Showing papers on "Oblique shock published in 1988"

Theory and simulation of collisionless parallel shocks

Abstract: This paper presents a self-consistent theoretical model for collisionless parallel shock structure, based on the hypothesis that shock dissipation and heating can be provided by electromagnetic ion beam-driven instabilities. It is shown that shock formation and plasma heating can result from parallel propagating electromagnetic ion beam-driven instabilities for a wide range of Mach numbers and upstream plasma conditions. The theoretical predictions are compared with recently published observations of quasi-parallel interplanetary shocks. It was found that low Mach number interplanetary shock observations were consistent with the explanation that group-standing waves are providing the dissipation; two high Mach number observations confirmed the theoretically predicted rapid thermalization across the shock.

Computer modeling of test particle acceleration at oblique shocks

Abstract: The present evaluation of the basic techniques and illustrative results of charged particle-modeling numerical codes suitable for particle acceleration at oblique, fast-mode collisionless shocks emphasizes the treatment of ions as test particles, calculating particle dynamics through numerical integration along exact phase-space orbits. Attention is given to the acceleration of particles at planar, infinitessimally thin shocks, as well as to plasma simulations in which low-energy ions are injected and accelerated at quasi-perpendicular shocks with internal structure.

Active current sheets near the Earth's bow shock

Abstract: We present here an investigation of “active current sheets” observed by the AMPTE UK spacecraft near the Earth's bow shock, concentrating on their macroscopic features and geometry. Events selected primarily by flow directions which deviate substantially from the Sun-Earth line show similar characteristics, including their association with an underlying macroscopic current sheet and a hot central region whose flow direction is organized, at least in part, by location relative to the inferred initial intersection point between the current sheet and the bow shock. This region is flanked by “edges” which, according to a Rankine-Hugoniot analysis, are often fast shocks whose orientation is consistent with that expected if a “bulge” on the bow shock convected past the spacecraft. We have found the magnetosheath manifestations of these events which we study in detail. We suggest that these events are the direct result of the disruption and reformation of the bow shock by the passage of an interplanetary current sheet, most probably a tangential discontinuity.

Combustion Processes in Supersonic Flow

Abstract: Three general classes of models that describe the processes occurring in diabatic flow in ducts having supersonic entry conditions are discussed. They are: integral techniques, finite-difference methods, and exact two-dimensional planar flame models formulated on the basis of instantaneous heat release. All three methods rigorously satisfy the conservation equations. The first two methods provide a basis for predicting and analyzing supersonic combustor performance. The careful interpretation and judicious use of experimental observations are crucial for the successful application of these methods. Comparisons of analytical and experimental results are presented, and generalized parametric studies are included. The third method is based on an idealized mixing and combustion model that may not be achievable, but nonetheless serves as a valuable analytical tool for explaining complex processes involving shock waves and heat addition. Results from four types of flow structures are discussed. Nomenclature A = cross-sectional area Af = projected area of inlet Aw = wall area

Shock waves in water

Abstract: The present paper gives a comprehensive examination of equations and charts for shock waves in water. The Tait equation of state is used in the analysis to describe the compressibility of water. The results for an oblique shock wave are presented in the hodograph plane where all possible velocity vectors downstream of the shock wave are seen to lay on a single curve (i.e., shock polar). The equation of the shock polar and the corresponding charts up to upstream Mach number of 3 are given, as well as a more convenient way of adapting the shock polar. The oblique shock‐wave detachment condition and the sonic flow condition downstream of a shock are also presented.

Shock effects in nonlinear chromatography

Abstract: Shocks are discontinuities of a function that appear under certain sets of experimental conditions, such as a shock wave. This ideal concept has to be completed by the more realistic notion of shock layer. In a shock layer the function (pressure for a shock wave, concentration in chromatography) varies very steeply, and all the points in the shock layer (e.g., in a concentration profile) move at almost the same velocity as the shock itself would in the ideal case. In nonlinear, ideal chromatography, the behavior of elution band profiles starts to deviate markedly from what takes place in linear chromatography as soon as a concentration shock forms. Under the influence of the axial diffusions and the mass transfer kinetics the actual band profiles deviate from those predicted by the ideal model. The shocks are replaced by shock layers, but their positions and migration rates are modified only very slightly. The importance of these shocks on the shape and migration rate of the bands is dramatic. Classical concepts such as those of retention time, column efficiency, and resolution must therefore be analyzed within the framework of the shock theory.

