Shock accelerated vortex ring

The interaction of a shock wave with a spherical density inhomogeneity leads to the development of a vortex ring through the impulsive deposition of baroclinic vorticity. The present fluid dynamics videos display this phenomenon and were experimentally investigated at the Wisconsin Shock Tube Laboratory's (WiSTL) 9.2 m, downward firing shock tube. The tube has a square internal cross-section (0.25 m x 0.25 m) with multiple fused silica windows for optical access. The spherical soap bubble is generated by means of a pneumatically retracted injector and released into free-fall 200 ms prior to initial shock acceleration. The downward moving, M = 2.07 shock wave impulsively accelerates the bubble and reflects off the tube end wall. The reflected shock wave re-accelerates the bubble (reshock), which has now developed into a vortex ring, depositing additional vorticity. In the absence of any flow disturbances, the flow behind the reflected shock wave is stationary. As a result, any observed motion of the vortex ring is due to circulation. The shocked vortex ring is imaged at 12,500 fps with planar Mie scattering.Comment: For Gallery of Fluid Motion 200

Cooling Effect of the Richtmyer-Meshkov Instability

We provide numerical evidence that the Richtmyer-Meshkov (RM) instability contributes to the cooling of a relativistic fluid. Due to the presence of jet particles traveling throughout the medium, shock waves are generated in the form of Mach cones. The interaction of multiple shock waves can trigger the RM instability, and we have found that this process leads to a down-cooling of the relativistic fluid. To confirm the cooling effect of the instability, shock tube Richtmyer-Meshkov instability simulations are performed. Additionally, in order to provide an experimental observable of the RM instability resulting from the Mach cone interaction, we measure the two particle correlation function and highlight the effects of the interaction. The simulations have been performed with an improved version of the relativistic lattice Boltzmann model, including general equations of state and external forces.Comment: 10 pages, 6 figure

A conservative sharp-interface method for compressible multi-material flows

In this paper we develop a conservative sharp-interface method dedicated to simulating multiple compressible fluids. Numerical treatments for a cut cell shared by more than two materials are proposed. First, we simplify the interface interaction inside such a cell with a reduced model to avoid explicit interface reconstruction and complex flux calculation. Second, conservation is strictly preserved by an efficient conservation correction procedure for the cut cell. To improve the robustness, a multi-material scale separation model is developed to consistently remove non-resolved interface scales. In addition, the multi-resolution method and local time-stepping scheme are incorporated into the proposed multi-material method to speed up the high-resolution simulations. Various numerical test cases, including the multi-material shock tube problem, inertial confinement fusion implosion, triple-point shock interaction and shock interaction with multi-material bubbles, show that the method is suitable for a wide range of complex compressible multi-material flows

Atwood ratio dependence of Richtmyer-Meshkov flows under reshock conditions using large-eddy simulations

We study the shock-driven turbulent mixing that occurs when a perturbed planar density interface is impacted by a planar shock wave of moderate strength and subsequently reshocked. The present work is a systematic study of the influence of the relative molecular weights of the gases in the form of the initial Atwood ratio A. We investigate the cases A = ± 0.21, ±0.67 and ±0.87 that correspond to the realistic gas combinations air–CO_2, air–SF_6 and H_2–air. A canonical, three-dimensional numerical experiment, using the large-eddy simulation technique with an explicit subgrid model, reproduces the interaction within a shock tube with an endwall where the incident shock Mach number is ~1.5 and the initial interface perturbation has a fixed dominant wavelength and a fixed amplitude-to-wavelength ratio ~0.1. For positive Atwood configurations, the reshock is followed by secondary waves in the form of alternate expansion and compression waves travelling between the endwall and the mixing zone. These reverberations are shown to intensify turbulent kinetic energy and dissipation across the mixing zone. In contrast, negative Atwood number configurations produce multiple secondary reshocks following the primary reshock, and their effect on the mixing region is less pronounced. As the magnitude of A is increased, the mixing zone tends to evolve less symmetrically. The mixing zone growth rate following the primary reshock approaches a linear evolution prior to the secondary wave interactions. When considering the full range of examined Atwood numbers, measurements of this growth rate do not agree well with predictions of existing analytic reshock models such as the model by Mikaelian (Physica D, vol. 36, 1989, p. 343). Accordingly, we propose an empirical formula and also a semi-analytical, impulsive model based on a diffuse-interface approach to describe the A-dependence of the post-reshock growth rate

