Showing papers on "Oblique shock published in 1973"

Structure of Shock Waves in Cylindrical Ducts

Abstract: Wall static and in-stream phot pressure distributions are presented for confined, nonreacting, supersonic flows in cylindrical sections wherein a shock structure has been stabilized. Based on an analysis of these measurements, the character of the wave structure is shown to be oblique rather than normal, with the flow remaining primarily supersonic downstream of the shock system. When additional cylindrical sections are either added or deleted the shock structure is, with the exception of slight changes due to the different initial conditions, independent of location in the duct. The parameters which govern the distance st, over which the pressure rise is spread, viz., Mach number, momentum thickness Reynolds number, duct diameter, and the momentum thickness of the upstream boundary layer, were varied as follows: 1.53 ^ Ma ^ 2.72, 5 x 10 ^ Ree ^ 6 x 10, 1.0 D 6.1 in., and 0.007 ^ 6 ^ 0.036 in. In each test the wave structure was generated by either lowering the pressure in the air supply system so that the cylindrical duct was, in effect, overexpanded when discharging to ambient conditions, or by throttling the flow leaving the duct. For a given pressure ratio across the disturbance, Pf/pa, st varies approximately directly with the product 0D and inversely with (Ma — l)Re0. A simple quadratic expression is presented which adequately represents this corespondence for the complete range of conditions tested and for data from the cited reference.

Shock Wave/Turbulent Boundary-Layer Interactions in Rectangular Channels

Abstract: Interaction regions created by the impingement of full span, externally generated, shock waves on a nozzle wall boundary layer were investigated. Incident shock strength was varied to produce unseparated, incipient, and fully separated flow fields. Significant departures from two-dimensionality were observed over the entire range of shock strengths tested and were identified with sidewall and corner boundary layer effects. However, comparisons of present centerline results with published two-dimensional data, obtained under similar test conditions and geometrical constraints, showed excellent agreement (e.g., incipient separation pressure levels, wall pressure distributions, free-interaction, and scale of the interaction region). This raises some question concerning the degree of two-dimensionality achieved in these previous investigations.

A Simple Correlation for Incipient-Turbulent Boundary-Layer Separation due to a Skewed Shock Wave

Abstract: References 1 Fingerson, L. M., "A Heat Flux Probe for Transient Measurements in High Temperature Gases," Ph.D. thesis, 1961, Univ. of Minnesota, Minneapolis, Minn.; also ARS Journal, Vol. 13, No. 11, Nov. 1962, p. 1709. 2 McCroskey, W. J., "Density and Velocity Measurements in HighSpeed Flows," AIAA Journal, Vol. 6, No. 9, Sept. 1968, pp. 1805-1808. 3 Horstman, C. C. and Kussoy, M. I, "Hypersonic Viscous Interaction on Slender Cones," AIAA Paper 68-2, New York, 1968. 4 Vas, I. E., "An Experimental Investigation of the Flow About a Slender Cone at Hypersonic Speeds," Ph.D. thesis, 1970, New York Univ., New York. 5 Becker, M., Papanikas, D. G., and Schweiger, G., "Experimental Study of the Flow Field in Front of Hemispheres in the Transition and Shock Formation Regime," presented at the 7th RGDS, July 1970, Deutsche Forschungsurid Versuchsanstalt fur Luftund Raumfahrt, (DFVLR) Porz-Wahn, W. Germany. 6 Harbour, P. J. and Lewis, J. H., "Preliminary Measurements of the Hypersonic Rarefield Flow Field on a Sharp Flat Plate Using an Electron Beam Probe," Rarefied Gas Dynamics, Supp. 4, Vol. 1, Academic Press, New York, 1967. 7 Petraites, R. J., "An Experimental Investigation of the Effects of Three-Dimensionality on the Flow Over a Flat Plate at M ~ 25," MSE thesis, Aug. 1972, Dept. of Aerospace and Mechanical Sciences, Princeton Univ., Princeton, N.J. 8 Dewey, C. F., Jr., "A Correlation of Convective Heat Transfer and Recovery Temperature Data for Cylinders in Compressible Flow," International Journal of Heat and Mass Transfer, Vol. 8, 1965, pp. 245-252. 9 Rubin, S. G., Rudman, S., Lin, T. C, and Pierucci, M., "Hypersonic Viscous-Inviscid Interaction by a New Type of Analysis," AGARD CP 30, Hypersonic Boundary Layers and Flow Fields, May 1968. 10 Mayne, A. W., Jr., Gilley, G. E., and Lewis, C. H., "Binary Boundary Layers on Sharp Cones in Low-Density Supersonic and Hypersonic Flow," AIAA Journal, Vol. 7, No. 4, April 1969, pp. 699-706.

