Showing papers on "Oblique shock published in 1983"

Evolution of ion distributions across the nearly perpendicular bow shock: Specularly and non‐specularly reflected‐gyrating ions

Abstract: Data from ISEE 1 and 2 spacecraft were used to study the evolution of the ion distributions in the perpendicular terrestrial bow shock. The plasma data were taken during passage of the spacecraft downstream of and through the shock. Solar wind ions had velocities ranging from Mach 2-12.4, and reflected ions featured a relative density of 1-3 percent of the solar wind density at Mach 2 to 15-25 percent at Mach 8-12. Computer simulations have indicated that the ions provide essential dissipation at the shock and gyrate about the magnetic field lines in the plasma rest frame at a speed twice that of the normal incident solar wind flow. The ion density decreases by up to two orders of magnitude at the forward end of the foot of the shock profile, suggesting that the ions are reflected by the shock specularly, and may enhance downstream ion thermalization.

Unsteadiness of the Separation Shock Wave Structure in a Supersonic Compression Ramp Flowfield

Abstract: Wall pressure fluctuations have been measured in a two-dimensional separated compression ramp-induced shock wave turbulent boundary-layer interaction The tests were made at a nominal freestream Mach number of 3 and at Reynolds numbers based on boundary-layer thickness of 78 X 10 and 14x 10 The wall temperature condition was approximately adiabatic Large-amplitude pressure fluctuations exist throughout the interaction, particularly near separation and reattachment In the upstream region of the flowfield, the unsteadiness of the separation shock wave structure generates an intermittent wall pressure signal Mean wall pressures in this region result from the superposition of the relatively low-frequency, large-amplitude, shock wave-induced fluctuations on the pressure signal of the undisturbed boundary layer This behavior is qualitatively similar to that observed in three-dimensional blunt fin-induced flows In these two flowfields, the length scale of the shock motion is a significant fraction of the distance from the interaction start to separation

Ions upstream of the Earth's bow shock: A theoretical comparison of alternative source populations

Abstract: The trajectories of ions reflected or leaked upstream from the earth's bow shock and subject solely to the Lorentz force in a steady interplanetary magnetic field B and the V x B electric field are studied theoretically. Expressions are obtained for the guiding center motion and gyromotion in a frame (the Hoffman-Teller frame) moving parallel to the shock surface with sufficient speed to transform the incident solar wind velocity into motion entirely along the interplanetary magnetic field. Equations are derived which transform these motions back to the observer's frame. The predicted upstream motions for four different source models for upstream ions are compared using these expressions: magnetic moment-conserving reflection of solar wind ions, specular reflection of solar wind ions, magnetic moment-conserving leakage of magnetosheath ions, and leakage of magnetosheath ions parallel to the shock normal.

The response of normal shocks in diffusers

Abstract: The frequency response of a normal shock in a diverging channel is calculated for application to problems of pressure oscillations in ramjet engines. Two limits of a linearized analysis arc discussed: one represents isentropic flow on both sides of a shock wave; the other may be a crude appr'l'I;imation to the influence of flow separation induced hy the wave. Numerical results arc given, and the influences of the shock wave on oscillations in the engine are discus,ed.

Backstreaming ions from oblique earth bow shocks

Abstract: One-dimensional, hybrid (particle ions, fluid electrons) numerical simulations of oblique shock structure are used to analyze the mechanism by which solar wind ions can be reflected off the earth's bow shock front and escape upstream. It is shown that no backstreaming ions are produced in the simulation over 50-90 degrees of theta(nB), the angle between the interplanetary magnetic field and the shock normal. Backstreaming ions are emitted for theta(nB) of 45 degrees or less, with characteristics in reasonable agreement with those of observed reflected ion streams. The simulated shock structure becomes rather turbulent as theta(nB) decreases from 45 to 30 degrees. Analysis of the backstreaming ion trajectories shows that all backstreaming ions are originally specularly reflected. The oblique shock structure and effects such as whistler formation and ion heating are discussed.

