Types Of Shock Waves Research Articles

Delta shock wave in the compressible Euler equations for a Chaplygin gas

We study the Riemann problem of the compressible Euler equations for the Chaplygin gas. With the analysis on the physically relevant region, we obtain two kinds of Riemann solutions by using the method of characteristic analysis. One composes of three contact discontinuities, and the other involves a delta shock wave in which both density and internal energy contain Dirac delta function simultaneously. We propose both generalized Rankine–Hugoniot relation and entropy condition for this type of delta shock wave. The numerical results coinciding with the theoretical analysis are also presented.

Generation of different types of surface acoustic waves by shock wave-Stone interaction

The generation of different types of surface acoustic waves (SAWs) in lithotripsy is investigated by numerical simulations using COMSOL, considering either the case of a weakly focused shock wave as an incident plane wave (in the focal plane) in shock wave lithotripsy (SWL) or a spherically divergent shock wave produced by a spark discharge in Nano Pulse Lithotripsy (NPL). The interaction of these two types of shock waves with an artificial kidney stone immersed in water may generate three different types of SAWs: namely, Scholte wave, acoustic surface evanescent wave (ASEW), and leaky Rayleigh wave (LRW). In particular, we examined the generation of SAWs on a flat, cylindrical, or spherical surface under different incident angles. It was found that the geometry and acoustic properties of the stone could significantly influence the types of SAWs generated and the resultant peak tensile stress produced at the stone-water boundary. Comparison with experimental measurements (i.e., Schlieren and photoelastic imaging) and stone fracture will also be made. [Work supported by NIH through 5R37DK052985-20.]

Characterisation of plasma synthetic jet actuators in quiescent flow

An experimental characterisation study of a large-volume three-electrode plasma synthetic jet actuator (PSJA) is presented. A sequential discharge power supply system is used to activate the PSJA. Phase-locked planar particle image velocimetry (PIV) and time-resolved Schlieren imaging are used to characterise the evolution of the induced flow field in quiescent flow conditions. The effect of orifice diameter is investigated. Results indicate three distinct features of the actuator-induced flow field. These are the initial shock waves, the high speed jet and vortex rings. Two types of shock waves with varied intensities, namely a strong shock wave and a weak shock wave, are issued from the orifice shortly after the ignition of the discharge. Subsequently, the emission of a high speed jet is observed, reaching velocities up to 130 m s−1. Pronounced oscillation of the exit velocity is caused by the periodical behaviour of capacitive discharge, which also led to the formation of vortex ring trains. Orifice diameter has no influence on the jet acceleration stage and the peak exit velocity. However, a large orifice diameter results in a rapid decline of the exit velocity and thus a short jet duration time. Vortex ring propagation velocities are measured at peak values ranging from 55 m s−1–70 m s−1. In the case of 3 mm orifice diameter, trajectory of the vortex ring severely deviates from the actuator axis of symmetry. The development of this asymmetry in the flow field is attributed to asymmetry in the electrode configuration.

Shock wave processes in collisional gas particle mixtures

Structures and propagation of shock waves in high density particle suspensions in gas are investigated theoretically and numerically. A physical and mathematical model which takes into account integral collisions between the particles on the basis of molecular-kinetic approaches of theory of granular materials is applied. The possibility of different types of shock waves, including double front structures is revealed. The role of particle collisions in the dynamics of particle dense layer expansion under an influence of divergent shock wave and in processes of shock wave diffraction past a backward-facing step is analyzed.

Expansion shock waves in regularized shallow-water theory.

We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularized shallow-water equations that include the Benjamin-Bona-Mahony and Boussinesq equations. An expansion shock exhibits divergent characteristics, thereby contravening the classical Lax entropy condition. The persistence of the expansion shock in initial value problems is analysed and justified using matched asymptotic expansions and numerical simulations. The expansion shock's existence is traced to the presence of a non-local dispersive term in the governing equation. We establish the algebraic decay of the shock as it is gradually eroded by a simple wave on either side. More generally, we observe a robustness of the expansion shock in the presence of weak dissipation and in simulations of asymmetric initial conditions where a train of solitary waves is shed from one side of the shock.

Supersonic Interference Flow Along the Corner of Intersecting Wedges

В качестве модели для изучения взаимодействия плоских скачков уплотнения в пространстве используется угловое тело, представляющее из себя два пересекающихся клина.

