Bow Shock Standoff Distance Research Articles

Non-monotonic dependence of the bow shock stand-off distance on the velocity of a CO2 flow about a sphere

A non-monotonic dependence of the bow shock stand-off distance around a spherical body recently observed in ballistic range experiments in CO2 is explained by a qualitative theoretical analysis and confirmed numerically. The analysis is based on the estimation of the average density in the shock layer with the Rankine–Hugoniot relations on the normal shock for chemically frozen and chemically equilibrium limits using a simplified chemistry model. The analysis reveals that a maximum of the density ratio across the shock and, therefore, a minimum of the stand-off distance as functions of the flight velocity are normally observed in CO2 and other gases, such as additionally considered N2, both in frozen and equilibrium flows. The low dissociation energy of CO2 results in relatively low flight velocities (around 5 km/s) at which the extrema are observed. It makes the effect more readily detectable in experiments in CO2 than in the Earth's atmosphere gases. The results of numerical simulations of the CO2 flow by solving the Navier–Stokes equations agree well with the ballistic range experiments and fully support the results of the theoretical analysis.

In situ plasma and neutral gas observation time windows during a comet flyby: Application to the Comet Interceptor mission

A comet flyby, like the one planned for ESA’s Comet Interceptor mission, places stringent requirements on spacecraft resources. To plan the time line of in situ plasma and neutral gas observations during the flyby, the size of the comet magnetosphere and neutral coma must be estimated well. For given solar irradiance and solar wind conditions, comet composition, and neutral gas expansion speed, the size of gas coma and magnetosphere during the flyby can be estimated from the gas production rate and the flyby geometry. Combined with flyby velocity, the time spent in these regions can be inferred and a data acquisition plan can be elaborated for each instrument, compatible with the limited data storage capacity. The sizes of magnetosphere and gas coma are found from a statistical analysis based on the probability distributions of gas production rate, flyby velocity, and solar wind conditions. The size of the magnetosphere as measured by bow shock standoff distance is 105–106km near 1au in the unlikely case of a Halley-type target comet, down to a nonexistent bow shock for targets with low activity. This translates into durations up to 103–104 seconds. These estimates can be narrowed down when a target is identified far from the Sun, and even more so as its activity can be predicted more reliably closer to the Sun. Plasma and neutral gas instruments on the Comet Interceptor main spacecraft can monitor the entire flyby by using an adaptive data acquisition strategy in the context of a record-and-playback scenario. For probes released from the main spacecraft, the inter-satellite communication link limits the data return. For a slow flyby of an active comet, the probes may not yet be released during the inbound bow shock crossing.

Mercury’s Bow Shock and Magnetopause Variations According to MESSENGER Data

Using data from the MESSENGER spacecraft magnetometer that describes the magnetopause and the bow shock crossing points of the Mercury’s magnetosphere, we have calculated the parameters of the paraboloids of revolution approximating the obtained points. For each spacecraft orbit, the subsolar magnetopause and bow shock standoff distances were obtained, based on the paraboloid parameters for each crossing point. The dependences of the magnetopause and bow shock subsolar standoff distances on the Mercury’s position relative to the Sun have been obtained. These profiles agree with decreases of the solar wind plasma dynamic pressure and the interplanetary magnetic field strength with heliocentric distance. The variations of the interplanetary and magnetosheath magnetic field were investigated. The average subsolar magnetosheath thickness and the value of the magnetic field jump at the bow shock during the transition from the upstream interplanetary magnetic field region to the magnetosheath were obtained.

Solar wind entry into Mercury’s magnetosphere: Simulation results for the second swingby of BepiColombo

Context. We use a global 3D hybrid plasma model to investigate the interaction between Mercury’s magnetosphere and the solar wind for the second BepiColombo swingby, evaluate magnetospheric regions, and study the typical energy profile of protons. Aims. The objective of this study is to gain a better understanding of solar wind entry and analyze simulated plasma data along a trajectory using BepiColombo swingby 2 conditions, with the goal of enhancing our comprehension of measurement data and potentially providing forecasts for future swingbys. Methods. To model Mercury’s plasma environment, we used the hybrid code AIKEF and developed a method to extract the particle (ion) data in order to compute the proton energy spectrum along the trajectory of BepiColombo during its second Mercury swingby on June 23, 2022. We evaluate magnetopause and bow shock stand-off distances under average upstream solar wind conditions with the Interplanetary Magnetic Field (IMF) condition derived from the BepiColombo magnetic field measurements during the second Mercury swingby. Results. We found that the magnetosheath on the quasi-perpendicular (dusk) side of the bow shock is thicker than that on the quasi-parallel (dawn) side, where a foreshock is formed. Multiple plasma populations can be extracted from our modeled energy spectra that assist in identifying magnetospheric regions. We observed protons of solar wind origin entering Mercury’s magnetosphere. Their energies range from a few electron volts in the magnetosphere up to 10 keV in the magnetosheath.

