HIGH-ORDER WENO SIMULATIONS OF THREE-DIMENSIONAL RESHOCKED RICHTMYER-MESHKOV INSTABILITY TO LATE TIMES:DYNAMICS,DEPENDENCE ON INITIAL CONDITIONS,AND COMPARISONS TO EXPERIMENTAL DATA

The dynamics of the reshocked multi-mode Richtmyer-Meshkov instability is investigated using 513 × 257^2 three-dimensional ninth-order weighted essentially nonoscil- latory shock-capturing simulations. A two-mode initial perturbation with superposed ran- dom noise is used to model the Mach 1.5 air/SF6 Vetter-Sturtevant shock tube experiment. The mass fraction and enstrophy isosurfaces, and density cross-sections are utilized to show the detailed flow structure before, during, and after reshock. It is shown that the mixing layer growth agrees well with the experimentally measured growth rate before and after reshock. The post-reshock growth rate is also in good agreement with the prediction of the Mikaelian model. A parametric study of the sensitivity of the layer growth to the choice of amplitudes of the short and long wavelength initial interfacial perturbation is also pre- sented. Finally, the amplification effects of reshock are quantified using the evolution of the turbulent kinetic energy and turbulent enstrophy spectra, as well as the evolution of the baroclinic enstrophy production, buoyancy production, and shear production terms in the enstrophy and turbulent kinetic transport equations.

Detonation initiation developing from the Richtmyer-Meshkov instability

Detonation initiation resulting from the Richtmyer-Meshkov instability is investigated numerically in the configuration of the shock/spark-induced-deflagration interaction in a combustive gas mixture. Two-dimensional multi-species Navier-Stokes equations implemented with the detailed chemical reaction model are solved with the dispersion-controlled dissipative scheme. Numerical results show that the spark can create a blast wave and ignite deflagrations. Then, the deflagration waves are enhanced due to the Richtmyer-Meshkov instability, which provides detonation initiations with local environment conditions. By examining the deflagration fronts, two kinds of the initiation mechanisms are identified. One is referred to as the deflagration front acceleration with the help of the weak shock wave, occurring on the convex surfaces, and the other is the hot spot explosion deriving from the deflagration front focusing, occurring on the concave surfaces.

Numerical investigation of Richtmyer-Meshkov instability driven by cylindrical shocks

In this paper, a numerical method with high order accuracy and high resolution was developed to simulate the Richtmyer-Meshkov（RM） instability driven by cylindrical shock waves. Compressible Euler equations in cylindrical coordinate were adopted for the cylindrical geometry and a third order accurate group control scheme was adopted to discretize the equations. Moreover, an adaptive grid technique was developed to refine the grid near the moving interface to improve the resolution of numerical solutions. The results of simulation exhibited the evolution process of RM instability, and the effect of Atwood number was studied. The larger the absolute value of Atwood number, the larger the perturbation amplitude. The nonlinear effect manifests more evidently in cylindrical geometry. The shock reflected from the pole center accelerates the interface for the second time, considerably complicating the interface evolution process, and such phenomena of reshock and secondary shock were studied.

The Richtmyer-Meshkov instability of a double-layer interface in convergent geometry with magnetohydrodynamics

The interaction between a converging cylindrical shock and double density interfaces in the presence of a saddle magnetic field is numerically investigated within the framework of ideal magnetohydrodynamics.Three fluids of differing densities are initially separated by the two perturbed cylindrical interfaces.The initial incident converging shock is generated from a Riemann problem upstream of the first interface.The effect of the magnetic field on the instabilities is studied through varying the field strength.It shows that the Richtmyer-Meshkov and Rayleigh-Taylor instabilities are mitigated by the field,however,the extent of the suppression varies on the interface which leads to non-axisymmetric growth of the perturbations.The degree of asymmetry of the interfacial growth rate is increased when the seed field strength is increased.

