Bulletin of the American Physical Society
73rd Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 22–24, 2020; Virtual, CT (Chicago time)
Session X03: FreeSurface Flows: General (10:45am  11:30am CST)Interactive On Demand

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X03.00001: A Numerical Study of Mass Transfer from Laminar Liquid Films Guangzhao Zhou, Andrea Prosperetti The process of a dissolved substance diffusing out of a liquid film in twodimensional, gravitydriven laminar flow down a vertical solid plane is numerically simulated. The fluid mechanic problem is solved separately subject to periodicity conditions in the flow direction. After steadystate is reached, many copies of the calculated flow fields are efficiently “glued” together to generate a long computational domain for simulation of mass transfer. This approach renders it possible to follow the diffusion process over a long distance and to elucidate its various stages. It is found that large and small waves, with a maximum liquid velocity larger or smaller than the wave speed, respectively, behave differently. For the latter, the Sherwood number reaches an asymptotic value by the time the film still contains a significant amount of solute. From this point on, the mass transfer is very similar to that of a flat film with a smaller thickness. For large waves, the contributions of the various parts of the wave evolve differently with time and conditions and may negatively affect the mass transfer process if they get out of balance. Thus, the presence of recirculation is, in and by itself, insufficient to judge the mass transfer performance of a falling film. [Preview Abstract] 

X03.00002: Coating flow in the presence of an irrotational airflow with circulation Andrew Mitchell, Brian Duffy, Stephen Wilson An analysis of steady coating flow of a thin film of a viscous fluid on the outside of a uniformly rotating horizontal circular cylinder in the presence of an irrotational airflow with circulation shows that the presence of the airflow can result in qualitatively different behaviour of the fluid film from that in classical coating flow. Fullfilm solutions corresponding to a continuous film of fluid covering the entire cylinder are possible only when the flux and mass of fluid do not exceed critical values, which are determined in terms of the parameters $F$ and $K$ representing the speed of the farfield airflow and the circulation of the airflow, respectively. The qualitative changes in the behaviour of the film thickness as $F$ and $K$ are varied are described. In particular, the film thickness can have as many as four stationary points and, in general, has neither toptobottom nor righttoleft symmetry. In addition, when the circulation of the airflow is in the same direction as the rotation of the cylinder the maximum mass of fluid that can be supported on the cylinder is always less than that in classical coating flow, whereas when the circulation is in the opposite direction the mass of fluid can be arbitrarily greater than that in classical coating flow. [Preview Abstract] 

X03.00003: Entropy: Combining Boundary Layers and DepthAveraged Models Benjamin Young, Stuart Dalziel, Nathalie Vriend Deriving robust and accurate closure laws for simplified models of complicated flows is still one of the most significant problems facing fluid dynamicists in the 21st century. Many approaches exist. Many of these approaches, however, often lack physicality, simplicity or are dependent on empirical data. This naturally leads to the question, `is there a general guiding principle that can be used to derive closure laws for any arbitrary flow model?’\\ We present a generic meanfield/maximum entropy approach that we apply to model the interaction between a boundary layer and free surface. We show that, amazingly, if entropy is maximized subject to meanfield conservation of mass, momentum and energy we can recover analytical solutions to both the NavierStokes equations and the granular $\mu(I)$ equations.\\ Finally, we apply our maximum entropy method to the `FreeSurface Blasius Problem’ and compare our model to both numerics and theory. We demonstrate that the meanfield/maximum entropy method is both highly accurate and predicts some previously unseen physical phenomena. [Preview Abstract] 

X03.00004: Novel air entrainment mechanism from a harmonically forced plunging liquid jet Sophia Relph, Kenneth Kiger, Akash Dhruv, Ilias Balaras The process of pouring molten metal for castings is highly susceptible to air entrainment. This has major ramifications for the quality of cast metal parts, as air and oxide inclusions induced during pouring can impact part strength and fatigue life. The current literature on air entrainment by disturbed plunging jets has largely relied on passively forced, uncontrolled jets where surface disturbances arise from unforced velocity fluctuations and little attempt is made to quantify the disturbance state of the jet. This work uses a wellcontrolled plunging jet with harmonically driven axisymmetric disturbances in order to investigate the specific processes by which disturbed jets entrain air, thus allowing air entrainment properties to be correlated with a repeatable jet disturbance state. The harmonically forced jet has led to the discovery of a novel free surface instability, which forces a transition from an axisymmetric free surface response to a threedimensional mode with a reduced entrainment threshold. Data on the free surface instability, as well as comparisons to the literature and to closely coordinated direct numerical simulations will be presented. [Preview Abstract] 

