Taylor Instability Research Articles

The effect of concentration-dependent diffusion on double-diffusive instability

The article studies the stability of a two-layer miscible system to the double-diffusive instability. The system is placed in a vertical Hele–Shaw cell and is composed of two homogeneous aqueous solutions initially separated by a narrow transient zone. We have restricted our consideration to the initially stable density stratification that precludes the Rayleigh–Taylor instability. The main objective of the study is to elucidate the effect of a concentration-dependent diffusion coefficient, which has been commonly ignored by researchers. Assuming linear dependence of the diffusion coefficient of each solute and using Picard's iteration scheme, we have derived a closed-form analytical expression for the time-dependent density profile. This permits the stability boundary to be established for a two-layer system with respect to the double-diffusive instability by taking into account the effect of a concentration-dependent diffusion coefficient. The obtained analytical result has been substantiated by the results of direct numerical simulation. The experiments have shown that a successive increase in the concentrations of both solutes, with their ratio remaining unchanged, can lead to opposite results. In the case of a NaNO3-H2SO4 pair, the two-layer system, being stable at low concentrations, becomes unstable as the concentrations proportionally increase, giving rise to convective motion in the form of salt fingers. On the contrary, a two-layer system consisting of LiCl and NaNO3 solutions is stabilized with increasing concentrations of dissolved substances. A further increase in the concentrations of these substances causes mechanical equilibrium breaking and subsequent formation of the so-called diffusive-layer convection. The experimental results are in good agreement with the theoretical predictions.

Hysteresis in a two-liquid whirlpool

This experimental study reveals a curious phenomenon—hysteresis in a lab-scale two-liquid flow. The rotating bottom disk drives a toroidal circulation of water–glycerin solution (lower fluid) and sunflower oil (upper fluid) in a vertical cylindrical container. As the rotation speeds up, the solution–oil interface and the oil–air (free) surface deform rising near the sidewall and depressing near the axis as typical of whirlpools. We choose that the oil–solution volume ratio be small (having in mined oil-pollution applications) but not too small (for convenient observation). As the rotation speeds up, the oil separates from the sidewall and collects in the solution funnel. Next, the interface touches the bottom, and this is the point of no return. The centrifugal force pushes the near-bottom oil to the periphery and the buoyancy pushes oil upward. The Rayleigh–Taylor instability breaks the interface, and oil droplets disperse in the solution. If before this breakdown, the rotation starts to decrease, the oil separates from the bottom at the angular velocity ω being remarkably smaller than that for which the oil touches the bottom. Therefore, the hysteresis is a capillary-induced phenomenon.

Characterization of the stability and dynamics of a laser-produced plasma expanding across a strong magnetic field

Magnetized laser-produced plasmas are central to many studies in laboratory astrophysics, in inertial confinement fusion, and in industrial applications. Here, we present the results of large-scale three-dimensional magnetohydrodynamic simulations of the dynamics of a laser-produced plasma expanding into a transverse magnetic field with a strength of tens of teslas. The simulations show the plasma being confined by the strong magnetic field into a slender slab structured by the magnetized Rayleigh–Taylor instability that develops at the plasma–vacuum interface. We find that when the initial velocity of the plume is perturbed, the slab can develop kink-like motions that disrupt its propagation.

Rayleigh–Taylor instability in impact cratering experiments

When a liquid drop strikes a deep pool of a target liquid, an impact crater opens while the liquid of the drop decelerates and spreads on the surface of the crater. When the density of the drop is larger than the target liquid, we observe mushroom-shaped instabilities growing at the interface between the two liquids. We interpret this instability as a spherical Rayleigh–Taylor instability due to the deceleration of the interface, which exceeds the ambient gravity. We investigate experimentally the effect of the density contrast and the impact Froude number, which measures the importance of the impactor kinetic energy to gravitational energy, on the instability and the resulting mixing layer. Using backlighting and planar laser-induced fluorescence methods, we obtain the position of the air–liquid interface, an estimate of the instability wavelength, and the thickness of the mixing layer. We derive a model for the evolution of the crater radius from an energy conservation. We then show that the observed dynamics of the mixing layer results from a competition between the geometrical expansion of the crater, which tends to thin the layer, and entrainment related to the instability, which increases the layer thickness. The mixing caused by this instability has geophysical implications for the impacts that formed terrestrial planets. Extrapolating our scalings to planets, we estimate the mass of silicates that equilibrates with the metallic core of the impacting bodies.

