Shock Location Research Articles

Martian Bow Shock and Magnetic Pileup Boundary Models Based on an Automated Region Identification

AbstractEmpirical models of bow shock and magnetic pileup boundary locations are typically based on the identification of individual boundary crossings and their subsequent fitting by properly chosen dependences. Such an approach, however, requires a large set of identified crossings, whose compilation can be easily a source of a significant bias. Moreover, the method is inherently biased by the spacecraft orbit: the more time the spacecraft spends in a given region, the more likely it is for a crossing to be identified in there. We use a different approach based on an automated region identification and Mars Atmosphere and Volatile Evolution (MAVEN) spacecraft data to derive empirical models of both the bow shock and magnetic pileup boundary locations around Mars. We use statistically known parameters in the solar wind, magnetosheath, and induced magnetosphere, along with the observed ratios of measured solar wind parameters, to automatically identify the region where the spacecraft is located at any given time. A simple empirical relation is then assumed for a boundary shape and location, and its free parameters are adapted to optimize the resulting model classification of individual data points. This procedure allows us to model both the bow shock and magnetic pileup boundary locations, reproducing successfully observed variations with the solar wind dynamic pressure, solar ionizing flux, and crustal magnetic fields. However, due to the sparse data coverage, the models are deemed unreliable beyond the terminator.

Influence of Geometric Parameters on Overall Performance of High Bypass Ratio Turbofan Nacelle and Exhaust System

In order to understand the coupled effect of the nacelle and exhaust system and to improve their overall performance, we studied the aerodynamic performance and the flow characteristics of the high bypass ratio turbofan nacelle and exhaust system by numerical simulation. The geometric parameters of a nacelle and exhaust system (e.g., the contraction ratio of the cowl afterbody and the fan nozzle exit angle) were investigated to evaluate their influence on the overall performance of the nacelle and exhaust system. The related flow mechanism was explored as well. The results show that the flow field of the nacelle and exhaust system under the mid-cruise condition exhibits characteristics of transonic flow. A stagnation zone exits at the nacelle lip and there is a velocity peak at the nacelle forebody. There exist a number of complex flow phenomena (such as shockwave, expansion wave, shear flow and shock wave-boundary layer interaction) in the downstream of the fan nozzle exit plane. The magnitude of the fan nozzle thrust or the intake ram drag is much higher than that of the additional drag, the nacelle drag or the core nozzle thrust. And for the nacelle drag, the friction drag of the cowl is in the same order of magnitude as the pressure drag of the cowl, the core cowl and the plug. But it is much larger than the friction drag of the core cowl and the plug. The effective thrust increases by 4.7% as the contraction ratio of the cowl afterbody increases; and it increases by 2.4% as the fan nozzle exit angle increases. The expansion degree of the fanjet flow, the shock wave strength and location, and the existence of the flow separation or second shock wave are influenced by the contraction ratio of the cowl afterbody and the fan nozzle exit angle. These phenomena have effects on the pressure distribution of the core cowl and the surrounding fanjet flow velocity, and hence they further affect the nacelle drag. The increase in the fan nozzle exit angle can noticeably reduce the thrust of the fan nozzle.

Development of a New Algorithm for Modeling Viscous Transonic Flow on Unstructured Grids at High Reynolds Numbers

Abstract This study investigates a new algorithm for modeling viscous transonic flow at high Reynolds number cases suitable for unstructured grids. The challenge of modeling viscous transonic flow around airfoils becomes intense at high Reynolds number cases due to a variety of flow regimes encountered, such as boundary layer growth and the shockwave/turbulent boundary-layer interaction, accompanied by large separation bubble. Therefore, it is highly demanded to develop robust and efficient models that can capture the shock-induced problems of turbulent flows for aircraft design purposes. The new model is essentially a hybrid algorithm to address the conflict between turbulence modeling and shock-capturing requirements. A skew-symmetric form of a collocated finite volume scheme with minimum aliasing errors was implemented to model the turbulent region in the combination of a semidiscrete, central difference scheme to capture discontinuities with adequately low numerical dissipation for the minimal effect on turbulent flows. To evaluate the effectiveness of the model, it was tested in three conventional cases. The computational results are close to measured data for predicting the shock locations. This implies that the model is able to predict the scale of the separation bubble and the main characteristics of turbulent transonic flow adequately.

