Showing papers on "Oblique shock published in 1972"

Instability of the interface of two gases accelerated by a shock wave

Abstract: Results are presented of an experimental study of the stability of the interface of two gases traversed by ashockwave. It is found that the interface is unstable both in the case of shock wave passage from the lighter to the heavier gas and for passage in the opposite direction. The interface disturbance grows linearly with time in the first approximation.

Study of waves in the earth's bow shock.

Abstract: Results of an examination of the perturbation vectors of waves upstream and downstream from the region of maximum compression in the bow shock on Ogo 5 under particularly steady solar-wind conditions. The polarization of the upstream waves was right-hand circular, and that of the downstream waves left-hand elliptical in the spacecraft frame. By observing that the polarization of the waves remained unchanged as the shock motion swept the wave structure back and forth across the satellite three times in eight minutes, it was found that the waves were not stationary in the shock frame. A study of the methods of determining the shock normal indicates that the normal estimated from a shock model should be superior to the normal based on magnetic coplanarity. The propagation vectors of the waves examined did not coincide with the shock-model normal, the average magnetic field, or the plasma-flow velocity. However, the major axis of the polarization ellipse of the downstream wave was nearly parallel to the upstream propagation vector.

Propagation of weak shock waves through turbulence

Abstract: The effect of turbulence on the structure of weak shock waves is investigated. The equilibrium structure is shown to be governed by a balance between nonlinear steepening and the turbulent scattering of acoustic energy out of the main wave direction. The scattered energy appears as perturbations behind the shock front. For conditions typical of sonic booms in atmospheric turbulence the wave structure is governed by a Burgers equation similar to that describing viscous shocks, except that parameters related to the turbulence appear instead of the viscosity coefficient. The magnitude of the perturbations following a shock is estimated from first-order scattering applied to a thickened shock. Predictions of shock thicknesses and perturbations compare favourably with available experimental data.

Structure of the Earth's bow shock

Abstract: Numerical simulations have provided detailed information of the microscopic processes that occur in a high Mach number oblique shock wave such as the bow shock. The gross feature of the ion dissipation is a strong interaction of the reflected ions with the whistler precursor, which can be explained by a nonlinear ion-ion counterstreaming instability. The instability simultaneously amplifies the magnetic oscillations of the whistler, which supports the strong magnetic turbulence at the bow shock. In addition, electrostatic substructures have been observed that significantly enhance the thermalization of the ion distribution on the Debye scale.

An investigation of shock strengthening in a conical convergent channel

Abstract: The behaviour of an initially plane, strong shock wave propagating into a conical convergence is investigated experimentally and theoretically. In the experiment a 10° half-angle cone is mounted on the end of a pressure-driven shock tube. Shock waves with initial Mach numbers varying from 6.0 to 10·2 are generated in argon a t a pressure of 1·5 Torr. During each run local shock velocities a t several positions along the cone axis are measured using a thin multi-crystal piezoelectric probe inserted from the vertex. This technique produces accurate velocity data for both the incident and reflected shock waves. In the corresponding analysis, a simplified characteristics method is used to obtain an approximate solution of the axisymmetric diffraction equations derived by Whitham (1959). Both the shock velocity measurements and the axisymmetric diffraction solution confirm that the incident shock behaviour is dominated by cyclic diffraction processes which originate at the entrance of the cone. Each diffraction cycle is characterized by Mach reflexion on the cone wall followed by Mach reflexion on the axis, These cycles evidently persist until the shock reaches the cone vertex, where the measured velocity has increased by as much as a factor of three. Real-gas effects, enhanced in the experiment by increasing the initial Mach number and decreasing the pressure, apparently alter the shock wave behaviour only in the region near the vertex. Velocity measurements for the reflected shock within the cone show that the shock velocity is nearly constant throughout most of the convergence length.

Binary index for assessing local bow shock obliquity

Abstract: The earth's collisionless plasma bow shock has, overall, a nonuniform structure whose magnetic profile is simultaneously that of a monotonic or laminar perpendicular shock and of a multigradient oblique shock, depending on the local orientation of the interplanetary field to the nominal shock surface. A 'pulsation index' Ip has been devised from empirical results to provide a simple convenient means of assessing the probable local character of the shock's structure; Ip = 0 or 1, according to whether local field geometry favors perpendicular or oblique structure, respectively, at a chosen point of observation on the nominal shock surface.

