Formation Of Bow Shock Research Articles

Experimental investigation of flow control of a curved-surface jet at Mach 5 hypersonic flow

Jet flow-control technology is a promising area of fluid research. In this work, the flow-control effect of a curved-surface jet in an incoming flow of Mach = 5 and its underlying control mechanism are experimentally studied using high-speed photography and dynamic force measurement. From the establishment of complete stability of the flow field, the evolutionary process can be roughly divided into five stages: two equilibrium stages (short and long term), jet acceleration stage, bow shock formation stage, interference removal stage, and stable state. By defining the pressure ratio (PR) as an independent variable, it is found that the flow control of the jet occurs through different wave-system structures. The interaction between the jet and the incoming flow produces an oblique shockwave and expansion waves. The shockwave generates thrust and forms a virtual rudder surface; the expansion waves interact with the backflow region and the separated shear layer to generate lift. Moreover, PR has an optimal solution of PRopt. When PR < PRopt, the effect of flow control is related to α, Ve, and ρe, and the greater the PR, the stronger the flow-control effect. When PR > PRopt, the flow-control effect is related to α and ρe, and the larger the PR, the weaker the effect of the shockwave and the stronger the effect of the expansion waves but the slower the growth. In experiments, the thrust, pitching moment, and lift increased by 17.43%, 17.75%, and 9.45%, respectively, because of the appearance of wave-system structure when PRopt = 201.32.

Development of a cometosheath at comet 67P/Churyumov-Gerasimenko

Context. The ionosphere of a comet is known to deflect the solar wind through mass loading, but the interaction is dependent on cometary activity. We investigate the details of this process at comet 67P using the Rosetta Ion Composition Analyzer. Aims. This study aims to compare the interaction of the solar wind and cometary ions during two different time periods in the Rosetta mission. Methods. We compared both the integrated ion moments (density, velocity, and momentum flux) and the velocity distribution functions for two days, four months apart. The velocity distribution functions were projected into a coordinate system dependent on the magnetic field direction and averaged over three hours. Results. The first case shows highly scattered H+ in both ion moments and velocity distribution function. The He2+ ions are somewhat scattered, but less so, and appear more like those of H2O+ pickup ions. The second case shows characteristic evidence of mass-loading, where the solar wind species are deflected, but the velocity distribution function is not significantly changed. Conclusions. The distributions of H+ in the first case, when compared to He2+ and H2O+ pickup ions, are indicative of a narrow cometosheath on the scale of the H+ gyroradius. Thus, He2+ and H2O+, with larger gyroradii, are largely able to pass through this cometosheath. An examination of the momentum flux tensor suggests that all species in the first case have a significant non-gyrotropic momentum flux component that is higher than that of the second mass-loaded case. Mass loading is not a sufficient explanation for the distribution functions and momentum flux tensor in the first case, and so we assume this is evidence of bow shock formation.

Three-dimensional analyses of an aspherical coronal mass ejection and its driven shock

Context. Observations reveal that shocks can be driven by fast coronal mass ejections (CMEs) and play essential roles in particle accelerations. A critical ratio, δ, derived from a shock standoff distance normalized by the radius of curvature (ROC) of a CME, allows us to estimate shock and ambient coronal parameters. However, true ROCs of CMEs are difficult to measure due to observed projection effects. Aims. We investigate the formation mechanism of a shock driven by an aspherical CME without evident lateral expansion. Through three-dimensional (3D) reconstructions without a priori assumptions of the object morphology, we estimate the two principal ROCs of the CME surface and demonstrate how the difference between the two principal ROCs of the CME affects the estimate of the coronal physical parameters. Methods. The CME was observed by the Sun Earth Connection Coronal and Heliospheric Investigation instruments and the Large Angle and Spectrometric Coronagraph. We used the mask-fitting method to obtain the irregular 3D shape of the CME and reconstructed the shock surface using the bow-shock model. Through smoothings with fifth-order polynomial functions and Monte Carlo simulations, we calculated the ROCs at the CME nose. Results. We find that (1) the maximal ROC is two to four times the minimal ROC of the CME. A significant difference between the CME ROCs implies that the assumption of one ROC of an aspherical CME could cause overestimations or underestimations of the shock and coronal parameters. (2) The shock nose obeys the bow-shock formation mechanism, considering the constant standoff distance and the similar speed between the shock and CME around the nose. (3) With a more precise δ calculated via 3D ROCs in space, we derive corona parameters at high latitudes of about −50°, including the Alfvén speed and the coronal magnetic field strength.

