree.

Partially ionized two-fluid shocks with collisional and radiative ionization and recombination – multilevel hydrogen model

ABSTRACT Explosive phenomena are known to trigger a wealth of shocks in warm plasma environments, including the solar chromosphere and molecular clouds where the medium consists of both ionized and neutral species. Partial ionization is critical in determining the behaviour of shocks, since the ions and neutrals locally decouple, allowing for substructure to exist within the shock. Accurately modelling partially ionized shocks requires careful treatment of the ionized and neutral species, and their interactions. Here we study a partially ionized switch-off slow-mode shock using a multilevel hydrogen model with both collisional and radiative ionization and recombination rates that are implemented into the two-fluid (PIP) code, and study physical parameters that are typical of the solar chromosphere. The multilevel hydrogen model differs significantly from magnetohydrodynamic (MHD) solutions due to the macroscopic thermal energy loss during collisional ionization. In particular, the plasma temperature both post-shock and within the finite-width is significantly cooler that the post-shock MHD temperature. Furthermore, in the mid to lower chromosphere, shocks feature far greater compression than their single-fluid MHD analogues. The decreased temperature and increased compression reveal the importance of non-equilibrium ionized in the thermal evolution of shocks in partially ionized media. Since partially ionized shocks are not accurately described by the Rankine-Hugoniot shock jump conditions, it may be incorrect to use these to infer properties of lower atmospheric shocks.

Theoretical Basis and Technical Method of Permeability Enhancement of Tectonic Coal Seam by High Intensity Acoustic Wave In Situ

Tectonic coal seams are characterized by soft, low permeability and high gas outburst. The traditional gas control method is the intensive drilling and extraction in this seam, which is not only large in engineering quantity, high in cost, difficult to form holes and low in extraction efficiency, but also easy to induce coal and gas outburst, which is a difficult problem for global coal mine gas control. To solve this difficult problem, the controllable shockwave equipment developed by the author’s team and successfully applied in the practice of permeability enhancement of coal seam, combined with the principles of shock vibration sound wave generation and shock wave attenuation and evolution in the rock stratum, a new idea of loading a controllable shock wave in the roof and floor of coal seam is proposed. The shock wave first attenuates and evolves into a high-strength sound wave in the roof and floor rock stratum, and then enters and loads into the coal seam to achieve the purpose of increasing permeability without damaging the physical properties of the tectonic coal seam and facilitating the opening of the original fractures. According to the new technical ideas, the implementation scheme and key parameters of the gas pre-extraction models in tectonic coal seam are designed, including the penetration drilling, roof and floor horizontal holes, shield tunneling and the high-strength acoustic wave of the working face, which provides a new technical approach to solve the problem of high efficiency and low cost gas extraction in the tectonic coal seam.

On kinematics of one‐dimensional radially symmetric shocks in non‐ideal reacting gases

In this manuscript, the advancement of one‐dimensional shock waves propagating through a non‐ideal reacting gas is examined. Considering the shock wave as a propagating discontinuity surface, a pair of evolution equations describing the strength of the shock and the first‐order discontinuity for variable initial data are obtained. The truncation approximations are used to obtain the exponent of shock velocity for the case of strong shock with constant initial data and compared with those exponents obtained from Guderley's scheme and Chisnell–Chester–Whitham (CCW) rule. The effects of non‐ideal and reaction parameters on the shock evolution in the case of arbitrary shock strength are examined and compared with those obtained from the CCW rule. Furthermore, the global behaviors of shock strength and induced discontinuity for different values of non‐ideal and reaction parameters are analyzed.