Showing papers on "Oblique shock published in 1977"

Oscillating delta wings with attached shock waves

Abstract: An unsteady flow theory is presented for studying the flowfield in the compression side of an oscillating flat delta wing with attached shock waves. Regular perturbation methods are used to analyze the in-phase and outof-phase flow components for small amplitudes and reduced frequencies. In particular, the out-of-phase flow is found to be "quasiconical," thus a pressure formulation can be realized. In the outboard region, where the crossflow is supersonic, exact solutions are found representing parallel surfaces of isobars. In the central region where the crossflow is subsonic, the problem is reduced to that of an ordinary-differential equation by a spanwise integration technique. Closed-form solutions are obtained for all cases. Numerical examples are presented to exhibit the dependence of the damping derivatives on several flow and geometrical parameters. Neutral damping boundaries are also given. It is found that the damping derivatives are generally less sensitive to the sweepback-angle and the freestream Mach number variations than to the mean-incidence variations, except near the shock detachment. Critical assessments, improvement schemes and future extensions were also discussed.

Evaluation of turbulence models for three primary types of shock-separated boundary layers

Abstract: Zero-equation (algebraic), one-equation (kinetic energy), and two-equation (kinetic energy plus length scale) turbulence eddy viscosity models were used in computing three basic types of shock-separated boundary-layer flows. The three basic types of shock boundary-layer interaction discussed are: (1) a normal shock wave at transonic speeds, (2) a compression corner shock at supersonic speeds, and (3) an incident oblique shock at hypersonic speeds. The models tested are simple, unmodified models used extensively for incompressible, unseparated flows. A comparison of computed and measured results for the compressible, separated flows described herein indicates that model performance is dependent on flow configuration with no distinct superiority of one model over the other for all three flow configurations.

Flow oscillations in a duct with a rectangular cross-section

Abstract: A two-dimensional configuration has been investigated in which air flows through a convergent nozzle and expands abruptly into a rectangular duct of larger cross-section which terminates in a plenum chamber. Three different types of oscillation have been observed in the downstream duct. At low plenumchamber pressures an oscillation occurs towards the exit of the duct as the boundary layer of the flow becomes alternately separated and attached. At increasing plenum pressure a shock-pattern oscillation takes place in which a change from a normal shock to oblique shocks occurs during a cycle. At still greater plenum pressures a base-pressure oscillation occurs which influences the entire duct flow downstream of the abrupt change in cross-section. The amplitudes of the oscillation can be as high as 10% of the rest state, and the frequency of the base-pressure oscillations can be predicted approximately from one-dimensional gasdynamic theory.The unsteady duct phenomena have been studied by synchronizing instantaneous pressures measured by quartz pressure transducers with interferograms obtained with a Mach–Zehnder interferometer.

The starting mechanism of wave-induced flow through a sharp-edged orifice

Abstract: Following weak plane shock diffraction at a knife-edge situated in a duct, a two-dimensional vortex sheet springs from the salient edge. The method of ‘vortex discretization’ is used, in conjunction with a Schwarz-Christoffel transformation, to develop a two-dimensional potential model for this constrained form of vortex generation. The analysis is independent of empirical parameters and describes, qualitatively, the pattern of streamlines through the orifice. Flow-visualization photographs are presented which illustrate the spiral shape of the starting vortex. Although of a limited nature, quantitative experimental vortex growth rates have been obtained and are compared with initial growth rates predicted theoretically. The results are discussed together with other aspects of the problem, including the limitations of the theory. An extension of vortex discretization is developed whereby the pressure distribution remote from the vortex sheet can be calculated. The combination of flow separation and the associated static wall pressure distribution gives theoretical insight into the mechanism of flow through an orifice.

Compression and rarefaction waves in shock-compressed metals

Abstract: The behavior of duralumin and copper is studied under conditions of specimen loading by two successive shock waves and during unloading after the shock compression. The amplitude of the first shock wave was 150–250 kbar. Direct measurements were performed of the difference in main stresses behind the shock front in duralumin. The results obtained do not agree with existing concepts of the behavior of solids under dynamic loading. Possible causes of this divergence are considered.