Multiple-Relaxation-Time Lattice Boltzmann Approach to Richtmyer-Meshkov Instability

The aims of the present paper are twofold. At first, we further study the Multiple-Relaxation-Time （MRT） Lattice Boltzmann （LB） model proposed in [Europhys. Lett. 90 （2010） 54003]. We discuss the reason why the Gram Schmidt orthogonalization procedure is not needed in the construction of transformation matrix M; point out a reason why the Kataoka-Tsutahara model [Phys. Rev. E 69 （2004） 035701（R）] is only valid in subsonic flows. The yon Neumann stability analysis is performed. Secondly, we carry out a preliminary quantitative study on the Richtmyer- Meshkov instability using the proposed MRT LB model. When a shock wave travels from a light medium to a heavy one, the simulated growth rate is in qualitative agreement with the perturbation model by Zhang-Sohn. It is about half of the predicted value by the impulsive model and is closer to the experimental result. When the shock wave travels from a heavy medium to a light one, our simulation results are also consistent with physical analysis.

The Growth of Richtmyer-Meshkov Instability under Multiple Impingements

The growth of multi-mode Richtmyer-Meshkov instability under multiple impingements and the effect of initial shock strength on the growth of RMI are numerically investigated. We obtain the time evolution of turbulent mixing zone width for initial shock with different strength. The results show that the turbulent mixing zone width grows in a different manner at different stage but strictly in a similar way for the initial shock with different strength. Also, the initial shock strength has a significant effect on the growth rate of turbulent mixing zone width, especially before reshock, but can not change the growth laws in the whole process.

Numerical simulations of Richtmyer-Meshkov instabilities using conservative front-tracking method

This paper presents the numerical simulations of two Richtmyer-Meshkov （RM） instability experiments using the conservative front-tracking method developed in （Mao, D. Towards front-tracking based on conservation in two space dimensions II, tracking discontinuities in capturing fashion. J. Comput. Phys., 226, 1550-1588 （2007））. The numerical results are compared with those obtained in （Holmes, R. L., Grove, J. W., and Sharp, D. H. Numerical investigation of Richtmyer-Meshkov instability using front-tracking. J. Fluid Mech., 301, 51-64 （1995））. The present simulations are generally in good agreement with those obtained by Holmes et al., and also capture the nonlinear and compessive phenomenon, i.e., the self-interactions of the transmitted and reflected wave edges, which was pointed out by Holmes et al. as the cause of the deceleration of the interfaces. However, the perturbation amplitudes and the amplitude growth rates of the interfaces obtained with the present conservative front-tracking method are a bit larger than those obtained by Holmes et al.

The Richtmyer–Meshkov instability of a 'V' shaped air/helium interface subjected to a weak shock

The Richtmyer-Meshkov instability ofa ‘V＇ shaped air/helium gaseous interface subjected to a weak shock wave is experimentally studied. A soap film technique is adopted to create a ‘V＇ shaped interface with accurate initial conditions. Five kinds of ‘V＇ shaped interfaces with different vertex angles are formed to highlight the effects of initial conditions on the flow characteristics. The results show that a spike is generated after the shock impact, and grows constantly with time. As the vertex angle increases, vortices generated on the interface become less noticeable, and the spike develops less pronouncedly. The linear growth rate of interface width after compression phase is estimated by a linear model and a revised linear model, and the latter is proven to be more effective for the interface with high initial amplitudes. The linear growth rate of interface width is, for the first time in a heavy/light interface configuration, found to be a non-monotonous function of the initial perturbation amplitude-wavelength ratio.

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

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.

