Separation Criteria for Off-Axis Binary Drop Collisions

Off-axis collisions of two equal size droplets are investigated numerically. Various governing processes in such collisions are discussed. Several commonly used theoretical models that predict the onset of separation after collision are evaluated based on the processes observed numerically. A separation criterion based on droplet deformation is found. The numerical results are used to assess the validity of some commonly used phenomenological models for drop separation after collision. Also, a critical Weber number for the droplet separation after grazing collision is reported. The effect of Reynolds number is investigated and regions of permanent coalescence and separation are plotted in a Weber-Reynolds number plane for high impact parameter collisions.

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The Splitting of Drops and Bubbles by Turbulent Fluid Flow

Journal of Fluids Engineering ◽

10.1115/1.3446958 ◽

1973 ◽

Vol 95 (1) ◽

pp. 53-60 ◽

Cited By ~ 136

Author(s):

M. Sevik ◽

S. H. Park

Keyword(s):

Reynolds Number ◽

Weber Number ◽

High Reynolds Number ◽

Air Bubbles ◽

Immiscible Liquids ◽

Turbulent Fluid Flow ◽

Liquid Drops ◽

A Value ◽

Critical Weber Number ◽

High Reynolds

The work of Hinze concerned with the splitting of drops and bubbles by turbulent flow has been extended. In particular, the breakup of air bubbles in the adjustment region of a high Reynolds number water jet has been observed. A critical Weber number of 1.3 was obtained from these experiments, whereas Hinze calculated a value of 0.59 based on tests involving the dispersion of various immiscible liquids. It was found that both Weber numbers could be predicted theoretically by considering the resonances of the liquid drops or gas bubbles.

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Numerical Investigation on Head-On Collisions of Binary Micro-Droplets by an Improved Multiphase Lattice Boltzmann Flux Solver

Volume 1: Micro/Nanofluidics and Lab-on-a-Chip; Nanofluids; Micro/Nanoscale Interfacial Transport Phenomena; Micro/Nanoscale Boiling and Condensation Heat Transfer; Micro/Nanoscale Thermal Radiation; Micro/Nanoscale Energy Devices and Systems ◽

10.1115/mnhmt2016-6533 ◽

2016 ◽

Author(s):

Y. Wang ◽

C. Shu

Keyword(s):

Reynolds Number ◽

Lattice Boltzmann ◽

Weber Number ◽

Density Ratio ◽

Distribution Functions ◽

Time Step ◽

Large Density ◽

Wide Range ◽

Large Density Ratio ◽

Critical Weber Number

Head-on collisions of binary micro-droplets are of great interest in both academic research and engineering applications. Numerical simulation of this problem is challenging due to complex interfacial changes and large density ratio between different fluids. In this work, the recently proposed lattice Boltzmann flux solver (LBFS) is applied to study this problem. The LBFS is a finite volume method for the direct update of macroscopic flow variables at cell centers. The fluxes of the LBFS are reconstructed at each cell interface through lattice moments of density distribution functions (DDFs). As compared with conventional multiphase lattice Boltzmann method, the LBFS can be easily applied to study complex multiphase flows with large density ratio. In addition, external forces can be implemented more conveniently and the tie-up between the time step and mesh spacing is also removed. Moreover, it can deal with complex boundary conditions directly as those do in the conventional Navier-Stokes solvers. At first, the reliability of the LBFS is validated by simulating a micro-droplet impacting on a dry surface at density ratio 832 (air to water). The obtained result agrees well with experimental measurement. After that, numerical simulations of head-on collisions of two micro droplets are carried out to examine different collisional behaviors in a wide range of Reynolds numbers and Weber numbers of 100 ≤ Re ≤ 2000 and 10 ≤ We ≤ 500. A phase diagram parameterized by these two control parameters is obtained to classify the outcomes of these collisions. It is shown that, at low Reynolds number (Re=100), two droplets will be coalescent into a bigger one for all considered Weber numbers. With the increase of the Reynolds number, separation of the collision into multiple droplets appears and the critical Weber number for separation is decreased. When the Reynolds number is sufficiently high, the critical Weber number for separation is between 20 and 25.

