Analysis Of Rayleigh-Taylor Instability Research Articles

Irrotational flow analysis of Rayleigh-Taylor instability in nanofluid layer with tangential magnetic field

The application of nanofluids in the presence of a magnetic field holds promise for advanced drug delivery systems, where controlled manipulation of magnetic nanoparticles within nanofluids can enhance targeted and localized drug delivery. This study explores the instability of a viscous fluid-nanofluid interface arranged in a planar configuration influenced by a tangential magnetic field using the irrotational flow theory. When the nanofluid is positioned above a viscous fluid, the interface is susceptible to the Rayleigh-Taylor instability. Employing linear stability theory, an explicit relationship connecting the perturbation growth parameter with the wavenumber is derived. Different dimensionless quantities such as the Atwood number, Weber number, Froude number, and Reynolds number are analyzed using stability plots. These plots provide valuable information about the behavior of interfaces. Increased magnetic field strength is observed to delay instability onset. Surface tension is found to stabilize the interface, whereas inertial forces destabilize it. This investigation contributes to understanding and controlling the interface dynamics in nanofluid systems.

Mantle thermochemical variations beneath the continental United States through petrologic interpretation of seismic tomography

The continental lithospheric mantle plays an essential role in stabilizing continents over long geological time scales. Quantifying spatial variations in thermal and compositional properties of the mantle lithosphere is crucial to understanding its formation and its impact on continental stability; however, our understanding of these variations remains limited. Here we apply the Whole-rock Interpretive Seismic Toolbox For Ultramafic Lithologies (WISTFUL) to estimate thermal, compositional, and density variations in the continental mantle beneath the contiguous United States from MITPS_20, a joint body and surface wave tomographic inversion for Vp and Vs with high resolution in the shallow mantle (60–100 km). Our analysis shows lateral variations in temperature beneath the continental United States of up to 800–900°C at 60, 80, and 100 km depth. East of the Rocky Mountains, the mantle lithosphere is generally cold (350–850°C at 60 km), with higher temperatures (up to 1000°C at 60 km) along the Atlantic coastal margin. By contrast, the mantle lithosphere west of the Rocky Mountains is hot (typically >1000°C at 60 km, >1200°C at 80–100 km), with the highest temperatures beneath Holocene volcanoes. In agreement with previous work, we find that the chemical depletion predicted by WISTFUL does not fully offset the density difference due to temperature. Extending our results using Rayleigh-Taylor instability analysis, implies the lithosphere below the United States could be undergoing oscillatory convection, in which cooling, densification, and sinking of a chemically buoyant layer alternates with reheating and rising of that layer.

Linear analysis of Rayleigh-Taylor instability in viscoelastic materials.

Rayleigh-Taylor instability (RTI) has become a powerful tool for determining the mechanical properties of materials under extreme conditions. In this paper, we first present the exact and approximate linear dispersion relations for RTI in viscoelastic materials based on the Maxwell and Kelvin-Voigt models. The approximate dispersion relation produces good predictions of growth rates in comparison with the exact one. The motion of the interface in Maxwell flow is mainly controlled by viscosity and elasticity dominates this behavior in Kelvin-Voigt flow. Since elasticity plays a distinct role from viscosity, cutoff wavelengths arise only in Kelvin-Voigt flow. The variation of the maximum growth rates and their corresponding wave numbers are also carefully studied. For both types of materials, viscosity suppresses the growth of instability, while elasticity speeds it up. This is at odds with the well-known understanding that elasticity suppresses hydrodynamic instabilities. The dependence of the maximum growth rate on slab thickness is also investigated for RTI in both types of flow, since the metal slab as a pusher has been extensively employed in high-energy-density physics. The model presented here allows study of more realistic situations by considering convergent effects and shock wave interactions, for the traditional potential flow theory is not suitable. To summary, it is able to provide guidances for future experimental designs for studies of materials under high strain and high strain rate conditions, as well as allow us to study RTI theoretically in more complicated conditions.

