Showing papers on "Oblique shock published in 1985"

Comparison of Finite Volume Flux Vector Splittings for the Euler Equations

Abstract: A flux-splitting method in generalized coordinates has been developed and applied to quasi-one-dim ensional transonic flow in a nozzle and two-dimensional subsonic, transonic, and supersonic flow over airfoils. Computational results using the Steger-Warming and Van Leer flux splittings are compared. Discussed are several advantages of a MUSCL-type approach (differencing followed by flux splitting) over a standard flux differencing approach (flux splitting followed by differencing) . With an approximately factored implicit scheme, spectral radii of 0.978-0.930 for a series of airfoil computations are obtained, generally decreasing as a larger portion of the flow becomes supersonic. The Van Leer splitting leads to higher convergence rates and a sharper representation of shocks, with at most two (but more often, one) zones in the shock transition. The second-order accurate one-sided-difference model is extended to a third-order upwind-biased model with a small additional computational effort. The results for both the second- and third-order schemes agree closely in overall features to a widely used central difference scheme, although the shocks are resolved more accurately with the flux splitting approach.

The unsteadiness of shock waves propagating through gas-particle mixtures

Abstract: A shock wave which is incident onto a gas-particle mixture or initiated within such a mixture needs a certain distance to reach a constant velocity. This effect is due to the inertia and the heat capacity of the particles. In general the shock wave is decelerated and the frozen pressure jump is decaying.

Conical similarity of shock/boundary-layer interactions generated byswept and unswept fins

Abstract: A parametric experimental investigation has been made of the class of three-dimensional shock wave/turbulent boundary layer interactions generated by swept and unswept leading-edge fins. The fin sweepback angles were 0-65 deg at 5, 9, and 15 deg angles of attack. Two equilibrium two-dimensional turbulent boundary layers with a freestream Mach number of 2.95 and a Reynolds number of 6.3 x 10 to the 7th/m were used as incoming flow conditions. All of the resulting interactions were found to possess conical symmetry of the surface flow patterns and pressures outside of an initial inception zone. Further, these interactions were found to obey a simple conical similarity rule based on inviscid shock wave strength, irrespective of fin sweepback or angle of attack. This is one of the first demonstrations of similarity among three-dimensional interactions produced by geometrically dissimilar shock generators.

A numerical study of oblique shock-wave reflections with experimental comparisons

Abstract: A direct comparison is made for several occurrences of oblique shock-wave reflections between interferometric results obtained at the University of Toronto Institute for Aerospace Studies (UTIAS) 10 cm x 18 cm hypervelocity shock tube and numerical results obtained by using a current computational method for solving the Euler equations. Very good qualitative agreement is obtained for equilibrium and frozen flow fields except in small regions where the experiments were dominated by viscous flow. The quantitative agreement is very close in some cases but can be out by 10-15% in cases with non-equilibrium flow or viscous structures or both. Additional parametrized sequences of calculations are presented to assess the utility of the present numerical method in constructing the various reflection- transition lines for perfect inviscid flows in the shock-wave Mach number, wedge-angle ($M\_s, \theta\_w$)-plane, and the validity of the `boundary- layer defect' theory.

Cylindrical sound wave generated by shock-vortex interaction

Abstract: The passage of a columnar vortex broadside through a shock is investigated. This has been suggested as a crude, but deterministic, model of the generation of 'shock noise' by the turbulence in supersonic jets. The vortex is decomposed by Fourier transform into plane sinusoidal shear waves disposed with radial symmetry. The plane sound waves produced by each shear wave/shock interaction are recombined in the Fourier integral. The waves possess an envelope that is essentially a growing cylindrical sound wave centered at the transmitted vortex. The pressure jump across the nominal radius R = ct attenuates with time as 1/(square root of R) and varies around the arc in an antisymmetric fashion resembling a quadrupole field. Very good agreement, except near the shock, is found with the antisymmetric component of reported interferometric measurements in a shock tube. Beyond the front r approximately equals R is a precursor of opposite sign, that decays like 1/R, generated by the 1/r potential flow around the vortex core. The present work is essentially an extension and update of an early approximate study at M = 1.25. It covers the range (R/core radius) = 10, 100, 1000, and 10,000 for M = 1.25 and (in part) for M = 1.29 and, for fixed (R/core radius) = 1000, the range M = 1.01 to infinity.

