Rayleigh-Taylor Instability Research Articles

A dusty rain falls on the nova V959 Monocerotis

ABSTRACT We present archival and ground-based infrared observations of the γ-ray-emitting nova V959 Mon, covering the period 100–4205 d after the 2012 eruption. We use these data to determine that the secondary in the nova system is a G5 main sequence star. Data from the NEOWISE survey reveal a significant increase in the emission at 3.4 and 4.6 $\, \mu$m at late (≳600 d) times, which we interpret as emission by dust. Other interpretations are considered but cannot be reconciled with the data. The presence of such late dust emission, and in particular its variation with time, are unprecedented in the context of novae. The behaviour of the dust emission suggests a qualitative interpretation in which ejecta from the 2012 eruption encounter denser pre-eruption circumbinary material, giving rise to Rayleigh–Taylor instabilities that cause clumps of dust-bearing material to fall back towards the central binary, the dust undergoing destruction by chemisputtering as it does so. The observed rise in the dust temperature, the decline in the nova-dust distance, and in the dust mass are consistent with this interpretation. Not all novae are expected to show this behaviour, but inspection of resources such as NEOWISE might reveal other novae post-eruption that do.

Viscous correction to the potential flow analysis of Rayleigh–Taylor instability in a Rivlin–Ericksen viscoelastic fluid layer with heat and mass transfer

AbstractThe current investigation focuses on examining viscous corrections for viscous potential flow (VCVPF) analysis concerning the Rayleigh–Taylor instability occurring at the interface of a Rivlin–Ericksen (R–E) viscoelastic fluid and a viscous fluid during the transfer of heat and mass between phases. The R–E model is a fundamental framework in the study of viscoelastic fluids, providing insights into their complex rheological behavior. It characterizes the material's response to both deformation and flow, offering valuable predictions for various industrial and biological applications. Within the framework of viscous potential flow (VPF) theory, viscosity is exclusively accounted for in the normal stress balance equation, disregarding the influence of shearing stress entirely. This study introduces a viscous pressure term into the normal stress balance equation alongside the irrotational pressure, presuming that this addition will improve the discontinuity of tangential stresses at the fluid interface. Through derivation of a dispersion relationship and subsequent theoretical and numerical stability analyses, the stability of the interface is investigated across various physical parameters. Multiple plots are generated using the dispersion relation, and a comparative analysis between VPF and VCVPF is conducted to establish improved stability criteria. The investigation highlights that the combined impact of heat/mass transport and shearing stress serves to delay the instability of the interface.

Investigation of effects of initial interface conditions on the two-dimensional single-mode compressible Rayleigh–Taylor instability: Based on the discrete Boltzmann method

The Rayleigh–Taylor (RT) instability in inertial confinement fusion implosions evolves at the unstable interface of two fluids when the light fluid is pushing the heavy one. The effects of the initial amplitude and transition layer on the compressible RT instability are investigated numerically by using the discrete Boltzmann method. On the one hand, during the RT evolution, higher initial amplitudes initially increase the global density gradient and non-equilibrium area, with a subsequent reversal. The increasing initial amplitude leads to an initial rise followed by a decline in the system’s maximum Mach number. On the other hand, the impact of the transition layer is generally opposite to the one of initial amplitude in the RT process. These findings offer significant insights into controlling and understanding RT instability in fusion implosion scenarios, emphasizing novel aspects relative to existing literature.

Condition for metal fragmentation during Earth-forming collisions

The long-term evolution of the deep Earth depends on its initial temperature and composition. These were set by the large planetary collisions that formed the Earth. After each collision, the metallic core of the impactor fell into a molten silicate magma ocean. Previous investigations showed that, as it sank, the impactor core fragmented into drops. The overall fragmentation of the core controlled the efficiency of chemical transfers between the impactor metal and the magma ocean, and, as a consequence, the composition of the Earth's core and mantle. However, because previous studies lack an impact stage, it is unclear whether the projectile core fragmented during the impact at Earth's surface, or deeper in the magma ocean.To answer this question, we conduct laboratory experiments modeling the collision of single-phase and two-phase impactors. In a first series of experiments, we investigate the impact of a single-phase centimetric liquid volume, representing the impactor core, onto a lighter immiscible liquid, representing the magma ocean. Our experiments approach the dynamical regime of planetary collisions for which inertia is large compared to surface tension. Varying the velocity and size of the impactor, we determine the conditions under which the impactor fragments into drops. We find that fragmentation occurs when the Froude number, which measures the relative importance of inertia to gravity, is larger than 40, regardless of surface tension. This fragmentation results from the growth of a turbulent Rayleigh-Taylor instability at the interface between the impacting liquid and the target pool. In contrast, when Fr<10, the impactor remains coherent. In a second series of experiments, we use two-phase impactors to show that these results hold for impactors that are differentiated into a core and a mantle.Applied to planet formation, our results suggest that the core of impactors less than 330 km in radius impacting at the escape velocity onto an Earth-sized planet fully fragments into droplets during the impact process, whereas the core of a giant Mars-sized impactor remains coherent. We derive a model for the depth at which the impactor core fragments in the magma ocean as a function of the impactor size and velocity. This model predicts that impactors with a radius less than 800 km fully fragment before reaching the bottom of the magma ocean. For velocities higher than twice the escape speed, some degree of fragmentation is unavoidable for any impactor size.

