Numerical Study On Turbulent Mixing Induced By Richtmyer-Meshkov Instability

Richtmyer-Meshkov(RM)instability refers to the growth of initial perturbations at a perturbed interface following an impulsive acceleration typically by a shock wave.During this process,various scales are developed and the flow can reach the turbulent state(called RM turbulence)under certain conditions.RM turbulence exists widely in inertial confinement fusion,scramjet and supernova explosion,and the relevant study is meaningful.Due to the complexity of RM turbulence,the relevant study poses a great challenge to experimental diagnostics and numerical simulation methods.The major difficulty of numerical simulation is the simultaneous handling of strong discontinuities and turbulent scales.On one hand,a certain amount of numerical dissipation should be retained in numerical scheme to inhibit the spurious oscillations near the discontinuities such as shock wave.On the other hand,sufficiently small dispersion and dissipation should be possessed in numerical scheme for accurate resolving of smallscale fluctuations(i.e.good spectral properties).In this thesis,a new type of high-order weighted compact nonlinear scheme(WCNS)based on nonlinear optimization is proposed,and then a three-dimensional compressible multi-species solver is developed based on the optimized WCNS.Then,numerical simulation of RM turbulent with three types of multi-mode initial perturbations is performed with the new solver.Special attention is paid to the evolution of RM turbulent mixing layer and the scale-to-scale energy transfer.Also,a phenomenological theory for structure functions of RM turbulence is developed.The main contents of the thesis are given below:1.A new nonlinear optimization strategy is proposed,based on which a WCNS with optimal spectral properties is constructed by considering the diversity of local flow structure and the influence of nonlinearity inherent in shock-capturing scheme.The optimization contains two steps:first,the dispersion parameter ηis optimized to obtain minimum dispersion;second,the dissipation parameter ξand the parameter C of the nonlinear weight function are adjusted depending on the flow conditions at each local region to realize adaptive dissipation.The optimized WCNS is extended to compressible multi-species flows by incorporating the double-flux algorithm.Numerical results of benchmark test cases indicate the new WCNS has good capability of capturing discontinuities while resolving more small-scale structures,which is suitable for numerical simulation of compressible turbulent mixing.2.The evolution of RM turbulent mixing with three types of multi-mode initial perturbations is simulated.First,the differences of mixing statistics within the mixing layer in the three cases are analyzed.It is found that the growth rate exponent in the broadband case is larger for the existence of initial large-scale perturbations,while the evolutions of the mixing width in the two high-wavenumber narrowband cases are the same.In the self-similar stage,both the decay exponent of turbulent kinetic energy and the asymptotic value of molecular mixing fraction are related to the growth exponent of the mixing width.Compared to the highwavenumber narrowband cases,the mixing layer in the broadband case has lower mixing efficiency,higher anisotropy and inhomogeneity.Then,the evolution of the subgrid-scale energy flux is investigated using coarse-graining approach.The deformation work and baropycnal work are found to have different preferences of the transfer direction in the spike and bubble regions.A priori test of a nonlinear model of baropycnal work in RM turbulence is performed for the first time,and high correlation results are obtained.The strain-enstrophy angle is introduced to explore the strain effect and rotation effect within the mixing layer.It is found that the deformation work is stronger in the strain-dominated region,while the baropycnal work has no clear preference between the strain effect and rotation effect.3.The scaling law of structure function of RM turbulence is investigated both numerically and theoretically.Results show that the scalar field exhibits a greater degree of intermittency than velocity field,under the current Mach number,and also the small-scale statistics suffer a larger influence of large scales.A phenomenological theory,which gives the spatial and temporal scaling laws of structure functions of velocity and scalar of RM turbulence,is developed for the first time by introducing an external agent.The spatial scaling exponents of structure functions from simulation deviate from the Kolmogorov exponents,but are quite close to the RM-modified anomalous exponents.This demonstrates the validity of the present phenomenological theory.