Sidewall Boundary-Layer Influence on Shock Wave/Turbulent Boundary-Layer Interactions

Abstract: Gl, G2 = shock generator # 1, # 2 M = Mach number P = pressure Re^ — freestream unit Reynolds number Redot = Reynolds number based on 60* S, R = separation, reattachment T = temperature W = test surface span x = axial coordinate xi = shock intercept with test surface in the absence of any boundary layer y* = vertical coordinate of sonic line a = shock generator angle of attack 6 = boundary-layer thickness 6* = displacement thickness 6 = momentum thickness

Annular Truncated Plug Nozzle Flowfield and Base Pressure Characteristics

Abstract: The flowfield and base pressure characteristics of an internal-external-expansion, truncated plug nozzle are described over the pressure ratio range from "open" wake to "closed" wake conditions. The effect of plug length on these characteristics, including the process of wake "closure" is also presented. An existing method for calculating the flowfield and base pressure, for closed wake operation, is modified to include the internal shock wave generated near the shroud exit. The supersonic portion of the flow is calculated using rotational axisymmetric method of characteristics. The technique of Hartree is employed so that the downstream characteristic point locations can be chosen to fit the developing flowfield. An overexpansion technique is used to detect the internal shock wave in the vicinity of the shroud exit so that its effect on the plug base pressure could be determined. Good agreement between the analytical results and experimental data is obtained for closed wake operations.

Shock Impingement Caused by Boundary-Layer Separation Ahead of Blunt Fins

Abstract: : High speed flow past a blunt protuberance on a surface results in a complex, three dimensional, inviscid-viscous interaction flow field. Characteristically, the interaction results in a separated flow region composed of horseshoe vortices near the surface, and a lambda-type shock pattern in the plane of symmetry ahead of the protuberance. The shock wave emanating from the separated flow region impinges on the bow shock ahead of the protuberance and causes intense heating and high pressures locally on the protuberance leading edge. The heating and pressure in this local area can be 10 times larger than the undisturbed stagnation line values; the amplification depends strongly on local flow conditions. Tests were conducted to examine and obtain a better understanding of these interaction flow fields; the most recent tests included detailed flow field surveys for Mach 3 flows ahead of blunt fins on a flat plate surface with turbulent boundary layers. (Author)

Solar wind interaction with the Earth's magnetic field: 3. On the Earth's bow shock structure

Abstract: A classification of earth's bow shock structures on the basis of upstream MA, β, Δ = ∠ Bn (angle between shock normal and magnetic field direction) has been found. Typical properties for each case are studied. In particular, the downstream turbulence present in has been positively correlated with upstream β. It is suggested that the shock precursor, as far as low-frequency waves are concerned, is always due to waves generated upstream and carried by the solar wind. The use of the shock velocity allows estimation of the shock thickness: if MA > 3, the shock is a few ion gyroradii thick.

