Showing papers on "Oblique shock published in 2003"

Shock waves, dead zones and particle-free regions in rapid granular free-surface flows

Abstract: Shock waves, dead zones and particle-free regions form when a thin surface avalanche of granular material flows around an obstacle or over a change in the bed topography. Understanding and modelling these flows is of considerable practical interest for industrial processes, as well as for the design of defences to protect buildings, structures and people from snow avalanches, debris flows and rockfalls. These flow phenomena also yield useful constitutive information that can be used to improve existing avalanche models. In this paper a simple hydraulic theory, first suggested in the Russian literature, is generalized to model quasi-two-dimensional flows around obstacles. Exact and numerical solutions are then compared with laboratory experiments. These indicate that the theory is adequate to quantitatively describe the formation of normal shocks, oblique shocks, dead zones and granular vacua. Such features are generated by the flow around a pyramidal obstacle, which is typical of some of the defensive structures in use today.

Large-Eddy Simulation of Supersonic Cavity Flowfields Including Flow Control

Abstract: Large-eddy simulations of supersonic cavity flowfields are performed using a high-order numerical method. Spatial derivatives are represented by a fourth-order compact approximation that is used in conjunction with a sixth-order nondispersive filter. The scheme employs a time-implicit approximately factored finite difference algorithm, and applies Newton-like subiterations to achieve second-order temporal and fourth-order spatial accuracy. The Smagorinsky dynamic subgrid-scale model is incorporated in the simulations to account for the spatially underresolved stresses. Computations at a freestream Mach number of 1.19 are carried out for a rectangular cavity having a length-to-depth ratio of 5:1. The computational domain is described by 2.06×10 7 grid points and has been partitioned into 254 zones, which were distributed on individual processors of a massively parallel computing platform. Active flow control is applied through pulsed mass injection at a very high frequency, thereby suppressing resonant acoustic oscillatory modes

Shock-wave-induced jetting of micron-size bubbles

Abstract: Free gas bubbles in water with radii between 7 and 55 µm subjected to a shock wave exhibit a liquid jetting phenomenon with the jet pointing in the direction of the propagating shock wave. With increasing bubble radius, the length of the jet tip increases and a lower estimate of the averaged jet velocity increases linearly from 20 to 150µm/s. At a later stage, the jet breaks up and releases micron-size bubbles. In the course of shock wave permeabilization and transfection of biological cells, this observation suggests a microinjection mechanism when the cells are near bubbles exposed to a shock wave.

Planar velocity measurements of a two-dimensional compressible wake

Abstract: The present study describes the application of particle image velocimetry (PIV) to investigate the compressible flow in the wake of a two-dimensional blunt base at a freestream Mach number M ∞=2. The first part of the study addresses specific issues related to the application of PIV to supersonic wind tunnel flows, such as the seeding particle flow-tracing fidelity and the measurement spatial resolution. The seeding particle response is assessed through a planar oblique shock wave experiment. The measurement spatial resolution is enhanced by means of an advanced image-interrogation algorithm. In the second part, the experimental results are presented. The PIV measurements yield the spatial distribution of mean velocity and turbulence. The mean velocity distribution clearly reveals the main flow features such as expansion fans, separated shear layers, flow recirculation, reattachment, recompression and wake development. The turbulence distribution shows the growth of turbulent fluctuations in the separated shear layers up to the reattachment location. Increased velocity fluctuations are also present downstream of reattachment outside of the wake due to unsteady flow reattachment and recompression. The instantaneous velocity field is analyzed seeking coherent flow structures in the redeveloping wake. The instantaneous planar velocity and vorticity measurements return evidence of large-scale turbulent structures detected as spatially coherent vorticity fluctuations. The velocity pattern consistently shows large masses of fluid in vortical motion. The overall instantaneous wake flow is organized as a double row of counter-rotating structures. The single structures show vorticity contours of roughly elliptical shape in agreement with previous studies based on spatial correlation of planar light scattering. Peak vorticity is found to be five times higher than the mean vorticity value, suggesting that wake turbulence is dominated by the activity of large-scale structures. The unsteady behavior of the reattachment phenomenon is studied. Based on the instantaneous flow topology, the reattachment is observed to fluctuate mostly in the streamwise direction suggesting that the unsteady separation is dominated by a pumping-like motion.

