Numerical Investigations Of The Interface Instability And Turbulent Mixing Impacted By Multiple Shocks

The interface instability and turbulent mixing are the classical fundamental hydrodynamic problems,and are also difficult but fascinating problems in hydrodynamic field.The interface instability and turbulent mixing impacted by multiple shocks exist in a variety of applications such as defense technology,inertial confinement fusion(ICF),astrophysics,etc.,meanwhile,they relate to many basic science fields including turbulence,compressible flow,shock dynamics,strong nonlinearity and so on,so they are very important for engineering and science.But because of the complex loading/unloading features and routes under the condition of multiple shocks,there is some serious challenges in the investigations.In this dissertation,a three-dimensional parallel numerical simulation method and program MVFT with high precision,which is applying to the compressible multi-viscous fluid and turbulence,is proposed.When the initial shock wave impacts the light/heavy fluid(Air/SF₆)interface,a multiple shock process with reflected shock wave and rarefaction wave will be produced between the downstream wall and interface.Then the evolution laws and statistics properties of interface instability and turbulent mixing impacted by this multiple shocks in planar and spherical convergent geometries are investigated by using the MVFT program respectively.First,a three-dimensional parallel large-eddy simulation program MVFT is proposed on the basis of compressible multi-viscous hydrodynamics program MVPPM with the fixed dynamic viscosity.On this basis,the MVFT program is developed to be a direct numerical simulation program by applying Chapman-Enskog gas viscosity model and diffusion model with molecule collision mechanism,and also be extended into spherical coordinates frame.Then the MVFT program is validated by comparing simulated results with linear and nonlinear theoretical models of single-mode Richtmyer-Meshkov(RM)instability and three typical experiments.For the turbulent mixing of light/heavy fluid under shock in planar geometry,after the impact of incident shock wave on the initial multi-mode perturbed Air/SF₆ interface,the multiple reflections of transmitted shock wave between the perturbed interface and downstream wall form the multiple loadings of shock/compression wave and rarefaction wave on the turbulent mixing zone(TMZ)alternately.Second,the evolution laws of TMZ width and statistics properties of complex flow in TMZ are mainly investigated,which illuminates the physical mechanism of the TMZ evolution under this multiple shocks.The growth of TMZ width shows that it is closely related to the multiple shocks process,the TMZ width grows as different ways in different stages.After the first shock,the RM instability happens,the TMZ width grows as a power law of time.The secondary loading of reflected shock wave(called reshock)also induces the RM instability,the TMZ width grows as a negative exponent law in time.When the reflected rarefaction wave(the third)collides with the interface from SF₆ to Air,it causes the Rayleigh-Taylor(RT)instability,and the TMZ width also grows as a negative exponent law but with a different growth factor.Subsequently,the impingement of reflected compression wave(the fourth)produces the RT stabilization effect which reduces the TMZ growth extremely combined with the effects of shock compression and peak-valley transformation in a very short time.Then the TMZ width grows as a linear way approximately and can not be influenced by the following reflected rarefaction and compression wave with lower and lower intensity.The statistics analysis exhibits that the statistics properties of TMZ are closely related to the multiple shocks process.The TMZ evolves asymmetrically and intermittently along the shock(streamwise)direction,the TMZ also evolves with statistical similar and anisotropic behavior.The materials mix well in the extent around the edges of TMZ,and mix badly in the middle extent of TMZ.Even though each loading can reinforce the turbulent intensity of TMZ,the mixing turbulence decays as a whole.The peaks of enstrophy,turbulent kinetic energy and dissipation rate and their integrals in the TMZ decay in a similar way to the growth of TMZ width.After the first shock,these statistics quantities decay as a power law of time.After the reshock(the second)and the reflected rarefaction wave(the third),they all decay as negative exponent laws but with different decaying factors.And then they decay asymptotically.That is to say the TMZ behaves in a statistically similar pattern.The streamwise and transverse components of turbulent kinetic energy,generalized Reynolds stress,enstrophy and the energy spectra of velocity fluctuations reveal that the evolutions of interface instability and induced turbulent mixing are anisotropic.The loading of reflected shock wave or compression wave weaken the anisotropy,but the loading of reflected rarefaction wave enhance the anisotropy.Third,for the interface instability and turbulent mixing with initial diffusive multi-modes Air/SF₆ interface impacted by implosion in the spherical convergent geometry,the combined complex loading/unloading process caused by the transmitted shock wave bouncing off the center after initial impact in spherical convergent geometry has been investigated.The results indicate that the shock loading features and routes,evolution laws,physical mechanism and statistics properties of TMZ in spherical convergent geometry are more complex and more different from that in planar geometry.After the initial implosion loading,the transmitted shock wave moves towards the center.When the transmitted shock wave bounces off,the secondary impact is produced,which is a combination of shock wave and Taylor wave,and forms the loading/unloading effects.The following impact repeats this loading/unloading process.The growth laws of TMZ width in spherical convergent geometry are also closely related to the multiple shocks loading features and routes.In this process of multiple loading/unloading and Bell-Plesset(BP)effect due to convergent geometry,the RM instability,RT instability,RT stabilization and BP effects coexist and compete each other,which result in the TMZ width growing in oscillatory way.The initial implosion loading causes the RM instability.When the interface accelerates toward the center,the RT instability is induced,it promotes the TMZ to grow combined with the BP effect.When the interface decelerates toward the center,the RT stabilization occurs and suppresses the growth of TMZ and even reduces its width.In the second reflected loading process,the reshock induces RM instability,and the Taylor wave leads to RT instability due to its unloading effect;likewise in the subsequent process of decelerated motion towards the center,the RT stabilization happens again and reduces the TMZ growth.The TMZ width repeats the aforementioned growth process.The statistics analysis also displays that the statistics properties of TMZ in spherical convergent geometry are closely related to the multiple shocks process.Like in planar geometry,the TMZ also evolves asymmetrically and intermittently along the shock(radial/streamwise)direction.The materials mix well in the extent around the edges of TMZ and badly in the middle extent of TMZ.The distributions of enstrophy,turbulent kinetic energy and generalized Reynolds stress,energy spectra,etc.exhibit that the TMZ evovles in statistically similar pattern and anisotropically.Each RT stabilization and reflected impact bouncing off the center all strengthen the anisotropy.When the turbulent mixing develops fully the energy spectra approach k^-1 scaling law at the inertial subrange.