Showing papers on "Oblique shock published in 1969"

Bow shock associated waves observed in the far upstream interplanetary medium

Abstract: Fifty orbits of Explorer 34 data have been used to study 0.01–0.05 Hz transverse waves in the interplanetary medium region between the bow shock and the spacecraft apogee of 34 RE. It is concluded that the waves are associated with the earth's bow shock since they only occur when projection of the interplanetary field observed at the spacecraft intersects the shock. The waves are observed 18.5% of the time when a total of 134 days of interplanetary data is considered, but more than 90% of the time when the field has the proper orientation with respect to the bow shock. On the basis of this result it is suggested that these waves with 20–100 second periods are a permanent feature of the solar wind-earth interaction. The transverse component of the waves is typically several gammas in amplitude in 4–8 gamma fields. The disturbance vector in the XY plane generally exhibits the same sense of rotation in a coordinate system where the field is oriented along the positive z axis. Attenuation of wave amplitudes with distance from the bow shock is estimated to be only a factor of 2 when the spacecraft is 15 RE from the bow shock. The absence of waves at particular field orientations, even though the field line intersects the shock, is interpreted as a propagation effect. This observation is the basis for calculations that yield an average velocity in the plasma frame of 2.7 ± 0.4 times the solar wind velocity. Whistler propagation and local generation by two-stream instability are discussed as alternate theoretical explanations for the presence of the waves. It is suggested that the data favor the latter mechanism.

Influence of Reflected Shock and Boundary‐Layer Interaction on Shock‐Tube Flows

Abstract: During the last decade the study of the interaction between normal shocks and boundary layers in the shock tube has been carried out by many research workers. This interest has been fostered by the requirement to understand the effects that this phenomenon may have on the flow properties in the region between the reflected shock and the end of the tube. This so‐called reflected shock region is important in chemical kinetics studies and as a reservoir of gas for hypersonic shock tunnels. In this paper a review is given of the various analyses of the problem together with the results of experimental studies. Reflected and transmitted shock bifurcation, the rate of growth of the bifurcated foot, and the effects of transition to turbulence are discussed. The influence of bifurcation on the flow in the shock tube is assessed, especially as a mechanism for transporting cold driver gas to the end plate, causing early cooling of the gas on the reflected shock region.

The interaction of shock waves and heat addition in the design of supersonic combustors

Abstract: Analytical models are needed that will permit the prediction of thrust efficiency of a supersonic combustor as a function of combustor geometry and heat release. An earlier, more general procedure for the one-dimensional analysis of supersonic combustors was developed on the basis of exponential pressure-area dependence. This paper extends that analysis by establishing three regimes for specific pseudo-one-dimensional solutions for thrust efficiency: (1) a low-heat-release regime in which the flow can be considered essentially shock-free; (2) an intermediate regime in which an oblique shock wave is sustained with a pressure ratio equal to or greater than that required for turbulent boundary-layer separation; and (3) a high-heat-release regime in which the combustion is preceded by a normal shock. The key to solution is the formulation for the wall-pressure force needed for the momentum equation. With it, a set of integral equations can be solved simultaneously for relationships between pressure ratio, total temperature ratio and area ratio across the combustor in the three regimes. It is argued that the most probable solutions are those that yield the lowest back pressure without violating the entropy limit (second law of thermodynamics). It is shown that such limiting processes, including shock waves, can yield higher over-all efficiencies than shock-free solutions, because the total pressure loss across the shock is more than compensated by the reduction in total pressure loss due to heat addition, which occurs at a lower Mach number. Results of a typical substantiating experiment falling in this class are presented, for a combustor-inlet Mach number of 3.2 and an alkyl borane fuel.

