Shock Theory Research Articles

EXPERIMENTAL STUDY ON CHIP FORMATION MECHANISM DUE TO SHOCK OF ULTRA-HIGH SPEED GRINDING

According to the theory of ultra-high speed shock, the phenomenon of ultra-high speed grinding from the collision between grain and workpiece is researched. In order to study the chip formation mechanism in ultra-high speed grinding, the experimental study on ultra-high speed shock grinding about four kinds of the engineering material such as carbon steel, natural marble, spring steel and high speed tool steel are performed, which is used veritable amorphous carborundum and CBN grains that adhered to the head of bullet whose size is 7.62 mm as abrasive material, and used the 81 type rifle as accelerator and charger. Some valuable results in experiment of ultra-high speed grinding are acquired and the results are analyzed in detail. The experimental results indicate that in ultra high speed shock grinding the contact point is produced high temperature instantaneously which attached or exceeded its melting point, thereby, the material of the contact zone between the bullet and the steel plate becomes mobile phase and the flow material leaves the matrix and becomes abrasive dust under the action of the grain and shock wave. The phenomenon on chip formation due to shock of ultra-high speed grinding is found, so the chip formation mechanism due to shock of ultra-high speed grinding is studied and disclosed from the deeper level, and the accuracy of "the model of mechanism of chip-formation due to shock in quasi-fluid phase on super-high speed grinding" is verified.

Closure to “Discussion of ‘The Resistance of Clamped Sandwich Beams to Shock Loading’ ” (2005, ASME J. Appl. Mech., 72, pp.)

The authors, Fleck and Deshpande (FD), are grateful for the interest shown in their work (1) by Tan et al. (2).The aim of the FD study (1) was to present a simple analytical framework in order to understand the sequence of deformation events in shock-loaded sandwich beams. The analytical framework, although limited in accuracy, provides physical insight and allows for the interpretation of full numerical simulations and experiments. We reply to the comments of Tan et al. (2) point by point.Points 1 and 2: We agree with Tan et al. (2) that the Taylor (3) analysis is of limited accuracy for strong air shocks. However, the FD analysis can handle strong air shocks provided one takes the transmitted impulse as an input to the model. This was done in the paper.Point 3: (i) A global energy balance is a possible assumption for the core compression phase, leading to an internally self-consistent theory. FD used it in order to obtain simple analytical expressions for the degree of core compression. Recently, the accuracy of this assumption in predicting the sandwich panel shock response has been assessed by Deshpande and Fleck (4) for the case of a foam core. For such a core, shock wave effects and rate effects are important. The simple energy balance then over-predicts the degree of core compression as it neglects additional mechanisms of dissipation (largely viscous we believe).Recall that the FD model was developed for lattice cores such as the corrugated core. The application of shock theory to those cores remains in open topic and hence FD used a simple energy balance argument to develop an initial understanding of the sandwich beam response.Point 3: (ii) Tan et al. (2) argue that large internal energy can accrue in a metallic foam made from a rate independent plastic solid material by a switch in the deformation mode from bending to stretching of the cell walls. It is difficult to see how this mechanism switch can explain increases in plastic work by an order of magnitude or more at high velocities. This can argued as follows. An ideal work calculation can be performed by equating the change in internal energy shown in the FE calculations of Tan et al. (2) to the degree of axial stretch of the cell walls of the foam in the extreme case of all the cell walls equally sharing this energy change. In the case of an impact velocity vo=200ms−1, each cell wall would need to undergo a nominal compressive strain of 0.991 or equivalently the cell walls thickening by more than a factor of 100. This is physically unrealistic and not borne out by experiment (5). It is the opinion of FD that a major component to the internal work in the simulations of Tan et al. (2) (Figs. 1 and 2) is from the artificial viscosity inherent in the explicit FE simulations using ABAQUS.Point 4: We agree that the dynamic strength of lattice cores can exceed the static strength. This can be due to rate sensitivity and∕or inertial effects. The FD analysis neglects both effects. Despite these simplifications (not inconsistencies) the model is remarkably robust.Comparison of the FD analysis with more sophisticated calculations and experiments remains an active research topic, and FD welcome such activity.

