Large Weber Numbers Research Articles

Numerical simulation of drop impingement and bouncing on a heated hydrophobic surface

The heat transfer of a single water droplet impacting on a heated hydrophobic surface is investigated numerically using a phase field method. The numerical results of the axisymmetric computations show good agreement with the dynamic spreading and subsequent bouncing of the drop observed in an experiment from literature. The influence of Weber number on heat transfer is studied by varying the drop impact velocity in the simulations. For large Weber numbers, good agreement with experimental values of the cooling effectiveness is obtained whereas for low Weber numbers no consistent trend can be identified in the simulations.

Implementation of a probabilistic surface density volume of fluid approach for spray atomisation

Eulerian Stochastic methods in Large Eddy Simulation context have been successfully used in reactive flows. They have been recently applied to spray atomisation, using surface and liquid volume as independent variables. These methods involve the solutions of Stochastic Partial Differential Equations, which are continuous in space and discontinuous in time. The implementation of these equations into a conventional finite volume solver can be challenging due to both the numerical diffusion of the scalar fields and the numerical integration of the stochastic source terms. This work presents the implementation and validation of the Eulerian Stochastic Fields surface/liquid volume atomisation method within the OpenFOAM framework. The paper discusses how algebraic compression methods can be used for the stochastic fields to minimise the numerical diffusion and the effects of the stochastic source term implementation. The model targets a-priori spray atomisation at large Weber numbers, although the implementation recovers the correct solution at low Weber model and captures correctly the capillary effects on liquid–gas interfaces. A turbulent liquid jet is used for validation and discussion of the accuracy and relative cost of the model implementation. The approach is then applied to a multi-hole gasoline direct injector where the agreement with experimental data showcases the capabilities of the solver for realistic injectors and atomisation regimes.

Pattern formation of quantum Kelvin-Helmholtz instability in binary superfluids

We study theoretically nonlinear dynamics induced by shear-flow instability in segregated two-component Bose-Einstein condensates in terms of the Weber number, defined by extending the past theory on the Kelvin-Helmholtz instability in classical fluids. Numerical simulations of the Gross-Pitaevskii equations demonstrate that dynamics of pattern formation is well characterized by the Weber number $We$, clarifying the microscopic aspects unique to the quantum fluid system. For $We \lesssim 1$, the Kelvin-Helmholtz instability induces flutter-finger patterns of the interface and quantized vortices are generated at the tip of the fingers. The associated nonlinear dynamics exhibits a universal behavior with respect to $We$. When $We \gtrsim 1$ in which the interface thickness is larger than the wavelength of the interface mode, the nonlinear dynamics is effectively initiated by the counter-superflow instability. In a strongly segregated regime and a large relative velocity, the instability causes transient zipper pattern formation instead of generating vortices due to the lack of enough circulation to form a quantized vortex per a finger. While, in a weakly segregating regime and a small relative velocity, the instability leads to sealskin pattern in the overlapping region, in which the frictional relaxation of the superflow cannot be explained only by the homogeneous counter-superflow instability. We discuss the details of the linear and nonlinear characteristics of this dynamical crossover from small to large Weber numbers, where microscopic properties of the interface become important for the large Weber number.

First order perturbation approach for the free surface flow over a step with large Weber number

The problem of two-dimensional free surface flow of inviscid and incompressible fluid over a step is considered. The flow is assumed to be as steady and irrotational, the effect of the surface tension is considered, but the gravity force is neglected. This problem is characterized by the nonlinear condition given by Bernoulli's equation on the unknown free surface, which can be considered as part of the solution. The main purpose of this work is to give an approximate solution of this problem, by using the Hilbert transformation and the perturbation technique; the results are calculated for a large values of the Weber number and small inclination angle of the step values. These results demonstrate that the used method is easily implemented, and provides approximate solutions to these kinds of problems.