Collisionless dissipation processes in quasi‐parallel shocks

Abstract: The evolution of collisionless, quasi-parallel shocks (the angle between the shock normal and the upstream magnetic field being less than 45 deg) is examined using two dimensional particle simulations. Reflected ions upstream from the shock are observed with average guiding center velocity and gyrational energy which agree well with the prediction of simple specular reflection. Strong ion heating through the shock ramp is apparently caused by large amplitude whistler turbulence. A flux of suprathermal electrons is also the magnetic field direction. Much stronger ion heating occurs in the shock than electron heating. The relevance of this work to the earth's bow shock is discussed.

On the structure of the magnetic slow switch‐off shock

Abstract: A particle code is used to simulate the evolution of a magnetic slow shock. The initial state is two uniform plasmas related by the Rankine-Hugoniot jump conditions and separated by a transition layer a few ion gyroradii thick. The code follows the evolution of the system in time. Two principal features of the results are the upstream escape of the hot shocked plasma and a damped, left-handed circularly polarized wave on the trailing edge of the shock. Analysis of the trailing wave train indicates that ion cyclotron interaction is important in heating the plasma. The upstream escape of particles results in a temporal broadening of the shock profile. The implications of the simulation results in magnetic merging processes in the neighborhood of an x type neutral point are described.

Impact of a liquid mass on a perfectly plastic solid

Abstract: The use of steady, normal and oblique shock configurations is explored in calculating the pressure and deformation produced by the impact of a liquid mass on a plane solid surface. Since pressures generated are very large, the change in bulk modulus of the liquid (water) is accounted for by using an equation of state following Field, Lesser & Davies (1979). The impact of a plane-ended liquid mass is analysed using a normal shock for the cases of a rigid surface and a perfectly plastic surface. For the former, it is found that pressures somewhat in excess of the ‘water-hammer’ pressure of linear acoustic theory are predicted, and for the latter there is a critical impact velocity below which no deformation occurs. Above this velocity the surface deforms at a constant rate, producing a pit with maximum depth at the centre. If the liquid mass is wedge-shaped then an oblique shock is formed, which is attached to the contact point provided that the impact Mach number is large enough, as originally shown by Heymann (1969). Pressure and deformation velocity can again be calculated for the cases of rigid and perfectly plastic surfaces respectively. For a rigid surface it is confirmed that pressures considerably in excess of the plane-ended case are produced at shock detachment. For the plastic surface, it is found that there is no critical impact velocity and deformation can occur at any velocity as shock detachment is approached. For a cylindrical liquid mass with a conical tip, the pit produced again has maximum depth at the centre, but with a considerably increased value. The possible use of these models for pitting caused by microjets associated with cavitation bubbles and by impact of liquid drops is discussed.

Shock-associated noise in supersonic jets

Abstract: This paper examines the fundamental mechanism of broadband shock noise in an improperly expanded supersonic jet. The study includes circular convergent and convergent-divergent nozzles. The main source of shock noise is determined to be the transient interaction between the shock front and the convected vorticity within the jet plume. The discussion of the noise generation mechanism is based on detailed numerical analysis, theoretical modeling, refined measurements of the jet mean flow, shock-cell structure, turbulence, and noise. Results in this study provide a broad-based generalization for the Harper-Bourne and Fisher analysis and prediction method.