Theory of Laminar Viscous-Inviscid Interactions in Supersonic Flow

Abstract: This investigation is concerned with those fluid-mechanical problems in which the pressure distribution is determined by the interaction between an external, supersonic inviscid flow and an inner, laminar viscous layer. The boundary-layer approximations are assumed to remain valid throughout the viscous region, and the integral or moment method of Lees and Reeves, extended to include flows with heat transfer; is used in the analysis. The general features of interacting flows are established, including the important distinctions between subcritical and supercritical viscous layers. The eigensolution representing self-induced boundary-layer flow along a semi-infinite flat plate is determined, and a consistent set of departure conditions is derived for determining solutions to interactions caused by external disturbances. Complete viscous-inviscid interactions are discussed in detail, with emphasis on methods of solution for both subcritical and supercritical flows. The method is also shown to be capable of predicting the laminar flow field in the near wake of blunt bodies. Results of the present theory are shown to be in good agreement with the measurements of Lewis for boundary-layer separation in adiabatic and non-adiabatic compression corners, and with the near-wake experiments of Dewey and McCarthy for adiabatic flow over a circular cylinder. Extensions of the method to flows with mass injection at the surface and to subsonic interactions are indicated.

Diffraction of a Shock Wave by a Cylinder

Abstract: The propagation of plane shock waves around cylinders of various radii was recorded with shadowgrams using a Cranz‐Schardin multiple spark camera and with single Mach‐Zehnder interferograms. The range of the incident shock Mach numbers extends from 1.04 to 2.2. Regular reflection and transition to Mach reflection are seen as the incident shock proceeds. From shadowgrams made at about 1 μsec intervals during this process the critical angle of transition was measured. The limiting angle of two shock theory fails to agree with the measured value. A theory of Whitham which requires the critical angle as well as the incident shock Mach number as initial values was applied to predict the triple point locus and the contour of the Mach stems. Numerical calculations using both the theoretical and the measured value of the critical angle for a fixed shock Mach number produced triple point loci lying close together. The predicted contour of the Mach stem and the density jump across it agree with the observations to ...

Molecular Velocity Distribution Function Measurements in a Normal Shock Wave

Abstract: Molecular velocity distribution functions have been measured throughout a normal, M = 1.59 helium shock wave that was formed in a low‐density wind tunnel. The measurements were obtained by using the electron beam fluorescence technique. Throughout the shock transition, distributions of random velocities were observed from directions both parallel and perpendicular to the flow. Also, direct measurements were made of the density and the flow velocity. The shock wave satisfied the continuity, momentum, and energy equations within the accuracy of the measurements. Parallel and perpendicular temperatures compare favorably to predictions derived from the Navier‐Stokes equations. In the upstream portion of the shock the distributions of parallel peculiar molecular velocities predicted according to the Chapman‐Enskog first iterate differ significantly from the experimental results, although as mentioned the second moments or temperatures agree with the Navier‐Stokes values.

Compressor for handling gases at velocities exceeding a sonic value

Abstract: In the fan portion of a turbofan engine, rotor blades comprise a primary cambered airfoil and an auxiliary airfoil. Where air flow exceeds a sonic velocity relative to the blades, the throat section between adjacent blades positions the normal air shock wave on the auxiliary airfoil. Each auxiliary airfoil forms a nozzle in combination with the pressure surface of its adjacent primary airfoil. This minimizes energy losses normally associated with such normal shock waves riding on the suction surfaces of cambered airfoils in regions of relatively thick boundary layer air. Lateral struts projecting from the primary airfoil, and used to position the auxiliary airfoil, create oblique shock waves which weaken the normal shock wave and minimize energy losses associated with a normal shock wave''s effect of distributing boundary layer air on an airfoil surface. These features are also effective in reducing the generation of noise.

Interpretation of pressure measurements behind the reflected shock in a rectangular shock tube.

Abstract: value of L/H = 10 to 12 as the value at which the type of cavity flow changes. Figure 5 indicates that much higher heating rates exist on the cavity floor for closed cavity flow, due to the reattachment region and increased heating in the downstream compression corner. (Note the similarity of heating distribution for L/H = 15 and 30 downstream corners with Fig. 1 for forward-facing steps.) The open cavity flow condition is seen to have relatively low heating rates (h/hQ < 0.5) over two-thirds of the floor, increasing to the order of attached flow heating near the downstream end. Similar heating distributions were obtained by Charwat et al. and Emery et al. for open cavity flow at Me = 2,9.