The properties and causes of rippling in quasi-perpendicular collisionless shock fronts

Abstract: . The overall structure of quasi-perpendicular, high Mach number collisionless shocks is controlled to a large extent by ion reflection at the shock ramp. Departure from a strictly one-dimensional structure is indicated by simulation results showing that the surface of such shocks is rippled, with variations in the density and all field components. We present a detailed analysis of these shock ripples, using results from a two-dimensional hybrid (particle ions, electron fluid) simulation. The process that generates the ripples is poorly understood, because the large gradients at the shock ramp make it difficult to identify instabilities. Our analysis reveals new features of the shock ripples, which suggest the presence of a surface wave mode dominating the shock normal magnetic field component of the ripples, as well as whistler waves excited by reflected ions. Key words. Space plasma physics (numerical simulation studies; shock waves; waves and instabilities)

Shock waves at microscales

Abstract: We present a model for the effects of scale, via molecular diffusion phenomena, on the generation and propagation of shock waves. A simple parametrization of the shear stresses and heat flux at the wall leads to the determination of new jump conditions, which show that, for a given wave Mach number at small scales, the resulting particle velocities are lower but the pressures are higher. Also, the model predicts that the flow at small scale is isothermal and that the minimum wave velocity can be subsonic. Experiments with a miniature shock tube using low pressures to simulate the effects of small scale have shown qualitative agreement with the proposed model. In fact, the effects of scale appear even more important than what has been incorporated in the model.

Interaction of a shock with a sphere suspended in a vertical shock tube

Abstract: Shock wave interaction with a sphere is one of the benchmark tests in shock dynamics. However, unlike wind tunnel experiments, unsteady drag force on a sphere installed in a shock tube have not been measured quantitatively. This paper presents an experimental and numerical study of the unsteady drag force acting on a 80 mm diameter sphere which was vertically suspended in a 300 mm x 300 mm vertical shock tube and loaded with a planar shock wave of M s = 1.22 in air. The drag force history on the sphere was measured by an accelerometer installed in it. Accelerometer output signals were subjected to deconvolution data processing, producing a drag history comparable to that obtained by solving numerically the Navier-Stokes equations. A good agreement was obtained between the measured and computed drag force histories. In order to interpret the interaction of shock wave over the sphere, high speed video recordings and double exposure holographic interferometric observations were also conducted. It was found that the maximum drag force appeared not at the time instant when the shock arrived at the equator of the sphere, but at some earlier time before the transition of the reflected shock wave from regular to Mach reflection took place. A negative value of the drag force was observed, even though for a very short duration of time, when the Mach stem of the transmitted shock wave relfected and focused at the rear stagnation point of the sphere.

Shock-Vortex Interactions at High Mach Numbers

Abstract: We perform a computational study of the interaction of a planar shock wave with a cylindrical vortex. We use a particularly robust High Resolution Shock Capturing scheme, Marquina's scheme, to obtain high quality, high resolution numerical simulations of the interaction. In the case of a very-strong shock/vortex encounter, we observe a severe reorganization of the flow field in the downstream region, which seems to be due mainly to the strength of the shock. The numerical data is analyzed to study the driving mechanisms for the production of vorticity in the interaction.

Numerical Study of Mixing Enhancement by Shock Waves in Model Scramjet Engine

Abstract: Anumerical study hasbeenconductedto investigatetheeffectofshockwaveson thesupersonichydrogen ‐airjet e ame stabilized in a Mach 2.5 circularcross-section combustor. Thenumerical model utilizes multispecies Navier ‐ Stokes equationswith detailed chemical reaction modelsand employsa k‐! shear stresstransport model. A wedge is mounted on the side wall of the combustor in order to e nd the interaction of the oblique shock waves with the hydrogen‐air jetlike e ame. The interaction between the shock waves and the mixing layer is classie ed according to the increasing tendency of the growth rate of the mixing layer downstream of the shock waves. It is found that the shock wavescreatea radially inward/outward aire owto thee ame and elongatea e ame-holding recirculation zone, and thus fuel ‐air mixing is enhanced signie cantly, resulting in improved combustion efe ciency. Also, the overall performance is investigated by changing the shock position and considering the mixing/combustion efe ciency and total pressure loss in a model scramjet combustor. Because there exists a tradeoff between the enhanced mixing/combustion efe ciency and the decreased total pressure recovery, it is suggested that the optimized shock position needs to be determined in order to obtain the maximum overall combustor performance using the overall performance index.