An update on non-stationary oblique shock-wave reflections: actual isopycnics and numerical experiments

Abstract: Nonstationary oblique shock-wave reflections over compressive wedges in air and argon were investigated using infinite-fringe interferometric techniques. These allowed direct, continuous and accurate observations of the isopycnics (lines of constant density) of the flow field. The initial pressures for these experiments were made as high as possible (15 to 250 torr) in order to increase the number of isopycnics and to enhance their details and distribution along the wedge surface over a shock-Mach-number range 2.0 < Ms [les ] 8.7. Included in the study were two cases of regular reflection (RR) and one of each single Mach reflection (SMR), complex Mach reflection (CMR) and double-Mach reflection (DMR) for air, and one RR, SMR, CMR and DMR for argon. These particular cases, which we investigated previously in N2 and Ar using a finite-fringe technique, have been used by computational fluid dynamicists to check their finite-difference results against our experimental data. It will be shown that the isopycnic structure previously reported by us differs in detail, in most cases, from that of the present study. The major difference arises from the fact that it was only possible previously to obtain discrete points on isopycnics and along the wedge surface. Consequently, the results obtained before were not as accurate. Comparisons were made of actual wall-density distributions with numerical simulations of the density contours of the various flows obtained by a number of authors. Each numerical method displays its advantages and disadvantages in describing the details of the flow fields. The present experimental results for air are new. They are of great interest from a practical viewpoint. The experiments in argon were redone to provide better data for a gas free from real-gas effects in the range of initial conditions considered, in order to simplify the computations in the numerical simulations. Although the recent numerical simulations are better than those reported previously, additional efforts are required to improve the predictions of the shape, location and values of the isopycnics and other flow isolines in the various regions and along the wall, and to render the predictions free of computer ‘noise’. It is worth noting that real-gas effects did not play any significant role in determining the various wave systems in RR, SMR, CMR and DMR; a different claim was made in our previous work. Relaxation of nitrogen in air can be seen however, at the highest shock Mach numbers (Ms = 7.19 and 8.70), with relaxation lengths in good agreement with accepted predictions.

Multiple spacecraft observations of interplanetary shocks: Characteristics of the upstream ULF turbulence

Abstract: All interplanetary shocks observed by ISEE-3 and either ISEE-1 or ISEE-2 or both in 1978 and 1979 are examined for evidence of upstream waves In order to characterize the properties of these shocks it is necessary to determine accurate shock normals An overdetermined set of equations were inverted to obtain shock normals, velocities and error estimates for all these shocks Tests of the method indicate it is quite reliable Using these normals the Mach number and angle were between the interplanetary magnetic field and the shock normal for each shock The upstream waves were separated into two classes: whistler mode precursors which occur at low Mach numbers and upstream turbulence whose amplitude at Mach numbers greater than 15 is controlled by the angle of the field to the shock normal The former waves are right hand circularly polarized and quite monochromatic The latter waves are more linearly polarized and have a broadband featureless spectrum

Lower hybrid drift instability with temperature gradient in a perpendicular shock wave

Abstract: Finite beta effects and an electron temperature gradient are included in the present study of the perpendicular bow shock geometry's lower hybrid instability, where the flute mode that is stable at the shock for constant electron temperature is destabilized in the case of a sufficiently great temperature gradient. Numerical solutions are given for cases in which the ion distribution is either drifting Maxwellian or consists of two Maxwellians, to represent the effect of reflected ions at the shock. A discussion is presented of the implications of results obtained for ion and electron heating and electron acceleration at the bow shock.

Shock dynamics in non-uniform media

Abstract: The theory of shock dynamics in two dimensions is reformulated to treat shock propagation in a non-uniform medium. The analysis yields a system of hyperbolic equations with source terms representing the generation of disturbances on the shock wave as it propagates into the fluid non-uniformities. The theory is applied to problems involving the refraction of a plane shock wave at a free plane gaseous interface. The ‘slow–fast’ interface is investigated in detail, while the ‘fast–slow’ interface is treated only briefly. Intrinsic to the theory is a relationship analogous to Snell's law of refraction at an interface. The theory predicts both regular and irregular (Mach) refraction, and a criterion is developed for the transition from one to the other. Quantitative results for several different shock strengths, angles of incidence and sound-speed ratios are presented. An analogy between shock refraction and the motion of a force field in unsteady one-dimensional gasdynamics is pointed out. Also discussed is the limiting case for a shock front to be continuous at the interface. Comparison of results is made with existing experimental data, with transition calculations based on three-shock theory, and with the simple case of normal interaction.