Experiments on transonic and supersonic turbulent boundary-layer separation

Abstract: Results of experimental investigations into turbulent boundary-layer behavior under the influence of pressure gradients and with separation are presented for transonic and supersonic flow fields. In the transonic case, an axisymmetric model was implemented consisting of an annular circular arc bump affixed to a circular cylinder aligned with the flow direction. For the supersonic separation study, an oblique shock wave impinging on the wind tunnel wall boundary layer was employed to cause separation. The mean streamwise and normal velocity components as well as the respective turbulence intensities were obtained with a two-color frequency shifted laser velocimeter.

Plane shock interacting with thermal layer

Abstract: Some extensions of Griffith’s work on shock/thermal layer interactions have been made. In particular, flow properties in a transition region between the foot of the shock and the thermal layer may be obtained; temperatures are reported.

Visualization of Shock Wave by Electric Discharge

Abstract: Theme O PTICAL systems such as schlieren systems, MachZehnder interferometers, and shadowgraphs have been used as typical methods to observe shock waves around models. However, any shock shape cannot necessarily be observed by these optical systems. For instance, it is difficult to measure a cross-section of a shock wave around a model, especially that around a winged body as shown in Fig. 1. In this case the shock shape in the shaded region (dotted line) cannot be observed by any optical method, because a part of the optical axes is intercepted by the body. In this paper, an observing method of shock waves by using an electric discharge has been tried. The principle of the method is based on the fact that a radiation intensity of an electric discharge depends on gas densities. When an electric discharge is generated across a shock wave, the radiation intensity in the shock layer is different from that in the freestream according to the difference of each density, consequently the location of the shock wave can be easily found by taking a photograph of this discharge column. Since the location of the electrodes may be chosen arbitrarily and the discharge column can be observed from any direction, it will be expected to be able to observe cross-sectional shock shapes or the shock wave in a shaded region as stated above. W I N G E D BODY

Radiation induced precursor flow field ahead of a Jovian entry body

Abstract: The change in flow properties ahead of the bow shock of a Jovian entry body, resulting from absorption of radiation from the shock layer, is investigated. Ultraviolet radiation is absorbed by the free stream gases, causing dissociation, ionization, and an increase in enthalpy of flow ahead of the shock wave. As a result of increased fluid enthalpy, the entire flow field in the precursor region is perturbed. The variation in flow properties is determined by employing the small perturbation technique of classical aerodynamics as well as the thin layer approximation for the preheating zone. By employing physically realistic models of radiative transfer, solutions are obtained for velocity, pressure, density, temperature, and enthalpy variations. The results indicate that the precursor flow effects, in general, are greater at higher altitudes. Just ahead of the shock, however, the effects are larger at lower altitudes. Pre-heating of the gas significantly increases the static pressure and temperature ahead of the shock for velocities exceeding 36 km/sec.

Normal shock wave-turbulent boundary layer interactions in transonic flow near separation

Abstract: The problem of a normal shock wave impinging on a flat plate, turbulent boundary layer is considered for the case where the external flow is transonic. Asymptotic methods are employed. It is shown that there are two outer regions, including the outer part of the boundary layer and the external flow, in which inviscid flow governing equations hold, and two regions near the wall, in which Reynolds and/or viscous stresses need be taken into account. The solutions in the outer regions lead to the pressure distribution on the wall, for which an analytical expression is presented, valid under those conditions when separation is imminent but has not yet occurred. The solutions valid in the inner regions lead to a separation criterion.

Blast waves with heat transfer

Abstract: A model is given for blast waves which are dominated by heat transfer rather than by shock heating and adiabatic expansion. The wave motion is attributed to a net heat flow W (watts/cm2) from the expanding hot core to the surrounding cold gas (density ρ1). The surface of the hot core is initially a supersonic heat wave without a shock. It changes into a subsonic heat wave with a leading shock after quickly passing through the detonation mode. A quantitative analysis of the space time trace near the detonation point yields the enthalpy hf and other parameters of the hot core, the thermal response function hf=f (W) of the background medium, and the blast wave energy E0=const ρ1V2sr3H (where Vs is the shock front velocity and rH is the radius of the hot core). The analysis shows the steady transition of such a blast wave from the early stage of a ’’thermal’’ wave with negligible mass motion to the late stage (which approaches ’’classical’’ blast waves) with negligible heat transfer. Applications to laser spa...

