Tadd Truscott

Water entry of spinning spheres

The complex hydrodynamics of water entry by a spinning sphere are investigated experimentally for low Froude numbers. Standard billiard balls are shot down at the free surface with controlled spin around one horizontal axis. High-speed digital video sequences reveal unique hydrodynamic phenomena which vary with spin rate and impact velocity. As anticipated, the spinning motion induces a lift force on the sphere and thus causes significant curvature in the trajectory of the object along its descent, similar to a curveball pitch in baseball. However, the splash and cavity dynamics are highly altered for the spinning case compared to impact of a sphere without spin. As spin rate increases, the splash curtain and cavity form and collapse asymmetrically with a persistent wedge of fluid emerging across the centre of the cavity. The wedge is formed as the sphere drags fluid along the surface, due to the no-slip condition; the wedge crosses the cavity in the same time it takes the sphere to rotate one-half a revolution. The spin rate relaxation time plateaus to a constant for tangential velocities above half the translational velocity of the sphere. Non-dimensional time to pinch off scales with Froude number as does the depth of pinch-off; however, a clear mass ratio dependence is noted in the depth to pinch off data. A force model is used to evaluate the lift and drag forces on the sphere after impact; resulting forces follow similar trends to those found for spinning spheres in oncoming flow, but are altered as a result of the subsurface air cavity. Images of the cavity and splash evolution, as well as force data, are presented for a range of spin rates and impact speeds; the influence of sphere density and diameter are also considered.

A spin on cavity formation during water entry of hydrophobic and hydrophilic spheres

United States. Office of Naval Research (University Laboratory Initiative Grant No. N00014-06-1-0445)

The upside-down water collection system of Syntrichia caninervis

Desert plants possess highly evolved water conservation and transport systems, from the root structures that maximize absorption of scarce ground water1–5, to the minimization of leaf surface area6 to enhance water retention. Recent attention has focused on leaf structures that are adapted to collect water and promote nucleation from humid air7–9. Syntrichia caninervis Mitt. (Pottiaceae) is one of the most abundant desert mosses in the world and thrives in an extreme environment with multiple but limited water resources (such as dew, fog, snow and rain), yet the mechanisms for water collection and transport have never been completely revealed. S. caninervis has a unique adaptation: it uses a tiny hair (awn) on the end of each leaf to collect water, in addition to that collected by the leaves themselves. Here we show that the unique multiscale structures of the hair are equipped to collect and transport water in four modes: nucleation of water droplets and films on the leaf hair from humid atmospheres; collection of fog droplets on leaf hairs; collection of splash water from raindrops; and transportation of the acquired water to the leaf itself. Fluid nucleation is accomplished in nanostructures, whereas fog droplets are gathered in areas where a high density of small barbs are present and then quickly transported to the leaf at the base of the hair. Our observations reveal natures optimization of water collection by coupling relevant multiscale physical plant structures with multiscale sources of water.

Cavity formation in the wake of a spinning sphere impacting the free surface

A spherical object impacting the free surface generatesboth a splash curtain and a subsurface air cavity. In the caseof a spinning sphere, the angular momentum combined withforward motion causes the sphere to move along a curvedpath, similar to a curve ball pitch in baseball. The hydrody-namics of a billiard ball diameter 5.7 cm impacting the freesurface with a downward vertical velocity of 7.5 m/s and aclockwise angular velocity of 232 rad/s are revealed throughhigh speed video imaging. The curved trajectory of thesphere is evident in Fig. 1. Figure 2 reveals the evolution ofthe splash curtain above the free surface as the sphere im-parts momentum into the fluid. Initially, at impact, the mo-mentum transfer forms a radial jet just above the free sur-face, until vertical growth outpaces radial expansion formingthe splash curtain Fig. 2 a . The curtain eventually col-lapses inward, forming a dome. As the sphere spins, it drawsfluid from the left side of the cavity causing the dome tobreakdown asymmetrically Fig. 2 b , in contrast to theaxis-symmetric dome in the case of surface impact by a non-spinning sphere. A bird’s eye view of the surface Fig. 3shows a wedge of fluid being pulled away from the left wallalong the equator of the sphere. The loss of fluid at the cavitywall hinders symmetrical growth of the splash curtain andresults in an asymmetrical collapse of the splash dome Fig.2 c . As the ball moves through the fluid, the wedgestretches and travels toward the right side of the cavity Fig.3 . Eventually the wedge impacts the opposite side of thecavity. This impact forces air to be ejected from the cavity;the ejected air forms a line of bubbles that can be seen atright in Fig. 1. As the ball travels along its curved trajectory,the cavity continues to elongate but no longer grows radially,eventually resulting in cavity pinch-off.Figure 1 was photographed by Brant Avondet and TaddTruscott.