Poverty and Witch Killing

Many observers have noted that poverty and violence go hand in hand. There is a strong negative relationship between economic growth and crime across countries, as well as across districts in India, and a link between low income and the occurrence of civil war.1 Yet existing studies are typically unable to resolve the key econometric identification issues of omitted variable bias and endogeneity. To illustrate, the unobserved quality of local government institutions may affect both income growth and crime rates, and poverty could lead to violence if desperate people with nothing to lose commit more crimes, but violence itself may in turn affect economic productivity. This paper uses local rainfall variation to identify the impact of income shocks on murder in a rural Tanzanian district.2 Extreme rainfall-resulting in drought or floods-is exogenous and is associated with poor harvests and near-famine conditions in the region, and a large increase in the murder of witches: there are twice as many witch murders in years of extreme rainfall as in other years. The victims are nearly all elderly women, typically killed by relatives. These econometric results, across 11 years in 67 villages, provide novel evidence on the role of income shocks in causing violent crime, and religious violence in particular, and also provide insights into witchcraft-an important social phenomenon in Africa rarely studied by economists. The view that economic conditions are a driving force behind witch murders is bolstered by the fact that most witch killing in Tanzania takes place in poor rural areas largely dependent on rain-fed agriculture, and that most victims in our sample are from poor households. However, it is difficult to definitively disentangle this income shock theory from alternative socio-cultural explanations. The concentration of Tanzanian witch murders in a region dominated by one particular ethnic group (the Sukuma), and the especially high number of witch murders in villages where indigenous religious beliefs are strong both point to the important role of non-economic factors. Economic theories and cultural theories are perhaps best viewed as complements: the empirical findings demonstrate the power of economics to rationalize a phenomenon that has previously been understood almost solely through a socio-cultural lens.3

Diamond port jet interaction with supersonic flow

Interaction flow field of the sonic air jet through diamond shaped orifices at different incidence angles (10 degrees, 27. 5 degrees, 45 degrees and 90 degrees) and total pressures (0. 10 MPa and 0. 46 MPa) with a Mach 5. 0 freestream was studied experimentally. A 90 degrees circular injector was examined for comparison. Cross-section Mach number contours were acquired by a Pitot-cone five-hole pressure probe. The results indicate that the low Mach semicircular region close to the wall is the wake region. The boundary layer thinning is in the areas adjacent to the wake. For the detached case, the interaction shock extends further into the freestream, and the shock shape has more curvature, also the low-Mach upwash region is larger. The vortices of the plume and the height of the jet interaction shock increase with increasing incidence angle and jet pressure. 90 degrees diamond and circular injector have stronger plume vorticity, and for the circular injector low-Mach region is smaller than that for the diamond injector. Tapered ramp increases the plume vorticity, and the double ramp reduces the level of vorticity. The three-dimensional interaction shock shape was modeled from the surface shock shape, the center plane shock shape, and cross-sectional shock shape. The shock total pressure was estimated with the normal component of the Mach number using normal shock theory. The shock induced total pressure losses decrease with decreasing jet incidence angle and injection pressure, where the largest losses are incurred by the 90 degrees, circular injector.

Nonlinear dynamics of two-dimensional undercompressive shocks

We consider the problem of a thin film driven by a thermal gradient with an opposing gravitational force. Under appropriate conditions, an advancing film front develops a leading undercompressive shock followed by a trailing compressive shock. Here, we investigate the nonlinear dynamics of these shock structures that describe a surprisingly stable advancing front. We compare two-dimensional simulations with linear stability theory, shock theory, and experimental results. The theory/experiment considers the propagation of information through the undercompressive shock towards the trailing compressive shock. We show that a local perturbation interacting with the undercompressive shock leads to nonlocal effects at the compressive shock.