Simulation of the Effects of Shock Wave Passing on a Turbine Rotor Blade

Abstract: The unsteady effects of shock waves and wakes shed by the nozzle guide vane row on the flow over a downstream turbine rotor have been simulated in a transient cascade tunnel. At conditions representative of engine flow, both wakes and shock waves are shown to cause transient turbulent patches to develop in an otherwise laminar (suction-surface) boundary layer. The simulation technique employed, coupled with very high-frequency heat transfer and pressure measurements, and flow visualization, allowed the transition initiated by isolated wakes and shock waves to be studied in detail. On the profile tested, the comparatively weak shock waves considered do not produce significant effects by direct shock-boundary layer interaction. Instead, the shock initiates a leading edge separation, which subsequently collapses, leaving a turbulent patch that is convected downstream. Effects of combined wake- and shock wave-passing at high frequency are also reported.

Specularly reflected ions, shock foot thicknesses, and shock velocity determinations in space

Abstract: The magnetic foot of a quasi-perpendicular, supercritical collisionless shock is spatially coincident with and caused by gyrating ions nearly specularly reflected from the shock. The reflected ions are turned around by the upstream magnetic field and returned to the shock after completing a partial gyration. An expression is derived for the turnaround distance of specularly reflected ions for arbitrary orientations of the incident velocity vector and the upstream magnetic field. This expression is then used to derive a formula for calculating the shock speed in the spacecraft frame from a single point measurement of the time required for the magnetic foot to transit a spacecraft. The derived formulas for turnaround distance and shock speed differ from previously published equations for these parameters and in some geometries give quantitatively very different results.

Shock acceleration of diffuse ions at the Earth's bow shock: Acceleration efficiency and A/Z enhancement

Abstract: Observations of particle spectra, intensity, and enhancement of alpha particles over protons at diffuse ion events at the quasi-parallel earth bow shock are compared to a Monte Carlo simulation of diffusive shock acceleration. The simulation includes the back reaction of accelerated particles on the shock structure, particle escape at an upstream free escape boundary, and a low energy per nucleon threshold for thermal leakage of downstream, shock-heated particles into the upstream region. The simulation assumes that the same scattering operator that gives rise to shock acceleration can also describe a viscous shock governed by hydrodynamic turbulence. This implies that accelerated ions can be drawn directly from the thermal solar wind with no separate superthermal seed population. Good agreement between the simulation and observations made during nearly radial magnetic field configurations lends support to thermal leakage of downstream, shock-heated ions as the mode of injection for diffusion ion events.

Modes of shock-wave oscillations on spike-tipped bodies

Abstract: The phenomenon of self-excited shock oscillations on a spike-tipped body at Mach 3 is investigated Various modes of shock oscillations are observed For some spike lengths, the shock oscillations are symmetric For other spike lengths, the shock structure oscillates asymmetrically with respect to the spike's axis In this case, experimental evidence confirms the presence of standing rotational waves on the body face and spike Spike configurations resulting in stable shock systems are also observed Holography and interferometry are used to obtain a detailed flow visualization

Hybrid simulation techniques applied to the earth's bow shock

Abstract: The application of a hybrid simulation model, in which the ions are treated as discrete particles and the electrons as a massless charge-neutralizing fluid, to the study of the earth's bow shock is discussed. The essentials of the numerical methods are described in detail; movement of the ions, solution of the electromagnetic fields and electron fluid equations, and imposition of appropriate boundary and initial conditions. Examples of results of calculations for perpendicular shocks are presented which demonstrate the need for a kinetic treatment of the ions to reproduce the correct ion dynamics and the corresponding shock structure. Results for oblique shocks are also presented to show how the magnetic field and ion motion differ from the perpendicular case.