Formation of Bow Shock Waves Around a Blunt Body in Magnetohydrodynamics Flows

The diffraction of a shock wave over a stationary body is a problem of interest associated with the starting of shock tubes and expansion tubes, which are well suited to studies of hypersonic magnetohydrodynamic flows. However, these facilities are characterized by very short test times. The transient parameters during the establishment of the detached bow shock in such impulsive facilities are important for both data processing and experimental design. In the present study, based on the low magnetic Reynolds number assumption and dipole magnetic field distribution, the influence of magnetic field on the diffraction of an incident shock wave over a sphere was studied numerically. The incident shock Mach number ranges from 11 to 15 under different magnetic field intensities. Time histories of the shock-detached distance and stagnation pressure were first obtained. Moreover, the time needed to establish the steady flows over the sphere was also displaced against the magnetic interaction parameter. The larger the magnetic interaction parameter, the longer the time needed to establish a steady bow shock for experiments, which further challenges the facilities to have sufficient test times for conducting hypersonic magnetohydrodynamic flow experiments.

Experimental observations of detached bow shock formation in the interaction of a laser-produced plasma with a magnetized obstacle

The magnetic field produced by planets with active dynamos, like the Earth, can exert sufficient pressure to oppose supersonic stellar wind plasmas, leading to the formation of a standing bow shock upstream of the magnetopause, or pressure-balance surface. Scaled laboratory experiments studying the interaction of an inflowing solar wind analog with a strong, external magnetic field are a promising new way to study magnetospheric physics and to complement existing models, although reaching regimes favorable for magnetized shock formation is experimentally challenging. This paper presents experimental evidence of the formation of a magnetized bow shock in the interaction of a supersonic, super-Alfvénic plasma with a strongly magnetized obstacle at the OMEGA laser facility. The solar wind analog is generated by the collision and subsequent expansion of two counter-propagating, laser-driven plasma plumes. The magnetized obstacle is a thin wire, driven with strong electrical currents. Hydrodynamic simulations using the FLASH code predict that the colliding plasma source meets the criteria for bow shock formation. Spatially resolved, optical Thomson scattering measures the electron number density, and optical emission lines provide a measurement of the plasma temperature, from which we infer the presence of a fast magnetosonic shock far upstream of the obstacle. Proton images provide a measure of large-scale features in the magnetic field topology, and reconstructed path-integrated magnetic field maps from these images suggest the formation of a bow shock upstream of the wire and as a transient magnetopause. We compare features in the reconstructed fields to two-dimensional MHD simulations of the system.

Evolution of heat transfer at the stagnation point during the detached bow shock establishment

The diffraction of a shock wave over a stationary body is a problem of interest associated with the starting of shock tubes and expansion tubes which are well suited to studies of hypersonic flows. However, these facilities are characterized by very short test times. The transient parameters during the establishment of the detached bow shock in such impulsive facilities are important for both data processing and experimental design. In the present study, numerical simulations are conducted to investigate the diffraction of a normal shock wave over a sphere and the subsequent transient phenomena in a viscous perfect-gas flow field. The incident shock Mach number ranges from 3 to 5 with a specific heat ratio of 1.4. Based on the theoretical description of the reflected shock position during bow shock formation, approximate solutions for the time histories of the stagnation-point heat flux are also derived. The analytical and numerical results agree well. The results show that the stagnation-point pressure and heat flux approach their steady-state values much more rapidly than the shock detachment distance does.