Numerical simulation of two-phase flow and droplet breakage of glycerin-water mixture and kerosene in the cyclone reactor

• The static pressure distribution conformed with the rules of the eddy field. • The vortex motion near the side wall was intense. • The droplet deformed, stretched, and broken. • The small surface tension and large Weber number promoted droplet breakage. A liquid-liquid cyclone reactor (LLCR) was designed to achieve mixing-reaction-separation integration during isobutane alkylation catalyzed by ionic liquids. However, studies of the droplets deformation and breakage in the kind of reactors are lacking. In this work, the research studied the velocity distribution, pressure field, and turbulent field to investigate the flow pattern and the main energy loss location in the LLCR through the computational fluid dynamics (CFD) method. The simulation results were verified by experiemnts to prove the correctness of the model. Then the deformation and breakage process of droplets, and the influencing factors of droplets breakage were studied by remodeling which was based on the tangential velocity distribution result of the three dimensional model. The three dimensional simulation results clearly showed that the pressure of the LLCR was mainly concentrated in the cone section and fluid turbulent motion was the most intense near the lateral wall. The reconstruct the results of the two dimensional model clearly showed that the deformation and breakage location of droplets were mainly occurred in the velocity boundary layer, while it was difficult to break in the mainstream region. In addition, low surface tension and high Weber number had a positive effect on droplet breakage.

Effects of surface subcooling on the spreading dynamics of an impact water droplet

Spontaneous spreading of a liquid droplet upon a cold solid surface is ubiquitous in nature as well as critical to many industrial technologies, while the mechanism of which still remains elusive. The role of surface subcooling in a water droplet spreading behavior upon impacting on a smooth silicon surface has been experimentally investigated. Under the subcooling condition of the substrate, in the low Weber number region, the non-dimensional maximum spreading diameter decreases with the surface subcooling due to a larger viscosity dissipation and higher surface tension. However, in the case of a high Weber number, the maximum spreading factor first descends and then increases with the increasing surface subcooling. This non-monotonic tendency is attributed to the competition between the increased maximum fingering length and the reduced maximum interior spreading diameter with an increase of the surface subcooling. A sufficiently large Weber number is the prerequisite for forming fingering patterns, and a high subcooling reinforces them due to the enhanced deceleration caused by a larger surface tension and viscosity. The time at maximum spreading barely changes with the impact velocity and slightly decreases with the surface subcooling depending on the droplet size. An improved correlation of the time at maximum spreading as a function of the maximum spreading factor, droplet size, impact velocity, and surface subcooling is proposed.

Leidenfrost drop impact on inclined superheated substrates

In real applications, drops always impact on solid walls with various inclinations. For the oblique impact of a Leidenfrost drop, which has a vapor layer under its bottom surface to prevent its direct contact with the superheated substrate, the drop can nearly frictionlessly slide along the substrate accompanied by spreading and retracting. To individually study these processes, we experimentally observe the impact of ethanol drops on superheated inclined substrates using high-speed imaging from two different views synchronously. We first study the dynamic Leidenfrost temperature, which mainly depends on the normal Weber number We⊥. Then, the substrate temperature is set to be high enough to study the Leidenfrost drop behavior. During the spreading process, drops are always kept uniform, and the maximum spreading factor Dm/D0 follows a power-law dependence on the large normal Weber number We⊥ as Dm/D0=We⊥/12+2 for We⊥ ≥ 30. During the retracting process, drops with low impact velocities become non-uniform due to the gravity effect. For the sliding process, the residence time of all studied drops is nearly a constant, which is not affected by the inclination and the We number. The frictionless vapor layer resulting in the dimensionless sliding distance L/D0 follows a power-law dependence on the parallel Weber number We|| as L/D0∝We||1/2. Without direct contact with the substrate, the behaviors of drops can be separately determined by We⊥ and We||. When the impact velocity is too high, the drop fragments into many tiny droplets, which is called the splashing phenomenon. The critical splashing criterion is found to be We⊥*≃ 120 or K⊥=We⊥Re⊥1/2≃ 5300 in the current parameter regime.

