Traveling Shock Wave Research Articles

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.

A Formation Mechanism for “Wrong Way” Radio Relics

Radio relics are typically found to be arc-like regions of synchrotron emission in the outskirts of merging galaxy clusters, bowing out from the cluster center. In most cases they show synchrotron spectra that steepen toward the cluster center, indicating that they are caused by relativistic electrons being accelerated at outward traveling merger shocks. A number of radio relics break with this ideal picture and show morphologies that are bent the opposite way and show spectral index distributions that do not follow expectations from the ideal picture. We propose that these “wrong way” relics can form when an outward traveling shock wave is bent inward by an infalling galaxy cluster or group. We test this in an ultra-high-resolution zoom-in simulation of a massive galaxy cluster with an on-the-fly spectral cosmic-ray model. This allows us to study not only the synchrotron emission at colliding shocks, but also their synchrotron spectra to address the open question of relics with strongly varying spectral indices over the relic surface.

Hybrid VOF–Lagrangian CFD Modeling of Droplet Aerobreakup

A hybrid VOF–Lagrangian method for simulating the aerodynamic breakup of liquid droplets induced by a traveling shock wave is proposed and tested. The droplet deformation and fragmentation, together with the subsequent mist development, are predicted by using a fully three-dimensional computational fluid dynamics model following the unsteady Reynolds-averaged Navier–Stokes approach. The main characteristics of the aerobreakup process under the shear-induced entrainment regime are effectively reproduced by employing the scale-adaptive simulation method for unsteady turbulent flows. The hybrid two-phase method combines the volume-of-fluid technique for tracking the transient gas–liquid interface on the finite volume grid and the discrete phase model for following the dynamics of the smallest liquid fragments. The proposed computational approach for fluids engineering applications is demonstrated by making a comparison with reference experiments and high-fidelity numerical simulations, achieving acceptably accurate results without being computationally expensive.

Characterization Of Shock Buffet On A Supercritical 2D Airfoil In Transonic Flow

The transonic flow over the supercritical OAT15A airfoil is investigated experimentally. Using time-resolved focusing schlieren sequences, we extracted the temporal evolution of the chordwise shock location for a wide range of combinations of Mach number and angle of attack. Based on this data, we identified the conditions of pre-buffet, buffet onset, fully-established buffet, and buffet-offset behavior. Key parameters characterizing most pronounced buffet behavior are presented and quantified in terms of the shock amplitude, its variation over multiple buffet cycles, and the associated frequency of the periodic shock oscillation. Fully-established buffet is identified at a Mach number of 0.72 and angle of attack of 5 deg. It is demonstrated that these operating conditions are characterized by a quasi-sinusoidal shock oscillation at a distinct frequency of 113 Hz, in good agreement with previous studies. This analysis reveals that the harmonic shock oscillation spanning a range of about 16.5% of the airfoil chord is accompanied by a coupled large-scale variation of the global flow topology. Both instantaneous and mean velocity components in the chordwise and vertical directions are discussed for representative phases of the buffet cycle. Instantaneous vector fields of both components provide insight into the flow organization throughout the buffet cycle and allow to identify the streamwise distance traveled by the shock wave within a full cycle. We can thus precisely capture the state of the shock wave and quantify the evolution of the shock-induced separation and the size of the turbulent wake. Severe variations of the flow topology are induced by the large-scale upstream and downstream shock displacement. The results show that incidents of massive flow separation are observed for shock positions being close to the upstream limit, and more general, that the wake influence is more pronounced when induced by an upstream traveling shock wave. Phase-averaged velocity profiles at significant locations along the airfoil suction side complement this analysis. Characteristic sets of velocity profiles are discussed in detail that allow to uniquely describe the development of the flow in each phase of the buffet cycle. Detailed contours and profiles of both velocity and Reynolds shear stress contributions across the wake region highlight the strong downstream influence the shock-induced turbulent wake. Phases of severe flow separation result in reverse flow persisting until the trailing edge which further substantiates the induced momentum deficit.

Waves in a Hyperbolic Predator–Prey System

We address a hyperbolic predator–prey model, which we formulate with the use of the Cattaneo model for chemosensitive movement. We put a special focus on the case when the Cattaneo equation for the flux of species takes the form of conservation law—that is, we assume a special relation between the diffusivity and sensitivity coefficients. Regarding this relation, there are pieces arguing for its relevance to some real-life populations, e.g., the copepods (Harpacticoida), in the biological literature (see the reference list). Thanks to the mentioned conservatism, we get exact solutions describing the travelling shock waves in some limited cases. Next, we employ the numerical analysis for continuing these waves to a wider parametric domain. As a result, we discover smooth solitary waves, which turn out to be quite sustainable with small and moderate initial perturbations. Nevertheless, the perturbations cause shedding of the predators from the main core of the wave, which can be treated as a settling mechanism. Besides, the localized perturbations make waves, colliding with the main core and demonstrating peculiar quasi-soliton phenomena sometimes resembling the leapfrog playing. An interesting side result is the onset of the migration waves due to the explosion of overpopulated cores.

