Showing papers on "Oblique shock published in 1971"
01 Jan 1971
TL;DR: In this paper, a modified Lax-Wendroff difference technique was used to detect shock wave interaction with laminar boundary layer on flat plate using modified Lazy Lazy Wasserstein difference technique.
Abstract: Shock wave interaction with laminar boundary layer on flat plate using modified Lax-Wendroff difference technique
409 citations
TL;DR: In this paper, a theory for the production and propagation of the shock wave associated with the supersonic elements of the axial flow compressor is presented, showing that the strength and positions of these shock waves are sensitive to small blade-to-blade differences found in practical builds.
96 citations
TL;DR: For example, increases in low energy cosmic ray intensity at front of propagating interplanetary shock waves were observed in this paper, showing that the cosmic ray is more sensitive to the propagation of inter-planetary shocks.
Abstract: Increases in low energy cosmic ray intensity at front of propagating interplanetary shock waves
83 citations
TL;DR: In this article, four anomalous Earth's bow shock locations observed during 1969 are studied, using plasma and magnetic field data from the European satellite HEOS-1, using magnetohydrodynamic equations, making use of the magnetosonic Mach number of the solar wind.
80 citations
TL;DR: In this paper, the authors present a theory of double-structured shock waves, which possess a precursor 'foot' due to the reflection of ions from a resistive shock front.
Abstract: This paper presents a theory of double-structured shock waves, which possess a precursor `foot' due to the reflection of ions from a resistive shock front. It is an extension of an earlier study by the author. Above a critical Alfven-Mach number MA the reflected ions generate a streaming instability with the electrons that results in the flow of a transverse electric current and a change in the magnetic field well ahead of the resistive front. The electrons in the foot are preheated by mixing with some hot downstream electrons that are assumed to be drawn forwards by the reflected ions. This model enables MA to be calculated as a function of β1, the upstream plasma beta. When a foot does develop, the theory enables its profile in magnetic field to be determined. The critical Alfven-Mach number MA at which the foot fully sumberges the resistive rise is also estimated, so that the upstream Alfven-Mach number MA1 of double-structured shocks satisfies doublehat-M. It is found that this range for MA1 narrows considerably with increasing β1; below doublehat-M is infinite. With doublehat-M, the shocks are fully developed ion reflecting shocks, with a thickness of order (c/ωpi), which is about the same as the length of the foot of the double-structured shocks. There is good agreement with the few available experimental results.
46 citations
TL;DR: In this article, a unified theory for supersonic and hypersonic flow with attached shock waves over the lower surface of a delta wing at an angle of attack is developed, where a linearized perturbation on a nonlinear flow field is first calculated and then strained and corrected so that the flow is matched continuously to the uniform flow.
Abstract: A unified theory is developed for supersonic and hypersonic flow with attached shock waves over the lower surface of a delta wing at an angle of attack. The flow field on the lower surface of a delta wing consists of uniform flow regions near the leading edges, where the cross flow is supersonic and a nonuniform flow region near the central part, where the cross flow is subsonic. In the nonuniform flow region, the theory is based on the assumption that the flow differs slightly from the corresponding two-dimensional flow over a flat plate. Thus a linearized perturbation on a nonlinear flow field is first calculated and then strained and corrected so that the flow is matched continuously to the uniform flow which is obtained exactly. When compared with available exact numerical solutions the theory gives, in all cases, almost identical results, except near the crossflow sonic line where existing numerical methods fail to produce a discontinuous slope in the pressure curve, whereas the present theory predicts such a discontinuity and shows that the slope has a square root singularity at the crossflow sonic line similar to that in the supersonic linear theory.
38 citations
TL;DR: In this article, the authors considered two instability mechanisms which could occur under the conditions found in a perpendicular collisionless shock wave and considered the effect of the voltage jump through the shock, and the density and magnetic field gradients at the shock front.
