Showing papers on "Oblique shock published in 1989"

Cyclic behavior at quasi-parallel collisionless shocks

Abstract: Large scale one-dimensional hybrid simulations with resistive electrons have been carried out of a quasi-parallel high-Mach-number collisionless shock. The shock initially appears stable, but then exhibits cyclic behavior. For the magnetic field, the cycle consists of a period when the transition from upstream to downstream is steep and well defined, followed by a period when the shock transition is extended and perturbed. This cyclic shock solution results from upstream perturbations caused by backstreaming gyrating ions convecting into the shock. The cyclic reformation of a sharp shock transition can allow ions, at one time upstream because of reflection or leakage, to contribute to the shock thermalization.

Numerical simulations of magnetized jets

Abstract: The present axisymmetric numerical simulations of light hypersonic jets allow unmagnetized jets and jets carrying a dynamically important magnetic field to be contrasted. After decelerating a weakly magnetized jet through a series of weak, oblique shocks, a Mach disk and a strong annular shock are encountered near the outer edges of the contact discontinuity separating the shocked fluid from the shocked ambient gas. Upon passing the annular shock, the gas quickly expands and enters a backflowing cocoon surrounding the jet. The overall speed of advance of the jet is reduced; matter near the jet axis which passes through the terminal Mach disk accumulates in a plug, and gas is discharged into the cocoon by the intermittent shedding of vortices. When magnetic stresses dominate, however, the jet is rapidly decelerated via a Mach disk and strong annular shock.

On the refraction of shock waves

Abstract: This paper discusses the refraction of plane shock waves in media with arbitrary equations of state. Previous work is reviewed briefly, then a rigorous definition of wave impedance is formulated. Earlier definitions are shown to be unsatisfactory. The impedance is combined with the boundary conditions at the media interface to study both head-on and oblique shock incidence. The impedance determines the nature of the reflected and transmitted waves, their intensities, and the fractions of energy and power that are reflected and transmitted. The refractive index is also defined and determines whether or not a wave will be refracted, and also helps determine whether the wave system will be regular or irregular. The fundamental law of refraction is derived and shown to be a consequence of the fact that an arbitrary point on a shock or an expansion wave follows a ray path of minimum time between any two points on the path. This is a generalization of Fermat's Principle to media that are deformed and convected by the waves propagating through them.

On the lengthscales of laminar shock/boundary-layer interaction

Abstract: The interaction of an oblique shock with a laminar boundary layer on an adiabatic flat plate is analysed by solving the Navier-Stokes equations numerically. Mach numbers range from 1.4 to 3.4 and Reynolds numbers range from 105 to 6 × 105. The numerical results agree well with experiments. The pressure distribution at the edge of the boundary layer is proposed as a sensitive indicator of the numerical resolution. Local and global properties of the interaction region are discussed. In the vicinity of the separation point, local scaling laws of the free interaction are confirmed. For the length of the separation bubble a new similarity law reveals a linear influence of the shock strength. A comparison with the triple-deck theory shows that, for finite Reynolds numbers, the triple deck tends to overestimate the lengthscale substantially and that this discrepancy increases with increasing Mach number. The triple-deck model of displacing the main part of the boundary layer is substantiated by the numerical results. An asymmetrical structure within the separation bubble causes a characteristic distribution of the wall shear stress.

On the effect of a tangential discontinuity on ions specularly reflected at an oblique shock

Abstract: A study is conducted for the case of a tangential discontinuity (TD) that convects into a shock at some arbitrary angle, in order to clarify events observed in proximity to the earth's bow shock. Very different behavior is noted to result depending on the sense of ion gyration relative to the TD. The fact that particles can be injected into the TD's plane, so that they travel upstream close to the TD, implies that active current sheet (ACS) events thus far assumed to be generated by the solar wind's interaction with a large-density reflected component are actually detached from the bow shock. In other geometries, ions stay close to the shock after their TD interaction, implying that ACS events are modifications of the shock.