Modulation of electron-acoustic waves in a plasma with kappa distribution

In the present work, employing a one dimensional model of an unmagnetized collisionless plasma consisting of a cold electron fluid, hot electrons obeying κ velocity distribution, and stationary ions, we study the amplitude modulation of an electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations of such a plasma, we obtained the nonlinear Schrödinger equation as the evolution equation. Seeking a harmonic wave solution with progressive wave amplitude to the evolution equation, as opposed to the plasma with vortex distribution, the amplitude wave assumes a shock wave type of solution. Finally, the modulational stability of the wave is studied and it is observed that the wave is modulationally stable for all admissible wave numbers.

Benefits of extracorporeal shockwave in the treatment of skin ulcers: a literature review

shockwave therapy (ESWT) has analgesic and anti-inflammatory effects. With the evolu - tion and comprehension of its biological and physical mechanisms, the application of ESWT on other pathologies has also been studied, especially in musculoskeletal diseases. Recently, studies on animal models have shown its angiogenic capacity and a higher rate of local re-epithelization. These small stud - ies led to few trials using low-energy, radial ESWT to treat problematic chronic skin ulcers. Skin ulcers have diverse etiologies, ranging from pressure ulcers, burns, venous or arterial ulcers, and even diabetic ulcers. Their treatment is usually a challenge, due to the long-term treatment and high costs. Objective: To review the literature and evaluate the efficacy of ESWT in caring for skin ulcers of various etiologies: diabetic ulcers, pressure ulcers, burns, post-traumatic ulcers, venous and arterial ulcers. Method: A lit- erature review was made, with only human trials included. Results: 9 articles were selected that fulfilled the eligibility criteria. The studies included evaluations of 788 patients. The manuscripts demonstrated a large variability regarding the interventions made. There was heterogeneity regarding intervention time, number of pulses, frequency of sessions, and also the number of sessions, energy density used, and the type of shock wave used in therapies. Some of the included trials found a higher rate of complete wound healing and faster epithelization in patients with chronic lesions, unresponsive to the traditional mea - sures. However, there were few studies in the literature with proper methodological quality. Conclusion: ESWT is a promising alternative for the treatment of patients unresponsive to conventional measures. The results are promising, although the evidence regarding wound healing and acceleration of wound healing is still limited. The studies selected did not report any significant side effects.

Ultrafast collisional ion heating by electrostatic shocks.

High-intensity lasers can be used to generate shockwaves, which have found applications in nuclear fusion, proton imaging, cancer therapies and materials science. Collisionless electrostatic shocks are one type of shockwave widely studied for applications involving ion acceleration. Here we show a novel mechanism for collisionless electrostatic shocks to heat small amounts of solid density matter to temperatures of ∼keV in tens of femtoseconds. Unusually, electrons play no direct role in the heating and it is the ions that determine the heating rate. Ions are heated due to an interplay between the electric field of the shock, the local density increase during the passage of the shock and collisions between different species of ion. In simulations, these factors combine to produce rapid, localized heating of the lighter ion species. Although the heated volume is modest, this would be one of the fastest heating mechanisms discovered if demonstrated in the laboratory.

Shock wave structure in a heterogeneous medium with two pressures

The shock wave motion of a mixture of a gas and fine solid particles is considered with allowance for the difference in velocities and the particle phase pressure, which is described by Anderson-type and other equations. Various forms of the equation of state for the particle phase are described. Graphical illustrations are given for the equation determining the composite type of this model with the particle phase pressure being neglected. Under certain assumptions, the complete model can be reduced to a hyperbolic system of equations. Types of shock waves formed in such a mixture are determined for this system of equations. The statements are illustrated by results of numerical simulations.

Novel shock wave excitation method for dynamic characterization of microstructures

A novel shock wave excitation method for dynamic characterization of MEMS microstructures was proposed. A typical shock wave excitation device mainly includes a needle electrode, a plate electrode, a high-voltage capacitor, a base structure and a feeder. The principle of this method is as follows. The testing microstructure was installed on the surface of the base structure supported by a rigid platform. The plate electrode was attached on the opposite surface. The needle electrode was mounted on the feeder. Adjusting the feeder, the shock wave will be generated as soon as the gap distance between two electrodes meets the requirements of electrical discharging. The base structure will be impacted by the shock wave. Thus the testing microstructure will be excited by the movement of the base structure. A dynamic measurement system for microcantilevers were developed. In the system, the shock wave excitation device was used to excite the testing microcantilevers. T-shaped piezoresistive microcantilevers were fabricated to get the vibration response. The experiments on the dynamic characteristics measurement for microcantilevers were carried out. The results show the shock wave excitation method is effective for MEMS dynamic characterization.

