Showing papers on "Oblique shock published in 1974"

30- to 100-keV protons upstream from the earth's bow shock

Abstract: Protons of 30 to 100 keV are found upstream from the bow shock whenever interplanetary magnetic fields connect the spacecraft and bow shock. The protons do not appear upstream of a boundary determined by the solar wind speed (the speed at which the interplanetary field is being convected) and an effective upstreaming velocity of 2.5 to 3 times the solar wind speed along the field lines. It is believed that (1) the lower-energy (3-4 keV) protons accelerated and reflected by the bow shock and (2) the Alfven waves observed upstream are in some way responsible for the origin of the 30- to 100-keV protons in very large regions upstream from the bow shock.

Effects of interplanetary shock waves on energetic charged particles

Abstract: Experimental data on the influence of interplanetary perpendicular and oblique shock waves on the ambient energetic protons are presented along with a theoretical analysis of the acceleration of particles in almost perpendicular shock waves. It was found that low-energy protons can be accelerated in perpendicular shock waves by repeated crossings of the shock front up to a maximum energy given by the product of their initial energy times the ratio of the magnetic fields. High-energy protons need to stay at the shock front for longer times than low-energy protons in order to reach the same relative energy gain. In the theoretical study of proton acceleration at almost perpendicular shock waves, it was found that protons reflected at shock waves with the angle between the upstream magnetic field and the shock normal greater than about 80 deg achieve large energy gains at the shock front. The larger this angle, the higher the energy gain. However, the reflection and energization of protons at these shock waves is not 'instantaneous', neither is it a one-step process: it is performed through repeated crossings of the shock front.

Motions of the bow shock induced by interplanetary disturbances

Abstract: Motivated by recent observations by Greenstadt and co-workers of very high bow shock ‘normal’ velocities, we investigate the reaction of the shock to changes in solar wind conditions for different bow shock locations. At low quiescent Mach numbers the shock is found to be much more sensitive to a given slow perturbation than it is at the normally occurring high Mach numbers. Thus under these circumstances even a smooth wavelike disturbance can cause high bow shock velocities. For high Mach numbers only impulsive perturbations like tangential discontinuities or occasional interplanetary shocks can induce high bow shock velocities. The former interaction is discussed in detail. Large induced shock velocities are possible, although very strong density discontinuities are needed to produce recently estimated average shock speeds of about 85 km/sec. Thus such high average shock velocities are difficult to understand. In this context also a qualitative discussion of the importance of oscillatory modes of the magnetosphere shock system is presented. The present work suggests average bow shock velocities of the order of 10 km/sec or somewhat larger. Much higher shock speeds should be the exception rather than the rule.

Oscillation Phenomena of Pseudo-Shock Waves

Abstract: In the previous paper, we presented the diffusion model of pseudo-shock waves, by which the time-mean static pressure distributions in pseudo-shocks could be explained. In the actual flow, however, the pseudo-shock wave is not steady, but oscillates about a mean position and causes the fluctuations of the local static pressures. In this paper the oscillation phenomena of pseudo-shocks in a straight pipe were experimentally investigated and the causes and the frequencies of oscillations were discussed. As the results, it was found that the oscillation of the pseudo-shock became stronger with the increasing Mach number and the maximum wall static pressure fluctuation induced by the oscillation amounted to about 60 per cent of the difference of static pressures before and behind the shock. Moreover, it was showed that this oscillating phenomena could be explained by the interaction of the shock with the small disturbances existing in the supersonic flow upstream the shock.

Mach Disk from Underexpanded Axisymmetric Nozzle Flow

Abstract: The flowfield associated with the underexpanded axisymmetric nozzle freejet flow including the appearance of a Mach disk has been studied. It is shown that the location and size of the Mach disk are governed by the appearance of a triple-point shock configuration and the condition that the central core flow will reach a state of 'choking at a throat'. It is recognized that coalescence of waves requires special attention and the reflected wave, as well as the vorticity generated from these wave interactions, have to be taken accurately into account. The theoretical results obtained agreed well with the experimental data.