Abstract: Two instability mechanisms which could occur under the conditions found in a perpendicular collisionless shock wave are considered. Both mechanisms are due to the negative energy character of the electron Bernstein waves propagating in the direction of the current flow in the shock. The effect of the voltage jump through the shock, and the density and magnetic field gradients at the shock front are considered. Both instability mechanisms occur only within a definite band of k values. The first mechanism is due to a resonance between the ion acoustic wave and one of the Bernstein harmonics and the second to resonant ions absorbing energy from a negative energy Bernstein mode. The first case requires Te≫Ti whereas the second case can occur for arbitrary values of the ratio Ti/Te, although the maximum effect occurs when this ratio is of order unity.
37 citations
TL;DR: In this paper, the diffraction of a shock of arbitrary strength by a plane interface separating two different fluids was calculated for the general case, and it was shown that for later times, the shock shape becomes tangent to the interface with decreasing strength there.
34 citations
TL;DR: Plate excitation by supersonic turbulent and shock boundary layers, measuring wall pressure fluctuation and panel displacement as mentioned in this paper, was used to measure wall pressure fluctuations and panel displacements.
29 citations
TL;DR: In this paper, the authors derived a differential equation relating the strain and strain gradient behind the wave when the region ahead is unstrained and at constant entropy, and used this equation to give conditions under which the wave will grow or decay at a given time.
27 citations
28 Mar 1971
TL;DR: In this paper, a numerical technique is presented for the calculation of steady inviscid transonic flows in turbomachinery cascades, wherein both subsonic and supersonic regions co-exist.
Abstract: A numerical technique is presented for the calculation of steady inviscid transonic flows in turbomachinery cascades, wherein both subsonic and supersonic regions co-exist. The problem is posed in the time-dependent form and the aysmptotic solution at large times provides the solution of the steady physical problems. The solutions for a hyperbolic nozzle cascade and two turbine cascades are compared with other analytical solutions and with an experimental result. The agreement appears to be very good. Some preliminary results are presented for a flow containing an oblique shock and its reflection. The computed results compare satisfactorily with the exact solution.Copyright © 1971 by ASME
TL;DR: Viscous slipstream flow downstream of triple shock wave intersection in supersonic diffuser air flow, using Pitot and static pressure probe measurements as discussed by the authors, using PPP measurements.
Abstract: Viscous slipstream flow downstream of triple shock wave intersection in supersonic diffuser air flow, using Pitot and static pressure probe measurements
TL;DR: In this article, the transient situation which follows when a plane normal shock wave is reflected (from a coplanar wall) into its own relaxation zone is examined theoretically, and approximate inner and outer solutions for the wall-pressure history are employed to establish the timewise variations in the thermodynamic state of the gas adjacent to the wall.
Abstract: The transient situation which follows when a plane normal shock wave is reflected (from a coplanar wall) into its own relaxation zone is examined theoretically. Approximate inner and outer solutions for the wall-pressure history are employed to establish the timewise variations in the thermodynamic state of the gas adjacent to the wall. Results for chemically relaxing O2 and vibrationally relaxing CO2 are compared with previous numerical solutions based on the method of characteristics, and the agreement is found to be excellent. The approximate technique is simple and requires only a minimum of computing time.
TL;DR: In this paper, the authors studied the Mach reflection of shock waves from a wedge under conditions in which the physical and chemical transformations in the gas heated by the shock wave play a significant role.
Abstract: The Mach reflection of shock waves in those cases in which the gas ideality condition is satisfied with high accuracy is well-known. The effects associated with the excitation of the internal degrees of freedom for the molecules lead to a qualitative change in the reflection pattern. The present study is an extension of [1, 2], devoted to the study of the Mach reflection of shock waves from a wedge under conditions in which the physical and chemical transformations in the gas heated by the shock wave play a significant role.