Numerical study of three-dimensional developments of premixed flame induced by multiple shock waves

The three-dimensional interactions of a perturbed premixed flame interface with a planar incident shock wave and its reflected shock waves are numerically simulated by solving the compressible,reactive Navier-Stokes equations with the high-resolution scheme and a single-step chemical reaction.The effects of the initial incident shock wave strength (Mach number) and the initial perturbation pattern of interface on the interactions are investigated.The distinct properties of perturbation growth on the flame interface during the interactions are presented.Our results show that perturbation growth is mainly attributed to the flame stretching and propagation.The flame stretching is associated with the larger-scale vortical flow due to RichtmyerMeshkov instability while the flame propagation is due to the chemical reaction.The mixing properties of unburned/burned gases on both sides of the flame are quantitatively analyzed by using integral and statistical diagnostics.The results show that the large-scale flow due to the vortical motion always plays a dominating role during the reactive interaction process;however,the effect of chemistry becomes more important at the later stage of the interactions,especially for higher Mach number cases.The scalar dissipation due to the molecular diffusion is always small in the present study and can be negligible.

Molecular dynamics simulation of cylindrical Richtmyer-Meshkov instability

The microscopic-scale Richtmyer-Meshkov(RM) instability of a single-mode Cu-He interface subjected to a cylindrically converging shock is studied through the classical molecular dynamics simulation. An unperturbed interface is first considered to examine the flow features in the convergent geometry, and notable distortions at the circular inhomogeneity are observed due to the atomic fluctuation. Detailed processes of the shock propagation and interface deformation for the single-mode interface impacted by a converging shock are clearly captured. Different from the macroscopic-scale situation, the intense molecular thermal motions in the present microscale flow introduce massive small wavelength perturbations at the single-mode interface, which later significantly impede the formation of the roll-up structure. Influences of the initial conditions including the initial amplitude,wave number and density ratio on the instability growth are carefully analyzed. It is found that the late-stage instability development for interfaces with a large perturbation does not depend on its initial amplitude any more. Surprisingly, as the wave number increases from 8 to 12, the growth rate after the reshock drops gradually. The distinct behaviors induced by the amplitude and wave number increments indicate that the present microscopic RM instability cannot be simply characterized by the amplitude over wavelength ratio(η). The pressure history at the convergence center shows that the first pressure peak caused by the shock focusing is insensitive to η, while the second one depends heavily on it.

Large-eddy simulations of the Richtmyer-Meshkov instability of rectangular interfaces accelerated by shock waves

A parallel algorithm and code MVFT(multi-viscous-fluid and turbulence) of large-eddy simulation(LES) is developed from our MVPPM(multi-viscous-fluid piecewise parabolic method),and performed to solve the multi compressible Navier-Stokes(N-S) equations.The effect of the unresolved subgrid-scale(SGS) motions on the large scales is represented by different SGS stress models in LES.A Richtmyer-Meshkov instability experiment of the evolution of a rectangular block of SF6,which occupies half of the height of the shock tube test section,following the interaction with a planar shock wave,is numerically and exhaustively simulated by this code.The comparison between experimental and simulated images of the evolving SF6 block shows that they are consistent.The numerical simulations reproduce the complex developing process of SF6 block,which grows overturningly.The geometric quantities that characterize the extents of SF6 block are also compared in detail between numerical simulations and experiment with good agreements between them,a quantitative demonstration of the developing law of SF6 block.There is an evident discrepancy between the three numerical simulations for the maximum position of the right edge of block at the late stage,because the right interface grows complicated and the dissipation is different for different SGS models.The SGS turbulent dissipation,molecular viscosity dissipation and SGS turbulent kinetic energy have been studied and analyzed.They have a similar distribution to the large eddy structures.The SGS turbulent dissipation is much greater than the molecular viscosity dissipation;the SGS turbulent dissipation of Vreman model is smaller than the Smagorinsky model.In general,the simulated results of Vreman SGS model are better compared with the dynamic viscosity and Smagorinsky SGS model.The vorticity and circulation deposition on the block interface have also been investigated.