Field aligned ion beams upstream of the Earth's bow shock: evidence for a magnetosheath source

Abstract: High time resolution ISEE-1 and -2 observations of upstream field-aligned ion beams at several crossings of the earth's bow shock indicate that some beams are due to high energy magnetosheath particles leaking through the shock into the upstream region. The distribution immediately downstream of these oblique shocks consists of a 'core' of directly transmitted, slightly heated ions, plus a crescent-shaped, high-velocity distribution, centered roughly on the magnetic field in the direction toward the upstream region, with a fairly well defined low velocity cutoff.

THE VELOCITY OF SOUND BEHIND STRONG SHOCK WAVES IN 2024 Al

Abstract: Rarefaction waves were produced by impacting a target with a thin plate. An optical technique was used to determine where the rarefaction from the back surface of the impactor overtook the shock wave induced in a step wedge target. Bromoform was placed on the front surface. When the shock reached the liquid it radiated steadily until the rarefaction from the impactor overtakes it. The times when this occurred were used to determine where the rarefaction just overtook the shock in the target, and thus the sound velocity. The leading edge of this rarefaction wave travels at longitudinal sound velocity in solids. This velocity increases smoothly with pressure until shock heating causes the material to melt. The data indicate that melting on the Hugoniot of 2024 Al begins at about 125 GPa and is completed at 150 GPa.

Stability of Shock Waves Attached to Wedges and Cones

Abstract: A numerical study of a reduced set of the Euler equations shows that both weak and strong attached shock waves are stable configurations depending on the boundary conditions imposed. The results obtained are in good agreement with experimental observations and with the minimum entropy principle. A heuristic ex- planation of the behavior observed is given in terms of quasistatic considerations. OR flow over a wedge or cone, whose deflection angle is less than the angle associated with shock detachment for the incoming supersonic flow, it is a well-known fact that the steady-state Euler equations admit two different solutions. Each solution is distinguished by the strength of the attached oblique shock. Thus a solution is labeled strong or weak if the shock-wave inclination is, respectively, greater than or less than the shock-wave inclination at detachment. For the strong shock solution, the flow is always subsonic downstream of the shock; for the weak shock solution, the flow is supersonic downstream of the shock, except for a small range of deflection angles in the neighborhood of the detachment angle where the weak shock is followed by subsonic flow. This small region will be ignored in the present work. The existence of multiple solutions has attracted considerable theoretical scrutiny, which has mainly succeeded in obscuring the problem. Indeed, our understanding of this problem has changed little since 1948, when Courant and Friedrichs1 wrote .. .The question arises which of the two actually occurs. It has frequently been stated that the strong one is unstable and that, therefore, only the weak one could occur. A convincing proof of this instability has apparently never been given. Quite aside from the question of stability, the problem of determining which of the possible shocks occurs cannot be formulated and an- swered without taking the boundary conditions at infinity into account. The confusion has come about because the question posed by Courant and Friedrichs and every succeeding investigator has not been the proper question to ask. The question should not be which solution actually occurs, since we have ex- perimental evidence2 that both the weak and the strong solutions do occur, but under what conditions do one or the other solutions occur. The answer to this latter question obviously depends on the boundary conditions, as already indicated by Courant and Friedrichs. Moreover, since the nature of steady-state solution is elliptic for the strong shock and hyperbolic for the weak shock, we should suspect that each problem is governed by a different set of boundary conditions. The purpose of this paper is, therefore, to study the stability of the weak and strong solutions with boundary conditions which are appropriate to each case under in- vestigation.

Injection slot location for boundary-layer control in shock-induced separation

Abstract: An experimental investigation of the effect of tangential air injection in controlling shock-induced turbulent boundary-layer separation is presented, in particular when the injection slot is located inside of what would otherwise have been the recirculating zone in a separated flow. The experiments were carried out at a freestream Mach number of 2.5 in the separated flow induced by a compression corner with a 20 ° angle. The observations made were wall static pressures, pitot profiles, and schlieren visualizations of the flow. The results show that the present location for injection is more effective in suppressing boundary-layer separation than the more conventional one, where the slot is located upstream of where separation would occur in the absence of injection.

