Mach Line Research Articles

Gradient Technique Theory: Tracing Magnetic Field and Obtaining Magnetic Field Strength

The gradient technique is a promising tool with theoretical foundations based on the fundamental properties of MHD turbulence and turbulent reconnection. Its various incarnations use spectroscopic, synchrotron, and intensity data to trace the magnetic field and measure the media magnetization in terms of Alfvén Mach number. We provide an analytical theory of gradient measurements and quantify the effects of averaging gradients along the line of sight and over the plane of the sky. We derive analytical expressions that relate the properties of gradient distribution with the Alfvén Mach number M A. We show that these measurements can be combined with measures of sonic Mach number or line broadening to obtain the magnetic field strength. The corresponding technique has advantages to the Davis–Chandrasekhar–Fermi way of obtaining the magnetic field strength.

Applicability analysis of inverse method of characteristics

The inverse method of characteristics (iMoC) is often employed to simulate the axisymmetric flow behind a predefined shock wave shape. Firstly, two marching schemes of iMoC were compared in this work: the intersection of the left- and right-running Mach lines and the intersection of the left-running Mach line and streamline. The intersection of the left-running Mach line and streamline is discovered to be simpler and more stable. Following that, the applicability of iMoC was analyzed by dividing the shock wave shapes into concave and convex curves, respectively. Based on the oblique shock relations, it is proved mathematically that iMoC is capable of computing the flow behind a concave shock wave. However, for the convex shock wave, if the shock wave angle declines too much along the axial coordinate, the clusters of left-running Mach lines may intersect, leading to iMoC failure. Furthermore, a method for enabling the implementation of iMoC is proposed by generating an expansion fan to replace the infeasible segment of the convex shock wave. Finally, computational fluid dynamics techniques were applied to validate the proposed methods and analysis. This study provides theoretical support to promote the application of iMoC in waverider and inward inlet design.

Refraction of Oblique Shock Wave on a Tangential Discontinuity

The refraction of an oblique shock wave on a tangential discontinuity dividing two gas flows with different properties is considered. It is shown that its partial reflection occurs with the exception of the geometrical diffraction of an oblique shock. Another oblique shock, expansion wave or weak discontinuity that coincides with the Mach line can act as a reflected disturbance. This study focuses on the relationships that define the type of reflected discontinuity and its parameters. The domains of shock wave configurations with various types of reflected discontinuities, including characteristic refraction and refraction patterns with a reflected shock and a reflected rarefaction wave, are analyzed. The domains of existence of various shock wave structures with two types of reflected disturbance, and the boundaries between them, are defined. The domains of parameters with one or two solutions exist for the characteristic refraction. Each domain is mapped by the type of refraction with regard to the Mach number, the ratio of the specific heat capacities of the two flows and the intensity of a refracted oblique shock wave. The conditions of the regular refraction and the Mach refraction are formulated, and the boundaries between the two refraction types are defined for various types of gases. Refraction phenomena in various engineering problems (hydrocarbon gaseous fuel and its combustion products, diatomic gas, fuel mixture of oxygen and hydrogen, etc.) are discussed. The result can be applied to the modeling of the shock wave processes that occur in supersonic intakes and in rotating and stationary detonation engines. The solutions derived can be used by other researchers to check the quality of numerical methods and the correctness of experimental results.

Постановка экспериментов для анализа возмущений головной ударной волны за счет присутствия частиц в сверхзвуковом потоке

The research in the field of devices and methods of experimental physics includes, in particular, the creation of installations for conducting experiments in the physics of multiphase nonequilibrium flows. Multiphase flow around bodies is of significant importance in various fields of technology, for example, in power engineering, contact visualization methods, aerosol technologies, in the application of various coatings, etc. In the high-speed two-phase flow around bodies, the physics of particle collisions with the surface and the interaction of flying particles with the head shock wave play an important role. Most of the experiments in this area, including the passage of the model through the zone of rain, snow, dust, cooled clouds, etc., are carried out in the reverse setting. In this case, the model is fixed, and the flow is made by one or another high-enthalpy aerodynamic installation. This approach does not correspond to the initial stage of the interaction formed before the entrance to the zone of the two-phase medium, between the head shock and the incident particle. Nevertheless, for some approaches, it is of interest to visually confirm the possibility of an oncoming particle being ejected at a supersonic speed by the front of the head shock wave and to see the deceleration of the model from the shadow pattern with a change in the Mach line. The paper considers a direct ballistic experiment which by shadow visualization tests the possibility of cavern formation near a body crossing the trajectory of the atmosphere saturated with dust particles

