Drag reduction by gas layers and streamlined air cavities attached to free-falling spheres

Abstract

The general objective of this thesis is to conduct experiments on sphere free-falling in liquid that advance our understanding of the drag reduction on solids moving in liquid by means of lubricating gas layers and attached streamlined air cavities. Part I of the thesis investigates the effect of thin air layers, naturally sustained on superhydrophobic surfaces, on the terminal velocity and drag force of metallic spheres free- falling in water. The surface of 20 mm to 60 mm steel or tungsten-carbide spheres is rendered superhydrophobic by a simple coating process that uses a commercially available hydrophobic agent. By comparing the free-fall of unmodified spheres and superhydrophobic spheres, in a 2.5 meters tall water tank, it is demonstrated that even a very thin air layer (~ 1 – 2 μm) that covers the freshly dipped superhydrophobic sphere, can reduce the drag force on the spheres by up to 80 %, at Reynolds numbers 105 to 3×105, owing to an early drag crisis transition. Part II of the thesis investigates the drag reduction by means of the dynamic Leidenfrost vapor-layer sustained on the surface of heated metallic spheres free-falling in a fluorocarbon liquid, FC-72 (perfluorohexane). In these experiments we employed two tall liquid tanks: a 3 meter tall 14 cm wide tank and a 2 meter tall 20 × 20 cm cross-section tank with a heater device. These tanks are significantly larger than the tanks used in prior studies and allow us to track the extended fall trajectories and to compare the drag on room-temperature no-vapor-layer spheres to that of heated Leidenfrost vapor-layer spheres. Analysis of the extended free-fall trajectories and acceleration, based on the sphere dynamic equation of motion, enables the accurate evaluation of the vapor-layer-induced drag reduction, without the need for extrapolation. We demonstrate that the drag on the Leidenfrost sphere in FC-72, can be as low as CD = 0.04 ± 0.01, or an order of magnitude lower than the values for the no-vapor-layer spheres in the subcritical Reynolds number range. This drag reduction extends into the supercritical Reynolds number range. The analysis method developed herein, to describe the sphere trajectories, can be applied in other related studies. Part III of the thesis examines a recently demonstrated phenomenon of the formation of stable-streamlined gas cavity following the impact of a heated Leidenfrost sphere on a liquid surface or a superhydrophobic sphere on water. The sphere encapsulated in a teardrop-shaped gas cavity was found to have near-zero hydrodynamic drag due to the self-adjusting streamlined shape and the free-slip boundary condition on the cavity interface. Here it is shown that such cavities can be formed following the water impact from a sufficient height of non-superhydrophobic spheres with water contact angles between 30° and 120°. In this case the streamlined cavity is attached just above the sphere’s equator, instead of entirely wrapping the sphere. Nevertheless, this sphere with attached cavity has near-zero drag and predetermined free-fall velocity in compliance with the Bernoulli law of potential flow. Last, the effect of surfactant addition to the water solution is investigated. The shape and fall velocity of the sphere with streamlined cavity formation were unaffected by the addition of low-surface-modulus synthetic surfactants, but was destabilised when a solution containing high-surface-modulus surfactants, such as soaps were used.