기총 폭발 하중에 대한 모델 수립과 구조 해석에 관한 연구

총구로부터 방출되는 폭발파에 대한 수학적 모델(GUNBLAST)을 수립하였으며, 폭발 하중에 대한 구조 응답 해석을 수행하였다. 폭발파는 자유영역 폭발파와 반사 폭발파로 구분되어질 수 있다. 본 연구에서는 스케일 기법을 이용하여 자유영역 폭발파 모델을 수립하였으며, 경사 충격파 이론과 전산유체역학(Computational Fluid Dynamics) 계산을 통하여 반사 충격파를 계산하였다. GUNBLAST는 두 가지의 구조 모델에 적용되었으며 구조 표면으로부터의 총구거리 변화에 따른 폭발파 특성을 파악하기 위하여 평판에 대한 적용을 통하여 균일하중조건과의 비교를 수행하였다. 또한 MSC/NASTRAN을 이용하여 12.7mm 기총을 장착한 비행기 날개 모델의 과도 응답 해석을 수행하였다. 결과적으로 이러한 폭발파는 랜덤진동과 항공기에 탑재된 장비에 고주파의 손상을 일으킬 수 있음을 확인하였다. A mathematical model, GUNBLAST, of blast waves emitted from a gun muzzle is established, and structural response analyses for the blast load are performed. The blast wave can be divided into two kinds of waves, free field and reflected blast waves. In this research, the free field blast wave model is established by the use of a scaling approach, and the reflected blast wave is calculated by using the oblique shock theory and computational fluid dynamic calculation. GUNBLAST is applied to two kinds of structural models. To investigate the effect of the muzzle distance from a structural surface, the blast waves on a plate for various muzzle distances are compared to uniform loads. Moreover, the transient response analysis of an aircraft wing model with a 12.7mm gun is carried out by using MSC/NASTRAN. From the results, it can be shown that the blast wave can cause broad random vibration and high frequency damage to equipments mounted in the aircraft.

Shock parameter calculations at weak interplanetary shock waves

Abstract. A large set of interplanetary shock waves observed using the Ulysses spacecraft is analysed in order to determine their local parameters. For the first time a detailed analysis is extended to the thermodynamic properties of a large number of events. The intention is to relate the shock parameters to the requirements set by MHD shock theory. A uniform approach is adopted in the selection of up and downstream regions for this analysis and applied to all the shock waves. Initially, the general case of a 3 component adiabatic plasma is considered. However, the calculation of magnetosonic and Alfvénic Mach numbers and the ratio of downstream to upstream entropy produce some unexpected results. In some cases there is no clear increase in entropy across the shock and also the magnetosonic Mach number can be less than 1. It is found that a more discerning use of data along with an empirical value for the polytropic index can raise the distribution of downstream to upstream entropy ratios to a more acceptable level. However, it is also realised that many of these shocks are at the very weakest end of the spectrum and associated phenomena may also contribute to the explanation of these results.

Stability of a Mach configuration

We prove the stability of a Mach configuration, which occurs in shock reflection off an obstacle or shock interaction in compressible flow. The compressible flow is described by a full, steady Euler system of gas dynamics. The unperturbed Mach configuration is composed of three straight shock lines and a slip line carrying contact discontinuity. Among four regions divided by these four lines in the neighborhood of the intersection, two are supersonic regions, and other two are subsonic regions. We prove that if the constant states in the supersonic regions are slightly perturbed, then the structure of the whole configuration holds, while the other two shock fronts and the slip line, as well as the flow field in the subsonic regions, are also slightly perturbed. Such a conclusion asserts the existence and stability of the general Mach configuration in shock theory. In order to prove the result, we reduce the problem to a free boundary value problem, where two unknown shock fronts are free boundaries, while the slip line is transformed to a fixed line by a Lagrange transformation. In the region where the solution is to be determined, we have to deal with an elliptic-hyperbolic composed system. By decoupling this system and combining the technique for both hyperbolic equations and elliptic equations, we establish the required estimates, which are crucial in the proof of the existence of a solution to the free boundary value problem. © 2005 Wiley Periodicals, Inc.

