Shock Shape Research Articles

Large-eddy simulation of a supersonic lifted jet flame: Analysis of the turbulent flame base

Large-eddy simulation of a supersonic hydrogen–air non-premixed lifted jet flame is reported in the configuration studied by Cheng et al. (1994). The emphasis of the study is on the mechanism driving flame stabilization. The resolution issue is first addressed by considering three meshes of, respectively, 4, 32 and 268 millions of cells. The highest resolution of 60 μm allows for resolving the flame with a reduced chemical kinetics. LES results are found in good agreement with experimental data and previous simulations of the literature. It is observed in the simulations that the highly unstable flame base exhibits a cyclic period of around 0.25 ms, with the transient occurence of shock diamonds. These shocks may enhance the mixing of the reactants and control the autoignition processes occurring in the vicinity of the burner exit. The flame also exhibits a transient bow shock shape structure. The dynamics of the turbulent flame base, and the fluctuations of its streamwise position, thus appears to be controlled by the intricate coupling between autoignition and the upstream propagation of strong pressure waves sustained by combustion, pertaining to an intermittent detonation-like mechanism. From these highly-resolved unsteady simulations, a scenario is drawn to explain the cyclic time evolution of the structure of the unsteady turbulent flame base, in direct relation with its fluctuating streamwise position.

Reflection of curved shock waves

Shock curvatures are related to pressure gradients, streamline curvatures and vorticity in flows with planar and axial symmetry. Explicit expressions, in an influence coefficient format, are used to relate post-shock pressure gradient, streamline curvature and vorticity to pre-shock gradients and shock curvature in steady flow. Using higher order, von Neumann-type, compatibility conditions, curved shock theory is applied to calculate the flow near singly and doubly curved shocks on curved surfaces, in regular shock reflection and in Mach reflection. Theoretical curved shock shapes are in good agreement with computational fluid dynamics calculations and experiment.

超音速パラシュートの開傘ダイナミクスに関する数値解析

This paper presents the recent efforts to characterize the maximum load experienced by a Disk-Gap-Band type parachute to support Mars landing mission currently considered at JAXA. We simulated the structure-flow interaction with CFD solver coupled with a mass-spring-damper structural model. The interaction was modeled using a 3D elastic canopy model and the immersed boundary method. Flow parameters were computed for a Mach 1.6 free stream condition. The flow field solution was post processed to yield the drag coefficient. In addition, experimental campaigns were conducted at JAXA supersonic wind tunnel facilities. The time histories of the drag coefficient were recorded; the shock shapes and the canopy opening process were visualized by Schlieren diagnostics to provide data and validate the numerical models. The computed averaged drag coefficient was found to be within 5% with the measurement. The breathing frequency computed from Fast Fourier Transform analysis was found to be a similar tendency with the experimental data.

Viscous Shock Layer Around Slender Bodies with Nonequilibrium Air Chemistry

A method has been developed which can reliably compute nonequilibrium viscous shock layer over blunt-nosed bodies. This method considerably improves computational efficiency, especially for long slender bodies. The shock shape is generated as a part of the solution in this method, and in the nose region, the shock shape is calculated from an algebraic relation and corrected by global passes through that region. The current algorithm yields a considerable decrease of more than 60% in CPU time relative to other VSL methods. In the present study, both seven and eleven species air models were tested. The seven species analysis includes N, O, N2, O2, NO, NO+ and e−. The eleven species analysis includes the same species plus N+, O+, $$\text{N}_{2}^{ + }$$ , $$\text{O}_{2}^{ + }$$ . The chemical reaction models for seven and eleven species are taken from Blottner and Gupta, respectively. The governing equations are solved with a spatial-marching, implicit, finite-difference method. The solution is obtained by solving a couple of normal momentum and continuity equations. The results of the present technique show good agreement compared to the STS_2 flight data and other numerical solutions.

The influence of IMF clock angle on the cross section of the tail bow shock

AbstractWe study effects of the interplanetary magnetic field (IMF) orientation on the terrestrial tail bow shock location and shape by using global MHD magnetosphere model and empirical bow shock models. It is shown that the tail bow shock cross section is well approximated by an ellipse with the direction of the major axis roughly perpendicular to the IMF clock angle direction. With the increasing IMF clock angle, the eccentricity of the bow shock cross section increases for northward IMF but decreases for southward IMF.