Colliding plasma structures: Current sheet and perpendicular shock

Abstract: They authors present results of a one-dimensional simulation of the interaction of a current sheet and a supercritical perpendicular shock in a collisionless plasma. The low-field region of the current sheet passes through the shock, allowing, for a short time, the complete reflection of the incident flow at the transition of the magnetic field to its downstream value. The counterstreaming ion beams relaunch the shock, while the low-field region remains downstream. The plasma in the low field region is unshocked but develops a complex multistream configuration, which in time develops to a more uniform distribution. They discuss the implications of the simulation results for observations within the magnetosheath and of active current sheets upstream of the bow shock.

Evolution of recurrent solar wind structures between 14 AU and the termination shock

Abstract: The solar wind conditions observed from Voyager 2 at approximately 14 AU are extrapolated to the region of the outer heliosphere bounded by the termination shock, using an MHD simulation model. Results from two simulation studies are presented for two sets of nearly recurrent solar wind interaction regions, with initial conditions generated from plasma and magnetic field data observed on March 1984 at 13.8 AU, and on November 1984 at 15.4, respectively. Each simulation describes an idealized recurrent solar wind structure in the supersonic region of the outer heliosphere out to the termination shock far beyond the present reaches of the Pioneer and Voyager spacecraft. It is shown that a collision between the forward shock and the reverse shock occurs approximately every 40 AU. When a forward shock interacts with the termination shock, the latter is weakened and moves outward; the termination shock is strengthened and moves inward when a reverse shock interacts with it.

Diffraction and transmission of a detonation into a bounding explosive layer

Abstract: The results of an experimental and analytical study of the propagation of a gaseous detonation past a bounding explosive layer are presented. Two adjacent 1.6 cm square detonation tubes, separated at the test section by a 50 nm thick cellulose film, were used to observe the interaction which occurs when a normal detonation in the primary gas comes into contact with a bounding explosive mixture. A pulsed argon ion laser and a high speed camera system were used to obtain Schlieren framing photographs of the interacting waves at 2μ sec intervals with an exposure time of 12 ns. Wave velocities and the pressure variation behind the incident detonation and the wave induced in the bounding gas were also determined. Experiments were made using a stoichiometric H 2 −O 2 mixture as the primary explosive, and using H 2 −O 2 mixtures with equivalence ratios ranging from 0.15 to 4.5 for the secondary bounding explosive. At the first instant of contact a bubble or blast wave was observed to propagate into the secondary explosive, and in some cases a micro-explosion in this bubble led to almost instant transition to oblique detonation. Otherwise an oblique shock is induced in the bounding explosive which is reflected from the shock tube wall. As the equivalence ratio of the bounding mixture increases, the reflection of the induced oblique shock changes from a regular to a Mach reflection, and in many cases a detonation is initiated behind the reflected wave. Shock polar analysis was used to compute the details of the interaction at the interface between the primary and secondary explosives. A simplified method for rapid computation of oblique detonation polars was developed for this purposes, and used to compute the conditions behind the induced oblique detonations and shock waves. There was good agreement between computed and measured shock angles; but computed oblique detonation angles, while showing the proper variation with the equivalence ratio, were always lower than the observed values. Calculation of induction lengths indicated that initiation was only possible behind reflected oblique shocks in agreement with experimental observation.

Characteristics of multiple shock wave/turbulent boundary layer interactions in rectangular ducts

Abstract: Multiple shock wave/turbulent boundary-layer interactions in a rectangular duct have been investigated using wall pressure measurements, surface oil flow visualization, spark schlieren photography, and laser Doppler velocimetry. Two undisturbed incoming Mach numbers were considered, Mach 2.45 and Mach 1.6. At Mach 2.45 the shock structure was a neutrally stable pattern of oblique shocks followed by repeated normal shocks with the level of flow confinement having only a small effect in the interaction. A large, three-dimensional separation region was observed. At Mach 1.6 the pattern consisted of a bifurcated normal shock followed by weaker, unbifurcated normal shocks. The boundary layer under the bifurcated shock was incipiently separated. In contrast to the Mach 2.45 case, the lower Mach number interaction was much steadier with the length of the interaction scaling directly with the level of flow confinement.