Passive Control of Shock Oscillation Around a Biconvex Circular Arc Airfoil in a Channel

A strong normal shock wave, generated on an airfoil, is responsible not only for limiting the aerodynamic performance but also for shock induced boundary layer separation. This shock induced boundary layer separation results aerodynamics instabilities (buffet), high cycle fatigue failure (HCF), nonsynchronous vibration (NSV), flutter and so on. In the present study, a numerical computation has been performed to control the unsteady shock oscillation over a 12% biconvex circular arc airfoil in a two dimensional channel. Reynolds averaged Navier-Stokes (RANS) equations with k-ω shear stress transport (SST) two equation turbulence model has been applied for computational analysis. To control the shock oscillation over a biconvex circular arc airfoil (referred as base airfoil), the geometry of the base airfoil has been modified by incorporating a cavity with two openings on both upper and lower surface of the airfoil. The cavity has been incorporated in such a manner that the mean position (along chord length) of the cavity is placed where the RMS of static pressure fluctuation on airfoil surface (for base airfoil) is maximum. The length and depth of the cavities are kept 10% and 2% of the chord length, respectively. The behavior of the shock wave oscillation has been studied for a particular pressure ratio (defined as the ratio of back pressure to inlet total pressure) of 0.69. The present study investigates the shock wave characteristics over (a) airfoil with no cavity (base airfoil) and (b) airfoil with cavity with 60% opening (60% of cavity length is open). The results showed that the incorporation of cavities on airfoil surfaces not only affect the flow field but also change the behaviour in a great extent. For pressure ratio 0.69, the flow field becomes steady for airfoil with cavities while for base airfoil the flow field was unsteady. The results also show that incorporation of a cavity on airfoil surfaces changes the type of shock wave from normal to λ shock wave.

Distribution Regularities of Shear Deformations in Incompressible Nonlinear Elastic Solids

The process of shock disturbances in incompressible nonlinear elastic medium is considered. For the case of one-dimensional deformation the two types of plane shock waves are shown, which carry shift deformations in the medium. The properties of these waves are described, their propagation velocities are calculated. The solution of the boundary problem of the interaction of two plane waves with different shear polarization is presented to demonstrate ways of using the obtained results.

Self-similar solutions for some nonlinear evolution equations: KdV, mKdV and Burgers equations

A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Burgers equations, with self-similar solutions is presented. The method employs ideas from symmetry reduction to space and time variables and similarity reductions for nonlinear evolution equations are performed. The obtained self-similar solutions of KdV and mKdV equations are related to Bessel and Airy functions whereas those of Burgers equation are related to the error and Hermite functions. These solutions appear as new types of solitary, shock and periodic waves. Also, the method can be applied to other nonlinear evolution equations in mathematical physics.

Shock wave generation and its influencing parameters based on diesel injector

Based on schlieren imaging method the shock wave generated by diesel injector has been investigated, and the influences of ambient gas property, the progress of the spray, ambient gas density and ambient gas temperature on shock wave have been analyzed. The results show that: the images of spray shock wave are cleaner using sulfur hexafluoride (SF6) as ambient gas than using the nitrogen (N2); at the beginning of injection, shock wave phenomenon does not generate immediately as the fuel leave the nozzle because of the needle movement, and the hesitation is decided by the injection condition and characteristics of injector. The generation of shock wave in the spray tip and the detachment of shock wave from the spray tip show little effect on the spray macroscopic characteristics. The ambient gas density and temperature have a significant effect on the maximum of spray tip velocity, types of shock wave and the detachment timing of shock wave from the spray tip.

Soft-Focused Extracorporeal Shock Waves Increase the Expression of Tendon-Specific Markers and the Release of Anti-inflammatory Cytokines in an Adherent Culture Model of Primary Human Tendon Cells

Focused extracorporeal shock waves have been found to upregulate the expression of collagen and to initiate cell proliferation in healthy tenocytes and to positively affect the metabolism of tendons, promoting the healing process. Recently, soft-focused extracorporeal shock waves have also been found to have a significant effect on tissue regeneration. However, very few in vitro reports have dealt with the application of this type of shock wave to cells, and in particular, no previous studies have investigated the response of tendon cells to this impulse. We devised an original model to investigate the in vitro effects of soft-focused shock waves on a heterogeneous population of human resident tendon cells in adherent monolayer culture. Our results indicate that soft-focused extracorporeal shock wave treatment (0.17 mJ/mm2) is able to induce positive modulation of cell viability, proliferation and tendon-specific marker expression, as well as release of anti-inflammatory cytokines. This could prefigure a new rationale for routine employment of soft-focused shock waves to treat the failed healing status that distinguishes tendinopathies.

