Bow Shock Front Research Articles

Алгоритми розрахунку надзвукового обтікан¬ня ракети-носія з кільцевим крилом

This paper presents algorithms to calculate supersonic flow about a prospective ring wing launch vehicle by the marching method and the relaxation method. The feature of the algorithms is the introduction of two computational subregions in the ring wing zone over the rocket airframe. In the marching algorithm, the computation region is reconstructed according to the position of the marching cross-section relative to the leading and trailing edge of the ring wing. When it finds itself at the leading edge of the ring wing, the computational region is split into a lower subregion between the rocket airframe and the downstream face of the ring wing and an upper subregion between the upstream face of the ring wing and the bow shock front. When the marching cross-section finds itself at the trailing edge of the ring wing, the lower and the upper computational subregions are merged into a single computational region. Based on the marching algorithm and using the authors’ rocket flow calculation program, software is developed for a fast numerical calculation of supersonic flow about ring wing rockets. For a particular ring wing rocket configuration, the paper presents the results of comparative calculations of supersonic flow about the rocket in the form of gas-dynamic parameter isolines in the flow field and the pressure distribution over the rocket airframe and the ring wing. The results for the marching method and the relaxation method are compared. It is shown that the ring wing is responsible for an undulatory pressure distribution between the rocket airframe and the downstream face of the ring wing. The marching method simulates the flow pattern between the rocket airframe and the downstream face of the ring wing more adequately, and its computation time is two orders of magnitude shorter than that of the relaxation method. The relaxation method should be used in the case of subsonic flows between the rocket airframe and the downstream face of the ring wing. The algorithm and software developed are recommended for parametric calculations of supersonic flow about ring wing rockets.

Estimation of the Propagation Time of the Solar Wind Pressure Pulse between a Shock Wave and the Magnetopause Based on Simultaneous Satellite and Ground-Based Observations

The propagation of solar wind inhomogeneities through the transition region between the bow shock front and the daytime magnetopause is an important link in the chain of solar-terrestrial connections. We analyzed a unique situation when two THEMIS satellites were near the bow shock during the solar wind pressure pulse, and the favorable location of the ground-based magnetometric equipment made it possible to determine the time of the solar wind impact on the magnetopause with greater accuracy than it was done previously. Based on the measurements, the propagation time of sudden impulse (SI) in the magnetosheath was estimated. The obtained value (~1 min) agrees with model calculations, but turns out to be 2–3 times less than that previously obtained by other authors also from satellite and ground-based observations. The propagation velocity of the solar wind in the magnetosheath (~280 km/s), the displacement velocity of the bow shock front to the Earth (~80 km/s), and the thickness of the magnetosheath at the location of the satellites (2.6–3.9RE) are determined.

Impact of a thermally stratified energy source on the bow shock wave and aerodynamic characteristics of a body

This paper presents numerical modelling of a thermally stratified energy source’s effect on the supersonic flow past a body “double-wedge - plate”. A multiple generation of the Richtmyer-Meshkov instabilities was obtained. These instabilities cause almost complete destruction of the bow shock front inside the source area and form a new multi-vortex mechanism of affecting the streamlined body. The defining parameters of the effect of stratified and homogeneous energy sources with equal values of total energy are analysed. The possibility of a significant decrease in the temperature at the vertex of the double-wedge and in the average front surface temperature due to the redistribution of source energy between layers has been established.

