Circular Shock Waves Research Articles

Circular dispersive shock waves in colloidal media

A dispersive shock wave (DSW), with a circular geometry, is studied in a colloidal medium. The colloidal particle interaction is based on the repulsive theoretical hard sphere model, where a series in the particle density, or packing fraction is used for the compressibility. Experimental results show that the particle interactions are temperature dependent and can be either repulsive or attractive, so the second term in the compressibility series is modified to allow for temperature dependent effects, using a power-law relationship. The governing equation is a focusing nonlinear Schrödinger-type equation with an implicit nonlinearity. The initial jump in electric field amplitude is resolved via a DSW, which forms before the onset of modulational instability. A semi-analytical solution for the amplitude of the solitary waves in a DSW of large radius, is derived based on a combination of conservation laws and geometrical considerations. The effect of temperature and background packing fraction on the evolution of the DSW and the amplitude of the solitary waves is discussed and the semi-analytical solutions are found to be very accurate, when compared with numerical solutions.

Transient SU/PG modelling of discontinuous wave propagation

This study proposed a transient 2-D hydrodynamic model adopting streamline upwind/Petrov-Galerkin (SU/PG) scheme for the analysis of discontinuous wave propagations by the sudden collapse of circular cylinder as well as by the dam break. The computation of sudden collapse in the circular cylinder problem identified both the outward-propagating circular shock waves and inward-propagating circular rarefaction waves. It was also confirmed that the advancing front and the depressive wave preserve the cylindrical symmetry, and the bore wave without oscillations was computed. The simulation results of the dam break shows that the bore and depressive waves which are propagating downstream and upstream, respectively are effectively developed and the shock front is sharply captured. The SU/PG scheme needs no tuning of adjustable parameters such as the artificial viscosity coefficient to be a viable option for accurate prediction of the flow characteristics in a discontinuous free surface case.

Feasibility of shock attenuation by simple obstacles in mitigating severe accident explosive loads

Fukushima severe accident showed that explosions are no longer exclusive in nuclear power plants and creative safety features would be beneficial to preserve the integrity of vital components against such explosions. Based on this motivation, simple obstacles are suggested as a means to attenuate shock waves that may arise from severe accident explosions and the effectiveness is investigated by computations employing fully compressible viscous Navier–Stokes equations of the FLUENT code. Two- and three-dimensional computations for a shock tube filled with air are performed and the computed peak pressure and arrival time are validated against existing experimental data and analyses. Effects of structural shapes and rectangular rigid obstacles on shock attenuation in simple geometries are preliminarily analyzed and the results show that the end wall peak pressure is reduced by about 18–30%. As a demonstration in a plant scale, a high pressure source of 0.2m radius semicircle is positioned at the bottom center of the two-dimensional hypothetical reactor cavity model (5.4m by 9.4m) and multiple rigid obstacles are positioned at the half-way between a reactor vessel and the pressure source. Incident circular shock wave is dispersed by the obstacles and the peak pressures at the reactor vessel bottom head center and the 45° regions are reduced by about 35% and 50%, respectively. This study implies the feasibility of simple obstacles for attenuating shock waves from the explosions expected under nuclear power plant severe accidents.

Semi-analytical solutions for dispersive shock waves in colloidal media

The diffractive resolution of a discontinuity at the edge of an optical beam in a colloidal suspension of spherical dielectric nanoparticles by a collisionless shock, or dispersive shock wave, is studied. The interaction of the nanoparticles is modelled as a hard-sphere gas with the Carnahan–Starling formula used for the gas compressibility. The governing equation is a focusing nonlinear Schrödinger-type equation with an implicit nonlinearity. It is found that the discontinuity is resolved through the formation of a dispersive shock wave which forms before the eventual onset of modulational instability. A semi-analytical solution is developed in the (1 + 1) dimensional case by approximating the dispersive shock wave as a train of uniform solitary waves. A semi-analytical solution is also developed for a (2 + 1) dimensional circular dispersive shock wave for the case in which the radius of the bore is large. Depending on the value of the background packing fraction, three qualitatively different solitary wave amplitude versus jump height diagrams are possible. For large background packing fractions a single stable solution branch occurs. At moderate values an S-shaped response curve results, with multiple solution branches, while for small values the upper solution branch separates from the middle unstable branch. Hence, for low to moderate values of the background packing fraction the dispersive shock bifurcates from the low to the high power branch as the jump height, the height of the input beam’s edge discontinuity, is increased. These multiple steady-state response diagrams, also typically found in combustion applications, are unusual in applications involving solitary waves. The predictions of the semi-analytical theory are found to be in excellent agreement with numerical solutions of the governing equations for both line and circular dispersive shock waves. The method used represents a new technique for obtaining semi-analytical results for a dispersive shock wave in a focusing medium.