Application of the sparse-Lagrangian multiple mapping conditioning approach to a model supersonic combustor

The Multiple Mapping Conditioning/Large Eddy Simulation (MMC-LES) model is extended for the first time to high-speed, compressible flow conditions and validated against non-reacting and reacting experimental data from a model supersonic combustor. The MMC-LES method solves the subgrid joint composition filtered density function through a Monte Carlo approach, and it permits a low-cost numerical implementation using a sparse distribution of stochastic Lagrangian particles. The sensitivity of results to the particle resolution is examined, and similar to past low-speed applications of MMC-LES, that sensitivity is found to be low. In comparison to the model equations for subsonic turbulent combustion conditions, the pressure work and viscous heating effects have been incorporated here to account for the effects of compressibility. As expected, the viscous heating effects are small for this flow case and can be ignored, while the pressure work is not negligible and makes a significant contribution at expansion fans and shock fronts where the magnitude of the pressure derivative term in non-reacting/reacting cases is as much as 23.8%/24.5% and 19.2%/18.6% of the stochastic particle standardized enthalpy, respectively. The MMC-LES predictions show good quantitative agreement with the available experimental data for the mean and root-mean-square of axial velocity, mean temperature, and wall pressure. Good qualitative comparison to the data is also observed for major flow characteristics, including location and size of shocks, expansion fans, and recirculation zone, and combustion characteristics such as flame lift-off distance. Although the effects of the pressure work on the mean flame lift-off distance are negligible, they have a significant influence on the predicted spatial fluctuations of the flame base.

The Downwind Solar Wind: Model Comparison with Pioneer 10 Observations

Abstract The solar wind in the upwind region has been well modeled using a pickup ion (PUI) mediated MHD model (Zank et al.). It suggests that PUIs have an important role in heating the solar wind in the outer heliosphere. However, the solar wind in the downwind region is not as well understood. Here, we compare the Zank et al. model with Pioneer 10 observations, which allows us to investigate the downwind solar wind out to 60 au. We use a model in which the hydrogen temperature is finite to obtain a proper hydrogen number density distribution in the downwind region and incorporate it into the model. Our results explain Pioneer 10 observations well and indicate that the heating due to PUIs is less effective than in the upwind region since the density of PUIs in the downwind region is less than the upwind PUIs density. We also derive parameters at several possible locations of the downwind termination shock.

Relocation of the 2018 Zakynthos, Greece, aftershock sequence: spatiotemporal analysis deciphering mechanism diversity and aftershock statistics

An Mw 6.8 earthquake occurred on October 25, 2018, 35 km offshore from the southwest coastlines of Zakynthos Island. The aftershock sequence appeared remarkably productive with six aftershocks of M ≥ 5.0 in the first month and tens of aftershocks with M ≥ 4.0 during the study period. The GCMT solution for the main shock suggests a very low angle plane (dip = 24°) for a dextral strike–slip faulting (rake = 165°). A similar solution is suggested for the largest aftershock (Mw 5.9) that occurred 5 days afterward. The proximity of the main shock location with the dextral active boundary of Kefalonia Transform Fault Zone (KTFZ) along with the Hellenic Subduction front supports this oblique faulting. The aftershock activity is comprised mostly in depths 5–12 km and forms eight distinctive clusters that accommodate regional strain and evidence strain partitioning. The role of stress transfer and statistical analysis are combined for detailing the highly productive aftershock sequence. Earthquake networks analysis reveals their random structure soon after the main shock, which became small-world structure after the first 200 days. Time series analysis constructed from the aftershock frequency and seismic moment release and manifested significant correlation among the eight seismicity clusters.

Modeling of cryogenic hydrogen releases

Hydrogen is likely to be stored and transported as a liquid with high densities to have sufficient hydrogen on-site and for efficient distribution. Thus, cryogenic hydrogen jets and dispersion characteristics need to be studied to quantify the risks of accidental releases. The present study modeled cryogenic hydrogen jets with stagnation temperatures around 50 K released from round nozzles at stagnation pressures of 2–10 bar. The instantaneous flow fields were modeled using the Large Eddy Simulation (LES) turbulence model to accurately and efficiently capture the flow characteristics. The numerical models were validated with experimental data. The concentration and velocity distributions show that the centerline mass fraction and velocity decay at similar rates to the decays for room temperature jets. The radial distributions of the mass fraction, temperature and velocity are Gaussian and self-similar. Additionally, the numerical model can reproduce the shock structures near the nozzle for these underexpanded cryogenic hydrogen jets. The location of the first normal shock was predicted to be closer to the nozzle than for room temperature jets. The present work can be used to develop and revise safety codes and standards for liquid hydrogen facilities.

