Delineation of the flow and mixing induced by Rayleigh–Taylor instability through tracers

Abstract

Rayleigh–Taylor-instability (RTI) induced flow and mixing are of great importance in both nature and engineering scenarios. To capture the underpinning physics, tracers are introduced to make a supplement to discrete Boltzmann simulation of compressible RTI flows. By marking two types of tracers with different colors, the tracer distribution provides a clear boundary of two fluids during the evolution. Fine structures of RTI flow and thermodynamic non-equilibrium behavior around the interface in a miscible two-fluid system are delineated. Distribution of tracers in their velocity phase space makes a charming pattern showing quite dense information on the flow behavior, which opens a new perspective for analyzing and accessing significantly deep insights into the flow system. RTI mixing is further investigated via tracer-defined local mixedness. The appearance of Kelvin–Helmholtz instability is quantitatively captured by the abrupt increase in mixedness averaged along the direction of acceleration. The role of compressibility and viscosity on mixing are investigated separately, both of which show a two-stage effect. The underlying mechanism of the two-stage effect is interpreted as the development of large structures at the initial stage and the generation of small structures at the late stage. At the late stage, for a fixed time, a saturation phenomenon of viscosity is found that a further increase in viscosity cannot lead to an evident decline in mixedness. The mixing statues of heavy and light fluids are not synchronous and the mixing of an RTI system is heterogeneous. The results are helpful for understanding the mechanism of flow and mixing induced by RTI.

Discrete Boltzmann modeling of Rayleigh-Taylor instability: effects of interfacial tension, viscosity and heat conductivity

“…The DBM method has been successfully applied to the study of fluid instability problems, and a series of research results and new insights are gained with its help [57][58][59][60][61]. Introducing the Van Der Waals (VDW) equation of state into the existing discrete Boltzmann BGK model for RTI systems and considering the contribution of the density gradient to the entropy and internal energy of the system, we can obtain the DBM model as shown in Eq.…”

Rayleigh-Taylor instability under multi-mode perturbation: discrete Boltzmann modeling with tracers

“…From Figure 1 (e)-(f), the tracer distribution patterns always shows a clear interface structure, even if there are a large number of separated and broken fluid areas in the flow field. Compared with singlemode perturbation [38] , the fluids mixing caused by multi-mode perturbation contains more abundant small structures and the interface shape and evolution are more complex, so the advantage of tracers to describe the fine structure is more fully reflected. Inevitably, there are some white noise spots on patterns of the tracers, and the resolution can be significantly improved by increasing the number of tracers.…”

“…While describing complex flows, tracers also provide an additional way to quantify the degree of mixing of light and heavy fluids. Zhang, et al [38] defined the local mixedness with the help of the location information of two types of tracers, additionally defined the averaged mixedness (AM):…”

“…Chen, et al [37] studied the specific heat ratio effect of RTI in compressible fluids, and discussed the variation of non-equilibrium strength with specific heat ratio. By introducing tracers in DBM, Zhang, et al [38] provided fine structure images with clear interfaces in RTI evolution, defined the mixing degree based on tracers, revealed the mixing process of light and heavy fluids, and further investigated the effect of compressibility and viscosity on RTI.…”

“…But these studies are basically based on single-mode perturbation. In this paper, we study the complex flow and mixing of multi-mode perturbation RTI based on the coupled modeling of DBM and tracers proposed by Zhang, et al [38] . The tracers provide a Lagrangian view of the same flow evolution.…”