Shock reflection transition in three-dimensional steady flow about interfering bodies

Abstract: A numerical study of the three-dimensional flowfield produced by the interaction of an axisymmetric shock and a planar wall is presented. These types of flowfields are encountered when a store is in close proximity to an aircraft. The flow is assumed inviscid and everywhere supersonic. This work is based upon the numerical solution of Euler's equations with all shock waves fit as discontinuiti es. The axisymmetric shock reflects from the plate first in a regular fashion, but, ultimately, this reflection becomes a Mach reflection. The transition from regular to Mach reflection and the subsequent development of a cross-sectional Mach disk is computed explicitly and studied in detail. The computational procedure is outlined and numerical results are compared with experimental data.

Experimental investigation of a two-dimensional shock-turbulent boundary layer interaction with bleed

Abstract: The two-dimensional interaction of an oblique shock wave with a turbulent boundary layer that included the effect of bleed was examined experimentally using a shock generator mounted across a supersonic wind tunnel The studies were performed at Mach numbers 2.5 and 2.0 and unit Reynolds number of approximately 2.0 x 10 to the 7th/meter. The study includes surface oil flow visualization, wall static pressure distributions and boundary layer pitot pressure profiles. In addition, the variation of the local bleed rates were measured. The results show the effect of the bleed on the boundary layer as well as the effect of the flow conditions on the local bleed rate.

Mechanism of Pseudo-shock Wave in Supersonic Jet

Abstract: Concerning the overexpanded supersonic jet, interaction between the normal shock wave immediately downstream of the D'Laval nozzle exit and the shear layer of the jet boundary was investigated experimentally. The following were demonstrated. (1) The normal shock wave changes into a pseudo-shock wave immediately after its occurrence in the flow, (2) the pseudo-shock wave is several jet diameters in length but somewhat shorter than the pseudo-shock wave in duct flow, (3) its pressure ratio is extremely small compared with that of the normal shock wave and nearly proportional to the Mach number immediately upstream of the pseudo-shockwave.

Computation of nonlinear supersonic potential flow over three-dimensional surfaces

Abstract: A fully implicit three dimensional marching technique is presented for the computation of inviscid supersonic flows. The nonconservative full potential equation is solved on spherical cross flow planes using standard transonic SLOR techniques. The three dimensional bow shock is fitted as a boundary with isentropic jump conditions and embedded shocks are captured. Applications of these techniques are presented for three dimensional bodies, wings, and wing-body configurations and the computed solutions are compared to experimental pressure data. Zero lift wave drag calculations are also presented and compared with measurements to evaluate the accuracy of the present techniques.

Numerical solution to the glancing sidewall oblique shock wave/turbulent boundary layer interaction in three dimension

Abstract: A supersonic three-dimensional viscous forward-marching computer design code called PEPSIS is used to obtain a numerical solution of the three-dimensional problem of the interaction of a glancing sidewall oblique shock wave and a turbulent boundary layer. Very good results are obtained for a test case that was run to investigate the use of the wall-function boundary-condition approximation for a highly complex three-dimensional shock-boundary layer interaction. Two additional test cases (coarse mesh and medium mesh) are run to examine the question of near-wall resolution when no-slip boundary conditions are applied. A comparison with experimental data shows that the PEPSIS code gives excellent results in general and is practical for three-dimensional supersonic inlet calculations.