Deceleration-stage Rayleigh–Taylor growth in a background magnetic field studied in cylindrical and Cartesian geometries

Experiments have identified the Rayleigh–Taylor (RT) instability as one of the greatest obstacles to achieving inertial confinement fusion. Consequently, mitigation strategies to reduce RT growth and fuel–ablator mixing in the hotspot during the deceleration phase of the implosion are of great interest. In this work, the effect of seed magnetic fields on deceleration-phase RT growth are studied in planar and cylindrical geometries under conditions relevant to the National Ignition Facility (NIF) and Omega experiments. The magnetohydrodynamic (MHD) and resistive-MHD capabilities of the FLASH code are used to model imploding cylinders and planar blast-wave-driven targets. Realistic target and laser parameters are presented that suggest the occurrence of morphological differences in late-time RT evolution in the cylindrical NIF case and a measurable difference in spike height of single-mode growth in the planar NIF case. The results of this study indicate the need for target designs to utilize an RT-unstable foam–foam interface in order to achieve sufficient magnetic field amplification to alter RT evolution. Benchmarked FLASH simulations are used to study these magnetic field effects in both resistive and ideal MHD.

Multiphysics analysis of thermal fluid in quasi-DC discharge in water

In the process of microsecond and millisecond pulsed discharge in water, a liquid low-density region will be formed by the effect of Joule heating. Then, thermal fluid is formed. Thermal fluid can influence the flow field and temperature distribution; and thus, it will affect the development of discharge. In this paper, the schlieren technology is used to observe the development of thermal fluid. The temperature field around the thermal fluid is calculated by the quantitative schlieren method. Finite element analysis is used to simulate the development of thermal fluid. Results show that the development of thermal fluid involves the coupling of electric fields, flow fields, and thermal fields. When there is an electric field, the movement of thermal fluid is mainly driven by the electric force, and it conforms to electrohydrodynamics. When the electric field disappears, the movement of thermal fluid is mainly driven by pressure. Due to Rayleigh–Taylor instability in the thermal fluid's head, the thermal fluid takes on a mushroom shape. The change in the thermal fluid's development direction on the side of the electrode leads to a short increase in the equivalent resistance of the gap. The study of thermal fluid is helpful to qualitatively understand quasi-DC discharge in water.

Research on ventilation and supercavitation mechanism of high-speed surface-piercing hydrofoil

Flow structures and hydrodynamic performance of high-speed surface-piercing hydrofoils were studied by numerical simulation, with an emphasis on the interaction mechanism between supercavitation and natural ventilation. Compared with the available experimental data, the numerical method could predict the cavitation and ventilation well. The numerical simulation results show that the flow over hydrofoil with blunt trailing edge is more conducive to separating. The semi-ogive hydrofoil was used to explore the influence of angles of attack on ventilation and cavitation. The ventilation rate increases with the increase in the angles of attack. At small attack angles (α = 0° and 2°), the regional ventilated flow is found in supercavitation. The vortex street structures and twin vortices closure mode are formed in the closure region of the supercavity. At moderate attack angles (α = 6° and 10°), the thickness of the undisturbed liquid sheet (δ) becomes thinner and the natural supercavitation transits to fully ventilated supercavitation through the cavitation-induced ventilation, but the ventilation position is different because of Taylor instability. The hydrodynamic coefficients remain relatively stable in natural supercavitation and the lift coefficient reduce to half of the original value when the supercavitation is fully ventilated, which are caused by the pressure changes on the suction and pressure surfaces.