Non-Fermi Power-Law Acceleration in Astrophysical Plasma Shocks

Collisionless plasma shock theory, which applies, for example, to the afterglow of gamma-ray bursts, still contains key issues that are poorly understood. In this Letter, we study charged particle dynamics in a highly relativistic collisionless shock numerically using ~109 particles. We find a power-law distribution of accelerated electrons, which upon detailed investigation turns out to originate from an acceleration mechanism that is decidedly different from Fermi acceleration. Electrons are accelerated by strong filamentation instabilities in the shocked interpenetrating plasmas and coincide spatially with the power-law-distributed current filamentary structures. These structures are an inevitable consequence of the now well-established Weibel-like two-stream instability that operates in relativistic collisionless shocks. The electrons are accelerated and decelerated instantaneously and locally: a scenery that differs qualitatively from recursive acceleration mechanisms such as Fermi acceleration. The slopes of the electron distribution power laws are in concordance with the particle power-law spectra inferred from observed afterglow synchrotron radiation in gamma-ray bursts, and the mechanism can possibly explain more generally the origin of nonthermal radiation from shocked interstellar and circumstellar regions and from relativistic jets.

Configuration of shock waves in two-dimensional overexpanded jets

An experimental and analytical study has been carried out to obtain the clear understanding of a shock wave transition associated with a steady two-dimensional overexpanded flow. Two-dimensional inviscid theory with respect to a shock wave reflection is used in the present study on the characteristic of shock waves. The results obtained from the flow analysis are compared with those obtained from flow visualizations. It is shown that in the region of regular reflection, the angle of an incident shock wave becomes lower than that calculated by two shock theory with an increment in the ratio p e/p b of the nozzle exit pressure p e to the back pressure p b. It is indicated that the configuration of shock waves in overexpanded jets is influenced by the divergent angle at the nozzle exit. Also it is shown from the flow visualization that a series of shock waves move into the nozzle inside with a decrease in pressure ratio p e/p b, even if the p e/p b is under overexpanded conditions.

Physical properties and behavior of shock waves

The distinguishing feature of a shock wave is its practically instantaneous rise in pressure. Its laws of propagation are different from those for ordinary, continuous-waveform sound waves, even when the sound wave amplitude is finite. The Rankine–Hugoniot shock relations connect the properties on either side of the shock, e.g., pressure, density, and particle velocity, with the shock velocity or Mach number. These relations are valid even for unsteady shocks, e.g., growing or decaying shocks. Weak shock theory provides a means of predicting the propagation of most steady and unsteady shocks that are encountered in acoustics, including those used in medicine. For example, in lithotripsy the focal pressure amplitude rarely exceeds 100 MPa; for such a shock the shock velocity is only ∼8% greater than the sound speed in water. Shock rise time τrise is an interesting property of shocks but often difficult to measure. For example, if the lithotripsy shock cited above was steady and in water, its rise time would be a few tens of picoseconds. When the shock is unsteady, τrise is much harder to predict.

From bench to bedside: Nonlinear bio-ultrasound

In the early 1960s, David Blackstock developed the weak shock theory which characterized the development and evolution of harmonics in a finite-amplitude propagating plane wave. Later work developed an understanding of beam patterns of the fundamental and higher harmonics from piston radiators. All of these concepts were germane to the field of bio-ultrasound. However, nonlinear effects were largely unexploited in bio-ultrasound until the 1980s, when the role of finite-amplitude mechanisms was recognized as an enhancer of heating and lesion production in high intensity applications. Later, in the 1990s, the role and the advantage of higher harmonics in ultrasonic imaging were developed. In particular, the higher harmonics generated by nonlinear effects, especially in the presence of aberrating tissue, were shown to produce dramatic increases in the resolution and contrast of ultrasound images in cardiology and other applications. Today, every high-end medical ultrasound scanner has the capability of ‘‘harmonic imaging’’ for improved image quality in a number of applications. The physics and technology of this remarkable development will be reviewed, along with the important guiding role of David Blackstock and his collaborators, particularly at UT Austin and at U. Rochester.