Numerical investigations of shock waves in gas-particle mixtures Evaluation of numerical methods for dusty-gas shock wave phenomena

Abstract: The propagation of shock waves in gas-particle mixtures in one- and two-dimensional geometries is numerically investigated. Two schemes for approximating conservation laws for particles, which are collectively treated as a continuum medium, are compared and discussed. Different models of the drag coefficient and Nusselt number, directly affecting the interaction between the gas and particle phases, are used for obtaining shock profiles, and the results are compared. The oblique shock reflections at a solid wedge in a gas-particle mixture are simulated. The results demonstrate that the reflection pattern changes as the shock propagates along the wedge, revealing strong non-selfsimilarity of the phenomenon.

Stephan's Quintet: The X-ray Anatomy of a Multiple Galaxy Collision

Abstract: Chandra observations of the compact galaxy group known as Stephan's Quintet (SQ) are presented. The major morphological features that were discovered with the ROSAT HRI are now imaged with higher resolution and S/N. The large scale shock (1. 5, ∼40 kpc if at 85 Mpc) is resolved into a narrow NS feature embedded in more extended diffuse emission (D ≥ 3 � ). The NS structure is somewhat clumpy, more sharply bounded on the W side and prominent only in the soft band (energies below ∼2 keV). Its observational properties are best explained as a shock produced by a high velocity encounter between NGC 7318b, a "new intruder", and the intergalactic medium in SQ. The shock conditions near the high speed intruder suggest that a bow shock is propagating into a pre-existing H  cloud and heating the gas to a temperature of 0.5 keV. The low temperature in the shock is a problem unless we postulate an oblique shock. One member, NGC 7319, hosts a Seyfert 2 nucleus, with an intrinsic luminosity LX = 10 43 erg s −1 , embedded in a region of more diffuse emission with 10 �� radius extent. The nuclear spectrum can be modeled with a strongly absorbed power-law typical of this class of sources. Several additional compact sources are detected including three in foreground NGC 7320. Some of these sources are very luminous and could be related to the ultraluminous X-ray sources found in nearby galaxies.

Viscous Shock Wave and Boundary Layer Solution to an Inflow Problem for Compressible Viscous Gas

Abstract: The inflow problem for a one-dimensional compressible viscous gas on the half line (0,+∞) is investigated. The asymptotic stability on both the viscous shock wave and a superposition of the viscous shock wave and the boundary layer solution is established under some smallness conditions. The proofs are given by an elementary energy method.

Flowfield Around Spike-Tipped Bodies for High Attack Angles at Mach 4.5

Abstract: The requirements for the design of a new short-range high-velocity missile are both the drag reduction and the correct information acquisition for the optoelectronic sensors embedded in the hemispherical nose. High anglesof attack must be studied to fulfill the maneuverability requirements of present and future missiles. A supersonic missile generates a bow shock around its blunt nose, which causes rather high surface pressure and temperature and, as a result, the development of high drag and damage of embedded sensors. The pressure and the temperature on the hemispherical nose surface can be substantially reduced if an oblique shock is generated by a forward-facing spike. Both the experiments and the computations are carried out to study the flowfield around three-dimensional blunt bodies equipped with forward-facing spikes for a large range of attack angles at a Mach number of 4.5. A blunt body, a classical disk-tip spike, a sphere-tip spike, and a biconical-tip spike are studied. The experiments involve high-pressure shock tunnel investigations using a shock tube facility. The differential interferometry technique is applied to visualize the flowfield around the different missile spike geometries. The differential interferogram pictures as well as surface pressure measurements are compared with numerical results. Numerical simulations based on steady-state three-dimensional Navier-Stokes computations are performed to predict the drag, the lift, and the pitching moment for the blunt body and for each spike-tipped missile. The computations allow one to bring out the advantages of each spike geometry in comparison to the blunt body.