Numerical and experimental investigation of multiple shock wave/turbulent boundary layer interactions in a rectangular duct

Abstract: : Multiple shock wave/turbulent boundary layer interactions in constant or nearly constant area supersonic duct flows occur in a variety of devices including scramjet inlets, gas ejectors, and supersonic wind tunnels. For sufficiently high duct exit pressures, a multiple shock wave/turbulent boundary layer interaction or shock train may form in the duct and cause a highly nonuniform, and possibly unsteady, flow at the duct exit. In this report, the mean flow characteristics of two shock train interactions, one with an initial Mach number of 2.5 the other at Mach 1.6, are investigated using spark Schlieren photography, surface oil flow visualization, and mean wall pressure measurements. The Mach 2.5 interaction was oblique and asymmetric in nature. A large separation occurs after the first oblique shock. The top and bottom wall boundary layer separation has been investigated, revealing that the shape of the reattachment lines and surface flow patterns for the two separation regions are quite different. This oblique shock flow pattern occurs in a neutrally stable fashion with each type of opposing separation region alternately existing on either the top or bottom wall during the course of a run. A small scale unsteadiness in the shock train location, with movement on the order of a boundary layer thickness, is also observed. In contrast, the Mach 1.6 interaction consists of repeated, symmetric normal shocks. The initial, bifurcated normal shock has a small separation region at its foot while the following weaker shocks do not separate the boundary layer. The number of shocks in the train and the overall length of the interaction increase as the boundary layer thickens in the duct.

Application of finite element and remeshing technique to shock interference on a cylindrical leading edge

Abstract: The problem of planar oblique shock impingement on a cylindrical leading edge in hypersonic flow is modeled using a Galerkin-Runge Kutta finite element method. The method utilizes a four stage Runge-Kutta time stepping scheme to solve the compressible Euler equations. Freestream Mach numbers of 6.5, 8.0 and 16.0 are studied. The computed surface pressure distributions consistently agree well with available experimental data. The peak pressure amplification ranges from 5.45 at M = 6.5 to approximately 17.0 at M = 16.0. Stagnation point heat transfer rate amplifications are calculated from the inviscid solution using the method of Fay and Riddell. The value and wall location of the peak pressure and heat transfer rate amplifications are extremely sensitive to the location of the impinging shock/bow shock intersection point.

Plasma waves in the range of the lower hybrid frequency: ISEE 1 and 2 observations at the Earth's bow shock

Abstract: This report presents a characterization of plasma wave noise in the range of the lower hybrid frequency associated with 65 crossings of earth's bow shock observed by the ISEE 1 and 2 satellites. Wave growth generally becomes detectable at the upstream edge of the shock foot, increases at the upstream edge of the shock ramp, peaks within the ramp, and then quickly decays to steady downstream values. The upstream extent of the noise is on the same order as that of specularly reflected gyrating ions. Similar profiles were observed in subcritical and supercritical shocks, and no special behavior was associated with the first critical Mach number. Spectra in the foot and ramp were similar in shape, although the noise was 1 to 2 orders of magnitude more intense in the shock ramps than in the feet. Electric field intensities are positively correlated with solar wind speed and inversely related to electron beta and Mach number. Magnetic components are positively correlated with Mach number and beta. The results are generally consistent with suggestions that the noise consists of lower hybrid waves driven by reflected gyrating ions in the foot, and by additional instabilities, such as the cross-field current, in the shock ramp.

Instability of the structure of strong oblique MHD cosmic-ray shocks

Abstract: A criterion of the instability of a flow of a thermal plasma and cosmic rays in front of an oblique MHD shock wave with respect to short-wavelength magnetosonic disturbances is derived. The dependence of a cosmic-ray diffusion tensor on a plasma density and a large-scale magnetic field is taken into account. The most unstable disturbances propagate at an angle to the magnetic field if diffusion is strongly anisotropic. In some cases the most strong instability connects with the off-diagonal terms of the diffusion tensor.

Shock wave derivatives

Abstract: A general theory is developed for obtaining the tangential and normal derivatives of thermodynamic and kinematic properties just downstream of a curved, unsteady shock wave. The flow upstream of the shock need not be steady or uniform and the gas need not be thermally or calorically perfect. Because of the complexity of the results, explicit formulas are provided for the above derivatives when the flow is steady and two‐dimensional or axisymmetric, and the gas is perfect.

Shock induced Rayleigh-Taylor instability in the presence of a boundary layer

Abstract: The aim of this work is an experimental study of the development of perturbations of a gaseous interface impulsively accelerated by a plane shock wave. The experiments are performed in a double diaphragm shock tube, where the second diaphragm is a very thin Mylar film which can be initially bulged because of a pressure difference between the two gases. The shape of the leading front of the contact zone is measured at three locations along the tube using a transversal array of heat transfer gauges. After the shock passage, the evolution of the interface is sensitive to vorticity production and boundary layer effects so that the impulsive Rayleigh–Taylor theory is inadequate for the description of this evolution. In particular, the predicted perturbation reversal when the shock wave passes from the heavy gas to the light one may not occur because of the boundary layer effect.