Multiple transonic shock-wave/turbulent boundary-layer interaction in a circular duct

Abstract: An experimental study is described in which detailed pitot, static, and wall pressure measurements have been obtained for multiple transonic shock-wave/turbulent boundary-layer interactions in a circular duct at a freestream Mach number of 1.49, a unit Reynolds number of 4.90xl0/m, and a blockage of 5.15%. The details of the flowfield show the formation of a series of normal shock waves with successively decreasing strength and decreasing distance between the successive shock waves up to the point where a terminal shock occurs. A one-dimensional flow model based on the boundary-layer displacement thickness is postulated to explain the formation of the series of normal shock waves. A comparison with the results from our previous study involving a single shock interaction suggests that the effect of increased blockage is to promote multiple shock interactions and produce a lower pressure recovery, a less retarded boundary-layer flow, and an increase in the overall length of the interaction.

Observations of 35‐ to 1600‐keV protons and low‐frequency waves upstream of interplanetary shocks

Abstract: The present investigation is concerned with a comparison of measurements of energetic protons in the range from 35 to 1600 keV and low-frequency waves (periods of approximately 6 s) on ISEE 3 associated with the passage of the large oblique shock of April 5, 1979, which exhibits an extended foreshock. An attempt is made to identify the energy of the particles which are responsible for the waves. Intensity profiles of both waves and particles as a function of upstream distance are compared, taking into account the relation between the energy of the particles and the period of the waves. The considered approach makes it possible to identify protons with energies of a few hundred keV as being responsible for the waves in the extended foreshock. It is believed that the high energy density of the high-energy solar flare protons preceding the shock could be responsible for 'seed' waves which provide the scattering centers necessary for the acceleration of the lower-energy protons via a first-order Fermi mechanism.

Shock drift acceleration in the presence of waves

Abstract: Attention is given to the initial results of a model designed to study the modification of the scatter-free, shock drift acceleration of energetic test particles by wave activity in the vicinity of a quasi-perpendicular, fast-mode MHD shock. It is emphasized that the concept of magnetic moment conservation is a valid approximation only in the perpendicular and nearly perpendicular regimes, when the angle theta-Bn between the shock normal and the upstream magnetic field vector is in the range from 70 deg to 90 deg. The present investigation is concerned with one step in a program which is being developed to combine the shock drift and diffusive processes at a shock of arbitrary theta-Bn.

Flowfield scaling in sharp fin-induced shock wave/turbulent boundary-layer interaction

Abstract: This paper presents the results of an experimental investigation of the three-dimensional interaction of a swept planar shock wave with a turbulent boundary layer. The shock wave was generated by a sharp, unswept fin mounted normal to a flat test surface. On the two test surfaces used, the incoming boundary layers varied in thickness by 3:1. In both cases, the freestream Mach number was nominally 3, the freestream Reynolds number 6.3 X 10 m~ *, and the wall temperature close to adiabatic. Detailed yaw angle and pitot pressure surveys in the two cases reveal a similar flowfield structure that can be correlated using a simple scaling technique.

Analysis of turbulent underexpanded jets. II - Shock noise features using SCIPVIS

Abstract: SCIPVIS, the computational model discussed by Dash et al. (1985), is assessed in predicting the complicated flow structure associated with shock-containing plumes. In addition, the analysis in this study examines this code's applicability as a basic part of a program for estimating broadband shock noise radiation. The results of this study show that excellent agreement exists between predicted and measured static pressure distributions for both underexpanded and overexpanded flow cases considered. Of the three turbulence closure models incorporated in the SCIPVIS code, the kW model of Spalding produces the most uniform agreement with measurement. The k-epsilon-2 model of Launder consistently overestimates plume spreading for supersonic jets with exit Mach numbers in the 1-2 range. Dash's (1983) k-epsilon-2-cc, compressibility-corrected version of Launder's model underestimates plume spreading. Good qualitative agreement was also obtained between the measured longitudinal turbulence intensity and that predicted by the code for the same trial case. Comparison of measured and predicted broadband shock noise spectrum peak values were found to be in excellent agreement. This utilized a variant of the Harper-Bourne and Fisher (1973) phase-array model: the effective shock spacing was reinterpreted as the value of the end of the plume potential core, determined herein by the SCIPVIS code.