Earth's bow shock and magnetopause in the case of a field-aligned upstream flow: Observation and model comparison

Abstract: [1] On 5 May 1996 the Interball-1 and IMP 8 spacecraft crossed the bow shock boundary. The upstream conditions were special in two factors: (1) the interplanetary magnetic field was anti-parallel to the solar wind flow within 15° and (2) the conditions were stable for a prolonged period (∼9 hours). At the nose of the magnetosphere, the Interball-1 data revealed that the magnetopause was farther outward by ∼2 RE than model predictions and the subsolar magnetosheath was unusually thin, at most 10% of the magnetopause standoff distance. Both results stand in contrast to predictions of existing magnetopause/bow shock models. Assuming a hyperboloidal (paraboloidal) shock wave, the calculated shock's standoff distance was 13.7 (13.6) RE, and the focus was located on the x axis at 4.5 (4.2) RE. On the basis of the IMP 8 observation, the bow shock flares significantly less than MHD simulations predict for a field-aligned bow shock at the magnetospheric flanks. This study discusses differences between the observations and existing MHD bow shock simulations for field-aligned upstream flow. Furthermore, it is suggested that the flow-aligned IMF orientation causes a significant change of the magnetopause shape into a bullet-like obstacle.

Stephan's Quintet: The X-ray Anatomy of a Multiple Galaxy Collision

Abstract: Chandra observations of the compact galaxy group known as Stephan's Quintet (SQ) are presented. The major morphological features that were discovered with the ROSAT HRI are now imaged with higher resolution and S/N. The large scale shock (1.5', ~40kpc if at 85 Mpc) is resolved into a narrow NS feature embedded in more extended diffuse emission (D>=3'). The NS structure is somewhat clumpy, more sharply bounded on the W side and prominent only in the soft band (energies below ~2 keV). Its observational properties are best explained as a shock produced by a high velocity encounter between NGC7318b, a ``new intruder'', and the intergalactic medium in SQ. The shock conditions near the high speed intruder suggest that a bow shock is propagating into a pre-existing HI cloud and heating the gas to a temperature of ~0.5 keV. The low temperature in the shock is a problem unless we postulate an oblique shock. One member, NGC7319, hosts a Seyfert 2 nucleus, with an intrinsic luminosity Lx=10^43 erg/s, embedded in a region of more diffuse emission with 10'' radius extent. The nuclear spectrum can be modeled with a strongly absorbed power-law typical of this class of sources. Several additional compact sources are detected including three in foreground NGC7320. Some of these sources are very luminous and could be related to the ultraluminous X-ray sources found in nearby galaxies.

A global solution to a two-dimensional Riemann problem involving shocks as free boundaries

Abstract: We present a global solution to a Riemann problem for the pressure gradient system of equations. The Riemann problem has initially two shock waves and two contact discontinuities. The angle between the two shock waves is set initially to be close to 180 degrees. The solution has a shock wave that is usually regarded as a free boundary in the self-similar variable plane. Our main contribution in methodology is handling the tangential oblique derivative boundary values.

Shock wave induced interaction of microbubbles and boundaries

Abstract: In the present study we experimentally investigate bubble dynamics after laser induced shock wave exposure in the vicinity of salt crystals suspended in water. High-speed microscopic images show aspherical collapse and rebound of single and multiple bubbles with initial radii between 5 and 150 μm. Radius time curves of bubbles close to one boundary are compared to the bubble dynamics of a spherical model. The bubble dynamics strongly depends on the position of neighboring bubbles and on the number of boundaries given by the surrounding salt grains. After excitation bubbles are drawn to the closest particles in their vicinity. Subsequent application of shock waves leads to jet formation against the rigid boundaries. The bubbles often tend to form in or migrate into cracks on the crystal surfaces and sometimes lead to the breakage of particles due to rapid bubble dynamics. Similar behavior may occur in other cases where material damage is induced by shock waves in liquids such as lithotripsy or shock wave cleaning applications.