Shapes of strong shock fronts in an inhomogeneous solar wind

Abstract: The shapes expected for solar-flare-produced strong shock fronts in the solar wind have been calculated, large-scale variations in the ambient medium being taken into account. It has been shown that for reasonable ambient solar wind conditions the mean and the standard deviation of the east-west shock normal angle are in agreement with experimental observations including shocks of all strengths. The results further suggest that near a high-speed stream it is difficult to distinguish between corotating shocks and flare-associated shocks on the basis of the shock normal alone. Although the calculated shapes are outside the range of validity of the linear approximation, these results indicate that the variations in the ambient solar wind may account for large deviations of shock normals from the radial direction.

The Interaction of a Reflected Shock Wave with the Boundary Layer in a Shock Tube

Abstract: The region behind the reflected shock in a shock tube is used as a reservoir of gas for a hypersonic tunnel and in chemical kinetics studies. In order to clarify the gas properties in this region, the interaction phenomenon of the reflected shock with the boundary layer must be made clear. Although many studies have been carried out about this interaction, they are not comprehensive. In this paper, this interaction was observed optically by schlieren method, and the growth rate of the bifurcation and the velocity of the reflected shock were clarified. Furhter, based on the present and previous experimental data, and modifying the previous flow models, a new flow model was presented on the interaction of the reflected shock with the boundary layer. The growth rate of the bifurcation and the velocity of the reflected shock calculated by this model are in fair by good agreement with experimental results.

Self-similar homothermal flow of self-gravitating gas behind shock wave

Abstract: Self-similar homothermal flows of self-gravitating gas behind the spherical shock wave propagating in a nonuniform atmosphere at rest are investigated. Using a similarity variable the solution corresponding to infinite star (ρ 1 ∝ r - w ) has been constructed. Both numerical and particular analytical solutions are obtained. These solutions are compared with the corresponding solutions of the adiabatic flow.

A discussion of interplanetary postshock flows with two examples

Abstract: Plasma and magnetometer observations of two types of flare-associated shock flows are described and compared with present models. One type represents a class of flows in which the shock is followed by a stream and separated from it by a region in which density, temperature, and speed decrease monotonically. Neither the blast wave model nor the two-stage model, in which the stream and the shock are attributed to the same flare, can quantitatively describe this class. The other type is characterized by a complex region between the shock and the following stream, which has many discontinuities and fluctuations but in which there is no increase in helium concentration. This class of event is not describable in terms of the conventional pictures presented, for example, by Hundhausen (1972). These two types of flow can be distinguished by using ground magnetograms, since the first type shows no sudden impulses following the shock, whereas the second type shows many.

Non-equilibrium dissociating nitrogen flow over a wedge

Abstract: Experimental results for dissociating nitrogen flow over a wedge, obtained in a free-piston shock tunnel, are described. Interferograms of the flow show clearly the curvature of the shock wave and the rise in fringe shift after the shock associated with the dissociation. It is shown that the shock curvature at the tip of the wedge can be used to calculate the initial dissociation rate and that it is a more sensitive indication of the rate than can be obtained from fringe shift measurements under the prevailing experimental conditions. Because the freestream dissociation fraction can be adjusted in the shock tunnel, the dependence on atomic nitrogen concentration of the dissociation rate can be determined by the shock curvature method. A detailed calculation of the flow field by an inverse method, starting from the measured shock shape, shows good agreement with experiments.