Many-body dissipative particle dynamics simulation of Newtonian and non-Newtonian nanodroplets spreading upon flat and textured substrates

To deposit droplets on substrates efficiently is critical for many technological and industrial applications, which requires a systematic understanding of the droplet spreading process. In the paper, mesoscopic modeling of viscous nanodroplets spreading on different solid surfaces has been conducted by many-body dissipative particle dynamics. The influence of fluid viscosity has been particularly analyzed by changing the interaction parameters and the maximum droplet spreading diameter has been obtained. The dimensionless maximum spreading diameter is correlated to the Reynolds numbers (Re) and Weber numbers (We) as βmax = 0.7Re0.1445We0.066. With the droplets partially attached by polymer chains to exhibit a shear-thinning non-Newtonian property, we demonstrate that the maximum spreading diameters are extremely different under a small initial kinetic energy, and gradually become consistent at a larger Weber number. Investigation of the spreading process on the intricate surfaces decorated by regular pillared structures shows a special expansion effect to improve the intrinsic wetting characteristic of the substrates, which is strongly controlled by the surface fraction of the pillared structures. Moreover, it is found that the fluid viscosity can profoundly affect the rebounding behavior of the droplet.

Numerical investigation of shear-flow free-surface turbulence and air entrainment at large Froude and Weber numbers

We investigate two-phase free-surface turbulence (FST) associated with an underlying shear flow under the condition of strong turbulence (SFST) characterized by large Froude ($Fr$) and Weber ($We$) numbers. We perform direct numerical simulations of three-dimensional viscous flows with air and water phases. In contrast to weak FST (WFST) with small free-surface distortions and anisotropic underlying turbulence with distinct inner/outer surface layers, we find SFST to be characterized by large surface deformation and breaking accompanied by substantial air entrainment. The interface inner/outer surface layers disappear under SFST, resulting in nearly isotropic turbulence with ${\sim}k^{-5/3}$ scaling of turbulence kinetic energy near the interface (where $k$ is wavenumber). The SFST air entrainment is observed to occur over a range of scales following a power law of slope $-10/3$. We derive this using a simple energy argument. The bubble size spectrum in the volume follows this power law (and slope) initially, but deviates from this in time due to a combination of ongoing broad-scale entrainment and bubble fragmentation by turbulence. For varying $Fr$ and $We$, we find that air entrainment is suppressed below critical values $Fr_{cr}$ and $We_{cr}$. When $Fr^{2}>Fr_{cr}^{2}$ and $We>We_{cr}$, the entrainment rate scales as $Fr^{2}$ when gravity dominates surface tension in the bubble formation process, while the entrainment rate scales linearly with $We$ when surface tension dominates.

Effect of heat and mass transfer on the instability of an annular liquid sheet

A temporal linear instability analysis has been conducted to investigate the effect of heat and mass transfer on the instability of an annular liquid sheet axially moving in the gas medium. The dispersion relation is obtained and solved numerically. Energy budget is calculated to provide physical insights of various instability driving mechanisms. The results show that heat and mass transfer promotes the wave growth rate mainly at small wave numbers. In contrast to the case without heat and mass transfer, the wave growth rate with strong heat and mass transfer peaks at zero wave number. Liquid viscosity is found to have a minimal stabilizing effect on the sheet instability. Regardless of the heat and mass transfer, increasing liquid Weber number suppresses the sheet instability below a crossover point of wave number at 1.15, and promotes the sheet instability above the crossover point. In the presence of strong heat and mass transfer, increasing gas-to-liquid density ratio reduces the wave growth rate at small wave numbers below 0.28, and beyond which increases the wave growth rate. Reducing sheet thickness promotes the sheet instability for all wave numbers. The energy budgets show that the inner gas disturbance is most responsible for promoting the wave growth rate at large liquid Weber numbers; and the inner interface dominates the outer one in destabilizing the annular liquid sheet.