Error Propagation Dynamics of PIV-based Pressure Field Calculations: How well does the pressure Poisson solver perform inherently?

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.

The water entry of slender axisymmetric bodies

We present a study of the forces, velocities, and trajectories of slender (length/diameter = 10) axisymmetric projectiles using an embedded inertial measurement unit (IMU). Three nose shapes (cone, ogive, and flat) were used. Projectiles were tested at vertical and oblique impact angles with different surface treatments. The trajectory of a half-hydrophobic and half-hydrophilc case impacting vertically was compared to the trajectory of symmetrically coated projectiles impacting the free surface at oblique angles. The oblique impact cases showed significantly more final lateral displacement than the half-and-half case over the same depth. The amount of lateral displacement was also affected by the nose shape, with the cone nose shape achieving the largest lateral displacement for the oblique entry case. Instantaneous lift and drag coefficients were calculated using data from the IMU for the vertical, half-and-half, and oblique entry cases. Impact forces were calculated for each nose shape and the flat nose shape experienced the largest impulsive forces up to 37 N when impacting vertically. The impact force of the flat nose decreased for the oblique entry case. The location of the center of pressure was determined at discrete time steps using a theoretical torque model and values from the IMU. Acoustic spectrograms showed that the sound produced during the water entry event predominately arises from the pinch-off for the cone and ogive nose shapes, with additional sound production from impact for the flat nose shape. Each test run was imaged using two Photron SA3 cameras.

Catastrophic cracking courtesy of quiescent cavitation

A popular party trick is to fill a glass bottle with water and hit the top of the bottle with an open hand, causing the bottom of the bottle to break open. We investigate the source of the catastrophic cracking through the use of high-speed video and an accelerometer. Upon closer inspection, it is obvious that the acceleration caused by hitting the top of the bottle is followed by the formation of bubbles near the bottom. The nearly instantaneous acceleration creates an area of low pressure on the bottom of the bottle where cavitation bubbles form. Moments later, the cavitation bubbles collapse at roughly 10 times the speed of formation, causing the bottle to break. The accelerometer data shows that the bottle is broken after the bubbles collapse and that the magnitude of the bubble collapse is greater than the initial impact. This fluid dynamics video highlights that this trick will not work if the bottle is empty nor if it is filled with a carbonated fluid because the vapor bubbles fill with the CO2 dissolved in the liquid, preventing the bubbles from collapsing. A modified cavitation number, including the acceleration of the fluid (a), vapor pressure (Pv), and depth of the fluid column (h), is derived to determine when cavity inception occurs. Through experimentation, visible cavitation bubbles form when the cavitation number is less than 0.5. The experiments, based on the modified cavitation number, reveal that the easiest way to break a glass bottle with your bare hands is to fill it with a non-carbonated, high vapor pressure fluid, and strike it hard.

