Session P16: Free-Surface Flows: Interaction with Physical Structures

Vented tube cavity deflation

When objects enter water, air cavities form and persist deep underwater. Cavities decrease drag for energy-saving applications but there are instances where it is beneficial to dissipate cavities before they collapse naturally. This research proposes a method of cavity dissipation by means of cavity deflation after water entry. The method utilizes a tube with radial vent holes attached to a spherical projectile in a manner to provide the air in the cavity a means to escape after deep seal. High-speed video and image processing are utilized to quantify cavity deflation. If the vented tube length is larger than the lower cavity length (at deep seal), the cavity will deflate. We propose a theoretical critical tube length required for deflation to occur for varying projectile sizes and impact conditions. Further, we show that the deflation amount is influenced by experimental parameters such as vented tube length, diameter and impact velocity. Finally, we find that cavity deflation reduces both noise and the forces on the sphere after deep seal.   

Reconfiguration of a Highly-Flexible Plate Impacting a Free Surface

Passive reconfiguration of flexible structures readily occurs in biological structures through fluids such as air and water. This phenomenon has been studied in detail to understand how structures such as seagrass and leaves conform to more streamline deformed structures under drag force in flow media. In this talk, the reconfiguration of highly flexible plates during water impact is experimentally investigated. The model is a V-shape wedge, which is made of two highly flexible cantilevered plates connected by a rigid bar at the apex. As the wedge falls into the water, the deformation of the flexible bottom plates due to impact is captured using high-speed photography. The displacement and acceleration of the model is recorded using a potentiometer and accelerometer, respectively. Particle Image Velocimetry (PIV) will be utilized to quantitatively evaluate the fluid velocity and pressure surrounding the plate. Simultaneous measurements are then analyzed to study the correlation between passive reconfiguration and hydrodynamic loading exerted to the plates. The experimental measurements and results presented in this talk will shed light on drag reduction techniques on highly-flexible plates near a free surface.   

Water entry of spheres into a rotating liquid

The transient cavity dynamics during water entry of a heavy, non-rotating sphere impacting a rotating pool of liquid is studied experimentally, numerically and theoretically. We show that the pool rotation advances the transition of the cavity type – from deep seal to surface seal – marked by a reduction in the transitional Froude number. The role of the dimensionless rotational number $\mathcal{S} = \omega R_0/U_0$ on the transient cavity dynamics is unveiled, where $R_0$ is the sphere radius, $\omega$ the angular speed of the liquid and $U_0$ the impact velocity. The rotating background liquid has two discernible effects on the cavity evolution. Firstly, an increase in the underwater pressure field due to centripetal effects; and secondly, a reduction in the pressure of airflow in the cavity neck near the water surface. The non-dimensional pinch-off time of the deep seal shows a robust 1/2 power-law dependence on the Froude number, but with a reducing prefactor for increasing $\omega$. Our findings reveal that the effects of a rotating background liquid on the water entry can be traced back to the subtle differences in the initial stage splash and the near-surface cavity dynamics.   

Computational investigation of water entry of solid objects with various nose curvatures

Water entry of solid objects is relevant in many applications. Following the impact of a solid on the

water free-surface, an air-entraining cavity forms. Previous studies have identified four general types of

cavities: deep, surface, shallow and quasi-static. Although with advancements in experimental methods,

image capturing techniques, and high performance computing the underlying physics are becoming better

understood, the challenge of predicting the resulting cavity shape still remains. The dynamics strongly

depend on fluid and solid properties, as well as impact parameters. To improve our understanding on cavity

formation and its shape, we present 3D multiphase flow simulations investigating the effect of nose shape

and Weber number on cavity formation. In our study, a stainless steel cylinder is used where the curvature

of the leading edge (nose) is varied from concave to convex, resulting in various cavity seals and splashing

crowns upon water entry.   