Investigating the effects of viscosity and density ratio on the numerical analysis of Rayleigh-Taylor instability in two-phase flow using Lattice Boltzmann method: From early stage to equilibrium state

The gravitational liquid-liquid two-phase flow was numerically investigated by using lattice Boltzmann method (LBM). The method was implemented for analyzing a model of Rayleigh-Taylor Instability (RTI). The feasibility of this present numerical approach was investigated by performing convergence test, and validating the obtained results with those obtained from experiments as well as other preceding numerical methods. Qualitative and quantitative comparisons were examined, whereby good agreements are noted for all cases. Parametric studies were also conducted by varying both of Reynolds and Atwood numbers to investigate the effects of viscosity and density ratio on the behavior of fluids interaction. Based on the obtained outcomes of this numerical approach, the present LBM was able to successfully simulate the complete phenomena during RTI, i.e.: the linear growth, secondary instability, bubble rising and coalescence, and liquid break-up, including turbulent mixing conditions as well as the equilibrium state. The finding obtained from this work might be beneficial in the investigation of parametric behavior in design of processes equipment such as for separator design.

Analysis of Rayleigh Taylor instability in nanofluids with rotation

<p style='text-indent:20px;'>This article focuses on the hidden insights about the Rayleigh-Taylor instability of two superimposed horizontal layers of nanofluids having different densities in the presence of rotation factor. Conservation equations are subjected to linear perturbations and further analyzed by using the Normal Mode technique. A dispersion relation incorporating the effects of surface tension, Atwood number, rotation factor and volume fraction of nanoparticles is obtained. Using Routh-Hurtwitz criterion the stable and unstable modes of Rayleigh-Taylor instability are discussed in the presence/absence of nanoparticles and presented through graphs. It is observed that in the absence/presence of nanoparticles, surface tension helps to stabilize the system and Atwood number has a destabilizing impact without the consideration of rotation factor. But if rotation parameter is considered (in the absence/presence of nanoparticles) then surface tension destabilizes the system while Atwood number has a stabilization effect (for a particular range of wave number). The volume fraction of nanoparticles destabilizes the system in the absence of rotation but in the presence of rotation the stability of the system is significantly stimulated by the nanoparticles.</p>

RAYLEIGH-TAYLOR INSTABILITY IN NANOFLUIDS THROUGH POROUS MEDIUM

RAYLEIGH-TAYLOR INSTABILITY IN NANOFLUIDS THROUGH POROUS MEDIUM

Rupture time of droplets impacted by a burst of picosecond laser pulses.

Liquid Sn droplets were irradiated with shaped bursts of picosecond laser pulses. The shapes of the deforming droplets following the impact of the recoil pressure induced by these bursts were imaged using a high-speed shadowgraph system. The rupture time t[over ̃]_{b} of the droplet expanding as a thin fluid film was measured for each case. A Rayleigh-Taylor instability analysis is done in order to determine the dependences governing t[over ̃]_{b}. The evidence supports the hypothesis that the initial perturbations of the developing Rayleigh-Taylor instabilities are on the order of the ablation depth and that there is a lower cutoff wavelength of these initial perturbations of ∼10μm.

Jetting of viscous droplets from cavitation-induced Rayleigh–Taylor instability

Liquid jetting and fragmentation are important in many industrial and medical applications. Here, we study the jetting from the surface of single liquid droplets undergoing internal volume oscillations. This is accomplished by an explosively expanding and collapsing vapour bubble within the droplet. We observe jets emerging from the droplet surface, which pinch off into finer secondary droplets. The jetting is excited by the spherical Rayleigh–Taylor instability where the radial acceleration is due to the oscillation of an internal bubble. We study this jetting and the effect of fluid viscosity experimentally and numerically. Experiments are carried out by levitating the droplet in an acoustic trap and generating a laser-induced cavitation bubble near the centre of the droplet. On the simulation side, the volume of fluid method (OpenFOAM) solves the compressible Navier–Stokes equations while accounting for surface tension and viscosity. Both two-dimensional (2-D) axisymmetric and 3-D simulations are performed and show good agreement with each other and the experimental observation. While the axisymmetric simulation reveals how the bubble dynamics results destabilizes the interface, only the 3-D simulation computes the geometrically correct slender jets. Overall, experiments and simulations show good agreement for the bubble dynamics, the onset of disturbances and the rapid ejection of filaments after bubble collapse. Additionally, an analytic model for the droplet surface perturbation growth is developed based on the spherical Rayleigh–Taylor instability analysis, which allows us to evaluate the surface stability over a large parameter space. The analytic model predicts correctly the onset of jetting as a function of Reynolds number and normalized internal bubble energy.