Cavitation onset caused by acceleration

Significance In this paper we propose an alternative derivation of the cavitation number and validate the threshold. The proposed dimensionless number is more suitable to predict the cavitation onset caused by a sudden acceleration rather than a large velocity as prescribed by the traditional cavitation number. Systematic experiments were conducted for validation, confirming that the alternative cavitation number predicts the threshold at which cavitation will occur (Ca<1). Striking the top of a liquid-filled bottle can shatter the bottom. An intuitive interpretation of this event might label an impulsive force as the culprit in this fracturing phenomenon. However, high-speed photography reveals the formation and collapse of tiny bubbles near the bottom before fracture. This observation indicates that the damaging phenomenon of cavitation is at fault. Cavitation is well known for causing damage in various applications including pipes and ship propellers, making accurate prediction of cavitation onset vital in several industries. However, the conventional cavitation number as a function of velocity incorrectly predicts the cavitation onset caused by acceleration. This unexplained discrepancy leads to the derivation of an alternative dimensionless term from the equation of motion, predicting cavitation as a function of acceleration and fluid depth rather than velocity. Two independent research groups in different countries have tested this theory; separate series of experiments confirm that an alternative cavitation number, presented in this paper, defines the universal criteria for the onset of acceleration-induced cavitation.

The water-entry cavity formed by low Bond number impacts

We examine the evolution of the water-entry cavity formed by millimetric steel spheres with hydrophobic coatings striking the water surface. The impact creates an axisymmetric air cavity that expands radially before closing under the combined influence of hydrostatic pressure, surface tension, and dynamic pressure. At low Bond numbers, B = gR2 / 1, where R is the sphere radius, the liquid density, the surface tension, and g the gravitational acceleration, cavity collapse is driven primarily by surface tension and possesses features not readily observed at high Bond numbers, B 1, including longitudinal cavity ripples and multiple pinchoffs. The cavity evolution at Weber number, W= U2R / =110, B=0.088, corresponding to R=0.80 mm, U =310 cm /s is shown in Fig. 1. The time between successive images is 0.94 ms. Longitudinal ripples are observed to propagate down the cavity walls at speeds less than that of the sphere. The cavity pinches off approximately halfway between the free surface and the sphere. The vertical retraction of the upper cavity results in a Worthington jet, while the lower cavity oscillates while remaining attached to the sphere. The cavity evolution at W=420, B=0.14, corresponding to R=1.0 mm, U=540 cm /s is shown in Fig. 2. Images were captured above and below the free surface with two synchronized cameras. The time between successive images is 1.9 ms. The impact generates a splash curtain that falls inward, creating a dome that seals the cavity from above. Once the cavity is sealed, the cavity pressure decreases as the sphere descends and the cavity volume increases. Note the Rayleigh–Taylor instability that develops, leading to a jet that penetrates the cavity from above. Eventually, pinchoff occurs at depth; this process is repeated several times, with each successive pinchoff producing a bubble of progressively decreasing volume.

Water entry of deformable spheres

When a rigid body collides with a liquid surface with sufficient velocity, it creates a splash curtain above the surface and entrains air behind the sphere, creating a cavity below the surface. While cavity dynamics have been studied for over a century, this work focuses on the water entry characteristics of deformable elastomeric spheres, which has not been studied. Upon free surface impact, elastomeric sphere deform significantly, resulting in large-scale material oscillations within the sphere, resulting in unique nested cavities. We study these phenomena experimentally with high speed imaging and image processing techniques. The water entry behavior of deformable spheres differs from rigid spheres because of the pronounced deformation caused at impact as well as the subsequent material vibration. Our results show that this deformation and vibration can be predicted from material properties and impact conditions. Additionally, by accounting for the sphere deformation in an effective diameter term, we recover previously reported characteristics for time to cavity pinch-off and hydrodynamic force coefficients for rigid spheres. Our results also show that velocity change over the first oscillation period scales with a dimensionless ratio of material shear modulus to impact hydrodynamic pressure. Therefore we are able to describe the water entry characteristics of deformable spheres in terms of material properties and impact conditions.