The detailed fluid mechanics of sperm propulsion are fundamental to our understanding of reproduction. In this paper, we aim to model a human sperm swimming in a microscope slide chamber. We model the sperm itself by a distribution of regularized stokeslets over an ellipsoidal sperm head and along an infinitesimally thin flagellum. The slide chamber walls are modelled as parallel plates, also discretized by a distribution of regularized stokeslets. The sperm flagellar motion, used in our model, is obtained by digital microscopy of human sperm swimming in slide chambers. We compare the results of our simulation with previous numerical studies of flagellar propulsion, and compare our computations of sperm kinematics with those of the actual sperm measured by digital microscopy. We find that there is an excellent quantitative match of transverse and angular velocities between our simulations and experimental measurements of sperm. We also find a good qualitative match of longitudinal velocities and computed tracks with those measured in our experiment. Our computations of average sperm power consumption fall within the range obtained by other authors. We use the hydrodynamic model, and a prototype flagellar motion derived from experiment, as a predictive tool, and investigate how sperm kinematics are affected by changes to head morphology, as human sperm have large variability in head size and shape. Results are shown which indicate the increase in predicted straight-line velocity of the sperm as the head width is reduced and the increase in lateral movement as the head length is reduced. Predicted power consumption, however, shows a minimum close to the normal head aspect ratio.

Measurements of the flow field around a model rotor descending axially into its own vortex wake have been performed using particle image velocimetry (PIV). At low descent rates, the expected cylindrical down-flow structure below the rotor is observed. At slightly higher descent rate, the flow enters the so-called vortex ring state (VRS) where the vorticity from the rotor accumulates into a toroidal structure near the rotor tips, and a large recirculation zone forms above the rotor disk. In the VRS, the flow below the rotor shows a significant upwards component, with a small up-flow zone penetrating right up to the rotor disk. Measurements show there to be a range of descent rates just before the onset of the VRS over which the flow may be interpreted to be in an incipient VRS condition. In this range, analyses of individual PIV measurements indicate that the flow near the rotor intermittently switches between the down-flow topology found at lower descent rates and the flow topology found in the fully developed VRS. The frequency of excursions of the flow into the VRS topology increases as the descent rate of the rotor is increased until, at high enough descent rate, the flow remains locked within its toroidal state.

The vortical flow originated from the tip of a NACA 0012 rectangular wing is described in its initial formation and development over a rounded and a squared tip. Smoke visualizations show the rolling-up kinematic and evolution of the vortical systems moving the plane towards the trailing edge. The presence of intense secondary vortices affects the primary vortex unsteadiness and shape during the formation and in the early wake. Stereoscopic Particle Image Velocimetry is used to describe vorticity, axial velocity and turbulent kinetic energy distributions of the vortex during the formation and in the early wake at different angles of attack of the wing. The rolling-up of the vorticity sheet around the vortex system is strongly influenced by the vortex shape and the intensity of secondary vortices. Turbulence coming from secondary structures and shear layers is wrapped into the roll-up of the vortex and high levels of turbulence are measured in the vortex core. However, a laminar vortex core is observed for the lower angle of attack in the early wake. Comparing the meandering of the vortex for the two wingtip geometries, two different sources of the vortex fluctuation in the wake are identified: the interaction of secondary vortices moving around the primary vortex and the rolling-up of the vorticity sheet. Lastly, measurements in the wake of the wing at zero incidence are also presented showing a distinctive counter rotating vortex pair.

No abstract

No abstract