Quantitative model for the generic 3D shape of ICMEs at 1 AU

Interplanetary imagers provide 2D projected views of the densest plasma parts of interplanetary coronal mass ejections (ICMEs) while in situ measurements provide magnetic field and plasma parameter measurements along the spacecraft trajectory, so along a 1D cut. As such, the data only give a partial view of their 3D structures. By studying a large number of ICMEs, crossed at different distances from their apex, we develop statistical methods to obtain a quantitative generic 3D shape of ICMEs. In a first approach we theoretically obtain the expected statistical distribution of the shock-normal orientation from assuming simple models of 3D shock shapes, including distorted profiles, and compare their compatibility with observed distributions. In a second approach we use the shock normal and the flux rope axis orientations, as well as the impact parameter, to provide statistical information across the spacecraft trajectory. The study of different 3D shock models shows that the observations are compatible with a shock symmetric around the Sun-apex line as well as with an asymmetry up to an aspect ratio around 3. Moreover, flat or dipped shock surfaces near their apex can only be rare cases. Next, the sheath thickness and the ICME velocity have no global trend along the ICME front. Finally, regrouping all these new results and the ones of our previous articles, we provide a quantitative ICME generic 3D shape, including the global shape of the shock, the sheath and the flux rope. The obtained quantitative generic ICME shape will have implications for several aims. For example, it constrains the output of typical ICME numerical simulations. It is also a base to develop deeper studies of the transport of high energy solar and cosmic particles during an ICME propagation, as well as for modeling and forecasting space weather conditions near Earth.

Dipole tilt controls bow shock location and flaring angle

The dipole tilt angle has been found to affect Earth’s bow shock. This work presents a quantitative relationship between the dipole tilt angle and the bow shock location and flaring angle. We collected a large data set of bow shock crossings from four different satellites (IMP 8, Geotail, Magion 4, and Cluster), including some recent crossings obtained during 2012–2013. The results from a statistical analysis demonstrate that: (1) the subsolar standoff distance increases but the flaring angle decreases with increasing dipole tilt angle; (2) when the dipole tilt angle changes sign from negative to positive, the dayside bow shock moves toward Earth and the shift can be as much as 2.29 R E, during which the flaring angle increases; and (3) the shape of bow shock in the northern and southern hemispheres differs. For the northern hemisphere bow shock, with increasing positive/negative dipole tilt angle, the flaring angle increases/decreases. While for the southern hemisphere, the trend is the opposite; with increasing positive/negative dipole tilt angle, the flaring angle decreases/increases. These results are helpful for future bow shock modeling that needs to include the effects of dipole tilt angle.

Global MHD simulations of Neptune's magnetosphere

AbstractA global magnetohydrodynamic (MHD) simulation has been performed in order to investigate the outer boundaries of Neptune's magnetosphere at the time of Voyager 2's flyby in 1989 and to better understand the dynamics of magnetospheres formed by highly inclined planetary dipoles. Using the MHD code Gorgon, we have implemented a precessing dipole to mimic Neptune's tilted magnetic field and rotation axes. By using the solar wind parameters measured by Voyager 2, the simulation is verified by finding good agreement with Voyager 2 magnetometer observations. Overall, there is a large‐scale reconfiguration of magnetic topology and plasma distribution. During the “pole‐on” magnetospheric configuration, there only exists one tail current sheet, contained between a rarefied lobe region which extends outward from the dayside cusp, and a lobe region attached to the nightside cusp. It is found that the tail current always closes to the magnetopause current system, rather than closing in on itself, as suggested by other models. The bow shock position and shape is found to be dependent on Neptune's daily rotation, with maximum standoff being during the pole‐on case. Reconnection is found on the magnetopause but is highly modulated by the interplanetary magnetic field (IMF) and time of day, turning “off” and “on” when the magnetic shear between the IMF and planetary fields is large enough. The simulation shows that the most likely location for reconnection to occur during Voyager 2's flyby was far from the spacecraft trajectory, which may explain the relative lack of associated signatures in the observations.

