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Experimental and Numerical Investigation of the Dynamics of Development of Rayleigh–Taylor Instability at Atwood Numbers Close to Unity

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Abstract

This paper presents the experimental and numerical results of studying the growth dynamics of the deterministic and given initial perturbations defined in a certain way. The formation, growth, and further evolution of inhomogeneities of the contact boundary occurs due to the development of the Rayleigh–Taylor instability (RTI) at the gas-liquid interface, and in particular (in this study), the air-water interface. The significant difference in the densities of the selected substances leads to a noticeable slowdown in the dynamics of the Kelvin–Helmholtz instability (KHI), which is responsible for the formation of mushroom-like structures, and, as a result, to the longer growth of water jets and the later moment of their destruction and transition to mixing. In this study, a quantitative comparison of the physical data recorded on the original experimental setup, which is described in this paper, with the calculated data obtained using various numerical methods is carried out. The numerical modeling is based on a complete 2D hydrodynamic model for describing the dynamics of the development of the RTI. The surface tension (water-air) and viscosity (water or air) are neglected in this study. The parameters of the development of the instability measured in the experiment and found in the calculations indicate satisfactory agreement between the obtained data. The quantitative results presented in this study justify the use of the classical hydrodynamics model to describe the movements of liquid and gas observed in this experiment and the fairly accurate numerical implementation of the corresponding model in the difference methods used here. The investigation of the development of turbulent mixing depending on well-defined initial conditions and the new regularities of the laws of mixing of the media of different densities that arise in this case is an important element in the study.

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ACKNOWLEDGMENTS

The multidimensional numerical calculations were carried out on the equipment installed in the Supercomputer Center for Collective Use of Keldysh Institute of Applied Mathematics, Russian Academy of Sciences and Russian Federal Nuclear Center, All-Russian Scientific Research Institute of Experimental Physics (VNIIEF). The authors thank the staff of these centers.

Funding

This study was supported as part of the scientific program of the National Center for Physics and Mathematics, Sarov, Nizhny Novgorod oblast.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    M. D. Bragin, N. V. Zmitrenko, P. A. Kuchugov & V. F. Tishkin

  2. Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia

    S. Yu. Gus’kov & R. A. Yakhin

  3. MIREA—Russian Technological Institute, Moscow, Russia

    I. G. Lebo

  4. Russian Federal Nuclear Center—VNIIEF, Sarov, Nizhny Novgorod oblast, Russia

    E. V. Levkina, N. V. Nevmerzhitskiy, O. G. Sin’kova, V. P. Statsenko, I. R. Farin & Yu V. Yanilkin

  5. Alekseev Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia

    I. R. Farin

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  1. M. D. Bragin
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Correspondence to M. D. Bragin, N. V. Zmitrenko or P. A. Kuchugov.

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Bragin, M.D., Gus’kov, S.Y., Zmitrenko, N.V. et al. Experimental and Numerical Investigation of the Dynamics of Development of Rayleigh–Taylor Instability at Atwood Numbers Close to Unity. Math Models Comput Simul 15, 660–676 (2023). https://doi.org/10.1134/S2070048223040038

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