On passive and active drag reduction of free-falling bodies in quiescent viscous fluid

Modes of drag reduction on surfaces interfacing with liquids have received a considerable amount of attention from researchers and industries due to the significantly associated advantages in terms of energy-savings and power consumption associated with various applications such as ships, underwater vehicles, piping infrastructures and microfluidic devices. One revolutionary technique to accomplish drag reduction on moving objects in liquids is to introduce a lubricating gas or vapour layer between the object surface and the ambient liquid via different strategies such as surface modification and by inducing the Leidenfrost effect. However, there are many open questions regarding the understanding, effectiveness and implementation of these drag reduction techniques. The main aim of the present study is to investigate the effect of various surface treatment techniques on the drag coefficient of a solid sphere and drag reduction by Leidenfrost effect on deformable liquid droplets in a free-falling experiment. This was accomplished by a newly designed and constructed experimental setup to facilitate the capture of the free-falling motion of both a solid sphere and a liquid droplet through a quiescent continuous viscous fluid phase in a vertical tank. The solid spheres used in the experiments were stainless-steel spheres with a diameter ranging from 4 mm to 7 mm. The spheres were surface-modified by a perflourodecyltrichlorosilane (FDTS) coating, roughened via an etching process and dry ice coating. No significant differences were found for the etched spheres compared with the unmodified spheres. Surprisingly, the drag coefficient of the FDTS sphere was increased by 13%. The dry ice coating successfully produced a substantial gas layer surrounding the free-falling spheres. However, due to issues with the uniformity of the coating, this method was abandoned. Following these, liquid gallium was used as the dispersed phase in free-falling deformable droplet experiments. Firstly, the effect of shape and deformation on the velocity and the drag coefficient of free-falling liquid gallium droplets in water were investigated for droplet diameters (spherical volume-equivalent) ranging from 2.67 mm to 5.56 mm under isothermal conditions with temperatures in the range of 30◦C to 70◦C. The initial shape of the droplets after detachment was found to be spherical. Spherical-oblate oscillations began immediately after the detachment of the droplet prior to the dampening of the oscillations into a final shape of an oblate-spheroid except for the smallest droplet size which remained spherical without any notable change in shape. It was found that the rhythmic change in shape induced the falling velocity to oscillate at a frequency double that of the aspect ratio. Moreover, increasing the viscosity ratio enhanced the amplitude of the oscillations. However, the oscillation frequencies were sensitive to the droplets’ size rather than their associated viscosity ratio. The experimental results reveal that for a deformed liquid gallium droplet with a terminal Reynolds number that varied in the range of 103 to 104, the drag coefficients were found to be larger than those associated with a solid sphere in the same Reynolds number range. Furthermore, the deformation is highly dependent on interfacial surface tension and inertial force, while the viscosity ratio and pressure distribution have negligible effect. Subsequently, the continuous phase was changed to a low boiling point perfluorinated liquid (FC-72) in order to investigate the drag reduction by Leidenfrost effect. The liquid gallium temperature was varied in the range of 40◦C to 170◦C to induce an inverted Leidenfrost effect. The fully-developed Leidenfrost regime was stable at a droplet temperature of 130◦C, and was illustrated by the vapour layer stream moving upward on the droplet surface. Unlike in water, the liquid gallium droplets in FC-72 formed a tear-drop shape. The drag coefficient calculated based on the maximum velocity achieved by the droplets revealed a drastic drag reduction of about 57% for the highest temperature droplet compared with the lowest temperature droplet. Numerical simulation based on the two-dimensional lattice Boltzmann model (LBM) was also carried out to study the velocity field and pressure distribution around a deformable droplet falling through an immiscible quiescent viscous liquid.