Numerical Modeling and Validation of Supersonic Two-Phase Flow of CO2 in Converging-Diverging Nozzles

Carbon dioxide is an attractive alternative to conventional refrigerants due to its low direct global warming effects. Unfortunately, CO2 and many alternative refrigerants have lower thermodynamic performance resulting in larger indirect emissions. The effective use of ejectors to recover part of the lost expansion work, which occurs in throttling devices, can close this performance gap and enable the use of CO2. In an ejector, the pressure of the motive fluid is converted into momentum through a choked converging-diverging nozzle, which then entrains and raises the energy of a lower-momentum suction flow. In a two-phase ejector, the motive nozzle flow is complicated by the nonequilibrium phase change affecting local sonic velocity and leading to various types of shockwaves, pseudo shocks, and expansion waves inside or outside the exit of the nozzle. Since the characteristics of the jet leaving the motive nozzle greatly affect the performance of the ejector, this paper focuses on the details of flow development and shockwave interaction within and just outside the nozzle. The analysis is based on a high-fidelity model that incorporates real-fluid properties of CO2, local mass and energy transfer between phases, and a two-phase sonic velocity model in the presence of finite-rate phase change. The model has been validated against the literature data for two-phase supersonic nozzles and overall ejector performance data. The results show that due to nonequilibrium effects and delayed phase change, the flow can choke well downstream of the minimum-area throat. In addition, Mach number profiles show that, although phase change is at a maximum near the boundaries, the flow first becomes supersonic in the interior of the flow where sound speed is lowest. Shock waves occurring within the nozzle can interact with the boundary layer flow and result in a ‘shock train’ and a sequence of subsonic and supersonic flow previously observed in single-phase nozzles. In cases with lower nozzle back pressure, the flow continues to accelerate through the nozzle and the exit pressure adjusts in a series of supersonic expansion waves.

The Weak and Strong Oblique Shock Waves Appeared on the Carbon Dioxide Two-phase Flow in the Ejector Refrigeration Cycle

After the Great East Japan Earthquake, the saving energy became the one of the most important issues. Especially, saving the electrical power for air-conditioning at summer time is a problem of great urgency. We have been developing the ejector refrigeration system which can improve coefficient of performance of refrigeration systems by converting exhausted expansion energy into useful pressure energy. The performance of the ejector is greatly affected by the pressure recovery at the mixing section in the ejector. It is elucidated by our recent research on the carbon dioxide refrigeration cycle that the pressure recovery at the ejector is performed by oblique shock waves appeared in the mixing section. The purpose of this research is to clarify the characteristics of the two-phase flow oblique shock waves in the supersonic carbon dioxide two-phase flow. It is shown by the theoretical analyses that the two types of oblique shock waves occur on the supersonic two-phase flow. One is the week shock wave behind of which the flow is still a subsonic state. The other is the strong oblique shock wave which has a large pressure recovery. And the experimental research also carried out by using the carbon dioxide two-phase flow channel. The theoretical results are compared with the experiment.

Experimental study on hysteresis phenomena of shock wave structure in an over-expanded axisymmetric jet

In recent studies on two-dimensional supersonic jets, it is reported that the hysteresis phenomenon for the reflection type of shock waves in the jet flow field is occurred under the quasi-steady flow condition and this phenomenon is affected by the transitional pressure ratio between the regular reflection and Mach reflection. However, so far, there are few researches on the hysteresis phenomenon for the transition of shock waves between regular and Mach reflection in over-expanded supersonic jets and the phenomenon has not been investigated satisfactorily. Therefore, the purpose of this study is to clarify the hysteresis phenomena for the reflection type of shock wave in the over-expanded axi-symmetric supersonic jet experimentally, and to discuss the relationship between hysteresis phenomenon and rate of the change of pressure ratio with time. Furthermore, the effect of Mach number at the nozzle exit on hysteresis loop was investigated for two kinds of nozzle.

Hysteretic phenomenon of shock wave in a supersonic nozzle

In recent years, hysteretic phenomena in fluid flow systems drew attention for their great variety of industrial and engineering applications. When the high-pressure gas is exhausted to atmosphere from the nozzle exit, the expanded supersonic jet with the Mach disk is formed at a specific condition. In two-dimensional expanded supersonic jet, the hysteresis phenomenon for the reflection type of shock wave is occurred under the quasi-steady flow and the transitional pressure ratio between the regular reflection and Mach reflection is affected by this phenomenon. However, so far, there are very few researches for the hysteretic phenomenon of shock wave in a supersonic internal flow and the phenomenon has not been investigated satisfactorily. The present study was concerned with the experimental and numerical investigations of hysteretic phenomena of shock wave in a supersonic nozzle, and discussed the relationship between hysteresis phenomenon and rate of the change of pressure ratio with time.