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Numerical study on Rayleigh-Taylor effect on cylindrically converging Richtmyer-Meshkov instability

Science China(Physics,Mechanics & Astronomy) 2019年第12期62卷 68-77页

作者： ZhiGang Zhai Fu Zhang ZhangBo Zhou JuChun Ding Chih-Yung Wen Department of Modern Mechanics University of Science and Technology of ChinaHefei 230026China Beijing Institute of Space Long March Vehicle Beijing 100076China Department of Mechanical Engineering The Hong Kong Polytechnic UniversityHong Kong 999077China

Evolution of a two-dimensional air/SF6 single-mode interface is numerically investigated by an upwind CE/SE method under a cylindrically converging circumstance. The Rayleigh-Taylor effect caused by the flow deceleration on the phase inversion(RTPI)is highlighted. The RTPI was firstly observed in our previous experiment, but the related mechanism remains unclear. By isolating the three-dimensional effect, it is found here that the initial amplitude(a0), the azimuthal mode number(k0) and the re-shocking moment are the three major parameters which determine the RTPI occurrence. In the variable space of(k0, a0), a critical a0 for the RTPI occurrence is solved for each k0, and there exists a threshold value of k0 below which the RTPI will not occur no matter what a0 is. There exists a special k0 corresponding to the largest critical a0, and the reduction rule of critical a0 with k0 can be well described by an exponential decay function. The results show that the occurrence of the RTPI requires a small a0 which should be less than a critical value, a large k0 which should exceed a threshold, and a right impinging moment of the re-shock which should be later than the RTPI occurrence. Finally, the effects of the incident shock strength, the density ratio and the initial position of the interface on the threshold value of k0 and on the maximum critical a0 are examined. These new findings would facilitate the understanding of the converging Richtmyer-Meshkov instability and would be helpful for designing an optimal structure of the inertia confinement fusion capsule.

关键词： converging shock wave Rayleigh-Taylor effect Richtmyer-Meshkov instability

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SOME MATHEMATICAL MODELS AND MATHEMATICAL ANALYSIS ABOUT Rayleigh-Taylor INSTABILITY

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Annals of Applied Mathematics 2019年第1期35卷 1-46页

作者： Boling Guo Binqiang Xie Institute of Applied Physics and Computational Math. China Academy of Engineering Physics South China Research Center for Applied Math.and Interdisciplinary Studies

In this paper we will review some mathematical models and mathematical analysis about Rayleigh-Taylor instability.

关键词： mathematical models mathematical analysis Rayleigh-Taylor instability

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External Magnetic Field Effects on the Rayleigh-Taylor Instability in an Inhomogeneous Rotating Quantum Plasma

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Journal of Modern Physics 2012年第11期3卷 1792-1801页

作者： G. A. Hoshoudy Department of Applied Mathematics Faculty of Science South Valley University Qena Egypt

The effects of external magnetic field effects on the Rayleigh-Taylor instability in an inhomogeneous stratified quantum plasma rotating uniformly are investigated. The external magnetic field is considered in both horizontal and vertical direction. The linear growth rate is derived for the case where a plasma with exponential density distribution is confined between two rigid planes at z=0 and z=h, by solving the linear QMHD equations into normal mode. Some special cases are particularized to explain the roles that play the variables of the problem. The results show that, the presence of both external horizontal and vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration. The maximum stability will happen in the case of wave number parallels to or in the same direction of external horizontal magnetic field.

关键词： Rayleigh-Taylor Instability Quantum Plasmas Magnetic Field

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Mixing Efficiency across Rayleigh-Taylor and Richtmeyer-Meshkov Fronts

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Open Journal of Fluid Dynamics 2015年第2期5卷 145-150页

作者： Jose Manuel Redondo Pilar Lopez Gonzalez-Nieto Jose Leandro Cano German Andres Garzon Applied Physics Department Politecnica University of Catalu&#241 a (UPC) Barcelona Spain Applied Mathematics Department Complutense University of Madrid (UCM) Madrid Spain Earth Physics Astronomy and Astrophsics II Department Complutense University of Madrid (UCM) Madrid Spain