Evolution of Earth-like extended exospheres orbiting solar-like stars

ABSTRACT Recent observations of the Earth’s exosphere revealed the presence of an extended hydrogenic component that could reach distances beyond 40 planetary radii. Detection of similar extended exospheres around Earth-like exoplanets could reveal crucial facts in terms of habitability. The presence of these rarified hydrogen envelopes is extremely dependent on the planetary environment, dominated by the ionizing radiation and plasma winds coming from the host star. Radiation and fast wind particles ionize the uppermost layers of planetary atmospheres, especially for planets orbiting active, young stars. The survival of the produced ions in the exosphere of such planets is subject to the action of the magnetized stellar winds, particularly for unmagnetized bodies. In order to address these star–planet interactions, we have carried out numerical 2.5D ideal MHD simulations using the pluto code to study the dynamical evolution of tenuous, hydrogen-rich, Earth-like extended exospheres for an unmagnetized planet, at different stellar evolutionary stages: from a very young, solar-like star of 0.1 Gyr to a 5.0 Gyr star. For each star–planet configuration, we show that the morphology of extended Earth-like hydrogen exospheres is strongly dependent on the incident stellar winds and the produced ions present in these gaseous envelopes, showing that the ionized component of Earth-like exospheres is quickly swept by the stellar winds of young stars, leading to large bow shock formation for later stellar ages.

Interstellar medium magnetic field in bow shock modelling

PurposeThis paper aims to demonstrate the impact of interstellar (IS) magnetic field on stellar shocks existence, shape and size in the stellar wind (SW) vs interstellar medium (ISM) numerical models.Design/methodology/approachComparison of hydrodynamics (HD) and magnetohydrodynamic (MHD) models results with or without ISM magnetic field, its intensity and ISM parameters.FindingsISM magnetic field facilitates formation and stabilises bow shocks around all astrophysical objects. ISM magnetic field may also be one of the reasons for a bow shock existence around the Sun.Practical implicationsISM magnetic field should be implemented in MHD and future kinetic numerical models of the SW interaction with ISM plasma.Originality/valueThis paper presents the results of HD and MHD models of bow shocks and the importance of ISM magnetic field implementation, according to astronomical bow shock observations. The study also presents a review of the most important papers showing the numerical results of bow shock formation.

The Shock Dynamics of Heterogeneous YSO Jets:3D Simulations Meet Multi-epoch Observations

Abstract High-resolution observations of young stellar object (YSO) jets show them to be composed of many small-scale knots or clumps. In this paper, we report results of 3D numerical simulations designed to study how such clumps interact and create morphologies and kinematic patterns seen in emission line observations. Our simulations focus on clump scale dynamics by imposing velocity differences between spherical, over-dense regions, which then lead to the formation of bow shocks as faster clumps overtake slower material. We show that much of the spatial structure apparent in emission line images of jets arises from the dynamics and interactions of these bow shocks. Our simulations show a variety of time-dependent features, including bright knots associated with Mach stems where the shocks intersect, a “frothy” emission structure that arises from the presence of the Nonlinear Thin Shell Instability along the surfaces of the bow shocks, and the merging and fragmentation of clumps. Our simulations use a new non-equilibrium cooling method to produce synthetic emission maps in Hα and [S ii]. These are directly compared to multi-epoch Hubble Space Telescope observations of Herbig–Haro jets. We find excellent agreement between features seen in the simulations and the observations in terms of both proper motion and morphologies. Thus we conclude that YSO jets may be dominated by heterogeneous structures and that interactions between these structures and the shocks they produce can account for many details of YSO jet evolution.