Linear stability of confined swirling annular liquid layers in the presence of gas velocity oscillations with heat and mass transfer

The linear stability of confined swirling annular liquid layers is studied in the presence of gas velocity oscillations with heat and mass transfer. The dispersion relation is obtained and is solved using Floquet theory. Results show that parametric instability regions appear when oscillations are considered and the oscillations play a destabilizing role. The forcing frequency controls the location of parametric instability regions and plays a slight destabilizing role. Heat and mass transfer has a stabilizing effect at small Weber numbers but a destabilizing effect at large Weber numbers. In addition, heat and mass transfer promotes the dispersion effect, vanishing the gap between the parametric and Kelvin-Helmholtz (K-H) instability regions. The effect of mode order is complex. The order n=0 is the most unstable. Rotating restrains the instability. The effect of confinement is complex. Confinement plays a stabilizing role at all the range of Weber numbers when ignoring heat and mass transfer. However, confinement promotes the instability at small Weber numbers but suppresses it at large Weber numbers when considering heat and mass transfer.

Effects of Asymmetric Gas Distribution on the Instability of a Plane Power-Law Liquid Jet

As a kind of non-Newtonian fluid with special rheological features, the study of the breakup of power-law liquid jets has drawn more interest due to its extensive engineering applications. This paper investigated the effect of gas media confinement and asymmetry on the instability of power-law plane jets by linear instability analysis. The gas asymmetric conditions mainly result from unequal gas media thickness and aerodynamic forces on both sides of a liquid jet. The results show a limited gas space will strengthen the interaction between gas and liquid and destabilize the power-law liquid jet. Power-law fluid is easier to disintegrate into droplets in asymmetric gas medium than that in the symmetric case. The aerodynamic asymmetry destabilizes para-sinuous mode, whereas stabilizes para-varicose mode. For a large Weber number, the aerodynamic asymmetry plays a more significant role on jet instability compared with boundary asymmetry. The para-sinuous mode is always responsible for the jet breakup in the asymmetric gas media. With a larger gas density or higher liquid velocity, the aerodynamic asymmetry could dramatically promote liquid disintegration. Finally, the influence of two asymmetry distributions on the unstable range was analyzed and the critical curves were obtained to distinguish unstable regimes and stable regimes.

Direct numerical simulation of droplet breakup in homogeneous isotropic turbulence: The effect of the Weber number

We report the direct numerical simulation of droplet breakup in forced homogeneous isotropic turbulence with a mass-conserving level set method. In particular, the effect of the Weber number on the interface morphology of droplet breakup and the interaction between vortical structures and the interface are addressed. The densities and viscosities are the same for both phases in the present simulations. It is found that with increasing the Weber number, the initially large-scale spherical droplet tends to break down into dispersed small droplets. Compared with the flow local topology in the carrier-phase turbulence, the local topology of the bi-axial strain is suppressed at the statistical stationary state inside the droplet. During the droplet breakup process, the vorticity tends to be tangent to the large-scale interface at the early stage, and subsequently the alignment is mitigated for large Weber numbers, because the small droplets with relatively strong surface tension and small local Weber numbers can resist the deformation induced by local turbulent straining motion in the statistically stationary state.