Heliosphere Configuration Insights from the Voyagers’ Heliopause Crossings and Solar Disturbance Propagations

The Voyager 1 and 2 (V1 and V2) crossings of the heliopause (HP) have generated new estimates of the shape of the heliosphere, helped elucidate plasma wave features, and helped clarify particle and field phenomena, all of which provide insights into the overall configuration of the heliosphere and its interaction with the local interstellar medium (LISM). Webber and Intriligator (2011) suggested a consistent offset in the V1 and V2 locations of the termination shock (TS), predicted a shrunken and squashed geometry of the heliosphere, and correctly predicted that V1 would encounter the HP in 2012.0 ± 1 year. Intriligator et al. (2005, 2008) examined how the Halloween 2003 solar events were manifested from the Sun to V1 and V2 at 92.6 and 73.2 AU, giving rise to Global Merged Interaction Regions (GMIRs) and to broad particle, plasma, and magnetic field offsets that could affect the configuration of the heliosphere. The 2012 solar events (Intriligator et al., 2015) appeared to cause a tsunami at V1 and V2 at 128.7 and 102.5 AU and emphasized that space weather often could be interpreted as TS or HP or heliospheric crossings. Washimi et al. (2017) suggested that further complications of these events could propagate from the LISM back into the heliosphere. We conclude that in addition to the LISM magnetic field, the size and shape of the heliosphere are affected on differing time and space scales by changes in the average solar wind dynamic pressure over solar cycles with changing configurations of coronal holes, by pressure increases from GMIRs, and by magnetohydrodynamic instabilities that may be enhanced by energetic neutral atoms formed in GMIRs. We suggest the value of additional simulations that would combine our use of source surface maps of solar activity with other computational refinements.

Variation in Fluid and Vasopressor Use in Shock With and Without Physiologic Assessment: A Multicenter Observational Study.

To characterize the association between the use of physiologic assessment (central venous pressure, pulmonary artery occlusion pressure, stroke volume variation, pulse pressure variation, passive leg raise test, and critical care ultrasound) with fluid and vasopressor administration 24 hours after shock onset and with in-hospital mortality. Multicenter prospective cohort study between September 2017 and February 2018. Thirty-four hospitals in the United States and Jordan. Consecutive adult patients requiring admission to the ICU with systolic blood pressure less than or equal to 90 mm Hg, mean arterial blood pressure less than or equal to 65 mm Hg, or need for vasopressor. None. Of 1,639 patients enrolled, 39% had physiologic assessments. Use of physiologic assessment was not associated with cumulative fluid administered within 24 hours of shock onset, after accounting for baseline characteristics, etiology and location of shock, ICU types, Acute Physiology and Chronic Health Evaluation III, and hospital (beta coefficient, 0.04; 95% CI, -0.07 to 0.15). In multivariate analysis, the use of physiologic assessment was associated with a higher likelihood of vasopressor use (adjusted odds ratio, 1.98; 95% CI, 1.45-2.71) and higher 24-hour cumulative vasopressor dosing as norepinephrine equivalent (beta coefficient, 0.37; 95% CI, 0.19-0.55). The use of vasopressor was associated with increased odds of in-hospital mortality (adjusted odds ratio, 1.88; 95% CI, 1.27-2.78). In-hospital mortality was not associated with the use of physiologic assessment (adjusted odds ratio, 0.86; 95% CI, 0.63-1.18). The use of physiologic assessment in the 24 hours after shock onset is associated with increased use of vasopressor but not with fluid administration.

Journal Vol – 15 No -7, July 2020 Journal > Journal > Journal Vol – 15 No -7, July 2020 > Page 6 PERFORMANCE AND EMISSION CHARACTERISTICS OF GASOLINE-ETHANOL BLENDS ON PFI-SI ENGINE Authors: D.Vinay Kumar ,G.Samhita Priyadarsini,V.Jagadeesh Babu,Y.Sai Varun Teja, DOI NO: https://doi.org/10.26782/jmcms.2020.07.00051 admin July 26, 2020 Abstract: Alcohol based fuels can be produced from renewable energy sources and