Thermo‐structural design of ZrB2–SiC‐based thermal protection system for hypersonic space vehicles

AbstractThe leading edges of hypersonic space vehicle experience high temperature and stress due to prevailing aerothermodynamic conditions of extreme heat flux and pressure. The design of thermal protection system (TPS) to protect the metallic airframe structure can ensure longer life and reliability under flight conditions. The effective design of TPS system requires the precise quantitative understanding of thermo‐mechanical stresses and deformation, which demands careful computational study under flight simulated conditions. In the above perspective, TPS design for a leading edge exposed to Mach 7 hypersonic flow for 250 seconds has been carried out by performing finite element‐based thermo‐structural analysis with pressure and heat flux estimated from computational fluid dynamics analysis (CFD). The fidelity and robustness of CFD scheme is established using grid independence and convergence analysis. CFD analysis effectively captures the formation of bow shock around the leading edge and stagnation region near its nose. For finite element analysis, high‐quality structural elements have been generated using HyperMesh to precisely model the thermo‐structural behavior of TPS. In our computational analysis, TPS is modeled as a three‐layered system with outermost layer of ZrB2‐SiC, middle layer of phenolic cork and innermost layer of Ti‐alloy. The analytical values of spatial variation of temperature, stress components, and displacement across the TPS have been critically analysed to rationalise specific structural configuration for better thermo‐structural stability. Together with temporal variation of temperature, the implication of such computational results has led us to propose a new design for TPS. The proposed TPS is capable of containing the stress and displacement within 32 MPa and 0.58 mm, respectively, when the leading edge is exposed to shock induced aero‐thermal heating as high as 2.11 MW/m2 and pressure of 72.8 kPa for a hypersonic cruise flight of 500 km range.

PLANETARY EMBRYO BOW SHOCKS AS A MECHANISM FOR CHONDRULE FORMATION

ABSTRACT We use radiation hydrodynamics with direct particle integration to explore the feasibility of chondrule formation in planetary embryo bow shocks. The calculations presented here are used to explore the consequences of a Mars-size planetary embryo traveling on a moderately excited orbit through the dusty, early environment of the solar system. The embryo’s eccentric orbit produces a range of supersonic relative velocities between the embryo and the circularly orbiting gas and dust, prompting the formation of bow shocks. Temporary atmospheres around these embryos, which can be created via volatile outgassing and gas capture from the surrounding nebula, can non-trivially affect thermal profiles of solids entering the shock. We explore the thermal environment of solids that traverse the bow shock at different impact radii, the effects that planetoid atmospheres have on shock morphologies, and the stripping efficiency of planetoidal atmospheres in the presence of high relative winds. Simulations are run using adiabatic and radiative conditions, with multiple treatments for the local opacities. Shock speeds of 5, 6, and 7 km s−1 are explored. We find that a high-mass atmosphere and inefficient radiative conditions can produce peak temperatures and cooling rates that are consistent with the constraints set by chondrule furnace studies. For most conditions, the derived cooling rates are potentially too high to be consistent with chondrule formation.

Mixing Characteristics of Inclined Fuel Injection via Various Geometries for Upstream-Fuel-Injected Scramjets

Efficient fuel/air mixing plays a crucial role in successful operation of hypersonic airbreathing engines, particularly scramjets, where fuel must be injected into high-speed crossflow and mixed with air at an extremely short timescale. This paper presents the results of a numerical study that investigates the effects of various orifice shapes on fuel mixing characteristics into hypersonic airflow at Mach 5, aiming at the application to scramjet operation with upstream fuel injection at Mach 10. The performance of the injectors at an inclination angle of 45 deg are assessed with respect to various criteria such as the mixing efficiency, streamwise circulation, total pressure recovery, fuel penetration, and spread. Streamwise slot injectors have been found to yield higher mixing efficiency than the other injectors tested (namely, square, circular, diamond, and triangular injectors), owing to the buffering effects. Apparent higher total pressure recovery has been obtained with these rectangular injectors, but their advantages have diminished significantly with the alignment of the trailing-edge position. The highest vertical penetration has been achieved by the square injector, whereas the performances of other injectors with a sharp leading edge have been found to be affected considerably by the axis switch phenomenon due to inclined injection at higher injection pressure. A major influence of the fore and aft shapes of the orifice has been observed on the three-dimensional bow shock formation and wake recirculation, respectively.

