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

2018 ◽  
Vol 846 ◽  
pp. 916-943 ◽  
Author(s):  
Qingyun Zeng ◽  
Silvestre Roberto Gonzalez-Avila ◽  
Sophie Ten Voorde ◽  
Claus-Dieter Ohl
Keyword(s):  
Bubble Dynamics ◽  
Stokes Equations ◽  
Droplet Surface ◽  
Taylor Instability ◽  
Bubble Collapse ◽  
Fluid Viscosity ◽  
Analytic Model ◽  
Radial Acceleration ◽  
Rayleigh Taylor Instability ◽  
Good Agreement

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.

scholarly journals Phase-field model for the Rayleigh–Taylor instability of immiscible fluids

2009 ◽  
Vol 622 ◽  
pp. 115-134 ◽  
Author(s):  
ANTONIO CELANI ◽  
ANDREA MAZZINO ◽  
PAOLO MURATORE-GINANNESCHI ◽  
LARA VOZELLA
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Stokes Equations ◽  
Phase Field Model ◽  
Terminal Velocity ◽  
Immiscible Fluids ◽  
Taylor Instability ◽  
Upper And Lower Bounds ◽  
Weakly Nonlinear ◽  
Rayleigh Taylor Instability

The Rayleigh–Taylor instability of two immiscible fluids in the limit of small Atwood numbers is studied by means of a phase-field description. In this method, the sharp fluid interface is replaced by a thin, yet finite, transition layer where the interfacial forces vary smoothly. This is achieved by introducing an order parameter (the phase-field) continuously varying across the interfacial layers and uniform in the bulk region. The phase-field model obeys a Cahn–Hilliard equation and is two-way coupled to the standard Navier–Stokes equations. Starting from this system of equations we have first performed a linear analysis from which we have analytically rederived the known gravity–capillary dispersion relation in the limit of vanishing mixing energy density and capillary width. We have performed numerical simulations and identified a region of parameters in which the known properties of the linear phase (both stable and unstable) are reproduced in a very accurate way. This has been done both in the case of negligible viscosity and in the case of non-zero viscosity. In the latter situation, only upper and lower bounds for the perturbation growth rate are known. Finally, we have also investigated the weakly nonlinear stage of the perturbation evolution and identified a regime characterized by a constant terminal velocity of bubbles/spikes. The measured value of the terminal velocity is in agreement with available theoretical prediction. The phase-field approach thus appears to be a valuable technique for the dynamical description of the stages where hydrodynamic turbulence and wave-turbulence come into play.

NUMERICAL SIMULATION OF RAYLEIGH–TAYLOR INSTABILITY BASED ON AN IMPROVED PARTICLE LEVEL SET METHOD

2014 ◽  
Vol 11 (04) ◽  
pp. 1350094 ◽  
Author(s):  
HUI TIAN ◽  
GUOJUN LI ◽  
XIONGWEN ZHANG
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Density Ratio ◽  
Immiscible Fluids ◽  
Taylor Instability ◽  
Wide Range ◽  
Particle Level ◽  
Rayleigh Taylor Instability ◽  
Particle Level Set Method

An improved particle correction procedure for particle level set method is proposed and applied to the simulation of Rayleigh–Taylor instability (RTI) of the incompressible two-phase immiscible fluids. In the proposed method, an improved particle correction method is developed to deal with all the relative positions between escaped particles and cell corners, which can reduce the disturbance arising in the distance function correction process due to the non-normal direction movement of escaped particles. The improved method is validated through accurately capturing the moving interface of the Zalesak's disk. Furthermore, coupled with the projection method for solving the Navier–Stokes equations, the time-dependent evolution of the RTI interface over a wide range of Reynolds numbers, Atwood numbers and Weber numbers are numerically investigated. A good agreement between the present results and the existing analytical solutions is obtained and the accuracy of the proposed method is further verified. Moreover, the effects of control parameters including viscosity, density ratio, and surface tension coefficient on the evolution of RTI are analyzed in detail, and a critical Weber number for the development of RTI is found.

