scholarly journals Numerical and Theoretical Investigation of Effect of Density Ratio on the Critical Weber Number of Droplet Breakup

2003 ◽  
Vol 40 (7) ◽  
pp. 501-508 ◽  
Author(s):  
Ri-Qiang DUAN ◽  
Seiichi KOSHIZUKA ◽  
Yoshiaki OKA
Keyword(s):  
Theoretical Investigation ◽  
Weber Number ◽  
Density Ratio ◽  
Droplet Breakup ◽  
Critical Weber Number

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

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.

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

2005 ◽  
Vol 473-474 ◽  
pp. 429-434 ◽  
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.

Nonlinear instability of plane liquid sheets

2000 ◽  
Vol 406 ◽  
pp. 281-308 ◽  
Author(s):  
SEYED A. JAZAYERI ◽  
XIANGUO LI
Keyword(s):  
Weber Number ◽  
Density Ratio ◽  
Perturbation Expansion ◽  
Liquid Sheet ◽  
Fundamental Wave ◽  
Liquid Density ◽  
Initial Amplitude ◽  
Nonlinear Stability Analysis ◽  
Liquid Sheets ◽  
Breakup Time

A nonlinear stability analysis has been carried out for plane liquid sheets moving in a gas medium at rest by a perturbation expansion technique with the initial amplitude of the disturbance as the perturbation parameter. The first, second and third order governing equations have been derived along with appropriate initial and boundary conditions which describe the characteristics of the fundamental, and the first and second harmonics. The results indicate that for an initially sinusoidal sinuous surface disturbance, the thinning and subsequent breakup of the liquid sheet is due to nonlinear effects with the generation of higher harmonics as well as feedback into the fundamental. In particular, the first harmonic of the fundamental sinuous mode is varicose, which causes the eventual breakup of the liquid sheet at the half-wavelength interval of the fundamental wave. The breakup time (or length) of the liquid sheet is calculated, and the effect of the various flow parameters is investigated. It is found that the breakup time (or length) is reduced by an increase in the initial amplitude of disturbance, the Weber number and the gas-to-liquid density ratio, and it becomes asymptotically insensitive to the variations of the Weber number and the density ratio when their values become very large. It is also found that the breakup time (or length) is a very weak function of the wavenumber unless it is close to the cut-off wavenumbers.

Liquid Jets in Subsonic Air Crossflow at Elevated Pressure

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
Jinkwan Song ◽  
Charles Cary Cain ◽  
Jong Guen Lee
Keyword(s):  
Weber Number ◽  
Momentum Flux ◽  
Drop Size ◽  
Density Ratio ◽  
Flux Ratio ◽  
Mie Scattering ◽  
Air Pressure ◽  
Scattering Intensity ◽  
Nozzle Orifice ◽  
Momentum Flux Ratio

The breakup, penetration, droplet size, and size distribution of a Jet A-1 fuel in air crossflow has been investigated with focus given to the impact of surrounding air pressure. Data have been collected by particle Doppler phased analyzer (PDPA), Mie-scattering with high speed photography augmented by laser sheet, and Mie-scattering with intensified charge-coupled device (ICCD) camera augmented by nanopulse lamp. Nozzle orifice diameter, do, was 0.508 mm and nozzle orifice length to diameter ratio, lo/do, was 5.5. Air crossflow velocities ranged from 29.57 to 137.15 m/s, air pressures from 2.07 to 9.65 bar, and temperature held constant at 294.26 K. Fuel flow provides a range of fuel/air momentum flux ratio (q) from 5 to 25 and Weber number from 250 to 1000. From the results, adjusted correlation of the mean drop size has been proposed using drop size data measured by PDPA as follows: (D0/D32)=0.267Wea0.44q0.08(ρl/ρa)0.30(μl/μa)-0.16. This correlation agrees well and shows roles of aerodynamic Weber number, Wea, momentum flux ratio, q, and density ratio, ρl/ρa. Change of the breakup regime map with respect to surrounding air pressure has been observed and revealed that the boundary between each breakup modes can be predicted by a transformed correlation obtained from above correlation. In addition, the spray trajectory for the maximum Mie-scattering intensity at each axial location downstream of injector is extracted from averaged Mie-scattering images. From these results, correlations with the relevant parameters including q, x/do, density ratio, viscosity ratio, and Weber number are made over a range of conditions. According to spray trajectory at the maximum Mie-scattering intensity, the effect of surrounding air pressure becomes more important in the farfield. On the other hand, effect of aerodynamic Weber number is more important in the nearfield.

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

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.

scholarly journals Numerical modelling of destruction of a drop of non-Newtonian fluid in a gas flow

2019 ◽  
Vol 196 ◽  
pp. 00042
Author(s):  
Anna Shebeleva ◽  
Andrey Minakov ◽  
Alexander Lobasov ◽  
Alexander Shebelev
Keyword(s):  
Weber Number ◽  
Gas Flow ◽  
Filter Cake ◽  
Droplet Breakup ◽  
Secondary Droplet ◽  
Large Solution ◽  
Secondary Droplets ◽  
Secondary Breakup ◽  
Les Model ◽  
Good Agreement

The research presents the numerical modeling findings of the secondary breakup of droplets of coal water slurries containing petrochemicals (CWSP) droplet with the filter cake content of 50 % for different Weber number values. The modeling method of the secondary droplet breakup is based on the VOF method for interface resolution, LES model for describing turbulence, and the technology of adapted dynamic grids. This technology enables the grid to be automatically concentrated in the region of large solution gradients during the calculation. The implementation of such a highly detailed grid allowed resolving secondary droplets with the dimensions down to 15 μm. We established the droplet breakup modes depending on the Weber number ranging from 36 to 342. The structure of the stream behind droplets was studied in detail and the numerical method was tested. The results are in good agreement with the results of known experiments.