Gravity Wave Breaking in Two-Layer Hydrostatic Flow

Abstract To better understand mountain-induced gravity wave breaking and potential vorticity generation in the troposphere, a two-layer hydrostatic flow over a three-dimensional Witch-of-Agnesi type of mountain is investigated. It is suggested that a two-layer model is the simplest model in which the partitioning of upper- and lower-level wave breaking and dissipation can be studied. High-resolution shallow water model runs are carried out with unsheared upstream flow and a wide variety of mountain heights. A regime diagram is constructed, in which gravity wave breaking is classified based on shock number, location, and type. It is demonstrated that different types of shocks identified in the numerical simulations can be consistently described using a shock regime diagram, derived from viscous shock theory. Four curious shock properties are shown to influence orographic flow: the steepening requirement, the tendency for external jumps to amplify shear, the bifurcation in external jumps, and the “double sh...

Numerical Investigation of Behaviour of Small Particle Passing through Normal Shock Wave (2nd Report, Behaviour of Small Particle Passing through Oscillating Shock Wave and Error in Measurement)

An anemometry using tracer particle, such as PIV and LDV, has some errors related to the deviation of particles from the stream, particularly around the large velocity gradient. But the reasonable correcting procedure has never been established. For a notable example, we have investigated the behavior of particle when it passes through a shock wave. In the first report, the effects of particle density and size are clarified by carrying out the simulation with the weak shock theory to the flow field and the BBO equation to the traveling particle. In the present paper, shock wave oscillation and nonuniforme particle size are taken into account, to realize the more exact experimental conditions. The results suggest that the turbulence detected in measurement contains the considerably large amount of errors concerning with the particle property used. In particular, the dispersion of particle diameter is more serious.

An active DNA transposon family in rice.

The publication of draft sequences for the two subspecies of Oryza sativa (rice), japonica (cv. Nipponbare) and indica (cv. 93-11), provides a unique opportunity to study the dynamics of transposable elements in this important crop plant. Here we report the use of these sequences in a computational approach to identify the first active DNA transposons from rice and the first active miniature inverted-repeat transposable element (MITE) from any organism. A sequence classified as a Tourist-like MITE of 430 base pairs, called miniature Ping (mPing), was present in about 70 copies in Nipponbare and in about 14 copies in 93-11. These mPing elements, which are all nearly identical, transpose actively in an indica cell-culture line. Database searches identified a family of related transposase-encoding elements (called Pong), which also transpose actively in the same cells. Virtually all new insertions of mPing and Pong elements were into low-copy regions of the rice genome. Since the domestication of rice mPing MITEs have been amplified preferentially in cultivars adapted to environmental extremes-a situation that is reminiscent of the genomic shock theory for transposon activation.

Model of plastic deformation for extreme loading conditions

We present a model of metallic plastic flow suitable for numerical simulations of explosive loading and high velocity impacts. The dependence of the plastic strain rate on applied stress at low strain rates is of the Arrhenius form but with an activation energy that is singular at zero stress so that the deformation rate vanishes in that limit. Work hardening is modeled as a generalized Voce law. At strain rates exceeding 109 s−1, work hardening is neglected, and the rate dependence of the flow stress is calculated using Wallace’s theory of overdriven shocks in metals [D.C. Wallace, Phys. Rev. B 24, 5597 (1981); 24, 5607 (1981)]. The thermal-activation regime is continuously merged into the strong shock limit, yielding a model applicable over the 15 decades in strain rate from 10−3 to 1012 s−1. The model represents all aspects of constitutive behavior seen in Hopkinson bar and low-rate data, including a rapid increase in the constant-strain rate sensitivity, with 10% accuracy. High-pressure behavior is controlled by the shear modulus, G(ρ,T), and the melting temperature, Tm(ρ). There are eleven material parameters in addition to G(ρ,T) and Tm(ρ). Parameters for Cu, U, Ta, Mo, V, Be, 304 SS, and 21-6-9 SS are provided.