Unsteady motion of shock waves in two dimensional transonic channel flows

Abstract: : Two dimensional unsteady transonic channel flow with a shock wave is considered for the so-called slowly varying time regime. Solutions are studied for two specific cases within this general time regime, the cases corresponding to small and large amplitude shock wave motions. For the large amplitude case, conditions are considered under which the shock wave travels upstream of the throat, disappears, and then reforms at the throat. A unified solution which covers both cases is developed. Numerical results are presented. A short discussion of shock induced separation in unsteady flows is given. (Author)

Condensation of H2O and D2O in Argon in the Centered Expansion Wave in a Shock Tube

Abstract: : Despite gasdynamic non-idealities in the flow produced in a shock tube, pressure measurements at three different locations in the driver section of the shock tube revealed that the expansion wave generated in relatively weak expansions could be viewed effectively as a simple centered expansion fan after an empirical shift of the actual origin of the expansion wave to a 'virtual' origin. The resulting centered expansion fan was used to study at two locations the condensation of H2O and D2O vapors in an excess of the carrier gas argon, with simultaneous pressure and light scattering measurements. The isentropic flow within the centered expansion fan was found to be preserved up to the point of the detectable onset of condensation by tailoring the onset conditions to occur at the tail of the expansion fan, thus rendering a simple analysis of the experiments possible. The onset conditions of H2O vapor were found to be in agreement with previous findings in supersonic nozzles and shock tubes, and they were well predicted by the so-called classical theory of homogeneous nucleation. The condensation of D2O vapor was found to exhibit similar trends as those of H2O vapor condensation despite the slight differences in physical properties between them due to isotopy. (Author)

Damping of a periodic sequence of weak shock waves in channels with “sound-absorbing” walls

Abstract: We solve two problems on the attenuation of infinite periodic sequences (periodic in time or in space) of disturbances containing weak shock waves and propagated in opposition to a current. In the first problem the disturbances are given as periodic functions of time at some \"initial\" cross section of a cylindrical channel. In the second problem we consider two-dimensional and, in general, nonstationary flow in a layer between two parallel plates which are regarded as \"lateral\" walls. At the same time, this flow is such that in a specially oriented rectangular coordinate system moving with constant velocity parallel to the lateral walls, it is stationary and periodic with respect to a variable taken along an axis parallel to the direction of motion of the coordinate system. Such flow takes place, for example, before an infinite periodic lattice of plane profiles in the case when the total velocity of the oncoming flow is supersonic while its component normal to the front of the lattice is subsonic.

Hypersonic flow with attached shock waves over plane delta wings

Abstract: A new form is given for the general solution to the thin-shock-layer equations for the flow over a nearly plane delta wing. Using this, the solution described conjecturally by Hayes & Probstein for symmetrical flow with attached shock waves over a plane delta wing is realized numerically. The flow construction devised for this purpose is applied also to yawed flows. The solutions obtained are found to agree moderately well with the results of numerical calculations from the full equations, but contain a number of anomalous features characteristic of the thin-shock-layer approximation.