Shock waves and drag in the numerical calculation of isentropic transonic flow

Abstract: Properties of the shock relations for steady, irrotational, transonic flow are discussed and compared for the full and approximate governing potential in common use. Results from numerical experiments are presented to show that the use of proper finite difference schemes provide realistic solutions and do not introduce spurious shock waves. Analysis also shows that realistic drags can be computed from shock waves that occur in isentropic flow. In analogy to the Oswatitsch drag equation, which relates the drag to entropy production in shock waves, a formula is derived for isentropic flow that relates drag to the momentum gain through an isentropic shock. A more accurate formula for drag, based on entropy production, is also derived, and examples of wave drag evaluation based on these formulas are given and comparisons are made with experimental results.

Jet-interaction-induced separation - The two-dimensional problem.

Abstract: An experimental study supporting the development of an analytical model for jet-interaction-induced separation of supersonic turbulent boundary layers is discussed. Extensive flat-plate tests were conducted at a Mach number of four and two Reynolds numbers. Surface pressures were recorded fore and aft of the four, sonic, normal jet slots tested. Shadowgraphs, taken through glass-ported side plates, were made of both the interacting and freejet plume characteristics. Generalized correlations showed that the entire problem scales directly with the observed shock heights and that these shock heights are predictable from freejet considerations.

Observation of nonuniform structure of the Earth's bow shock correlated with interplanetary field orientation

Abstract: Explorer 33 and 35 magnetometers, on the western and eastern flanks of the earth's bow shock, respectively, observed the boundary concurrently between 0130 and 0430 UT, Oct. 30, 1968. Contrasting shock structures were recorded. Explorer 35 saw a quiet abrupt shock, whereas Explorer 33 saw an irregular noisy boundary with much upstream wave activity. The interplanetary field was roughly in the average archimedean spiral angle and was therefore approximately tangent to the shock at Explorer 35 and normal to the shock at Explorer 33. Gross motions and variable tilting of the aberrated shock probably contributed to the peculiar sequence of shock crossings at the two spacecraft. The observations support a model of the shock in which perpendicular and oblique collisionless structures coexist and form a nonuniform magnetosheath outer boundary.

Perturbation solution for growth of nonlinear shock waves in a lattice

Abstract: A perturbation solution is obtained for the propagation of longitudinal shock waves in a one‐dimensional lattice with a velocity step applied to the first mass. The nonlinear part of the elastic interaction force is assumed to be of parabolic form. The growth of particle velocity at the head of the wave and the noticeable high‐frequency contributions travelling behind, that arise due to nonlinearity, have been observed previously in numerical studies and are found also in the perturbation solution. Within the range of validity of the solution, the nonlinear growth of maximum particle velocity at the head of the shock wave is shown to increase with distance into the lattice as the two‐thirds power.

Propagation and Growth of Shock Waves in Inhomogeneous Fluids

Abstract: The propagation of a shock discontinuity into a fluid region at rest with a spatially dependent density and entropy distribution is considered. Representing the shock wave as a propagating singular surface, a differential equation is derived for the strength of the shock in terms of the density gradient behind the shock and a “critical density gradient.” The growth and decay behavior of the wave is discussed for two different conditions ahead of the wave and it is found that, under certain circumstances, a characteristic shock strength may exist which markedly affects the character of the critical density gradient (and thus the growth and decay behavior of the wave).

Corotating shock structures

Abstract: Consideration of observed interplanetary shocks leads to the conclusion that a corotating forward shock has not been unambiguously identified at 1 AU A reverse shock identified in September 1967 is a likely candidate for a corotating structure

A Study of Unsteady Transonic Flows with Shock Waves in Two Dimensional Channels.

Abstract: : A two dimensional unsteady transonic flow of a perfect gas with constant specific heats is considered, with solutions found in the form of perturbations from a uniform, sonic, isentropic flow. Longitudinal viscous stress terms are included so that shock waves can be considered. The case where the characteristic time of a temporal flow disturbance is large compared to the time taken by a sonic disturbance to cross the transonic regime is considered. A similarity solution involving an arbitrary function of time is found and it is shown that this solution corresponds to unsteady channel flows with shock waves, for the case where the walls are in general not stationary. Solutions are presented for thick (shock fills transonic region) and thin (shock tends to a discontinuity) shock waves in unsteady flows, both for decelerating and accelerating channel flows. For the thin shock case, both numerical and asymptotic solutions are given. (Author)

Propagation of shock waves in bubble–liquid mixtures

Abstract: In this paper experiments are described on shock waves in a mixture of an aqueous solution of glycerine and small air bubbles. Bubble size, shock strength and volumetric air content are varied during these experiments. Results are given concerning the measured shock velocity, the shock thickness and the occurrence of pressure waves at the back side of the shock. These results are compared with those of previous theoretical work by the author. Good agreement with theory is found regarding shock velocity and shock thickness. The pressure waves predicted by theory do appear indeed, but are attenuated considerably stronger than according to the theory.

