Interaction Of Planar Shock Wave Research Articles

Interaction of planar shock wave with three-dimensional heavy cylindrical bubble

Interactions of a planar shock wave with two-dimensional (2D), three-dimensional (3D) concave, and 3D convex SF6 cylindrical bubbles surrounded by air are studied both experimentally and numerically. The effects of initial interface curvature on the bubble deformation and wave propagation are highlighted. The cylindrical bubbles are generated by a wire-restriction method based on the soap-film technique, and their shapes are well controlled by adjusting the pressure difference across the interface. The high-speed schlieren results demonstrate that the evolving interfaces develop more symmetrically than previous studies as they are free of holder and fewer disturbance waves are generated. Typical evolution processes of the 2D bubble such as the jet formation and vortex pair formation are clearly captured. Compared with the 2D case, the oppositely (identically) signed principal curvatures of the concave (convex) boundary produce more complicated high pressure fields and 3D additional baroclinic vorticity. For 3D cases, the numerical results show that the wave patterns in the symmetry or boundary slice are distinct from the 2D case owing to the 3D movement of the generated waves, and the jet structure presents an evident three dimensionality. In particular, for the concave bubble, a certain slice between the boundary and symmetry slices presents the fastest-developing jet, while for the convex case the fastest jet emerges at the boundary slice. The upstream interface along the symmetry slice of the concave (convex) bubble moves faster (slower) than that of the 2D case, which is reasonably predicted by a 3D theoretical model.

Numerical investigation on the interaction of planar shock wave with an initial ellipsoidal bubble in liquid medium

This paper performs numerical investigations on the interaction of shock wave with an ellipsoidal bubble in liquid medium. The governing equations, including the conservative Euler equations and the non-conservative transport equation of the liquid volume fraction, are discretized based on the finite volume method. A tangent of hyperbola for interface capturing (THINC) interface reconstruction scheme is employed for the phasic densities and the liquid volume fraction to maintain the interface sharpness. The major-axis (z-axis) of the bubble is parallel to the incident planar shock wave. Different collapse behaviors are observed for two ellipsoidal geometries, named as the disk-like bubble and rugby-like one. Different collapse patterns of an initial ellipsoidal bubble are presented and the manifestation is that the transverse jets pierce the bubble differently, classified as along the centerline, off-centerline along the circumferential direction or along the meridian line if the aspect ratio is varied. For the disk-like bubble, it presents the strongest collapsing process under certain eccentricity, characterized by the highest water hammer pressure under the same incident shock strength. The second sheeting jet is an important factor that leads to the collapse of the remaining bubbles pierced by the first transverse jet.

Study on Mach stems induced by interaction of planar shock waves on two intersecting wedges

The properties of Mach stems in hypersonic corner flow induced by Mach interaction over 3D intersecting wedges were studied theoretically and numerically. A new method called “spatial dimension reduction” was used to analyze theoretically the location and Mach number behind Mach stems. By using this approach, the problem of 3D steady shock/shock interaction over 3D intersecting wedges was transformed into a 2D moving one on cross sections, which can be solved by shock-polar theory and shock dynamics theory. The properties of Mach interaction over 3D intersecting wedges can be analyzed with the new method, including pressure, temperature, density in the vicinity of triple points, location, and Mach number behind Mach stems. Theoretical results were compared with numerical results, and good agreement was obtained. Also, the influence of Mach number and wedge angle on the properties of a 3D Mach stem was studied.

Experimental investigation on the interaction of planar shock wave with cylindrical gaseous inhomogeneity

The interaction of a planar shock wave (Mach number of 1.2) with a gas cylinder (helium cylinder or SF6 cylinder) is experimentally studied using the high-speed schlieren photography. Because the soap film has less influence on the interface evolution than the solid diaphragm and the soap film cylinder can effectively suppress the gas exchange at the interface compared with the diaphragm-less cylinder, a circular wire-restriction method of using the soap film technique is introduced to generate the interface separating the experimental gas from the ambient gas. Illuminated by a DC source, the evolution of the gas cylinder accelerated by a shock wave is captured by the high-speed video camera in a single test run and the wave patterns are also observed. It is shown from the results that the SF6 cylinder is firstly compressed and accelerated by the shock, and then a jet is formed at the downstream interface due to the transmitted shock focusing. Subsequently, induced by the vorticity, the cylinder is developed into a mushroom shape and finally the turbulent mixing occurs. After the impact of the shock wave, the helium cylinder is firstly accelerated and the reversal phase occurs at the upstream interface. Afterwards, a jet is generated from the upstream interface and gradually tears through the downstream interface. Eventually, the interface is developed into two independent vortexes. Compared with the previous studies, the results in this work behave more symmetry and fewer disturbances are generated in the flow field due to the absence of the holder. Moreover, the variation of the interface scales with time is measured from which the changes of the interface can be well interpreted. At last, the shock and interface velocities in SF6 case obtained in the experiment are found to have a satisfactory agreement with the theoretical prediction from one-dimensional gas dynamics, which verifies the interface formation method to some extent.