Phase-field formulated meshless simulation of Rayleigh-Taylor instability problem

The interface between two immiscible Newtonian liquids with different densities and the same viscosity, influenced by gravity, is based on the Phase-Field Method (PFM) formulation. The solution of the related governing coupled Navier-Stokes (NS) and Cahn-Hillard (CH) equations is structured by the meshless Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO). The variable density is involved in the inertial and buoyancy terms (non-Boussinesq formulation). The related moving boundary problem is handled through single-domain, irregular, fixed node arrangement in two-dimensional Cartesian coordinates. The meshless DAM uses weighted least squares approximation on overlapping subdomains, polynomial shape functions of second-order and Gaussian weights. Implicit time discretisation is performed for the NS and CH equations in the momentum predictor and Phase-Field (PF) variable corrector steps of PISO, while the momentum corrector steps solve the NS equation explicitly. This solution procedure has improved stability compared to Chorin’s pressure-velocity coupling, previously used in meshless solutions of related problems. The Rayleigh-Taylor instability problem simulations are performed for an Atwood number of 0.76. The DAM parameters (shape parameter of the Gaussian weight function and number of nodes in a local subdomain) are the same as in the author’s previous studies on single-phase flows. The simulations did not need any upwinding in the range of the simulations. The results compare well with the mesh-based finite volume method studies performed with the open-source code Gerris.

Shape stability of a microbubble in a power–law liquid

The onset of non-spherical oscillations of a microbubble in an unbounded power–law liquid, important for biomedical ultrasound applications, is studied. Two sets of evolution equations are obtained from the equation of motion: a Rayleigh Plesset-type equation for the spherical oscillations and an equation for the non-spherical oscillations. The non-spherical oscillations are modeled using the perturbation method via the Legendre polynomials. Two kinds of instabilities, namely parametric and Rayleigh-Taylor instabilities, are investigated. A higher power–law index causes the damping of the oscillations for both spherical and non-spherical oscillations. The power–law index damping effect depends on the ultrasonic drive frequency. At natural frequency, the amplitude of the perturbations is high compared to the non-resonant cases. At a low consistency index, the damping effect of the power–law index decreases. Unlike Newtonian liquids, the viscosity of power–law liquids is affected by the frequency of the acoustic field, thereby affecting Rayleigh-Taylor instability.

Non-locality of mean scalar transport in two-dimensional Rayleigh–Taylor instability using the macroscopic forcing method

The importance of non-locality of mean scalar transport in two-dimensional Rayleigh–Taylor Instability (RTI) is investigated. The macroscopic forcing method is utilized to measure spatio-temporal moments of the eddy diffusivity kernel representing passive scalar transport in the ensemble averaged fields. Presented in this work are several studies assessing the importance of the higher-order moments of the eddy diffusivity, which contain information about non-locality, in models for RTI. First, it is demonstrated through a comparison of leading-order models that a purely local eddy diffusivity is insufficient to capture the mean field evolution of the mass fraction in RTI. Therefore, higher-order moments of the eddy diffusivity operator are not negligible. Models are then constructed by utilizing the measured higher-order moments. It is demonstrated that an explicit operator based on the Kramers–Moyal expansion of the eddy diffusivity kernel is insufficient. An implicit operator construction that matches the measured moments is shown to offer improvements relative to the local model in a converging fashion.

Mixing, heating and ion-neutral decoupling induced by Rayleigh-Taylor instability in prominence-corona transition regions.