Passive control of transonic flow fields with shock wave using non-equilibrium condensation and porous wall

When non-equilibrium condensation occurs in a supersonic flow field, the flow is affected by the latent heat released. In the present study, in order to control the transonic flow field with shock wave, a condensing flow was produced by an expansion of moist air on a circular bump model and shock waves were occurred in the supersonic parts of the fields. Furthermore, the additional passive technique of shock / boundary layer interaction using the porous wall with a cavity underneath was adopted in this flow field. The effects of these methods on the shock wave characteristics were investigated numerically and experimentally. The result obtained showed that the total pressure loss in the flow fields might be effectively reduced by the suitable combination between non-equilibrium condensation and the position of porous wall.

Effect of nonequilibrium condensation of moist air on transonic flow fields

When condensation occurs in a supersonic flow field, the flow is affected by the latent heat released. In the present study, a condensing flow was produced by an expansion of moist air in nozzle with circular bump models and shock waves occurred in the supersonic parts of the flow fields. The experimental investigations were carried out to show the effects of initial conditions in the reservoir and nozzle geometries on the shock wave characteristics and the turbulences in the flow fields. Furthermore, in order to clarify the effect of condensation on the flow fields with shock waves, Navier-Stokes equations were solved numerically using a 3rd-order MUSCL type TVD finite-difference scheme with a second order fractional step for time integration. As a result, the effect of condensation on the aspect of flow field has been clarified.

On shock waves in a confined reflector

The main objective of the present work is to carry out experimental studies concerning generation of polygonal-shaped shock waves in a procedure introduced by Apazidis and Lesser [N. Apazidis, M.B. Lesser, On generation and convergence of polygonal-shaped shock waves, J. Fluid Mech. 309 (1996) 301–309]. In this procedure an expanding circular cylindrical shock wave with constant Mach number distribution is generated at the center of a confined air-filled chamber. The chamber boundary has the form of a slightly perturbed circle. The shock reflects off the boundary and converges in the inner of the chamber into a polygonal shape. For this experimental study, an air-filled chamber was designed and manufactured. Shocks were generated by means of an electric discharge. A schlieren system with camera and delayed flash device, was used in order to visualize the process. Equipment for time control and measuring was also used. The experimental results of the current investigation confirmed the theoretical predictions obtained in earlier studies of similar problems. The major new result showed that it is possible to generate polygonal-shaped shocks with sharp corners and plane sides by means of reflection from a smooth boundary. The shock strength was estimated to M=1.1 and the observed shock form confirmed the earlier theoretical predictions. The proposed experimental procedure showed to be a simple, stable, repeatable and reliable method to produce highly symmetrical polygonal-shaped converging shocks.

201 湿り空気の非平衡凝縮が遷音速流れ場に及ぼす影響

When condensation occurs in a transonic flow fields, the flow is affected by the latent heat released. In the present study, a condensing flow was produced by an expansion of moist air in transonic flow fields using circular bump model and shock waves were occurred in the supersonic parts of the fields. The experimental investigations were caned out to show the effects of initial conditions and note geometries on the shock wave characteristics and the turbulences in the flow fields.

Oscillation of Circular Shock Waves with Upstream Nonuniformity.

Until to the authors' previous reports on the oscillation of circular shock waves, investigations have been concerned with situations where the upstream flow is uniform, and oscillation and deformation are induced by only downstream conditions. However in the centrifugal compressor, the flow into the diffuser becomes nonuniform due to the impeller wake and the stall in the upstream impeller, which causes deformation and oscillation of the shock wave. Here, the above effects are considered. The upstream disturbance was generated by cylindrical bars. An imperfectly circular shock wave was induced by the wake, and the oscillation state, along with the modes caused by forced oscillation, was investigated experimentally. It was found that the basic mode of oscillation is predominant and that the oscillation is weaker than in the case of a uniform upstream.

Oscillation of Circular Shock Waves with Upstream Nonuniformity.