Resolving the Bow Shock and Tail of the Cannonball Pulsar PSR J0002+6216

We present X-ray and radio observations of the recently discovered bow-shock pulsar wind nebula (PWN) associated with PSR J0002+6216, characterizing the PWN morphology, which was unresolved in previous studies. The multifrequency, multiepoch Very Large Array (VLA) radio observations reveal a cometary tail trailing the pulsar and extending up to 5.′3, with multiple kinks along the emission. The presented radio continuum images from multiconfiguration broadband VLA observations are one of the first results from the application of multiterm multifrequency synthesis deconvolution in combination with the AWProject gridder implemented in the Common Astronomy Software Applications (CASA) package. The X-ray emission observed with Chandra extends to only 21″, fades quickly, and has some hot spots present along the extended radio emission. These kinks could indicate the presence of density variations in the local interstellar medium or turbulence. The bow-shock standoff distance estimates a small bow-shock region with a size of 0.003–0.009 pc, consistent with the pulsar spin-down power of = 1.51 × 1035 erg s−1 estimated from timing. The high-resolution radio image reveals the presence of an asymmetry in the bow-shock region, which is also present in the X-ray image. The broadband radio image shows an unusually steep spectrum along with a flat-spectrum sheath, which could indicate varying opacity or energy injection into the region. Spatially resolved X-ray spectra provide marginal evidence of synchrotron cooling along the extended tail. Our analysis of the X-ray data also shows that this pulsar has a low spin-down power and one of the lowest X-ray efficiencies observed in these objects.

Experimental Investigation of Flow Interaction Dynamics in Supersonic Retropropulsion

Supersonic retropropulsion experiments were performed using a 12.7-cm-diameter 70 deg sphere–cone body with a single jet in the center of the model with a 4:1-area-ratio Laval nozzle directed into a Mach 4 freestream. Data were acquired using high-speed schlieren imaging and direct axial force measurements. Spectral analyses of the total axial force, jet total pressure, and bow shock standoff distance were performed, resulting in the observation of three characteristic modes. For all tests, a dominant frequency in the axial force, independent of the jet and tunnel flow, of 1.9 kHz was observed, which was determined to be a structural vibration mode. A mode at 4.2 kHz in the axial force is observed to correspond to the motion of flow structures, suggesting a coupling between the jet flow and the freestream. A dependency on the presence of the jet and the selection of jet gas is shown for a 13.7 kHz mode, indicating it is acoustic in nature. Proper orthogonal decomposition on the schlieren image data is used to show that the flowfield structures in which dominant modes manifest are dependent on the thrust coefficient.

Near-surface gas discharge effect on a steady bow shock wave position in a supersonic flow past a cylindrically blunted body in the air

The problem of the bow shock wave control using a near-surface gas discharge in a supersonic flow past a semi-cylindrical body at Mach number M = 4 in the air is investigated experimentally and numerically. The possibility of controlling the position of a steady bow shock wave and the characteristics of a streamlined body by creating a volumetric plasma region using a surface gas discharge organized on the entire front surface of the body is shown. An increase in the stand-off distance of a steady bow shock is experimentally and numerically obtained, which is the greater, the higher the discharge power and the greater the adiabatic index in the plasma region created by the discharge. A comparison of the numerical and experimental data showed good agreement. It is established that the relative value of the steady bow shock stand-off distance increases linearly in the power range from 1.5 × 105 to 2.4 × 105 W at the discharge current from 430 to 670 A, and the adiabatic index in the plasma region can be estimated as 1.3. It is also found that at higher values of the discharge power, the adiabatic index in the plasma region decreases. The average plasma parameters were expressed as functions of the discharge specific power and the adiabatic index. The mechanism of the gas discharge effect on the bow shock wave is established, and it is shown that the plasma parameters in the region created by the discharge, including the degree of ionization and the degree of nonequilibrium, affect the position of the steady bow shock wave.