Numerical Study of Strong Plasma Shock Waves Produced in an Electromagnetic Shock Tube

Abstract: A set of two-fluid Navier-Stokes equations with classical physical transport coefficients is used to compute the evolution and structure of collisional plasma shock waves in an electromagnetic shock tube. Shock speeds up to 200 cm/microsec and shocked-plasma temperatures of the order of kilovolts are studied. A strong transverse bias magnetic field is employed, which significantly alters the size and shape of the shock profiles, when compared with the zero bias field case. The wave structure is different from that of a two-fluid gasdynamic shock without transverse magnetic field. Especially significant is the effect of the small ion Larmor radius in reducing the gasdynamic shock thickness by at least an order of magnitude in the transverse shock case, which permits collisional shocks to have thicknesses much smaller than the post-shock mean free path. These collisional shock waves produce very hot ions, the ion temperature increasing with shock speed, although the formation time and distances also increase substantially with shock speed.

Magnetic probes with nanosecond response time for plasma experiments.

Abstract: Small magnetic probes for use in a collisionless shock experiment have been constructed. The method of building the coil, connecting it to the oscilloscope, shielding and enclosing the probe, calibration, and testing of the time response with a fast square wave pulse and a sampling oscilloscope are described. These probes, with response times of

Shock‐Induced Dynamics of a Low‐Density Heated‐Fluid Element

Abstract: The dynamic behavior of a two‐dimensional, heated, turbulent fluid element which is instantaneously set into motion relative to its surroundings by the passage of a reflected shock wave has been studied in a shock tube. It is demonstrated that the dynamics of this fluid element are similar to those encountered in the study of gravitational thermals, and that the shock tube may be used to extend the range of experimental parameters under which “thermal‐like” phenomena can be investigated. An exploding wire was used to generate the clearly defined heated element. Data obtained from high‐speed (22 000 pictures/sec) interferograms indicate that the effective radius (re) of the heated element varies linearly with its horizontal displacement (x), i.e., re = αx, where α, the entrainment coefficient, is a constant. The coefficient α is shown to vary approximately linearly in the range 0.15 ≲ α ≲ 0.50 with increasing shock strength. The observed temporal growth of the heated element was compared with that predicte...

An experimental study of hypersonic wakes behind wedges at angle of attack

Abstract: Experimental measurements of mean flow properties of hypersonic wakes behind wedges of 20° included angle were conducted for angles of attack up to 25° at Mach number 6, with Reynolds number based on wedge base height ranging from 7,000 to 55,000. The near and far wake structures were determined, including streamlines and velocity profiles, over a down-stream distance of 60 base heights. The base pressure is insensitive to incidence within about 17°. At higher incidence, flow separation occurs on the leeward surface. The near wake flow field changes accordingly. The far viscous wake (x/H > 4) changes with increasing incidence because of the increasing differences of the inviscid flow quantities at the leeward and windward edges of the viscous wake. The wake static pressure, which increases with incidence, viscous wake edge velocities, edge Mach number, edge temperatures and flow inclination of the real flow (directed towards the leeward side) compare favorably with a simple inviscid shock expansion model. In the laminar wake flows the wake widths, minimum velocities, minimum Mach numbers and maximum temperatures change little with incidence. However, in the transitional wake flows, the “break-away” phenomenon is observed and transition from laminar to turbulent flow moves upstream as angle of attach increases.

Laboratory Study of High-beta Plasma Shock Waves.

Abstract: A plasma wind tunnel has been used to generate shock waves at rest in the laboratory reference frame. The upstream pressure ratio beta is in the range 1-3, and the Mach number based on the fast magnetosonic wave speed is 3 to 5. The shock wave is formed by letting the plasma 'wind' impinge on the field of a magnetic obstacle. The resulting shock is primarily transverse, and exhibits a thickness of 0.8 to 1.2 times the ion inertial length c/ omega pi. The shock thickness decreases with increasing Mach number, and increases as the ion mass is increased. Measured values of upstream and downstream magnetic field particle density, and temperature agree with those calculated from the shock conservation relations. Magnetic fluctuations in the shock front are observed, with frequencies near the ion cyclotron frequency. Comparisons of these results with those of other experiments, and with the Earth's bow shock, are made.

