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...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.展开更多
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 ...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.展开更多
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 cylin...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.展开更多
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 foun...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).展开更多
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 flui...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.展开更多
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 com...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.展开更多
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 ...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.展开更多
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 ...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.展开更多
A program MVFT3D of large-eddy simulation is developed and performed to solve the multi compressible Navier- Stokes equations. The SGS dissipation and molecular viscosity dissipation have been analyzed, and the former...A program MVFT3D of large-eddy simulation is developed and performed to solve the multi compressible Navier- Stokes equations. The SGS dissipation and molecular viscosity dissipation have been analyzed, and the former is much larger than the later. Our test shows that the SGS dissipation of Vreman model is smaller than the Smagorinsky model. We mainly simulate the experiment of fluid instability of shock-accelerated interface by Poggi in this paper. The decay of the turbulent kinetic energy before the first reflected shock wave–mixing zone interaction and its strong enhancement by re-shocks are presented in our numerical simulations. The computational mixing zone width under double re-shock agreement well with the experiment, and the decaying law of the turbulent kinetic energy is consistent with Mohamed and Larue’s investigation. Also, by using MVFT3D we give some simulation results of the inverse Chevron model from AWE. The numerical simulations presented in this paper allow us to characterize and better understand the Richtmyer-Meshkov instability induced turbulence, and the code MVFT3D is validated.展开更多
Suppression of the hydrodynamic instabilities involved in the inertial confinement fusion has attracted much attention but remains a challenge.In this work,we report the first theoretical analysis and experimental val...Suppression of the hydrodynamic instabilities involved in the inertial confinement fusion has attracted much attention but remains a challenge.In this work,we report the first theoretical analysis and experimental validation on attenuating the instability growth of a shock-accelerated fluid layer through a second shock impact.An analytical model is established to predict linear growth rates of the perturbations at two interfaces of the layer by considering both the effects of interface coupling and reverberating waves.Theoretically,there are nine possibilities for simultaneously attenuating the instability growths of perturbations at the two interfaces.Accordingly,shock-tube experiments are specially designed and conducted,and nine possibilities are all realized by experiments,which verifies the reliability of the analytical model and also demonstrates the feasibility of attenuating the instability growth of a fluid layer via double shock.展开更多
The rapid cycling synchrotron(RCS)at the China spallation neutron source operates as a high-intensity proton accelerator.The coupled bunch instability was observed during RCS beam commissioning,which significantly lim...The rapid cycling synchrotron(RCS)at the China spallation neutron source operates as a high-intensity proton accelerator.The coupled bunch instability was observed during RCS beam commissioning,which significantly limited the beam power.To investigate the dynamics of instability under an increased beam power,a pulsed octupole magnet with a gradient of 900 T/m^(3) was developed.The magnet system integrated an octupole magnet with a pulsed power supply.The field was carefully measured to examine the performance before its installation into the tunnel.After the installation of the magnets,beam measurements were performed to confirm the effectiveness of the instability mitigation on an actual proton beam.The measurement results show that the instability can be suppressed using the pulsed octupole magnet,particularly at the highenergy stage in an acceleration cycle,meeting the requirements for stable operation of the accelerator.Additionally,when the instability is completely suppressed through chromaticity optimization,octupole magnets can significantly enhance the RCS transmission efficiency,which is crucial for controlling beam loss.The pulsed octupole magnet offers significant progress in beam stability in the RCS,providing valuable experience for further beam power enhancement.展开更多
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 int...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.展开更多
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 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.展开更多
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 decelerat...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.展开更多
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 compres...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.展开更多
The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produ...The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms=1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock with the material interface, and effect of initial perturbation modes on R-M instability are investigated numerically. It is noted that the shock refraction is a main physical mechanism of the initial phase changing of the material surface. The multiple interactions of the reflected shock from the origin with the interface and the R-M instability near the material interface are the reason for formation of the spike-bubble structures. Different viscosities lead to different spike-bubble structure characteristics. The vortex pairing phenomenon is found in the initial double mode simulation. The mode interaction is the main factor of small structures production near the interface.展开更多
