The Richtmyer-Meshkov Instability On Minimum-surface Featured Interface

When an interface separating two different fluids is impulsively accelerated, the interface is hydrodynamically unstable, and the turbulent mixing dominates the flow eventually, which is known as Richtmyer-Meshkov instability (RMI). A great attention is attracted on RMI all over the world due to the applications in scientific and engineer-ing fields, such as the compressible turbulent flow, the supersonic combustion ramjet and the inertial confinement fusion. Although the two-dimensional (2D) RMI was ex-tensively studied in the previous work, researches on fundamental mechanisms in the three-dimensional (3D) RMI were still limited. In the present work, experimental and theoretical investigations are performed on the interaction of a shock wave with the3D gaseous cylinder and the3D perturbed interface with minimum-surface feature.A novel method to generate the gaseous interface with the minimum-surface fea-ture is developed by soap film technique in shock-tube experiments. The geometry of the discontinuous interface can be controlled by its boundaries, which are fixed on the experimental facility. The formed interface can be accurately described by mathemati-cal formula. By changing the shape of the boundaries, two types of interfaces with the minimum-surface feature are realized in the3D RMI experiments. It is confirmed by experiments that there are less disturbances in the flow field and the formed interface evolves more symmetrically due to the lack of support in the new method.The interaction of a planar shock wave with a gaseous cylinder is experimentally studied and it is found that the initial shape of cylinders could affect the instability evolution. In the case of3D cylinder with the minimum-surface feature, the interfacial evolution varies with the cross-section of the cylinder whether the gas inside is sulfur hexafluoride (SF6) or helium (He), which is found to be closely related to the initial geometry of the cylinder. As the incident shock wave passes through the cylindrical inhomogeneity, the components of vorticity deposited on the interface are not only along the axial direction, but also along the circumferential direction. Because the principal curvatures of the interface with minimum-surface feature are in different directions, the instability evolution induced by the two components of deposited vorticity is suppressed by each other, resulting in the instability growth slower than that in the corresponding2D configuration.The interaction between a planar shock wave and a sinusoidal bounded interface with the minimum-surface feature is experimentally studied. In the case of air/SF6inter- face, the growth rate of perturbations in current3D configuration decreases about40%in amplitude comparing to the corresponding2D single-mode configuration. A theoret-ical model, which illustrates the effects of principal curvatures, is then developed and validated by the experimental results. In the case of SF6/air interface, the perturbation decreases in amplitude until its phase is reversed. The growth of perturbation ampli-tude, when nondimensionalized by the modified3D impulsive model using the average of pre-and post-shock perturbation amplitude, collapses into one curve.In the theoretical study, a linear model to predict the RMI evolution of arbitrary shapes is proposed by the linear stability analysis in the3D RMI system, and the3D RMI is found to be quite dependent on the principal curvatures of the shocked interface. A nonlinear model is proposed by matching the linear model to the asymptotic solution in order to predict the nonlinear RMI behavior. The linear and nonlinear models are then validated by the experimental results.The interaction of a cylindrical shock wave with a spherical SF6bubble is experi-mentally studied. It is found that the transmitted shock wave focuses inside the bubble and a jet at the downstream of the spherical interface is induced by the pressure jump. When the incident shock transmits toward the converging center, the shock strength in-creases and the pressure jump induced by the focusing of shock is stronger than that in the configuration of a planar shock wave, so that the velocity of jet is higher. When the incident shock is reflected at the converging center, the reflected shock transmits back-wards and the shock strength decreases. As the reflected shock impacts the vortex ring, the flow becomes chaotic and turbulent mixing occurs eventually. The experimental results provide a fundamental base for the study of the interaction between a perturbed interface and the complex curved shock wave.In the present dissertation, effects of three dimensions on two classical RMI prob-lems, i.e. the interaction of shock waves with the cylindrical inhomogeneity and per-turbed interface, are investigated. The study provides a new method to research the3D RMI. Because the disturbance induced by the supporting device on the instability is largely lessened owing to the membrane formation method in the experiment, the evo-lution of the shocked interface appears more symmetric than the previous results. The experimental results can be served as a good benchmark for numerical codes and3D RMI models.