GEOMETRY ANALYSIS OF SUPERSONIC FLOW AROUND TWO AXIALLY SYMMETRICAL BODIES USING THE DIGITAL IMAGE PROCESSING METHOD

The scientific paper covers the research of the geometric laws of the intersection of two angle shock waves formed upon supersonic flow with zero incidence of two bodies. The positions of shock waves engaging with the surfaces of the models of axially symmetrical bodies are determined. Systems of analysis and decision support are based on the involvement of photographs (video frames) processing results by the image intensity parameter. This method facilitates the identification of the shock wave angle with a higher rate of probability, and, therefore, the more precise definition of the engagement points of the shock wave with the researched surface. This paper analyses the video frames of the interaction of shock waves using the digital image processing method by the image intensity parameter, the formulas determining the intersection point of shock waves, that occur upon the supersonic motion of two axially symmetric bodies near each other, are determined. The positions of the point of contact of the outgoing shock wave with the surface of the second object were determined, factoring in the difference in the the incoming and outgoing shock wave angles. The availability of sufficient statistics allowed to identify theoretical relationships between the gas flow rate, the geometric parameters of objects, the distances between them, density, pressure and image intensity in photographs. The method of digital image processing can be applied to the analysis of shock waves during the flow around a supersonic stream of bodies with a "blunt" end. The shock wave front in this case is described by a secondorder curve, upon the analysis of which it is necessary to select a portion of this curve, replacing it with some accuracy by a straight line segment (Mach line).

Nonlinear unsteady streaks engendered by the interaction of free-stream vorticity with a compressible boundary layer

The nonlinear response of a compressible boundary layer to unsteady free-stream vortical fluctuations of the convected-gust type is investigated theoretically and numerically. The free-stream Mach number is assumed to be of $O(1)$ and the effects of compressibility, including aerodynamic heating and heat transfer at the wall, are taken into account. Attention is focused on low-frequency perturbations, which induce strong streamwise-elongated components of the boundary-layer disturbances, known as streaks or Klebanoff modes. The amplitude of the disturbances is intense enough for nonlinear interactions to occur within the boundary layer. The generation and nonlinear evolution of the streaks, which acquire an $O(1)$ magnitude, are described on a self-consistent and first-principle basis using the mathematical framework of the nonlinear unsteady compressible boundary-region equations, which are derived herein for the first time. The free-stream flow is studied by including the boundary-layer displacement effect and the solution is matched asymptotically with the boundary-layer flow. The nonlinear interactions inside the boundary layer drive an unsteady two-dimensional flow of acoustic nature in the outer inviscid region through the displacement effect. A close analogy with the flow over a thin oscillating airfoil is exploited to find analytical solutions. This analogy has been widely employed to investigate steady flows over boundary layers, but is considered herein for the first time for unsteady boundary layers. In the subsonic regime the perturbation is felt from the plate in all directions, while at supersonic speeds the disturbance only propagates within the dihedron defined by the Mach line. Numerical computations are performed for carefully chosen parameters that characterize three practical applications: turbomachinery systems, supersonic flight conditions and wind tunnel experiments. The results show that nonlinearity plays a marked stabilizing role on the velocity and temperature streaks, and this is found to be the case for low-disturbance environments such as flight conditions. Increasing the free-stream Mach number inhibits the kinematic fluctuations but enhances the thermal streaks, relative to the free-stream velocity and temperature respectively, and the overall effect of nonlinearity becomes weaker. An abrupt deviation of the nonlinear solution from the linear one is observed in the case pertaining to a supersonic wind tunnel. Large-amplitude thermal streaks and the strong abrupt stabilizing effect of nonlinearity are two new features of supersonic flows. The present study provides an accurate signature of nonlinear streaks in compressible boundary layers, which is indispensable for the secondary instability analysis of unsteady streaky boundary-layer flows.