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Direct numerical simulation of the droplet deformation in the external flow at various Reynolds and Weber numbers

10.5194/egusphere-egu2020-7775 ◽

2020 ◽

Author(s):

Anna Zotova ◽

Yuliya Troitskaya ◽

Daniil Sergeev ◽

Alexander Kandaurov

Keyword(s):

Experimental Data ◽

Numerical Simulation ◽

Reynolds Number ◽

Direct Numerical Simulation ◽

Software Package ◽

Weber Number ◽

Deformation Mode ◽

Stationary Flow ◽

External Flow ◽

Droplet Deformation

A lot of experimental works is devoted to studying behaviour of a droplet in the flow of the external medium. It is shown in [1] that mode of the deformation of droplet in the stationary flow is affected by the Weber number and the Reynolds number. The authors distinguish two types of the droplet deformation in the external flow: the dome-shaped deformation and the bowl-shaped one.Using the Basilisk software package, direct numerical simulation of the process of deformation of liquid drop in the gas stream was carried out. We examined the problem of the following geometry: a drop of liquid with diameter of 5 mm was placed in the gas stream at the speed of 30 m/s. The density of liquid and gas correspond to the density of water and air, the viscosity of liquid is equal to the viscosity of water. The viscosity of gas and the surface tension at the interface between liquid and gas are determined by the set values of the Reynolds (50 - 3000) and the Weber (2 - 30) numbers. Two main modes of the drop deformation were observed: the dome-shaped deformation and the bowl-shaped one, there is a transitional deformation mode between them. The map of deformation modes is constructed for comparison with the experimental data available in the literature. It was found that the dependence of the Weber number corresponding to the transition from one deformation mode to another on the Reynolds number is well described by the power law proposed in the literature.&#160;This work was supported by the RFBR projects 19-05-00249, 18-35-20068, 18-55-50005, 18-05-60299, 20-05-00322 (familiarization with the Basilisk software package) and the Grant of the President No. MK-3184.2019.5, work on comparison with experimental data was supported by the RSF project No. 18-77-00074, carrying out numerical experiment was supported by the RSF project No. 19-17-00209, A.N. Zotova is additionally supported by the Ministry of Education and Science of the Russian Federation (Government Task No. 0030-2019-0020). The authors are grateful to the FCEIA employee: UNR - CONICET (Rosario, Rep. Argentina) Dr. Ing. C&#233;sar Pairetti.[1] Hsiang, L.-P., Faeth, G. M., Int. J. Multiphase Flow 21(4), 545-560 (1995).

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Penetration Dynamics of Solid Particles into Liquids High-Speed Experimental Results and Modelling

Materials Science Forum ◽

10.4028/www.scientific.net/msf.473-474.429 ◽

2005 ◽

Vol 473-474 ◽

pp. 429-434 ◽

Cited By ~ 9

Author(s):

Olga Verezub ◽

György Kaptay ◽

Tomiharu Matsushita ◽

Kusuhiro Mukai

Keyword(s):

Contact Angle ◽

Particle Size ◽

Aqueous Solutions ◽

Particle Velocity ◽

Weber Number ◽

High Speed ◽

Solid Particles ◽

Bulk Liquid ◽

Distilled Water ◽

Critical Weber Number

Penetration of model solid particles (polymer, teflon, nylon, alumina) into transparent model liquids (distilled water and aqueous solutions of KI) were recorded by a high speed (500 frames per second) camera, while the particles were dropped from different heights vertically on the still surface of the liquids. In all cases a cavity has been found to form behind the solid particle, penetrating into the liquid. For each particle/liquid combination the critical dropping height has been measured, above which the particle was able to penetrate into the bulk liquid. Based on this, the critical impact particle velocity, and also the critical Weber number of penetration have been established. The critical Weber number of penetration was modelled as a function of the contact angle, particle size and the ratio of the density of solid particles to the density of the liquid.