1.3 kW monolithic linearly polarized single-mode master oscillator power amplifier and strategies for mitigating mode instabilities

We report on the high-power amplification of a 1064 nm linearly polarized laser in an all-fiber polarizationmaintained master oscillator power amplifier,which can operate at an output power level of 1.3 kW.The beam quality(M^2) was measured to be <1.2 at full power operation.The polarization extinction rate of the fiber amplifier was measured to be above 94% before mode instabilities(MIs) set in,which reduced to about 90% after the onset of MI.The power scaling capability of strategies for suppressing MI is analyzed based on a semianalytical model,the theoretical results of which agree with the experimental results.It shows that mitigating MI by coiling the gain fiber is an effective and practical method in standard double-cladding large mode area fiber,and,by tight coiling of the gain fiber to the radius of 5.5 cm,the MI threshold can be increased to three times higher than that without coiling or loose coiling.Experimental studies have been carried out to verify the idea,which has proved that MI was suppressed successfully in the amplifier by proper coiling.

Numerical study on the turbulent mixing of planar shock-accelerated triangular heavy gases interface

The interaction of a planar shock wave with a triangle-shaped sulfur hexafluoride (SF6) cylinder surrounded by air is numerically studied using a high resolution finite volume method with minimum dispersion and controllable dissipation reconstruction.The vortex dynamics of the Richtmyer-Meshkov instability and the turbulent mixing induced by the KelvinHelmholtz instability are discussed.A modified reconstruction model is proposed to predict the circulation for the shock triangular gas-cylinder interaction flow.Several typical stages leading the shock-driven inhomogeneity flow to turbulent mixing transition are demonstrated.Both the decoupled length scales and the broadened inertial range of the turbulent kinetic energy spectrum in late time manifest the turbulent mixing transition for the present case.The analysis of variable-density energy transfer indicates that the flow structures with high wavenumbers inside the Kelvin-Helmholtz vortices can gain energy from the mean flow in total.Consequently,small scale flow structures are generated therein by means of nonlinear interactions.Furthermore,the occasional 'pairing' between a vortex and its neighboring vortex will trigger the merging process of vortices and,finally,create a large turbulent mixing zone.

Mode coupling in converging Richtmyer-Meshkov instability of dual-mode interface

The converging Richtmyer-Meshkov(RM)instability on single-and dual-mode N2/SF6 interfaces is studied by an upwind conservation element and solution element solver.An unperturbed case is first considered,and it is found that the shocked interface undergoes a long-term deceleration after a period of uniform motion.The evolution of single-mode interface at the early stage exhibits an evident nonlinearity,which can be reasonably predicted by the nonlinear model of Wang et al.(Phys Plasmas 22:082702,2015).During the deceleration stage,the perturbation amplitude drops quickly and even becomes a negative(phase inversion)before the reshock due to the Rayleigh-Taylor(RT)stabilization.After the reshock,the interface experiences a phase inversion again or does not,depending on the reshock time.The growth of the second-order harmonic in the deceleration stage clearly reveals the competition between the RT effect and the nonlinearity.For dual-mode interfaces,the growth of the first mode(wavenumber k1)relies heavily on the second mode(wavenumber k2)due to the mode coupling effect.Specifically,for cases where k2 is an even or odd multiple of k1,the growth of the first mode is inhibited or promoted depending on its initial amplitude sign and the phase difference between two basic waves,while for cases where k2 is a non-integer multiple of k1,the second mode has negligible influence on the first mode.Through a systematic study,signs of perturbation amplitudes of the generated k2−k1 and k2+k1 waves are obtained for all possible dual-mode configurations,which are reasonably predicted by a modified Haan model(Phys Fluids B 3:2349-2355,1991).