X03.00005: Scaling and modeling of air entrainment volume from vortex interactions with a free surface Kelli Hendrickson, Xiangming Yu, Dick Yue Understanding air entrainment from vortex interactions with a free surface is a critical component for predicting air entrainment in civil, environmental, ocean and naval engineering applications with direct impact on turbulent dissipation and airsea interaction. We use highresolution 3D direct numerical simulation of individual vortex interactions with a free surface to study the air entrainment characteristics as a function of the vortex parameters. The numerical method utilizes conservative Volume of Fluid (cVOF) to capture the interface on a Cartesian grid and informed component labeling (ICL) to quantify the entrainment characteristics. Our particular interest lies in understanding the total volume of air entrainment due to underlying vortical interactions. By varying the vortex Froude number, Weber number, Reynolds number, and incidence angle, we establish the dependence of the initial onset entrainment volume as a linear function of the vortex circulation flux Froude number. We define a critical value and relative depth below which vortex interactions with a free surface do not entrain air. Finally, we show the applicability of the scaling and model within the context of quasisteady breaking waves generated by a fullysubmerged circular cylinder. [Preview Abstract] 

X03.00006: Optimal Capillarity Rheometry for Newtonian Fluids Subramaniam Balakrishna, William Schultz The differential analysis of McCarroll et al (2016) expands upon the Capillary Breakup Rheometry (Mckinley and Tripathi (2000)) to determine the surface tension to viscosity ratio of an unsteady stretched Newtonian filament free surface. Our analysis is valid during and after stretch and hence no longer relies on breakup. Challenges associated with the choice of stretch history are twofold: `rapid stretching' is viscous dominated and results in a nearly cylindrical free surface while `slow stretching' results in a quasistatic profile with hard to measure viscous effects. We focus on parametric strategies that optimize rheometry.~ [Preview Abstract] 

X03.00007: Oblateprolate Faraday waves on a spherical drop: precession, torsion and symmetry breaking Laurette Tuckerman, Antoine Mille, Jalel Chergui, Damir Juric When a spherical drop is subjected to an oscillating radial force, surface waves are excited whose pattern depends on the forcing frequency and amplitude. For frequencies leading to spherical harmonic degree $\ell=2$, the Faraday instability leads to a periodic oscillation between axisymmetric prolate and oblate shapes (EboAdou et al. JFM 2019). We find that this regime is succeded by several further transitions: (1) precession of the drop, (2) breaking of axisymmetry leading to a general ellipsoid, and (3) torsion leading to elongation and rupture. [Preview Abstract] 

X03.00008: Gravitycapillary hexagonal waves generated by sinusoidal wavemaker oscillation Chang Xu, Marc Perlin Crosswaves are standing waves with crests perpendicular to a wavemaker; they are subharmonic waves excited by parametric instability. The modulational and chaotic behaviors of nonlinear crosswaves have been studied widely since the 1970s. When surface tension is negligible, crosswaves are usually trapped near the wavemaker and often exhibit a long modulation. However, investigation of capillary effects on crosswaves is lacking. In this work, we study crosswaves that are highly dependent on surface tension as well as gravity. By oscillating a plate vertically with frequencies of 25Hz to 45Hz at one end of a rectangular basin, a new progressive wave pattern is realized. Unlike most crosswaves that occur adjacent to the wavemaker, these wave patterns travel downstream in the form of a hexagonal pattern. To quantify the surface elevations, the water surface is measured using a synthetic Schlieren technique. Experiments show that two oblique progressive waves with subharmonic frequency are generated. They form a hexagonal pattern when the lateral components of these waves are in resonance with the parametric sloshing modes of the tank, which then causes a selective amplification of subharmonics. [Preview Abstract] 

X03.00009: Analysis of Thin Leaky Dielectric Layers Subject to an Electric Field Matthew Keith, Alexander Wray, Stephen Wilson We investigate a bilayer of liquid and gas contained between two planar electrodes subject to a normal electric field described by the TaylorMelcher leaky dielectric model. We use both the full Stokes flow formulation and the longwave approximation to explore the linear stability of the system. Nonlinear calculations reveal four qualitatively different behaviours, namely, the return of the liquidgas interface to its flat state, asymptotic thinning, contact with the upper wall, and singular touchdown behaviour. The appropriate parameter planes are determined numerically. Of particular interest are the interfacial dynamics of these four behaviours, which we investigate both analytically and numerically. In particular, we investigate the longtime behaviour in the asymptotic thinning regime and the onset of sliding. Additionally, we explore the selfsimilar dynamics of the interface during touchdown and upperwall contact. Finally, we explore the limiting cases of a perfectly conducting liquid and a highly conducting liquid and gas, both of which are commonly observed physically, which allow for additional analytical and numerical progress. [Preview Abstract] 

X03.00010: Identifying Surface Expressions of Submerged Bottom Features Using Machine Learning Saksham Gakhar, Jeffrey Koseff, Nicholas Ouellette Laboratory experiments were carried out in an openchannel recirculating water flume for different bottom treatments and a variety of flow conditions. We acquired overhead images of the free surface downstream of the bottom features and used these to train convolutional neural network based classifiers. Using these classifiers, we demonstrate that information acquired at the surface alone can be used to differentiate between the physical features that lie at the bottom boundary. We show that although external physical processes such as winds can modulate the free surface, they do not necessarily eliminate the freesurface signature of the submerged bottom features. Our results provide strong motivation for future studies that probe the physical processes responsible for transporting information about the bottom of the flow to the surface. [Preview Abstract] 