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Numerical Simulation of Droplet Generation in Series Co-Flow Capillaries

ASME 2009 Second International Conference on Micro/Nanoscale Heat and Mass Transfer, Volume 1 ◽

10.1115/mnhmt2009-18377 ◽

2009 ◽

Author(s):

Yanxi Song ◽

Jinliang Xu

Keyword(s):

Reynolds Number ◽

Disperse Phase ◽

Weber Number ◽

Three Dimensional ◽

Continuous Phase ◽

Disperse Flow ◽

Double Emulsions ◽

Wide Range ◽

In Series ◽

Dispersed Phases

We study the production and motion of monodisperse double emulsions in microfluidics comprising series co-flow capillaries. Both two and three dimensional simulations are performed. Flow was determined by dimensionless parameters, i.e., Reynolds number and Weber number of continuous and dispersed phases. The co-flow generated droplets are sensitive to the Reynolds number and Weber number of the continuous phase, but insensitive to those of the disperse phase. Because the inner and outer drops are generate by separate co-flow processes, sizes of both inner and outer drops can be controlled by adjusting Re and We for the continuous phase. Meanwhile, the disperse phase has little effect on drop size, thus a desirable generation frequency of inner drop can be reached by merely adjusting flow rate of the inner fluid, leading to desirable number of inner drops encapsulated by the outer drop. Thus highly monodisperse double emulsions are obtained. It was found that only in dripping mode can droplet be of high mono-dispersity. Flow begins to transit from dripping regime to jetting regime when the Re number is decreased or Weber number is increased. To ensure that all the droplets are produced over a wide range of running parameters, tiny tapered tip outlet for the disperse flow should be applied. Smaller the tapered tip, wider range for Re and we can apply.

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Cavity Detachment from a Wedge with Rounded Edges and the Surface Tension Effect

Journal of Marine Science and Engineering ◽

10.3390/jmse9111253 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1253

Author(s):

Yuriy N. Savchenko ◽

Georgiy Y. Savchenko ◽

Yuriy A. Semenov

Keyword(s):

Surface Tension ◽

Weber Number ◽

Solution Process ◽

Cavity Flow ◽

Surface Tension Effect ◽

Force Coefficient ◽

Hodograph Method ◽

Wide Range ◽

Critical Weber Number ◽

Cavity Boundary

Cavity flow around a wedge with rounded edges was studied, taking into account the surface tension effect and the Brillouin–Villat criterion of cavity detachment. The liquid compressibility and viscosity were ignored. An analytical solution was obtained in parametric form by applying the integral hodograph method. This method gives the possibility of deriving analytical expressions for complex velocity and for potential, both defined in a parameter plane. An expression for the curvature of the cavity boundary was obtained analytically. By using the dynamic boundary condition on the cavity boundary, an integral equation in the velocity modulus was derived. The particular case of zero surface tension is a special case of the solution. The surface tension effect was computed over a wide range of the Weber number for various degrees of cavitation development. Numerical results are presented for the flow configuration, the drag force coefficient, and the position of cavity detachment. It was found that for each radius of the edges, there exists a critical Weber number, below which the iterative solution process fails to converge, so a steady flow solution cannot be computed. This critical Weber number increases as the radius of the edge decreases. As the edge radius tends to zero, the critical Weber number tends to infinity, or a steady cavity flow cannot be computed at any finite Weber number in the case of sharp wedge edges. This shows some limitations of the model based on the Brillouin–Villat criterion of cavity detachment.

