Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II

We report the first measurements of the perturbation amplitude in the converging Richtmyer-Meshkov instability in a semiannular shock tube. At early stages, the amplitude growth agrees well with the impulsive model considering the geometrical convergence effect. A quick decrease of the growth rate at late time, even to be negative, before the reshock is observed for the first time. The reduction of the growth rate is ascribed to the Rayleigh-Taylor stabilization caused by the interface deceleration motion only presented in the converging circumstance. By reasonably evaluating the Rayleigh-Taylor stabilization, a modified model based on the Bell equation is proposed, which well predicts the perturbation growth in a converging geometry from early to late stages before the reshock. It is also found that the flow compressibility is significant in the converging Richtmyer-Meshkov instability.

Measurement of a Richtmyer-Meshkov Instability at an Air-SF_{6} Interface in a Semiannular Shock Tube.

Richtmyer–Meshkov (RM) instability is regarded as a central role for understanding the hydrodynamic processes involved in inertial confinement fusion, supersonic combustion and supernova explosion....

https://journals.sagepub.com/doi/pdf/10.1177/0954406217727305

Review of experimental Richtmyer–Meshkov instability in shock tube: From simple to complex:

The Richtmyer–Meshkov instability on a three-dimensional single-mode light/heavy interface is experimentally studied in a converging shock tube. The converging shock tube has a slender test section so that the non-uniform feature of the shocked flow is amply exhibited in a long testing time. A deceleration phenomenon is evident in the unperturbed interface subjected to a converging shock. The single-mode interface presents three-dimensional characteristics because of its minimum surface feature, which leads to the stratified evolution of the shocked interface. For the symmetry interface, it is quantitatively found that the perturbation amplitude experiences a rapid growth to a maximum value after shock compression and finally drops quickly before the reshock. This quick reduction of the interface amplitude is ascribed to a significant Rayleigh–Taylor stabilization effect caused by the deceleration of the light/heavy interface. The long-term effect of the Rayleigh–Taylor stabilization even leads to a phase inversion on the interface before the reshock when the initial interface has sufficiently small perturbations. It is also found that the amplitude growth is strongly suppressed by the three-dimensional effect, which facilitates the occurrence of the phase inversion.

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Long-term effect of Rayleigh-Taylor stabilization on converging Richtmyer-Meshkov instability

Ritchmyer–Meshkov instability on an air/SF interface is experimentally studied in a coaxial converging shock tube by a high-speed laser sheet imaging technique. An unperturbed case is first examined to obtain the characteristics of the converging shock and the shocked interface. For sinusoidal interfaces, the wave pattern and the interface morphology of the whole process are clearly observed. It is quantitatively found that the perturbation amplitude first decreases due to the shock compression, then experiences a rapid growth to a maximum value and finally drops quickly before the reshock. The reduction of growth rate is ascribed to the Rayleigh–Taylor stabilization caused by the interface deceleration motion that is present in the converging circumstance. It is noted that the influence of the wavenumber on the amplitude growth is very little before the reshock, but becomes significant after the reshock.

Experimental study on a sinusoidal air/SF interface accelerated by a cylindrically converging shock

The interaction of cylindrical converging shock waves with a polygonal heavy gas cylinder is studied experimentally in a vertical annular diaphragmless shock tube. The reliability of the shock tube facility is verified in advance by capturing the cylindrical shock movements during the convergence and reflection processes using high-speed schlieren photography. Three types of air/SF6 polygonal interfaces with cross-sections of an octagon, a square and an equilateral triangle are formed by the soap film technique. A high-speed laser sheet imaging method is employed to monitor the evolution of the three polygonal interfaces subjected to the converging shock waves. In the experiments, the Mach number of the incident cylindrical shock at its first contact with each interface is maintained to be 1.35 for all three cases. The results show that the evolution of the polygonal interfaces is heavily dependent on the initial conditions, such as the interface shapes and the shock features. A theoretical model for circulation initially deposited along the air/SF6 polygonal interface is developed based on the theory of Samtaney & Zabusky (J. Fluid Mech., vol. 269, 1994, pp. 45–78). The circulation depositions along the initial interface result in the differences in flow features among the three polygonal interfaces, including the interface velocities and the perturbation growth rates. In comparison with planar shock cases, there are distinct phenomena caused by the convergence effects, including the variation of shock strength during imploding and exploding (geometric convergence), consecutive reshocks on the interface (compressibility), and special behaviours of the movement of the interface structures (phase inversion).

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Experimental investigation of cylindrical converging shock waves interacting with a polygonal heavy gas cylinder

Richtmyer-Meshkov (RM) instability occurs when an initially perturbed interface separating two different fluids is impulsively accelerated by a shock wave. If the density gradient of the interface and the pressure gradient of the shock wave are misaligned, baroclinic vorticity will be deposited in the flow, enhancing the interpenetration and mixing between two fluids. Up till now, the RM instability has been studied experimentally, numerically and theoretically due to the extensive applications in scientific and industrial fields, such as internal confinement fusion, supernova explosion, and the mixing of fuels in the scramjet.

Tong Long

Papers

Experimental investigation of cylindrical converging shock waves interacting with a polygonal heavy gas cylinder

Richtmyer-Meshkov Instability of a Multimode Interface Accelerated by a Toroidal Shock Wave