scholarly journals Breakup of a liquid rivulet falling over an inclined plate: Identification of a critical Weber number

2017 ◽  
Vol 29 (5) ◽  
pp. 052101 ◽  
Author(s):  
Rajesh K. Singh ◽  
Janine E. Galvin ◽  
Greg A. Whyatt ◽  
Xin Sun
Keyword(s):  
Weber Number ◽  
Inclined Plate ◽  
Critical Weber Number

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.

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.

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.

scholarly journals Viscoelastic effects on the jetting–dripping transition in co-flowing capillary jets

2008 ◽  
Vol 610 ◽  
pp. 249-260 ◽  
Author(s):  
J. M. MONTANERO ◽  
A. M. GAÑÁN-CALVO
Keyword(s):  
Dispersion Relation ◽  
Weber Number ◽  
Temporal Stability ◽  
Temporal Analysis ◽  
Viscoelastic Effects ◽  
Critical Weber Number ◽  
Lateral Mode ◽  
Spatio Temporal ◽  
Capillary Jets ◽  
Axisymmetric Perturbations

Linear hydrodynamics stability analysis is used to determine the influence of elasticity on the jetting–dripping transition and on the temporal stability of non-axisymmetric modes in co-flowing capillary jets. The critical Weber number for which axisymmetric perturbations undergo a transition from convective to absolute instability is calculated from the spatio-temporal analysis of the dispersion relation for Oldroyd-B liquids, as a function of the density and viscosity ratios, and the Reynolds and Deborah numbers. Elasticity increases the critical Weber number for all cases analysed and, consequently, fosters the transition from jetting to dripping. The temporal analysis of the dispersion relation for them= 1 lateral mode shows that elasticity does not affect its stability.

Splashing of droplets impacting superhydrophobic substrates

2019 ◽  
Vol 870 ◽  
pp. 175-188 ◽  
Author(s):  
Enrique S. Quintero ◽  
Guillaume Riboux ◽  
José Manuel Gordillo
Keyword(s):  
Interfacial Tension ◽  
Critical Condition ◽  
Weber Number ◽  
Atmospheric Conditions ◽  
Ohnesorge Number ◽  
A Value ◽  
Consistent Model ◽  
Self Consistent ◽  
Critical Weber Number ◽  
Good Agreement

A drop of radius $R$ of a liquid of density $\unicode[STIX]{x1D70C}$, viscosity $\unicode[STIX]{x1D707}$ and interfacial tension coefficient $\unicode[STIX]{x1D70E}$ impacting a superhydrophobic substrate at a velocity $V$ keeps its integrity and spreads over the solid for $V<V_{c}$ or splashes, disintegrating into tiny droplets violently ejected radially outwards for $V\geqslant V_{c}$, with $V_{c}$ the critical velocity for splashing. In contrast with the case of drop impact onto a partially wetting substrate, Riboux & Gordillo (Phys. Rev. Lett., vol. 113, 2014, 024507), our experiments reveal that the critical condition for the splashing of water droplets impacting a superhydrophobic substrate at normal atmospheric conditions is characterized by a value of the critical Weber number, $We_{c}=\unicode[STIX]{x1D70C}\,V_{c}^{2}\,R/\unicode[STIX]{x1D70E}\sim O(100)$, which hardly depends on the Ohnesorge number $Oh=\unicode[STIX]{x1D707}/\sqrt{\unicode[STIX]{x1D70C}\,R\,\unicode[STIX]{x1D70E}}$ and is noticeably smaller than the corresponding value for the case of partially wetting substrates. Here we present a self-consistent model, in very good agreement with experiments, capable of predicting $We_{c}$ as well as the full dynamics of the drop expansion and disintegration for $We\geqslant We_{c}$. In particular, our model is able to accurately predict the time evolution of the position of the rim bordering the expanding lamella for $We\gtrsim 20$ as well as the diameters and velocities of the small and fast droplets ejected when $We\geqslant We_{c}$.

The TAR Model for Calculation of Droplet/Wall Impingement

1998 ◽  
Vol 120 (3) ◽  
pp. 593-597 ◽  
Author(s):  
Haitao Xu ◽  
Yongchang Liu ◽  
Ping He ◽  
Haiqing Wang
Keyword(s):  
Weber Number ◽  
Experimental Results ◽  
Droplet Radius ◽  
Hydrodynamic Behavior ◽  
New Model ◽  
Wall Impingement ◽  
Critical Weber Number ◽  
Wall Interaction

In this paper, we present a new model, called the TAR model, for calculation of droplet/wall impingement. Using this model, we find that the critical Weber number for rebound is not a constant. It varies with the droplet radius. For large drops, the critical Weber numbers and rebound velocities predicted by the TAR model agree with experimental results very well. Whereas, the predicted hydrodynamic behavior of small droplets is very different from that of large drops. This conclusion is significant for modeling engine spray/wall interaction.

Numerical Simulation of Droplet Flows and Evaluation of Interfacial Area

2002 ◽  
Vol 124 (3) ◽  
pp. 576-583 ◽  
Author(s):  
T. Watanabe ◽  
K. Ebihara
Keyword(s):  
Lattice Boltzmann ◽  
Weber Number ◽  
Volume Fraction ◽  
Interfacial Area ◽  
Force Balance ◽  
Two Phase ◽  
Critical Weber Number ◽  
Boltzmann Method ◽  
Droplet Flows ◽  
Good Agreement

Droplet flows with coalescence and breakup are simulated numerically using the lattice Boltzmann method. It is shown that the rising velocities are in good agreement with those obtained by the force balance and the empirical correlation. The breakup of droplets after coalescence is simulated well in terms of the critical Weber number. A numerical method to evaluate the interfacial area and the volume fraction in two-phase flows is proposed. It is shown that the interfacial area corresponds to the shape, the number and the size of droplets, and the proposed method is effective for numerical evaluation of interfacial area even if the interface changes dynamically.

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