Research at the Experimental Hydrodynamics Laboratory

Free Surface Hydrodynamics

Water Entry by Spheres      Breaking Waves     Naval Ballistics

Cover of the Gallery of Fluid Motion, Physics of Fluids, 2006 image taken from our winning gallery poster (2005).

Water Entry by Spinning and Non-spinning Spheres T. T. Truscott & A. H. Techet Summary The complex hydrodynamics of water entry by a spinning sphere are investigated experimentally for low Froude numbers. Standard billiard balls are fired down at the free surface with controlled spin around one 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 curve ball pitch in baseball. The splash and cavity dynamics are highly altered, however, for the spinning case compared to impact of a sphere without spin. Depending on the spin rate, the splash curtain and cavity form and collapse asymmetrically with a persistent wedge of fluid emerging across the center of the cavity. 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 across a range of spin rates for a constant impact speed.  Relevant parameters include the Froude Number at impact: Fr = Vo/sqrt(gd) and the Spin Parameter: S = ωr/Vo, where ω is the rotation rate of the sphere (rad/s) and r = d/2 is the sphere radius, Vo is the impact velocity and g is gravity. Spin parameter is simply the ratio of the tangential surface velocity to the downward/forward motion of the sphere. CHECK OUT THE HiGH-SPEED VIDEOS BELOW! Cover of the Gallery of Fluid Motion, Physics of Fluids, 2006 image taken from our winning gallery poster showing the splash generated by a spinning sphere. Spinning Spheres Spin greatly affects the trajectory of the sphere after impact. The lift force resulting from the sphere’s rotation, causes the cavity formed with the hydrophobic sphere to curve. The inertially driven features are consistent with the non-spinning sphere (e.g. cavity collapse, etc), however several major differences can be seen in the case of spin. The billiard balls in the videos below impact the free surface at about 1.7 m/s, the same speed as the non-spinning spheres in the videos above. Again the sphere on the left is hydrophilic and the sphere in the videos on the right is hydrophobic. The spheres are both spinning at ~100 rad/s.   In the hydrophobic case, the spinning motion causes a wedge of fluid to cut through the middle of the cavity, due to the no-slip condition on the sphere. This wedge impacts the far wall of the cavity, resulting in a line of bubbles, which eject out on the left side of the cavity (see videos of hydrophobic sphere, side view). From the top the cavity cross section looks like a cardiod shape. The wedge has completely split the cavity into two. Surface coating and impact velocity can dramatically affect cavity formation during water entry of spheres. Duez et al. present a theoretical limit, dependent on impact velocity and surface static wetting angle, below which air cavities no longer form. We show that transverse spin alters the spheres surface velocity distribution to straddle this theoretical limit, resulting in cavity formation over half of the sphere and none on the other half, and yields similar results to the case of a sphere dropped without spin, at the same impact speed, when its surface is half hydrophilic and half hydrophobic. The ultimate finding presented herein reveals the dramatic similarities between the effect of surface conditions, specifically static wetting angle, and the effect of spin on the formation of both the water entry cavity and the wedge. Through images obtained from high speed video, we demonstrate the ability to produce a fluid wedge that bisects the cavity without using spin, by dropping a half-and-half sphere that has a hydrophobic surface treatment on one hemisphere (left) and a hydrophilic treatment (right) on the other. (Movies are Quicktime MOV files). (N.B. Movies files cannot be used or posted elsewhere without permission from the authors.) Hydrophilic Hydrophobic Half-and-Half (no spin) (top view)    (side view)     Image series of spinning spheres with increading spin parameters from Truscott & Techet (2009) JFM. Note the spheres are spinning in the opposite direction from the videos above. Non-spinning Spheres Simply changing the surface coating on a sphere yields vastly differing results, even for the case without spin. The videos below show an impact of a billiard ball that is not spinning.  The billiard ball has markings on it for image detection.  It is falling at about 1.7 m/s.  The top images are viewed directly from above. The sphere in the videos on the left was cleaned such that it was hydrophilic (static contact angle less than 90 degrees). No splash/cavity results up to a critical impact velocity. The videos on the right show a sphere that has been coated with a hydrophobic surface treatment. The static contact angle is approximately 120 degrees. For hydrophobic spheres, a cavity nearly always results. Hydrophilic Hydrophobic (top view)   (side view)    APS Gallery of Fluid Motion Video 2008   PIV of the radial and vertical velocity magnitudes (left and center) and vorticity (right) around a sphere entering the water forming a vapor cavity in it’s wake. Publications.htmlPublications.htmlshapeimage_2_link_0
Cover from the 25 April 2009 (vol. 625) cover of Journal of fluid mechanics taken from our work on spinning spheres. Our paper [2.11] on this topic appears in this issue. Publications.htmlshapeimage_3_link_0