Mechanism analysis of magnetohydrodynamic shock control in hypersonic flow

The effects of external magnetic fields on the shock-wave configuration at hypersonic plasma flow field are investigated in this paper. A series of numerical simulations over various geometry configurations, namely, a blunt body and a fixed-geometry inlet forebody, have been conducted by varying the applied magnetic field under different freestream conditions. Results show that magnetohydrodynamic shock control capabilities under three types of magnetic field are ranked from weak to strong as dipole magnet, solenoid magnet, and uniform magnet field. Under the same applied magnetic field, it is easier to deflect the shock at a relatively high altitude condition, compared with the low altitude case. The bow shock standoff distance is dependent on the distribution of counter-flow Lorentz force right after shock in the stagnation region. For the oblique shock control, the function of two components of Lorentz force is different that the counter-flow one decelerates the flow and increases the shock-wave angle, while the normal one squeezes the oblique shock and deflects the streamlines.

Hypervelocity Spherically-Blunted Cone Flows in Mars Entry Ground Testing

Bow-shock standoff distances over sphere and spherically-blunted cone geometries were examined through experiments in two facilities capable of high-stagnation enthalpy hypersonic flows simulating Mars planetary entry conditions. High-speed and high-resolution schlieren images were obtained in the California Institute of Technology T5 reflected shock tunnel and the Hypervelocity Expansion Tube to examine facility independence of the measurements. Accompanying reacting Navier–Stokes simulations were carried out. A recently developed unified model for sphere and sphere–cone behavior was first verified for high-stagnation enthalpy flows through simulations with thermal and chemical nonequilibrium. Shock standoff distance measurements in both facilities were found to be in good agreement with model predictions. The need to account for the divergence of the streamlines in conical nozzles was highlighted and an existing model extended to account for changes in shock curvature between parallel and conical flows. The contributions of vibrational and chemical nonequilibrium to the stagnation-line density profile were quantified using the simulation results comparing three chemical kinetic models.

Remote sensing of cometary bow shocks: modelled asymmetric outgassing and pickup ion observations

ABSTRACT Despite the long escort by the ESA Rosetta mission, direct observations of a fully developed bow shock around 67P/Churyumov–Gerasimenko have not been reported. Expanding on our previous work on indirect observations of a shock, we model the large-scale features in cometary pickup ions, and compare the results with the ESA Rosetta Plasma Consortium Ion Composition Analyser ion spectrometer measurements over the pre-perihelion portion of the escort phase. Using our hybrid plasma simulation, an empirical, asymmetric outgassing model for 67P, and varied interplanetary magnetic field (IMF) clock angles, we model the evolution of the large-scale plasma environment. We find that the subsolar bow shock standoff distance is enhanced by asymmetric outgassing with a factor of 2 to 3, reaching up to $18\,000\, \rm {km}$ approaching perihelion. We find that distinct spectral features in simulated pickup ion distributions are present for simulations with shock-like structures, with the details of the spectral features depending on shock standoff distance, heliocentric distance, and IMF configuration. Asymmetric outgassing along with IMF clock angle is found to have a strong effect on the location of the spectral features, while the IMF clock angle causes no significant effect on the bow shock standoff distance. These dependences further complicate the interpretation of the ion observations made by Rosetta. Our data-model comparison shows that the large-scale cometary plasma environment can be probed by remote sensing the pickup ions, at least when the comet’s activity is comparable to that of 67P, and the solar wind parameters are known.

Numerical simulation of mono-disperse gravity-driven granular flow around a wedge using two-fluid model

The numerical simulation of glass beads granular flow around a wedge located in a rectangular channel is performed by the Two-Fluid Model (i.e. the Euler-Euler approach) aiming to make a comparison between the numerical and the available experimental data. The channel is tilted against the horizon making the glass beads fall under the action of the gravity force. The numerical simulation shows the glass beads structure that resembles a bow shock wave around the wedge. The computed bow shock stand-off distance is compared to the data extracted from the experimental results. The details of the comparison between the numerical and the experimental data are discussed.

Hybrid modeling of cometary plasma environments

Context. The ESA Rosetta probe has not seen direct evidence of a fully formed bow shock at comet 67P/Churyumov–Gerasimenko (67P). Ion spectrometer measurements of cometary pickup ions measured in the vicinity of the nucleus of 67P are available and may contain signatures of the large-scale plasma environment. Aims. The aim is to investigate the possibility of using pickup ion signatures to infer the existence or nonexistence of a bow shock-like structure and possibly other large-scale plasma environment features. Methods. A numerical plasma model in the hybrid plasma description was used to model the plasma environment of a comet. Simulated pickup ion spectra were generated for different interplanetary magnetic field conditions. The results were interpreted through test particle tracing in the hybrid simulation solutions. Results. Features of the observed pickup ion energy spectrum were reproduced, and the model was used to interpret the observation to be consistent with a shock-like structure. We identify (1) a spectral break related to the bow shock, (2) a mechanism for generating the spectral break, and (3) a dependency of the energy of the spectral break on the interplanetary magnetic field magnitude and bow shock standoff distance.