Simulation of ligament mode breakup of molten slag by spinning disk in the dry granulation process

This paper performed the numerical investigations on the physical mechanism of ligament mode breakup of molten slag at the spinning disk edge by volume of fluid methodology, the piecewise line interface calculation scheme is utilized to track the air-slag interface location. Ligament spacing, length and tip diameter, and droplet size have been analyzed, a ligament spacing model for viscous fluids is developed theoretically based on Rayleigh Taylor instability analysis. Viscosity always produces a damping effect on the ligament spacing and the appearance of ligament. The ratio of ligament length and tip diameter is proportional to We0.447. Due to the circumferential surface tension, the ligaments tend to a pinch-off type droplet formation mode, and the breakup of ligament is a final result of destabilization of capillary waves. Due to ligament stretching caused by centrifugal effect, the pinch-off capillary wavelength is about 2.2–3.1 times of the ligament tip diameters. However, the actual dominant mode is the short-wave mode driven by propagative capillary wave from the ligament tip.

Study on Electrohydrodynamic Rayleigh-Taylor Instability with Heat and Mass Transfer

The linear analysis of Rayleigh-Taylor instability of the interface between two viscous and dielectric fluids in the presence of a tangential electric field has been carried out when there is heat and mass transfer across the interface. In our earlier work, the viscous potential flow analysis of Rayleigh-Taylor instability in presence of tangential electric field was studied. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer coefficient, and vapour fraction on the stability of the system. It has been observed that heat transfer and electric field both have stabilizing effect on the stability of the system.

Liquid-metal plasma-facing component research on the National Spherical Torus Experiment

Liquid metal plasma-facing components (PFCs) have been proposed as a means of solving several problems facing the creation of economically viable fusion power reactors. Liquid metals face critical issues in three key areas: free-surface stability, material migration and demonstration of integrated scenarios. To date, few demonstrations exist of this approach in a diverted tokamak and we here provide an overview of such work on the National Spherical Torus Experiment (NSTX). The liquid lithium divertor (LLD) was installed and operated for the 2010 run campaign using evaporated coatings as the filling method. Despite a nominal liquid level exceeding the capillary structure and peak current densities into the PFCs exceeding 100 kA m−2, no macroscopic ejection events were observed. The stability can be understood from a Rayleigh–Taylor instability analysis. Capillary restraint and thermal-hydraulic considerations lead to a proposed liquid-metal PFCs scheme of actively-supplied, capillary-restrained systems. Even with state-of-the-art cooling techniques, design studies indicate that the surface temperature with divertor-relevant heat fluxes will still reach temperatures above 700 °C. At this point, one would expect significant vapor production from a liquid leading to a continuously vapor-shielded regime. Such high-temperature liquid lithium PFCs may be possible on the basis of momentum-balance arguments.

Viscous Potential Flow Analysis of Rayleigh-Taylor Instability of Cylindrical Interface

The present paper deals with the study of Rayleigh-Taylor instability at the cylindrical interface using viscous potential flow theory. In the inviscid potential flow theory, the viscous term in Navier-Stokes equation vanishes as viscosity is zero. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in viscous potential flow theory and tangential stresses are not considered. A dispersion relation is derived and stability is discussed in terms of various parameters such as Ohnesorge number, density ratio etc. A condition for neutral stability is obtained and it is given in terms of critical value of the wave number. It is observed that the Ohnesorge number has destabilizing effect while inner fluid fraction has stabilizing effect on the stability of the system.

基于小波变换的信号去噪在瑞利泰勒不稳定性定标实验中的应用

基于小波变换的信号去噪在瑞利泰勒不稳定性定标实验中的应用

Linear Rayleigh-Taylor instability analysis of double-shell Kidder’s self-similar implosion solution

This paper generalizes the single-shell Kidder’s self-similar solution to the double-shell one with a discontinuity in density across the interface. An isentropic implosion model is constructed to study the Rayleigh-Taylor instability for the implosion compression. A Godunov-type method in the Lagrangian coordinates is used to compute the one-dimensional Euler equation with the initial and boundary conditions for the double-shell Kidder’s self-similar solution in spherical geometry. Numerical results are obtained to validate the double-shell implosion model. By programming and using the linear perturbation codes, a linear stability analysis on the Rayleigh-Taylor instability for the double-shell isentropic implosion model is performed. It is found that, when the initial perturbation is concentrated much closer to the interface of the two shells, or when the spherical wave number becomes much smaller, the modal radius of the interface grows much faster, i.e., more unstable. In addition, from the spatial point of view for the compressibility effect on the perturbation evolution, the compressibility of the outer shell has a destabilization effect on the Rayleigh-Taylor instability, while the compressibility of the inner shell has a stabilization effect.