This study explores nonlinear development of the magnetized Rayleigh-Taylor instability (RTI) in a prominence-corona transition region. Using a two-fluid model of a partially ionized plasma, we compare RTI simulations for several different magnetic field configurations. We follow prior descriptions of the numerical prominence model (Popescu Braileanu et al. 2021 Astron. Astrophys. 646, A93(doi:10.1051/0004-6361/202039053),Popescu Braileanu et al. 2021 Astron. Astrophys. 650, A181 (doi:10.1051/0004-6361/202140425)and Popescu Braileanu et al. 2023 Astron. Astrophys. 670, A31(doi:10.1051/0004-6361/202142996)) and explore the charged-neutral fluid coupling and plasma heating in a two-dimensional mixing layer for different magnetic field configurations. We also investigate how the shear in magnetic field surrounding a prominence may impact the release of the gravitational potential energy of the prominence material. We show that the flow decoupling is strongest in the plane normal to the direction of the magnetic field, where neutral pressure gradients drive ion-neutral drifts and frictional heating is balanced by adiabatic cooling of the expanding prominence material. We also show that magnetic field within the mixing plane can lead to faster nonlinear release of the gravitational energy driving the RTI, while more efficiently heating the plasma via viscous dissipation of associated plasma flows. We relate the computational results to potential observables by highlighting how integrating over under-resolved two-fluid sub-structure may lead to misinterpretation of observational data. This article is part of the theme issue 'Partially ionized plasma of the solar atmosphere: recent advances and future pathways'.

The influence of thermal pressure gradients and ionization (im)balance on the ambipolar diffusion and charge-neutral drifts.

Solar partially ionized plasma is frequently modelled using single-fluid (1F) or two-fluid (2F) approaches. In the 1F case, charge-neutral interactions are often described through ambipolar diffusion, while the 2F model fully considers charge-neutral drifts. Here, we expand the definition of the ambipolar diffusion coefficient to include inelastic collisions (ion/rec) in two cases: a VAL3C one-dimensional model and a 2F simulation of the Rayleigh-Taylor instability (RTI) in a solar prominence thread based on [Lukin et al. 2024 Phil. Trans. R. Soc. A 382, 20230417. (doi:10.1098/rsta.2023.0417)]. On one side, we evaluate the relative importance of the inelastic contribution, compared to elastic and charge-exchange collisions. On the other side, we compare the contributions of ion/rec, thermal pressure, viscosity and magnetic forces to the charge-neutral drift velocity of the turbulent flow of the RTI. Our analysis reveals that the contribution of inelastic collisions to the ambipolar diffusion coefficient is negligible across the chromosphere, allowing the classical definition of this coefficient to be safely used in 1F modelling. However, in the transition region, the contribution of inelastic collisions can become as significant as that of elastic collisions. Furthermore, we ascertain that the thermal pressure force predominantly influences the charge-neutral drifts in the RTI model, surpassing the impact of the magnetic force. This article is part of the theme issue 'Partially ionized plasma of the solar atmosphere: recent advances and future pathways'.

Multi-scale simulation of microstructural evolution for molten U–Zr–O ternary system

The morphological evolution of the molten corium is critical to the success of the “in-vessel retention” (IVR) strategy, which is of great significance for the safety of the nuclear industry under severe accidents. However, the direct observation of microstructural evolution by experiments is impossible in extreme conditions. Herein, a multi-scale simulation approach was employed to investigate the microstructural evolution and related mechanisms for the molten U–Zr–O ternary system. First, based on the reported calculated phase diagram, a simplified free energy formula describing a phase diagram of U–Zr–O was determined, where only liquid phases are focused. Then, the atomic diffusion coefficients were calculated by ab-initio molecular dynamics simulations. Based on such information, a homemade phase-field model was developed, which was coupled with Cahn–Hillard and Navier–Stokes equations. Accordingly, the microstructural evolution of molten U–Zr–O materials was systematically investigated. The results reveal that the evolution of the molten core was driven by both the decreasing free energy and gravity potential, accessing the final morphology of the system as a two-layer structure, including a metallic layer and an oxidized layer. Moreover, diverse intermediate morphologies could be observed from different initial component distributions, although their average compositions were identical. Finally, some intermediate simulated microstructural patterns agreed well with experimental observation, demonstrating the unstable structures captured by experiments and the validity of the simulations. The present study provides an effective approach to investigate the microstructural evolution of molten core and a guideline for optimizing the IVR strategy based on different morphologies in the corium.