Compressibility effects in Rayleigh–Taylor instability-induced flows

2010 ◽  
Vol 368 (1916) ◽  
pp. 1681-1704 ◽  
Author(s):  
S. Gauthier ◽  
B. Le Creurer
Keyword(s):  
Compressible Flows ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Density Fluctuations ◽  
Taylor Instability ◽  
Turbulent Regime ◽  
Developed Turbulence ◽  
Perfect Fluids ◽  
Rayleigh Taylor Instability ◽  
Compressibility Effects

We present a tentative review of compressibility effects in Rayleigh–Taylor instability-induced flows. The linear, nonlinear and turbulent regimes are considered. We first make the classical distinction between the static compressibility or stratification, and the dynamic compressibility owing to the finite speed of sound. We then discuss the quasi-incompressible limits of the Navier–Stokes equations (i.e. the low-Mach number, anelastic and Boussinesq approximations). We also review some results about stratified compressible flows for which instability criteria have been derived rigorously. Two types of modes, convective and acoustic, are possible in these flows. Linear stability results for perfect fluids obtained from an analytical approach, as well as viscous fluid results obtained from numerical approaches, are also reviewed. In the turbulent regime, we introduce Chandrasekhar’s observation that the largest structures in the density fluctuations are determined by the initial conditions. The effects of compressibility obtained by numerical simulations in both the nonlinear and turbulent regimes are discussed. The modifications made to statistical models of fully developed turbulence in order to account for compressibility effects are also treated briefly. We also point out the analogy with turbulent compressible Kelvin–Helmholtz mixing layers and we suggest some lines for further investigations.

scholarly journals Variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells. Part 2. Nonlinear simulations

2013 ◽  
Vol 721 ◽  
pp. 295-323 ◽  
Author(s):  
M. O. John ◽  
R. M. Oliveira ◽  
F. H. C. Heussler ◽  
E. Meiburg
Keyword(s):  
Oil Recovery ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Viscous Fingering ◽  
Variable Density ◽  
Taylor Instability ◽  
Constant Density ◽  
Streamwise Vorticity ◽  
Miscible Displacements ◽  
Rayleigh Taylor Instability

AbstractDirect numerical simulations of the variable density and viscosity Navier–Stokes equations are employed, in order to explore three-dimensional effects within miscible displacements in horizontal Hele-Shaw cells. These simulations identify a number of mechanisms concerning the interaction of viscous fingering with a spanwise Rayleigh–Taylor instability. The dominant wavelength of the Rayleigh–Taylor instability along the upper, gravitationally unstable side of the interface generally is shorter than that of the fingering instability. This results in the formation of plumes of the more viscous resident fluid not only in between neighbouring viscous fingers, but also along the centre of fingers, thereby destroying their shoulders and splitting them longitudinally. The streamwise vorticity dipoles forming as a result of the spanwise Rayleigh–Taylor instability place viscous resident fluid in between regions of less viscous, injected fluid, thereby resulting in the formation of gapwise vorticity via the traditional, gap-averaged viscous fingering mechanism. This leads to a strong spatial correlation of both vorticity components. For stronger density contrasts, the streamwise vorticity component increases, while the gapwise component is reduced, thus indicating a transition from viscously dominated to gravitationally dominated displacements. Gap-averaged, time-dependent concentration profiles show that variable density displacement fronts propagate more slowly than their constant density counterparts. This indicates that the gravitational mixing results in a more complete expulsion of the resident fluid from the Hele-Shaw cell. This observation may be of interest in the context of enhanced oil recovery or carbon sequestration applications.

scholarly journals Transition stages of Rayleigh–Taylor instability between miscible fluids

2001 ◽  
Vol 443 ◽  
pp. 69-99 ◽  
Author(s):  
ANDREW W. COOK ◽  
PAUL E. DIMOTAKIS
Keyword(s):  
Growth Rates ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Density Ratio ◽  
Reynolds Numbers ◽  
Taylor Instability ◽  
Initial Growth ◽  
Mixing Zone ◽  
Miscible Fluids ◽  
Rayleigh Taylor Instability

Direct numerical simulations (DNS) are presented of three-dimensional, Rayleigh–Taylor instability (RTI) between two incompressible, miscible fluids, with a 3:1 density ratio. Periodic boundary conditions are imposed in the horizontal directions of a rectangular domain, with no-slip top and bottom walls. Solutions are obtained for the Navier–Stokes equations, augmented by a species transport-diffusion equation, with various initial perturbations. The DNS achieved outer-scale Reynolds numbers, based on mixing-zone height and its rate of growth, in excess of 3000. Initial growth is diffusive and independent of the initial perturbations. The onset of nonlinear growth is not predicted by available linear-stability theory. Following the diffusive-growth stage, growth rates are found to depend on the initial perturbations, up to the end of the simulations. Mixing is found to be even more sensitive to initial conditions than growth rates. Taylor microscales and Reynolds numbers are anisotropic throughout the simulations. Improved collapse of many statistics is achieved if the height of the mixing zone, rather than time, is used as the scaling or progress variable. Mixing has dynamical consequences for this flow, since it is driven by the action of the imposed acceleration field on local density differences.