Mixing generated by gravitational acceleration and the role of local turbulence measured through multifractal methods is examined in numerical experiments of Rayleigh-Taylor and Richtmyer-Meshkov driven front occurring at density interfaces. The global advance of the fronts is compared with laboratory experiments and Nusselt and Sherwood numbers are calculated in both large eddy simulation (LES) and kinematic simulation KS models. In this experimental method, the mixing processes are generated by the evolution of a discrete set of forced turbulent plumes. We describe the corresponding qualitative results and the quantitative conclusions based on measures of the density field and of the height of the fluid layers. We present an experimental analysis to characterize the partial mixing process. The conclusions of this analysis are related to the mixing efficiency and the height of the final mixed layer as functions of the Atwood number, which ranges from 9.8 × 10−3 to 1.34 × 10−1.

关键词： Rayleigh-Taylor Instability Richtmyer-Meshkov Instability Mixing Efficiency Front Evolution Fractal Dimension

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Mechanism of the Large Surface Deformation Caused by Rayleigh-Taylor Instability at Large Atwood Number

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Journal of Applied Mathematics and Physics 2014年第10期2卷 971-979页

作者： Yikai Li Akira Umemura Department of Aerospace Engineering Nagoya University Nagoya Japan

Studying the dynamical behaviors of the liquid spike formed by Rayleigh-Taylor instability is important to understand the mechanisms of liquid atomization process. In this paper, based on the information on the velocity and pressure fields obtained by the coupled-level-set and volume-of- fluid (CLSVOF) method, we describe how a freed spike can be formed from a liquid layer under falling at a large Atwood number. At the initial stage when the surface deformation is small, the amplitude of the surface deformation increases exponentially. Nonlinear effect becomes dominant when the amplitude of the surface deformation is comparable with the surface wavelength (~0.1λ). The maximum pressure point, which results from the impinging flow at the spike base, is essential to generate a liquid spike. The spike region above the maximum pressure point is dynamically free from the bulk liquid layer below that point. As the descending of the maximum pressure point, the liquid elements enter the freed region and elongate the liquid spike to a finger-like shape.

关键词： Fluid Mechanics Multi-Phase Flow Rayleigh-Taylor Instability Spike Formation

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Rayleigh-Taylor Instability of Magnetized Plasma through Darcy Porous Medium

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Journal of Modern Physics 2014年第5期5卷 186-197页

作者： Gamal Abdallah Hoshoudy Department of Applied Mathematics and Computer Science Faculty of Science South Valley University Kena Egypt

Effects of horizontal and vertical magnetic field components on the Rayleigh-Taylor instability of stratified incompressible plasmas layer of variable density through Darcy porous medium are studied. The basic magnetohydrodynamic (MHD) set of equations has been constructed and linearized. Then the linear normalized growth rate is obtained analytically as a function of the physical parameters of the system considered. Numerical calculations have been performed to see the effects of various parameters on the normalized growth rate of Rayleigh-Taylor instability.(For more information,please refer to the PDF.)

关键词： Rayleigh-Taylor Instability Magnetized Plasmas Darcy Porous Media

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Quantum Effects on the Rayleigh-Taylor Instability of Viscoelastic Plasma Model through a Porous Medium

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Journal of Modern Physics 2011年第10期2卷 1146-1155页

作者： Gamal A. Hoshoudy 不详

The stability of stratified of incompressible, viscoelastic plasma through a porous medium in the presence of the quantum mechanism is considered. The dispersion relation is obtained using the normal mode technique. The behavior of growth rate with respect to the quantum effect, strain retardation time and stress relaxation time are examined in the presence of porosity of the porous medium, the medium permeability, kinematic viscosity. It is shown that, the presence of quantum term stabilizes a certain wave number band, whereas the system is unstable for all wave numbers in the absence of quantum term. The considered parameters beside the quantum term will bring about more stability on the considered system.