This study investigates numerically the coupling effect on the evolution of Richtmyer-Meshkov instability at double heavy square bubbles.Five scenarios are considered,each with varying initial separations S/L(where L ...This study investigates numerically the coupling effect on the evolution of Richtmyer-Meshkov instability at double heavy square bubbles.Five scenarios are considered,each with varying initial separations S/L(where L demotes the side length of the square)ranging from 0.125 to 1.0.Squares are filled with SF6gas,and are enclosed by N2gas.The simulations of shock-induced multispecies flow are performed by solving the two-dimensional compressible Euler equations with a higher-order explicit modal discontinuous Galerkin solver.The simulations demonstrate that the flow morphology resulting from the coupling effect is highly dependent on the separation between two squares.When the separation is large,the squares experience a weaker coupling effect and evolve independently.While,as the separation reduces,the coupling effect manifests earlier in the interaction and becomes more substantial.As a result,this phenomenon greatly intensifies the motion of inner upstream/downstream vortex rings towards the symmetry axis,leading to the emergence of multiple jets such as the twisted downward,upward,and coupled jets.A thorough exploration of the coupling effect of double squares is conducted by analyzing the vorticity production.Notably,a significant quantity of vorticity is produced along the squares interface for smaller separation.Further,these coupling effects result in various interface features(upstream/downstream movement,and height/width evolution),and temporal variations of various spatially integrated fields.Finally,the analysis of the flow structure also considers the interaction between two more flow parameters,the Mach and Atwood numbers,in order to evaluate the coupling effects.展开更多
The influence of the squeeze film between the tube and the support structure on flow-induced vibrations is a critical factor in tube bundles subjected to two-phase cross-flow.This aspect can significantly alter the th...The influence of the squeeze film between the tube and the support structure on flow-induced vibrations is a critical factor in tube bundles subjected to two-phase cross-flow.This aspect can significantly alter the threshold for fluidelastic instability and affect heat transfer efficiency.This paper presents a mathematical model incorporating the squeeze film force between the tube and the support structure.We aim to clarify the mechanisms underlying fluidelastic instability in tube bundle systems exposed to two-phase flow.Using a self-developed computer program,we performed numerical calculations to examine the influence of the squeeze film on the threshold of fluidelastic instability in the tube bundle system.Furthermore,we analyzed how the thickness and length of the squeeze film affect both the underlying mechanisms and the critical velocity of fluidelastic instability.展开更多
We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of plana...We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components,such as a disturbed onedimensional(1D)steady shock wave,we conduct a formal asymptotic analysis for the Euler system and associated numerical methods.This analysis aims to illustrate the discrepancies among various low-dissipative numerical algorithms.Furthermore,a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable algorithms.To verify the stability mechanism,a consistent,low-dissipation,and shock-stable HLLC-type Riemann solver is presented.展开更多
基金performed under the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344
文摘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.
基金The project supported by the National Natural Science Foundation of China(90205027 and 10632090)
文摘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.
基金The project supported by the National Natural Science Foundation of China (10176033, 10135010 and 90205025)The English text was polished by Yunming Chen
文摘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.
基金the National Natural Science Foundation of China(Grants 11802304 and 11625211)the Science Challenging Project(Grant TZ2016001).
文摘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).
基金This work was supported by the KAUST Office of Spon-sored Research under Award No.URF/1/2162-01.
文摘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.
基金This work was supported by the National Natural Science Foundation of China(Grants 11772329 and 11625211).
文摘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.
基金Support by the Science Foundations of Laboratory of Computational Physics,Science Foundation of China Academy of Engineering Physics under Grant Nos.2009A0102005,2009B0101012National Basic Research Program of China under Grant No.2007CB815105National Natural Science Foundation of China under Grant Nos.11074300,11075021,and 11071024
文摘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.
文摘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.
文摘A program MVFT3D of large-eddy simulation is developed and performed to solve the multi compressible Navier- Stokes equations. The SGS dissipation and molecular viscosity dissipation have been analyzed, and the former is much larger than the later. Our test shows that the SGS dissipation of Vreman model is smaller than the Smagorinsky model. We mainly simulate the experiment of fluid instability of shock-accelerated interface by Poggi in this paper. The decay of the turbulent kinetic energy before the first reflected shock wave–mixing zone interaction and its strong enhancement by re-shocks are presented in our numerical simulations. The computational mixing zone width under double re-shock agreement well with the experiment, and the decaying law of the turbulent kinetic energy is consistent with Mohamed and Larue’s investigation. Also, by using MVFT3D we give some simulation results of the inverse Chevron model from AWE. The numerical simulations presented in this paper allow us to characterize and better understand the Richtmyer-Meshkov instability induced turbulence, and the code MVFT3D is validated.
基金supported by the National Natural Science Foundation of China(Grant Nos.12372281,12102425,12388101,and 123B2034)the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB0620201)the Youth Innovation Promotion Association CAS。
文摘Suppression of the hydrodynamic instabilities involved in the inertial confinement fusion has attracted much attention but remains a challenge.In this work,we report the first theoretical analysis and experimental validation on attenuating the instability growth of a shock-accelerated fluid layer through a second shock impact.An analytical model is established to predict linear growth rates of the perturbations at two interfaces of the layer by considering both the effects of interface coupling and reverberating waves.Theoretically,there are nine possibilities for simultaneously attenuating the instability growths of perturbations at the two interfaces.Accordingly,shock-tube experiments are specially designed and conducted,and nine possibilities are all realized by experiments,which verifies the reliability of the analytical model and also demonstrates the feasibility of attenuating the instability growth of a fluid layer via double shock.
基金supported by the Guangdong Basic and Applied Basic Research Foundation,China(No.2021B1515140007).