Nonequilibrium Radio Frequency Discharge Plasma Effect on Conical Shock Wave: M = 2.5 Flow

Abstract: An experimental study of shock modie cation in an M =2:5 supersonic e ow of nonequilibrium plasma over a cone is discussed. The experiments are conducted in a nonequilibrium plasma supersonic wind tunnel. Recent experiments at the Ohio State University using a supersonic plasma e ow over a quasi-two-dimensional wedge showed that an oblique shock can be considerably weakened by a transverse rf discharge plasma. The previously observed shock weakening, however, has been found consistent with a temperature rise in the boundary layers heated by the discharge. In thepresent study, theboundary-layereffects on theshock waveare reduced by placing an entire cone model into a supersonic inviscid core e ow. The electron density in the supersonic plasma e ow in the test section is measured using microwave attenuation. The ionization fraction in the discharge is in the same range as in the previous plasma shock experiments, up to ne/N =(1.2‐3.0)£10 i7 . The results do not show any detectable shock weakening by the plasma. This strongly suggests that the previously observed shock weakening and dispersion in nonequilibrium plasmas are entirely due to thermal effects.

Shock Wave Modification Method and System

Abstract: A shock wave in a gas is modified by emitting energy to form an extended path in the gas; heating gas along the path to form a volume of heated gas expanding outwardly from the path; and directing a path. The volume of heated gas passes through the shock wave and modifies the shock wave. This eliminates or reduces a pressure difference between gas on opposite sides of the shock wave. Electromagnetic, microwaves and/or electric discharge can be used to heat the gas along the path. This application has uses in reducing the drag on a body passing through the gas, noise reduction, controlling amount of gas into a propulsion system, and steering a body through the gas. An apparatus is also disclosed.

Mechanism of Shock Wave Oscillation in Transonic Diffusers

Abstract: Self-excited shock wave oscillation in a two-dimensional transonic diffuser is investigated experimentally and analytically. In theexperiments, the temporal position of a shock wave is recorded by a high-speed charge-coupled device camera combined with a schlieren system, simultaneously measuring the e uctuation of the static pressure on the diffuser wall. The temporal variation of the static pressure is also measured to obtain the propagation of pressure disturbances. The results show that a pressure disturbance is generated near the stem of the shock wave and is convected in the downstream direction. In thedownstream region wheretheboundary layer becomes highly turbulent, another disturbance is generated that propagates upstream and causes the shock wave to oscillate. One-dimensional Euler equations are solved numerically, and the power spectral density distribution of the shock wave oscillation is calculated. The numerical results agree very well with the experiments. It is also shown that the present calculation can explain the shock wave oscillation in the diffusers reported so far.

Normal Shock/Boundary-Layer Interaction Control Using Aeroelastic Mesoflaps

Abstract: A normal shock/boundary-layer interaction control technique termed mesoflaps for aeroelastic recirculating transpiration has been investigated in a planar Mach 1.37 wind tunnel. In this flow-control system, an array of small flaps is mounted over a cavity; the flaps deflect aeroelastically under the pressure loads imposed by the normal shock, thereby allowing recirculation from downstream of the shock to upstream. Qualitative analysis of the mesoflap control was investigated with spark shadowgraph visualizations and oil-streak surface-flow visualizations, whereas quantitative analysis was achieved by measuring surface pressure distributions and boundary-layer velocity profiles. Nine different mesoflap arrays were investigated, in addition to the solid-wall reference case. It was found that flap thickness and, therefore, transpiration rate, had a demonstrable effect on static and total pressure recovery, in addition to boundary-layer integral properties. Although some of the arrays did not provide a performance benefit, one particular flap array was found to have significantly higher static and total pressure recoveries than the solid-wall reference case, while simultaneously demonstrating a reduction in boundary-layer momentum thickness and unchanged displacement thickness.

