Experimental And Numerical Study On Converging Richtmyer-Meshkov Instability

When an interface separating fluids with different properties is accelerated by a shock wave, the amplitudes of initial perturbations on the interface will grow with time, and turbulent mixing between fluids will eventually occur at the late stages due to the appearance of many small random vortices in the flow field. This shock-interface inter-action is often termed as Richtmyer-Meshkov (RM) instability. Due to the applications in both natural and engineering fields, extensive studies on the RM instability have been carried out. In previous work, most studies have paid attention to the RM in-stability induced by the planar shock wave, while the RM instability under converging shock conditions has been seldom investigated. However, in many applications, such as weapon explosion and inertial confinement fusion (ICF), the instability is generally in-duced by converging shock waves. As a consequence, it is crucial to investigate the RM instability induced by converging shock waves. For this purpose, in this thesis, we first design and manufacture a new semi-annular converging shock tube and experimentally investigate the evolution of a single-mode interface impacted by cylindrical converging shock waves. Then, we perform numerical simulations on this problem based on a new solver HOWD (high order WENO and double-flux methods) that can be used for sim-ulating the compressible multicomponent flow with high order accuracy by combining the WENO reconstruction and the double flux method. Moreover, HOWD is adopted to investigate the interaction of a planar shock wave with a three-dimensional gas cylinder. The three-dimensional gas cylinders with convex or concave shapes are considered to illustrate the effect of three-dimensional effects on the gas cylinder evolution.In experimental aspect, a semi-annular converging shock tube is designed and con-structed, which is convenient for producing cylindrical converging shock waves. Based on the shock tube structure, a new drawer-like interface formation device is designed, where a gas interface can be easily formed and placed in the test section. Therefore, it is possible for us to perform the RM instability experiments under cylindrical converging shock conditions in this shock tube. As a validation, the pressure histories along the test section and the schlieren frames of the converging shock wave during the shock propagation in the test section are obtained.The RM instability of an air/SF6 single-mode gaseous interface accelerated by con-verging shock waves is conducted in the semi-annular converging shock tube, and the complete evolution of the interface deformation and the shock propagation is obtained. The variation of the perturbation amplitudes with time is calculated, and three novel mechanisms including Bell-Plesset (BP) effect, Rayleigh-Taylor (RT) effect and sec-ondary instability effect in the converging RM instability are highlighted. Then, the effects of initial conditions (such as the perturbation amplitude, the wave number and the shock strength) on the interface evolution and perturbation growth are discussed.In numerical aspect, a new solver HOWD is developed, which can well capture not only the shock wave and the contact surface, but also the small scale vertical structures in flow field, by combining the WENO reconstruction and the double flux method. Classical examples have been used to verify the capability of the HOWD to simulate the RM instability. The development of the single-mode gaseous interface impacted by cylindrical converging shock waves is also investigated by the numerical simulation based on the HOWD. In the beginning, the numerical results are in good agreement with numerical ones. However, the difference between them increases after the distorted interface being impacted by the reflected shock wave. This phenomenon illustrates that more physical factors, such as real gas effect and boundary effect, should be considered in the numerical simulations of the converging RM instability.The HOWD is adopted to investigate the interaction of planar shocks with three-dimensional gas cylinders, and the numerical results coincide well with the experimen-tal ones in both qualitative and quantitative ways, further verifying the reliability of the numerical method. From the numerical results, one can find that in concave cylinder the boundary plane evolution is promoted, while the symmetry plane evolution is sus-pended. In convex cylinder, on the contrary, the boundary plane evolution is suspended, while the symmetry plane evolution is promoted. These phenomena may result from the difference in the pressure and vorticity distributions caused by the three-dimensional effects of the cylinder.In conclusion, the evolution of an air/SF6 single-mode interface accelerated by cylindrical converging shock waves is obtained in the semi-annular converging shock tube, and the influences of three novel mechanisms of BP effect, RT effect and sec-ondary instability effect on the interface perturbation growth are analyzed. Then the effects of initial conditions (perturbation amplitude, wave number and shock strength) on the RM instability is systematically investigated. Moreover, the developed HOWD is adopted to simulate the interaction of a planar shock with a three-dimensional gas cylinder, and the results show that the interface evolution will be greatly disturbed by initial three-dimensionality of the cylinder.