Bow shock stand-off distance for subsonic decelerating bodies

Projectile accelerations above $$500~\hbox {ms}^{-2}$$ are commonly encountered in aerodynamic applications, but suitable validation data are rare in this regime. Experimental transonic velocity range data for a sphere decelerating under its own drag have been used to validate a numerical model for decelerating objects. The validated model is then used to explore the flow field ahead of objects decelerating from supersonic to subsonic Mach numbers. To model the non-inertial frame of the projectile, source terms were included in the momentum and energy equations in a computational fluid dynamics model. In decelerating cases, the bow shock formed in supersonic flight persists in the subsonic regime. The differences in the flow field between the steady and unsteady cases are explained using the concept of flow history. In the experiment, a tubular insert was present near the observation window in the ballistic range. The insert was numerically modelled, and it is shown that the resulting bow shock behaviour can be explained in terms of the Kantrowitz criterion, in conjunction with flow history. The RAE2822 aerofoil was used to explore the effects of shock overtaking and propagation during deceleration from supersonic to low subsonic Mach numbers. In this case, the bow shock wave persists from the initial supersonic speed to projectile Mach numbers lower than 0.4. The expansion wave and tail shock are shown to overtake the decelerating projectile and propagate forward, behind the bow shock.

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.

COMPRESSIBLE FLOW IN FRONT OF AN AXISYMMETRIC BLUNT OBJECT: ANALYTIC APPROXIMATION AND ASTROPHYSICAL IMPLICATIONS

ABSTRACT Compressible flows around blunt objects have diverse applications, but current analytic treatments are inaccurate and limited to narrow parameter regimes. We show that the gas-dynamic flow in front of an axisymmetric blunt body is accurately derived analytically using a low order expansion of the perpendicular gradients in terms of the parallel velocity. This reproduces both subsonic and supersonic flows measured and simulated for a sphere, including the transonic regime and the bow shock properties. Some astrophysical implications are outlined, in particular for planets in the solar wind and for clumps and bubbles in the intergalactic medium. The bow shock standoff distance normalized by the obstacle curvature is in the strong shock limit, where g is the compression ratio. For a subsonic Mach number M approaching unity, the thickness δ of an initially weak, draped magnetic layer is a few times larger than in the incompressible limit, with amplification .

THE PLASMA ENVIRONMENT IN COMETS OVER A WIDE RANGE OF HELIOCENTRIC DISTANCES: APPLICATION TO COMET C/2006 P1 (MCNAUGHT)

On 2007 January 12, comet C/2006 P1 (McNaught) passed its perihelion at 0.17 AU. Abundant remote observations offer plenty of information on the neutral composition and neutral velocities within 1 million kilometers of the comet nucleus. In early February, the Ulysses spacecraft made an in situ measurement of the ion composition, plasma velocity, and magnetic field when passing through the distant ion tail and the ambient solar wind. The measurement by Ulysses was made when the comet was at around 0.8 AU. With the constraints provided by remote and in situ observations, we simulated the plasma environment of Comet C/2006 P1 (McNaught) using a multi-species comet MHD model over a wide range of heliocentric distances from 0.17 to 1.75 AU. The solar wind interaction of the comet at various locations is characterized and typical subsolar standoff distances of the bow shock and contact surface are presented and compared to analytic solutions. We find the variation in the bow shock standoff distances at different heliocentric distances is smaller than the contact surface. In addition, we modified the multi-species model for the case when the comet was at 0.7 AU and achieved comparable water group ion abundances, proton densities, plasma velocities, and plasma temperatures to the Ulysses/SWICS and SWOOPS observations. We discuss the dominating chemical reactions throughout the comet-solar wind interaction region and demonstrate the link between the ion composition near the comet and in the distant tail as measured by Ulysses.

Experimental investigation of flow past simple model bodies in hypersonic wind tunnels at similar values of the Mach and Reynolds numbers but at different physical flow velocities

The pressure distributions over the surfaces of simple model bodies, such as hemisphere, wedge, and cone, and the bow shock stand-off distances from these bodies are investigated in hypersonic wind tunnels with similar-in-value Mach and Reynolds numbers but considerably different flow velocities (u = 790 to 5950 m/s). These are the tunnels with an ohmic heater and electric-arc and MHD gas flow accelerators. Flow pattern visualization followed by photometering measurements are used for determining the bow shock stand-off distance. At low gas densities the method of anomalous dispersion of the sounding radiation is employed for visualizing the flow. The pressure distributions over the body surfaces and the bow shock stand-off distances are calculated from the Navier-Stokes equations and thin viscous shock layer (TVSL) theory. The measured parameter values are in agreement with those calculated from Navier-Stokes equations. For the cone and the wedge the discrepancy is within 10%.