Experimental analysis of the evaporation regimes of an axially grooved heat pipe at small tilt angles

Using a high-speed digital microscope, visualization experiments of the vapor-liquid two-phase flow and heat transfer in an axially grooved heat pipe are conducted to investigate the evaporation regimes that occur at small tilt angles. The effects of the heat load and tilt angle on these evaporation regimes are analyzed. The evaporation regimes are further quantitatively characterized with a regime diagram developed based on the Bond number and Weber number. The results indicate that, unlike in a horizontal position, the evaporation regime of a grooved heat pipe with a small tilt angle can include corner-film evaporation induced by the combination of gravity and capillary force in addition to pool-surface evaporation and fin-film evaporation. Corner-film evaporation is the characteristic evaporation regime of an axially grooved heat pipe with a small tilt angle, and it exhibits random oscillatory motion of the vapor-liquid interface. Pool-surface evaporation is observed at small Weber numbers, corner-film evaporation occurs at large Weber numbers when the Bond number is approximately greater than 0.003, and fin-film evaporation occurs at medium Weber numbers.

Towards enhanced bubble detachment within a thin liquid film by electrowetting with voltage modulation

This paper extends our previous bubble actuation study using a simple constant voltage by including the oscillating effect created by voltage modulation. Rather than normal contact angle change due to the constant voltage, voltage modulation exhibits preferable characteristics of periodical contact angle variation which is proved to be helpful for bubble detachment within a thin liquid film. Different waveform and frequency modulations were evaluated to acquire an optimal signal input for the purpose of inducing the maximum oscillation effects with which bubble detachment in a thin liquid film can be enhanced. The thick liquid film results show that the square waveform coupled with a frequency of 1 Hz allows for maximum contact angle change scope and induces the largest vertical bubble velocity. With the optimal signal, the tests of bubble detachment within a thin liquid film were conducted and characterized. Three different bubble detachment modes were observed and classified as follows: direct detachment, delayed detachment, and non-detachment. The actuation mechanism of the electrowetting effect on the bubble behavior within a thin liquid film was analyzed. The dimensionless parameter, Weber number, was used to characterize the bubble deformation. A high-speed frame analysis shows that a Weber number greater than 0.5 × 10−3 is necessary to break the energy barrier of the ultra-thin film and achieve the direct detachment mode. It is expected that a proper electrowetting actuation mechanism causing a relatively large Weber number can effectively enhance the bubble detachment within a thin liquid film which will provide promising applications to improve two-phase heat transfer.

Drop impact onto a thin film: Miscibility effect

In this work a systematic experimental study was performed to understand the process of liquid drop impact onto a thin film made of a different liquid from drop. The drop and film liquids can be miscible or immiscible. Three general outcomes of deposition, crown formation without splashing, and splashing, were observed in the advancing phase of the drop impact onto a solid surface covered by either a miscible or an immiscible thin film. However, for a miscible film, a larger Weber number and film thickness are needed for the formation of a crown and splashing comparing with immiscible cases. The advancing phase of drop impact onto a thin immiscible film with a large viscosity is similar to that of drop impact onto a dry surface; for a miscible film viscous film, the behavior is far from that of a dry surface. The behavior of liquid lamella in the receding phase of drop impact onto a thin miscible film is reported for the first time. The results show that immiscibility is not a necessary condition for the existence of a receding phase. The existence of a receding phase is highly dependent on the interfacial tension between the drop and the film. The miscibility can significantly affect the receding morphology as it will cause mixing of the two liquids.

Experimental study on thermo-hydrodynamic behaviors in miniaturized two-phase thermosyphons

In this paper, the thermo-hydrodynamic behaviors in miniaturized two-phase thermosyphons are experimentally investigated by a visualization system. The effects of heat load and channel dimension on the thermo-hydrodynamic behaviors are examined and further quantitatively recognized by a state diagram depending on the Weber number and Bond number. In addition, the vapor–liquid two-phase flow, heat transfer regimes and thermal performances are analyzed and discussed. The results indicate that, differing from the conventional two-phase thermosyphon, the state of working fluid in a miniaturized two-phase thermosyphon is no longer only in a fashion of pool and annular-flow states, but also in a fashion of oscillation state. The oscillation state is the characteristic two-phase flow regime of a miniaturized two-phase thermosyphon and possesses the feature of random formation and oscillatory motion of liquid plug in minichannels. The pool state occurs at small Weber number, the annular-flow state is observed at large Weber number, and the oscillation state takes place at medium Weber number when Bond number is approximately smaller than 0.7. The thermal performance of oscillation state is better than that of pool state but is less powerful than that of annular-flow state. The heat transfer regimes are the film evaporation and condensation combined with thermal conduction in the pool state, the forced evaporation and condensation in the oscillation state, and the film evaporation and condensation in the annular-flow state, respectively.

