A simple but effective technique is proposed to generate cylindrical converging shock waves. The shock dynamics is employed to design a curved wall profile of the test section in a shock tube. When a planar shock wave propagates forward along the curved wall, the disturbances produced by the curved wall would continuously propagate along the shock surface and bend the shock wave. As an example, the wall profile for an incident shock Mach number of M 0 = 1.2 and a converging angle of 15°is tested numerically and experimentally. Both numerical and experimental results show a perfect circular shock front, which validates our method.In some applications of shock tube such as inertial confinement fusion, 1 supernova explosion, 2 and shock wave lithotripsy, 3 converging shocks are needed in order to concentrate energy in a small volume. However, it is difficult to generate a cylindrical converging shock wave in an ordinary shock tube due to the initial shape imperfections and the nonlinear wave interactions. 4-6 Experiments of cylindrical converging shock waves interacting with cylindrical bubble have been conducted in an annual coaxial vertical diaphragmless shock tube. 5 A suggestion of gas lens to generate a cylindrical converging shock wave in a twodimensional wedge geometry was proposed by Dimotakis and Samtaney. 6 This consideration can produce a perfect cylindrical converging shock wave theoretically, although the related experimental results have not yet been found from the open publications. In this letter, a simple but effective technique is proposed in order to avoid difficulties in the formation of cylindrical converging shock wave. Specifically, we apply shock dynamics to design a wall profile with a special shape, which transfers the planar shock wave in a shock tube to a cylindrical one.The shock dynamics is a simple and useful theoretical tool to analyze the process of the propagation of shock waves in various phenomena such as diffraction, reflection, refraction, interaction, and so on. Particularly, the theory of disturbance propagating on shock surface presented by Whitham 7 provides us with such a possibility to analyze complicated phenomena of shock diffraction and interaction. The Chester-Chisnell-Whitham ͑CCW͒ relation is the basis of shock dynamics for the case of a uniform quiescent gas ahead of shock, which refers to Chester, 8 Chisnell, 9 and Whitham, 7,10,11 who obtained the same relation using different methods, independently. According to the shock dynamics, when a planar shock wave propagates forward along a continuously concave wall, the disturbances produced by the curved wall would continuously propagate along the shock front and bend the shock wave such that the contact edge of the wall and the shock wave can keep vertically propagating forward. In order to obtain a perfect cylindrical convergent shock wave, the curvature of the profile line should be calculated by shock dynamics. Only a very brief introduction of the shock dynamics is provided here. The method by applying shock dynam...
In our previous work, the technique of generating cylindrical converging shock waves based on shock dynamics theory was proposed. In the present work, a further study is carried out to assess the influence of several parameters including the converging angle θ0, the incident planar shock Mach number M0, and the shock tube height h on the wall profile and the converging shock wave. Combining the high-speed schlieren photography and the numerical simulation with the shock dynamics theory, the characteristics of wall profiles, cylindrical converging shock waves, and thermodynamic properties for different controllable parameters are analyzed. It is found that these parameters have great effects on shapes of the wall profile and experimental investigation favors large values of M0 and h and moderate θ0. The experimental sequences of schlieren images indicate that the shocks moving in the converging part are of circular shapes, which further verifies the method in our previous work. In addition, the changes of the shock Mach number, pressure, temperature, and density are obtained quantitatively. The results show that higher pressure and temperature can be reached in the converging part at the same distance to the center of convergence for larger incident shock Mach numbers, larger shock tube heights, or smaller converging angles. All the database will be useful for understanding the shock focusing and further investigating the Richtmyer-Meshkov instability induced by the converging shock waves.
A compact all-fiber displacement interferometer (AFDI) system, working at 1550 nm, has been developed and tested, and its working fundamentals will be introduced in this letter. In contrast with other models of fiber-optic velocity interferometer system, AFDI adopts a single-mode optic fiber pigtail as the detect head, diameter of which is only 1 mm, to collect directly the reflect laser beam from the moving surface, which makes this instrument have some unique advantages in observing the point movements of a small flyer. Preliminary experiments using this instrument to measure the velocity history of a small aluminum thin foil driven by a nanosecond pulse laser were conducted successfully, the precise velocity history profile deduced from the sharp interference fringes and the nanometer resolution in displacement gives an eloquent proof of its eminent abilities. The field depth (approximately 2 mm) of our AFDI is a little smaller than the DISAR [Weng et al., Appl. Phys. Lett. 89, 111101 (2006)] system, but its compact structure makes it much convenient to operate. Further applications for multipoints velocity history measurements of small targets are under consideration.
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