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Reynolds Number and Roughness Effects on Turbocompressor Performance: Numerical Calculations and Measurement Data Evaluation

Volume 2C: Turbomachinery ◽

10.1115/gt2020-14653 ◽

2020 ◽

Author(s):

Fabian Dietmann ◽

Michael Casey ◽

Damian M. Vogt

Keyword(s):

Reynolds Number ◽

Measurement Data ◽

Theoretical Models ◽

Design Flow ◽

Flow Coefficient ◽

Low Flow ◽

Roughness Effects ◽

Flow Channels ◽

Compressor Performance ◽

Low Flow Coefficient

Abstract Further validation of an analytic method to calculate the influence of changes in Reynolds number, machine size and roughness on the performance of axial and radial turbocompressors is presented. The correlation uses a dissipation coefficient as a basis for scaling the losses with changes in relative roughness and Reynolds number. The original correlation from Dietmann and Casey [6] is based on experimental data and theoretical models. Evaluations of five numerically calculated compressor stages at different flow coefficients are presented to support the trends of the correlation. It is shown that the sensitivity of the compressor performance to Reynolds and roughness effects is highest for low flow coefficient radial stages and steadily decreases as the design flow coefficient of the stage and the hydraulic diameter of the flow channels increases.

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Laminar to Turbulent Buoyant Vortex Ring Regime in Terms of Reynolds Number, Bond Number, and Weber Number

Journal of Fluids Engineering ◽

10.1115/1.4038661 ◽

2018 ◽

Vol 140 (5) ◽

Cited By ~ 1

Author(s):

Xueying Yan ◽

Rupp Carriveau ◽

David S. K. Ting

Keyword(s):

Reynolds Number ◽

Vortex Ring ◽

Weber Number ◽

High Speed ◽

Reynolds Numbers ◽

Bond Number ◽

Vortex Rings ◽

Transition Regime ◽

Turbulent Vortex ◽

Buoyant Vortex Rings

When buoyant vortex rings form, azimuthal disturbances occur on their surface. When the magnitude of the disturbance is sufficiently high, the ring will become turbulent. This paper establishes conditions for categorization of a buoyant vortex ring as laminar, transitional, or turbulent. The transition regime of enclosed-air buoyant vortex rings rising in still water was examined experimentally via two high-speed cameras. Sequences of the recorded pictures were analyzed using matlab. Key observations were summarized as follows: for Reynolds number lower than 14,000, Bond number below 30, and Weber number below 50, the vortex ring could not be produced. A transition regime was observed for Reynolds numbers between 40,000 and 70,000, Bond numbers between 120 and 280, and Weber number between 400 and 800. Below this range, only laminar vortex rings were observed, and above, only turbulent vortex rings.

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Influence of Liquid Properties on Energy Conversion During Crown Evolution Following Drop Impact Upon Films

Journal of Fluids Engineering ◽

10.1115/1.4044441 ◽

2019 ◽

Vol 142 (1) ◽

Author(s):

Yujia Zhang ◽

Peiqing Liu ◽

Qiulin Qu ◽

Fanglin Liu ◽

Ramesh K. Agarwal

Keyword(s):

Reynolds Number ◽

Energy Conversion ◽

Weber Number ◽

Stokes Equations ◽

Drop Impact ◽

Navier Stokes ◽

Impact Process ◽

Vof Model ◽

The Moment ◽

The Impact

Abstract The energy conversion is proposed to analyze the effects of liquid properties on the formation of an ejecta sheet, prompt splashing, and crown evolution. The incompressible laminar Navier–Stokes equations coupled with the volume-of-fluid (VOF) model are solved numerically in an axisymmetric frame to simulate the impact process. Based on the energy conversion curves and liquid–gas interface shapes, the Weber number is shown to be the main dimensionless quantity controlling the impact process, especially with regard to crown evolution. However, the Reynolds number does have some influence on the drop impact process, especially during the stage of ejecta sheet formation and prompt splashing. By studying energy conversion during the impact process, the crown evolution is shown to be accelerated significantly with decreasing Weber number, but is hardly affected by the Reynolds number. A linear relation is found between the time to the moment of crown stabilization (when the crown height reaches its maximum value) and the square root of the Weber number. The relationship between the Weber number and the energy distribution at the moment of crown stabilization is also studied.

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