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.

High temperature effects in moving shock reflection with protruding Mach stem

The influence of high temperature effects on the protrusion of Mach stem in strong shock reflection over a wedge was numerically investigated. A two-dimensional inviscid solver applies finite volume method and unstructured quadrilateral grids were employed to simulate the flow. Theoretical analysis was also conducted to understand the phenomenon. Both numerical and theoretical results indicate a wall-jet penetrating forward is responsible for the occurrence of Mach stem protrusion. The protrusion degree seems to depend on the thermal energy buffer capacity of the testing gas. Approaches to increase the energy buffer capacity, such as vibrational relaxation, molecular dissociation, and increase of frozen heat caoacitv, all tend to escalate the orotrusion effect.

Numerical study on shock-dusty gas cylinder interaction

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.

On transition of type V interaction in double-wedge flow with non-equilibrium effects

The transition between regular reflection （RR） and Mach reflection （MR） of type V shock-shock interaction on a double-wedge geometry with high temperature non-equilibrium effects is investigated by extended shock-polar method and numerical simulation. First, the critical angles of transition from detachment criterion and yon Neumann criterion are determined by the extended shock-polar method considering the non-equilibrium effects. Then wave patterns and the transition process are numerically obtained. Results of the critical transition angles from shock-polar calculation and numerical simulation show evident disagreement, indicating transition mechanism between RR and MR of type V interaction is changed. By comparing with the frozen counterpart, it is also found that non-equilibrium effects lead to a larger critical wedge angle and a larger hysteresis interval.

Review on hydrodynamic instabilities of a shocked gas layer

Hydrodynamic instabilities induced by a shock wave can be observed in both natural phenomena and engineering applications,and are frequently employed to study gas dynamics, vortex dynamics, and turbulence. Controlling these instabilities is very desirable, but remains a challenge in applications such as inertial confinement fusion. The field of “shock-gas-layer interaction” has experienced rapid development, driven by advances in experimental and numerical techniques as well as theoretical understanding. This domain has uncovered a diverse array of wave patterns and hydrodynamic instabilities, such as reverberating waves, feedthrough, abnormal and freeze-out Richtmyer-Meshkov instability, among others. Studies have shown that it is possible to suppress these instabilities by appropriately configuring a gas layer. Here we review the recent progress in theories,experiments, and simulations of shock-gas-layer interactions, and the feedthrough mechanism, the reverberating waves and their induced additional instabilities, as well as the convergent geometry and reshock effects, are focused. The conditions for suppressing hydrodynamic instabilities are summarized. The review concludes by highlighting the challenges and prospects for future research in this area.

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.

Interaction of strong converging shock wave with SF6gas bubble

Interaction of a strong converging shock wave with an SF6 gas bubble is studied, focusing on the effects of shock intensity and shock shape on interface evolution. Experimentally, the converging shock wave is generated by shock dynamics theory and the gas bubble is created by soap film technique. The post-shock flow field is captured by a schlieren photography combined with a high-speed video camera. Besides, a three-dimensional program is adopted to provide more details of flow field. After the strong converging shock wave impact, a wide and pronged outward jet, which differs from that in planar shock or weak converging shock condition, is derived from the downstream interface pole. This specific phenomenon is considered to be closely associated with shock intensity and shock curvature. Disturbed by the gas bubble, the converging shocks approaching the convergence center have polygonal shapes, and the relationship between shock intensity and shock radius verifies the applicability of polygonal converging shock theory. Subsequently, the motion of upstream point is discussed, and a modified nonlinear theory considering rarefaction wave and high amplitude effects is proposed. In addition, the effects of shock shape on interface morphology and interface scales are elucidated. These results indicate that the shape as well as shock strength plays an important role in interface evolution.

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.