The interaction of a planar shock wave with a dusty-gas cylinder is numerically studied by a compressible multi-component solver with an adaptive mesh refinement technique. The influence of non-equilibrium effect caus...The interaction of a planar shock wave with a dusty-gas cylinder is numerically studied by a compressible multi-component solver with an adaptive mesh refinement technique. The influence of non-equilibrium effect caused by the particle relaxation, which is closely related to the particle radius and shock strength, on the evolution of particle cylinder is emphasized. For a very small particle radius, the particle cloud behaves like an equilibrium gas cylinder with the same physical properties as those of the gas-particle mixture. Specifically, the transmitted shock converges continually within the cylinder and then focuses at a region near the downstream interface, producing a local high pressure zone followed by a particle jet. Also, noticeable secondary instabilities emerge along the cylinder edge and the evident particle roll-up causes relatively large width and height of the shocked cylinder. As the particle radius increases, the flow features approach those of a frozen flow of pure air, e.g., the transmitted shock propagates more quickly with a weaker strength and a smaller curvature, resulting in an increasingly-weaken shock focusing and particle jet. Also, particles would escape from the vortex core formed at late stages due to the larger inertia, inducing a greater particle dispersion. It is found that a large particle radius as well as a strong incident shock can facilitate such particle escape. The theory of Luo et al.(J. Fluid Mech., 2007) combined with the SZ circulation model ( J. Fluid Mech., 1994) can reasonably explain the high dependence of particle escape on the particle radius and shock strength.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
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 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 of a planar shock with SF_(6)/Ar/He dual interfaces(SF_(6)/Ar interface is sinusoidal and Ar/He interface is unperturbed)is numerically studied with a compressible multi-component flow solver that is c...The interaction of a planar shock with SF_(6)/Ar/He dual interfaces(SF_(6)/Ar interface is sinusoidal and Ar/He interface is unperturbed)is numerically studied with a compressible multi-component flow solver that is capable of simultaneously capturing discontinuities and resolving small-scale smooth structures.Six cases with different interface distances and incident shock strengths are considered.For all cases,after the shock impact,the amplitude of the first interface reduces gradually to zero(i.e.,phase inversion)and then increases continuously in the negative direction.The rarefaction wave(RW2)reflected from the second interface promotes or suppresses the development of the first interface depending on the interface distance(D).Specifically,if D is small,RW2 arrives at the first interface at a time before phase inversion,and thus promotes the instability growth at the first interface.If D is large,RW2 encounters the first interface at a time after phase inversion,and thus suppresses the instability growth.A theoretical model for the critical distance,under which the first interface just completes phase inversion at the arrival time of RW2,is developed.With this model,one can regulate the instability growth at the first interface by giving a desired D.The development of the second interface belongs to non-standard Richtmyer-Meshkov instability,which depends heavily on the phase of the rippled transmitted shock.It is found that the model of Ishizaki(Phys.Rev.E 53,R5592,1996)fails to predict the perturbation growth of the second interface for cases where the transmitted shock is at phase 2 due to the ignorance of baroclinic vorticity.A new model considering the combined effects of baroclinic vorticity,velocity perturbation,and pressure disturbance is proposed,which gives a reasonable prediction of perturbation growth at the second interface.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grants 11802304 and 11625211)the Science Challenging Project (Grant TZ2016001).
文摘The interaction of a planar shock wave with a dusty-gas cylinder is numerically studied by a compressible multi-component solver with an adaptive mesh refinement technique. The influence of non-equilibrium effect caused by the particle relaxation, which is closely related to the particle radius and shock strength, on the evolution of particle cylinder is emphasized. For a very small particle radius, the particle cloud behaves like an equilibrium gas cylinder with the same physical properties as those of the gas-particle mixture. Specifically, the transmitted shock converges continually within the cylinder and then focuses at a region near the downstream interface, producing a local high pressure zone followed by a particle jet. Also, noticeable secondary instabilities emerge along the cylinder edge and the evident particle roll-up causes relatively large width and height of the shocked cylinder. As the particle radius increases, the flow features approach those of a frozen flow of pure air, e.g., the transmitted shock propagates more quickly with a weaker strength and a smaller curvature, resulting in an increasingly-weaken shock focusing and particle jet. Also, particles would escape from the vortex core formed at late stages due to the larger inertia, inducing a greater particle dispersion. It is found that a large particle radius as well as a strong incident shock can facilitate such particle escape. The theory of Luo et al.(J. Fluid Mech., 2007) combined with the SZ circulation model ( J. Fluid Mech., 1994) can reasonably explain the high dependence of particle escape on the particle radius and shock strength.
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 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 National Natural Science Foundation of China(Grant Nos.12122213,12072341,and 91952205).
文摘The interaction of a planar shock with SF_(6)/Ar/He dual interfaces(SF_(6)/Ar interface is sinusoidal and Ar/He interface is unperturbed)is numerically studied with a compressible multi-component flow solver that is capable of simultaneously capturing discontinuities and resolving small-scale smooth structures.Six cases with different interface distances and incident shock strengths are considered.For all cases,after the shock impact,the amplitude of the first interface reduces gradually to zero(i.e.,phase inversion)and then increases continuously in the negative direction.The rarefaction wave(RW2)reflected from the second interface promotes or suppresses the development of the first interface depending on the interface distance(D).Specifically,if D is small,RW2 arrives at the first interface at a time before phase inversion,and thus promotes the instability growth at the first interface.If D is large,RW2 encounters the first interface at a time after phase inversion,and thus suppresses the instability growth.A theoretical model for the critical distance,under which the first interface just completes phase inversion at the arrival time of RW2,is developed.With this model,one can regulate the instability growth at the first interface by giving a desired D.The development of the second interface belongs to non-standard Richtmyer-Meshkov instability,which depends heavily on the phase of the rippled transmitted shock.It is found that the model of Ishizaki(Phys.Rev.E 53,R5592,1996)fails to predict the perturbation growth of the second interface for cases where the transmitted shock is at phase 2 due to the ignorance of baroclinic vorticity.A new model considering the combined effects of baroclinic vorticity,velocity perturbation,and pressure disturbance is proposed,which gives a reasonable prediction of perturbation growth at the second interface.