Prediction of Hypersonic Laminar Boundary-Layer/Shock-Wave Interactions

Abstract: UMERICAL solution of the compressible timedependent Navier-Stokes equations is one method of obtaining the theoretical solution of the interaction of an oblique shock wave and a laminar boundary layer. MacCormack1 and MacCormack and Baldwin2 used the method of MacCormack 3 to generate solutions for low supersonic Mach numbers. The purpose of this Synoptic is to ascertain the validity of the MacCormack algorithm for laminar boundary-layer/shock-wave interactions in the hypersonic regime. Results of several numerical solutions were compared with experimental data from the von Karman Facility (VKF) Hypersonic Wind Tunnel (B) and the Langley Research Center (LRC) Mach 8 Variable Density Tunnel. Agreement between the numerical solution and the data was generally satisfactory, although the extent of separation was under predicted in interactions with large separated regions. When applied to hypersonic interactions having large separated and recirculating regions, the method gave marginal performance. Lack of spatial resolution in the longitudinal direction is the suspected cause of the discrepancies. Contents The MacCormack method, which is an explicit, split, twostep algorithm, was used to solve the laminar, compressible, time-dependent Navier-Stokes equations expressed in conservative form. The equations, together with the details of the algorithm, are given by MacCormack. 2 Because of the difficulty in maintaining laminar flow throughout hypersonic boundary-layer/shock-wave interactions for strong shock waves and moderate-to-high Reynolds numbers, the incident shock angles (Fig. 1 for schematic) in this study are limited to a maximum of 16 deg and the Reynolds numbers to a maximum of 106/ft. The computed pressure ratio at the wall, pw/pw, is compared with measured data of an AEDC-VKF Tunnel B experiment in Fig. I.4 Agreement is excellent particularly near the peak pressure location where the correct shape is generated, and in the midrange where the correct pressure gradient is obtained. No evidence of separation was obvious from the data, and no separated region was predicted by the program.

Shock propagation in variable area ducts with phase changes: an extension of Chisnell's method

Abstract: Chisnell's approximating ordinary differential equation for the motion of a shock in a variable area duct is generalized to allow for phase changes behind the shock.

Initial flow model in shock tubes

Abstract: Introduction A the perturbational phenomena of the flow generated by the incident shock wave in a shock tube, one of the most important comes from the noninstantaneous opening of the diaphragm. The flow has a three-dimensional behavior in the first instants of the rupture and compression waves continually arise next to the diaphragm during the opening, generate first a shock wave, accelerate and strengthen this wave. Many experiments, both old and new, have shown the importance of these effects. The formation process of a plane shock wave is confined in a small length of the tube, but the acceleration process may require a large tube length, depending on initial conditions, diaphragm material and shape, and the tube itself. White's model is an approximation of the formation process; in the x,t diagram, compression waves are assumed to coalesce in a single point where the shock possesses its final and constant value, but the acceleration process is not taken into account. More recently, the "multistage" model may be considered as an improvement of White's model but it is still a discontinuous model. In the present model, the flow regime is related to the opening process itself. Boundary-layer effects are neglected, although it would not be too difficult to include them. In the same way, the formation phase itself will not be taken into account, but a numerical method of determination of the flow variables is developed in order to describe the acceleration phase.

Steady plasma flow with a shock in a mirror

Abstract: Based on scaled version of the equations of ideal magnetohydrodynamics it is shown how to construct a steady flow with a shock in a mirror. The upstream state is supersonic, but essentially arbitrary. The shock must be Mach number one on axis although the Mach number may rise rapidly off axis. The shock is extremely effective in converting the directed streaming energy of flow into randomized thermal energy. Such flow patterns may be of interest in very long theta pinches where quasi‐steady flow may obtain or in plasma gun devices where the gun injects a plasma along a magnetic field.

Transition from Mach to regular reflection and domains of various mach reflection configurations

Abstract: We have investigated different reflection configurations associated with the quasisteady reflection of shock waves from a plane corner in a shock tube.

Shock tensors and shock polars

Abstract: A refraction law for the velocity at an oblique shock in a compressible fluid is derived in dyadic form similar to that for refraction of light rays at an interface. The shock tensor embodies only the assumptions of conservation of mass and equality of tangential velocity components. Given the shock inclination and density ratio, a quadratic equation in the ratio of the flow speeds can be found with flow turning angle as a parameter. Analysis of the two solutions shows that they lie on a circle in the polar plane, a result independent of the equation of state or other conservation laws. If the density ratio is allowed to vary, a pencil of circles is generated in the hodograph plane ; or, equivalently a right, elliptic cone with two nappes appears in the three-space formed when the density ratio coordinate is added at right angles to the hodograph plane. The further requirements that momentum and energy be conserved taken together with weak restrictions on the functional form of the equation of state are sufficient to permit the development of a general theory of shock polars. The allowed shock states are seen to lie on the space curve formed by intersection of a surface called the Hugoniot cylinder with the elliptic cone. The projection of this space curve on the hodograph plane is the shock polar. The theory is applied to the special case of a polytropic gas by way of illustration.