Computational Evaluation of Shock Wave Interaction with a Liquid Droplet

This article represents the natural continuation of the work by Rossano and De Stefano (2021), dealing with the computational fluid dynamics analysis of a shock wave interaction with a liquid droplet. Differently from our previous work, where a two-dimensional approach was followed, fully three-dimensional computations are performed to predict the aerodynamic breakup of a spherical water body due to the impact of a traveling shock wave. The present engineering analysis focuses on capturing the early stages of the breakup process under the shear-induced entrainment regime. The unsteady Reynolds-averaged Navier–Stokes approach is used to simulate the mean turbulent flow field in a virtual shock tube device with circular cross section. The compressible-flow-governing equations are numerically solved by means of a finite volume method, where the volume of fluid technique is employed to track the air–water interface. The proposed computational modeling approach for industrial gas dynamics applications is verified by making a comparison with reference numerical data and experimental findings, achieving acceptably accurate predictions of deformation and drift of the water body without being computationally cumbersome.

Non-Symmetrical Collapse of an Empty Cylindrical Cavity Studied with Smoothed Particle Hydrodynamics

The non-symmetrical collapse of an empty cylindrical cavity is modeled using Smoothed Particle Hydrodynamics. The presence of a nearby surface produces an anisotropic pressure field generating a high-velocity jet that hits the surface. The collapse follows a different dynamic based on the initial distance between the center of the cavity and the surface. When the distance is greater than the cavity radius (detached cavity) the surface is hit by traveling shock waves. When the distance is less than the cavity radius (attached cavity) the surface is directly hit by the jet and later by other shock waves generated in the last stages of the of the collapse. The results show that the surface is hit by a stronger shock when distance between the center of the cavity and the surface is zero while showing more complex double peaks behavior for other distances.

Combustion mode and wave multiplicity in rotating detonative combustion with separate reactant injection

Abstract Numerical simulations with detailed chemistry are conducted for two-dimensional rotating detonative combustion with separate injection of fuel and oxidant. The influences of the fuel and oxidant compositions on combustion mode and detonation wave multiplicity are studied. It is found that in the parts of the flow beyond the fuel refill zone, there are two distinct, highly inhomogeneous zones with fuel-rich and fuel-lean compositions, respectively. Both detonative and deflagrative regimes are observed and proceed mostly under a premixed combustion mode with the deflagration confined mostly to the fuel-lean zone. The results from our simulations show that limited H2 is detonated or deflagrated close to stoichiometric conditions and more than 70% of H2 is detonated or deflagrated under fuel-lean conditions. Over 70% of the detonated H2 is consumed in a premixed combustion mode. Our analysis also suggests that the detonation fraction increases with increased inlet pressure, decreased inlet temperature or increased injection orifice number. Additionally, the range of mixture fraction over which the composition is detonable is narrower than the range for deflagration. The number of detonation waves increases with increased oxygen mass fraction in the oxidant stream, with the additional waves being formed by mutual enhancement of an explosive hot spot and a travelling shock wave. Stabilization of the multiple waves follows a chaotic period involving both co-rotating and counter-rotating waves. Furthermore, the deficit of the detonation speed relative to the ideal Chapman − Jouguet value increases with the number of waves but also decreases monotonically with the level of reactant mixing. The reactant mixing effects along the detonation wave height are further discussed through quantifying the statistics of height-wise mixture fraction, heat release rate and OH mass fraction.

