The Principal Curvature Effect On Richtmyer-Meshkov Instability

When an initially perturbed interface is impulsively accelerated, the interface is hy-drodynamically unstable, the perturbation amplitude increases, fluid mixing becomes severe and eventually develops into turbulent flow. This phenomenon is known as Richtmyer-Meshkov (RM) instability. It plays an important role in the scientific and engineering areas, such as the inertial confinement fusion, the supersonic combustion ramjet and the supernova explosion in astrophysics. Much attention has been paid to the RM instability since its concept was proposed.For the past few decades, the issues on the RM instability have been extensively studied concentrating mainly on the two-dimensional (2D) cases. While the RM in-stability is intrinsically a three-dimensional (3D) phenomenon in both the nature and engineering environments. The studies on the 3D RM instability are mainly restricted by the experimental measurement, the computation resource and the complexity of the modelling.The RM instability is known to be affected severely by the initial interface shape. The 3D interfaces possess a number of different features comparing with the 2D cases. For a 3D interface, the interface curvature at every point should be represented by two principal curvatures, and the combining form of the two principal curvatures affects the perturbation significantly. Based on our previous work, experimental and numerical methods are adopted in the present work to further investigate the effect of principal curvature on interface evolution. Through this study, the mechanism of interface evo-lution should be well understood and the theoretical model will be validated.1. The interface formation method using the soap film technique to create a single-mode interface with minimum-surface feature is improved in this work. As a consequence, the wave pattern during the shock-interface interaction and the in-terface morphology at very early stage can be clearly captured compared with the previous work. Both light/heavy and heavy/light interfaces are experimentally studied using the improved device in the horizontal shock tube facility, and the whole evolving process is recorded, providing a database for the validation of numerical method.2. Numerical method is used in the present work to obtain physical parameters in the flow field. The 3D unsteady compressible Euler equations with the ideal gas law as the equation of state are appropriately adopted. Level set method and real ghost fluid method (rGFM) are used to capture the interface that initially separates different gases. The governing equation and the level set function are solved by a fifth-order weighted essentially non-oscillatory (WENO) scheme in uniform cu-bic cells and advanced in time by the third-order Runge-Kutta method. OpenMP is adopted to improve the computational efficiency. The numerical simulations clearly reproduce the interface evolution and present a detailed 3D wave struc-ture, expand the understanding of RM instability of the minimum-surface featured single mode interface.3. Numerical methods are adopted to simulate the interaction of a shock with an interface with different principle curvatures. In this work, three kinds of inter-face are considered, i.e., an interface with identical signed principal curvatures (3D single mode interface), with opposite signed principal curvatures (minimum-surface featured single mode interface) and with one zero-valued principal cur-vature (2D single mode interface), and perturbation amplitudes of the interfaces are extracted from the symmetry planes. It is found that, comparing with the 2D single mode interface, the perturbation growth rate is enhanced for the case with identical signed principal curvatures, while suppressed and even delayed for the case with opposite signed principal curvatures. The numerical results agree well with the experimental results which confirms the feasibility and reliabili-ty of the experimental method and validates the effectiveness of the theoretical model proposed in previous work. By analyzing the wave structure and vorticity distribution, the mechanisms that affect the perturbation growth is illustrated.4. For a light/heavy case, six types of 3D interfaces with different principal curva-ture combining forms are designed and simulated. Evolution of the interface and perturbation amplitudes at different positions are compared and analyzed. It is found that, the principal curvature effect is a local effect, once an interface pos-sesses regions with identical signed principal curvatures and regions with opposite signed principal curvatures, the growth rates at different positions will develop d-ifferently. In a global view, for interfaces with the same maximum perturbation amplitude, the one with opposite signed principal curvatures possesses slower perturbation amplitude growth rate and slower interface area growth rate than the one without opposite signed principal curvatures. The results show that the 2D interface is the most stable one compared with the 3D interface with any kind of principle curvature form.experimental and numerical methods are both adopted to investigate the 3D effect, especially the principle curvature effect of initial interface, on the interface evolution. The relationship between the interface principle curvature and the perturbation growth is given. Through this study, it is anticipated that the growth rate of interface perturbation will be controlled by adjusting the interface principle curvature, which is quite benefical for the interface design in engineering areas.