Effect of Atwood number on convergent Richtmyer-Meshkov instability

Developments of two-dimensional single-mode light/heavy interfaces driven by convergent shock waves are numerically investigated,focusing on the effect of the Atwood number on the Rayleigh-Taylor stabilization,the compressibility and the nonlinearity.Five different test gases,including C〇2,Kr,R22,R12 and SF6,are considered with air as the ambient gas.It is clarified for the first time that the unperturbed interface begins to decelerate when the shock focuses at the convergence center,and the acceleration during the deceleration phase is proportional to the Atwood number.During the first reshock,the interface moves outwards with a deceleration until it starts moving inwards.When the initial interface is weakly disturbed,a more obvious amplitude reduction is observed for the case with a larger Atwood number before the reshock,which means that the Rayleigh-Taylor stabilization is stronger.To assess the effect of the Atwood number on the compressibility and the nonlinearity,three models,including a linear incompressible model,a nonlinear incompressible model and a linear compressible model,are adopted to predict the amplitude growth before the reshock.The results show that the nonlinearity is weak,and is almost not influenced by the Atwood number before the reshock.The compressibility,however,greatly changes the amplitude growth.As the Atwood number increases,the compressibility plays a less significant role in the amplitude growth because a heavier gas is harder to be compressed.Although a gas with a larger specific heat ratio is also difficult to be compressed,the specific heat ratio plays a minor role to the compressibility relative to the Atwood number.During the reshock,the amplitude grows linearly until the nonlinearity in the cases with large Atwood numbers is strong enough to reduce the amplitude growth rate.

Flux Limiter Lattice Boltzmann for Compressible Flows

In this paper, a new flux limiter scheme with the splitting technique is successfully incorporated into a multiple-relaxation-time lattice Boltzmann （LB） model for shacked compressible flows. The proposed flux limiter scheme is efficient in decreasing the artificial oscillations and numerical diffusion around the interface. Due to the kinetic nature, some interface problems being difficult to handle at the macroscopic level can be modeled more naturally through the LB method. Numerical simulations for the Richtmyer-Meshkov instability show that with the new model the computed interfaces are smoother and more consistent with physical analysis. The growth rates of bubble and spike present a satisfying agreement with the theoretical predictions and other numerical simulations.

Experimental investigation on the properties of liquid film breakup induced by shock waves

We experimentally observed properties of liquid film breakup for shock-wave-initiated disturbances in air at normal temperature and pressure.The tested liquids include water and various glycerol mixtures.High speed camera and multiple-spark high speed camera were utilized to record the process of liquid film breakup.A phase Doppler particle analyzer was also used to record droplet size and velocity.The experimental results show that liquid viscosity plays a vital role in the deformation,breakup and atomization of liquid films.After the interaction of shock waves,the droplet size of various glycerol mixtures is significantly smaller than either water or glycerol.Richtmyer-Meshkov instability is an important factor in the breakup and atomization of liquid films induced by shock waves.Furthermore,a dispersal model is established to study breakup mechanisms of liquid films.The correlation between droplet size and velocity is revealed quantitatively.The research results may provide improved understanding of breakup mechanisms of liquid films,and have important implications for many fields,especially for heterogeneous detonations of gas/liquid mixtures.

Numerical Simulations of the Richtmyer-Meshkov Instability of Solid-Vacuum Interface

The Richtmyer-Meshkov instability of interfaces separating elastic-plastic materials from vacuum is investigated by numerical simulation using a multi-material solid mechanics algorithm based on an Eulerian framework.The research efforts are directed to reveal the influence of the initial perturbation and material strength on the deformation of the perturbed interface impacted by an initial shock.By varying the initial amplitude(kx0)of the perturbed interface and the yield stress(sY),three typical modes of interface deformation have been identified as the broken mode,the stable mode and the oscillating mode.For the broken mode,the interface width(i.e.,the bubble position with respect to that of the spike)increases continuously resulting in a final separation of the spike from the perturbed interface.For the stable mode,the interface width grows to saturation and then maintains a nearly constant value in the long term.For the oscillating mode,the wavy-like interface moving forward obtains an aperiodic oscillation of small amplitude,namely,the interface width varies in time slightly around zero.The intriguing difference of the typical modes is interpreted qualitatively by comparing the early-stage wave motion and the commensurate pressure and effective stress.Further,the subsequent interface deformation is illustrated quantitatively via the time series of the interface positions and velocities of these three typical modes.

Mixing Efficiency across Rayleigh-Taylor and Richtmeyer-Meshkov Fronts

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&minus;3 to 1.34 × 10&minus;1.