Shock-wave-induced mixing enhancement in scramjet combustors

Abstract: An experimental study of the interaction between a weak shock wave and a supersonic shear layer was carried out to determine the possibility of shock-induced mixing enhancement. A supersonic (Mach 2.5) stream of nitrogen was mixed with a sonic helium jet downstream of a rearward-facing step to simulate the mixing region in the vicinity of a SCRAMJET flameholder. A small wedge was used to generate an oblique shock wave that impinges on the mixing layer. Schlieren flow visualization and Rayleigh scattering concentration measurements were carried out. The results indicate that significant spreading of the shear layer may occur downstream of the shock/shear layer interaction region. Further study is required to determine the mechanism of the observed spreading and the extent of the increase in mixing efficiency. Since there are shock-induced losses, an optimum mixing enhancement configuration will have to be determined before the method can be validated and successfully implemented in a SCRAMJET combustor.

On the structure of resistive MHD intermediate shocks

Abstract: An overview is presented of the resistive steady state structure of intermediate MHD shocks, ie, shocks that effect a transition from super-alfvenic to sub-alfvenic flow The results are presented in terms of magnetic hodograms in which the two components of the magnetic field tangential to the shock surface are plotted against each other By performing fixed-point analysis in this plane, at the possible upstream and downstream states of these shocks, and by solving the one-dimensional, steady state, resistive, nonviscous MHD equations numerically, it is found that three basic types of hodogram topology exist, describing the resistive intermediate shock structure These topologies are characterized by the normal flow speed (in the shock frame) relative to the fast-wave speed and the sound speed at the upstream and downstream states Fast-mode and slow-mode shocks are contained within these hodograms as well In brief summary, it is found that all intermediate shocks that have an upstream normal flow speed, νx1, less than the local small-amplitude fast-mode wave speed, cf1, and a downstream normal flow speed, νx2, greater than the local small-amplitude slow-mode wave speed, cs2, have a unique magnetic structure consisting mainly of a rotation of the tangential magnetic field, accompanied by a more or less pronounced change in field magnitude This type of shock is called a subfast (νx1 cs2) intermediate shock A subfast strong intermediate shock has νx1 cf1) The structures of both weak (νx2>cs2) and strong (νx2 c1) to subsonic (νx2

Vortex paradigm for shock-accelerated density-stratified interfaces

Abstract: Numerical simulations are reported that capture the observations of Haas and Sturtevant (1985) when a planar shock accelerates an inclined planar interface between two media. A vortex paradigm is presented for interpreting the evolution of shock-accelerated density-stratified interfaces beyond early times. The simulations illustrate the paradigm and are in good agreement with the results of Haas and Sturtevant. Color images of space-time diagrams of the one-space integrated vorticity function are given to show the primary and secondary features of the emerging vortex structures.

Laser-induced iodine fluorescence technique for quantitative measurement in a nonreacting supersonic combustor

Abstract: A nonintrusive optical technique, laser-induced iodine fluorescence (LIIF), is demonstrated in the quantitative study of the compressible flowfield in a steady, nonreacting supersonic combustor. Measurements of density, temperature, and velocity were made with the calibrated technique for two combustor operating conditions. Measurements were first conducted in the supersonic flow over a rearward-facing step for comparison with calculated pressure profiles. The second operating condition was staged, transverse injection behind a rearwardfacing step at an injection dynamic pressure ratio of 1.20. These experimental results demonstrate the capability of the technique for making accurate, spatially resolved measurements of gasdynamic variables in the complex supersonic flowfield. Complete data sets to be generated with this technique will be used to validate computational fluid dynamic (CFD) codes for supersonic combustor flowfields, prior to the inclusion of chemical reaction.

Separation shock dynamics in Mach 5 turbulent interactions induced by cylinders

Abstract: Wall pressure fluctuations have been measured under the unsteady separation shock in interactions generated by unswept circular cylinders. Models were tested in the turbulent boundary layers on the tunnel floor and on a full-span flat plate. The freestream unit Reynolds number was 53×10 6 m -1 , and the wall temperature approximately adiabatic. Distributions of the shock frequency, shock period, and shock speeds in the upstream and downstream directions have been calculated

An Implementation of a Grid-Independent Upwind Scheme for the Euler Equations

Abstract: A scheme for the twedimensional Euler equations that uses flow parameters to determine the direction for upwind-differencing is described. This approach reduces the grid-dependence of conventional schemes. Upwinding at the local flow angle and the local pressure-gradient angle is tested. The upwindbiased fluxes are calculated with Roe's approximate Riemann solver. A centered flux is used for the component normal to the upwinding direction. Results for a first-order scheme show significant improvement over conventional grid-aligned upwinding. Specifically, oblique shock waves are less diffused. Preliminary results for a second-order scheme are also included.