Influence of Particle on Gas Detonation by Shock

There exist evidence, that the gaseous detonation passing through a cloud of solid particles could be attenuated or even suppressed. Contrary to these known works, in the present article, we have found that just one single 160-micron particle can serve as a trigger for the detonation onset. By numerical simulation, we have obtained that there are the concentration ratio limits, in which single particle is enough to initiate gaseous detonation, although without particle the detonation is not ignited in the same conditions in a tube of restricted size. In other words, the presence of a solid particle in the combustible mixture could decrease significantly the ignition delay time. Using of temperature pattern visualization, we have demonstrated that the ignition arises in the subsonic region located between the particle and the bow shock front. The approximations of the used model are discussed. It is shown that used assumptions are valid within investigated time intervals. The work performed with use of the supercomputer resources Interdepartmental Supercomputer Center Russian Academy of Sciences (ISC RAS)

Interstellar Medium Parameters in Front of the External Bow Shock

We know that it is the front of the Earth’s bow shock where the solar wind kinetic energy flux is transformed into the other kinds the most intensively. In our previous studies, we obtained important relationships that enable calculating the key parameters at transition through the Earth’s bow shock front. One of the most important sources of information on physical processes at the heliosphere boundary are the Voyager 1 and 2 spacecrafts. Since both the solar wind and interstellar medium are supersonic streams, two shocks are formed when flowing around the heliopause. The internal shock, in which the solar wind decelerates to subsonic velocity, is called the heliospheric shock. In the external bow shock, the interstellar gas supersonic flux is decelerated. The aim of this paper is to generalize the previously obtained equations to the processes in the external bow shock region. If Voyager-1 was equipped with a greater set of measuring instruments, we could have already provided estimations of the interstellar medium key parameters, and described in physical terms what this medium is, using relationships and equations from our studies.

MHD heat flux mitigation in hypersonic flow around a blunt body with ablating surface

One of the possible applications of magnetohydrodynamic flow control is considered. Namely, the surface heat flux mitigation by means of magnetohydrodynamic (MHD) interaction in hypersonic flow around a blunt body. The 2D computational model realizes a coupled solution of chemically non-equilibrium ionized airflow in magnetic field. Heat- and mass-transfer due to the ablation of materials from the body surface is taken into account.Two cases of free-stream flow conditions are considered: moderate free-stream velocity (7500 m s−1) case and high free-stream velocity (11 000 m s−1) case. It is shown that the first flow case results in moderate ionization in the shock layer, while the second flow case results in high ionization. In the first case, the Hall effect is significant, and effective electrical conductivity in the shock layer is rather low. In the second case, the Hall effect reduces, and effective conductivity is high. Even if the Hall effect is strong, as in the first case, intensive MHD deceleration of the flow behind the shock is provided due to the presence of insulating boundaries, the bow shock front and non-conductive wall of the blunt body. In the second case, high effective conductivity provides a high intensity of MHD flow deceleration. In both cases, a strong effect of MHD interaction on the flow structure is observed. As a consequence, a noticeable reduction of the surface heat flux is revealed for reasonable values of magnetic induction. The new treatment of mechanism for the surface heat flux reduction is proposed, which is different from commonly used one assuming that MHD interaction increases the bow shock stand-off distance, and, consequently results in a decrease of the mean temperature drop across the shock layer. The new effect of ‘saturation of heat flux’ is discussed.

Limits of shock wave ignition of hydrogen–oxygen mixture in the presence of particles

It is a well known fact that the cloud of non-reacting particles in the flow weakens or even suppresses the detonation. Contrary to this phenomenon there are experimental data showing that the presence of solid particles in the combustible mixtures shorten significantly the ignition delay time. In other words particles could promote the initiation of detonation. This paper analyzes numerically the phenomenon of detonation initiation behind the shock wave in the combustible mixture containing only one solid particle. Numerical results demonstrate a significant degree of lowering of ignition limits. Namely, it is shown that it becomes possible to ignite the gaseous mixture much earlier due to the shock wave interaction with solid particle surface. It is found that ignition arises in subsonic region located between the particle and the bow shock front.