Transmission of singularities through a shock wave and the sound generation

Abstract: The interaction of a plane shock wave of finite strength with a vortex line, point vortex, doublet or quadrupole of weak strength is studied Based upon the physical condition that a free vortex line cannot support a pressure difference, rules are established which define the change of the linear intensity of the segment of the vortex line after its passage through the shock The rules for point vortex, doublet, and quadrupole are then established as limiting cases These rules can be useful for the construction of the solution of the entire flow field and for its physical interpretation However, the solution can be obtained directly by the technique developed for shock diffraction problems Explicit solutions and the associated sound generation are obtained for the passage of a point vortex through the shock wave

Super‐Alfvénic flow and collision free shock wave in a plasma wind tunnel

Abstract: A super‐Alfvenic and supersonic flow in a plasma wind tunnel were studied experimentally The wind tunnel was constructed for the studies of the magnetohydrodynamic shock waves and wakes, and has features such as quasisteady flow and low fluctuation level The Alfven Mach number MA and ion acoustic Mach number M covered in the present experiment are MA = 1−4 and M = 2−6 A standing shock wave was found downstream of the magnetic‐nozzle exit The shock wave is collision free and the normal of the wavefront is parallel to the magnetic field Macroscopic features of the shock wave were discussed with reference to the theoretical predictions of the magnetohydrodynamic and collision‐free shock waves

On the shock-on-shock interaction problem

Abstract: The unsteady, inviscid flowfield that results when a supersonic vehicle strikes a planar oblique shock wave, though difficult to simulate experimentally, is quite easy to model and compute numerically. The complicated flowfield, which contains multiple shock wave interactions, is determined using a second-order, shock-capturing, finite-difference approach which solves the time-dependent Euler equations under a self-similar transformation. A series of numerical results for a simple two-dimensional wedge is presented which describes the entire disturbed region, including the wave structure, and shows good agreement with the available two- and three-dimensional experimental data.-

Some Extensions of Thin-Shock-Layer Theory

Abstract: In the usual form of thin-shock-layer theory it is assumed that the flow about a lifting body can be expanded in terms of the inverse density ratio across a basic oblique shock wave lying in the plane of the leading edges of the body. In this paper it is shown that more accurate results can be obtained by moving the basic shock closer to the calculated shock wave below the body. The results obtained show why the original form of thin-shock-layer theory often gave good agreement with experiment in conditions which appeared to be outside the range of validity of the theory.

Three dimensional flows around airfoils with shocks

Abstract: The present work describes a mathematical model and numerical scheme for the computer-aided calculation of two- and three-dimensional transonic flow over an isolated yawed wing with oblique shock waves and a trailing vortex sheet The flow is modeled by the potential equation for irrotational flow which is hyperbolic at supersonic points and elliptic at subsonic points A coordinate-invariant difference scheme is used in which retarded difference formulas are constructed to conform with the local flow direction The resulting 'rotated' difference scheme allows complete flexibility in the choice of a coordinate system Shock waves are located automatically in the form of compression bands spread over a few mesh widths The scheme has proven to be stable and convergent throughout the transonic range Calculations have been performed for Mach number up to 12 and yaw angles up to 60 deg, the likely operating range of a yawed-wing transport designed to fly at supersonic speeds Calculations becomes less accurate towards upper end of range, because the difference scheme is first-order accurate in the supersonic range

Hypersonic flows generated by parabolic and paraboloidal shock waves

Abstract: A computer algorithm has been developed to determine the blunt-body flowfields supporting symmetric parabolic and paraboloidal shock waves at infinite free-stream Mach number. Solutions are expressed in an analytic form as high-order power series, in the coordinate normal to the shock, whose coefficients can be determined exactly. Analytic continuation is provided by the use of Pade approximations. Test cases provide solutions of very high accuracy. In the axisymmetric case for gamma equals 715 the solution has been found far downstream, where it agrees with the modified blast-wave results. For plane flow, on the other hand, a limit line appears within the shock layer, a short distance past the sonic line, suggesting the presence of an imbedded shock. Local solutions in the downstream limit are discussed.