Shock diffraction in channels with 90° bends

Abstract: A study has been made of how initially planar shocks in air propagate around 90° bends in channels of nearly rectangular cross-section. In shallow bends for which the radius of curvature R is much greater than the radius r of the channel, the shock recovers from a highly curved profile at the start of the bend to regain planarity towards the end of the bend. This occurs on account of the acceleration of the triple point across the channel following its interaction with the expansion waves generated at the convex wall. In sharp bends the shock profiles retain their pronounced curvature for some distance downstream of the bend.At the start of a shallow bend (R/r ≈ 6) the shock at the concave wall, initial Mach number M0, accelerates to Mw = 1.15M0 and remains at this value until towards the end of the bend it begins to attenuate. At the convex wall, shocks of M0 > 1.7 attenuate to Mw = 0.7M0 and propagate at this value for some distance around the bend. In the early stages of a sharper bend (R/r ≈ 3) the shock at the concave wall strengthens to Mw = 1.3M0, remaining at this value for some distance downstream of the bend. At the convex wall the shock decelerates to 0.6M0.Whitham's (1974) ray theory is shown to predict with reasonable accuracy the Mach numbers of the wall shocks at both surfaces for both bends tested and the range of incident shock velocities used, 1.2 2 over the initial stages of the bend.

Second-order effects related to a model for a parallel shock

Abstract: Second-order effects are calculated for a low-frequency electromagnetic instability due to an ion beam in a plasma. This instability is a characteristic of a parallel shock model that includes an ion reflecting electrostatic subshock. The analysis is similar to that done by S. P. Gary, but a counterstreaming configuration is chosen that is homogeneous in time and that has specially growing modes. Among other effects, energy is transferred from the incoming main plasma ions to the beam ions. Electron pressure effects are calculated and are small for low frequencies. The application of this model to the earth's bow shock is discussed.

Mach reflection flowfields associated with strong shocks

Abstract: : The Mach reflection associated with the passage of a shock wave over a wedge is treated in the limit of an ideal gas and a strong shock. In this limit, flow properties are functions only of wedge angle theta and the ratio of specific heats gamma. Numerical results are presented for gamma = 9/7, 7/5, and 5/3. Wedge angles are noted at which the transition from regular to double-Mach, to complex-Mach, and to simple-Mach reflection occurs. Characteristic velocities in the recirculation region associated with Mach reflection are estimated. Local surface pressure maxima, at the upstream and downstream edge of the recirculation region, are also estimated. The scale of the recirculation region increases with decrease in gamma, in accord with experimental observations. The wedge solution is used on a piecewise basis to estimate height-of-burst (HOB) flow fields. Normalized results are presented for HOB triple-point trajectory and surface pressure variation with range. The present results provide a convenient characterization of Mach reflection flow fields associated with both wedge and HOB flows. Validation of the HOB solution, however, is needed.

Turbulence measurements in two shock-wave/shear-layer interactions

Abstract: Measurements of the longitudinal component of the mass-flow fluctuations have been made in an 8° compression corner flow and a reattaching shear layer at a Mach number of approximately 2.9 and unit Reynolds number of about 7 × 107 m−1. The data includes turbulence intensities and probability density distributions. Significant turbulence amplification occurs in both interactions. A qualitative explanation in terms of direct shock effects, extra strain rates, and their relative contribution, is suggested.

On the propagation of weak and moderately strong, curved shock waves

Abstract: In this paper we concern ourselves with the theoretical description of curved converging shock waves, where nonlinear interaction effects, between the shock fronts and the flow behind them, and refraction effects are equally important. In a non-viscous, isoenergetic and isentropic flow the problem can be described by a nonlinear wave equation for the pressure field. This equation then admits an analytical solution with the help of the method of strained coordinates provided that the nonlinear terms contain only derivatives with respect to two independent variables. This restrictive condition is approximately fulfilled if the incoming wave is only slightly curved.Replacing in the solution the strained coordinates – which themselves depend on the solution – by physical coordinates, we get an accurate description of the transition from the shock pattern obtained by the geometric-acoustics approach (very weak shocks) to the pattern determined by Whitham's shock dynamics (strong shocks). Furthermore, the solution describes the complete flow field and agrees very favourably with experimental data by Sturtevant & Kulkarny.