Journal Vol – 15 No -7, July 2020 Journal > Journal > Journal Vol – 15 No -7, July 2020 > Page 6 PERFORMANCE AND EMISSION CHARACTERISTICS OF GASOLINE-ETHANOL BLENDS ON PFI-SI ENGINE Authors: D.Vinay Kumar ,G.Samhita Priyadarsini,V.Jagadeesh Babu,Y.Sai Varun Teja, DOI NO: https://doi.org/10.26782/jmcms.2020.07.00051 admin July 26, 2020 Abstract: Alcohol based fuels can be produced from renewable energy sources and

Accretion Flow Evolution of a New Black Hole Candidate MAXI J1348–630 during the 2019 Outburst

Abstract Galactic black hole (BH) candidate MAXI J1348–630 was recently discovered by MAXI and Swift/BAT satellites during its first outburst in 2019 January, which continued for ∼4 months. We study the spectral and timing properties of the source in detail. The combined 1–150 keV Swift/XRT, Swift/BAT, and MAXI/GSC spectra are investigated with the two-component advective flow (TCAF) solution. Physical flow parameters of TCAF, such as the Keplerian disk accretion rate, the sub-Keplerian halo accretion rate, the shock location, and the shock compression ratio, are estimated from our spectral fits. Based on the variation of flux in soft and hard X-ray ranges, the hardness ratio, TCAF model fitted accretion rates, and the accretion rate ratio, we show how the source evolved through four spectral states, viz., hard, hard-intermediate, soft-intermediate, and soft, in rising and declining states. Low-frequency quasi-periodic oscillations are observed in two observations during the rising phase of the outburst. From the spectral analysis, we estimate the mass of the BH to be M ⊙. We also find that the viscous timescale in this outburst is ∼3.5 days. The distance of the source is also estimated as 5–10 kpc from state transition luminosity.

Properties of two-temperature magnetized advective accretion flow around rotating black hole

ABSTRACT We study the two-temperature magnetized advective accretion flow around the Kerr black holes (BHs). During accretion, ions are heated up due to viscous dissipation, and when Coulomb coupling becomes effective, they transfer a part of their energy to the electrons. On the contrary, electrons lose energy due to various radiative cooling processes, namely bremsstrahlung, synchrotron, and Comtonization processes, respectively. To account for the magnetic contribution inside the disc, we consider the toroidal magnetic fields which are assumed to be dominant over other components. Moreover, we adopt the relativistic equation of state to describe the thermal characteristics of the flow. With this, we calculate the global transonic accretion solutions around the rotating BHs. We find that accretion solution containing multiple critical points may harbour shock wave provided the standing shock conditions are satisfied. Further, we investigate the shock properties, such as shock location (xs) and compression ratio (R) that delineate the post-shock corona (hereafter PSC) and find that the dynamics of PSC is controlled by the flow parameters, such as accretion rate (${\dot{m}}$) and magnetic fields (β, defined as the ratio of gas pressure to the magnetic pressure), etc. Finally, we calculate the emission spectra of the accretion flows containing PSC and indicate that both ${\dot{m}}$ and β play the pivotal roles in explaining the spectral state transitions commonly observed for BH X-ray binaries.

Convexity of Self-Similar Transonic Shocks and Free Boundaries for the Euler Equations for Potential Flow

We are concerned with geometric properties of transonic shocks as free boundaries in two-dimensional self-similar coordinates for compressible fluid flows, which are not only important for the understanding of geometric structure and stability of fluid motions in continuum mechanics but also fundamental in the mathematical theory of multidimensional conservation laws. A transonic shock for the Euler equations for self-similar potential flow separates elliptic (subsonic) and hyperbolic (supersonic) phases of the self-similar solution of the corresponding nonlinear partial differential equation in a domain under consideration, in which the location of the transonic shock is apriori unknown. We first develop a general framework under which self-similar transonic shocks, as free boundaries, are proved to be uniformly convex, and then apply this framework to prove the uniform convexity of transonic shocks in the two longstanding fundamental shock problems -- the shock reflection-diffraction by wedges and the Prandtl-Meyer reflection for supersonic flows past solid ramps. To achieve this, our approach is to exploit underlying nonlocal properties of the solution and the free boundary for the potential flow equation.

