Kinetics of Rayleigh−Taylor instability in van der Waals fluid: the influence of compressibility

Abstract

Early studies on Rayleigh−Taylor instability (RTI) primarily relied on the Navier−Stokes (NS) model. As research progresses, it becomes increasingly evident that the kinetic information that the NS model failed to capture is of great value for identifying and even controlling the RTI process; simultaneously, the lack of analysis techniques for complex physical fields results in a significant waste of data information. In addition, early RTI studies mainly focused on the incompressible case and the weakly compressible case. In the case of strong compressibility, the density of the fluid from the upper layer (originally heavy fluid) may become smaller than that of the surrounding (originally light) fluid, thus invalidating the early method of distinguishing light and heavy fluids based on density. In this paper, tracer particles are incorporated into a single-fluid discrete Boltzmann method (DBM) model that considers the van der Waals potential. By using tracer particles to label the matter-particle sources, a careful study of the matter-mixing and energy-mixing processes of the RTI evolution is realized in the single-fluid framework. The effects of compressibility on the evolution of RTI are examined mainly through the analysis of bubble and spike velocities, the ratio of area occupied by heavy fluid, and various entropy generation rates of the system. It is demonstrated that: (i) compressibility has a suppressive effect on the spike velocity, and this suppressive impact diminishes as the Atwood number (At) increases. The influence of compressibility on bubble velocity shows a staged behavior with increasing At. (ii) The impact of compressibility on the entropy production rate associated with the heat flow ({\dot{S}}_{\mathrm{N}\mathrm{O}\mathrm{E}\mathrm{F}}) is related to the stages of RTI evolution. Moreover, this staged impact of compressibility on {\dot{S}}_{\mathrm{N}\mathrm{O}\mathrm{E}\mathrm{F}} varies with At. Compressibility exhibits an inhibitory effect on the entropy production rate associated with viscous stresses ({\dot{S}}_{\mathrm{N}\mathrm{O}\mathrm{M}\mathrm{F}}). (iii) By incorporating the morphological parameter of the proportion of area occupied by heavy fluid (A_h), it is observed that the first minimum point of \mathrm{d}{A}_h/\mathrm{d}t can serve as a criterion for identifying the point at which bubble velocity reaches its first maximum value. The series of physical cognition provides a more accurate understanding of the RTI kinetics and a helpful reference for the development of corresponding regulation techniques.

Graphical abstract

Keywords

discrete Boltzmann method / Rayleigh−Taylor instability / compressibility effect / tracer particles

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Declarations

The authors declare that they have no competing interests and there are no conflicts.

Acknowledgements

The authors thank Yanbiao Gan, Feng Chen, Chuandong Lin, Huilin Lai, Zhipeng Liu, Ge Zhang, Yiming Shan, Dejia Zhang, Jiahui Song, Hanwei Li, Yingqi Jia, and Xuan Zhang for helpful discussions on DBM. This work was supported by the National Natural Science Foundation of China (Grant Nos. 12172061, 12102397, and 12101064), the Opening Project of State Key Laboratory of Explosion Science and Safety Protection (Beijing Institute of Technology) (Grant No. KFJJ23-02M), the Foundation of National Key Laboratory of Shock Wave and Detonation Physics (Grant No. JCKYS2023212003), and the 2023 Computational Physics Key Laboratory Youth Fund Sponsored Project (Grant No. 6241A05QN23001).

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