Rayleigh–Taylor instability of viscoelastic drops at high Weber numbers

Movies of the breakup of viscous and viscoelastic drops in the high-speed airstream behind a shock wave in a shock tube have been reported by Joseph, Belanger & Beavers (1999). They performed a Rayleigh–Taylor stability analysis for the initial breakup of a drop of Newtonian liquid and found that the most unstable Rayleigh–Taylor wave fits nearly perfectly with waves measured on enhanced images of drops from the movies, but the effects of viscosity cannot be neglected. Here we construct a Rayleigh–Taylor stability analysis for an Oldroyd-B fluid using measured data for acceleration, density, viscosity and relaxation time λ1. The most unstable wave is a sensitive function of the retardation time λ2 which fits experiments when λ2/λ1 = O(10-3). The growth rates for the most unstable wave are much larger than for the comparable viscous drop, which agrees with the surprising fact that the breakup times for viscoelastic drops are shorter. We construct an approximate analysis of Rayleigh–Taylor instability based on viscoelastic potential flow which gives rise to nearly the same dispersion relation as the unapproximated analysis.

Rayleigh–Taylor instability analysis of targets with a low-density ablation layer

Irregularities on the outer surface of Inertial Confinement Fusion (ICF) capsules accelerated by laser irradiation are amplified by the Rayleigh–Taylor instability (RTI), which occurs at the ablation front (ablative RTI), where density gradient and acceleration have the same direction. The analytic stability theory of subsonic ablation fronts, for Froude number larger than one, shows that the main stabilization mechanisms are blowoff convection (rocket effect equilibrating the gravity force) and ablation (Sanz 1994; Betti et al. 1996). Blowoff convection and ablation are enhanced if the ablator material is mixed with high-Z dopants. The latest enhances radiation emission setting the ablator on a higher adiabat, lowering its density, and increasing the ablation velocity. When such an ablator is used to push a solid deuterium-tritium (D–T) shell, the D–T-ablator interface becomes classically unstable. The aim of this paper is to investigate the stability of such a configuration, represented by a low-density ablator pushing a heavier shell, and study the interplay between the classical and ablative RTIs occurring simultaneously. The stability analysis is carried out using a sharp boundary model (Piriz et al. 1997), which contains all the basic physics of the RTI in ICF.

The breakup of bubbles into jets during submerged gas injection

There has never been any fundamental explanation presented for the transition from the bubbling regime to the jetting regime when gas is injected into liquid at high velocity through submerged tuyeres. This is an important issue in metallurgical processes, since the flow regime is known to influence refining rates, refractory erosion, and the penetration of the liquid into the tuyere. Based on the observation that many small droplets of liquid and gas bubbles are formed to create the jets, a combined Kelvin-Helmholtz and Rayleigh-Taylor instability analysis has been applied to bubbles forming at submerged tuyeres. For particular wavelengths of disturbances, the interface will be unstable and create bubbles and droplets. The critical injection velocity for instability depends on surface tension, tuyere diameter, and the gas-to-liquid density ratio, which can be summarized by We = 10.5(ρ*)−1/2, where We is the Weber number based on the gas velocity and density and tuyere diameter, and ρ* is the gas-to-liquid density ratio. The importance of surface tension had not been appreciated previously for this regime of gas injection. There is considerable controversy in the literature concerning the measurement of the transition from bubbling to jetting. The 70 pct “linking” point, proposed by Ozawa and Mori, describes the situation where 70 pct of the bubbles link with the preceding bubbles and produce a reasonably steady jet. The theoretical correlation developed above predicts the velocity to reach this point ±20 pct (95 pct confidence level) in a variety of systems from six different groups of workers. The theoretical analysis demonstrates that the instabilities are primarily capillary in nature, not gravity waves, which explains the observation that orientation has little effect on the jetting transition.