A new measurement technique to reconstruct the density field of the shock-wave/boundary-layer interaction (SWBLI) in a confined duct is proposed. With this technique, it is possible to quantitatively capture in detail the structures of the density field both in the regions of the shock-systems in the central core and boundary-layer flows near the duct wall concurrently. The novel feature of the proposed technique is to make use of the schlieren images with the rainbow filters of the vertical and horizontal cutoff settings and then to reconstruct the two-dimensional density field integrated over the line-of-sight direction using the corresponding filter calibration curves. The proposed technique is applied for the first time to a shock train in a constant-area straight duct under the upstream condition of the shock train: the freestream Mach number is 1.42, the incoming boundary layer thickness normalised by the duct half height is 0.175, and the corresponding unit Reynolds number $Re/m$ is $2.99 \times 10^7$ m-1. The calculated isopycnic field depicts the streamwise and transverse density variations inside the shock train, the mixing region after the shock train, and the boundary-layer of the interaction region. This technique is shown to be capable of identifying the locations of shocks in a shock train more precisely than a conventional approach measuring the static pressure distribution along the duct wall. In addition, various quantitative visual representations such as a shadowgraphy and a bright-field schlieren can be extracted from the density field acquired by the present approach, and the spatial evolution of the shape and strength of each shock constituting the shock train as well as the boundary layer flow properties can be quantitatively clarified.

A shock-induced separation loss reduction method, using local blade suction surface shape modification (smooth ramp structure) with constant adverse pressure gradient with the consideration of radial equilibrium effect to split a single shock foot into multiple weaker shock wave configuration, is investigated on the NASA Rotor 37 for promoting aerodynamic performance of a transonic compressor rotor. Numerical investigation on baseline blade and improved one with blade modification on suction side has been conducted employing the Reynolds-averaged Navier–Stokes method to reveal flow physics of ramp structure. The results indicate that the passage shock foot of baseline is replaced with a family of compression waves and a weaker shock foot generating moderate adverse pressure gradient on ramp profile, which is beneficial for mitigating the shock foot and shrinking flow separation region as well. In addition, the radial secondary flow of low-momentum fluids within boundary layer is decreased significantly in the region of passage shock-wave/boundary-layer interaction on blade suction side, which mitigates the mass flow and mixing intensity of tip leakage flow. With the reduction of flow separation loss induced by passage shock, the adiabatic efficiency and total pressure ratio of improved rotor are superior to baseline model. This study herein implies a potential application of ramp profile in design method of transonic and supersonic compressors.

In this work we present experimental results on the behavior of diamond at megabar pressure. The experiment was performed using the PHELIX facility at GSI in Germany to launch a planar shock into solid multi-layered diamond samples. The target design allows shock velocity in diamond and in two metal layers to be measured as well as the free surface velocity after shock breakout. As diagnostics, we used two velocity interferometry systems for any reflector (VISARs). Our measurements show that for the pressures obtained in diamond (between 3 and 9 Mbar), the propagation of the shock induces a reflecting state of the material. Finally, the experimental results are compared with hydrodynamical simulations in which we used different equations of state, showing compatibility with dedicated SESAME tables for diamond.

The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we consider a ‘spherical piston’ problem for the relativistic Euler equations, which describes the wave motion produced by a sphere expanding into an infinite surrounding medium. We use the reflected characteristics method to construct a global piecewise smooth solution with a single shock of this spherical piston problem, provided that the speed of the sphere is a small perturbation of a constant speed.

Production of high dynamic pressure using a strong shock wave is a topic of high relevance for high-energy-density physics, inertial confinement fusion, and materials science. Although the pressures in the multi-Mbar range can be produced by the shocks generated with a large variety of methods, the higher pressures, in the sub-Gbar or Gbar range, are achievable only with nuclear explosions or laser-driven shocks. However, the laser-to-shock energy conversion efficiency in the laser-based methods currently applied is low and, as a result, multi-kJ multi-beam lasers have to be used to produce such extremely high pressures. In this paper, the generation of high-pressure shocks in the newly proposed collider in which the projectile impacting a solid target is driven by the laser-induced cavity pressure acceleration (LICPA) mechanism is investigated using two-dimensional hydrodynamic simulations. A special attention is paid to the dependence of shock parameters and the laser-to-shock energy conversion efficiency on the impacted target material and the laser driver energy. It has been found that both in case of low-density and high-density solid targets, the shock pressures in the sub-Gbar range can be produced in the LICPA-based collider with the laser energy of only a few hundreds of joules, and the laser-to-shock energy conversion efficiency can reach values of 10–20%, by an order of magnitude higher than the conversion efficiencies achieved with other laser-based methods used so far.