Investigation of radiative bow-shocks in magnetically accelerated plasma flows

We present a study of the formation of bow shocks in radiatively cooled plasma flows. This work uses an inverse wire array to provide a quasi-uniform, large scale hydrodynamic flow accelerated by Lorentz forces to supersonic velocities. This flow impacts a stationary object placed in its path, forming a well-defined Mach cone. Interferogram data are used to determine a Mach number of ∼6, which may increase with radial position suggesting a strongly cooling flow. Self-emission imaging shows the formation of a thin (<60 μm) strongly emitting shock region, where Te ∼ 40–50 eV, and rapid cooling behind the shock. Emission is observed upstream of the shock position which appears consistent with a radiation driven phenomenon. Data are compared to 2-dimensional simulations using the Gorgon MHD code, which show good agreement with the experiments. The simulations are also used to investigate the effect of magnetic field in the target, demonstrating that the bow-shocks have a high plasma β, and the influence of B-...

STELLAR SIGNATURES OF AGN-JET-TRIGGERED STAR FORMATION

To investigate feedback between relativistic jets emanating from Active Galactic Nuclei (AGN) and the stellar population of the host galaxy, we analyze the long-term evolution of the galaxy-scale simulations by Gaibler et al. (2012) of jets in massive, gas-rich galaxies at z ~ 2 - 3 and of stars formed in the host galaxies. We find strong, jet-induced differences in the resulting stellar populations of galaxies that host relativistic jets and galaxies that do not, including correlations in stellar locations, velocities, and ages. Jets are found to generate distributions of increased radial and vertical velocities that persist long enough to effectively extend the stellar structure of the host. The jets cause the formation of bow shocks that move out through the disk, generating rings of star formation within the disk. The bow shock often accelerates pockets of gas in which stars form, yielding populations of stars with significant radial and vertical velocities, some of which have large enough velocities to escape the galaxy. These stellar population signatures can serve to identify past jet activity as well as jet-induced star formation.

Erratum: Detecting floating black holes as they traverse the gas disc of the Milky Way

A population of intermediate-mass black holes (BHs) is predicted to be freely floating in the Milky Way (MW) halo, due to gravitational wave recoil, ejection from triple BH systems, or tidal stripping in the dwarf galaxies that merged to make the MW. As these BHs traverse the gaseous MW disk, a bow shock forms, producing detectable radio and mm/sub-mm synchrotron emission from accelerated electrons. We calculate the synchrotron flux to be $\sim \rm 0.01-10\, mJy$ at GHz frequency, detectable by Jansky Very Large Array, and $\sim 10-100\,\mu\rm Jy$ at $\sim10^{10}-10^{12} \,\rm Hz$ frequencies, detectable by Atacama Large Millimeter/sub-millimter Array. The discovery of the floating BH population will provide insights on the formation and merger history of the MW as well as on the evolution of massive BHs in the early Universe.

MAGNETOSPHERIC STRUCTURE AND ATMOSPHERIC JOULE HEATING OF HABITABLE PLANETS ORBITING M-DWARF STARS

We study the magnetospheric structure and the ionospheric Joule Heating of planets orbiting M-dwarf stars in the habitable zone using a set of magnetohydrodynamic (MHD) models. The stellar wind solution is used to drive a model for the planetary magnetosphere, which is coupled with a model for the planetary ionosphere. Our simulations reveal that the space environment around close-in habitable planets is extreme, and the stellar wind plasma conditions change from sub- to super-Alfvenic along the planetary orbit. As a result, the magnetospheric structure changes dramatically with a bow shock forming in the super-Alfvenic sectors, while no bow shock forms in the sub-Alfvenic sectors. The planets reside most of the time in the sub-Alfvenic sectors with poor atmospheric protection. A significant amount of Joule Heating is provided at the top of the atmosphere as a result of the planetary interaction with the stellar wind. For the steady-state solution, the heating is about 0.1-3\% of the total incoming stellar irradiation, and it is enhanced by 50\% for the time-dependent case. The significant Joule Heating obtained here should be considered in models for the atmospheres of habitable planets in terms of the thickness of the atmosphere, the top-side temperature and density, the boundary conditions for the atmospheric pressure, and particle radiation and transport.

