Session J26: Flow Instability: Rayleigh-Taylor II

Rayleigh-Taylor Instability : Bubble-Spike asymmetry in transitional regime

In Inertial confinement fusion (ICF) applications and astrophysical flows, Rayleigh Taylor instability (RTI) occurs over a wide range of Mach, Reynolds and Knudsen numbers. The  objective of the current study is to establish RTI characteristics in the continuum-rarefied transitional regime at different Mach and Reynolds numbers. The Gas Kinetic Scheme is used to perform numerical simulations of RTI in the continuum and transitional regimes. At a given Mach number, decreasing Reynolds number results in increasing Knudsen number. At each Mach number, there exists a critical Reynolds number (Re_cr) below which flow is dominated by diffusive transport characteristic of rarefied flows. In the transitional regime (near

Re_cr), significant bubble-spike asymmetry is observed. It is shown that the spike side is dominated by diffusive transport, whereas the bubble side is advective in nature. The metrics characterizing the advective and diffusive domains in this transitional regime are identified. The results of this study can lead to a more comprehensive understanding of RTI over a wide range of Mach and Knudsen numbers.   

Ribbing instability in the rotating drag-out problem

We study experimentally and numerically the flow around a rotating wheel, when this wheel is partially immersed in a liquid reservoir. Two liquids are used: water, and an 80 times more viscous mixture of water and UCON oil. For large enough rotation rates, the initially 2D liquid film entrained along the wheel destabilizes into several parallel liquid ribs. These ribs are reminiscent of the fingers forming in the printer's instability, but in a strongly inertial limit. We measure the spacing between these ribs as a function of wheel velocity, viscosity and depth of immersion (up to 50% of wheel radius). A 3D numerical simulation is carried out with Basilisk for the conditions of the experiment: this simulation shows a good agreement with experimental results, and yields insight into the mechanism of rib formation. We will show that this mechanism relies on the variations of pressure within the liquid film, as it is extracted from the bath. We will discuss the implications of this mechanism for predicting the wavelength of this ribbing instability.   

Data-Driven Low-Order Modeling of the Rayleigh-Taylor Transition to Turbulence

We consider a data-driven, low-order modeling approach to the Rayleigh-Taylor (RT) transition to turbulence. Towards this, a suite of Direct Numerical Simulations (DNS) of low Atwood number RT flows was performed. This dataset was parametrized by four non-dimensional quantities characterizing the initial conditions and emphasizing the inertial and diffusive regimes of growth of the mixing region.

A related talk in this session presents results on a Bayesian approach to inferring the initial conditions (IC) using a neural network trained to map IC and time to a handful of domain-averaged scalars that characterize the instantaneous state of the system---length of the mixing zone, turbulent kinetic energy and dissipation and others.

In this talk, we pursue the analysis further by considering data-driven modeling of the dynamical evolution and transition to turbulence in the suite of RT simulations.

While we are ultimately interested in developing improved mix-models, here we present preliminary results on modeling the dynamical evolution of the same set of domain-averaged scalars using a variety of methods ranging from neural-ODEs to attention mechanisms. We expect that further data-driven modeling of the residual with respect to state of the art RANS models will lead to such improved mix models.   

Numerical simulations of non-premixed Rayleigh-Taylor flames

Using detailed 3D numerical simulations of a non-premixed, Rayleigh-Taylor (RT) flame, we have identified new mechanisms for stabilization and destabilization of the underlying flow¹. The flow is initialized with a sharp interface separating the fuel and oxidizer streams, that supports multimode perturbations. The simulations were performed using the astrophysical FLASH code, with appropriate modifications² to support accurate computations of chemically reacting flows with heat release. In particular, molecular transport of mass, momentum and heat are implemented through a newly developed, flux-based solver compatible with Adaptive Mesh Refinement for efficient computations. The Atwood number driving the instability growth is varied by changing the concentration of Nitrogen in both the fuel and oxidizer streams. The flame is initiated by auto-ignition of a combustible mixture produced initially by physical diffusion and later sustained by the mixing process associated with the RT instability. The problem setup is of relevance to several applications including ultra-compact combustors (UCC) which experience high-g loading of magnitude ~ 10⁴g₀ across the fuel-air interface, which could be susceptible to RT mixing.