Simultaneous Observation of a Moreton Wave on 1997 November 3 in Hα and Soft X-Rays

We report the observation of a Moreton wave in Hα (line center and ±0.8 A) with the Flare Monitoring Telescope at the Hida Observatory of Kyoto University at 4:36-4:41 UT on 1997 November 3. The same region (NOAA Active Region 8100) was simultaneously observed in soft X-rays with the soft X-ray telescope on board Yohkoh, and a wavelike disturbance (X-ray wave) was also found. The position of the wave front as well as the direction of propagation of the X-ray wave roughly agree with those of the Moreton wave. The propagation speeds of the Moreton wave and the X-ray wave are about 490 ± 40 and 630 ± 100 km s-1, respectively. Assuming that the X-ray wave is an MHD fast-mode shock, we can estimate the propagation speed of the shock, on the basis of MHD shock theory and the observed soft X-ray intensities ahead of and behind the X-ray wave front. The estimated fast shock speed is 400-760 km s-1, which is in rough agreement with the observed propagation speed of the X-ray wave. The fast-mode Mach number of the X-ray wave is also estimated to be about 1.15-1.25. These results suggest that the X-ray wave is a weak MHD fast-mode shock propagating through the corona and hence is the coronal counterpart of the Moreton wave.

Particle Image Velocimetry in Mach 3.5 and 4.5 Shock-Tunnel Flows

For the e rst time, a particle image velocimetry (PIV) system was used to study high-Mach-number e ows in a shock-tunnel facility with velocities of more than 1.5 km/s and measuring times in the millisecond range. An application of PIV to such a transient high-speed e ow is considerably more dife cult than to a continuous e ow because no online adjustments of the optics and the particle seeding can be done. Additionally, a proper seeding and timingofthefacility iscrucial.Firstwewilldiscussthemeasured velocity e eldbehind acontoured Lavalnozzle (design Mach number4.5 ). The measurement data show that thee owe eld at the nozzleexit is parallel to the nozzle axis and homogeneous as expected from supersonic nozzle theory. The average measured velocity corresponds very well to the calculated e ow velocity. The results are compared to measurements made with a conical Mach 3.5 nozzle that exhibits a diverging e owe eld. A wedge was further introduced into the parallel Mach 4.5 nozzle e ow to study the seed particle performance downstream of an oblique shock. The measured results are also in good agreement with calculated velocities from oblique shock theory. PIV has, therefore, proven to be an efe cient measurement method for high-speed and short-duration simulation facilities.

Low power BL Lacertae objects and the blazar sequence

The spectral properties of blazars seem to follow a phenomenological sequence according to the source luminosity. By inferring the source physical parameters through (necessarily) modeling of the blazar spectra, we have previously proposed that the sequence arises because the particles responsible for most of the emission suffer increasing radiative losses as the luminosity increases. Here we extend those results by considering the widest possible range of blazar spectral properties. We find a new important ingredient for shaping the spectra of the lowest power objects, namely the role of a finite timescale for the injection of relativistic particles. Only high energy particles radiatively cool over such a timescale leading to a break in the particle distribution: particles with this break energy are those emitting most of the power, and this gives rise to a link between blazar spectra and total energy density inside the source, which controls the cooling timescale. The emerging picture requires two phases for the particle acceleration: a first pre–heating phase in which particles reach a characteristic energy as the result of balancing heating and radiative cooling, and a more rapid acceleration phase which further accelerate these particles to form a power law distribution. While in agreement with standard shock theory, this scenario also agrees with the idea that the luminosity of blazars is produced through internal shocks, which naturally lead to shocks lasting for a finite time.

An experimental approach to the study of the sedimentation of dispersed particles in a centrifugal field

On the basis of an especially developed centrifuge, a PC-controlled separation analyser has been assembled for the continuous registration of particles' sedimentation process in a fluid, caused by centrifugal acceleration. The system enables the parallel investigation of up to eight samples. During the centrifugation, the radial and temporal variation of light transmission through the samples is registered by means of a CCD line detector. Experiments were carried out with the separation analyser on manipulated rigid and sphered red blood cells for the verification of an established one-dimensional mixture fluid model. In particular, the influence of particle volume concentration as well as of the angular velocity on the sedimentation process was investigated. Justification could be furnished for the one-dimensional model based on the theory of kinematic waves and shocks. In addition, an algorithm has been developed for the experimental determination of the suspension's effective or apparent viscosity.