Application of an All-Speed Implicit Finite-Volume Algorithm to Rayleigh–Taylor Instability

2015 ◽  
Vol 12 (03) ◽  
pp. 1550018 ◽  
Author(s):  
Ilyas Yilmaz ◽  
Firat Oguz Edis ◽  
Hasan Saygin
Keyword(s):  
Mach Number ◽  
Finite Volume ◽  
Turbulent Mixing ◽  
Stokes Equations ◽  
Baroclinic Instability ◽  
Three Dimensional ◽  
Taylor Instability ◽  
Fully Implicit ◽  
Energy Conserving ◽  
Rayleigh Taylor Instability

We present a three-dimensional Direct Numerical Simulation (DNS) study of Rayleigh–Taylor Instability (RTI) using an all-speed, fully implicit, nondissipative and discrete kinetic energy conserving algorithm. In order to perform this study, an in-house, fully parallel, finite-volume, DNS solver, iDNS, which solves the set of time-dependent, compressible Navier–Stokes equations with gravity was developed based on the present algorithm and the PETSc parallel library. It is shown that the algorithm is able to capture the correct physics of the baroclinic instability and turbulent mixing. Compressibility (i.e., high Mach number) has been found more effective on the development of the flow after the diffusive growth phase passed. An increase in bubble growth rate together with a decrease in turbulent mixing was also observed at Mach number 1.1.

Flow Induced Dynamics of a Pinned Droplet on the Surface of a Channel

2005 ◽  
Author(s):  
Amirreza Golpaygan ◽  
Nasser Ashgriz
Keyword(s):  
Surface Tension ◽  
Stokes Equations ◽  
Liquid Droplet ◽  
Equilibrium Shape ◽  
High Surface ◽  
Droplet Surface ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Droplet Deformation ◽  
Newtonian Liquids

Dynamic behavior of a droplet adhering to the surface of a channel has been modeled under the influence of surrounding fluid. The numerical solution is based on solving Navier-Stokes equations for Newtonian liquids. The study includes the effect of interfacial forces with constant surface tension, also effect of adhesion between the wall and droplet accounted by implementing contact angle at the wall. The Volume-Of-Fluid method is used to numerically determine the deformation of free surface. Droplet deformation and final shapes have been predicted. A reduction in the surface tension allows the droplet to deform much easier. However, an increase in the fluid viscosity, although increases the shear force on the droplet, may not result in the deformation at high surface tension. It is shown that deformation of droplet significantly influences structure of channel flow. Effects of liquid droplet and channel fluid properties, namely density and viscosity, inlet velocity, surface tension and channel geometry on dynamics of the problem have been studied. Two different outcomes have been considered: the first one droplet with equilibrium shape and the other one when breakup of the droplet occurs. The border line between the disintegration region and equilibrium region is determined for different droplet surface tensions.

Numerical Solution on Spherical Vacuum Bubble Collapse Using MPS Method

2009 ◽  
Author(s):  
Wenxi Tian ◽  
Suizheng Qiu ◽  
Guanghui Su ◽  
Yoshiaki Oka
Keyword(s):  
Bubble Dynamics ◽  
Bubble Diameter ◽  
Liquid Pool ◽  
Bubble Collapse ◽  
Bubble Liquid ◽  
Mps Method ◽  
Noncondensable Gas ◽  
Cavitation Phenomenon ◽  
Rebound Phenomenon ◽  
Good Agreement

In this study, the vacuum bubble collapse in liquid pool has been simulated using MPS code. The liquid is described using moving particles and the bubble-liquid interface was set to be vacuum pressure boundary without interfacial heat mass transfer. The motion and location of interfacial particles can be competent in configurating the topological shape of vacuum bubble. The time dependent bubble diameter, interfacial velocity and bubble collapse time were obtained under wide parametric range. The comparison with Rayleigh’s prediction showed a good agreement which validates the applicability and accuracy on MPS method in solving present momentum problems. The potential void-induced water hammer pressure pulse was also evaluated which is instructive for cavitaion erosion study. The bubble collapse with noncondensable gas has also been simulated and the rebound phenomenon was successfully captured which is similar with vapor-filled cavitation phenomenon. The present study exhibits some fundamental characteristics of vacuum bubble hydrodynamics and it is also expected to be instructive for further applications of MPS method to in complicated bubble dynamics.

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