Features in the Behavior of the Solar Wind behind the Bow Shock Front near the Boundary of the Earth’s Magnetosphere

Macroscopic discontinuous structures observed in the solar wind are considered in the framework of magnetic hydrodynamics. The interaction of strong discontinuities is studied based on the solution of the generalized Riemann–Kochin problem. The appearance of discontinuities inside the magnetosheath after the collision of the solar wind shock wave with the bow shock front is taken into account. The propagation of secondary waves appearing in the magnetosheath is considered in the approximation of one-dimensional ideal magnetohydrodynamics. The appearance of a compression wave reflected from the magnetopause is indicated. The wave can nonlinearly break with the formation of a backward shock wave and cause the motion of the bow shock towards the Sun. The interaction between shock waves is considered with the well-known trial calculation method. It is assumed that the velocity of discontinuities in the magnetosheath in the first approximation is constant on the average. All reasonings and calculations correspond to consideration of a flow region with a velocity less than the magnetosonic speed near the Earth–Sun line. It is indicated that the results agree with the data from observations carried out on the WIND and Cluster spacecrafts.

Fine structure of the interplanetary shock front according to measurements of the ion flux of the solar wind with high time resolution

According to the data of the BMSW/SPEKTR-R instrument, which measured the density and velocity of solar wind plasma with a record time resolution, up to ~3 ×10–2 s, the structure of the front of interplanetary shocks has been investigated. The results of these first investigations were compared with the results of studying the structure of the bow shocks obtained in previous years. A comparison has shown that the quasi-stationary (averaged over the rapid oscillations) distribution of plasma behind the interplanetary shock front was significantly more inhomogeneous than that behind the bow-shock front, i.e., in the magnetosheath. It has also been shown that, to determine the size of internal structures of the fronts of quasi-perpendicular (θBN > 45°) shocks, one could use the magnetic field magnitude, the proton density, and the proton flux of the solar wind on almost equal terms. A comparison of low Mach (МА < 2), low beta (β1 < 1) fronts of interplanetary and bow shocks has shown that the dispersion of oblique magnetosonic waves plays an essential role in their formation.

Origin of the backstreaming ions in a young Hot Flow Anomaly

We analyze an event in front of the bow shock observed by Cluster spacecraft on 22.02.2006. This event has many attributes of Hot Flow Anomaly at early stage of development including strong upstream beam and disturbed magnetic profile with increased magnetic field at one or two sides as observed by 4 Cluster spacecraft. The angle between the magnetic field vectors at two sides of the current sheet was ~10°. The minimum magnetic field magnitude within HFA was ~1nT. The shock at two sides of the HFA was quasi-perpendicular. Upstream beam was observed on the leading side of the HFA. Parameters and velocity distributions of solar wind ions and of upstream ions observed on C1 and C3 spacecraft are analyzed separately in order to trace their changes across the event. The goal of this analysis was to get more information about the source of upstream beam. The beam evolved from the start of its observation till the HFA encounter being initially energetic and nearly mono-energetic. Its mean energy continuously decreased and energy spectrum widened as HFA approached spacecraft. First observation of particular energy that diminished with approaching the HFA varied linearly with gyro-radius of ions. The energy spectra of integrated beam (for all observation) and the energy spectrum of the beam observed just in front of HFA are very similar to the magnetosheath ion energy spectrum observed after bow shock crossing at ~1h after observation of the HFA. Lowest energies in the beam were observed within HFA only. Highest density and pressure of upstream beam are found in the current sheet itself. We suggest that the upstream beam is the result of the magnetosheath ions leakage through the region of HFA crossing with the bow shock front.

Study and comparison of the parameters of five hot flow anomalies at a bow shock front

Five hot flow anomalies (HFA) recorded by the Tail Probe of the INTERBALL satellite in 1996 are analyzed in present work. For the five chosen events the authors determined the characteristics of current sheets whose interaction with the bow shock front led to formation of an HFA, as well as the directions of external electric fields and the directions of motion of these HFAs over a shock front. The analysis of plasma convection in an HFA body is carried out; the average velocities of plasma motion in the HFA are determined in a coordinate system linked with the normal to a current layer and with the normal to the bow shock. According to the character of plasma convection in an HFA body, these five events may be divided into two types, which also differ in the direction of the motion over the front of the bow shock. In the first-type HFAs, the convection of plasma has a component directed from the intermediate region confirming its identification as a source of energy for the formation of an HFA. In the second-type HFAs, plasma motion from the intermediate region in leading and trailing parts is less expressed. This fact, as well as the great variation of peculiar velocities in the body of anomalies, allowed the assumption that second-type anomalies are nonstationary. Evidence is presented that the anomalies considered in the paper are bordered with shocks formed in solar wind passing a large-scale, decelerated body of heated plasma.

