skip to main content

Attention:

The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Thursday, October 10 until 2:00 AM ET on Friday, October 11 due to maintenance. We apologize for the inconvenience.


This content will become publicly available on December 11, 2024

Title: Direct numerical simulations of compressible three-layer Rayleigh-Taylor instability
Multi-fluid mixing in a system with three stratified layers is explored using two-dimensional compressible direct numerical simulations (DNS) by solving fully compressible multi-species Navier-Stokes equations. All configuration cases under investigation consist of at least one acceleration-driven Rayleigh-Taylor unstable interface where the direction of the acceleration is from the heavier to the lighter fluids to initiate the chaotic mixing. The DNS are initialized with isopycnic background stratification, where the species densities of the three fluids are initially constant over the domain, and also they are benefited from the adaptive mesh refinement (AMR) to reduce the computational cost. We investigate four cases with the global Atwood number of 0.04 where the stratified layers along the acceleration direction (from bottom to top) have heavy-intermediate-light, heavy-light-light, heavy-light-intermediate, and heavy-light-heavy densities, and each case is studied with two different distances between the first and third fluid layers. It is found that the globally unstable case with heavy-intermediate-light densities, which has two unstable interfaces, exhibits symmetric mixing during the flow evolution and eventually behaves similarly to the classical two-layer Rayleigh-Taylor instability (RTI) flows. This finding is consistent with the observation in previous three-layer RTI experiments. The case with heavy-light-light densities is performed for comparison purposes, and it practically only has a single-stratified interface similar to the two-layer RTI problem. For the remaining two cases, the top interface of the three-layer RTI is stably stratified. It is shown that for the cases where the top interface is neutrally stratified (e.g., heavy-light-light case) or weakly stratified (e.g., heavy-light-intermediate case), upward pure fluids penetration is larger compared to the heavy-light-heavy case, whose top interface is initially strongly stable. In addition to the study on large-scale RTI entrainment, we also present mixedness and vortical dynamics of the flows.  more » « less
Award ID(s):
2234415
NSF-PAR ID:
10479455
Author(s) / Creator(s):
; ;
Publisher / Repository:
2024 AIAA SciTech Forum
Date Published:
Format(s):
Medium: X
Location:
Orlando, Florida
Sponsoring Org:
National Science Foundation
More Like this
  1. Rayleigh–Taylor instability, RTI, occurs at the interface separating two fluids subjected to acceleration when the density gradient and the acceleration are in opposite directions. Previous scientific research primarily considered RTI under the incompressible assumption, which may not be valid in many high-energy-density engineering applications and astrophysical phenomena. In this study, the compressibility effects of the background isothermal stratification strength on multi-mode two-dimensional RTI are explored using fully compressible multi-species direct numerical simulations. Cases under three different isothermal Mach numbers – Ma=0.15,  0.3,  and  0.45 – are investigated to explore weakly, moderately, and strongly stratified compressible RTI, respectively, at an Atwood number of 0.04. Unlike incompressible RTI, an increase in the flow compressibility through the strength of the background stratification can suppress the RTI growth and can lead to a termination of the RTI mixing layer growth with a highly molecularly mixed state. Our findings suggest that even at the chosen relatively low Atwood number, the variable-density effects can be significantly enhanced due to an increase in the background stratification for the compressible RTI as different spatial profiles become noticeably asymmetric across the mixing layer for the strongly stratified case. In addition, this study compares the chaotic behavior of the cases by studying the transport of the turbulent kinetic energy as well as the vortex dynamics. The Reynolds number dependence of the results is also examined with three different Reynolds numbers, and the findings for the large-scale mixing and flow quantities of interest are shown to be universal in the range of the Reynolds numbers studied.

     
    more » « less
  2. We derive interface models for three-dimensional Rayleigh–Taylor instability (RTI), making use of a novel asymptotic expansion in the non-locality of the fluid flow. These interface models are derived for the purpose of studying universal features associated with RTI such as the Froude number in single-mode RTI, the predicted quadratic growth of the interface amplitude under multi-mode random perturbations, the optimal (viscous) mixing rates induced by the RTI and the self-similarity of horizontally averaged density profiles and the remarkable stabilization of the mixing layer growth rate which arises for the three-fluid two-interface heavy–light–heavy configuration, in which the addition of a third fluid bulk slows the growth of the mixing layer to a linear rate. Our interface models can capture the formation of small-scale structures induced by severe interface roll-up, reproduce experimental data in a number of different regimes and study the effects of multiple interface interactions even as the interface separation distance becomes exceedingly small. Compared with traditional numerical schemes used to study such phenomena, our models provide a computational speed-up of at least two orders of magnitude. 
    more » « less
  3. Abstract