Up to the authors' previous reports on the oscillation of the circular shock waves, the investigations have been concerned with situations where the upstream flow is uniform, and oscillation and deformation were induced by only downstream conditions. But in the centrifugal diffuser of a centrifugal compressor, the flow into the diffuser becomes nonuniform due to the impeller wake and the stall in the upstream impeller, which causes deformation and oscillation of the shock wave. Here, the above effects are considered, and the upstream disturbance is generated by cylindrical bars. The imperfect circular shock wave was induced by the effect of the wake, and the oscillation state, along with the oscillation modes caused by forced oscillation, is investigated experimentally. It was found that the basic mode of the oscillation is predominant and that the oscillation is weaker than in the case of uniform upstream.

Resonance of Circular Shock Waves

Resonance of Circular Shock Waves

Oscillation of Nearly Circular Shock Waves

Oscillation modes of nearly circular shock waves in supersonic radial flow were investigated both theoretically and experimentally. The shock waves deformed from circular shape were obtained by the asymmetric back pressure produced by down-stream obstacles. Oscillation modes of the shock waves were investigated by means of statical study of the phase function and mean coherence in each static mode. The oscillation consisted of mode 0 and the same mode as the original static shape. The frequency of each static mode depended on the deformation from the real circle.

Resonance of circular shock wave.

In supersonic centrifugal compressors or disc MHD power generators, oscillation modes of the circular shock wave can be caused by the static change or the dynamic change of the back pressure. While previous studies, which included only the former effects, were carried out both experimentally and theoretically, the latter effects of forced oscillation are considered here. The excitation of the back pressure fluctuation in a downstream stagnation chamber was accomplished by rotating a butterfly valve. The pressure fluctuation was measured to investigate the resonance of the circular shock wave at concentric positions in the vicinity of the first shock and in the downstream stagnation chamber. A-D-converted signals were statistically correlated to extract the spacial oscillation modes. Resonance was confirmed to occur when the excitation frequency was near the natural frequency of mode 0. Furthermore, the small pertubation of the higher harmonic modes in the downstream stagnation chamber influenced the oscillation modes of the circular shock wave.

Oscillation of nearly circular shock waves.

Oscillation modes of nearly circular shock waves in supersonic radial flow were investigated both theoretically and experimentally. The shock waves deformed from circular shape were obtained by the asymmetric back pressure produced by downstream obstacles. Oscillation modes of the shock waves were investigated by use of the statistical study of the phase function and the mean coherence in each static mode. The oscillation consisted of mode 0 and the same mode as the original static shape. The frequency of each static mode depended on the deformation from the real circle.

Oscillation of Circular Shock Wave

Oscillation modes of a circular shock wave in supersonic radial flow were studied both experimentally and theoretically. The pressure fluctuation was measured on concentric positions to investigate modes of a circular shock wave in case of mean radii of 70 and 77 mm, and the A-D converted signals were statistically correlated. A simple model of an oscillating shock wave was proposed. Frequency of the oscillation increased from low to high values with the increase in its radius. The oscillation was mainly consisted of mode 0 superposed by modes of 1, 2 and 4. The mode 1 is considered to be weak. The experimental frequency of each mode agreed well with the theoretical results.

Oscillation of circular shock wave.

Oscillation modes of a circular shock wave in supersonic radial flow were studied both experimentally and theoretically. The pressure fluctuation was measured on concentric positions to investigate modes of a circular shock wave in case of mean radii of 70 and 77 mm, and the A-D converted signals were statistically correlated. A simple model of an oscillating shock wave was proposed. Frequency of the oscillation increased from low to high values with the increase in its radius. The oscillation was mainly consisted of mode 0 superposed by modes of 1, 2 and 4. The mode 1 is considered to be weak. The experimental frequency of each mode agreed well with the theoretical results.

Model for Converging Detonations in Solid Explosives

The fluid-dynamic equations which describe converging detonation fronts in high explosives are solved over a coordinate system that changes from circular to a pleated pattern as the detonation converges. There are three reasons for introducing such a coordinate system rather than making the usual assumption that when a spherical or cylindrical explosive charge is initiated simultaneously on its curved surface the detonation front maintains its symmetry as the detonation converges to the center: (1) Calculations made elsewhere show that a converging circular shock wave is unstable. (2) Calculations in this paper show that if spherical or cylindrical symmetry is maintained, density and velocity become infinite, but if the detonation front folds these quantities remain finite except at a few points which can be removed by cuts. The average fluid velocity remains almost constant over 99% of the detonation front. (3) Experiments indicate that a cylindrical detonation front becomes rather symmetrically deformed.