Shock wave generator

Abstract: A shock wave generator for the fragmentation of concrements, having a light-pulse-transmiting light guide and a converter arranged at the distal light guide end and having an ionization surface which, when a light pulse impinges, initiates a shock wave in the surrounding fluid, as well as having a shock wave outlet zone. In order to increase its efficiency and durability, the generator is constructed such that the ionization surface extends obliquely sloped with respect to the beaming axis of the impinging light pulse and the shock wave outlet zone is arranged in the direct shock wave beaming area of the ionization surface, thereby permitting a largely unhindered, low-loss propagation for the shock wave to the application point.

Numerical Simulations of Interaction between Stellar Wind and Interstellar Medium

Abstract: Hydrodynamic interaction between supersonic spherical wind emitted from an astronomical object and a uniform streaming flow is simulated numerically assuming the flow to be axisymmetric, adiabatic and inviscid. Examples of such a phenomenon are a comet in the solar wind, and the solar wind or a stellar wind in an interstellar medium. Three cases of the incident flow, i.e., subsonic, supersonic and hypersonic flow, are considered. Discontinuities in the flow, i.e., a bow shock, a contact surface, an inner shock, a Mach disc and a slip surface are identified. The contact surface and the slip surface are found to be Kelvin- Helmholtz unstable. Other instabilities occurring near the stagnation region and the inner shock are also found.

Stability of shock waves

Abstract: The progress already made in studies of the stability of shock waves and some tasks for the future are reviewed. The following aspects of the problem are discussed: 1) stability of shock waves as hydrodynamic discontinuities irrespective of the events which occur in the relaxation zone of a wave (this aspect includes also the problem of stability of a shock wave sustained by a piston and anomalies in the reaction of a wave to external perturbation, including reflection and refraction of perturbations); 2) stability of flow in the relaxation zone (structural stability) of a shock wave. The stress is on the theoretical side of the problem. However, potential practical realization of the shock-wave instability criteria are also considered. Schemes of decay of unstable shock-wave discontinuities are discussed.

Experimental and numerical investigation of an oblique shock wave/turbulent boundary layer interaction with continuous suction

Abstract: An numerical and experimental investigation has been conducted into the interaction of an incident oblique shock wave with a turbulent boundary layer, for the cases of a rough plate and a porous plate with suction, at a nominal Mach number of 2.5 and flow deflection angles of 0, 4, 6, and 8 deg. Attention is given to the pitot pressure profiles, wall static pressures, and porous plate local bleed distributions measured for the two plates. Suction is found to increase the strength of the incident shock required to separate the boundary layer; for all shock strengths tested, separation is completely eliminated.

Multispacecraft observations of energetic ions upstream and downstream of the bow shock

Abstract: Simultaneous measurements of energetic protons and alpha particles were obtained inside and outside of the magnetopause and upstream and downstream of the bow shock. In the magnetosheath, no gradient or streaming is found in the upstream direction. The present results are consistent with first-order Fermi acceleration at the bow shock and subsequent downstream convection, and exclude the possibility of a magnetospheric source for these particles.

Formation of double layers within an oblique collisionless shock.

Abstract: Simulations show that for shock waves propagating obliquely to a magneticfield (angles from 55/degree/ to 80/degree/ for the parameters run), a double layer formsat the shock front and plays an important role in the shock dynamics. Electronsare strongly accelerated through the double layer and scattered off ion andmagnetic field fluctuations behind the shock. Some ions are reflected by thedouble layer and the jump in magnetic field. For these investigations, electronheating is the major dissipation.

Compressible Flowfield Characteristics of Butterfly Valves

Abstract: The results of an experimental investigation into the flowfield characteristics of butterfly valves under compressible flow operating conditions are reported. The experimental results include Schlieren and surface flow visualizations and flowfield static pressure distributions. Two valve disk shapes have been studied in a planar, two-dimensional test section: a generic biconvex circular are profile and the midplane cross-section of a prototype butterfly valve. The results demonstrate that under certain conditions of operation the butterfly valve flowfield can be extremely complex with oblique shock waves, expansion fans, and regions of flow separation and reattachment