Magnetic structure of ionizing shock waves Part 3. Normal shocks

Abstract: Normal ionizing shock waves are considered as a subclass of oblique shocks in which the upstream transverse magnetic field component is zero; i.e. the upstream field is normal to the plane of the shock. Non-trivial (switch-on) normal shocks involve a non-zero downstream transverse field component; magnetically trivial normal shocks are simply gas shocks with an imbedded constant normal magnetic field. As with oblique shocks, switch-on normal ionizing shock waves are plane- polarized, provided the conductivity is a scalar. Ohmic structures are discussed for several values of shock Alfv en number, treating the electric field as a free parameter, as usual. For Alfv en numbers extending from zero to two (for the infinite-Mach-number case), there is always a finite range of E field values. Above two, only the gas shock exists, and this requires a unique electric field value. Because the magnetic field magnitude increases through switch-on shocks, there is no mechanism available for converting magnetic energy into thermal energy, as is the case for oblique or skew shocks. Thus, there is no significant downstream heating above the viscous temperature; and, in some cases, slight downstream cooling may even occur. Expansion shocks are not possible in this geometry. Previous studies are reviewed in the light of structural requirements, and some erroneous results are clarified; in particular, it should be noted that MHD switchon solutions for the pre-ionized case are not imbedded in the family of ionizing switch-on solutions.

Flow velocity measurements in a t tube.

Abstract: The flow velocity of a T‐tube plasma has been measured by recording the attenuation of a known shock wave propagating through the T‐tube flow. This technique yields results with typical accuracies of 0.1 km/sec which is about 10% of the velocity of the probing shock. The interpretation of the results invites a comparison of the T‐tube flow field with an overexpanded detonation or breakdown wave in the high‐velocity regime and with a radiation driven shock front in the low‐velocity regime.

Strong mass injection at the surface of a blunt body in a supersonic flow

Abstract: The case of supersonic flow over a blunt body when another gas is injected through the surface of the body in accordance with a given law is theoretically investigated If molecular transport processes are neglected, the flow between the shock wave and the surface of the body should be regarded as two-layer, that is, as consisting of the flow in the shock layer between the shock wave and the contact surface and the flow in the layer of injected gas A numerical solution of the problem is obtained near the front of the body and its accuracy is estimated Approximate analytic solutions are obtained in the injected-gas layer: a constant-density solution and a solution of the boundary-layer type in the local similarity approximation Near the flow axis the numerical and analytic solutions are fairly close, but at a distance from the axis the assumptions made reduce the accuracy of the approximate solutions The flow in question can serve as a gas-dynamic model of a series of problems describing the radiant heating of blunt bodies in a hypersonic flow In the presence of intense radiative heat transfer, vaporization is so great that the thickness of the vapor layer is comparable with the thickness of the shock layer Moreover, the thermal shielding of various kinds of obstacles in channels through which a radiating plasma flows can be organized by means of the forced injection of a strong absorber The formulation of a similar problem was reported in [1], but the results of the solution were not given A two-layer model of the flow of an ideal gas over a blunt body was used in [2, 3] for the analysis of radiative heat transfer In [2] the neighborhood of the stagnation point is considered In [3] preliminary results relating to two-layer flow over blunt cones are presented The solution is obtained by Maslen's approximate method

Investigation of a Supersonic Surface Jet—Hypersonic Flow Interaction with Axial Symmetry

Abstract: An experimental investigation of axially symmetric slot injection of a supersonic jet into a hypersonic stream has been carried out A cone of 5° half angle was constructed in such a way that jet injection at six different angles could be provided. The throat areas and exit areas of the slots were the same in all cases, and provided a nominal jet Mach number of (2)*. The freestream Mach number was 6 in all cases. The boundary layer at the point of injection was fully turbulent Optical investigations were made, and surface pressure distributions were obtained. Stagnation temperature and stagnation pressure surveys were made downstream of the injection point, the results being reduced by digital computer to provide mass flux profiles. The results indicate that three basic types of interaction occur depending on the angle of the jet. Equations describing the displacement of the dividing streamline for each of the three interaction types are established empirically, and the streamline displacement is compared to separation and shock displacement scales. Jet mass entrainment is also examined. It is tentatively concluded that jets of intermediate angle hold promise of advanced propulsion applications, while jets at small angles provide stable films, as necessary in thermal protection applications.

Radiating‐Conducting Thick‐Transparent Normal Shock Solution

Abstract: An approximate solution for the radiating and conducting flowfield behind hypervelocity normal shock waves is presented. The solution is used to investigate the effects of conduction and uncertainty in radiative properties upon the flowfield enthalpy variation.