Nanosecond (ns) pulsed dielectric barrier discharge (DBD) actuator in a laminar flat plate boundary layer is investigated numerically in an attempt to gain some new insights into the understanding of ns DBD actuation mechanism. Special emphasis is put on the examination, separation and comparison of behaviors of discharge induced micro shock wave and residual heat as well as on the investigation of response of external flow to the two effects. The shock wave is found to introduce highly transient, localized perturbation to the flow and be able to significantly alter the flow pattern shortly after its initiation. The main flow tends to quickly recover to close to its undisturbed state due to the transient nature of perturbation. However, with the shock decay and final disappearance, another perturbation source in the vicinity of discharge region, which contains contribution from both residual heat and shock, becomes increasingly pronounced and eventually develops into a perturbation wave train in the boundary layer. The perturbation is relatively weak and may not be a Tollmien-Schlichting (TS) wave and not trigger the laminar-turbulent transition of boundary layer. Instead, it is more likely to manipulate the flow stability to achieve the strong control authority of this kind of actuation in the case of flow separation control. In addition, a parametric study over the different electrical and hydrodynamic parameters is also conducted.

In nature, when hazardous geophysical granular flows (e.g. a snow avalanche) impact on an obstacle as they stream down a slope, rapid changes in flow depth, direction and velocity will occur. It is important to understand how granular material flows around such obstacles in order to enhance the design of defense structures. In this study, a three dimensional (3-D) Smoothed Particle Hydrodynamics (SPH) model is developed to simulate granular flow past different types of obstacles. The elastic–perfectly plastic model with implementation of the Mohr–Coulomb failure criterion is applied to simulate the material behavior, which describes the stress states of soil in the plastic flow regime. The model was validated by simulating the collapse of a 3-D column of sand with two different aspect ratios; the results showed that the SPH method is capable of simulating granular flow. The model is then applied to simulate the gravity-driven granular flow down an inclined surface obstructed by a group of columns with different spacing, a circular cylinder and a tetrahedral wedge. The numerical results are then compared with experimental results and two different numerical solutions. The good agreements obtained from these comparisons demonstrate that the SPH method may be a powerful method for simulating granular flow and can be extended to design protective structures.

In the present paper, the problem on normal low-velocity impact of a solid upon an isotropic spherical shell is studied without considering the changes in the geometrical dimensions of the contact domain. At the moment of impact, shock waves (surfaces of strong discontinuity) are generated in the target, which then propagate along the shell during the process of impact. Behind the wave fronts up to the boundary of the contact domain, the solution is constructed with the help of the theory of discontinuities and one-term ray expansions. The ray method is used outside the contact spot, but the Laplace transform method is applied within the contact region. As a result, the exact solution of the contact force is determined as a function of time. This model is intended to be used in simulating crash scenarios in frontal impacts, and to provide an effective tool to estimate the severity of effect on the human head and to estimate brain injury risks.

An improved method of space-time conservation element and solution element (CE/SE) is developed to solve the equations of conservation laws in fluid dynamics. The present method substantially differs in both concept and methodology from the traditional CE/SE method. In this paper the improved second-order CE/SE method is presented in a hexahedral grid. Furthermore, the present CE/SE method was successfully applied to solve the interaction problem of shock waves and detonation. Several numerical examples were also given. Numerical results have compared with the results of experiments and other computational methods. The compared results have shown a good agreement. The improved CE/SE method has higher accuracy and becomes a more prospective scheme.