Influence of gas flow on performance of ``Confined'' atomization nozzles

Abstract: Supersonic gas jets in “confined” nozzles were studied by Schlieren photography in blank atomizing tests (i.e., no liquid present). Tests in nitrogen at 1.56 MPa pressure showed that changes in the geometry of a nozzle altered the wave pattern and the height of the supersonic region in the jet. In particular, the protrusion height of the metal delivery tube (above the gas exit) had a profound influence. An expansion wave formed at the tip of the nozzle when the protrusion height was too high, and the jet became subsonic in a short distance. Longer supersonic wave patterns were observed at lower protrusion heights following the appearance of a shock wave at the tip of the nozzle. These results correlated well with the atomizing performance of the same nozzles determined previously. The nozzles which had long supersonic flow regions corresponded to those which produced fine powders, and short supersonic regions were associated with reduced efficiency in performance. This indicated that the preservation of high velocities in the gas was of primary importance for effective liquid breakup in atomization. A procedure (based on the characteristics solution of supersonic flow) was developed for assessing flow conditions in atomizing nozzles and for calculating the optimum height of the delivery tube for a given geometry to obtain the longest supersonic jet.

Preliminary study of the interactions caused by crossing shock waves and a turbulent boundary layer

Abstract: The subject research, the first phase of an extended study of the interaction of crossing shock waves with a turbulent boundary layer, has revealed the complexity of the resulting flow. Detailed surface visualization and mean wall static pressure distributions show little resemblance to the inviscid flow approximation, and the exploratory high frequency measurements show that the flow downstream of the theoretical inviscid shock crossing position has a significant unsteady characteristic. Further developments of the (unsteady) high frequency measurements are required to fully characterize the unsteadiness and the requirements to include this component in flowfield modeling.

Whistler wave bursts upstream of the Uranian bow shock

Abstract: Observations of magnetic field wave bursts upstream of the Uranian bow shock are reported which were recorded prior to the inbound shock crossing. Three wave types are identified. One exhibits a broad spectral enhancement from a few millihertz to about 50 mHz and is seen from 17 to 10 hr prior to the inbound shock crossing. It is argued that these waves are whistler waves that have propagated upstream from the shock. A second wave type has a spacecraft frame frequency between 20 and 40 mHz, is seen only within or immediately upstream of the shock pedestal, is right-hand polarized in the spacecraft frame, and has a typical burst duration of 90 s. The third wave type has a spacecraft frame frequency of about 0.15 Hz, is seen exclusively within the shock pedestal, is left-hand polarized in the spacecraft frame, and has a burst duration lasting up to 4 min. It is argued that the low-frequency bursts are whistler waves with phase speed comparable to, but in excess of, the solar wind speed.

Chemistry associated with hypersonic vehicles

Abstract: A series of chemical equilibrium, chemical nonequilibrium, and thermal nonequilibrium calculations are performed for various chemical processes related to a Single Stage To Orbit Hydrogen Fueled Airbreathing Hypersonic Vehicle (SSTOHFAHV). The processes include air dissociation downstream of a 60and 30-deg oblique shock and Hi-air combustion. The calculations are applied to two typical SSTOHFAHV trajectories.

The Role of Oblique Reflection Shocks in Astrophysical Jets

Abstract: Les simulations de jets hydrodynamiques montrent que les modes de reflexion predits par la theorie lineaire ne sont pas disruptifs mais saturent a des amplitudes finies au travers de la formation d'ondes de choc obliques. Les proprietes de ces ondes de choc sont etudiees

Development of a navier-stokes code on a connection machine

Abstract: Governing Equations The results of adaptation of a 2-D NavierStokes code on a 16000-processor Connection Machine CM2 are presented. The Navier-Stokes code solves the two-dimensional, unsteady, compressible, viscous-flow equations of fluid dynamics for flow past arbitrary bodies by use of an explicit, finite-volume multistage, Runge-Kutta time-stepping scheme. The implementation strategies on CM2 are discussed. The code conversion issues such as domain decomposition and boundary-condition implementation, are highlighted. The performance of the code is evaluated by calculating the flowfield of the impingement of an oblique shock on a flat plate. Runtime comparisons are made on VAX8800, Convex CX-2, Cray X-MP, and CM2.