A survey of solar wind conditions at 5 AU: a tool for interpreting solar wind-magnetosphere interactions at Jupiter

We examine Ulysses solar wind and interplanetary magnetic field (IMF) observations at 5 AU for two ~13 month intervals during the rising and declining phases of solar cycle 23 and the predicted response of the Jovian magnetosphere during these times. The declining phase solar wind, composed primarily of corotating interaction regions and high-speed streams, was, on average, faster, hotter, less dense, and more Alfvenic relative to the rising phase solar wind, composed mainly of slow wind and interplanetary coronal mass ejections. Interestingly, none of solar wind and IMF distributions reported here were bimodal, a feature used to explain the bimodal distribution of bow shock and magnetopause standoff distances observed at Jupiter. Instead, many of these distributions had extended, non-Gaussian tails that resulted in large standard deviations and much larger mean over median values. The distribution of predicted Jupiter bow shock and magnetopause standoff distances during these intervals were also not bimodal, the mean/median values being larger during the declining phase by ~1 – 4%. These results provide data-derived solar wind and IMF boundary conditions at 5 AU for models aimed at studying solar wind-magnetosphere interactions at Jupiter and can support the science investigations of upcoming Jupiter system missions. Here, we provide expectations for Juno, which is scheduled to arrive at Jupiter in July 2016. Accounting for the long-term decline in solar wind dynamic pressure reported by McComas et al. (2013), Jupiter’s bow shock and magnetopause is expected to be at least 8 – 12% further from Jupiter, if these trends continue.

Flowfield Establishment in Hypervelocity Shock-Wave/Boundary-Layer Interactions

Shock/boundary-layer interactions generated over double-wedge and double-cone models in high-enthalpy, hypersonic flows are known to be sensitive to the thermochemical state of the gas. In this study, the transient evolution of shock interactions and separated flow is examined in nitrogen and air freestream conditions with stagnation enthalpies ranging from 2 to and Mach numbers from 4 to 7. The time-dependent flowfield and associated time scales required to reach mean values for both viscous and inviscid processes are investigated using fast-response thermocouples and high-speed schlieren and chemiluminescence imaging. In all cases, the oblique/bow-shock triple point is observed to propagate upstream to a mean location as the bow-shock standoff distance increases with time. For all freestream conditions, the triple point reaches a mean position in less time for the conical than the wedge flow. Distinct differences between nitrogen and air both in the evolution and mean flow features are observed in the highest-enthalpy test case. The triple-point establishment time is greater in nitrogen than air, corresponding to an increased bow-shock standoff distance, whereas the viscous establishment times in the region of peak heating are comparable. Although the observed dependence on freestream composition and enthalpy can be used to quantify the effect of thermochemistry, we note the time scales for viscous and inviscid processes are of the same order of magnitude for all conditions studied. Normalized establishment times of 2–8 are measured, in reasonable agreement with existing experimental data from surface gauges (6–11).

Active current sheets and candidate hot flow anomalies upstream of Mercury's bow shock

Hot flow anomalies (HFAs) represent a subset of solar wind discontinuities interacting with collisionless bow shocks. They are typically formed when the normal component of the motional (convective) electric field points toward the embedded current sheet on at least one of its sides. The core region of an HFA contains hot and highly deflected ion flows and rather low and turbulent magnetic field. In this paper, we report observations of possible HFA‐like events at Mercury identified over a course of two planetary years. Using data from the orbital phase of the MESSENGER mission, we identify a representative ensemble of active current sheets magnetically connected to Mercury's bow shock. We show that some of these events exhibit magnetic and particle signatures of HFAs similar to those observed at other planets, and present their key physical characteristics. Our analysis suggests that Mercury's bow shock does not only mediate the flow of supersonic solar wind plasma but also provides conditions for local particle acceleration and heating as predicted by previous numerical simulations. Together with earlier observations of HFA activity at Earth, Venus, Mars, and Saturn, our results confirm that hot flow anomalies could be a common property of planetary bow shocks and show that the characteristic size of these events is controlled by the bow shock standoff distance and/or local solar wind conditions.