01 Apr 1971
TL;DR: In this paper, an experimental study was made of the interaction of an oblique shock with the bow shock of the blunt leading edge, and the interactions were classified according to the interference patterns described by Edney.
Abstract: : An experimental study was made of the interaction of an oblique shock with the bow shock of blunt leading edge. The interactions were classified according to the interference patterns described by Edney. Peak heating rates 5.5 times those of the blunt leading edge alone were studied. All interactions appeared to be unsteady except when the slipstream of the interaction passed above the blunt leading edge. (Author)
TL;DR: In this article, the reflection of a finite elastic plane shock wave at a plane boundary is examined and a semi-inverse method of solution is used, where only angles of incidence which are less than a critical angle are considered in detail.
TL;DR: The situation which arises from the regular reflection of a curved shock from a straight rigid boundary is analyzed in this article, where the relation between the curvatures of the incident shock and reflected shock has been derived.
Abstract: The situation which arises from the regular reflection of a curved shock from a straight rigid boundary is analyzed. In particular, the relation between the curvatures of the incident shock and reflected shock has been derived. The nature of the curvature of the reflected shock has also been analyzed.
TL;DR: In this paper, a difference scheme of second-order accuracy for axially symmetric flows containing shock waves was described, and applied to the interaction of a shock wave with the end of a cylinder moving at supersonic speed.
Abstract: We describe a difference scheme of second-order accuracy for calculating axially symmetric flows containing shock waves, and we apply our computational results to the interaction of a shock wave with the end of a cylinder moving at supersonic speed.
TL;DR: In this paper, an equation for magnetogasdynamic shock polar, given in terms of magnetic induction polar variables (i.e., the magnet induction polar), is obtained, and the evolutionary and entropy non-decrease conditions are assumed to admit immediate geometrical interpretation.
Abstract: An equation for magnetogasdynamic shock polar, given in terms of magnetic induction polar variables (i.e. the magnetic induction polar), is obtained. Evolutionary and entropy non-decrease conditions, given in terms of these polar variables, assume a very simple form, and admit immediate geometrical interpretation. It is found that this magnetic induction polar is far more natural and convenient to use than the shock polar given in terms of conventional velocity polar variables.
TL;DR: In this paper, the effect of thermal radiation on the structure of normal shock waves in gas-particle flows is analyzed, restricted to conditions at which the gas flow can be decoupled from the particle flow and where the gas contribution to radiation is negligible.
Abstract: The effect of thermal radiation on the structure of normal shock waves in gas-particle flows is analyzed. The study is restricted to conditions at which the gas flow can be decoupled from the particle flow and where the gas contribution to radiation is negligible. An approximate closed-form solution, derived for a gray, absorbing particle cloud, demonstrates that, within the limits of the analysis and for a given shock Mach number, radiative influences increase with increasing stagnation temperature and particle diameter and decreasing pressure and particle loading. The radiation-affected regions were found to extend large distances upstream of the gas phase discontinuity. Results from numerical calculations are in substantial agreement with those of the approximate theory. Decreasing the shock Mach number, at constant pressure, stagnation temperature, particle loading, and particle diameter, increased the fraction of the particle temperature rise across the shock occurring upstream of the gas phase discontinuity. Nomenclature
TL;DR: In this paper, an axisymmetric blunt body or a symmetric profile is located in a uniform supersonic combustible gas mixture stream with the parameters M1, p1, and T1.
Abstract: Assume an axisymmetric blunt body or a symmetric profile is located in a uniform supersonic combustible gas mixture stream with the parameters M1, p1, and T1. A detached shock is formed ahead of the body and the mixture passing through the, shock is subjected to compression and heating. Various flow regimes behind the shock wave may be realized, depending on the freestream conditions. For low velocities, temperatures, or pressures in the free stream, the mixture heating may not be sufficient for its ignition, and the usual adiabatic flow about the body will take place. In the other limiting case the temperature behind the adiabatic shock and the degree of gas compression in the shock are so great that the mixture ignites instantaneously and burns directly behind the shock wave in an infinitesimally thin zone, i. e., a detonation wave is formed. The intermediate case corresponds to the regime in which the width of the reaction zone is comparable with the characteristic linear dimension of the problem, for example, the radius of curvature of the body at the stagnation point.
