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Front. Phys.    2025, Vol. 20 Issue (1) : 11201    https://doi.org/10.15302/frontphys.2025.011201
Kinetics of Rayleigh−Taylor instability in van der Waals fluid: the influence of compressibility
Jie Chen1,2, Aiguo Xu2,3,4,5(), Yudong Zhang6, Dawei Chen2, Zhihua Chen1
1. National Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing 210094, China
2. National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
3. State Key Laboratory of Explosion Science and Safety Protection, Beijing Institute of Technology, Beijing 100081, China
4. HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China
5. National Key Laboratory of Shock Wave and Detonation Physics, Mianyang 621999, China
6. School of Mechanics and Safety Engineering, Zhengzhou University, Zhengzhou 450001, China
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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 ( S˙ NOEF) is related to the stages of RTI evolution. Moreover, this staged impact of compressibility on S˙ NOEF varies with At. Compressibility exhibits an inhibitory effect on the entropy production rate associated with viscous stresses ( S˙ NOMF). (iii) By incorporating the morphological parameter of the proportion of area occupied by heavy fluid ( Ah), it is observed that the first minimum point of dAh/dt 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.
Keywords discrete Boltzmann method      Rayleigh−Taylor instability      compressibility effect      tracer particles     
Corresponding Author(s): Aiguo Xu   
Just Accepted Date: 05 August 2024   Issue Date: 23 August 2024
 Cite this article:   
Jie Chen,Aiguo Xu,Yudong Zhang, et al. Kinetics of Rayleigh−Taylor instability in van der Waals fluid: the influence of compressibility[J]. Front. Phys. , 2025, 20(1): 11201.
 URL:  
https://academic.hep.com.cn/fop/EN/10.15302/frontphys.2025.011201
https://academic.hep.com.cn/fop/EN/Y2025/V20/I1/11201
Fig.1  (a) DBM simulation study and (b) flowchart of DBM simulation.
Fig.2  (a) The computational domain with [0, 1]×[−4, 4]. Red represents heavy fluid, and blue represents light fluid. (b−e) The density profile at x = 0 across various Ma conditions for At = 0.1, 0.25, 0.5, and 0.7, respectively.
Fig.3  The spike and bubble velocity under various Ma conditions for (a) At = 0.1, (b) At = 0.25, (c) At = 0.5, and (d) At = 0.7. The horizontal gray dashed line represents the bubble-saturated velocity predicted by potential flow models.
Fig.4  The contour plots of the compressive ( VC, left half) and solenoidal ( VS, right half) components of vertical velocity for At = 0.1. From (a) to (f): t = 1, 2, 3, 4, 5, and 6, respectively. From (1) to (4): Ma = 0.3, 0.5, 0.7, and 0.9, respectively. The dark lines represent the interface of the heavy and light fluids.
Fig.5  The contour plots of the compressive ( VC, left half) and solenoidal ( VS, right half) components of vertical velocity for At = 0.7. From (a) to (f): t = 1, 2, 3, 4, 5, and 6, respectively. From (1) to (4): Ma = 0.3, 0.5, 0.7, and 0.9, respectively. The dark lines represent the interface of the heavy and light fluids.
Fig.6  The VS profiles along the vertical lines across the bubble ( x = 1, denoted by dash lines) and spike (x = 0.5, denoted by solid lines) tips for At = 0.7. From (a) to (f): t = 1, 2, 3, 4, 5, and 6, respectively. The circles marked on the VS profile denote the vertical position of the bubble and spike tips at each moment.
Fig.7  The pressure contour at the initial time for At = 0.7. From (a) to (d): Ma = 0.3, 0.5, 0.7, and 0.9, respectively. The dark lines represent the interface of the heavy and light fluids.
Fig.8  The evolution of the proportion of area occupied by the heavy fluid Ah for (a) At = 0.1, (b) At = 0.25, (c) At = 0.5, and (d) At = 0.7.
Fig.9  The evolution of dAh/dt for (a) At = 0.1, (b) At = 0.25, (c) At = 0.5, and (d) At = 0.7.
Fig.10  Evolution of dAh/dt and Vbubble for At = 0.7 and Ma = 0.7. The vertical grey dash-dot line represents the moment t = 2.0.
Fig.11  The evolution of S˙NOEF for (a) At = 0.1, (b) At = 0.25, (c) At = 0.5, and (d) At = 0.7.
Fig.12  The evolution of |∇T|total2 for (a) At = 0.1, (b) At = 0.25, (c) At = 0.5, and (d) At = 0.7.
Fig.13  The contour plots of |∇ T|2 for At = 0.7 under two Ma conditions: (a) Ma = 0.3 and (b) Ma = 0.9. From (1) to (6): t = 1, 2, 3, 4, 5, and 6, respectively. The dark lines represent the interface of the heavy and light fluids.
Fig.14  The evolution of L for (a) At = 0.1, (b) At = 0.25, (c) At = 0.5, and (d) At = 0.7.
Fig.15  The evolution of dL/dt for (a) At = 0.1, (b) At = 0.25, (c) At = 0.5, and (d) At = 0.7.
Fig.16  The evolution of d|∇T| t ot al2/dt for (a) At = 0.1, (b) At = 0.25, (c) At = 0.5, and (d) At = 0.7.
Fig.17  The contour plots of (a) | ∇T|2 and (b) T for At = 0.7 at t = 4. From (1) to (3): Ma = 0.3, 0.5, and 0.9, respectively.
Fig.18  The evolution of S˙NOMF for (a) At = 0.1, (b) At = 0.25, (c) At = 0.5, and (d) At = 0.7.
Fig.19  The evolution of (∇ u:∇u)total for (a) At = 0.1, (b) At = 0.25, (c) At = 0.5, and (d) At = 0.7.
Fig.20  The evolution of d(∇ u:∇ u)total/ dt for (a) At = 0.1, (b) At = 0.25, (c) At = 0.5, and (d) At = 0.7.
Fig.21  The contour plots of ∇ u:∇ u for At = 0.1 and Ma = 0.3. From (a) to (f): t = 1, 2, 3, 4, 5, and 6, respectively.
Fig.22  The contour plots of ∇ u:∇ u for At = 0.7 under two Ma conditions: (a) Ma = 0.3, (b) Ma = 0.9. From (1) −(6): t = 1, 2, 3, 4, 5, and 6, respectively. The dark lines represent the interface of the heavy and light fluids.
  Fig.A1 Schematic of discrete velocities.
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