AbstractWhen an interface separating two fluids of different densities is impacted by a shock wave, initial perturbations on the interface grow continuously with time and later induce a flow transition to turbulent mixing. This type of hydrodynamic instability is usually known as the Richtmyer-Meshkov (RM) instability in honor of Richtmyer who first reported theoretical and numerical studies on this problem and Meshkov who later gave an experimental confirmation. The RM instability has become increasing attrac- tive due to its significance in many natural phenomena and engineering applications such as inertial confinement fusion (ICF), supersonic combustion, supernova explosion and extracorporeal shock wave lithotripsy. A large number of experimental, numerical and theoretical studies on RM instability have been reported and these studies mainly focused on the development of a single-mode interface (i.e., the single-mode RM insta- bility) for its simple mathematical form. However, in realities such as ICF and superno- va explosion, the initial interface usually presents a multi-mode or random perturbation. So far, the study of multi-mode RM instability is scarce due to its high complexity. It is therefore highly desirable to perform the study on RM instability at a multi-mode interface. Also, most of previous studies considered the RM instability induced by a planar shock wave. This is not the case in man-made applications (e.g. ICF) where the interfacial instability is usually triggered by a converging shock wave. Hence, this thesis focuses on the RM instability on a multi-mode interface and under a cylindrically converging shock wave. Considering that the multi-mode interface evolution is much more complex than the single-mode counterpart and also the RM instability induced by a converging shock wave is far more complicated than that induced by a planar shock, we study this problem step by step. The whole work can be divided into four parts:
1) High-fidelity experiments of the RM instability on an air/SF6 single-mode in- terface are first carried out in a planar shock tube. The soap-film technique is extended to create a single-mode interface which is free of supporting mesh, short-wavelength perturbations, gas diffusion and three-dimensionality. The clear interface evolution structures are well captured. An agreement between the linear growth rate obtained from experiments and the impulsive model is attained, which indicates that the experi- mental method is trustworthy. Then, the amplitude growths of the overall perturbation amplitude as well as the individual growths of bubble and spike are measured from experiment and the latest nonlinear theory for RM instability is validated. Also, the interface contours are extracted from the schlieren images and a Fourier analysis was performed to acquire the amplitude growth of the first three harmonics. The results are compared with the perturbation model for RM instability at the weakly nonlinear stage for model valiation.
2) The RM instability on a dual-mode interface with controllable initial conditions is experimentally investigated in a planar shock tube. The effects of wave number and phase of the basic modes on the instability evolution are emphasized. A Fourier analysis of the interface shapes extracted from schlieren images is performed to obtain the time- variant amplitude growth of the basic modes. A nonlinear model considering both the mode-coupling mechanism and the growth saturation is proposed, which well predicts the growths of basic modes. A parametric study on the dual-mode RM instability is performed via numerical simulation. The growth of total mixing zone of the dual-mode interface is also analysed.
3) Evolution of a single-mode interface triggered by a cylindrically converging shock was numerically investigated, which was compared with the single-mode inter- face evolution induced by a planar shock wave. The converging RM instability is more complicated than the planar counterpart. Several physical mechanisms, including the geometry effect, the Rayleigh-Taylor (RT) effect, the nonlinear effect, and the com- pressible effect were found to be pronounced in the converging case. Generally, the geometry effect and the nonlinear effect play an important role on the interface evo- lution in the early stage, while the RT effect and the compressible effect dominate the late-time interface evolution. The interface amplitude growth under converging shock condition and planar shock condition are extracted from experiments, and the differ- ences between the converging RM instability and the planar RM instability were quan- titatively discussed.
4) The developments of single- and dual-mode interfaces impacted by a converging shock wave are experimentally investigated in a semi-annular converging shock tube. A Fourier analysis of the interface contours extracted from experiment is performed, and visible differences between the amplitude growth of each basic mode of a dual-mode interface and that of the corresponding single-mode interface are observed. Compared with the planar RM instability, the converging counterpart produces different mode- coupling effects. Also, numerical simulations were performed for a parametric study. The effects of the initial wave number and the relative phase on the RM instability development are discussed.
|Date of Award||31 May 2020|
|Supervisor||Xisheng Luo (Chief supervisor), Juchun DIng (Co-supervisor) & Chih-yung Wen (Co-supervisor)|
- Richtmyer-Meshkov instability
- single-mode interface
- dual-mode inter- face
- converging shock
- shock-tube experiment