On the Interaction of Shock Waves with Contact Surfaces Between Gases of Different Densities

Abstract: The interaction of shock waves with a contact surface between gases of different densities has been studied experimentally and theoretically. The basic mechanism for the instability of perturbations at the interface is baroclinic vorticity generation resulting from the misalignment of the pressure gradient of the shock and the density gradient of the interface. In the present study, the effects of interface density contrast and initial thickness, and incident wave strength on the development of the instability at the interface are investigated. The experiments were performed in a new vertical shock tube facility where the interaction of a shock wave with either a discontinuous interface, formed by a thin (0.5 µm) plastic membrane, or a continuous interface, created by retracting a metal plate initially separating the two gases, was studied. Air was used on one side of the interface and either helium, carbon dioxide, refrigerant-22 or sulphur hexafluoride was used on the other side as the test gas. Experiments to study the time evolution of quasi-sinusoidal perturbations on a continuous interface have shown that the growth rates are reduced as the interface thickness is increased. It has been observed that growth rates of perturbations of wavelength λ ~ 25 mm on interfaces of thickness δ ~ 10 mm are about three times smaller than those predicted by the linear theory for the impulsive acceleration of discontinuous interfaces. A new model that accounts for the growth rate reduction caused by the presence of a finite density gradient on the interface has been proposed, and good agreement was obtained with the present experimental results. Experiments were also performed to observe the schlieren visual thickness of plane discontinuous or continuous interfaces with random small-scale perturbations after interaction with the incident shock wave and its reverberations. The interface was initially located near the end wall of the shock tube to permit the observation of the development of the interface phenomena after the arrival of the incident shock and its reverberations. It is found that the interaction of a shock wave with a discontinuous interface causes the appearance of a turbulent mixing zone between the two gases, whose growth rate slows down as time increases, owing to a decrease in turbulence intensity and the action of viscosity. Because of the large uncertainty associated with the measurements a short time after the interaction with the incident shock, the accurate determination of a possible universal power law governing the thickening of the interface is not feasible. Results for the interaction of the first reverberation of the primary wave with the already turbulent interface have demonstrated that this growth is sensitive to the initial pre-growth state of the interface. It also appears that the thickening of the turbulent mixing zone is accomplished by the merging of large structures within the interface. However, since the energy available for the turbulent motions at the impulsively accelerated interface remains constant after the interaction with the shock and also depends on the wavelength of the initial perturbation, it is not certain whether the development of mixing at the interface achieves an asymptotic stage of self-similar turbulence independent of initial conditions, as has been observed for the gravity-driven interfaces. Also, it has been found that the growth rates measured in the present experiments with discontinuous interfaces are nearly an order of magnitude lower than those reported by previous investigators. The continuous interfaces formed by the retracting plate are smoothed by molecular diffusion, and thus the combination of low density gradient and small initial perturbations is such that they exhibit growth only after being perturbed by acoustic noise introduced by the reverberation of waves between the interface, the side walls and the end of the shock tube. The development of viscous boundary layers on the side walls of the test section can cause the bifurcation of waves reflected from the end wall of the shock tube, and, thereafter, the formation of wall bubbles and interface contaminating jets. Moreover, the generation of vortical structures by the baroclinic instability excited by the interaction of reflected waves with the distorted interface within the boundary layer has been demonstrated. Significant contamination of the test gas can by achieved by these structures, even if reflected-wave bifurcation is absent. Moreover, the strain induced by the vorticity in these wall structures tends to thin the interface; the magnitude of this effect on the growth rates in the present plane interface experiments is estimated to be of order 10% for discontinuous interfaces and 50% for continuous interfaces.

Improvements and applications of a streamwise upwind algorithm

Abstract: An improved streamwise upwind algorithm has been used to study conical flow fields. In the present method, additional terms have been introduced in the cross-flow direction to prevent solution decoupling in supersonic flows, and the local Mach number is taken into account in order to evaluate the rotated differencing. It is found that the formula captures oblique shock waves in the same manner as Roe's (1986) formula, has good convergence properties, and accurately computes shear flows.

Turbulent Shock — Boundary-Layer Interaction with Control Theory and Experiment

Abstract: Experimental and theoretical investigations are presented concerning the two-dimensional turbulent shock-boundary-layer interaction at a curved wall with passive flow control through ventilation in the shock region. The theoretical flow simulation is based on an iteration method, coupling a boundary layer integral solution with an embedded interference model for the viscid flow and the non-linear potential solution for the inviscid flow.