Probing the thermodynamic conditions of the heliosheath plasma by shock wave propagation

Context. The pressure equilibrium between the inner heliosheath and the outer heliosheath (referred to as the local interstellar medium) is an eminent theoretical and practical problem; theoretical, because the relevant pressure carriers have to be identified, and practical, because data must be gathered in order to confirm such a pressure equilibrium. The problem is closely connected with the stability of the heliopause, that is, of the tangential discontinuity between these two counterflowing media, and is of utmost importance for understanding the stability of the whole circumsolar plasma structure. Aims. In this paper we analyze the thermodynamic conditions of the multi-fluid plasma between the solar wind termination shock and the heliopause determining the total heliosheath pressure. We look into this problem from a theoretical standpoint and revisit theoretical descriptions of the solar wind plasma after its passage over the solar wind termination shock, thereafter forming the subsonic heliosheath region. Methods. Hereby we take into account the 3D magnetohydrodynamics shock conditions and the resulting 3D temperature structure of the downstream plasma flow. We use a kind of seismological procedure to probe the heliosheath plasma by inquiring into the propagation conditions of traveling shock wave perturbations in this predetermined 3D heliosheath plasma structure. We discuss the fact that the front geometry of such a traveling shock wave most probably does not remain spherical, if it was to begin with, due to asymmetric shock propagation conditions. In contrast, the wave front is likely to become strongly deformed into an upwind bulge. Results. Concerning the plasma pressure, in addition to solar wind and pick-up proton pressures, we have to take into account the solar wind electron pressure which as a surprise turns out to be of comparable magnitude. As a consequence, the characteristic propagation speed of the traveling shock wave in the weakly magnetized heliosheath plasma is given as a mixed speed expressed by the sound speeds of the protons and the electrons. We describe local low-energy proton density signatures that can be found in Voyager-2 proton data as a consequence of traveling shock wave passages and show that the total local plasma pressure can be directly derived from them.

Origin and chaotic propagation of multiple rotating detonation waves in hydrogen/air mixtures

The origin and chaotic propagation of multiple detonative waves in the two-dimensional modelled rotating detonation combustor fueled by premixed hydrogen/air mixtures are numerically investigated with detailed chemical mechanism. The discrete reactants inlets are adopted, to mimic the spatial non-uniformity of the propellant in the practical Rotating Detonation Engine (RDE) combustor. The emphasis is laid on the mechanism to induce the new detonation waves in the RDE and the influence of the reactant non-uniformity in RDE on the critical detonation combustion dynamics. The numerical experiments show that the stability and number of the rotating detonation wave are affected by the inlet total pressures and reactant equivalence ratios. The RDE with high inlet total pressure would experience chaotic instability before reaching stable propagation of detonation waves in near-stoichiometric mixtures, while for the RDE with low inlet total pressure, no chaotic propagation transient after the detonation initiation is observed. It is found that the chaotic propagation stage is responsible for the variation of the rotating detonative wave number and propagation direction. Frequent detonation extinction, re-ignition and re-orientation, irregular reactants refill zones, co-rotating and counter-rotating detonation waves are observed during chaotic stage. The explosive spots arising during this stage, which may initiate new detonation waves, result from the mutual enhancement between the travelling shock waves and the deflagrative fronts. Furthermore, the predictability of the chaotic detonation wave propagation is further confirmed in terms of the initial and boundary conditions, mesh and chemical mechanism. It is also found that the fuel equivalence ratio has a considerable impact on the number of the stabilized detonation wave and velocity deficit.

Improved scaling laws for the shock-induced dispersal of a dense particle curtain

Experiments were performed within Sandia National Labs’ Multiphase Shock Tube to measure and quantify the shock-induced dispersal of a shock/dense particle curtain interaction. Following interaction with a planar travelling shock wave, schlieren imaging at 75 kHz was used to track the upstream and downstream edges of the curtain. Data were obtained for two particle diameter ranges ($d_{p}=106{-}125$, $300{-}355~\unicode[STIX]{x03BC}\text{m}$) across Mach numbers ranging from 1.24 to 2.02. Using these data, along with data compiled from the literature, the dispersion of a dense curtain was studied for multiple Mach numbers (1.2–2.6), particle sizes ($100{-}1000~\unicode[STIX]{x03BC}\text{m}$) and volume fractions (9–32 %). Data were non-dimensionalized according to two different scaling methods found within the literature, with time scales defined based on either particle propagation time or pressure ratio across a reflected shock. The data show that spreading of the particle curtain is a function of the volume fraction, with the effectiveness of each time scale based on the proximity of a given curtain’s volume fraction to the dilute mixture regime. It is seen that volume fraction corrections applied to a traditional particle propagation time scale result in the best collapse of the data between the two time scales tested here. In addition, a constant-thickness regime has been identified, which has not been noted within previous literature.