Numerical analysis of shock interaction with a spherical bubble

Two-dimensional and three-dimensional computational fluid dynamics studies of a spherical bubble impacted by a supersonic shock wave (Mach 1.25) have been performed to fully understand the complex process involved in shock–bubble interaction (SBI). The unsteady Reynolds-averaged Navier–Stokes computational approach with a coupled level set and volume of fluid method has been employed in the present study. The predicted velocities of refracted wave, transmitted wave, upstream interface, downstream interface, jet, and vortex ring agree very well with the relevant available experimental data. The predicted non-dimensional bubble and vortex velocities are also in much better agreement with the experiment data than values computed from a simple model of shock-induced Rayleigh–Taylor instability (the Richtmyer–Meshkov instability). Comprehensive flow visualization has been presented and analyzed to elucidate the SBI process from the beginning of bubble compression (continuous reflection and refraction of the acoustic wave fronts as well as the location of the incident, refracted and transmitted waves at the bubble compression stage) up to the formation of vortex rings as well as the production and distribution of vorticity. Furthermore, it is demonstrated that turbulence is generated with some small flow structures formed and more intensive mixing, i.e., turbulent mixing of helium with air starts to develop at the later stage of SBI.

A spectral element-based phase field method for incompressible two-phase flows

In this paper, we propose a spectral element-based phase field method by solving the Navier–Stokes/Cahn–Hilliard equations for incompressible two-phase flows. The high-order differential nonlinear term of the Cahn–Hilliard equation poses a great challenge for obtaining numerical solutions, so the Newton–Raphson method is adopted to tackle this conundrum. Furthermore, we employ the time-stepping scheme to decouple the Navier–Stokes equations to favor the computations with large density and viscosity contrast, in terms of both stability and convergence efficiency. In addition, the continuum surface tension model is used to account for the tangential component of the interfacial force, and thus our numerical method has the ability to simulate thermocapillary flows. We present four examples to demonstrate the interface capture accuracy of the proposed method. The shape of the rotating Zalesak's disk is accurately preserved by the present method even for two periods, which implies less dissipation and higher accuracy at long time numerical simulation. It is also noted that the present method with fourth-order element can achieve similar accuracy with the consistent scheme by evaluating the convective fluxes with the fifth-order weighted essentially non-oscillatory scheme. Moreover, the proposed method appears to comply well with mass conservation. And the results of thermocapillary flow test show good agreement with theoretical prediction. Finally, the rising bubble and Rayleigh–Taylor instability are considered to verify the proposed method for complex changes in interfacial topology, as well as its performance under large density and viscosity contrasts and high Reynolds number conditions.

Evaporation of Three-Dimensional Wavy Liquid Film Entrained by Turbulent Gas Flow

A film cooling technique using a liquid film subjected to a hot gas flow in a turbulent condition is theoretically investigated. We successfully incorporate the two essential factors for the evaporating liquid film, droplet entrainment and three-dimensional film architecture, allowing for the physically consistent straightforward formulation. The validity of the present model is conveyed by reproducing combustion test results conducted for two types of flight-model bipropellant thrusters, in which the film length or dryout point shortens approximately inversely proportional to the combustion pressure. The underlying scenario to determine the film length is revealed. The gas flow initiates the originally smooth liquid film to be destabilized by Kelvin–Helmholtz instability in the axial direction and accelerates the wave crests leading to Rayleigh–Taylor instability in the transverse direction. Superposing the two types of waves produces three-dimensional cusps on the film as roots of entrained droplets. The convective heat transfer evaporating the liquid film is enhanced by the entrainment, reducing the net film flow rate, and by the cusp structure, enlarging the area of liquid/gas interface along the transverse direction in particular.