Method and structure for reduction of shock waves

Abstract: A method of and apparatus for reducing shock waves created by solid bodies having supersonic speed relative to a gas, and reducing and even eliminating the sonic boom which accompanies the shock waves. The nose or leading portion of the moving body, be it a body of revolution, or an airfoil lifting body, or be it another moving body, is provided with blunt configuration at its leading portion to create a detached ''''normal'''' shock wave. A three-step thermodynamic cycle is applied to the gas (i.e., air) flow surrounding the moving body. The three steps are (1) compression of the gas, caused by the moving body, (2) heating of the compressed gas by addition of heat, and (3) expansion of the compressed gas to hear its original pressure. In air, for example, a blunt nose flying body at supersonic speeds creates a high compression zone (stagnation zone) between the shock wave and the nose of the body. Heat is applied, e.g., by burning fuel, electricity, or nuclear radiation, to the stagnation zone of high pressure, resulting in a substantial decrease of static pressure immediately in front of the blunt nose. The heat can be applied to the compressed air zone from forwardly projecting structures suitably shaped to create only low intensity shock waves. The applied heat decreases the static pressure at the nose zone, in turn decreasing the high air drag, and also decreasing the intensity of the shock wave ahead of the flying body, thereby decreasing the intensity of the part of the shock wave which reaches the ground, resulting in a reduction in sonic boom.

Investigations of the Aerodynamic Characteristics of the Shock Tubes : (Part 2,On the Formation of Shock Waves)

Abstract: To explain the mechanism of the shock formation in a simple shock tube, the multi-stage model was presented, which improved White's theory, and some numerical calculations were carried out. Simple and White's theories correspond respectively to the case of zero or one stage of the present multi-stage model. The shock Mach number calculated by the multi-stage model is always larger than that obtained by the White's model. The difference between them becomes large as the diaphragm pressure ratio increases. Further in order to express the variation of the shock Mach number along the tube a function II (x) was proposed. By using this function, the phenomenon that shocks stronger than that predicted by the simple theory would possibly happen was discussed.

Laboratory study of turbulence in collision-free shocks.

Abstract: In an earlier paper the authors describe a plasma wind tunnel that produces a steady collision‐free flow. A shock wave standing in front of a magnetic obstacle was produced in this flow. The changes in magnitude and direction of the magnetic field across the shock wave were found to be in agreement with values predicted using the magnetohydrodynamic Rankine‐Hugoniot relations. This work has been extended using electric field measurements to determine the over‐all flow patterns. The electron density has been measured with a laser interferometer, and the density ratio across the shock wave has been found to be consistent with the shock wave equations. The power spectra of the magnetic and electric fluctuations have been measured. These fluctuations are consistent with whistler waves standing in the shock front. The power spectrum shows large variations with position in the shock with the highest frequencies appearing near the toe of the shock wave. The amplitude and frequency variation of the power spectrum is quite similar to space data where the latter is available. The electric field fluctuations are found to be proportional to the magnetic fluctuations with a proportionality constant equal to the flow velocity. The absolute magnitude of the magnetic turbulence is too low to absorb all of the dissipation required for the shock wave and a simple model using wave‐particle interactions is suggested.

The diffraction accompanying the regular reflexion of a plane obliquely impinging shock wave from the walls of an obtuse wedge

Abstract: The diffraction problem of a plane shock wave at the apex of an obtuse wedge treated by Lighthill (1950) is extended by assuming that the shock wave strikes the walls of the obtuse wedge at some finite oblique angle of incidence (not exceeding the critical angle). Transformations similar to that performed in the above-mentioned paper lead to a non-symmetrical boundary-value problem for an analytic function of a complex variable having a non-homogeneity in the form of a delta-function. It was found possible to extend, for the case considered, the method developed by Lighthill and construct the solution in almost as simple a form as given in the above-mentioned paper. The case of three-dimensional stationary flow is considered when the line of reflexion makes a finite angle with the edge of the wedge.