Effect of nose shape on the shock standoff distance at nearsonic flows

This paper describes a numerical solution of the bow shock shape ahead of some blunt and sharp axisymmetric noses containing sphere, blunt cone, and sharp cone at steady transonic flow in the Mach number range of 1.01 to 1.2. For validating the results, one sphere and three blunt cones are modeled, and their shock standoff distance is compared with other experimental and numerical studies. The flow over other noses with similar geometric parameters is then solved and compared with each other. In this study, the Reynolds-averaged Navier—Stokes equations are solved using the Spalart—Allmaras turbulence model. The purpose of this study is to determine the shock standoff distance for some blunt and sharp noses at low supersonic free flight speed. The shock standoff distance is determined from the Mach number curve on the symmetry line. The present numerical simulations reach down to M8=1.01 a range where it is almost very difficult to set in experimental studies. The shock wave locations were found to agree well with previous numerical and experimental studies. Our results are closer to the experimental results compared to other numerical studies. In addition, the results for shock standoff distances over paraboloids in these speed ranges have not been previously published as far as we know.

Flow Field Analysis on the Stagnation Streamline of a Blunt Body

The hypersonic flow on the stagnation streamline of a blunt body is analyzed with quasi one-dimensional (1-D) Navier-Stokes equations approximated by adopting the local similarity to the two-dimensional (2-D)/axisymmetric Navier-Stokes equations. The governing equations are solved using the implicit finite volume method. The computational domain is confined from the stagnation point to the shock wave, and the shock fitting method is used to find the shock position. We propose a boundary condition at the shock, which employs the shock wave angle in the vicinity of the stagnation streamline using the shock shape correlation. As a result of numerical computation conducted for the hypersonic flow over a sphere, the proposed boundary condition is shown to improve the accuracy of the prediction of the shock standoff distance. The quasi 1-D Navier-Stokes code is efficient in computing time and is reliable for the flow analysis along the stagnation streamline and the prediction of heat flux at the stagnation point in the hypersonic blunt body flow.

Shape and position of Earth’s bow shock near-lunar orbit based on ARTEMIS data

Abstract Earth’s bow shock is the result of interaction between the supersonic solar wind and Earth’s magnetopause. However, data limitations mean the model of the shape and position of the bow shock are based largely on near-Earth satellite data. The model of the bow shock in the distant magnetotail and other factors that affect the bow shock, such as the interplanetary magnetic field (IMF) B y , remain unclear. Here, based on the bow shock crossings of ARTEMIS from January 2011 to January 2015, new coefficients of the tail-flaring angle α of the Chao model (one of the most accurate models currently available) were obtained by fitting data from the middle-distance magnetotail (near-lunar orbit, geocentric distance - 20 R E> X > - 50 R E). In addition, the effects of the IMF B y on the flaring angle α were analyzed. Our results showed that: (1) the new fitting coefficients of the Chao model in the middle-distance magnetotail are more consistent with the observed results; (2) the tail-flaring angle α of the bow shock increases as the absolute value of the IMF B y increases. Moreover, positive IMF B y has a greater effect than negative IMF B y on flaring angle. These results provide a reference for bow shock modeling that includes the IMF B y .

Numerical investigation on the thermal protection mechanism for blunt body with forward-facing cavity

Numerical experiments are carried out using the standard hypersonic ballistic-type model (HB-2) to investigate the effect of forward-facing cavity on the aerodynamic heating. A general concept is proposed which utilizes the flow disturbances generated passively in the nosed subsonic region to weaken the detached shock wave. Several aspects are mainly studied, including shock shape and standoff distance, surface heat flux and pressure, flowfield feature and cooling mechanism. The numerical results indicate that shock strength and standoff distance increase with an increase in the L/D ratio of the cavity. Interestingly, a bulge structure of the detached shock associated with a deep cavity is observed for the first time. Local surface heat flux and pressure around the concave nose are much lower respectively than those at the stagnation point of the baseline model. In addition, both surface heat and pressure reductions are proportional to the L/D ratio. A negative heating phenomenon may occur in the vicinity of a sharp lip or on the base wall of a deep cavity. If the L/D ratio exceeds 0.7, the detached shock appears as a self-sustained oscillation which can be referred to as the cooling mechanism.

Simulation of Shock Wave Assisted Free and Shape Forming of Metallic Plates in a Shock Tube

Due to their complexity, certain engineering problems like finding shock strength, Mach number etc. and the interaction of shock wave with a structure in free and restricted metal forming techniques cannot be achieved in a single experimentation, these can be obtained only through a number of trials and that leads to increase in cost and time. In such cases both cost and time can be reduced by adopting numerical simulations. In this projectcommercial software ANSYS is used to simulate the propagation shock wave through a shock tube, free and shape forming of metallic plates subjected to this shock wave. Shock Mach numbers up to 2.12 have been generated by varying the driver to driven pressure ratios. Thin copper plates of diameter 60mm and thickness of 0.5mm and 0.3mm are subjected to shock wave loadingin order to form into dies.These dies,madeof structural steel are modelled with pre-defined shapes. The plate peakoverpressures ranging from 9 to 20bar have been generated.The midpoint deflection, Von Mises stress and strain are calculated for free forming copper plates. The simulated results are compared with the experimental values available in literature. The simulated results match well with the experimental values.