Bow shock and its interaction with interplanetary shocks

Abstract: Harbingers of significant magnetospheric motions consist of the interactions of interplanetary discontinuities with the standing bow shock. The most common discontinuity is the tangential discontinuity. Less frequent in occurrence, but of major significance to subsequent magnetospheric dynamics, is the flare-generated interplanetary shock wave and its initiation of bow shock and magnetopause motion toward Earth. Early studies utilized the ordinary gas-dynamic analogy of the well-known Riemann splitting of an initial discontinuity (i.e., bow shock) into a reflected shock (the moving bow shock) and the transmitted shock (the inward-moving interplanetary shock). It was shown that order-of-magnitude pressure increases at the subsolar point of the magnetopause are readily found for typical shock-on-shock studies. Phenomenological studies also demonstrated, in agreement with observations, that the magnetopause motion could be predicted on the basis of quasi-static variation of the solar wind dynamic pressure. Recent hydromagnetic studies (for the simplified case of perpendicular shocks) have extended the theory to predict bow shock and magnetopause velocities which appear to be observed by spacecraft. Such one-dimensional studies provide upper limits for all average plasma parameters within the region of the Sun-Earth axis. The general case of the time-dependent interaction in three dimensions has, as yet, not been done. Nevertheless, the general configurational and plasma details are, in principle, amenable to examination with the use of multiple spacecraft measurements during the interaction and the ensuing dynamic motions on a time scale of tens of min to the several hr required for the magnetopause to move to smaller geocentric distances. The physical processes of various energy transfers from kinetic to thermal and magnetic as predicted by the hydromagnetic theory could then be assessed by study of the plasma average velocity, direction of flow, magnetic field, temperature, and density. The magnetosheath plasma properties following such interactions could, on a more speculative note, provide new boundary conditions (associated with appropriate magnetosheath and magnetosphere magnetic field polarities) which could, in turn, initiate and drive the reconnection process within the magnetopause.

Three-Dimensional Separation for Interaction of Shock Waves with Turbulent Boundary Layers

Abstract: For the interaction of shock waves with turbulent boundary layers, obtained experimental three-dimensional separation results and correlations with earlier two-dimensional and three-dimensional data are presented. It is shown that separation occurs much earlier for turbulent three-dimensional than for two-dimensional flow at hypersonic speeds.

On the possibility of turbulent thickening of weak shock waves

Abstract: This paper examines the possible thickening of an initially sharp sonic boom by the turbulence it encounters in passing to the ground. Three apparently different viewpoints, all indicating substantial thickening, are shown to be actually identical and to give an irrelevant upper bound on wave thickness. All three approaches describe only the apparent mean diffusion induced by random convection of a sharp wave about its nominal position. Although a wave-front folding mechanism ultimately accounts for an apparent thickening as individual rays are weakened and tangled by turbulence, this process is too slow to be effective in the practical boom situation. The paper then considers what linear thickening of a wave packet results from propagation trough atmospheric turbulence and concludes that, in the relevant limit, a wave may be thickened by a factor of about 2 at the most. The conclusion is therefore reached that atmospheric turbulence cannot be the cause of the thousandfold discrepancy between the measured wave fronts and their Taylor thickness.

Laminar electrostatic shock waves generated by an ion beam

Abstract: Strong laminar electrostatic shock waves have been experimentally observed when an ion beam is injected into a collisionless plasma. The structure of the shock is qualitatively different from one with a trailing wave train. A density depression follows behind the shock front, and no trailing wave train due to wave dispersion is found. A significant amount of ions reflected from and transmitted through the shock front form a precursor. The critical Mach number above which no shock is formed is found to be 1.5. Numerical simulations reported here reproduce the experimental observations very well. An analysis based on the water‐bag model accounts for the observed value of the critical ion‐beam velocity which gives the critical Mach number. It also points out that the reflected ions play an essential role in the persistence of the shock.

Turbulence in electrostatic ion acoustic shocks

Abstract: Three types of collisionless electrostatic ion‐acoustic shocks are investigated using the University of California, Los Angeles, double plasma device: (a) laminar shocks; (b) small amplitude turbulent shocks in which the turbulence is confined to be upstream of the shock potential jump; and (c) large amplitude turbulent shocks in which the wave turbulence occurs throughout the shock transition. The wave turbulence is generated by ions which are reflected from the shock potential; linear theory spatial growth increments agree with experimental values. The experimental relationship between the shock Mach number and the shock potential is shown to be inconsistent with theoretical shock models which assume that the electrons are isothermal. Theoretical calculations which assume a trapped electron equation of a state and a turbulently flattened velocity distribution function for the reflected ions yields a Mach number vs potential relationship in agreement with experiment.

Parallel high β shocks and relaxation phenomena

Abstract: The structure of collisionless shocks propagating parallel to the magnetic field is discussed in the case of a large ratio of plasma pressure to magnetic pressure. The theory makes use of the basic ideas of Kennel and Sagdeev and it is shown that their shock model is to be interpreted in terms of relaxation shocks. The calculations are based on a purely macroscopic set of equations including finite Larmor radius effects. The resulting shock structure is determined both in a quasilinear WKB-type approximation and through a direct numerical integration of the basic non-linear equations. The results from both methods agree fairly well, although the level of the turbulence is high. It is argued that strong parallel shocks have a double structure, where the main transition is followed by a broad relaxation wave. It is suggested that the magnetosheath should be considered as the relaxation zone of the Earth's bow shock.