Aeroacoustics of supersonic jet flows from a contoured plug-nozzle

Abstract: The results of an experimental study of the acoustic far-field, the shock-associated noise, and the nature of the repetitive shock structure of supersonic jet flows issuing from a plug-nozzle having an externally expanded contoured plug with a pointed termination, operated at a range of supercritical pressure ratios £ = 2.0 to 4.5, are reported. The supersonic jet flow from the contoured plug-nozzle (CPN) is shown to be shock free and virtually wakeless at pressure ratio £ = 3.60 (fully expanded jet flow Mach number M7 = 1.49). As compared with the noise characteristics of underexpanded jet flows from an "equivalent" convergent nozzle, substantial reductions in the overall sound pressure levels (OASPL's) are achieved at all observation angles in the entire range of the pressure ratios. The typical bucket-type behavior of the OASPL vs MJ9 characteristic of supersonic jet flows from the contoured convergent-divergent (CD) nozzle, is not observed for the CPN operated over a range of supercritical pressure ratios. At the off-design conditions, the noise reductions for the CPN are higher than for the equivalent contoured CD nozzle. Moreover, the noise intensity of the CPN nozzle jet flows scales to the second power of the shock-strength related parameter 0 = (M/ 1)' and not to the fourth power as observed for the underexpanded jet flows from a convergent round nozzle. Similarly, the OASPL's of the CPN scale to ft =MJ-Md and not to /3? as reported for the contoured CD nozzle where Md is the design Mach number of either the CPN or the contoured CD nozzle.

Compressible rotational flows generated by the substitution principle

Abstract: A theory is developed for compressible rotational flow that is based on the substitution principle. The theory encompasses a formula for the transformation of the vorticity under the principle. Solutions are found for four rotational flows. These are the rotational counterparts of a parallel flow, flow behind a planar oblique shock wave, Prandtl–Meyer flow, and Taylor–Maccoll flow. A surprising variation of the vorticity is found for the planar oblique shock wave and the Prandtl–Meyer flow. Irrotational flow behind a curved shock wave, where the upstream flow is rotational, is examined and shown not to be possible.

Ptindamental Problem In Computing Radiating Flow Fields With Thick Shock Waves

Abstract: Possible reasons for the failure of the Navier-Stokes equations to yield realistic profiles of the temperature and density through the structure of a hypersonic shock wave are investigated. Models for bulk viscosity in a monatomic gas are examined which yield a realistic thickness for the shock-wave density profile, but not the temperature profile, and hence are not satisfactory. A tentative computational model for nitrogen is explored which yields considerably more realistic results than the Navier-Stokes equations. This model involves a nonlinear stress-strain tensor, nonlinear heat flux vector, and nonequilibrium rotational energy.

Shock wave source having central locating system & disposed in a cavity free of shock waves

Abstract: A shock wave source for disintegrating a calculus has a centrally disposed cavity in which a locating system for identifying the position of the calculus is disposed. The shock wave source has an emission surface, from which shock waves are emitted into a coupling agent in the shock wave source. The emission surface is angled in the direction of shock wave propagation, so that the shock waves emitted therefrom diverge. A focusing element is provided which focuses the shock waves onto the calculus, the focusing element having a structure which, in addition to focusing the shock waves, compensates for the divergence of the shock waves. Due to the divergence of the shock waves, the central cavity in which the locating system is disposed is maintained free of shock waves.

Plasma Heating by a Magnetosonic Shock Wave through Resonant Ion Acceleration

Abstract: Resonant wave-particle interactions in magnetosonic shock waves are studied by theory and simulation The number of ions trapped by a perpendicular laminar shock in a finite beta plasma is evaluated, and the amount of shock heating due to resonant ion acceleration is analytically obtained in terms of the Alfven Mach number and upstream plasma parameters Some effects of trapped ions on shock waves are also discussed In addition, it is shown that a laminar oblique shock can reflect some electrons by a magnetic mirror effect, in spite of a large positive potential in the shock region These theoretical predictions are confirmed by a fully electromagnetic particle simulation with full ion and electron dynamics in one spatial dimension

Shock wave generator for an apparatus for non-contact disintegration of concrements, present in a body

Abstract: The shock wave generator has a fluid-filled housing (9) with an outlet aperture (10) for shock waves and a shock wave source (12, 13, 14) arranged opposite this aperture, and means (18) for focusing the shock waves on a focus F, a plate-shaped body (19) being arranged between the shock wave source (12, 13, 14) and the focus F, and possessing a cross-sectional surface area less than that of a shock wave emanating from the shock wave source (12, 13, 14). The plate-shaped body (19) is made from a material whose acoustic impedance essentially corresponds to that of the fluid, and in which the speed of sound propagation differs from that in the fluid.