On inhibition of the Rayleigh–Taylor instability by a horizontal magnetic field in ideal MHD fluids with velocity damping

It is still open whether the inhibition phenomenon of the Rayleigh–Taylor (RT) instability by a horizontal magnetic field can be mathematically verified for a non-resistive magnetohydrodynamic (MHD) fluid in a two-dimensional (2D) horizontal slab domain, since it was roughly verified in the linearized case by Wang in [43]. In this paper, we show that this inhibition phenomenon can be rigorously verified in the (nonlinear) inhomogeneous, incompressible, inviscid case with velocity damping. More precisely, we show that there is a critical number mC, such that if the strength |m| of a horizontal magnetic field is bigger than mC, then the small perturbation solution around the magnetic RT equilibrium state is exponentially stable in time. Moreover, we also provide a nonlinear instability result for the case |m|∈(0,mC). Our instability result reveals that a horizontal magnetic field can not inhibit the RT instability, if it's strength is too small.

Numerical investigation on the coupled mechanisms of bubble breakup in a venturi-type bubble generator

ABSTRACT The bubble breakup mechanism in a venturi-type bubble generator is a hot research topic, and the bubble breakup mechanisms induced by the axial regional flow field characteristics has long been studied and debated. A coupled volume of fluid and large eddy simulation numerical simulation method was conducted within the OpenFOAM® framework to track the two-phase interfaces and transient turbulence characteristics of the flow field in a venturi-type bubble generator. A turbulence inlet database was established to ensure the reliability of the numerical solution and the economy of the calculation. The results indicated that the bubble breakup induced by the axial regional flow field characteristics of the divergent section can be divided into a steady-state disturbed breakup pattern and an unsteady-state disturbed breakup pattern macroscopically, the latter playing a dominant role in generating fine bubbles. Furthermore, a series of typical bubble breakup processes were captured via a Lagrangian approach that showed that interfacial instability played an important role at each stage of bubble transport: Kelvin–Helmholtz instability caused bubbles to detach from the gas film during the steady-state disturbed breakup pattern, and Rayleigh–Taylor instability induced the deformation of detached bubbles in the unsteady-state disturbed region. Additionally, viscous shear force strengthened the interfacial instability in the binary breakup process, and turbulent fluctuations and collisions contributed to the shattering of defective bubbles. Moreover, a shearing-off process tended to occur in regions with small vorticity fluctuations, therefore playing a small role in creating large clusters of bubbles.

Investigation into the formation of Ni splats plasma-sprayed on to mild steel and stainless steel substrates

The present study investigates the splat formation behaviour of Ni particles plasma sprayed onto AISI 1008 mild steel and 316 austenitic stainless steel substrates to draw a comparative analysis of splat formation on both surfaces. A range of analytical techniques were used to analyse the surface and cross-sectional characteristics of the splats formed on both substrates. Most of the splats observed on both of the substrates were halo type splats driven by Rayleigh–Taylor instabilities. A linear relationship was identified between the size of the central core of the splats and their outer ring of debris, which was distinct for each substrate. The diffusion profile, obtained through STEM-EDS analysis, revealed a higher degree of diffusion across the interface between splat and stainless steel substrate as compared to mild steel, suggesting a better bond efficiency for stainless steel. Cross-sectional observations, together with theoretical calculations, showed evidence of substrate melting as well as the presence of metallurgical bonds for both mild steel and stainless steel substrates.

Topology and cavitation number characteristics of the gaseous jet-induced tail cavity under co-flow

The tail cavity as induced by submerged gaseous jets on the bottom of axisymmetric vehicles is studied in a water tunnel over Froude numbers, which denote co-flow velocities, between 4.8 < Fr < 16.0, and the jet stagnation to ambient pressure ratio in a convergent–divergent nozzle between 1.7 < p0/p∞ < 14.5. The shadowgraph topology of the induced tail cavity falls into three consecutive categories on the regime map: intact cavity, partially broken cavity (PBC), and pulsating foamy cavity. Both the Fr and p0/p∞ are essential drivers for the topology and length of the tail cavity within the current scope. The length of PBC holds a logarithmic relationship to p0/p∞. The fluctuation intensity of the cavitation number is under heavy influence from Fr and p0/p∞ and is regarded as a direct and reliable measurement of jet/closure interaction intensity. Under high Fr, the Rayleigh–Taylor instability is dominant at the cavity surface, which leads to a significant amount of bubble shedding and adds to the total cavity gas leakage. From the perspective of the vehicle, the characteristics of its bottom pressure depend on the cavity regime. The characteristics of jet-induced tail cavity established in the presented study should be helpful for the design and control of submarine vehicles propelled by rockets and supersonic jets.