Transition from dripping to jetting

1999 ◽  
Vol 383 ◽  
pp. 307-326 ◽  
Author(s):  
CHRISTOPHE CLANET ◽  
JUAN C. LASHERAS
Keyword(s):  
Weber Number ◽  
Free Edge ◽  
Newtonian Liquid ◽  
Inviscid Limit ◽  
Inertia Effects ◽  
Wide Range ◽  
Critical Weber Number ◽  
Experimental Values ◽  
Outside Diameter ◽  
Good Agreement

We consider the critical Weber number (Wec≡ ρV20D/σ) at which the transition from dripping to jetting occurs when a Newtonian liquid of density ρ and surface tension σ is injected with a velocity V0 through a tube of diameter D downward into stagnant air, under gravity g. We extend Taylor's (1959) model for the recession speed of a free edge, and obtain in the inviscid limit an exact solution which includes gravity and inertia effects. This solution provides a criterion for the transition which is shown to occur at a critical Weber numberformula herewhere Bo and Boo are the Bond numbers (Bo≡[ρgD2/(2σ)]1/2), respectively based on the inside and outside diameter of the tube, and K is a constant equal to 0.37 for the case of water injected in air. This critical Weber number is shown to be in good agreement with existing experimental values as well as with new measurements performed over a wide range of Bond numbers.

On the Critical Weber Number for Coarse Water Formation in Steam Turbines

1979 ◽  
Vol 21 (5) ◽  
pp. 353-356 ◽  
Author(s):  
C. S. Ow ◽  
R. I. Crane
Keyword(s):  
Weber Number ◽  
Maximum Size ◽  
Distribution Functions ◽  
Steam Turbines ◽  
Wet Steam ◽  
Nonlinear Parameters ◽  
Upper Limit ◽  
Water Formation ◽  
Critical Weber Number ◽  
Cumulative Mass

The widely quoted experiments of Moore et al. indicate that the largest stable drops resulting from atomization behind a blade, in typical low-pressure wet-steam flows, can be described by a constant critical Weber number, Wec, of about 21, obtained graphically by fitting upper-limit distribution functions (ULDF) to measured spectra. A non-subjective re-analysis of these data has been made, using Marquardt's algorithm for the least-squares estimation of nonlinear parameters to improve the fitting. It is shown that optimization of the ULDF fit increases Wec considerably in the case of supersonic blade-exit flow. However, replacement of the computed maximum size by that corresponding to a given cumulative mass is necessary to avoid distortion of the result by the small fraction of total mass contained in the largest drops. A cumulative mass of 99.9 per cent consistently gives Wec values near 21, confirming Moore's result, but indicating the need for further work on the Mach-number dependence of Wec.

A Direct Numerical Simulation of the Unsteady Development of a Deformable Rising Bubble in a Quiescent Liquid

2008 ◽  
Author(s):  
Alpana Agarwal ◽  
C. F. Tai ◽  
J. N. Chung
Keyword(s):  
Weber Number ◽  
Bubble Dynamics ◽  
Stokes Equations ◽  
Control Volume ◽  
Density Ratio ◽  
Simulation Method ◽  
Liquid Pool ◽  
Accurate Information ◽  
Two Phase ◽  
Wide Range

An accurate finite-volume based numerical method for the simulation of an isothermal two-phase flow, consisting of a deformable bubble rising in a quiescent, unbounded liquid, is presented. This direct simulation method is built on a sharp interface concept and developed on an Eulerian, Cartesian fixed grid with a cut-cell scheme and marker points to track the moving interface. The unsteady Navier-Stokes equations in both liquid and gas phases are solved separately. The mass continuity and momentum flux conditions are explicitly matched at the true phase boundary to determine the interface shape and movement of the bubble. The highlights of this method are that it utilizes a combined Eulerian-Lagrangian approach, and is capable of treating the interface as a sharp discontinuity. A fixed underlying grid is used to represent the control volume. The interface, however, is denoted by a separate set of marker particles which move along with the interface. A quadratic curve fitting algorithm with marker points is used to yield smooth and accurate information of the interface curvatures. This numerical scheme can handle a wide range of density and viscosity ratios. The bubble is assumed to be spherical and at rest initially, but deforms as it rises through the liquid pool due to buoyancy. Additionally, the flow is assumed to be axisymmetric and incompressible. The bubble deformation and dynamic motion are characterized by the Reynolds number, the Weber number, the density ratio and the viscosity ratio. The effects of these parameters on the translational bubble dynamics and shape are given and the physical mechanisms are explained and discussed. Results for the shape, velocity profile and various forces acting on the bubble are presented here as a function of time until the bubble reaches terminal velocity. The range of Reynolds numbers investigated is 1 < Re < 100, and that of Weber number is 1 < We < 10.

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