This paper presents the results of numerical simulations on the characteristics of hydraulic shockwaves in an inclined chute contraction. A two-dimensional numerical hydraulic simulation model is used to simulate the hydraulic shockwaves, based on the finite-volume multi-stage (FMUSTA) scheme proposed by Guo et al. [1]. This numerical model has been proved having good ability in simulating hydraulic shockwaves through the comparison with the exact solution of idealized shockwaves in a horizontal contraction provided by Ippen and Dawson [2], and the comparison with experimental results provided in the companion paper by Jan et al. [3]. The simulated shockwave parameters such as the shock angle, maximum shockwave height and maximum shockwave position for various conditions are compared with those calculated by the empirical relations obtained in the companion paper. The numerical results validate the applicability of these empirical relations and also extend their applicability to higher approach Froude numbers.

Le dimensionnement des structures immergées vis-à-vis des effets d'une explosion sous-marine constitue une exigence forte pour un constructeur de navires militaires. La présente étude s'intéresse à la description de l'interaction entre une coque élastique immergée et une onde acoustique se propageant dans le fluide. En utilisant un modèle linéaire pour le fluide et la structure, il est possible de proposer une description du problème couplé dont la résolution peut être conduite avec une méthode semi-analytique. Les inconnues du problème (pour le fluide : champ de pression incident, champ de pression réfléchi, champ de pression rayonné ; pour la structure : champ de déplacement radial et ortho radial) sont écrites sous la forme d'un développement en série de Fourier de la variable angulaire. L'évolution des différents champs est décrite dans le domaine de Laplace par transformation des équations temporelles du problème couplé. Une application est proposée ici au cas de deux coques couplées par un fluide. La méthode de calcul ainsi proposée est implantée dans un code de calcul MATLAB qui peut ainsi être utilisé en bureau d'études pour le pré-dimensionnement de coques de sous-marins.

We consider the Euler equations for compressible fluidsin a nozzle whose cross-section is variable and may contain discontinuities.We view these equations as a hyperbolic system in nonconservative formand investigate weak solutions in the sense of Dal Maso, LeFloch and Murat [J. Math. Pures Appl.74 (1995) 483–548].Observing that the entropy equality has a fully conservative form,we derive a minimum entropy principle satisfied by entropy solutions.We then establish the stability of a class of numerical approximations for this system.

The Smooth Particle Hydrodynamics (SPH) impact code (Benz & Asphaug 1994) has been developed for the simulation of impacts and collisions involving brittle solids in the strength-and gravity-dominated regime. In the latter regime, the gravitational overburden is used to increase the fracture threshold. In this paper, we extend our numerical approach to include the effect of porosity at a sub-resolution scale by adapting the so-called P -α model (Herrman 1969). Using our extended 3D SPH impact code, we investigated collisions between porous bodies to examine the sensitivity of collisional outcomes to the degree of porosity. Two applications that illustrate the capabilities of our approach are shown: 1) the modeling of a Deep Impact-like impact and 2) the computation of the amount of momentum transferred to an asteroid following the impact of a high velocity projectile.

The approach to the ultimate strength of metals is determined experimentally. The strength of the materials and the strain rate were determined from the free surface velocity time history, which was measured with an optically recording velocity interferometer system. The dynamic strength was measured at strain rates in the domain of 5·106 to 5·108 s−1. The necessary tension to break the metal (spall) and the very high strain rates were achieved using high-powered lasers in nanosecond and picosecond regimes. The measurements at strain rates larger than 108 s−1 were achieved for the first time. The ultimate strength of metals was calculated using a realistic wide-range equation of state. Our experiments indicate that under very fast tension processes, the dynamic strength of materials is determined not by the macroscopic defects but by atomic quantum mechanical processes described by the equation of state of the material. The rate of the process is described by the strain rate, and at strain rates higher than 5·107 s−1, the atomic forces are dominating the dynamic strength of materials.

A physical mechanism that can result in the generation of extended expanding atmospheres is discussed. The process involves the unloading of stellar material following the arrival of a shock wave at the edge of the star. The basic principles are developed from a discussion of a simplified case that has been studied in the laboratory; they are then applied to the atmosphere of a star. A radiation-hydrodynamics computation of a model cepheid is then used to obtain quantitative atmospheric profiles. The computed continuum and spectral lines during the unloading process are then examined. A discussion of the possibility that the unloading process occurs in stars other than cepheids suggests the existence of a shock visibility factor associated with ionization or dissociation in the region behind the shock front and leads to a possible alternate interpretation of the variable star instability strips in the H-R diagram.