Electron plasma wave shocks in a collisionless plasma

Abstract: A large-amplitude electron plasma wave in a bounded collisionless plasma is observed to steepen and form a shock with a trailing wave train. The dependence of the Mach number and the period of the wave train on the shock amplitude shows that the shock structure is related to solitary waves. For a larger-amplitude shock, however, the trailing wave train is small or disappears, and a potential jump followed by large-amplitude oscillations propagating with a slower velocity than that of the shock front is observed. The amplitude of the oscillations is sufficiently large to trap a significant number of electrons and to form vortices in phase space.

Reynolds Number Effects on the Shock Wave-Turbulent Boundary Layer Interaction at Transonic Speeds.

Abstract: : A Ludwieg tube experiment is described in which the pertinent features of the shock wave-boundary layer interaction on an airfoil are simulated with a two-dimensional flat plate in a supersonic nozzle. The nozzle is modified to impress an airfoil pressure distribution on the flat plate that is typical of a cruising flight condition. A normal shock wave is positioned at a fixed location on the plate, and measurements are made in the vicinity of the shock wave-boundary layer interaction zone.

Calculation of Turbulent Boundary-Layer Shock-Wave Interaction

Abstract: The value of the logarithmic-shock-polar diagram has been illustrated by its use in two examples, one of which could have necessitated the use of iteration, and one which did not. It can be further utilized to evaluate the two types of threeshock-configuration encountered in shock interaction, i.e., weak oblique wave striking a strong shock, and a weak oblique wave striking another oblique wave of the same family. Both of these have the necessary contact discontinuity line, the first in the form of a shear layer, and the second in the form of an expansion wave. The logarithmic-shock-polar family can be used to estimate the results of reflections from shock waves and expansion waves from a solid wall, or from a free shear layer. These represent all the uses of shock interaction at a point necessary to explain any of Edney's six distinct types of shock a) Flow over double wedge. b) "Logarithmic-Shock-Polar" for flow over double wedge.

Second sound in a solid under shock compression

Abstract: The propagation of a strong shock wave in a perfect, three-dimensional crystalline lattice is studied by means of molecular-dynamical calculations The results show that behind the shock front there is a region of thermal relaxation which increases with time The thermally relaxed region, therefore, propagates with a velocity lower than that of the shock front It is believed that the wave-like propagation of this thermally equilibrated region is a natural extension of second sound from the conventional low-temperature, low-pressure regime to the high-temperature, high-pressure regime The implication of this phenomenon on PVT calculations from shock-wave data is discussed briefly

Stationary shocks and toroidal diffusion

Abstract: For a resistive plasma of stellarator or low‐temperature tokamak type, the quasistationary equilibrium is rotating at the reduced sound speed Bθνth/Bz, and has a slow (acoustic branch) shock fixed in space. Dissipation in the shock can increase plasma loss by an order of magnitude over the Pfirsch‐Schluter rate. For a very weak shock, the loss rate scales with the resistivity as η4/3; for a stronger (but still weak) shock, it scales as η3/2 . On the diffusion time scale, flow along the lines of force must develop.

Structure and luminosity of strong shock waves in air

Abstract: A set of numerical computations of the thermal structure and optical luminosity of strong shock waves in air is described. The model includes radiation transport coupled with hydrodynamics under assumed conditions of steady flow. With shock velocities above 10 km/sec a thermal precursor develops ahead of the shock front, and increases in prominence with increasing shock strength. For velocities above 50 km/sec the precursor is partially opaque to visible light and the computed brightness is smaller than that of a blackbody at the shock temperature. At higher velocities the brightness decreases with increasing shock strength. Steady solutions could not be found for velocities above 80 km/sec.

Computer programs for predicting supersonic and hypersonic interference flow fields and heating

Abstract: This report describes computer codes which calculate two-dimensional shock interference patterns. These codes compute the six types of interference flows as defined by Edney (Aeronaut. Res. Inst. of Sweden FAA Rep. 115). Results include properties of the inviscid flow field and the inviscid-viscous interaction at the surface along with peak pressure and peak heating at the impingement point.