关键词： Rayleigh-Taylor Instability Viscoelastic Quantum Plasm

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Rayleigh-Taylor Instability in Magnetized Plasma

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World Journal of Mechanics 2014年第8期4卷 260-272页

作者： G. A. Hoshoudy Department of Applied Mathematics and Computer Science Faculty of Science South Valley University Kena Egypt

The Rayleigh-Taylor instability in stratified plasma has been investigated in the presence of combined effect of horizontal and vertical magnetic field. The linear growth rate has been derived for the case where plasma with exponential density distribution is confined between two rigid planes by solving the linear MHD equations into normal mode. Some special cases have been particularized to explain the roles the variables of the problem play;numerical solutions have been made and some stability diagrams are plotted and discussed. The results show that, the growth rate depends on the horizontal and vertical components of magnetic field and also depends on the parameter λ*=λLD ?(λ is constant and LD is the density-scale length). The maximum instability happens at λ*=-0.5 and to get more stability model we select?λ* such that it is different than?λ*=-0.5. The vertical magnetic field component have a greater effect than the horizontal magnetic field component in the case of large wavelength, while in the case of short wavelength, the horizontal magnetic field components have greater effect than the vertical magnetic field component.

关键词： Rayleigh-Taylor Instability Plasma Horizontal and Vertical Magnetic Field

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Expansion of Linear Analysis of Rayleigh-Taylor Interface Instability of Metal Materials

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World Journal of Mechanics 2018年第4期8卷 94-106页

作者： Xinbo Bai Tao Wang Yuxuan Zhu Guoqiang Luo College of Physical Science and Technology Sichuan University Chengdu China Institute of Fluids Physics China Academy of Engineering Physics Mianyang China State Key Laboratory of Advanced Technology for Materials Synthesis and Processing Wuhan University of Technology Wuhan China

The linear analysis of the Rayleigh-Taylor instability in metal material is extended from the perfect plastic constitutive model to the Johnson-Cook and Steinberg-Guinan constitutive model, and from the constant loading to a time-dependent loading. The analysis is applied to two Rayleigh-Taylor instability experiments in aluminum and vanadium with peak pressures of 20 GPa and 90 GPa, and strain rates of 6 × 106 s−1 and 3 × 107 s−1 respectively. When the time-dependent loading and the Steinberg-Guinan constitutive model are used in the linear analysis, the analytic results are in close agreement with experiments quantitatively, which indicates that the method in this paper is applicable to the Rayleigh-Taylor instability in aluminum and vanadium metal materials under high pressure and high strain rate. From these linear analyses, we find that the constitutive models and the loading process are of crucial importance in the linear analysis of the Rayleigh-Taylor instability in metal material, and a better understanding of the Rayleigh-Taylor instability in metals is gained. These results will serve as important references for evolving high-pressure, high-strain-rate experiments and numerical simulations.

关键词： Linear Analysis Rayleigh-Taylor Instability Time-Dependent Loading Constitutive Model

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Electrostatic Rayleigh-Taylor Mode in Electron-Positron-Ion Quantum Plasma

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Journal of Modern Physics 2017年第4期8卷 636-653页

作者： Sajad Ali Mushtaq Ahmad Department of Physics FPNS Abdul Wali Khan University Mardan Pakistan Department of Physics FBAS International Islamic University (IIUI) Islamabad Pakistan

Electrostatic Rayleigh-Taylor (ERT) mode/instability is studied in a non-uni-form quantum magnetoplasma, whose constituents are electrons and positrons with fraction of ions. The effects of quantum corrections (i.e. Bohm potential and temperature degeneracy) and magnetic field on ERT mode are investigated with astrophysical plasma application. A generalized dispersion relation is deduced under the drift wave approximation. The presence of positron makes the dispersion relation a cubic equation. Different roots of both real and imaginary parts of the RT mode are examined by applying the Cardano’s method of solving the cubic equation. The dispersion relation and the growth rates of RT instability are examined both analytically and numerically with effects of electron and positron density, and magnetic field variations. It is shown that the magnetic field and positron density have stabilizing effectuates on ERT mode while due to electron density the mode becomes unstable. The present work is antici-pated to be of physical relevance in the studies of laboratory laser-produced plasmas as well as in the study of compact magnetized astrophysical objects like white dwarfs.

关键词： Rayleigh-Taylor Instability Drift Wave Approximation Quantum Magneto Hydrodynamics Cardano’s Method

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