Multi-scale evolution of Kelvin–Helmholtz waves at the Earth's magnetopause during southward IMF periods

At the Earth's low-latitude magnetopause, the Kelvin–Helmholtz instability (KHI), driven by the velocity shear between the magnetosheath and magnetosphere, has been frequently observed during northward interplanetary magnetic field (IMF) periods. However, the signatures of the KHI have been much less frequently observed during southward IMF periods, and how the KHI develops under southward IMF has been less explored. Here, we performed a series of realistic 2D and 3D fully kinetic simulations of a KH wave event observed by the Magnetospheric Multiscale (MMS) mission at the dusk-flank magnetopause during southward IMF on September 23, 2017. The simulations demonstrate that the primary KHI bends the magnetopause current layer and excites the Rayleigh–Taylor instability (RTI), leading to penetration of high-density arms into the magnetospheric side. This arm penetration disturbs the structures of the vortex layer and produces intermittent and irregular variations of the surface waves which significantly reduces the observational probability of the periodic KH waves. The simulations further demonstrate that in the non-linear growth phase of the primary KHI, the lower-hybrid drift instability (LHDI) is induced near the edge of the primary vortices and contributes to an efficient plasma mixing across the magnetopause. The signatures of the large-scale surface waves by the KHI/RTI and the small-scale fluctuations by the LHDI are reasonably consistent with the MMS observations. These results indicate that the multi-scale evolution of the magnetopause KH waves and the resulting plasma transport and mixing as seen in the simulations may occur during southward IMF.

Terminal velocities and vortex dynamics of weakly compressible Rayleigh–Taylor Instability

The evolution of Rayleigh–Taylor instability (RTI) for weakly compressible fluids was numerically simulated using the smooth particle hydrodynamics method. It was found that the speed of spikes and bubbles in most cases will reach a stable value, which is called terminal speed. The calculated terminal speed of the bubble was found to be systematically higher than the theoretical model based on the potential flow hypothesis. This deviation could be modified by including the vortex effect on the terminal speed of the bubble. A significant correlation between the bubble speed and the vorticity in the bubble head was found during the whole evolution of RTI. The analysis of the vortex dynamics in the bubble head region during the terminal speed stage shows that there is a balance between the baroclinic production, viscous dissipation, and convective transport of the vorticity.

Growin: Modeling ionospheric instability growth rates

Seasonal and zonal climatologies of Rayleigh–Taylor growth rates under geomagnetically quiet conditions during solar minimum and solar moderate conditions as a function of local time and altitude are calculated using open source data and software. It is under the action of the Rayleigh–Taylor instability that plumes of depleted plasma, or plasma bubbles, are understood to develop in the bottomside of the equatorial ionosphere. The growin python module utilizes other Heliophysics python modules to collate and process vertical plasma drift to drive the SAMI2 is Another Model of the Ionosphere (SAMI2) model and subsequently calculate the flux tube integrated Rayleigh–Taylor growth rate. The process is repeated for two different types of drift inputs: the Fejer–Scherliess model and measured drifts from the Communication/Navigation Outage Forecasting System (C/NOFS). These growth rates are compared to bubble occurrence frequencies obtained from a dataset of bubbles detected by the C/NOFS satellite. There is an agreement between periods of strong positive instability growth and high frequencies of bubble occurrence in both low and moderate solar activity conditions when using C/NOFS drifts. Fejer–Scherliess drifts are only in agreement with bubble occurrence frequencies during moderate solar activity conditions. Bubble occurrence frequencies are often above 25%, even when growth rates in the bottomside F region are negative. The climatological nature of the growth rates discussed here begs further study into the day-to-day variability of the growth rate and its drivers.