Shock system of February 2, 1969

Abstract: The shock system observed in the solar wind by Pioneer 9 and Ogo 5 on Feb. 2, 1969, consisted of the following major discontinuities: a forward slow shock; a forward fast shock; a tangential discontinuity at which the density dropped sharply and the flow direction changed; a tangential discontinuity at which the magnetic field strength jumped to an unusually high value; two closely spaced tangential discontinuities that bracketed a region of even greater field strength and that fronted a region of very cool, very dense, helium-enriched plasma; a reverse fast shock of low Mach number; and a second reverse fast shock of very low Mach number. The event had aspects of both corotating and flare-induced shock systems; it is suggested that the source of the disturbances was a flare occurring at or near an M region.

Test gas properties behind a decelerating shock wave in a shock tube

Abstract: Measurements of electron density behind a shock wave in air are presented. Operating conditions are such that shock‐wave deceleration, boundary‐layer mass loss, and chemical nonequilibrium are important in the determination of the development of the electron density behind the shock wave. A one‐dimensional unsteady analysis is described. Calculated electron density is compared with experimental values. Agreement is within a factor of 2. The difference is probably attributable to expansion waves embedded in the test gas.

Numerical solution for the inviscid supersonic flow in the corner formed by two intersecting wedges.

Abstract: The inviscid, interference corner flow generated by two intersecting wedges immersed in a supersonic stream is obtained by use of a second-order, shock-capturing, finite-difference approach. The governing equations are solved iteratively in conical coordinates to yield the flow structure consisting of multiple shock and slip surfaces. The numerical results for shock wave and slip surface position and structure, pitot pressure traverses, and surface pressure distributions are compared with experimental data obtained over a wide range of Reynolds numbers. The comparisons show the best agreement with the high Reynolds number (greater than 3,000,000) results for which the boundary layer is turbulent.

Interaction of interplanetary MHD shock waves with the magnetopause

Abstract: The interaction between a shock-wave and the magnetopause is formulated on the basis of one-dimensional magnetohydrodynamics. The magnetopause is assumed to be a tangential discontinuity, and the magnetic field is limited to the case of perpendicularity. Both the forward and reverse shocks' impact on the magnetopause are considered and analyzed separately. The forward shock-magnetopause interaction results in a transmitted shock, a tangential discontinuity, and a simple rarefaction wave. The reverse shock-magnetopause interaction creates a transmitted shock, a tangential discontinuity, and a reflected wave. The propagation of an SSC signal which is related to an interplanetary shock-induced geomagnetic storm's onset-time on Earth is discussed in general terms. It was found in earlier work (Shen and Dryer, 1972) that the propagation velocity of an inter-planetary shock is decreased by about 10∼15% following its impact with the earth's bow shock; the present study shows that its velocity is then suddenly increased by a factor of two to three after impact with the magnetopause. The fast propagating shock-wave inside the magnetosphere degenerates into a hydromagnetic wave as it advances into an increasing intensity of the distorted dipole geomagnetic field.

Reflection of a plane shock wave from a rigid concave wall

Abstract: We present the results of an experimental study of the reflection of a plane stationary shock wave with Mach number in the range 1.21–1.35 from a rigid cylindrical concave wall. The experiments were carried out in a shock tube. In experimental shock tube technology the reflection of a shock wave from a rigid wall is often used for obtaining high temperatures [1]. This circumstance is associated with the fact that the temperature behind the reflected wave is significantly higher than that behind the incident wave.

Relaxation and none quilibrium radiation behind shock waves in air

Abstract: This article discusses relaxation behind shock waves in air at velocities from 8 to 12 km/sec. Profiles are obtained for the parameters of the gas behind the front. The populations of the radiating states of the atoms and the molecules are calculated. In a number of spectral ranges the intensity of the radiation passes through a maximum exceeding the equilibrium level. A comparison is made with experimental data obtained in shock tubes. The radiant heat fluxes from the relaxation zone are calculated. The contribution of this radiation to the radiative heating of blunt bodies with flow around them at hypersonic velocities is evaluated.