High time resolution plasma wave and magnetic field observations of the Jovian bow shock

Abstract: High time resolution (60 ms) Voyager magnetometer and plasma wave measurements of a strong (fast Mach number 16), quasi-perpendicular Jovian bow shock reveal an abrupt change in the plasma wave spectrum at the leading edge of the shock foot. Upstream electron plasma waves terminate at the leading edge, and are replaced by a lower-frequency broadband spectrum of ion-acoustic-like waves, which terminates at the main shock ramp. The clear association with the foot region of the lower frequency component suggests that it is generated by reflected ions. If the upstream plasma waves are generated by an escaping electron heat flux, their termination at the leading edge suggests that electrons are heated by the low-frequency waves in the shock foot.

Analysis of unsteady inviscid diffuser flow with a shock wave

Abstract: A finite difference scheme with a shock-fitting algorithm has been used to investigate unsteady inviscid now with a shock in an inlet diffuser. The flowfield consists of three different regions: the supersonic and the subsonic regions, and a region containing both air and liquid fuel droplets, separated by a normal shock wave and a fuel injection system. The analysis is based on a two-phase, quasi-one-dimensional model. The response of a shock wave to various disturbances has been studied, including large-amplitude periodic oscillations and pulse perturbations.

The propagation and growth of whistler mode waves generated by electron beams in earth's bow shock

Abstract: In this study, the propagation and growth of whistler mode waves generated by electron beams within earth's bow shock is investigated using a planar model for the bow shock and a model electron distribution function. Within the shock, the model electron distribution function possesses a field-aligned T greater than T beam that is directed toward the magnetosheath. Waves with frequencies between about 1 and 100 Hz with a wide range of wave normal angles are generated by the beam via Landau and anomalous cyclotron resonances. However, because the growth rate is small and because the wave packets traverse the shock quickly, these waves do not attain large amplitudes. Waves with frequencies between about 30 and 150 Hz with a wide range of wave normal angles are generated by the beam via the normal cyclotron resonance. The ray paths for most of these waves are directed toward the solar wind although some wave packets, due to plasma convection travel transverse to the shock normal. These wave packets grow to large amplitudes because they spend a long time in the growth region. The results suggest that whistler mode noise within the shock should increase in amplitude with increasing upstream theta sub Bn. The study provides an explanation for the origin of much of the whistler mode turbulence observed at the bow shock.

Interaction of air shock waves with porous compressible materials

Abstract: J. J. Keller, "Nonlinear acoustic resonances in shock tubes with varying cross-sectional area," Z. Angew. Math. Phys., 28, No. i, 107 (1977). L. P. Gor'kov, "Nonlinear acoustic oscillations of a gas column in a closed tube," Inzh. Zh., 3, No. 2 (1963). W. Chester, "Resonant oscillations in closed tubes," J. Fluid Mech., 18, Part ii (1964). A. N. Kraiko and A. L. Ni, "Nonlinear acoustics approximation in problems of gas oscillations in tubes," Prikl. Mat. Mekh., 44, No. 1 (1980). A. L. Ni, "Nonlinear resonant oscillations of a gas in a tube under the action of a periodically varying pressure," Prikl. Mat. Mekh., 47, No. 4 (1983). Sh. U. Galiev, N. A. Ii'gamov and A. V. Sadykov, "Periodic shock waves in a gas," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2 (1970). M. P. Mortell and B. R. Seymour, "A finite-rate theory of quadratic resonance in a closed tube," J. Fluid Mech., 112, 411 (1981).

A simple model for the formation of “reflected,” “intermediate,” and “diffuse” ion distributions upstream of Earth's bow shock

Abstract: Detailed energetic ion and low-frequency wave experiments on ISEE 1, 2, and 3, have established correlations between the types of ion populations and waves observed to exist in the earth's foreshock region. The present calculation has the objective to quantitatively test the picture obtained for the earth's foreshock region. An analysis is conducted of the coupled spatial and temporal evolution of upstream protons and hydromagnetic waves by means of a simple model in which the protons are represented by counterstreaming beams which resonate with hydromagnetic waves, exciting the outward propagating modes and damping the inward propagating modes at a single wave number.