Initial propagation of impulsively generated converging cylindrical and spherical shock waves

Abstract: An analytical description for the initial phases of collapse of a spherical or cylindrical shock wave in a perfect gas is given in the present paper. The shock wave is initiated by the instantaneous and uniform deposition of a finite quantity of energy per unit surface area at a finite radius R0. For the initial shock motion where xs = (Rs - R0)/R0 is small, analytical solutions are obtained by a power-series expansion of the dependent variables in xs. The classical self-similar solution for a strong planar blast wave is recovered as the present zero-order solution. Non-similar effects arising from both finite shock strengths and the presence of a characteristic length R0 are accounted for simultaneously in the present perturbation scheme. The analysis is carried out up to third order in xs. For very large values of the initiation energy where the shock wave remains strong throughout its collapse, it is found that the present perturbation solution can adequately describe a significant portion of the collapse processes. The solution indicates that the shock decays rather rapidly initially and later begins to accelerate as a result of the additional adiabatic compression of the shocked states due to flow-area convergence. However, for weak initiation where the energy released is small, the present perturbation solution is an asymptotic series and diverges very rapidly as the shock propagates away from the wall. The range of validity then is limited to very small values of xs.

A closed-form solution to oblique shock-wave properties.

Abstract: Oblique shock wave properties with free stream Mach number and flow deflection angle as independent variables, noting explicit solution

Optimal shapes of bodies with attached shock waves

Abstract: We consider the problem of finding the shape of two-dimensional and axisymmetric bodies having minimal wave drag in a supersonic perfect gas flow. The solution is sought among bodies having attached shock waves. The limitations on the body contour are arbitrary: these constraints may be body dimensions, volume, area, etc. Such problems with arbitrary isoperimetric conditions may be solved by the method suggested in [1, 2]. This method involves the use of the exact equations of gasdynamics which describe the flow as additional constraints. This method was developed further in [3–6] in the solution of several problems.

Expansion and thermalization processes of plasma flow on the bsg-ii device.

Abstract: The expansion process of a collision-dominated theta-pinch plasma in a homogeneous magnetic channel and the thermalization process of the kinetic energy of this plasma flow by a magnetic mirror field are studied on the BSG-II device. Previously it was reported that shock phenomena due to a mirror field were observed by several methods of measurement. In this paper four experimental results are presented: (1) the expansion of plasma along the homogeneous magnetic channel is adiabatic; it is well described by a model for one-dimensional isentropic flow of collision-dominated plasma; (2) the flow is supersonic and the occurrence of a shock in front of the mirror field is in accordance with a criterion concerning the supersonic-sonic transition of plasma flow; (3) the rate of plasma loss through the mirror field is reduced by the occurrence of the shock; (4) the values of the plasma parameters measured before and behind the shock front satisfy the Rankine-Hugoniot relations, though plasma pressure, flow velocity and Mach number are time-dependent.

Oblique hydromagnetic shock waves.

Abstract: An experiment is described in which shock waves are propagated in a magnetized hydrogen plasma with Alfven Mach numbers up to M{sub A} = 5 and at angles a to the magnetic field from 90 Degree-Sign to 40 Degree-Sign . The plasma of density {approx}5 x 10{sup 14} cm{sup 3} and temperature {approx}1 eV is created in a pyrex chamber of 45 cm diameter and 93 cm length by means of an oscillatory z -discharge. The initial magnetic field is 500-1000 G. A curved magnetic piston is driven into the plasma by exciting a rapidly rising {theta} -current in a single-turn loop of short axial length arranged round the tube on its midplane. A curved shock front propagates ahead of the piston in the manner of a bow wave. Magnetic and electric probes are used to study the development and structure of the shock front. On the midplane the front has the monotonie field jump typical of propagation perpendicular to the field, but for propagation at an angle to the field a radically different structure is seen. Ahead of the main jump in field and density there is a large-amplitude, circularly polarized oscillation which is identified as a highfrequency Alfven ('whistler') wave propagating at the same speed as the shock. The wavelength {lambda} is given by {lambda} Almost-Equal-To (2{pi} cos{alpha})/(M2{sup 2}{sub A}-1){sup Vulgar-Fraction-One-Half} * (c)/{omega}{sub pi}. The results are compared with numerical computations of shock structure using hydromagnetic equations. To account for the observed structure, it is necessary to invoke collisionless effects. (author)

Flow perturbations generated by a shock wave interacting with an entropy wave

Abstract: Numerical results for perturbed downstream flow field resulting from entropy wave interaction with normal shock and oblique shock generated by wedge flow

Determination of the shock wave parameters in materials preserved in cylindrical bombs

Abstract: 1. It has been found that in cylinders of inert materials arranged along the axis of the charge, the detonation waves of cylindrical charges excite conical shock waves with the formation of a head wave. 2. It has been shown that head waves occur in solid, liquid, and porous substances. 3. It has been established that the propagation velocity of the triple-shock configuration is equal to the detonation velocity of the explosive charge employed. This makes it possible to estimate the shock wave parameters in substances whose shock adiabats are known.