Development of a simplified one-dimensional CDA bubble model

Sodium-cooled fast reactors (SFRs) have high safety with an extremely low probability of a core disruptive accident (CDA). However, from a defense-in-depth perspective, the CDA sequence is still worth studying. Severe accidents in SFRs, such as unprotected loss of flow, might lead to a CDA during which fuel and some fission products could be instantly released from a large CDA bubble through potential leak paths in the top shield structure. Therefore, a reasonable prediction of dynamic behavior of a large-scale bubble within the sodium pool is vital for accurately evaluating the migration of source terms. In this study, we propose a simplified one-dimensional CDA bubble model that can handle heat and mass transfer in two-phase multicomponent materials in different computational domains during the rising of bubbles through the sodium pool toward the cover-gas region. In this model, an entrainment model based on the Rayleigh–Taylor instability and Kelvin–Helmholtz instability was used to explain the coolant entrainment through the gas/liquid boundary and jet fragmentation. The model also addresses the mitigation effect of non-condensable gases on the condensation of fuel, steel and sodium vapor at bubble interface. We evaluated the model using a past experiment on the expansion of a two-phase, large bubble with high pressure in a stagnant liquid pool conducted by Purdue University in the late 1970 s using a 1/7-scale model of Clinch River Breeder Reactor. Good agreement with the experimental data demonstrates that the developed model can reasonably represent the essential characteristics of dynamic behavior of a large, high-pressure bubble with heat and mass transfer in two-phase multicomponent materials. This is valuable for evaluating the migration of the source terms, which will be carried out in future studies.

On development of lattice-Boltzmann method based multi phase flow solver

A numerical methodology based on lattice Boltzmann and level set function is presented to simulate the two-phase flows with stringent density and viscosity ratio. Two different strategies - single grid (SGLBLS) and dual grid (DGLBLS) are used. For accurate computation of interfacial forces in DGLBLS, the level set equations are solved on a uniform grid which is twice that for lattice-Boltzmann equations. The code validation and performance of SGLBLS and DGLBLS is carried on three different problems: Young’s Laplace law, 2D rising bubble and Rayleigh–Taylor instability. The results show that the representation of the interface is more accurate in DGLBLS with significantly less mass error - establishing it as an accurate method to handle stringent density and viscosity ratio. The comparison between DGLBLS and SGLBLS shows that the DGLBLS leads to a large improvement in the accuracy of the results with only slight increase in the computational cost.

An edge-based interface tracking (EBIT) method for multiphase-flow simulation with surface tension

We present a novel Front-Tracking method, the Edge-Based Interface Tracking (EBIT) method for multiphase flow simulations. In the EBIT method, the markers are located on the grid edges and the interface can be reconstructed without storing the connectivity of the markers. This feature makes the process of marker addition or removal easier than in the traditional Front-Tracking method. The EBIT method also allows almost automatic parallelization due to the lack of explicit connectivity.In a previous journal article we have presented the kinematic part of the EBIT method, that includes the algorithms for piecewise linear reconstruction and advection of the interface. Here, we complete the presentation of the EBIT method and combine the kinematic algorithm with a Navier–Stokes solver. A circle fit is now implemented to improve the accuracy of mass conservation in the reconstruction phase. Furthermore, to identify the reference phase and to distinguish ambiguous topological configurations, we introduce a new feature: the Color Vertex. For the coupling with the Navier–Stokes equations, we first calculate volume fractions from the position of the markers and the Color Vertex, then viscosity and density fields from the computed volume fractions and finally surface tension stresses with the Height-Function method. In addition, an automatic topology change algorithm is implemented into the EBIT method, making it possible the simulation of more complex flows. The two-dimensional version of the EBIT method has been implemented in the free Basilisk platform, and validated with seven standard test cases: stagnation flow, translation with uniform velocity, single vortex, Zalesak's disk, capillary wave, Rayleigh-Taylor instability and rising bubble. The results are compared with those obtained with the Volume-of-Fluid (VOF) method already implemented in Basilisk.

Numerical Simulation of the Interaction between a Planar Shock Wave and a Cylindrical Bubble

Three-dimensional (3D) computational fluid dynamics (CFD) simulations have been carried out to investigate the complex interaction of a planar shock wave (Ma = 1.22) with a cylindrical bubble. The unsteady Reynolds-averaged Navier–Stokes (URANS) approach with a level set coupled with volume of fluid (LSVOF) method has been applied in the present study. The predicted velocities of refracted wave, transmitted wave, upstream interface, downstream interface, jet, and vortex filaments are in very good agreement with the experimental data. The predicted non-dimensional bubble and vortex velocities also have great concordance with the experimental data compared with a simple model of shock-induced Rayleigh–Taylor instability (i.e., Richtmyer–Meshkov instability) and other theoretical models. The simulated changes in the bubble shape and size (length and width) against time agree very well with the experimental results. Comprehensive flow analysis has shown the shock–bubble interaction (SBI) process clearly from the onset of bubble compression up to the formation of vortex filaments, especially elucidating the mechanism on the air–jet formation and its development. It is demonstrated for the first time that turbulence is generated at the early phase of the shock cylindrical bubble interaction process, with the maximum turbulence intensity reaching about 20% around the vortex filament regions at the later phase of the interaction process.