CHARACTERIZATION OF THE INNER KNOT OF THE CRAB: THE SITE OF THE GAMMA-RAY FLARES?

One of the most intriguing results from the gamma-ray instruments in orbit has been the detection of powerful flares from the Crab Nebula. These flares challenge our understanding of pulsar wind nebulae and models for particle acceleration. We report on the portion of a multiwavelength campaign using Keck, HST, and Chandra concentrating on a small emitting region, the Crab's inner knot, located a fraction of an arcsecond from the pulsar. We find that the knot's radial size, tangential size, peak flux, and the ratio of the flux to that of the pulsar are correlated with the projected distance of the knot from the pulsar. A new approach, using singular value decomposition for analyzing time series of images, was introduced yielding results consistent with the more traditional methods while some uncertainties were substantially reduced. We exploit the characterization of the knot to discuss constraints on standard shock-model parameters that may be inferred from our observations assuming the inner knot lies near to the shocked surface. These include inferences as to wind magnetization, shock shape parameters such as incident angle and poloidal radius of curvature, as well as the IR/optical emitting particle enthalpy fraction. We find that while the standard shock model gives good agreement with observation in many respects, there remain two puzzles: (a) The observed angular size of the knot relative to the pulsar--knot separation is much smaller than expected; (b) The variable, yet high degree of polarization reported is difficult to reconcile with a highly relativistic downstream flow.

Using an acoustic sensor and accelerometer to measure the downhole impact frequency of a hydraulic impactor

As an efficient drilling technology, percussion-rotary drilling technology depends extensively on the core component, a hydraulic impactor located at the bottom of the well, to realize its performance. As the most important parameter of the hydraulic impactor, the impact frequency directly reflects the efficiency with which rocks are broken. Furthermore, the impact frequency of the impactor running at the bottom of the well most accurately reflects the real working situation of the hydraulic impactor and the actual drilling process. Several methods have been employed to measure impact frequencies, including a stress wave method, a displacement measurement, and an electromagnetic induction method. However, given the limitations of the testing principle and the test equipment size, most of these methods can only be used to measure the impact frequency of the hydraulic impactor on the ground, i.e., outside the well. To directly obtain the impact frequency of the hydraulic impactor at the bottom of the well, this paper suggests two new test methods, namely, an acoustic sensor method and an accelerometer method, based on actual project experience. The acoustic sensor method measures the impact frequency by processing the acoustic data resulting from the hydraulic impactor's vibration, while the accelerometer method measures the impact frequency by processing the accelerometer data of the hydraulic impactor's vibration. The acoustic sensor method is simple and practical with regard to its programming and operation and can be further divided into two methods, namely, a non-threshold decibel sensor method and a threshold acoustic sensor method. The accelerometer method can be applied both downhole and on the ground. In addition, the ballistic work value obtained using the accelerometer method can be compared to that obtained using the acceleration sensor under the same conditions (including the impact of the pump, the shock shape, the formation conditions, and the hole deviation angle). Laboratory tests and field works were performed after the testing equipment was calibrated. The test results show that both test methods can meet the requirements in terms of required measurement errors. Moreover, the measurements obtained using the accelerometer method and the non-threshold decibel sensor method are more accurate than those obtained using the threshold acoustic sensor method when working downhole, and the threshold acoustic sensor method is more suitable for impact frequency measurements obtained on the ground.