BOW SHOCK FRAGMENTATION DRIVEN BY A THERMAL INSTABILITY IN LABORATORY ASTROPHYSICS EXPERIMENTS

The role of radiative cooling during the evolution of a bow shock was studied in laboratory-astrophysics experiments that are scalable to bow shocks present in jets from young stellar objects. The laboratory bow shock is formed during the collision of two counter-streaming, supersonic plasma jets produced by an opposing pair of radial foil Z-pinches driven by the current pulse from the MAGPIE pulsed-power generator. The jets have different flow velocities in the laboratory frame and the experiments are driven over many times the characteristic cooling time-scale. The initially smooth bow shock rapidly develops small-scale non-uniformities over temporal and spatial scales that are consistent with a thermal instability triggered by strong radiative cooling in the shock. The growth of these perturbations eventually results in a global fragmentation of the bow shock front. The formation of a thermal instability is supported by analysis of the plasma cooling function calculated for the experimental conditions with the radiative packages ABAKO/RAPCAL.

Detailed kinematic investigation of Herbig-Haro objects in the northeast region of NGC7129

Using the Fabry-Perot scanning interferometer at the SAO RAS 6-m telescope, we studied a number of Herbig-Haro objects in the northeast region of NGC7129. We detected a helicoidal flow in HH234, consisting of separate high-speed knots propagating within the cavity in the interstellar medium created by the outflow. HH235 consists of at least five knots, each of which form its own bow shock front. The direction of these fronts together with the NW-SE oriented high-velocity core of the flow indicate the location of a possible source. The origin of the objects HH105 and HH821 is discussed as well. Possible Herbig-Haro outflow sources in this region are located further north of the cluster center in the vicinity of the active star V350 Cep, except for HH234 with a known source. It can be considered ascertained that the NGC7129 region consists of several star-forming cores, in which multiple outflows from stars of different masses are present.

The magnetic hole as plasma inhomogeneity in the solar wind and related interplanetary medium perturbations

We considered magnetic hole-type plasma structures with a constant total pressure, which are often observed in the flux of the solar wind. The interaction between a linear magnetic hole and the front of the primary or bow shock wave before the Earth’s magnetosphere was studied, and the appearance of a fast shock wave in the magnetosheath and displacement of the bow shock front in the direction of the Earth’s magnetosphere is described. The magnetic hole in the scope of the MHD theory is considered a plasma inhomogeneity bounded by two tangential discontinuities: the front and rear boundaries. Based on the MHD theory of nonlinear interactions of solar wind discontinuity structures with a magnetic hole, the appearance of new automodel and MHD shock waves inside the magnetic hole is shown. The obtained results, which provide evidence of a change in the configuration of the magnetic hole and a displacement of the bow shock front due to the perturbation from the solar wind, are qualitatively verified in many aspects by observations performed earlier by the Cluster and ACE spacecrafts.

Bow shock: Power aspects

It is clear that the primary energy source for magnetospheric processes is the solar wind, but the process of energy transfer from the solar wind into the magnetosphere, or rather, to convecting magnetospheric plasma, appears to be rather complicated. Bow shock is a powerful transformer of the solar wind kinetic energy into the gas dynamic and electromagnetic energy. A jump of the magnetic field tangential component at front crossing means that the front carries an electric current. The solar wind kinetic energy partly transforms to gas kinetic and electromagnetic energy during its passage through the bow shock front. The transition layer (magnetosheath) can use part of this energy for accelerating of plasma, but can conversely spend part its kinetic energy on the electric power generation, which afterwards may be used by the magnetosphere. Thereby, transition layer can be both consumer (sink) and generator (source) of electric power depending upon special conditions. The direction of the current behind the bow shock front depends on the sign of the IMF Bz-component. It is this electric current which sets convection of plasma in motion.