    Fluids with different densities often coexist in subsurface fractures and lead to variable‐density flows that control subsurface processes such as seawater intrusion, contaminant transport, and geologic carbon sequestration. In nature, fractures have dip angles relative to gravity, and density effects are maximized in vertical fractures. However, most studies on flow and transport through fractures are often limited to horizontal fractures. Here, we study the mixing and transport of variable‐density fluids in vertical fractures by combining three‐dimensional (3D) pore‐scale numerical simulations and visual laboratory experiments. Two miscible fluids with different densities are injected through two inlets at the bottom of a fracture and exit from an outlet at the top of the fracture. Laboratory experiments show the emergence of an unstable focused flow path, which we term a “runlet.” We successfully reproduce the unstable runlet using 3D numerical simulations and elucidate the underlying mechanisms triggering the runlet. Dimensionless number analysis shows that the runlet instability arises due to the Rayleigh‐Taylor instability (RTI), and flow topology analysis is applied to identify 3D vortices that are caused by the RTI. Even under laminar flow regimes, fluid inertia is shown to control the runlet instability by affecting the size and movement of vortices. Finally, we confirm the emergence of a runlet in rough‐walled fractures. Since a runlet dramatically affects fluid distribution, residence time, and mixing, the findings in this study have direct implications for the management of groundwater resources and subsurface applications.

     
    more » « less
  4. Abstract

    The Rayleigh–Taylor (RT) instability is ubiquitously observed, yet has traditionally been studied using ideal fluid models. Collisionality can vary strongly across the fluid interface, and previous work demonstrates the necessity of kinetic models to completely capture dynamics in certain collisional regimes. Where previous kinetic simulations used spatially and temporally constant collision frequency, this work presents five-dimensional (two spatial, three velocity dimensions) continuum-kinetic simulations of the RT instability using a more realistic spatially varying collision frequency. Three cases of collisional variation are explored for two Atwood numbers: low to intermediate, intermediate to high, and low to high. The low-to-intermediate case exhibits no RT instability growth, while the intermediate-to-high case is similar to a fluid-limit kinetic case with interface widening biased toward the lower-collisionality region. A novel contribution of this work is the low-to-high collisionality case that shows significantly altered instability growth through an upward movement of the interface and damped spike growth due to increased free-streaming particle diffusion in the lower region. Contributions to the energy flux from the non-Maxwellian portions of the distribution function are not accessible to fluid models and are greatest in magnitude in the spike and regions of low collisionality. Increasing the Atwood number results in greater RT instability growth and reduced upward interface movement. Deviation of the distribution function from Maxwellian is inversely proportional to collision frequency and concentrated around the fluid interface. The linear phase of RT instability growth is well described by theoretical linear growth rates accounting for viscosity and diffusion.

     
    more » « less
  5. This work numerically investigates the role of viscosity and resistivity in Rayleigh–Taylor instabilities in magnetized high-energy-density (HED) plasmas for a high Atwood number and high plasma beta regimes surveying across plasma beta and magnetic Prandtl numbers. The numerical simulations are performed using the visco-resistive magnetohydrodynamic equations. Results presented here show that the inclusion of self-consistent viscosity and resistivity in the system drastically changes the growth of the Rayleigh–Taylor instability (RTI) as well as modifies its internal structure at smaller scales. It is seen here that the viscosity has a stabilizing effect on the RTI. Moreover, the viscosity inhibits the development of small-scale structures and also modifies the morphology of the tip of the RTI spikes. On the other hand, the resistivity reduces the magnetic field stabilization, supporting the development of small-scale structures. The morphology of the RTI spikes is seen to be unaffected by the presence of resistivity in the system. An additional novelty of this work is in the disparate viscosity and resistivity profiles that may exist in HED plasmas and their impact on RTI growth, morphology and the resulting turbulence spectra. Furthermore, this work shows that the dynamics of the magnetic field is independent of viscosity and likewise the resistivity does not affect the dissipation of enstrophy and kinetic energy. In addition, power law scalings of enstrophy, kinetic energy and magnetic field energy are provided in both the injection range and inertial sub-range, which could be useful for understanding RTI induced turbulent mixing in HED laboratory and astrophysical plasmas and could aid in the interpretation of observations of RTI-induced turbulence spectra. 
    more » « less