Formation and propagation of cylindrical shock waves in a pulsed induction discharge

An experimental investigation was made into the formation and propagation of cylindrical collapsing shock waves in a pulsed induction gas discharge. The shock fronts were made visible and their propagation velocity measured by means of the schlieren method in conjunction with high-speed cine photography in the photoscanning regime and frame-by-frame detection, which made it possible, using the experimental data, to analyze the formation and propagation of the shock waves. A physical picture of the individual stages in the development of the discharge is given on the basis of the experimental results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 129–133, January–February, 1981.We are thankful to Yu. P. Raizer for helpful discussions of the work.     

Hysteresis phenomenon at interaction of shock waves generated by a cylinder array

This paper describes investigations of the interaction between bow shock waves generated by cylindrical bodies in a supersonic flow. Numerical simulations are performed using the inviscid Euler equations for cylinders whose axes are parallel to each other and normal to the flow direction. Mostly an infinite periodical cylinder array is considered, but the case of two cylinders is also briefly discussed. Three different regimes of the shock wave interaction, a regular interaction, a Mach interaction, and a choked flow, have been observed for the flow through the periodical cylinder array. In the case of the flow around two bodies, the choked flow is replaced by a regime with a collective bow shock. The transition between different flow regimes is studied by varying the inflow Mach number or the distance between the cylinders. A hysteretic behavior at the transition between the regular and Mach interactions has been observed. The transition is governed by the theoretical detachment and von Neumann criteria based on the local shock wave inclination at the interaction point.     

Focusing shock waves generated by an accelerating projectile

Unsteady flow fields past a projectile either in parabolic motion or in accelerated motion are investigated numerically, with special attention to shock wave focusing phenomena induced by the motions. The two-dimensional Euler equations are solved by a moving-cell, MUSCL TVD finite-volume method with Steger-Warming flux-vector splitting. The pattern of shock wave focusing induced by the projectile is found to be similar to that of shock waves reflected from a concave wall observed in a laboratory experiment using a shock tube. Effects of projectile shapes and trajectories on focusing are also examined.     

Comparison of different methods of measurement of pressure of underwater shock waves generated by electrical discharge

Different methods for measurement of strong underwater shock waves pressure pulses with peak pressures of up to 200 MPa and rise time of tens to hundreds of nanoseconds are described and compared. The experimental techniques include direct methods of pressure measurement using various electromechanical gauges such as quartz, carbon-based, and commercially available PCB gauges, and nondirect methods based on measurement of the velocity of the shock wave such as time-of-flight and fast-streak photography. Advantages and disadvantages of the used gauges and methods are discussed. The shock waves were produced by underwater electrical discharge (discharge current amplitude ≤100 kA, pulse duration ≤5 μs) initiated by an exploding wire. A good correspondence between the pressure amplitudes measured by the various gauges and methods was observed. The obtained dependence of the shock wave pressure on the distance from the discharge channel was found to be best fitted by a r ^−0.7 law. It is also shown that none of these methods can be used to determine the time evolution of the pressure behind the front of the shock wave.     

The interaction between shock waves and foam in a shock tube

An experimental study and a numerical simulation were conducted to investigate the mechanical and thermodynamic processes involved in the interaction between shock waves and low density foam. The experiment was done in a stainless shock tube (80 mm in inner diameter, 10 mm in wall thickness and 5 360 mm in length). The velocities of the incident and reflected compression waves in the foam were measured by using piezo-ceramic pressure sensors. The end-wall peak pressure behind the reflected wave in the foam was measured by using a crystal piezoelectric sensor. It is suggested that the high end-wall pressure may be caused by a rapid contact between the foam and the end-wall surface. Both open-cell and closed-cell foams with different length and density were tested. Through comparing the numerical and experimental end-wall pressure, the permeability coefficients α and β are quantitatively determined.     

Two-dimensional self-similar flows generated by the interaction between a shock and low-density gas regions

A plane time-dependent flow generated by the interaction between a normal shock and a low-density gas region occupying a quarter of the plane is theoretically investigated. Numerical simulation is performed on the basis of the Euler equations. It is established that after the shock has come in contact with the low-density region two-dimensional self-similar flows of different type can develop. On regular interaction the original shock is refracted on the low-density region with the matching of the accelerated and original shock and the refracted contact discontinuity at a common point. On irregular interaction a complicated flow occurs; it includes curved and oblique shocks, a contact discontinuity with points of inflection, multiple matching points, a high-pressure jet, and a layered vortex. The jet and vortex structures are investigated in detail. The tendency of the gasdynamic structure development with variation in the control parameters of the problem is determined. A simplified, near-analytical technique for estimating the slopes of the main shocks and the gas parameters behind them is proposed.     