Dripping instability of a two-dimensional liquid film under an inclined plate

It is known that the dripping of a liquid film on the underside of a plate can be suppressed by tilting the plate so as to cause a sufficiently strong flow. This paper uses two-dimensional numerical simulations in a closed-flow framework to study several aspects of this phenomenon. It is shown that, in quasi-equilibrium conditions, the onset of dripping is closely associated with the curvature of the wave crests approaching a well-defined maximum value. When dynamic effects become significant, this connection between curvature and dripping weakens, although the critical curvature remains a useful reference point as it is intimately related to the short length scales promoted by the Rayleigh–Taylor instability. In the absence of flow, when the film is on the underside of a horizontal plate, the concept of a limit curvature is relevant only for small liquid volumes close to a critical value. Otherwise, the drops that form have a smaller curvature and a large volume. The paper also illustrates the peculiarly strong dependence of the dripping transition on the initial conditions of the simulations. This feature prevents the development of phase maps dependent only on the governing parameters (Reynolds number, Bond number, etc.) similar to those available for film flow on the upper side of an inclined plate.

Propagation of premixed hydrogen-air flame initiated by a planar ignition in a closed tube

Numerical simulations were used to study the dynamics of premixed flames propagating after planar ignition in a closed tube filled with stoichiometric hydrogen-air mixture. The two-dimensional fully compressible reactive Navier–Stokes equations coupled to a calibrated chemical-diffusive model were solved using a high-order numerical method and adaptive mesh refinement. The results show that the flame evolves from an initially planar flame to a double-cusped tulip flame, subsequently to a multi-cusped tulip flame, and finally to a series of distorted tulip flames (DTFs). The DTF forms one after another until the end of combustion. The initial flame lips of the double-cusped tulip flame are produced due to the stretching effect of nonuniform flow caused by the wall friction. The multi-cusped tulip flame forms as secondary cusps are created on the leading flame tips near the sidewalls. The formation of DTFs here is thought to be closely connected to pressure waves generated in the flame propagation process. The first DTF is caused by the combined effects of the vortex motions and the Rayleigh–Taylor (RT) instability driven by pressure waves, while the subsequent DTFs form due to reverse flows and RT instability. Nevertheless, both the vortex motions and reverse flows are essentially induced by the interactions between pressure waves and flow fields. Furthermore, the numerical results were compared to that in the case with a semicircular ignition. It was found that although there are significant differences in the early flame acceleration and tulip formation stages between the two differently shaped ignitions, the dynamics of DTFs are substantially consistent.

Rayleigh–Taylor instability of classical diffusive density profiles for miscible fluids in porous media: a linear stability analysis

A Rayleigh–Taylor instability typically develops when a denser layer overlies a less dense one in the gravity field. In that case, the initial base state density profile is a step function for which linear stability analysis results are well known. We investigate here analytically the linear stability analysis of other classical diffusive density profiles for porous media flows. We find that, for a species A initially distributed in the upper half of the domain with an initial concentration profile of \((-X)^m\) for \(0<m<1\) where X is the vertical coordinate, and absent from the bottom half of the domain, for large times the eigenfunctions grow like \(\exp \left( \omega _0 T^{(m+1)/2} + \omega _1 \ln (T) \right) \) where \(\omega _0\) and \(\omega _1\) are constants and T is time. Thus, the growth rate defined by \((1/A) (\mathrm{{d}}A/\mathrm{{d}}T)\) decays like \(c_1 T^{(m-1)/2} +c_2 T^{(m-2)/3}\) whilst the maximum growing wavenumber scales with \(T^{(m-2)/6}\). These results are compared to the growth rates obtained using numerical linear stability analysis. Our analytical predictions provide a set of generalised results that pave the way to the analysis of Rayleigh–Taylor instabilities of nontrivial density profiles.