Observation and analysis of the Mach reflection of weak uniform plane shock waves. Part 1. Observations

Abstract: Shock fronts and fluid-particle trajectories throughout a two-dimensional shock wave flow have been measured by multiple schlieren photography in a detailed study of the Mach reflection from a 10° wedge of plane uniform shocks with Mach numbers of 1.105, 1.240 and 1.415. Correction of optical distortions throughout the field of view permitted the positions and shapes of the shock fronts and the magnitudes and directions of the particle velocities to be measured with a high degree of accuracy. No departure from self-similarity of the flow fields could be detected. The cross-sections of the reflected shocks were found to be circular and centred on a point which moved with the velocity of the flow behind the incident shock. The triple-point trajectories were linear. The velocity of the curved Mach stem shock was found to be constant at any one height above the wedge surface and to decrease monotonically with height. A deviation from perpendicularity was noticed where the Mach stems met the surface of the wedge, the shocks having a slight forward inclination of as much as 1°. The experimental results cannot be completely explained using the classical three-shock theory and an alternative model for weak Mach reflection is developed in Part 2 of this paper.

Observation and analysis of the Mach reflection of weak uniform plane shock waves. Part 2. Analysis

Abstract: A non-stationary approach to the reflection of weak plane shocks is suggested as an alternative to the usual pseudo-stationary transformation For regular reflection the non-stationary model produces results which are identical to those obtained using the pseudo-stationary assumption, but with simpler algebra For weak Mach reflections, where the predictions of the pseudo-stationary model are in disagreement with experimental results, the non-stationary model predicts accurately the observed shapes and positions of the reflected and Mach stem shocks and the spatially varying flow properties behind these shocks However, the non-stationary model predicts that the gas flows above and below the contact surface, relative to the triple point, are not quite parallel Parallel flows could be obtained only in the limiting case of grazing incidence, when the reflected shock was sonic The model is based on the experimental results presented in Part 1 of this paper

A Detailed Numerical, Graphical, and Experimental Study of Oblique Shock Wave Reflections

Abstract: An extensive series of numerical calculations of oblique-shock-wave reflections in air and argon have been performed using a version of the second-order Eulerian Godunov scheme for inviscid compressible flow. This scheme is among the best of the upwind schemes developed in recent years. The results have been compared with the best available interferometric data from the UTIAS 10 cm x 18 cm shock tube, for fifteen different cases. The objective of this portion of the study was to assess the accuracy of the computer code in computing two-dimensional shocked flow of an inviscid perfect gas. A significant portion of our analysis is devoted to the question of the extent of influence of viscous and vibrational nonequilibrium effects on the experimental flow fields. Further parametrized series of calculations were performed in an effort to study the feasibility of numerically constructing inviscid transition lines in the (M/sub s/, theta/sub w/)-plane. Good agreement with analytic predictions was found for low values of M/sub s/ and, as might be expected, there are substantial discrepancies for M/sub s/ = 8.75. The possibility of using such numerical results in the formulation of accurate transition criteria is discussed. Overall, the computer code has been found to representmore » a significant predictive capability. The future extension of the code to permit the detailed modelling of nonequilibrium and viscous effects is, however, an important objective. 32 refs., 236 figs.« less

Experimental and numerical investigation of a shock wave impingementon a cylinder

Abstract: This paper presents an experimental study and a numerical simulation of the impingement of an oblique shock wave on a cylinder. The investigation was undertaken to attain two goals. The first goal was to experimentally investigate and document the complex three-dimensional shock wave and boundary-layer interaction occurring in practical problems, such as the shock-wave impingement from the Shuttle nose on an external fuel tank, and store interference on a supersonic tactical aircraft. The second goal was to carry out a comparison of experimental measurements and numerical computations of such complex flows. The experimental results revealed a complex flowfield with two separation zones, regions of cross flow, reflected shocks, and expansion fans. The numerical predictions agreed surprisingly well with the measured results, both on the surface and in the flowfield. However, some important flow details, such as the size and extent of the separation, and the reflected shock-wave system, were not predicted.