Shock Induced Starting of Gasdynamic Laser Nozzles.

Abstract: : Dynamic processes occurring in single and multiple arrays of contoured Mach 3.2 rapid expansion, two-dimensional, supersonic nozzles during the passage of strong shock waves were investigated. Two sizes of single throat nozzles were tested. Their throat openings were 0.276 and 0.069 inch. The multiple nozzle array used had nine parallel nozzles of the smaller size arranged to simulate the flow channel of a gas dynamic laser. Several series of schlieren photographs were taken of the flow field within the nozzles. A fully started condition evidenced by uniform supersonic flow was observed in the small single nozzle and the multiple throat array approximately 80 microseconds after the passage of Mach 2.33 shock waves. The large single nozzle was not fully started by Mach 3.0 incident shocks. The dynamic flow initiation process was found to be strongly influenced by the strength and frequency of transverse wave reflections in the nozzle inlets. The larger single nozzle's failure to start is believed to be due to the fact that its larger inlet size reduced the frequency of these reflections by an amount which prevented the rapid increase in effective reservoir pressure necessary for supersonic flow initiation. A novel digital time delay computer was designed and built to facilitate making closely spaced photographs of the flow patterns.

Supersonic‐subsonic flow transition and shock formation and propagation in a dense plasma beam

Abstract: The axial flow of a supersonic high density plasma beam into an asymmetric mirror machine has been investigated experimentally. It has been found that in front of the second mirror peak, two supersonic‐subsonic flow transitions and shock formations occur. The subsequent motion upstream, of the first and stronger shock front has been measured by the time‐of‐flight method through diamagnetic loop and electric double probe signals. The shock front speed has been found to be one third the speed of sound in the neighborhood of the sonic transition and decreases to zero ahead of the upstream mirror.

Interaction between an external compression shock and a blunt body in a hypersonic stream

Abstract: A complex shock configuration with two triple points can occur during the interaction between an external oblique compression shock and the detached shock ahead of a blunt body (for instance, ahead of a wing or stabilizer edge). This results in the formation of a high-pressure, low-entropy supersonic gas jet [1–6]. Here two flow modes are possible [1], which differ substantially in the intensity of the thermal and dynamic effects of the stream on the blunt body: mode I corresponds to the impact of a supersonic jet [2–6], while the supersonic jet in mode II does not reach the body surface in the domain of shock interaction because of curvature under the effect of a pressure drop. Conditions for the realization of the above-mentioned flow modes are investigated experimentally and theoretically, and an approximate method is proposed to determine the magnitude of the compression shock standoff in the interaction domain. Blunt bodies with plane and cylindrical leading edges are examined. The results of a computation agree satisfactorily with experimental data.

Estimates of Turbulent Boundary Layer Behind a Shock Wave Moving with Uniform Velocity.

Abstract: : A theory, previously presented by the author, concerning turbulent boundary-layer development behind a shock moving with uniform speed is briefly reviewed. Numerical results for boundary-layer properties are presented for shock propagation in air at Mach numbers in the range 1.01 or = M sub S or = 20. The heat transfer results are in good agreement with the shock tube wall heat transfer measurements of Hartunian et al., which were made in the range 3 or = M sub S = 8. Approximate analytical expressions for turbulent boundary-layer properties are deduced, and estimates of the wall temperature variation with distance behind the shock (assumed small) are given. Effects of blowing (wall ablation) are also estimated. The need for experimental data to confirm large Mach number and blowing effects predictions is also noted. (Author)

