Jumping drops on the surface of the water

2020 ◽  
Vol 15 (3-4) ◽  
pp. 228-231
Author(s):  
A.G. Terentiev
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Theoretical Model ◽  
Drop Size ◽  
Initial Conditions ◽  
Water Drop ◽  
Numerical Calculations ◽  
Rise Height

The paper proposes a theoretical model for the bouncing of a water drop on a free surface. The motion of a drop in air is described by the usual equations connecting the forces of inertia, gravity, and Stokes (viscosity resistance). The drop is considered spherical with a given surface tension. Numerical calculations were carried out using the same algorithm, but with different initial conditions. Some conditions are set for the droplet disintegration, others for the droplet reflection from the free surface. It is shown that the disintegration of a drop occurs periodically with a decrease in the drop size and an increase in the drop rise height. In the interval between droplet decays, periodic reflection from the free surface occurs with a decrease in the rise height.

scholarly journals The breakup of levitating water drops observed with a high speed camera

2011 ◽  
Vol 11 (19) ◽  
pp. 10205-10218 ◽  
Author(s):  
C. Emersic ◽  
P. J. Connolly
Keyword(s):  
Size Distribution ◽  
High Speed ◽  
Drop Size ◽  
Initial Conditions ◽  
Water Drop ◽  
Liquid Water Content ◽  
Drop Size Distribution ◽  
High Speed Camera ◽  
Size Distributions ◽  
Drop Size Distributions

Abstract. Collision-induced water drop breakup in a vertical wind tunnel was observed using a high speed camera for interactions between larger drop sizes (up to 7 mm diameter) than have previously been experimentally observed. Three distinct collisional breakup types were observed and the drop size distributions from each were analysed for comparison with predictions of fragment distributions from larger drops by two sets of established breakup parameterisations. The observations showed some similarities with both parameterisations but also some marked differences for the breakup types that could be compared, particularly for fragments 1 mm and smaller. Modifications to the parameterisations are suggested and examined. Presented is also currently the largest dataset of bag breakup distributions observed. Differences between this and other experimental research studies and modelling parameterisations, and the associated implications for interpreting results are discussed. Additionally, the stochastic coalescence and breakup equation was solved computationally using a breakup parameterisation, and the evolving drop-size distribution for a range of initial conditions was examined. Initial cloud liquid water content was found to have the greatest influence on the resulting distribution, whereas initial drop number was found to have relatively little influence. This may have implications when considering the effect of aerosol on cloud evolution, raindrop formation and resulting drop size distributions. Calculations presented show that, using an ideal initial cloud drop-size distribution, ~1–3% of the total fragments are contributed from collisional breakup between drops of 4 and 6 mm.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

A note on the instabilities of a horizontal shear flow with a free surface

2000 ◽  
Vol 406 ◽  
pp. 337-346 ◽  
Author(s):  
L. ENGEVIK
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Shear Flow ◽  
Velocity Profile ◽  
Froude Number ◽  
The Other ◽  
Algebraic Equations ◽  
Horizontal Shear ◽  
Analytical Treatment ◽  
Unstable Region

The instabilities of a free surface shear flow are considered, with special emphasis on the shear flow with the velocity profile U* = U*0sech2 (by*). This velocity profile, which is found to model very well the shear flow in the wake of a hydrofoil, has been focused on in previous studies, for instance by Dimas & Triantyfallou who made a purely numerical investigation of this problem, and by Longuet-Higgins who simplified the problem by approximating the velocity profile with a piecewise-linear profile to make it amenable to an analytical treatment. However, none has so far recognized that this problem in fact has a very simple solution which can be found analytically; that is, the stability boundaries, i.e. the boundaries between the stable and the unstable regions in the wavenumber (k)–Froude number (F)-plane, are given by simple algebraic equations in k and F. This applies also when surface tension is included. With no surface tension present there exist two distinct regimes of unstable waves for all values of the Froude number F > 0. If 0 < F [Lt ] 1, then one of the regimes is given by 0 < k < (1 − F2/6), the other by F−2 < k < 9F−2, which is a very extended region on the k-axis. When F [Gt ] 1 there is one small unstable region close to k = 0, i.e. 0 < k < 9/(4F2), the other unstable region being (3/2)1/2F−1 < k < 2 + 27/(8F2). When surface tension is included there may be one, two or even three distinct regimes of unstable modes depending on the value of the Froude number. For small F there is only one instability region, for intermediate values of F there are two regimes of unstable modes, and when F is large enough there are three distinct instability regions.

scholarly journals Unsteady flow induced by a withdrawal point beneath a free surface

2005 ◽  
Vol 47 (2) ◽  
pp. 185-202 ◽  
Author(s):  
T. E. Stokes ◽  
G. C. Hocking ◽  
L. K. Forbes
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Unsteady Flow ◽  
Critical Values ◽  
The Other ◽  
Withdrawal Rate ◽  
Steady Solutions

AbstractThe unsteady axisymmetric withdrawal from a fluid with a free surface through a point sink is considered. Results both with and without surface tension are included and placed in context with previous work. The results indicate that there are two critical values of withdrawal rate at which the surface is drawn directly into the outlet, one after flow initiation and the other after the flow has been established. It is shown that the larger of these values corresponds to the point at which steady solutions no longer exist.

Differentiating Freezing Drizzle and Freezing Rain in HRRR Model Forecasts

2021 ◽  
Author(s):  
Sarah Tessendorf ◽  
Allyson Rugg ◽  
Alexei Korolev ◽  
Ivan Heckman ◽  
Courtney Weeks ◽  
...  
Keyword(s):  
Drop Size ◽  
Prediction Models ◽  
Water Drop ◽  
Weather Prediction ◽  
Supercooled Liquid ◽  
Drop Diameter ◽  
Aircraft Icing ◽  
Freezing Rain ◽  
Primary Focus

AbstractSupercooled large drop (SLD) icing poses a unique hazard for aircraft and has resulted in new regulations regarding aircraft certification to fly in regions of known or forecast SLD icing conditions. The new regulations define two SLD icing categories based upon the maximum supercooled liquid water drop diameter (Dmax): freezing drizzle (100–500 μm) and freezing rain (> 500 μm). Recent upgrades to U.S. operational numerical weather prediction models lay a foundation to provide more relevant aircraft icing guidance including the potential to predict explicit drop size. The primary focus of this paper is to evaluate a proposed method for estimating the maximum drop size from model forecast data to differentiate freezing drizzle from freezing rain conditions. Using in-situ cloud microphysical measurements collected in icing conditions during two field campaigns between January and March 2017, this study shows that the High-Resolution Rapid Refresh model is capable of distinguishing SLD icing categories of freezing drizzle and freezing rain using a Dmax extracted from the rain category of the microphysics output. It is shown that the extracted Dmax from the model correctly predicted the observed SLD icing category as much as 99% of the time when the HRRR accurately forecast SLD conditions; however, performance varied by the method to define Dmax and by the field campaign dataset used for verification.

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