Shape effects in the water entry of panels

We consider the water entry of falling two-dimensional rigid panels with low deadrise angles. Through theory and experiment, we examine the influence of panel shape on purely vertical trajectories and assess the effectiveness of the Wagner model, which assumes ideal fluid and imposes severe approximations on the geometric aspects of the problem.  Despite these limitations, the model has been surprisingly successful in describing qualitative and approximating quantitative aspects of the pressure during forced water entry of wedges.  In the present work, we provide analytical solutions for the free trajectories of a class of surfaces, and compare with tabletop-scale experiments with several drop heights.  One of the more interesting testable predictions is that surfaces whose profile curves upwards more strongly than a parabola will continue to accelerate, while profiles of weaker power will decelerate.   

The effect of pitch angle on the oblique impact of a flexible plate on a water surface

The oblique impact of a flexible rectangular plate (length 108 cm, width 41 cm) on a water surface is studied experimentally. The plate is made of 6061 aluminum with a thickness of 6.61 mm and is mounted to a dynamometer through a pinned connection along each of the short edges. The undeformed plate is tilted with a nonzero pitch angle (α) relative to the still water surface while the two short edges remain horizontal and perpendicular to the motion trajectory of the plate. During the impact, the horizontal and vertical components of the plate velocity are kept constant between the passage of the two short edges through the still water level. Time resolved measurements of the impact force and moment, the under-plate spray root and the out-of-plane plate deflection are performed. By varying the impact velocity and the pitch angle, the effect of several parameters is explored. It is found that the effect of the normal impact velocity dominates at a single pitch angle over the given range of plate motion trajectories. With the same magnitude of the normal velocity, a smaller pitch angle results in a stronger impact, featured by greater impact force and stronger interaction between the fluid motion and the structural dynamics.   

Flapping, Flexible Plates in Close Proximity to a Free Surface

Deriving inspiration from manta rays, reconfiguration of flexible structures can provide desirable thrust to serve as an alternative propulsion method. The scope of the research project includes understanding the fluid-structure interaction of a very flexible flapping plate with prescribed vertical oscillatory motion. This talk will consist of an exploration of passive reconfiguration of the flapping plate at various distances from the free surface. Plate deformation will be significant due to the low flexural rigidity of the structure. The deforming side view of the plate will be measured using high-speed video images and a gradient based edge detection technique. Measurements of the surrounding fluid will include drag on the plate, fluid pressure, and fluid velocity surrounding the plate. At distances far away from the free surface, the flapping plates will reconfigure to a streamlined shape which decrease drag on the structure. As the structure is raised in the water column, the deformed shape will change based on its proximity to the free surface as waves are generated.   

Rotation in Soft Lubricated Hertzian Contacts

Forces associated with relative sliding of lubricated soft surfaces are relatively well understood. However, experiments show that the surface deformation can also produce an elastohydrodynamic torque, which  has only been characterized in the limit of non-conforming surfaces (Saintyves et al. 2020). In this work, we analyze this torque on a lubricated cylinder sliding parallel to the surface of an elastic substrate, for the full range of sliding velocities from low-velocity Hertzian contact to high-velocity non-conforming contact. We numerically solve Reynolds lubrication theory in the thin fluid layer, coupled with the equilibrium equations of the elastic solid, both for a thin elastic layer and a thick elastic substrate. We then use these solutions to calculate the resulting rotation rate when the cylinder is freely suspended in the fluid.  In the limit of small sliding velocities, which corresponds to a vanishingly thin film of entrained fluid, we show that the cylinder rotates as if it were purely rolling. The dimensionless rotation rate  decreases at larger sliding speeds due to an increase in the fluid layer thickness and non-conformality of the surfaces.  We find agreement of the rotation rate with experiments and develop analytical approximations in the limits of small and large sliding velocities. Our results suggest opportunities to control elastohydrodynamic lubrication through the application of external torques.    