X03.00011: Wave damping of a sloshing wave by an interacting turbulent vortex flow Francisco Reyes, Vicente Torrejón, Claudio Falcón We report on the enhancement of the hydrodynamic damping of gravity waves at the surface of a fluid layer as they interact with a turbulent vortex flow in a sloshing experiment. Gravity surface waves are excited by oscillating horizontally a square container holding our working fluid (water). At the bottom of the container, 4 impellers in a quadrupole configuration generate a vortex array at moderate to high Reynolds number, which interact with the wave. We measure the surface fluctuations using different optical nonintrusive methods and the local velocity of the flow. In our experimental range, we show that as we increase the angular velocity of the impellers, the gravity wave amplitude decreases without changing the oscillation frequency nor generating transverse modes. This wave dissipation enhancement is contrasted with the increase of the turbulent velocity fluctuations from PIV measurements. To rationalize the damping enhancement a periodically forced shallow water model including viscous terms is presented, which is used to calculate the sloshing wave resonance curve. The calculated curve is then used to relate the turbulent velocity fluctuations with the enhanced shallow water viscous friction coefficient, which are shown to be proportional between themselves. [Preview Abstract] 

X03.00012: Interfacial Mixing by Marangoni Surfers Clement Gouiller, Christophe Ybert, Cecile CottinBizonne, Romain Volk, Mickael Bourgoin, Florence Raynal Marangoni effects constitute a major source of interfacial flows, classically induced by a local release of heat or surfactant. When this release originates from a particle floating at the fluid surface, particle sources additionally selfpropel generating complex flows and dynamics. In the present work, we pour glassbubbles at the surface to reveal interfacial mixing properties induced by interfacial swimmers. Experimentally, we access their dynamics, the floaters concentration and velocity fields to get insights into the interfacial transport properties. From the concentration field standard deviation, we evidence that the system reaches a steadystate of incomplete floaters mixing after a few minutes. We provide a model, in good agreement with the experiments, that predicts the value of the standard deviation reached. Qualitatively, we rationalize the steadystate as a competition between mixing by the random motion of many stirrers and unmixing due to the Marangoni flow structure around a swimmer, which constantly rejuvenate gradients in the form of a depleted area around each particle. Finally, examination of the energy spectra reveals complex multiscale properties with some analogy with turbulent mixing despite no inertial turbulence occurs in the subphase. [Preview Abstract] 

X03.00013: Gas exchange in an interfaciallydriven bioreactor Shannon Griffin, Joe Adam, Patrick McMackin, Frank Riley, Amir Hirsa Gas transfer at interfaces is a limiting factor in the performance of many chemical reactors and bioreactors. The knifeedge surface viscometer (KEV) is a fluid physics apparatus in which a thin, rotating ring at the interface of a liquid conveys shear and mixing to the bulk fluid via surface shear viscosity and secondary inertial flow. KEVs can function as chemical reactors or bioreactors driven by prescribed interfacial shear rates. This investigation focuses on the effects of interfacial shear on gas transfer using a KEV. Simulations using COMSOL were compared to CO$_{\mathrm{2}}$ gas transfer experiments with varying Reynolds (Re) and Boussinesq (Bq) numbers. Results show a monotonic increase in gas transfer with increasing Re and increasing Bq, as measured by the time required to reach steadystate gas concentration in the KEV. These results are relevant to applications and future studies in chemical reactors, bioreactors, and gas transfer in microgravity studied using the ringsheared drop (RSD). A containerless bioreactor launched to the ISS in 2019, the RSD was originally designed to study amyloid fibrillization without interaction with solid walls. [Preview Abstract] 

X03.00014: Air cushioning and impact pressures during a wedge slamming on water Utkarsh Jain, Vladimir Novakovic, Hannes Bogaert, Devaraj van der Meer The water entry of a wedge has become a model test in marine and naval engineering research. Wagner theory, originating in 1932, predicts impact pressures, and accounts for contributions to the total pressure arising from various flow domains in the vicinity of the wetting region on the wedge. Here we study the slamming of a wedge and a cone with a deadrise angle of 10 degrees. Using a linear motor, a constant, wellcontrolled velocity is maintained throughout the impact event. Using an inhouse visualisation technique, we reveal that aircushioning under the cone causes a significant deflection of the water surface prior to impact. Pressures at two locations on the impactor are measured during and after impact. Pressure timeseries from the two impactors are discussed using appropriate hydrodynamic pressure, and inertial time scales. The nondimensionalised pressure time series are compared to composite Wagner solutions (Zhao & Faltinsen 1993). It is shown that, without a single free parameter, the spaceaveraged composite solutions reproduce the measurements near perfectly well, and a finite size of the sensor is why the peak pressure has a nonsingular rise. Approximations made in the innerdomain for extending the Wagner model to threedimensions are experimentally justified. [Preview Abstract] 
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