An experimental and numerical investigation of the dependency on the initial conditions of the Richtmyer-Meshkov instability

Abstract

International audienceThe nonlinear evolution of 2D single-mode Richtmyer-Meshkov instabilities is investigated through experiments in shock tube and numerical simulations. In our shock tube, the interface is materialized by a thin membrane attached to a stereo-lithographed grid. The purpose of this study is to compare experimental and numerical results, verify that using a higher Mach number for the incident shock wave (M-isw) than in a previous study [C. Mariani, M. Vandenboomgaerde, G. Jourdan, D. Souffland, and L. Houas, ``Investigation of the Richtmyer-Meshkov instability with stereolithographed interfaces,'' Phys. Rev. Lett. 100, 254503 (2008)] drastically reduces the deleterious effects of the membrane remnants, explore the effect of a high initial amplitude at the interface on the growth of the perturbation, and understand the lack of roll-up structures in the nonlinear phase of the instability. Using grayscale gradient rather than gray level, a new processing of the raw pictures is developed. Numerical simulations run with the TRICLADE code show that adding short-wavelength (swl) perturbations to the single-mode interface is necessary to understand the morphology of the experimental pictures. Through these comparisons, a minimal description of the swl perturbations is proposed. The experimental growth rates are correctly predicted by the TRICLADE code. Positive agreements are also obtained by models only if they take into account the effect of a high initial amplitude. A first result is the agreement that we obtain between experiment, simulations, and models indicates that the membrane remnants no longer influence the global dynamics of the instability. This is due to the increase of M-isw from 1.15 to 1.45. Another result of this investigation is that swl perturbations disrupt the spikes which grow at the interface and prevent the appearance of roll-up structures. Numerical simulations show the importance of a diffuse transition layer at the initial interface as a stabilizing process of the swl perturbations. In our case, only such a layer would allow the roll-up structures to grow. Finally, our analysis confirms that, when they are present at the same time, the swl perturbations distort the long wavelength perturbations, and that the latter decreases the growth of the former. (C) 2014 AIP Publishing LLC

Nonlinear growth of the converging Richtmyer-Meshkov instability in a conventional shock tube

“…As a result, the feed-back on the first harmonics stays low: the influence of the grid on the first harmonics remains limited. These conclusions are in accordance with the ones which were drawn from a previous study [34] in the planar case: the grid adds short-wavelength (swl) perturbations to the singlemode interface with low feed-back on the fundamental mode. Another way to check that our experiment is a good approximation of the canonical single mode problem is to reconstruct the shape of the interface with the first three modes.…”

The effect of initial conditions on mixing transition of the Richtmyer–Meshkov instability

“…It is noteworthy that the spectrum of small-amplitude short-wavelength perturbations observed is inevitable in real-life experiments where the interface is machine made. In fact, it has been shown that running numerical simulations with the addition of such residual perturbations to single-mode interfaces is necessary to understand the morphology of the experimental picture (Vandenboomgaerde et al 2014). As such, the deviation in experiments herein from the ideal case of a pure single-mode perturbation allows us to complement single-mode work by improving them to be closer to reality.…”

“…Since the interface formed is not perfectly sinusoidal, the presence of a spectrum of residual small-amplitude short-wavelength perturbations (Vandenboomgaerde et al 2014) and multi-mode fronts observed can cause mode coupling (Rupert 1991) in the nonlinear late-time growth regime. Large scales develop by means of a bubble-competition mechanism (Zufiria 1988) and vortex pairing.…”

Experimental and Numerical Investigation of the Growth of an Air/SF6 Turbulent Mixing Zone in a Shock Tube

“…More precisely, the building blocks of the egg-box initialization contain two sine functions in each direction a 0 cos 2px=m ð ÞÀ 1=5 ð Þ ð cos 2px=m ð Þ Þþa 0 cos 2py=m ð ÞÀ 1=5 ð Þcos 2py=m ð Þ ð corresponding to the first harmonics of j cos px=m ð Þj or j cos py=m ð Þj. However, such a representation may not be the most realistic [22]. Furthermore, schlieren pictures ( Fig.…”