Detecting floating black holes as they traverse the gas disc of the Milky Way

A population of intermediate-mass black holes (BHs) is predicted to be freely floating in the Milky Way (MW) halo, due to gravitational wave recoil, ejection from triple BH systems, or tidal stripping in the dwarf galaxies that merged to make the MW. As these BHs traverse the gaseous MW disk, a bow shock forms, producing detectable radio and mm/sub-mm synchrotron emission from accelerated electrons. We calculate the synchrotron flux to be $\sim \rm 0.01-10\, mJy$ at GHz frequency, detectable by Jansky Very Large Array, and $\sim 10-100\,\mu\rm Jy$ at $\sim10^{10}-10^{12} \,\rm Hz$ frequencies, detectable by Atacama Large Millimeter/sub-millimter Array. The discovery of the floating BH population will provide insights on the formation and merger history of the MW as well as on the evolution of massive BHs in the early Universe.

Can the magnetic field in the Orion arm inhibit the growth of instabilities in the bow shock of Betelgeuse?

Many evolved stars travel through space at supersonic velocities, which leads to the formation of bow shocks ahead of the star where the stellar wind collides with the interstellar medium (ISM). Herschel observations of the bow shock of $\alpha$-Orionis show that the shock is almost free of instabilities, despite being, at least in theory, subject to both Kelvin-Helmholtz and Rayleigh-Taylor instabilities. A possible explanation for the lack of instabilities lies in the presence of an interstellar magnetic field. We wish to investigate whether the magnetic field of the interstellar medium (ISM) in the Orion arm can inhibit the growth of instabilities in the bow shock of $\alpha$-Orionis. We used the code MPI-AMRVAC to make magneto-hydrodynamic simulations of a circumstellar bow shock, using the wind parameters derived for $\alpha$-Orionis and interstellar magnetic field strengths of $B\,=\,1.4,\, 3.0$, and $5.0\, \mu$G, which fall within the boundaries of the observed magnetic field strength in the Orion arm of the Milky Way. Our results show that even a relatively weak magnetic field in the interstellar medium can suppress the growth of Rayleigh-Taylor and Kelvin-Helmholtz instabilities, which occur along the contact discontinuity between the shocked wind and the shocked ISM. The presence of even a weak magnetic field in the ISM effectively inhibits the growth of instabilities in the bow shock. This may explain the absence of such instabilities in the Herschel observations of $\alpha$-Orionis.

Transient bow shock around a cylinder in a supersonic dusty plasma

Visual observations of the formation of a bow shock in the transient supersonic flow of a dusty plasma incident on a biased cylinder are presented. The bow shock formed when the advancing front of a streaming dust cloud was reflected by the obstacle. After its formation, the density jump of the bow shock increased as it moved upstream of the obstacle. A physical picture for the formation of the electrohydrodynamic bow shock is discussed.

THE GALACTIC CENTER CLOUD G2—A YOUNG LOW-MASS STAR WITH A STELLAR WIND

We explore the possibility that the G2 gas cloud falling in towards \sgra is the mass loss envelope of a young TTauri star. As the star plunges to smaller radius at 1000 to 6000 \kms, a strong bow shock forms where the stellar wind is impacted by the hot X-ray emitting gas in the vicinity of \sgra. For a stellar mass loss rate of $4\times10^{-8}$ \msun per yr and wind velocity 100 \kms, the bow shock will have an emission measure ($EM = n^2 vol$) at a distance $\sim10^{16}$ cm, similar to that inferred from the IR emission lines. The ionization of the dense bow shock gas is potentially provided by collisional ionization at the shock front and cooling radiation (X-ray and UV) from the post shock gas. The former would predict a constant line flux as a function of distance from \sgra, while the latter will have increasing emission at lesser distances. In this model, the star and its mass loss wind should survive pericenter passage since the wind is likely launched at 0.2 AU and this is much less than the Roche radius at pericenter ($\sim3$ AU for a stellar mass of 2\msun). In this model, the emission cloud will probably survive pericenter passage, discriminating this scenario from others.