Classical Solutions of Rayleigh–Taylor instability for inhomogeneous incompressible viscous fluids in bounded domains

Classical Solutions of Rayleigh–Taylor instability for inhomogeneous incompressible viscous fluids in bounded domains

Heat transfer and transport property contrast effects on the compressible Rayleigh-Taylor instability

Heat transfer and transport property contrast effects on the compressible Rayleigh-Taylor instability

The Effect of Spatially Varying Collision Frequency on the Development of the Rayleigh–Taylor Instability

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.

The ISPH simulation of Rayleigh-Taylor instability and multi-phase flow within porous media

The present study applies the incompressible smoothed particle hydrodynamics (ISPH) method to simulate multi-phase flow instabilities, specifically Rayleigh-Taylor instability (RTI) and mixing in a sloshing tank, within various porous media. This study is the first numerical attempt to simulate RTI in diverse porous structures. Porous media are modeled with the non-Darcy approach based on linear and nonlinear factors. The Smagorinsky model is employed to implement turbulence stress. Two validation tests were performed to verify the effectiveness of the ISPH technique, the first evaluating pressure over still water in a tank, the second RTI in free fluid, and excellent agreement was obtained in both tests. The results indicate that porosity parameters play a crucial role in controlling the RTI phenomenon and mixing in the sloshing tank. Low porosity leads to high porous resistance, which significantly reduces RTI development and the mixing processes between the two fluids by hindering the interaction of the heavier and lighter fluids. This study shows the effectiveness of the ISPH method in handling complex interfaces in two-phase mixing flows within porous media.

Non-circular pressure swirl nozzles injecting into stagnant air

As far as we are aware, all the previous studies have focused on circular injectors. Here, the effect of non-circular orifice shape on pressure swirl injector was investigated experimentally. For this purpose, three injectors; circular, square and rectangular were manufactured. The nozzles had the same cross-sectional area. Water was used as the working fluid and tests were conducted at room temperature and pressure. The Weber number varied from 484 to 1936. Flow parameters of the swirl jets were obtained by an in-house image processing code. The measured parameters were: discharge coefficient, spray angle, breakup length, lateral spread, SMD of drops and wavelength of surface waves formed on the cone. The influence of nozzle shape on all these parameters are discussed.A new breakup regime morphology for non-circular pressure swirl nozzles was defined. At lower Weber numbers, the air core was trapped inside the liquid sheet and relatively large ligaments were formed and separated from the edges (fiber breakup regime). As the Weber number was increased Rayleigh-Taylor instability produced cell-like structures near the nozzle exit. These cell-like structures eventually broke up at the thickened edges of the cells and formed Christmas tree like structures (Christmas tree regime). We found that all the measured flow parameters can best be correlated as a function of Reynolds number and Weber number based on liquid sheet thickness at nozzle exit. All these correlations were reported. Breakup length and lateral spread were heavily influenced by the breakup regime. In fiber breakup regime the breakup length and lateral spread increased with increasing Weber number. However, in Christmas tree (cellular) breakup regime, breakup length and lateral spread decreased with increasing Weber number.

Hybrid LBM-FVM solver for two-phase flow simulation

In this paper, we introduce a hybrid LBM-FVM solver for two-phase fluid flow simulations in which interface dynamics is modeled by a conservative phase-field equation. Integrating fluid equations over time is achieved through a velocity-based lattice Boltzmann solver which is improved by a central-moment multiple-relaxation-time collision model to reach higher accuracy. For interface evolution, we propose a finite-volume-based numerical treatment for the integration of the phase-field equation: we show that the second-order isotropic centered stencils for diffusive and separation fluxes combined with the WENO-5 stencils for advective fluxes achieve similar and sometimes even higher accuracy than the state-of-the-art double-distribution-function LBM methods as well as the DUGKS-based method, while requiring less computations and a smaller amount of memory. Benchmark tests (such as the 2D diagonal translation of a circular interface), along with quantitative evaluations on more complex tests (such as the rising bubble and Rayleigh-Taylor instability simulations) allowing comparisons with prior numerical methods and/or experimental data, are presented to validate the advantage of our hybrid solver. Moreover, 3D simulations (including a dam break simulation) are also compared to the time-lapse photography of physical experiments in order to allow for more qualitative evaluations.