Experimental investigation of the interaction of shock waves with textiles

Experimental studies have been performed to investigate the pressure amplification experienced behind a textile when exposed to a shock wave. Three textiles with different masses and air permeabilities were studied. Mach numbers for tests varied between 1.23 and 1.55. The distance between the back wall and the textile was varied between 3 and 15 mm. It was found that in most cases the presence of the textile led to a pressure amplification at the back wall. This amplification was dependent on the textile, Mach number and distance from the back wall. The processes causing the pressure amplification were identified by analysing pressure traces and contact shadowgraphs. It was found that when the incident wave impinges on the textile, a part is reflected upstream and a part is transmitted through the textile. The transmitted portion reflects back and forth in the gap between the textile and the back wall leading to a back wall pressure trace with a stepped profile. In addition, the textile moves towards the back wall causing compression waves to propagate towards the back wall. The combination of the stepped profile and the compression waves cause the pressure amplification. The contribution of each mechanism depends on the textile properties. Approximate wave diagrams have been constructed. Tests involving multiple layers of textiles are also discussed. Received 17 October 2000 / Accepted 2 February 2001     

The interaction between shock waves and solid spheres arrays in a shock tube

When a shock wave interacts with a group of solid spheres, non-linear aerodynamic behaviors come into effect. The complicated wave reflections such as the Mach reflection occur in the wave propagation process. The wave interactions with vortices behind each sphere‘s wake cause fluctuation in the pressure profiles of shock waves. This paper reports an experimental study for the aerodynamic processes involved in the interaction between shock waves and solid spheres. A schlieren photography was applied to visualize the various shock waves passing through solid spheres. Pressure measurements were performed along different downstream positions. The experiments were conducted in both rectangular and circular shock tubes. The data with respect to the effect of the sphere array, size, interval distance, incident Mach number, etc., on the shock wave attenuation were obtained.     

Investigations of shock wave interaction with nanosecond surface discharge

Non-stationary plane shock wave interaction with localized nanosecond-lasting surface discharges was investigated. Pulse discharge plasma glow evolution was recorded with a CCD camera and gas flow evolution was recorded with laser shadowgraphy. CFD simulations of pulse energy deposition near the horizontal wall surface in front of the shock wave were carried out. Non-stationary 2D symmetrical flow dynamics were studied and analysis of the instantaneous surface discharge energy rate through CFD and shadow images matching was carried out.     

Experimental study of shock waves from the interaction of a supersonic plasma jet with an ambient gas

Preliminary results of the interaction of a supersonic, radiatively cooled plasma jet with an ambient gas are presented. The experimental setup consists of a radial foil, a mum-thick aluminium disc held between two concentric electrodes and subjected to a 1.4 MA, 250-ns current pulse from the MAGPIE generator. The plasma flow, with typical velocities of ~70?C90?km/s, is produced by the J?× B force acting on the plasma ablated from the foil. A jet is formed from the convergence of this ablated plasma on the axis of the system. A new setup allows the jet to interact with an argon ambient (particle density N ~10^16-17 cm^?3) from a supersonic gas nozzle (Mach ~9). First results are characterised by the presence of several (previously unseen) shock structures, which are formed from the interaction of the jet with the argon ambient.     

Certain three-dimensional flows with Mach interaction of shock waves

In [1, 2] it is shown that there is a range of values of the Mach number and geometric parameters for which flow past conical bodies is realized with plane attached shocks and regular intersection of the shocks in space. In the present article we determine the class of solutions corresponding to flow past conical star-shaped bodies with a configuration of the shocks in space of the Mach type.     

Regular oblique interaction of shock waves coming from the same direction in a conducting medium with a magnetic field

The regular interaction of two plane MHD shock wave fronts overtaking one another at an arbitrary angle is investigated within the framework of the ideal magnetohydrodynamic model. The self-similar solution in which all the discontinuities are explicitly distinguished is obtained by means of a computer. The solution is analyzed over a wide range of the key parameters.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 127–143, November–December, 1995.