Pitot and static observations in compressible flow

Abstract: In transonic and supersonic flow, the readings of pitot and static tubes are affected by shock waves formed by the measuring instruments introduced into the stream. This chapter describes a shock wave as a narrow zone, crossing the streamlines, through which occur sharp increases in pressure, density, and temperature, accompanied by an abrupt degradation of energy and decrease of velocity. The component of velocity normal to the shock wave is supersonic upstream of the wave and subsonic immediately downstream. These shock waves affect the pressures acting both at the mouth of the pitot tube and at the orifice of the static tube. The relationship between the total pressure and the pitot pressure in supersonic flow can be obtained with sufficient accuracy from the assumption that the shock wave formed ahead of the pitot tube is normal to the stagnation stream tube. In supersonic flow, static tubes with a variety of head shapes can record the free-stream static pressure accurately provided that the static holes are sufficiently far downstream. In some circumstances, it might be convenient to use a probe that can measure static pressure, within an acceptable tolerance, at both subsonic and supersonic speeds. Hess and Smith have shown that such a probe, with a circular cross-section, can be designed theoretically by suitable shaping in a diametrical plane, that is, by an appropriate variation of diameter with downstream distance.

Choking Phenomena of Flows in a Shock Tube

Abstract: If the flow area of a duct is reduced beyond a limiting value, the flow will be choked and, after a transient period of wave propagation, it will become steady and the flow rate will be decreased. At present, however, the choking phenomenon is not well understood. In this paper, the limiting conditions and the strength of a shock wave which propagates upstream when choking occurs are calculated, assuming that the flow is one-dimensional. Next, the transient flows around six kinds of wedges which were set in the low pressure channel of a shock tube were observed optically both by the schlieren method and a Mach-Zehnder interferometer. As the results, the choking process of the flow and the effect of the choking on the shape and behavior of the reflected shock wave were clarified. When the flow is choked at the wedge section, the experimental results of the velocity of the reflected shock wave agree well with the values calculated by the present one-dimensional method.

Weak shocks in open-ended ducts with complex geometry

Abstract: The dynamics of weak shocks in ducts of complex geometry and the sound radiation produced by the reflection of a weak shock from the open end of a duct have been investigated. Duct geometries include expansion chambers with and without inlet or outlet tubes extended and enclosed perforated tubes. Internal and external pressure histories of the interaction of weak shocks with simple muffler elements have been recorded using a standard one-shot shock tube and a resonating shock tube. The excitation shock Mach number ranged from 1.05 to 1.55. Analytical investigations, including a synthesis of existing works on internal weak-shock interactions of an acoustic treatment of the sound radiation produced by weak shock waves, are presented. Combining the above analyses, models for the reduction in radiated sound per unit of incident shock amplitude, as a result of inserting a muffler between the source and the tailpipe exit, are developed. For expansion chambers with and without extensions, the dependence of the transmitted and reflected waves and of the radiated sound on area ratio is compared with predictions. In particular, measured transmission coefficients for expansion chambers agree reasonably well with the predictions for all shock strengths; however, for large area ratios, the predicted sound attenuation is not observed, as waves diffracted at the upstream junction cause more sound to be radiated. For expansion chambers with internal extensions, sound attenuation is increased for low incident shock strengths; while for increasing incident shock strength, the internal transmission characteristics deteriorate, the reducing the sound attenuation. For enclosed perforated tubes, the dependence of the transmitted and reflected waves and of the radiated sound on the perforated area ratio and incident shock strength is compared with predictions. For perforated tubes with infinite enclosure, the transmission and reflection coefficients depend on both incident shock strength and perforated area ratio, as predicted. However, agreement with data is obtained only after inserting a perforated discharge coefficient with the perforated area ratio in the theory. The reduction of sound radiation with perforated area ratio is measured for one incident shock strength and then compared with predictions. For small area ratios, there is agreement but for large area ratios the measurements show that less sound is radiated than predicted. For large area ratios, gradual compressions with smooth fronts (not shock fronts) are transmitted, resulting in less radiated sound. Enclosures have no effect on the sound attenuation for small perforate area ratios; however, as the perforate area ratio increases, the enclosure eventually inhibits further increase in sound attenuation.