Application of flux vector splitting methods with SST turbulence model to wall-bounded flows

An explicit 3D Reynolds Averaged Navier-Stokes solver SURFS3D has been developed and run on a structured grid. A 4-stage Runge-Kutta (RK) method is used for the time integration and OpenMP is used to parallelize the solver. This is used as a platform to compare Van Leer’s Flux Vector Splitting Method (VLFVSM) to a variant of Liou’s Advection Upstream Splitting with velocity and pressure diffusion (AUSM+-up2). The code results are validated for wall bounded flows. Menter’s k−ω Shear Stress Transport (SST) turbulence model is employed and validated for turbulent flows. The SST turbulence model is selected due to its capability to predict the shock location and separation location in adverse pressure gradient accurately. The validation cases are laminar and turbulent incompressible flows and turbulent supersonic flow over flat plate, transonic flow over an axisymmetric bump, and supersonic flow over a blunt bi-conic configuration. It is observed that VLFVSM+SST lacks accurate viscous prediction capability for the wall-bounded flows at low speeds compared to AUSM +-up2+SST, which works well at low speed. In transonic flow conditions, both schemes perform well. AUSM +-up2 scheme exhibits mild carbuncle problem for Mach 3.0 flow over a blunt biconic configuration, whereas, VLFVSM is free from this problem. Overall, the SST turbulence model performance is good for all the validation cases studied.

Unsteady characteristics of compressible reattaching shear layers

Compressible reattaching flows occur in many aerospace applications and are characterized by high aerothermal loads at reattachment and a broad range of characteristic time scales. The flowfield in this study involves a separated shear layer reattaching onto a 20° ramp at a freestream unit Reynolds number of 6.7 × 107 m−1 and Mach number of 2.9. Delayed detached eddy simulations were carried out using OVERFLOW 2.2K by Leger et al. [“Detached-eddy simulation of a supersonic reattaching shear layer,” AIAA J. 55, 3722–3733 (2017)], and the corresponding results were analyzed to determine the unsteady features of this flowfield using statistical techniques. The simulations were run for long integration times, which ensured sufficient temporal resolution of low-frequency unsteadiness in the range of St=O(0.01). The mean flow data highlighted essential flow components such as an expansion fan at the separation point, a large recirculation vortex, and a reattachment shock. Fourier analysis of wall pressure data revealed several high energy frequency bands, which appeared to correspond to separation bubble breathing, shear-layer flapping, and shedding of vortices from the recirculation zone. The spectra also highlighted the possible presence of Rossiter modes, suggesting a feedback mechanism through the recirculation zone. Correlations in the shear-layer and recirculation zone confirmed the presence of large-scale turbulence structures, with an increase in length and time scales downstream. The spectra of reattachment shock location suggested a broadband nature of the oscillations. The role of upstream events on the same was investigated by examining coherence, conditional averages, and correlations. A similar exercise was carried out to investigate the nature of unsteadiness at the mean reattachment location.

Learning from Friends in a Pandemic: Social Networks and the Macroeconomic Response of Consumption

This paper studies how social communications via networks affect agents' expectations and macroeconomic shock propagation mechanisms. First, we construct a new measure of shocks to the social network using Facebook's Social Connectedness Index (SCI), which measures the number of county-to-county friendship ties. Using plausibly exogenous variation in the exposure of counties to COVID-19 shocks in their social network, we find that a 10% rise in the number of SCI-weighted cases and deaths is associated with a 0.15% and 0.42% decline in consumption expenditures, respectively. These effects are concentrated among consumer goods \& services that rely more on social-contact. Second, we augment a quantitative pandemic-consumption model under incomplete markets with a tractable mechanism of belief formation through social communications. The model is general enough to nest a number of workhorse theories of expectation formations featuring overreaction, rational updating, and/or stickiness. We find that, while social communication slows the speed of aggregate belief adjustment in responses to fundamentally relevant shocks, it also moderates overreaction to local noise in aggregation. We demonstrate how the dynamic and average size of aggregate responses depend on the location of the initial shocks and the network structure.

Factors Associated With the Use of Bare Metal Stents in Patients With ST Elevation Myocardial Infarction