01 Jan 1971
TL;DR: In this article, the problem of interaction of an inhomogeneity frozen into the solar wind with the bow shock has been investigated, and five linearly independent types of frozen-in inhomogeneities have been investigated.
Abstract: The problem of interaction of an inhomogeneity frozen into the solar wind with the bow shock has been investigated. These frozen‐in tangential discontinuities produce ripples that move along the shock, ripples that can cause magnetosonic waves in the downstream medium. There are five linearly independent types of frozen‐in inhomogeneities. Of the five inhomogeneities, those involving changes in the magnitude of density or velocity produce magnetosonic waves of largest amplitude. Other inhomogeneities are substantially less effective in producing magnetosonic waves in the magnetosheath. For normal solar wind parameters, a 10% density inhomogeneity upstream typically produces a magnetosonic wave with |δB| = 0.03 Bs where Bsis the field strength in the magnetosheath. A 30° fluctuation in magnetic field direction upstream typically produces a magnetosonic wave downstream with magnetic amplitude ≃ 10−3 Bs. However, for certain angles between the upstream magnetic field and the shock, the efficiency of conversi...
TL;DR: In this paper, the generation of acoustic waves during the interaction of a reflected normal shock front generated in a shock tube, and a two-dimensional highly heated turbulent fluid element are reported.
Abstract: The generation of acoustic waves during the interaction of a reflected normal shock front generated in a shock tube, and a two‐dimensional highly heated turbulent fluid element are reported. The heated gaseous element was created at a predetermined time by exploding a fine‐gauge copper wire in the drift flow of the incident shock wave. The transient interaction phenomena were systematically recorded using both μsec spark schlieren and interferometric photographs, as well as a high‐speed framing camera in conjunction with an interferometer and schlieren optical system. These data revealed that (1) a cylindrical progressive band of acoustic waves centered on the transmitted heated element is generated behind the reflected shock front. The leading edge of the acoustic‐wave front was found to have an alternate compression‐rarefraction type of density distribution along its circumference. (2) The reflected normal shock wave is distorted during its passage through the heated element. (3) The dynamic behavior of the heated element is radically altered. The density amplitude distribution through the acoustic‐wave system is shown to be in general agreement with the analytical predictions of Chisnell [Proc. R. Soc. Lond. 232, 350(1955)], which were based upon shock‐contact surface interaction theory.
TL;DR: In this paper, an experimental study was made of the shock wave projected into free water from the end of a hydrodynamic conical shock tube driven by a high explosive, which was made with small piezoelectric and piezoresistive gauges arrayed about two different shock tube configurations.
Abstract: An experimental study was made of the shock wave projected into free water from the end of a hydrodynamic conical shock tube driven by a high explosive. Pressure‐time measurements were made with small piezoelectric and piezoresistive gauges arrayed about two different shock tube configurations. For one tube, designed on a very small scale, results showed that a remnant of the sector shock front propagated undisturbed over the length of the water tank (20 cone lengths). This was demonstrated by the fact that attenuation with distance along the extended cone axis closely approximated the accepted relationship P ∝ R−1.13 for explosion shock waves in free water. On‐axis data for the other tube whose shock wave energy was three orders of magnitude greater than the first, showed very rapid attenuation beyond the cone mouth. Both cone results are consistent with existing theory that defines the undisturbed shock front region in terms of cone parameters—length, angle, and amount of explosive—that affect shock energy and geometry. Results for the first cone on attenuation of pressure with angle to the axis also were consistent with the predicted angular extent of the undisturbed front region. At 30°, attenuation was about 75%.