Transformation of solar wind energy into the energy of magnetospheric processes

When the solar wind flows round the magnetosphere, its flow structure and interplanetary magnetic field lines are affected. This indicates the appearance of an electric current system in near-Earth space. the magnetized solar wind plasma moving at the solar wind velocity in the coordinate system of near-earth bow shock induces an electric field in this system. When crossing the bow shock front at the nose point, the tangential magnetic field component increases nearly four times, and the magnetic field energy density—15 times.

Nonlinear phenomena related to the solar shock motion in the Earth’s magnetosphere

The motion of the MHD nonlinear shock in the Earth’s magnetosphere is considered in the scope of magnetic hydrodynamics. This wave comes from the solar wind and is refracted into the magnetosphere, generating a fast return rarefaction wave. It has been indicated that a wave refracted into the magnetosphere is a weak fast dissipative shock, propagating in magnetospheric plasma at a velocity higher than its propagation velocity in a solar wind stream. The wave motion near the Earth-Sun line with regard to the effect of the geomagnetic field transverse component is described. In this case, shock damping follows the generalized Crussard-Landau law and a wave retains its shock character up to the plasmapause, interacting with this region when an arbitrary MHD discontinuity is disintegrated. It is stated that an MHD shock loses its shock character when moving in a strongly inhomogeneous plasma within the plasmasphere and a weak shock reflected from the plasmapause can combine with a return secondary shock in the magnetosheath, promoting the experimentally observed backward motion of the bow shock front.

On one mechanism for the generation of a reverse solar wind shock in the magnetosheath in front of the Earth’s magnetosphere

A possible mechanism for the generation of a reverse fast shock in the magnetosheath in the solar wind flow around the Earth’s magnetosphere is considered. It is shown that such a shock can emerge through the breaking of a nonlinear fast magnetosonic compression wave reflected from the magnetopause toward the bow shock rear. In this case, the magnetopause is represented as a tangential discontinuity with a zero normal magnetic field component at it and the mechanism under consideration is assumed to be secondary with respect to the sudden disturbance of the bow shock-Earth’s magnetosphere system by a nonstationary solar wind shock. A possible confirmation of the process under study by in-situ SC3 experimental observations of the bow shock front motion on the Cluster spacecraft is pointed out.

Dynamics of ion sound waves in the front of the terrestrial bow shock

Abstract. Single spacecraft measurements from the Cluster 3 satellite are used to identify nonlinear processes in ion-sound turbulence observed within the front of the quasiperpendicular terrestrial bow shock. Ion sound waves possess spatial scales that are too small for the efficient use of multipoint measurements on inter-satellite separation scales. However, it is shown how frequency domain modelling can be applied to single spacecraft electric field data obtained using the EFW internal burst mode. The resulting characteristics of the nonlinear processes are used to argue about the possible wave sources and investigate their dynamics.

Dependence of the power consumed by the magnetosphere on the solar wind parameters

The results of the previous studies, where the expressions were obtained for the electric current, which is generated at the bow shock front and is closed through the magnetosphere, and for the magneto-pause potential as a function of such solar wind parameters as the plasma density and velocity and the IMF intensity, are used. The power (W) consumed by the magnetosphere is equal to the Poynting vector flux S through the magnetopause. According to the special case of the Poynting theorem applied by Heikkila to the-magnetosphere, the energy flux can be expressed in terms of the electric potential (the integration is carried out over the entire surface of the magnetosphere). As a result, the required dependence, which is quadratic with respect to the IMF Bz component, has been obtained for W. It is discussed why the magnetosphere is energy-isolated at the northward IMF Bz component despite this.