文摘The rapid cycling synchrotron(RCS)at the China spallation neutron source operates as a high-intensity proton accelerator.The coupled bunch instability was observed during RCS beam commissioning,which significantly limited the beam power.To investigate the dynamics of instability under an increased beam power,a pulsed octupole magnet with a gradient of 900 T/m^(3) was developed.The magnet system integrated an octupole magnet with a pulsed power supply.The field was carefully measured to examine the performance before its installation into the tunnel.After the installation of the magnets,beam measurements were performed to confirm the effectiveness of the instability mitigation on an actual proton beam.The measurement results show that the instability can be suppressed using the pulsed octupole magnet,particularly at the highenergy stage in an acceleration cycle,meeting the requirements for stable operation of the accelerator.Additionally,when the instability is completely suppressed through chromaticity optimization,octupole magnets can significantly enhance the RCS transmission efficiency,which is crucial for controlling beam loss.The pulsed octupole magnet offers significant progress in beam stability in the RCS,providing valuable experience for further beam power enhancement.
基金supported by the China Postdoctoral Science Foundation(Grant No.2016M602026)the National Natural Science Foundation of China(Grant Nos.11625211,and 11621202)+1 种基金the Science Challenge Project(Grant No.TZ2016001)the Fundamental Research Funds for the Central Universities
文摘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.
基金supported by the National Natural Science Foundation of China(Nos.12172353,92052301,11621202 and 12202436)the Science Challenge Project(No.TZ2016001)the National Science Foundation(No.CBET0755269).
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.11772329,11802304,and U1530103)the Science Challenge Project(Grant No.TZ2016001)the Research Grants Council,Hong Kong(Grant No.152151/16E)
文摘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.
基金supported by the National Natural Science Foundation of China (Grant No. 10672151)the Foundation of China Academy of Engaineering Physics (Grant No. 2008B0202011)the Fundamental Quality and Reliability of National Defence Science and Technology Industry of China (Grant No. Z112009B004)
文摘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.
基金supported by the Special Funds for Major State Basic Research Projects(Grant No.G1999032805)National Natural Science Foundation of China(Grant Nos.10176033,90205025)National High-Tech ICF Committee in China.
文摘The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms=1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock with the material interface, and effect of initial perturbation modes on R-M instability are investigated numerically. It is noted that the shock refraction is a main physical mechanism of the initial phase changing of the material surface. The multiple interactions of the reflected shock from the origin with the interface and the R-M instability near the material interface are the reason for formation of the spike-bubble structures. Different viscosities lead to different spike-bubble structure characteristics. The vortex pairing phenomenon is found in the initial double mode simulation. The mode interaction is the main factor of small structures production near the interface.
基金the funding through the German Research Foundation within the research unit DFG-FOR5409。
文摘This study investigates numerically the coupling effect on the evolution of Richtmyer-Meshkov instability at double heavy square bubbles.Five scenarios are considered,each with varying initial separations S/L(where L demotes the side length of the square)ranging from 0.125 to 1.0.Squares are filled with SF6gas,and are enclosed by N2gas.The simulations of shock-induced multispecies flow are performed by solving the two-dimensional compressible Euler equations with a higher-order explicit modal discontinuous Galerkin solver.The simulations demonstrate that the flow morphology resulting from the coupling effect is highly dependent on the separation between two squares.When the separation is large,the squares experience a weaker coupling effect and evolve independently.While,as the separation reduces,the coupling effect manifests earlier in the interaction and becomes more substantial.As a result,this phenomenon greatly intensifies the motion of inner upstream/downstream vortex rings towards the symmetry axis,leading to the emergence of multiple jets such as the twisted downward,upward,and coupled jets.A thorough exploration of the coupling effect of double squares is conducted by analyzing the vorticity production.Notably,a significant quantity of vorticity is produced along the squares interface for smaller separation.Further,these coupling effects result in various interface features(upstream/downstream movement,and height/width evolution),and temporal variations of various spatially integrated fields.Finally,the analysis of the flow structure also considers the interaction between two more flow parameters,the Mach and Atwood numbers,in order to evaluate the coupling effects.
基金financially supported by the National Natural Science Foundation of China(Grant No.12072336).
文摘The influence of the squeeze film between the tube and the support structure on flow-induced vibrations is a critical factor in tube bundles subjected to two-phase cross-flow.This aspect can significantly alter the threshold for fluidelastic instability and affect heat transfer efficiency.This paper presents a mathematical model incorporating the squeeze film force between the tube and the support structure.We aim to clarify the mechanisms underlying fluidelastic instability in tube bundle systems exposed to two-phase flow.Using a self-developed computer program,we performed numerical calculations to examine the influence of the squeeze film on the threshold of fluidelastic instability in the tube bundle system.Furthermore,we analyzed how the thickness and length of the squeeze film affect both the underlying mechanisms and the critical velocity of fluidelastic instability.
基金Project supported by the National Natural Science Foundation of China(Nos.12471367 and12361076)the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Nos.NJZY19186,NJZY22036,and NJZY23003)。
文摘We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components,such as a disturbed onedimensional(1D)steady shock wave,we conduct a formal asymptotic analysis for the Euler system and associated numerical methods.This analysis aims to illustrate the discrepancies among various low-dissipative numerical algorithms.Furthermore,a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable algorithms.To verify the stability mechanism,a consistent,low-dissipation,and shock-stable HLLC-type Riemann solver is presented.