Particle Concentrations in High Mach Number, Two-Phase Flows

Abstract: : An experimental and theoretical study of the behavior of solid particles in high speed flow systems has been conducted. A new drag coefficient correlation which allows greater accuracy in the prediction of particle trajectories over a wide range of slip Mach number and slip Reynolds number was formulated. A variety of basic two-phase flow situations, i.e., uniform flow, Prandtl-Meyer expansion, and oblique shock, was investigated by varying the initial particle velocity and particle radius. In addition, the effect of different gases and different particles on the two-phase flow characteristics was investigated, and significant differences were noted. The exploratory experimental studies conducted in this investigation substantiate that a test facility suitable for the study of particle trajectories has been developed and that accurate particle concentration profiles can be obtained with the laser scattering technique.

Supersonic Flow of a Dusty Gas over a Slender Wedge

Abstract: Effects of solid or liquid particles contained in a gas are investigated for supersonic flow over a slender wedge by a perturbation method. The frozen shock wave, attached to the leading edge, decays with distance from the surface and bends backward. Various manners of the change in flow variables of the gas, depending on the properties of the mixture and the Mach number, in the relaxation zone behind the frozen shock wave are illustrated by examples. The development of the dispersed shock wave far from the wedge is studied too by the method of matched expansions.

Behaviour of the acceleration and shock waves in materials with internal state variables

Abstract: The explicit expressions for the change in the amplitudes of one-dimensional acceleration and shock waves propagating through arbitrary homogeneous materials described by the strain and internal state variables/parameters/are derived. The existence of a critical amplitude β for the acceleration wave and a critical strain gradient λ for the shock wave is established. For an infinitesimal shock wave the general form of the solution of the governing differential equation is furnished. The differential equations for the amplitudes of these two kind of waves are applied to an elastic-viscoplastic material.

On the local time dependence of the bow shock wave structure

Abstract: In the first 6 months after its launch, Ogo 3 crossed the earth's bow shock over 500 times. From this group, a set of 494 shock crossings were chosen for analysis. These crossings, as they were recorded by the UCLA/JPL search coil magnetometer, were scanned and classified according to the nature of the plasma waves detected near the shock. More than 85% of the shocks detected fell into a single category showing the predominance of two independent wave trains near the shock, the higher frequency appearing upstream and the lower downstream. The other 15%, which constitute an upper limit, appear to be composed of shocks dominated by a single wave pattern and of chaotic shocks showing no orderly progression of wave frequencies as the shock was penetrated. This division of wave pattern was found to occur at all local times, that is, in all regions where the satellite penetrated the shock.

Flowfield Analysis for Successive Oblique Shock Wave-Turbulent Boundary-Layer Interactions

Abstract: A computation procedure is described for predicting the flowfields which develop when successive interactions between oblique shock waves and a turbulent boundary layer occur. Such interactions may occur, for example, in engine inlets for supersonic aircraft. Computations are carried out for axisymmetric internal flows at M 3.82 and 2.82. The effect of boundary layer bleed is considered for the M 2.82 flow. A control volume analysis is used to predict changes in the flow field across the interactions. Two bleed flow models have been considered. A turbulent boundary layer program is used to compute changes in the boundary layer between the interactions. The results given are for flows with two shock wave interactions and for bleed at the second interaction site. In principle the method described may be extended to account for additional interactions. The predicted results are compared with measured results and are shown to be in good agreement when the bleed flow rate is low (on the order of 3% of the boundary layer mass flow), or when there is no bleed. As the bleed flow rate is increased, differences between the predicted and measured results become larger. Shortcomings of the bleed flow models at higher bleed flow rates are discussed.

Motion of an explosive-induced plane shock wave

Abstract: A plane, unsupported, Chapman-Jouguet detonation in a condensed explosive drives a decelerating shock into a semi-infinite inert of lower shock impedance. A previously reported exact solution for a portion of this one-dimensional time-dependent problem is extended to the entire flow field, and some numerical results are given. The solution has the form of a small set of first-order ordinary differential equations for the shock, and a similar set for each particle path.