Experimental study on the interaction of planar shock wave with polygonal helium cylinders

The evolution of a polygonal helium cylinder impacted by a planar weak shock wave is investigated experimentally. Three different polygonal interface shapes including a square, an equilateral triangle and a diamond are formed by the soap film technique, where thin pins are used as edges to connect the adjacent sides of soap films. Shock tube experiments are conducted to obtain sequences of schlieren images using a high-speed video camera. In each case, the development of the wave system and the evolution of the polygonal helium cylinder subjected to a planar shock wave with a Mach number of \(1.21\pm 0.03\) are obtained in a single test. For comparison, numerical simulations are also performed using the two-dimensional and axisymmetric vectorized adaptive solver (VAS2D). The variations of the interface properties including the displacement, the length and the height of the distorted interfaces in the three cases are given. For the square helium cylinder, two counter-rotating vortices connected by a thin link can be observed. The height of the distorted interface always increases, and its length first decreases and then increases. In the triangle case, an air jet is formed quickly and moves downwards within the volume and eventually encounters the downstream interface, resulting in a bulge on the downstream interface. In the diamond case, the upstream interface quickly forms a re-entrant air jet similar to that in the triangle case, and the downstream interface becomes flat. The circulation in the three cases is calculated numerically, revealing the main driving mechanism of the development of the shocked polygonal interface. This work exhibits the great potential of the experimental method in studying shock–polygonal interface interactions in the case of slow/fast (air/helium) situations.

Velocity scaling of a shock wave reflected off a circular cylinder

Two different approaches are undertaken to investigate the interaction of planar shock waves with circular cylinders. Experiments are conducted in a shock-tube apparatus equipped with a schlieren-based optical system to monitor the interaction, and numerical simulations are carried out using an in-house computer code to simulate similar problems. The incident shock-wave Mach number is varied in the range 1.1-1.4. Excellent agreement is found between the simulations and the experiments in terms of shock patterns, even though the model is based on an inviscid approach. Quantitative comparisons between the experimental results for different initial conditions (shock-wave strength, cylinder diameter, and working gas) are made to find the physical parameters affecting the path of the reflected shock. An approximate universal relation is derived, which predicts the reflected-shock trajectory along the axis of symmetry as a function of the incident-shock Mach, the diameter of the cylinder, and the gas properties. This relation is valid in the vicinity of the cylinder in the range of 0.1-5 D, where D is the cylinder diameter. It is found that the reflected shock from the cylinder evolves as in the case of a reflected-shock wave from a planar wall multiplied by a reduction factor, which depends on the incident-shock Mach number and the ratio of specific heats.

The interaction of planar shock waves with multiphase saturated flexible porous materials – a numerical investigation

The three-dimensional governing macroscopic equations of the flow field which is developed when an elasto-plastic highly deformable open-cell porous medium whose pores are uniformly filled with liquid and gas is struck head-on by a planar shock wave, are developed using a multiphase approach. The one-dimensional version of these equations is solved numerically using an arbitrary Lagrangian Eulerian (ALE) based numerical code. The numerical predictions are compared qualitatively to experimental results from various sources and good agreements are obtained. This study complements our earlier studies in which we solved, using an ALE-based numerical code, the one-dimensional governing equations of the flow field which is developed when an elasto-plastic flexible open-cell porous medium, capable of undergoing extremely large deformations, whose pores are saturated with gas only, is struck head-on by a planar shock wave.

Bubble dynamics, shock waves and sonoluminescence

Sound and light emission by bubbles is studied experimentally. Single bubbles kept in a bubble trap and single lasergenerated bubbles are investigated using ultrafast and highspeed photography in c...

Head-on interaction of planar shock waves with ideal rigid open-cell porous materials. Analytical model

An analytical model for predicting the flow field which results immediately after the dead-on collision of planar shock waves with ideal rigid porous materials in the vicinity of the porous material/air interface was developed. In addition, a simplified empirical method for readily estimating the enhanced pressure peak at the shock-tube end-wall is proposed. The predictions of the proposed analytical and empirical models were compared to experimental results. The agreement was found to be good to excellent.

Dust entrainment by means of a planar shock induced vortex over loose dust layers

The recent study of Ben-Dor and Rayevsky (1994) regarding the interaction of planar shock waves with high density layers was reconsidered in order to demonstrate a possible dust entrainment mechanism which has not received appropriate attention so far. It was shown that, as a result of the interaction, a large vortex is generated. This vortex could in fact contribute to the entrainment of dust when planar shock waves interact with loose dusty layers.

Head-on interaction of planar shock waves with polyurethane foams — a semi-empirical model

A semi-empirical model for calculating the velocity of the compaction wave which is transmitted into a polyurethane foam struck head-on by a planar shock wave is developed on the basis of some experimental observations. The compaction wave induced velocity and the induced density are determined. Predictions of the model are compared to experimental results and found to be satisfactory.