Molecular dynamics investigation of the shock response of silica aerogels

Highly-nanoporous low-density silica aerogel is an excellent candidate for shock wave and high-energy absorption applications. In the present work, high-velocity shock compression of a wide range of silica aerogel densities from 209 to 847 kg m−3 were analysed according to the reverse ballistic approach using molecular dynamics (MD) simulations at various particle velocities. The computed shock velocities from bin-density distribution diagrams increase linearly with the particle velocities. For the considered particle velocities in a wide range from 10 to 120 Å ps−1 for silica aerogel of density 209 kg m−3, the generated shock velocities, as well as the intercept and the slope of their linear variations, were in excellent agreement with the previous macroscopic experiments reported in the literature. Moreover, the von Mises stress values for low-density aerogels increase slowly due to the less resistance for atom movements, as well as the maximum reached values were lesser compared to the values for high-density aerogels. This work showed that the shock wave travelling in macroscopic experiments of silica aerogel can be predicted at the nanoscale using all-atom simulations with the remarkable agreement.

Stellar Energetic Particles in the Magnetically Turbulent Habitable Zones of TRAPPIST-1-like Planetary Systems

Abstract Planets in close proximity to their parent star, such as those in the habitable zones around M dwarfs, could be subject to particularly high doses of particle radiation. We have carried out test-particle simulations of ∼GeV protons to investigate the propagation of energetic particles accelerated by flares or traveling shock waves within the stellar wind and magnetic field of a TRAPPIST-1-like system. Turbulence was simulated with small-scale magnetostatic perturbations with an isotropic power spectrum. We find that only a few percent of particles injected within half a stellar radius from the stellar surface escape, and that the escaping fraction increases strongly with increasing injection radius. Escaping particles are increasingly deflected and focused by the ambient spiraling magnetic field as the superimposed turbulence amplitude is increased. In our TRAPPIST-1-like simulations, regardless of the angular region of injection, particles are strongly focused onto two caps within the fast wind regions and centered on the equatorial planetary orbital plane. Based on a scaling relation between far-UV emission and energetic protons for solar flares applied to M dwarfs, the innermost putative habitable planet, TRAPPIST-1e, is bombarded by a proton flux up to 6 orders of magnitude larger than experienced by the present-day Earth. We note two mechanisms that could strongly limit EP fluxes from active stars: EPs from flares are contained by the stellar magnetic field; and potential CMEs that might generate EPs at larger distances also fail to escape.

Optical diagnostic systems based on Shenguang III

Optical diagnostic system plays an important role in inertial confinement fusion (ICF) experiment. Some key physical quantities and parameters in fusion can be diagnosed intuitively. In this review, three typical diagnostic systems on Shengang III facility are introduced, including imaging velocity interferometer system for any reflector (VISAR), fusion-reaction diagnostic system and backscatter light diagnostic system. VISAR can be used to measure velocity of free surface or shock wave traveling history in transparent media, which is an important diagnostic technique for shock wave velocity regulation, material compression characteristics and radiation temperature measurement. The fusion reaction-history diagnostic system can be used to accurately measure the fusion rate of ICF experiment. It’s a key diagnostic technique to study implosion dynamics and understand the mixed effect. Backscatter light diagnostic system is capable to measuring the energetic quotient stimulated by laser and plasma interaction (LPI), which produce important supports for calculating the coupling efficiency of driven laser and target.

Mottled Protoplanetary Disk Ionization by Magnetically Channeled T Tauri Star Energetic Particles

Abstract The evolution of protoplanetary disks is believed to be driven largely by angular momentum transport resulting from magnetized disk winds and turbulent viscosity. The ionization of the disk that is essential for these processes has been thought to be due to host star coronal X-rays but could also arise from energetic particles produced by coronal flares, or traveling shock waves, and advected by the stellar wind. We have performed test-particle numerical simulations of energetic protons propagating into a realistic T Tauri stellar wind, including a superposed small-scale magnetostatic turbulence. The isotropic (Kolmogorov power spectrum) turbulent component is synthesized along the individual particle trajectories. We have investigated the energy range [0.1–10] GeV, consistent with expectations from Chandra X-ray observations of large flares on T Tauri stars and recent indications by the Herschel Space Observatory of a significant contribution of energetic particles to the disk ionization of young stars. In contrast with a previous theoretical study finding a dominance of energetic particles over X-rays in the ionization throughout the disk, we find that the disk ionization is likely dominated by X-rays over much of its area, except within narrow regions where particles are channeled onto the disk by the strongly tangled and turbulent magnetic field. The radial thickness of such regions is 5 stellar radii close to the star and broadens with increasing radial distance. This likely continues out to large distances from the star (10 au or greater), where particles can be copiously advected and diffused by the turbulent wind.

