Session AK: Free Surface Flows I

Droplet Impact Onto A Flat Plate: Inclined Verses Moving Surfaces

Much research has been conducted on the impact of droplets normal to flat surfaces. However, very little research has been carried out on oblique impacts, even though they occur frequently in nature and industry. We experiment with the effects of tangential and normal impact velocities on the behavior of a droplet as it impacts a flat plate. The plate is inclined in the first case, and in the second case the plate is rotated via an electric motor. The asymmetric nature of the impact causes asymmetric splashing, such that under certain conditions only part of the rim splashes. Using a high-speed camera, we demonstrate that the splash threshold of inclined and moving surfaces are quantitatively similar, with only small differences. We also develop a phase diagram of splashing showing which phase occurs given a tangential and normal impact velocity. Such a phase diagram is useful for both engineering design and for the evaluation of splash-prediction models.   

Shallow-angle water entry of ballistic projectiles

The water-entry of ballistic projectiles is investigated using high-speed digital imaging. Projectiles enter the water at shallow angles to the free surface, $5^{\circ}-15^{\circ}$, without ricochet at Mach numbers between 0.3 and 2.0. Projectile dynamics, critical entry angle, and cavity growth are discussed. Geometric modifications to a projectile allow it to travel large distances underwater assuming a sufficiently large air-cavity is formed after impact, which dramatically decreases drag on the projectile. Results show that successful water-entry occurs for projectiles with modified tip geometries at Mach numbers ranging from 0.3 to 2; these projectile modifications include tip geometry and material properties. A theoretical cavity model compares well with the experimental data and will be discussed for a range of experimental conditions.   

Open-Channel Capillary Flow in Helical Support Structures

When gravitational effects are negligible compared to capillary effects, it is possible to achieve capillary flow in a helical wire support. The global dynamics of open-channel capillary flow in helical support structures are modeled by one-dimensional continuity and momentum equations where the pressure is related to the local curvature of the free surface. Equal volumetric flow rates at entrance and exit are prescribed. The pressure difference across the interface, or Laplace pressure, is predicted as a function of the helix geometry and contact angle. Local flow analysis (FEM) has been performed to determine viscous losses as a function of the dimensions of the support and the configuration of the free surface, where the free surface shapes are taken to be the equilibrium shapes computed for static conditions. The global model predicts that for a given helix geometry and contact angle and for a given flow rate below a critical value, there exists a range of channel volumes that give a stable flow. Preliminary experimental evidence suggests that a channel with an imposed flow rate can adjust its volume to achieve stable flow.   

Experimental measurement of vorticity flux across the interface of an unsteady breaking wave

The nature of the vorticity and vorticity flux on the air and water side of an unsteady breaking wave is examined using fully time-resolved Particle Image Velocimetry (PIV), with the aim of better understanding the physics of air-sea interaction. Results reveal regions of strong vorticity in the air, in the absence of wind, as well as distinct vortical regions in the water beneath the crest region, which persist through the breaking process; these regions of vorticity are mechanisms for mixing and transport. The near-surface vorticity is correlated with the viscous flux of vorticity at the surface on both sides of the air-water interface to gain further insight into the physical processes during breaking. The method used to calculate vorticity flux follows the methods presented in previous work [1,2]. Using this analysis, the physical flow characteristics associated with the vorticity flux can also be examined. [1] Gharib, M. and A. Weigand, \textit{J. Fluid Mech}. 321:59--86 (1996). [2] Dabiri, D. and M. Gharib, \textit{J. Fluid Mech}. 330:113-139 (1997).   

Playing with inclined circular hydraulic jumps

We have investigated the structure of the circular hydraulic jump, when the jet impacts an inclined plate. At low plate slope, quasi-circular shapes, evolving towards elliptic shapes are observed. At moderate inclinations, the upper and lower jumps become markedly different, and the lower jump is even rejected to infinity when a critical inclination is reached. Above this critical inclination, the jump is coupled to an outer dewetting contact line to give a specific object (expanding impact sheet feeding a curved rim in which the liquid is flowing tangentially). In this regime, both the position and curvature of the upper jump follows unusual scalings with the flow rate that completely differ from those observed on horizontal plates. Finally we have looked to metastable drops trapped in the circular jump at very small inclinations. As reported in a previous APS, the lowest position in the jump can become unstable and the drops oscillate around the jump perimeter. We show that this behavior requires very specific conditions of surface tension and viscosity and propose simple interpretations for the instability mechanism.   

Deformation of a liquid surface induced by an air jet

An experimental and theoretical study is performed to characterize the depression of a liquid surface due to an air jet exiting a nozzle from above. The Reynolds number of the jet is confined to a moderate range($\sim $100). In order to obtain more stable surface profiles, we use a viscous fluid (silicone oil) instead of water. Based on the data acquired from experiments, we find how the depth and diameter of the cavity are dependent on the radius and height of the nozzle, and the exit velocity of the jet. Theoretical explanations are provided both in the two dimensional (2-D) and three dimensional (3-D) cases. In the 2-D case, a free surface equation and the asymptotic expansion of its solution are obtained by employing a conformal mapping method. In the 3-D case where this technique fails, we propose a different model using an exact axisymmetric solution to Euler's equation.   

Flow patterns in free liquid film exposed to temperature gradient

Thermocapillary-driven flow induced in a free thin liquid film under a temperature gradient parallel to the free surfaces is examined with experimental and numerical approaches. Under a small temperature gradient, a two-dimensional flow inside the film is realized in which the fluid returns in the middle region of the film. By increasing the temperature gradient, instability takes place to realize a three-dimensional flow. The authors will introduce a unique flow pattern in the presentation.   

The impact of surface conditions on gas exchange across an air/water interface during mixed convection

The effect of surface conditions on the transport of oxygen across an air/water interface was investigated experimentally for mixed convection conditions. A wind/water tunnel was used to gather the requisite data and the resulting Sherwood numbers are presented as a function of the Rayleigh and Reynolds numbers. Wind speeds for both clean and surfactant covered surfaces were varied from 1 to 4 m/s in increments of 1 m/s. Water surfaces devoid of surfactant monolayers were studied, along with oleyl alcohol covered water surfaces. The surfactant monolayer existing on a tap water surface was also studied. The results show the effect of surface conditions, as well as the relative importance of free and forced convection on gas exchange.   

Surface flow, shapes and stability of rotating triangles on a water surface

We present an experimental study of polygons forming at the free surface of a water flow driven by a rotating bottom and confined to a stationary cylinder, as described in Jansson et al., Phys. Rev. Lett. {\bf 96}, 174502 (2006). In particular, we study the case of a triangular structure, either completely floating or with a dry center. For these structures, we present measurements of the surface flows, the surface shapes and the process of structure formation, and we analyze our results in terms of a collection of discrete vortices. We show that partial blocking of the surface flow destroys the triangular structure and reestablishes the circular symmetry.