¹N. Attal, P. Ramaprabhu, Physica D, 404, 132353, (2020)

²N. Attal, P. Ramaprabhu et al., Comp. & Fluids, 107, 59-76, (2015)   

Experimental Detection of Large-Scale Flow Structures in Rayleigh–Taylor instability

Here we examine the  large-scale structures that develop in Rayleigh–Taylor instability (RTI) experiments. Our experimental setup is comprised of two layers of fluid separated by a polycarbonate barrier at mid-depth of an acrylic tank. A statically unstable stratification is set up across the barrier such that when the barrier is removed RTI develops. Velocity and density data are collected using simultaneous particle image velocimetry and planar laser induced fluorescence. 

 

Large-scale structures are found using a Lagrangian-filtering based technique, which allows us to divide the flow into two structure fields b⁺ (downward moving) and b^- (upward moving). The experimentally determined b^± fields show reasonable agreement with previous numerical work and the mean per-structure average profiles show good agreement with theoretical predictions from two-fluid two-structure models. Thus, providing physical evidence for their existence across the mixing zone.    

Numerical Investigation of the Rayleigh-Taylor Instability Under Sharp and Sinusoidal Acceleration Switches

We study the dynamic properties of an interfacial flow between heavy and light incompressible fluids, which becomes Rayleigh-Taylor (RT) unstable when the system is subjected to an external acceleration field in the opposite direction of the density gradient. We perform implicit large eddy simulations (ILES) of RT instability under time-dependent sharp and smooth acceleration reversals. The majority of RT instability studies under variable acceleration have used a series of step functions. However, it is conjectured that a sinusoidal profile, which allows a smoother transition from acceleration to deceleration or vice versa, would better represent these transitions in real applications. We examine the performance of the length scale, Z(t), computed by integrating the time-variable acceleration over time in capturing RTI dynamics. In addition, we will discuss the time evolution of various parameters, including mass flux, Reynolds stress anisotropy tensor, and molecular mixing, to further discuss RTI mixing dynamics.   

Comparison of RANS Model and Self-Similarity Predictions Corresponding to Small Atwood Number, Transitional Rayleigh–Taylor Mixing

Profiles of mean and turbulent fields across the mixing layer obtained from direct numerical simulation data [O. Schilling and N. J. Mueschke, Physics of Fluids 22, 105102 (2010)] corresponding to a small Atwood number, transitional Rayleigh–Taylor mixing experiment in a water channel facility are compared to the profiles predicted by three- and four-equation mechanical–scalar Reynolds-averaged Navier–Stokes models and to analytical self-similar profiles [O. Schilling, Physics of Fluids 33, 085129 (2021)] at various times. The models are initialized in several different ways, and both time-dependent and constant model coefficients are used. It is shown that all profiles are in very good agreement. Many self-similar quantities are evaluated as a function of time using the time-dependent model coefficients, and are compared to their values using late-time constant coefficients, and are also compared to the dynamic model predictions and DNS data.   

Selecting optimal state variables for the Rayleigh-Taylor transition to turbulence

We propose a state variable identification method relying on a Bayesian approach in order to model the Rayleigh-Taylor (RT) transition to turbulence. Neural networks are used to emulate a large data-set of RT direct numerical simulations determined by their initial conditions. Using this surrogate model and an efficient MCMC algorithm, we infer the perturbed initial interface from the knowledge of several state variable candidates. From the posterior probability distributions, we then assess the ability of given state variables to predict accurately the evolution of the mixing layer. It is shown that a reduced number of variables allows to model efficiently the RT transition to turbulence, enabling extensions of classical mixing models to capture it.   

Analysis of a Multiphase Radiation-Driven Rayleigh-Taylor Instability

The physics of multiphase (particle-gas) Radiation-driven Rayleigh-Taylor Instability (RRTI) are central to understanding various astrophysical phenomena, especially the dust-laden stellar winds of asymptotic giant branch stars. While previous studies have examined the formation of instabilities during the initial stages of dust condensation, none have fully accounted for the multiphase effects, such as velocity slip between the dust and gas, that introduce additional complexity to the instability. When the dust and gas are not fully coupled, particles will detach from the flow field and may be concentrated in clusters. This study delves into the multiphase RRTI, concentrating on the role of high-opacity dust particles and their influence on the instability and its associated hydrodynamic growth. Numerical simulations are performed in the FLASH code and use an added radiation-particle coupling mechanism for this study. We examine the consequences of velocity equilibration rate, arising due to varying particle sizes, and how these different amounts of slip impact the dynamics and evolution of the RRTI. The effect of competing gravitational and radiation accelerations will be discussed and the effect of radiation heating of the gas and resulting gas buoyancy explored. The knowledge obtained from our research can improve astrophysical models and simulation techniques, allowing more precise depictions of the complex dynamics stemming from particle-gas-radiation interactions.