Simulation of binary droplet collisions with the entropic lattice Boltzmann method

The recently introduced entropic lattice Boltzmann method (ELBM) for multiphase flows is extended here to simulation of droplet collisions. Thermodynamically consistent, non-linearly stable ELBM together with a novel polynomial equation of state is proposed for simulation large Weber and Reynolds number collisions of two droplets. Extensive numerical investigations show that ELBM is capable of accurately capturing the dynamics and complexity of droplet collision. Different types of the collision outcomes such as coalescence, reflexive separation, and stretching separation are identified. Partition of the parameter plane is compared to the experiments and excellent agreement is observed. Moreover, the evolution of the shape of a stable lamella film is quantitatively compared with experimental results. The end pinching and the capillary-wave instability are shown to be the main mechanisms behind formation of satellite droplets for near head-on and off-center collisions with high impact parameter, respectively. It is shown that the number of satellite drops increases with increasing Weber number, as predicted by experiments. Also, it is demonstrated that the rotational motion due to angular momentum and elongation of the merged droplet play essential roles in formation of satellite droplets in off-center collisions with an intermediate impact parameter.

Electrokinetic instability of liquid micro- and nanofilms with a mobile charge

The instability of ultra-thin films of an electrolyte bordering a dielectric gas in an external tangential electric field is scrutinized. The solid wall is assumed to be either a conducting or charged dielectric surface. The problem has a steady one-dimensional solution. The theoretical results for a plug-like velocity profile are successfully compared with available experimental data. The linear stability of the steady-state flow is investigated analytically and numerically. Asymptotic long-wave expansion has a triple-zero singularity for a dielectric wall and a quadruple-zero singularity for a conducting wall, and four (for a conducting wall) or three (for a charged dielectric wall) different eigenfunctions. For infinitely small wave numbers, these eigenfunctions have a clear physical meaning: perturbations of the film thickness, of the surface charge, of the bulk conductivity, and of the bulk charge. The numerical analysis provides an important result: the appearance of a strong short-wave instability. At increasing Debye numbers, the short-wave instability region becomes isolated and eventually disappears. For infinitely large Weber numbers, the long-wave instability disappears, while the short-wave instability persists. The linear stability analysis is complemented by a nonlinear direct numerical simulation. The perturbations evolve into coherent structures; for a relatively small external electric field, these are large-amplitude surface solitary pulses, while for a sufficiently strong electric field, these are short-wave inner coherent structures, which do not disturb the surface.

Experiments on the fragmentation of a buoyant liquid volume in another liquid

AbstractWe present experiments on the instability and fragmentation of volumes of heavier liquids released into lighter immiscible liquids. We focus on the regime defined by small Ohnesorge numbers, density ratios of the order of one, and variable Weber numbers. The observed stages in the fragmentation process include deformation of the released fluid by either Rayleigh–Taylor instability (RTI) or vortex ring roll-up and destabilization, formation of filamentary structures, capillary instability, and drop formation. At low and intermediate Weber numbers, a wide variety of fragmentation regimes is identified. Those regimes depend on early deformations, which mainly result from a competition between the growth of RTI and the roll-up of a vortex ring. At high Weber numbers, turbulent vortex ring formation is observed. We have adapted the standard theory of turbulent entrainment to buoyant vortex rings with initial momentum. We find consistency between this theory and our experiments, indicating that the concept of turbulent entrainment is valid for non-dispersed immiscible fluids at large Weber and Reynolds numbers.