Clumpy and fractal shocks, and the generation of a velocity dispersion in molecular clouds

We present an alternative explanation for the nature of turbulence in molecular clouds. Often associated with classical models of turbulence, we instead interpret the observed gas dynamics as random motions, induced when clumpy gas is subject to a shock. From simulations of shocks, we show that a supersonic velocity dispersion occurs in the shocked gas provided the initial distribution of gas is sufficiently non-uniform. We investigate the velocity size-scale relation $\sigma \propto r^{\alpha}$ for simulations of clumpy and fractal gas, and show that clumpy shocks can produce realistic velocity size-scale relations with mean $\alpha \thicksim 0.5$. For a fractal distribution, with a fractal dimension of 2.2 similar to what is observed in the ISM, we find $\sigma \propto r^{0.4}$. The form of the velocity size-scale relation can be understood as due to mass loading, i.e. the post-shock velocity of the gas is determined by the amount of mass encountered as the gas enters the shock. We support this hypothesis with analytical calculations of the velocity dispersion relation for different initial distributions. A prediction of this model is that the line-of sight velocity dispersion should depend on the angle at which the shocked gas is viewed.Comment: 11 pages, 17 figures, accepted for publication in MNRA

Experiments on the Richtmyer–Meshkov instability: Small-scale perturbations on a plane interface

This paper reports the results of measurements of the "visual thickness," obtained from flow visualization experiments by the schlieren method, of initially plane interfaces between two gases under impulsive accelerations. It is found that when such interfaces are processed by just one incident shock wave of strength of order Ms=1.5, their thickness increases slowly and they require observation over extended times; their growth rates are found to slow down with time, in agreement with simple theoretical arguments. The observed growth rates of thin interfaces formed by plastic membranes have been found to be substantially smaller than that reported by previous investigators. Also, thick, diffusively smoothed interfaces initially grow much more slowly than the discontinuous ones do. In these experiments, it is found that wall vortices formed by shock wave/boundary-layer interaction at the interface grow much more rapidly than the shock-processed interfaces in the bulk of the fluid. These wall structures can reduce the apparent growth of interfaces by vorticity-induced strain and impair the observation of the relevant interface phenomena

X-ray measurements of growth rates at a gas interface accelerated by shock waves

A new experimental technique to measure the density of a high atomic number gas at a shock-accelerated interface has been developed and demonstrated. It is based on the absorption of x rays by the high atomic number gas, and it was implemented in a vertical square shock tube. The object of the study was the turbulent entrainment and mixing of shock-accelerated air/xenon interfaces prepared by retracting a metal plate, initially separating the two gases, prior to the release of the shock wave. Interfaces of two types, quasi-sinusoidal and nominally flat, were examined. The amplitude of large wavelength (25–100 mm) perturbations on the interface, and the thickness of the interface were measured. An integral definition for the interface mean line was adopted, making it possible to study and time evolution of the individual Fourier modes of the perturbations. A new integral definition for the interface thickness was proposed, making it feasible to study for the first time the time evolution of the thickness of quasi-sinusoidal interfaces. Images of interfaces after interacting with a series of weak waves reverberating between the interface and the shock tube end wall were obtained. The perturbations are studied at the late stages of their evolution, when their amplitude is no longer small compared to their wavelength. Consequently, the measured growth rates of the modal amplitudes are smaller than those predicted by the impulsive model based on the small amplitude approximation. In the case of nominally flat interfaces, the thickness is observed to grow linearly at rates comparable to values previously reported

Study of detonation interactions inside a 2-D ejector using detonation transmission tubing

Study of detonation interactions inside a two-dimensional ejector using detonation transmission tubing was reported. The main objective of the ejector assembly in the study is to make the flow-field as close to 2-D as possible. Optical-grade Perspex sheets with a thickness of 10 mm were used on both sides of the nozzle to allow visualization of the flow. Wall pressure measurements were conducted at the locations. The NONEL tube was flush with the entrance of the nozzle. The signal to begin pressure measurements and image acquisition was obtained through a Kulite XT-190 transducer. The detonation was initiate by an electronic blasting machine, DynoStart 2, with a capacitance of 0.2μF and an output voltage of 2500 V. High-speed shadowgraphy was employed to visualize the flow. The results show that the effects of 3-D flow at the initial stage of the detonation affect the incident shock front and the reflected shock wave system at the nozzle entrance