[Paper Review] Delineation of the flow and mixing induced by Rayleigh-Taylor instability through tracers

Ge Zhang, Aiguo Xu+4 more|arXiv (Cornell University)|Dec 31, 2019

Fluid Dynamics and Turbulent Flows87 references22 citations

TL;DR

This study introduces tracers into a discrete Boltzmann model (DBM) to visualize and quantify flow structures and mixing dynamics in compressible Rayleigh-Taylor instability (RTI). By tracking colored tracers, the method reveals fine-scale flow patterns and thermodynamic nonequilibrium behavior, while a tracer-defined mixedness metric uncovers a two-stage mixing evolution driven by large-scale initial structures and small-scale late-stage turbulence. The key contribution is the identification of a viscosity saturation effect and distinct compressibility/viscosity two-stage influences on mixing, offering new insight into RTI-driven mixing mechanisms.

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 RTI in compressible flows. Via marking two types of tracers with different colors, the tracer distribution provides a clear boundary of two fluids during the RTI evolution. Fine structures of the flow and thermodynamic nonequilibrium behavior around the interface in a miscible two-fluid system are delineated. Distribution of tracers in its 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 mixedness averaged align the direction of the pressure gradient. The role of compressibility and viscosity on mixing are investigated separately, both of which show 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 further increase of viscosity cannot see an evident decline in mixedness. The mixing statues of heavy and light fluids are not synchronous and the mixing of a RTI system is heterogenous. The results are helpful for understanding the mechanism of flow and mixing induced by RTI.

Motivation & Objective

• To investigate the detailed flow and mixing dynamics induced by Rayleigh-Taylor instability (RTI) in compressible, miscible fluid systems.
• To overcome limitations of traditional Navier-Stokes models in capturing thermodynamic nonequilibrium (TNE) effects at fluid interfaces.
• To develop a tracer-based method for visualizing fine-structure evolution and interfacial behavior in RTI with high spatiotemporal resolution.
• To quantify the effects of compressibility and viscosity on RTI mixing using a new mixedness metric derived from tracer distribution.
• To reveal the underlying physical mechanisms behind the two-stage mixing behavior observed in RTI systems.

Proposed method

• Tracers are introduced into a multiple-relaxation-time discrete Boltzmann model (DBM) to track fluid interface evolution and distinguish between heavy and light fluid regions.
• Two types of tracers are colored differently to provide a clear visual boundary between fluids during RTI development.
• A local mixedness metric χp is defined based on the spatial distribution of tracers, enabling quantitative analysis of mixing degree at each point in the domain.
• The mixedness is averaged vertically and analyzed along the horizontal direction to detect the onset and intensity of Kelvin-Helmholtz instability (KHI).
• Statistical analysis is performed using different-sized spatial cells (n = 1.0 and 8.0) to evaluate the robustness of mixedness profiles and avoid over-smoothing or excessive fluctuation.
• A scale analysis using optimal exponential fitting (χp = χ0 + C0·exp(t*/t0)) is applied to extract characteristic time scale t0 and characteristic mixedness C0 as functions of viscosity and compressibility.

Experimental results

Research questions

• RQ1 How do tracers enhance the visualization and quantification of flow structures and interfacial dynamics in RTI?
• RQ2 What is the role of compressibility in the two-stage evolution of RTI mixing, and how does it affect the characteristic time scale t0 and mixedness C0?
• RQ3 How does viscosity influence RTI mixing, and what causes the observed two-stage behavior and viscosity saturation effect?
• RQ4 Can the tracer-based mixedness metric reliably detect the onset and intensity of Kelvin-Helmholtz instability (KHI) in RTI systems?
• RQ5 What physical mechanisms underlie the transition from large-scale to small-scale structure dominance in RTI mixing?

Key findings

• The tracer method successfully reveals fine-structure flow patterns and thermodynamic nonequilibrium (TNE) behavior at the fluid interface, particularly in velocity phase space, providing rich insights into RTI dynamics.
• The mixedness χp increases nearly exponentially with time, indicating a characteristic time scale t0 that decreases monotonically with increasing compressibility.
• Viscosity exhibits a two-stage effect on mixedness: initially increasing mixedness due to enhanced large-structure penetration, then decreasing it due to suppression of small-scale structures, culminating in a viscosity saturation effect beyond which further increases in viscosity do not reduce mixedness.
• The characteristic time scale t0 increases with viscosity initially and then slightly decreases, while characteristic mixedness C0 shows a similar two-stage trend, indicating distinct physical mechanisms at early and late stages.
• The mixedness profile averaged along the horizontal direction reveals the onset of Kelvin-Helmholtz instability (KHI), with intensity quantified by the average mixedness aligned with the pressure gradient direction.
• Heavy and light fluid mixing is asynchronous, and the mixing process is heterogeneous, with the system showing distinct behaviors depending on the fluid's compressibility and viscosity.