Interferometric CT measurement of three-dimensional flow phenomena on shock waves and vortices discharged from open ends

Abstract: Three-dimensional flow phenomena are observed in a shock tube experiment for shock waves and vortices discharged from a square open end and a pair of circular open ends by using an interferometric CT (Computed Tomography) technique. To take multidirectional finite-fringe interferograms for a three-dimensional flow field, we introduce a rotating duct model in the test section of the shock tube. The experiments are performed for incident shock Mach numbers 1.50 and 1.30 in nitrogen gas of 98 kPa initial pressure. Good quality CT images of the density distribution are obtained by carefully selecting the projection images for a reproducible flow within a prescribed accuracy. The three-dimensional flow features are clearly visualized for a vortex ring, a secondary shock wave, shock-vortex interaction, and shock-shock interaction through the pseudo-color image of density distribution and the isopycnic surface. Their meanings in gas dynamics and shock dynamics are discussed. We demonstrate that studies of various three-dimensional problems in shock dynamics are possible using the present CT technique.

Three‐dimensional modeling of Earth's bow shock: Shock shape as a function of Alfvén Mach number

Abstract: [1] Earth's bow shock changes its three-dimensional (3-D) location in response to changes in the solar wind ram pressure Pram, Alfven Mach number M A , magnetic field orientation, fast mode Mach number M ms , and sonic Mach number M S . Using shock locations from global 3-D ideal MHD simulations [Cairns and Lyon, 1995], empirical models are derived for the 3-D shape and location of Earth's bow shock in the near-Earth regime as a function of solar wind conditions. Multiple simulations with different M A and Pram but two orientations of the interplanetary magnetic field B IMF are analyzed: θ IMF = 45° and 90° with respect to the solar wind direction v sw . Models for the (paraboloid) flaring parameter b s as a function of M A , azimuthal angle Φ, and θ IMF = 45° or 90°, show b s decreasing with M A , corresponding to the shock becoming blunter and less swept back (with a larger cross section), as expected. Together with models for the shock's standoff distance (which increases with decreasing M A ) the models for b s (M A , Φ) predict the shock's 3-D location. Variations of by with Φ represent eccentricities in the shock's cross section (i.e., a departure from circularity), with the shock extending further perpendicular to v ms (the fast mode speed) than parallel, as M A → 1. An additional effect is observed in which the shock shape is skewed for θ IMF = 45° (but not for θ IMF = 90°) in the plane containing B IMF and v sw . These latter two effects are consistent with the fast mode velocity varying with propagation direction relative to B IMF .

Self-induced oscillations in the shock wave flow pattern formed in a stationary supersonic flow over a double wedge

Abstract: Numerical simulations of a two-dimensional supersonic flow of an inviscid perfect gas over a double wedge in the Mach numbers range 5⩽M⩽9, revealed the existence of self-induced oscillations in the shock wave flow pattern in a narrow range of geometrical parameters.

Bow shock motions observed with CLUSTER

Abstract: [1] The Cluster mission allows the determination not only of the bow shock crossing position but also, with a simple timing method and a reasonable confidence, the shock normal and the velocity along this normal. We apply this technique to a series of eleven consecutive bow shock crossings which occurred during a time interval of approximatively two and a half hours on 31 March 2001. We fit, on a distance versus time frame, the position of the bow shock subsolar point by imposing that the time derivatives at the crossings be equal to the shock speeds we determine. The curve we obtain this way represents global oscillations of the bow shock with a typical amplitude that compares quite well to the prediction of standard gasdynamic models which take into account the upstream solar wind plasma conditions.

Positron acceleration to ultrarelativistic energies by a shock wave in a magnetized electron–positron–ion plasma

Abstract: Positron acceleration in oblique shock waves is studied with relativistic, electromagnetic, particle simulations with full particle dynamics. In the simulations, some positrons have been accelerated to energies γ∼600, where γ is the Lorentz factor. The electric field parallel to the magnetic field plays an essential role in the acceleration; it prevents some positrons from passing through the shock wave. For certain shock propagation velocities and angles, these positrons stay around the shock front for long periods of time, moving roughly parallel to the external magnetic field, and gain great energies. These properties are in good agreement with a proposed acceleration model.