Fully kinetic simulations of collisionless, mesothermal plasma emission: Macroscopic plume structure and microscopic electron characteristics

This paper presents a fully kinetic particle particle-in-cell simulation study on the emission of a collisionless plasma plume consisting of cold beam ions and thermal electrons. Results are presented for both the two-dimensional macroscopic plume structure and the microscopic electron kinetic characteristics. We find that the macroscopic plume structure exhibits several distinctive regions, including an undisturbed core region, an electron cooling expansion region, and an electron isothermal expansion region. The properties of each region are determined by microscopic electron kinetic characteristics. The division between the undisturbed region and the cooling expansion region approximately matches the Mach line generated at the edge of the emission surface, and that between the cooling expansion region and the isothermal expansion region approximately matches the potential well established in the beam. The interactions between electrons and the potential well lead to a new, near-equilibrium state different from the initial distribution for the electrons in the isothermal expansion region. The electron kinetic characteristics in the plume are also very anisotropic. As the electron expansion process is mostly non-equilibrium and anisotropic, the commonly used assumption that the electrons in a collisionless, mesothermal plasma plume may be treated as a single equilibrium fluid in general is not valid.

Dynamic sliding of frictionally held bimaterial interfaces subjected to impact shear loading

The fast frictional sliding along an incoherent interface of a bimaterial system composed of a Homalite and a steel plate is studied experimentally in a microsecond time-scale. The plates are held together by a static uniform compressive pre-stress while dynamic sliding is initiated by asymmetric impact. The full-field technique of dynamic photoelasticity is simultaneously used with a local technique of velocimetry based on laser interferometry. In the case where the impact loading is applied to the Homalite plate, a shear Mach line originates from a disturbance propagating along the interface supersonically with respect to the dilatational wave speed of Homalite and it crosses the P-wave front. The sliding starts well behind the P-wave front in Homalite and it propagates with a supershear speed with respect to Homalite. A fast interface wave and a wrinkle-like opening pulse (detachment wave) travelling along the interface are observed. When the impact loading is applied to the steel plate, the local sliding velocity measurement reveals that sliding initiates with the arrival of the P-wave front in the steel plate.

Particle Velocimetry and Photoelasticity Applied to the Study of Dynamic Sliding Along Frictionally-Held Bimaterial Interfaces: Techniques and Feasibility

A laser interferometry-based technique was developed to locally measure the in-plane components of particle velocity in dynamic experiments. This technique was applied in the experimental investigation of dynamic sliding along the incoherent (frictional) interface of a Homalite–steel bimaterial structure. The bimaterial specimen was subjected to uniform compressive stress and impact-induced shear loading. The evolution of the dynamic stress field was recorded by high-speed photography in conjunction with dynamic photoelasticity. The combination of the full-field technique of photoelasticity with the local technique of velocimetry was proven to be a very powerful tool in the investigation of dynamic sliding. A relatively broad loading wave with an eye-like structure emanated from the interface. The particle velocity measurements established that sliding started behind the eye-like fringe pattern. It propagated with supershear speed with respect to Homalite. A shear Mach line originating from the sliding tip is visible in the photoelastic images. A vertical particle velocity measurement revealed the existence of a wrinkle-like pulse traveling along the bimaterial interface. The wrinkle-like pulse followed the initial shear rupture tip and propagated at a specific subshear speed.

Interaction of Sound from Supersonic Jets with Nearby Structures

We numerically solve a model of sound generated in an ideally expanded two-dimensional supersonic (Mach 2) jet. Two configurations are considered: 1) a free jet and 2) an installed jet with a nearby array of flexible aircraft type panels. In the later case the panels vibrate in response to loading by sound from the jet, and the full coupling between the panels and the jet is simulated, accounting for panel response and radiation as well as the jet acoustics. We consider the long time behavior of the jet/panel system and present results for the flowfield and far-field pressure and the vibration of, and radiatlon from, the panels. The pressure within the jet changes from a nearly discrete spectrum peaked at a preferred frequency f * , which depends on properties of the jet, to a continuous spectrum as downstream distance increases. The far-field pressure is characterized by a highly directional beaming of sound with a spectral peak at f * within the Mach line and a lower-level breakup into small-scale structures away from the Mach line. We show that the location of the panels relative to the Mach line is critical in determining panel response. Panels located upstream of the Mach line are subject to a low-level continuous spectrum loading and exhibit a comparable response. In contrast, panels located within the Mach line are subject to a high-level loading due to the intense Mach wave radiation of sound peaked at f * and exhibit a comparable response. The panels radiate in a simil ion to the sound in the particular, the is a strong beaming of sound waves at frequency f * from the ex ted panels Mach-angle-from the bounding wall, indicating a significant effect of Mach wave radiation both interior spectral content in the supersonic regime.