Finite dimensional models of the hydraulic hammer effect and solar tower control

The occurrence of traveling shock waves associated to the sudden opening or closing of a valve, known as the hammer effect, is important from the perspective of control design because it imposes an upper bound constraint on the maximum bandwidth achievable for the controlled system. This article addresses the problem of characterizing hydraulic hammer effect of the heating fluid in a solar power tower. The transfer function that relates the increments of the pressure inside the pipe and the fluid velocity is computed, as well as its poles and zeros. In this way, it is possible to obtain finite dimensional linear approximations for this transfer function with a prescribed complexity. As an application, the traveling waves of pressure and velocity of a fluid used for temperature control in a typical solar tower circuit are simulated.

Unsteady supercritical/critical dual flowpath inlet flow and its control methods

The characteristics of unsteady flow in a dual-flowpath inlet, which was designed for a Turbine Based Combined Cycle (TBCC) propulsion system, and the control methods of unsteady flow were investigated experimentally and numerically. It was characterized by large-amplitude pressure oscillations and traveling shock waves. As the inlet operated in supercritical condition, namely the terminal shock located in the throat, the shock oscillated, and the period of oscillation was about 50 ms, while the amplitude was 6 mm. The shock oscillation was caused by separation in the diffuser. This shock oscillation can be controlled by extending the length of diffuser which reduces pressure gradient along the flowpath. As the inlet operated in critical condition, namely the terminal shock located at the shoulder of the third compression ramp, the shock oscillated, and the period of oscillation was about 7.5 ms, while the amplitude was 12 mm. At this condition, the shock oscillation was caused by an incompatible backpressure in the bleed region. It can be controlled by increasing the backpressure of the bleed region.

Lithotripter shock wave interaction with a bubble near various biomaterials

Following previous work on the dynamics of an oscillating bubble near a bio-material (Ohl et al 2009 Phys. Med. Biol. 54 6313–36) and the interaction of a bubble with a shockwave (Klaseboer et al 2007 J. Fluid Mech. 593 33–56), the present work concerns the interaction of a gas bubble with a traveling shock wave (such as from a lithotripter) in the vicinity of bio-materials such as fat, skin, muscle, cornea, cartilage, and bone. The bubble is situated in water (to represent a water-like biofluid). The bubble collapses are not spherically symmetric, but tend to feature a high speed jet. A few simulations are performed and compared with available experimental observations from Sankin and Zhong (2006 Phys. Rev. E 74 046304). The collapses of cavitation bubbles (created by laser in the experiment) near an elastic membrane when hit by a lithotripter shock wave are correctly captured by the simulation. This is followed by a more systematic study of the effects involved concerning shockwave bubble biomaterial interactions. If a subsequent rarefaction wave hits the collapsed bubble, it will re-expand to a very large size straining the bio-materials nearby before collapsing once again. It is noted that, for hard bio-material like bone, reflection of the shock wave at the bone—water interface can affect the bubble dynamics. Also the initial size of the bubble has a significant effect. Large bubbles (∼1 mm) will split into smaller bubbles, while small bubbles collapse with a high speed jet in the travel direction of the shock wave. The numerical model offers a computationally efficient way of understanding the complex phenomena involving the interplay of a bubble, a shock wave, and a nearby bio-material.

Interaction of a shock wave with an array of particles and effect of particles on the shock wave weakening

Two-phase systems that involve gas-particle or gas-droplet flows are widely used in aerospace and power engineering. The problems of weakening and suppression of detonation during saturation of a gas or liquid flow with the array of solid particles are considered. The tasks, associated with the formation of particles arrays, dust lifting behind a travelling shock wave, ignition of particles in high-speed and high-temperature gas flows are adjoined to safety of space flight. The mathematical models of shock wave interaction with the array of solid particles are discussed, and numerical methods are briefly described. The numerical simulations of interaction between sub- and supersonic flows and an array of particles being in motionless state at the initial time are performed. Calculations are carried out taking into account the influence that the particles cause on the flow of carrier gas. The results obtained show that inert particles significantly weaken the shock waves up to their suppression, which can be used to enhance the explosion safety of spacecrafts.

On Some Aspects of Tsunami Waves Propagation in Ocean

Interest in transoceanic tsunami wave propagation has been revived recently. By adopting the World Geodetic System 1984 Earth model, this article presents a method to solve shallow-water long-wave equations on an ellipsoidal surface. Method of characteristics on a regular grid coupled with Strang-type splitting results in finite difference schemes with order (2, 2) accuracy both in space and time. Discontinuous solution (traveling shock wave) which may represent one kind of tsunami bore-propagating bore front step is discussed.