A 2D Loosely Coupled Model of a Vertical Wedge

Fluid-structure interactions are a fundamental problem in the context of naval vehicles and are increasingly challenging to examine when structures are highly deformable. A partitioned, loosely-coupled procedure is used to numerically predict the dynamics of a thin, flexible plate subjected to water entry. The fluid subdomain is solved using a nonlinear hydrodynamic model based on Vorus (1996) and later expanded on by Xu (1998) and Judge (2000). The model is often viewed as a computationally practical compromise between the exact solution to the nonlinear, ideal flow boundary-value problem and the Wagner (1932) family of asymptotic theories. The structural subdomain is solved using a finite element plate model formulated for large, dynamic displacements. Material nonlinearities are not considered in this work, but the elastic modulus will be varied as a function of time to study the impact of stiffness control on plate dynamics. Validation of the water entry portion of the code will be performed against existing experimental data for a pair of plates forming a V-shaped wedge. These will be conducted for two types of boundary conditions: (1) closed boxed, fixed on all edges, and (2) cantilevered, fixed on one edge and free on all other edges.   

Experimentally obtained velocity and pressure fields of an open channel flow around a cylinder using RIM-SPIV

The quantification of velocity and pressure fields over streambeds is important for predicting sediment mobility and water exchange between stream and sediment interstitial spaces. The latter is typically referred as hyporheic flow, which consists of surface water that flows through the streambed sediment pores. In this paper, we report an experimental investigation of the time-averaged velocity and pressure field, quantified in a set of laboratory experiments using stereo Particle Image Velocimetry with a refractive index-matched fluid, for an open channel flow around a submerged vertical cylinder as a model for plant stalk over a plane bed of coarse granular sediment.  Full velocity and pressure fields were generated up to and around the cylinder and directly adjacent to the steam bed. The pressure field was calculated from the velocity field using an Omni-Directional, Rotating Ray integration methodology to solve the Reynolds-averaged Navier-Stokes equations. This is the first time that such a velocity and pressure field is characterized experimentally for a free surface flow with irregular floor contour.   

Air Entrainment Measurements of a Ship Hull Turbulent Boundary Layer

Air entrainment occurs in turbulent free-surface boundary layers that grow along the hulls of ships. The boundary layer characteristics and air entrainment depend on the ship speed and position along the hull. A ship boundary layer simulation device consisting of a surface-piercing stainless-steel belt driven from rest by two vertically oriented rollers generates a temporally evolving boundary layer that emulates the spatially evolving boundary layer of a ship hull. The radius, depth, and streamwise position of bubbles entrained into the belt's boundary layer are extracted from images captured by a stationary high-speed camera recording at 1000 fps for 10 s in runs with final belt speeds ranging from 3.5 m/s to 5 m/s. Five runs at each belt velocity were performed to reach statistical convergence of the bubble measurements. Bubbles with radii down to 0.25 mm are resolved within the effective camera field of view (3.52 cm x 5.67 cm) and depth of field (6.5 cm). The bubbles in each image are tracked across the measurement area and the vertical and horizontal components of the bubble velocities are determined from the trajectories. Bubble characteristics are explored as functions of bubble radius and depth.   

Does an air-layer cushion hydrodynamic slamming loads?

Hydrodynamic slamming events are found in the crashing of waves against coastal/breakwater structures, against the walls of shipping containers due to sloshing of liquid cargo, when a diver lands onto water, or during the splash-down landing of sea planes and spacecrafts. In all such events, the ambient air is trapped between the liquid and the impactor on its own accord, but its role in affecting the hydrodynamic loads is not clear. The highest loads are produced when the impact is perfectly parallel - this appears contradictory to the presence of a trapped air `cushioning' layer, which is also the thickest under the same conditions. We shed light on this feature of solid-liquid slamming loads by performing careful experiments with a flat plate that is made to slam perfectly parallel on a bath of water. In the absense of a cushioning air layer, a parallel impact would produce loads with a time singularity, but spatially uniform across the impactor. Whereas with the air cushioning layer, different regions of the plate contact the liquid at different times, such that the loading has a non-uniform spatial distribution. We show how the intially entrapped air-layer's shape, and its time evolution effects the impact pressures at different locations on the plate. Using high-fidelity sensors, we show that at the location where the air layer is at its thickest, there is a very clear reduction of the time-integrated loads (or pressure impulses).