A hybrid CFD/characteristics method for fast characterization of hypersonic blunt forebody/inlet flow

A hybrid CFD/characteristic method (CCM) was proposed for fast design and evaluation of hypersonic inlet flow with nose bluntness, which targets the combined advantages of CFD and method of characteristics. Both the accuracy and efficiency of the developed CCM were verified reliably, and it was well demonstrated for the external surfaces design of a hypersonic forebody/inlet with nose bluntness. With the help of CCM method, effects of nose bluntness on forebody shock shapes and the flowfield qualities which dominate inlet performance were examined and analyzed on the two-dimensional and axisymmetric configurations. The results showed that blunt effects of a wedge forebody are more substantial than that of related cone cases. For a conical forebody with a properly blunted nose, a recovery of the shock front back to that of corresponding sharp nose is exhibited, accompanied with a gradually fading out of entropy layer effects. Consequently a simplification is thought to be reasonable for an axisymmetric inlet with a proper compression angle, and a blunt nose of limited radius can be idealized as a sharp nose, as the spillage and flow variations at the entrance are negligible, even though the nose scale increases to 10% cowl lip radius. Whereas for two-dimensional inlets, the blunt effects are substantial since not only the inlet capturing/starting capabilities, but also the flow uniformities are obviously degraded.

Strong coronal channelling and interplanetary evolution of a solar storm up to Earth and Mars.

The severe geomagnetic effects of solar storms or coronal mass ejections (CMEs) are to a large degree determined by their propagation direction with respect to Earth. There is a lack of understanding of the processes that determine their non-radial propagation. Here we present a synthesis of data from seven different space missions of a fast CME, which originated in an active region near the disk centre and, hence, a significant geomagnetic impact was forecasted. However, the CME is demonstrated to be channelled during eruption into a direction +37±10° (longitude) away from its source region, leading only to minimal geomagnetic effects. In situ observations near Earth and Mars confirm the channelled CME motion, and are consistent with an ellipse shape of the CME-driven shock provided by the new Ellipse Evolution model, presented here. The results enhance our understanding of CME propagation and shape, which can help to improve space weather forecasts.

Effects of the interplanetary magnetic field clock angle on the shape of bow shock

Using the global magnetohydrodynamics (MHD) simulation model, we investigated the effects of the interplanetary magnetic field (IMF) clock angle on the shape of bow shock, including its rotational asymmetry and subsolar point. For general northward IMF (z component B z > 0), the rotational symmetry of the bow shock is broken by the effects of fast magnetosonic Mach number (M ms), and the cross-sectional line of the bow shock is an ellipse with the semi-major axis along the direction perpendicular to the IMF. The ratio or D-value between semi-major and semi-minor axis can be used to illustrate the extent of asymmetry of the bow shock. On the basis of the multiple parameters fitting, we obtain the changing relationship of both semi-axes with the clock angle and the distance away from the Earth. For general southward IMF (B z 0, and decreases with the increasing IMF clock angle for B z < 0.

The shape of the Venusian bow shock at solar minimum and maximum: Revisit based on VEX observations

Several factors control the bow shock position at Venus, including short-term period responses (solar wind dynamic pressure) and long-term period variations (solar activity). Based on Venus Express (VEX) observations, we revisit the influence of solar activity on the Venusian bow shock location, by accurately determining not only the shock terminator distance but also the subsolar point with a three-parameter fit (TPF) method. At the same time, VEX covers a larger range of solar zenith angles (SZA) at the Venusian bow shock (from about 10 to 135 degrees) than the Pioneer Venus Orbiter (PVO) spacecraft. Fitting results display that the Venusian bow shock is farther away from Venus at solar maximum than at solar minimum. The subsolar stand-off distance increases from 1.364 planetary radii at solar minimum to 1.459RV at solar maximum, while the terminator shock distance changes from 2.087RV to 2.146RV. Inspection of the bow shock and the induced magnetosphere boundary (IMB) locations clearly shows a positive correlation for every orbit, while the average bow shock location is not responsive to changes in the solar wind dynamic pressure.

Numerical simulations of Mach stem formation via intersecting bow shocks

Hubble Space Telescope observations show bright knots of Hα emission within outflowing young stellar jets. Velocity variations in the flow create secondary bow shocks that may intersect and lead to enhanced emission. When the bow shocks intersect at or above a certain critical angle, a planar shock called a Mach stem is formed. These shocks could produce brighter Hα emission since the incoming flow to the Mach stem is parallel to the shock normal. In this paper we report first results of a study using 2-D numerical simulations designed to explore Mach stem formation at the intersection of bow shocks formed by hypersonic “bullets” or “clumps”. Our 2-D simulations show how the bow shock shapes and intersection angles change as the adiabatic index γ changes. We show that the formation or lack of a Mach stem in our simulations is consistent with the steady-state Mach stem formation theory. Our ultimate goal, which is part of an ongoing research effort, is to characterize the physical and observational consequences of bow shock intersections including the formation of Mach stems.