BackgroundDrug eluting stents (DES) are used in the majority of patients undergoing percutaneous coronary intervention (PCI). Factors associated with the use of bare metal stents (BMS) for patients undergoing primary PCI for ST elevation myocardial infarction (STEMI) have not been adequately explored. The objective of this study was to evaluate factors associated with BMS use in STEMI patients undergoing primary PCI. MethodsPatients undergoing primary PCI for STEMI between January 2008 and February 2015 were retrospectively identified. Patients who received both a DES and BMS were included in the DES group and patients receiving balloon angioplasty only were excluded. Baseline demographics, angiographic variables, procedure related variables and in-hospital events were collected. Multivariate analysis was performed to identify factors associated with BMS use. ResultsEight hundred and sixty-five patients underwent primary PCI for STEMI during the study period. Seventy-two patients (8.3%) received balloon angioplasty only and were excluded, yielding 793 patients for the study cohort. Three hundred fifty-two patients (44%) received BMS and 441 patients (56%) received DES. Patients receiving DES had a higher prevalence of diabetes mellitus, prior myocardial infarction, prior PCI, left anterior descending artery culprit location and Medicaid Insurance compared to those receiving BMS. Patients receiving BMS had a higher prevalence of cardiogenic shock and right coronary artery culprit location. Unadjusted in-hospital mortality was significantly higher for patients receiving BMS compared to patients receiving DES, 11.1% vs 3.2%, respectively, p < 0.0001. Multivariate predictors of BMS use were cardiogenic shock (OR 30.3; 95% CI 11.25 to 81.73) and diabetes mellitus (OR 2.99; 95% CI 1.04 to 8.64). ConclusionIn a contemporary series of patients undergoing primary PCI for STEMI, BMS were used in 44% of patients and independent factors associated with BMS use were cardiogenic shock and diabetes mellitus.

Interactions between a shock and turbulent features in a Mach 2 compressible boundary layer

Large field-of-view (FOV) particle image velocimetry experiments are conducted in the vicinity of a shock wave boundary layer interaction (SWBLI) at Mach 2. The current FOV covers up to 30 boundary layer thicknesses ( ), comprising of upstream and downstream regions relative to the SWBLI, thereby allowing the turbulent boundary layer and shock to be simultaneously captured. The relationship between the boundary layer features and the instantaneous shock location is directly quantified, with the aim of better understanding the mechanisms responsible for oscillation of the reflected shock. The results show that the reflected shock location is clearly influenced by the instantaneous state of the incoming boundary layer. It is found that passage of low-/high-momentum very-large-scale turbulent features through the SWBLI region causes the reflected shock to move upstream/downstream of the mean location. Moreover, interaction with the shock is found to introduce additional velocity fluctuations across a range of spanwise length scales within the boundary layer. The spanwise scales smaller than one recover within one downstream of the SWBLI region. However, at larger spanwise wavelengths, two persistent modes at approximately one and six are observed, where they remain correlated for a longer streamwise extent ( ) than the other spanwise modes. The wall pressure measurements indicate that the low-frequency fluctuations arising from the oscillating shock foot are due to dampening of high-frequency contents beyond the critical frequency associated with the unstable global mode. Thus, the results suggest that low-frequency pressure oscillations are not necessarily an independent phenomenon from the turbulent features entering the SWBLI region and interacting with the shock. Instead, a large scale separation between their dominant time scales is due to the critical frequency of the unstable global mode occurring at frequencies that are orders of magnitudes slower than the dominant frequency of the very-large-scale features.

Influence of the Interplanetary Magnetic Field Cone Angle on the Geometry of Bow Shocks

Abstract The frozen-in interplanetary magnetic field (IMF) in the solar wind is one of the most important parameters affecting the Earth’s space weather. In the early studies of the IMF’s influence on space weather, significant effects of the north–south component of the IMF B Z were emphasized, while the radial component of the IMF B X was largely ignored. However, the IMF near the Earth is not always dominated by the north–south component of the IMF B Z , and the radial component of the IMF B X also plays an important role. However, while the effects of the IMF B X (cone angle) on the magnetopause have been studied in recent years, there has been much less effort to quantify the B X (cone angle) effects on the bow shock. In this paper, using the bow shock crossing data from multiple satellites, we investigate the IMF cone angle effect on the dayside and nightside of the bow shock. Our results show that under the radial IMF condition, the dayside of the bow shock is located closer to the Earth than the average. At the same time, on the nightside, the bow shock is farther away from the Earth than the average. The mechanism explaining the bow shock location under the radial IMF is not completely understood. We believe that the magnetosonic Mach number and unusual conditions of the magnetosheath, especially for low dynamic pressure, play an important role. In the future, more work is needed to describe the reactions of the Earth’s magnetosphere to different IMF orientations, especially to the radial IMF.

Parametric Study on Thrust Vectoring with a Secondary Injection in a Convergent–Divergent Nozzle

AbstractThis work investigated the performance of thrust vectoring with a secondary injection in a convergent–divergent nozzle. Analytical modeling was conducted to determine the shock location and...