Magnetohydrodynamic shock waves in non-aligned flow.

Abstract: Steady shock discontinuity in perfectly conducting gas flow in arbitrarily oriented magnetic field for various Mach numbers

Turbulent shear layer reattachment downstream of a backward-facing step in confined supersonic axisymmetric flow

Abstract: The reattachment of a supersonic jet with a turbulent boundary layer abruptly expanding into an axisymmetric parallel diffuser has been experimentally investigated using a surface-flow technique. Measurements were made in the started condition, where the blowing pressure is sufficiently high to establish an oblique shock system in the diffuser. The proposed reattachment criterion correlates present measurements in terms of the diffuser area ratio, and also those of other workers for unconfined flow in terms of the free stream Mach number after separation. As already reported for unconfined flow, it is found that disturbances downstream of reattachment do not affect the upstream region.

Effects of oblique shock waves in the near field of rocket plumes

Abstract: Rocket nozzle originated oblique shock waves effect on near-field plume inpingement flows, heat transfer and pressure distribution

Shock-wave shapes on hypersonic axisymmetric power-law bodies

Abstract: Shock wave shapes over axisymmetric power law bodies in hypersonic flow, noting asymptotic flow theory implications

Structure of Strong Shock Waves

Abstract: A model is proposed for the structure of strong shock waves which explicitly accounts for the existence of a near molecular beam, hypersonic flow upstream, and of a subsonic, hot continuum flow downstream. This is accomplished by considering the conversion of the beam into the continuum through collisions. Appropriate continuum equations are derived including the input of mass, momentum, and energy from the beam particles. The particles in the molecular beam are assumed to be converted into members of the continuum in a single collision; and the collision transport phenomena associated with the continuum are assumed to be governed by the Chapman‐Enskog expressions. Comparisons with other models for shock structure and with experimental results are given. In view of its simplicity the present model should be applicable to other hypersonic, rarefied flow problems.

Flow Field behind a Shock Wave in a Low‐Pressure Test Gas

Abstract: A study is made of the two‐dimensional flow field resulting from boundary‐layer growth in the driven gas of a shock tube. Attention is given to circular as well as to rectangular shock tubes. Formulas that describe the axial and transverse velocity components near the shock front are developed and are evaluated numerically. The properties of the two‐dimensional flow field are discussed. It is found that the flow is nearly one‐dimensional at distances greater than a tube radius from the shock front. In the region near the shock front, averaging of the perturbations gives results identical to those of Mirels' quasi‐one‐dimensional theory. An approximate description of the entire flow field can be obtained by taking the average velocity provided by Mirels' theory, and by superimposing the two‐dimensional flow pattern stretched axially so as to conform to the prescribed average. The details of the flow field provided in the present paper can, therefore, be considered a complement to Mirels' work.

Interaction of an Advancing Shock Front with a Concentrated Heat (Entropy) Source

Abstract: The results of an experimental investigation conducted in a shock tube on the interaction of a reflected normal shock front with a two‐dimensional highly heated thin gaseous filament are reported. The heated gaseous filament was created at a predetermined time either by exploding a fine gauge copper wire or by an arc discharge between two thin needle electrodes in the drift flow of the incident shock wave. The transient interaction phenomena were recorded systematically by spark interferometric and schlieren techniques. These data revealed that; (a) A cylindrical band of acoustic waves centered on the transmitted (interacted) heated filament is generated behind the reflected shock front. On the basis of the analysis of the interferometric data, the leading acoustic wave front was found to have an alternate compression‐rarefaction type of density distribution along its circumference. (b) Owing to its passage through the heated filament, the reflected normal shock becomes distorted. (c) The interacted heated gaseous filament split into two vortexlike flow regions.