Calculation of three-dimensional shock/turbulent boundary-layer interaction generated by sharp fin

Abstract: A three-dimensio nal oblique shock/turbulent boundary-layer interaction is computed using a hybrid explicitimplicit numerical algorithm for the compressible Navier-Stokes equations. The flow configuration consists of a sharp fin or wedge, attached normal to a flat plate. The deflection of the wedge generates an oblique shock wave that interacts with the turbulent boundary layer on the flat plate. Computed results are obtained at Mach number M^ = 3 for a wedge angle of 10 deg and Reynolds number of Re8oo = 2.8 X 10s based on the undisturbed boundary-layer thickness 8^ upstream of the sharp fin. These results, together with the results of a previous computation for the same configuration at Re^ = 9.3 X 10s, are compared to the recent experimental data of McClure and Dolling. The computed results are in generally good agreement with the experiment and predict with reasonable accuracy the recovery of the boundary layer to a nominal two-dimensional state downstream of the interaction. Contour plots of various flow variables are employed to investigate the flow structure for the Re8oo = 2.8 X 105 case and to compare with the model developed by Oskam, et al. based upon experimental measurements at Re6oQ = 9.3 X 10s.

Computation of the tip vortex off a low-aspect-ratio wing

Abstract: The viscous transonic flow around a low-aspect-ratio wing has been computed using an implicit, threedimensional, *'thin-layer" Navier-Stokes solver The grid around the geometry of interest is obtained numerically as a solution to a Dirichlet problem for the cube The geometry chosen for this study is a low-aspect-ratio wing with large sweep, twist, taper, and camber The topology chosen to wrap the mesh around the wing with good tip resolution is a C-O-type mesh Using this grid, the flow around the wing was computed for a freestream Mach number of 082 at an angle of attack of 5 deg At this Mach number, an oblique shock forms on the upper surface of the wing, and a tip vortex and three-dimensional flow separation off the wing surface are observed Particle path lines indicate that the three-dimensional flow separation on the wing surface is a part of the root of the tip-vortex formation The lifting of the tip vortex before the wing trailing edge is clearly observed by following the trajectory of particles released around the wing tip

A major shock‐associated energetic storm particle event wherein the shock plays a minor role

Abstract: The energetic particle event associated with the quasi-perpendicular interplanetary shock which passed ISEE 3 on June 6, 1979, is characterized by persistent beamlike antisunward particle fluxes on both sides of the shock. We found that the shock has no significant nonadiabatic effects on the energetic particles near 1 AU. The lack of particles with pitch angles larger than 60° accounts for the absence of signatures of shock drift acceleration. The adiabatic behavior of the bulk of the particles at the shock offers a unique opportunity to understand the role of the postshock magnetic regime. A recently formed magnetic discontinuity just downstream from the shock forms an effective obstacle for particles, particularly those with a small gyroradius. From the spatial dependence of the particle population in front of the magnetic discontinuity we derived the escape probability for particles to cross the discontinuity. Strong anisotropic particle bursts are observed as intensity spikes (duration less than 1 min) both upstream and downstream from the shock. Velocity dispersion in some of these spikes is consistent with impulsive release at the magnetic discontinuity. We propose that the spikes are accomplished by a disturbance propagating along the discontinuity which develops a normal component perhaps accompanied by induced electric fields, thus enabling, in particular, low-energy particles with their small gyroradii to cross and stream into the upstream region. The energetic particle fluxes in this event are among the highest we have observed at ISEE 3. These fluxes are not produced by shock acceleration near 1 AU, but originate somewhere else far downstream from the magnetic discontinuity. From what we have learned from the unambiguous particle population signatures in this event, we believe that most shock-associated particle events cannot be understood on the basis of shock interactions alone; rather, the intensity history of energetic particles below 1 MeV is determined by the complete ensemble of magnetic structures embedded in the compressed plasma well behind the shock.