Unsteady Aerodynamic Response Of Two-dimensional Subsonic And Supersonic Oscillating Cascades With Chordwise Displacement And Flexible Deformation

In this paper the double linearization theory applied to lightly loaded two-dimensional subsonic and supersonic cascades undergoing oscillation with chordwise displacement or flexible deformation is presented. Numerical computation based on this theory have been conducted to demonstrate parametric dependence of the unsteady aerodynamic work on blades. The translational oscillation can be destabilized by chordwise displacement for both subsonic and supersonic cascades. The contribution of chordwise displacement to the unsteady aerodynamic work is strongly dependent upon the phase difference between the chordwise and normal components of the blade motion. The unsteady aerodynamic work for flexible blade motion also is substantially influenced by steady loading. For the supersonic cascades, the effect of displacement of Mach line reflection points due to the chordwise blade motion gives a significant contribution to the unsteady aerodynamic force.

HOW THE MACH PHENOMENON AND SHAPE AFFECT THE RADIOGRAPHIC APPEARANCE OF SKELETAL STRUCTURES

The shape of skeletal structures and their position relative to the x‐ray beam have a considerable effect on their radiographic appearance. Depending on the thickness of the cortical or subchondral bone, skeletal structures display the characteristics of either homogeneous or compound lamellar structures. Convex homogeneous structures are associated with a negative Mach line, and concave homogeneous structures are associated with a positive Mach line. Convex compound lamellar structures are associated with a negative Mach band and visualization of the lamina (subchondral or cortical bone) is reduced. Concave compound lamellar structures are associated with a positive Mach band and visualization of the lamina is enhanced. The combined effect of Mach phenomenon, shape, and thickness enhances visualization of some skeletal surfaces and make others imperceptible. These principles are very useful to correctly identify complex skeletal structures and avoid misinterpretations.

THE MACH PHENOMENON

Mach bands are optical illusions produced by an extensive lateral inhibition network within the retina. They are seen on every radiograph. Both positive and negative Mach bands can be seen at a boundary, but only one type is usually seen at boundaries created by biological structures because of their shape. Convex structures are associated with a negative Mach line and concave structures are associated with a positive Mach line. Using this principle, the shape of unknown structures can be deduced and structures of known shape can be more accurately identified. Sometimes, Mach lines can be very prominent and be perceived as real structures. Ways to make the distinction between Mach lines and real opacities are described. Understanding the Mach phenomenon improves accuracy of radiographic interpretation.

Unsteady aerodynamic analysis of two-dimensional subsonic and supersonic cascades oscillating with chordwise displacement or nonrigid deformation.

This paper presents the double linearization theory applied to lightly loaded two-dimensional subsonic and supersonic cascades undergoing oscillation with chordwise displacement or nonrigid deformation. Numerical computation based on this theory has been conducted to study parametric dependence of unsteady aerodynamic work on blades. Chordwise displacement can be favorable or unfavorable for stabilizing the translational oscillation, depending upon the phase difference between the chordwise and normal components of the blade motion. For supersonic cascades, the effect of displacement of Mach line reflection points due to the chordwise blade motion gives significant contribution to unsteady aerodynamic forces. The unsteady aerodynamic work for nonrigid blade motion is also substantially influenced by steady loading.

Linearized Magnetogasdynamic Relaxing Flow over a Wedge in a Non‐Equilibrium Oncoming Stream

AbstractA linearized solution has been obtained for a steady, non‐equilibrium, magnetogasdynamic flow of a conducting fluid with infinite conductivity over a wedge where the oncoming flow is assumed to be in a non‐equilibrium state and the uniform magnetic field is aligned to the uniform fluid stream in the undisturbed state. The effects due to viscosity, heat conduction and diffusion have been neglected. The solution reduces to the previous result of Vincenti [13] for non‐magnetic case as a special case. It further reduces to the previous result of Clarke [2] for an equilibrium free stream. The variations of the velocity disturbance along the initial frozen Mach line and the pressure coefficient as well as relaxation parameter on the surface of the wedge have been studied. The pressure coefficient becomes negative under certain conditions.

4 二重露光ホログラフィー干渉計によるウォータージェットの可視化計測

Recently, water jet is intensively used in the mechanical engineering and medical application as well. However, the structure and movement of the high speed water jet itself are not clear cut yet.This paper is mainly concerned, by using double exposure holographic interferometry, with the structure and velocity decay of high speed water jet. Experiments were conducted In an Aqua-Jet-Cutter at injection pressure about 230MPa, and with a 0.25mm diameter nozzle. It is found that the water jet velocity is estimated by measuring the angle of the Mach line generated around the jet.

The appearance of liquid surfaces and layers in routine radiographs.

Image features in the radiograph produced by deformation of a liquid surface by surface tension and by the density gradient in a diffusion layer may present unexpected difficulty of interpretation. Such features have been analysed in model experiments, which have been reported earlier. The aim of the present investigation was to examine the occurrence and the clinical implications of corresponding phenomena in routine radiographs. In the human body liquid surfaces and diffusion layers can occur only in cavities, both normal and abnormal. A liquid surface tends to extend up a cavity wall to form a meniscoid or, if the cavity is small enough, a discoid. The liquid surface continues further up the wall as a liquid film. The shape of the meniscoid and the discoid varies with the shape and inclination of the wall. Most of the image features of interest are produced by rays that are tangential to a horizontal surface, a meniscoid, a discoid or a concave wall, any of which is visualized as an internal boundary with a light Mach line. When the wall is convex towards the cavity the meniscoid is saddle-shaped and an external boundary with a dark Mach line is produced. The horizontal part of a liquid surface can be touched only if it is at the same level as the focus of the roentgen tube. A liquid surface at any other level can be touched in its meniscoid only by rays that are not horizontal. It is reproduced as an internal boundary, slightly concave upwards; above this boundary the rest of the liquid surface is reproduced as a wedge field.(ABSTRACT TRUNCATED AT 250 WORDS)

Radiographic demonstration of a liquid surface bounded by a wet solid surface.

At the line of contact between a liquid surface and a bounding wet solid wall deformation of the surface is produced by surface tension, and this deformation gives rise to various features in the radiograph. For the interpretation of these image features a detailed analysis was performed by means of model experiments. Tubes and rods of methyl acrylate with different diameters and covered with wet sheets of porous paper were used. The tubes were partly filled with water. In some cases a rod was placed concentrically or eccentrically inside the tube. The shape of the image of the liquid surface in vertical and inclined models was examined by conventional radiographic technique and computed tomography. At the walls the surface tension resulted in formation of meniscoids. When the distance between solid walls was short enough adjacent meniscoids joined to form a discoid. The shape of the meniscoid and discoid varied with the shape and inclination of the walls. Distinct boundaries representative of the shape and position of the surface were produced only from those places where the beam was tangential to the surface. When the surface was concave towards the gas in the direction of the beam an internal boundary with a light Mach line was produced. When the surface was convex towards the gas in the direction of the beam an external boundary with a dark Mach line was produced. A boundary was straight when the surface was plane or was part of a cylindric surface. The seemingly simple form of the liquid surface gave rise to surprisingly complex boundary formations, which are analyzed in detail. The findings reported may have a variety of implications for the interpretation of clinical radiographs and may act as a key for the reconstruction of the structures reproduced.

Weak Nonlinear Shock Waves in Steady Two-Dimensional Flow of a Non-Equilibrium Gas along a Curved Wall

The behaviour of the characteristic solution in the neighbourhood of the first frozen Mach line is investigated for the two-dimensional steady supersonic flow of a non-equilibrium gas along a curved wall. We assume that the gas is in non-equilibrium with a finite reaction rate and various transport effects are negligible. It is found that when the wall is a continuous curved bend, the first spatial derivatives of gas properties at the first frozen Mach line depend on the relaxation length and the curvature of the wall shape at the beginning of the bend. The position of breakdown of the solution and the conditions necessary for no shock to form on the first frozen Mach line are obtained. For a concave wall with a sharp corner, a frozen shock wave emanating from the corner is formed. The shape of this frozen shock wave is also obtained. Further, the solution in the linearized case is obtained.

Solution of variational problems of gasdynamics of supersonic nonequilibrium flows

The problem of the optimization of the supersonic portion of a nozzle for gas flow in the case of certain nonequilibrium processes was solved in [1, 2]. The authors examined the flow scheme in which the closing Mach line of the first family arrives at the initial rarefaction wave fan. At the same time, in [3] in the solution of the analogous problem for the case of gas flow with foreign particles it was shown that it is advisable to consider also a different scheme, in which the closing characteristic arrives at the axis of symmetry outside the initial rarefaction wave fan. In the following we present results of a study of such a scheme for gas flow with nonequilibrium processes taking place. The necessary conditions which define the optimum contour are obtained and, in particular, the conditions which define the coordinate x and the magnitude of the angle at the corner points.