Eric A. Gillies

Hydrodynamic propulsion of human sperm

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.

Alleviation of Airfoil Dynamic Stall Moments via Trailing-Edge-Flap Flow Control

Trailing-edge-flap flow control for the mitigation of large negative pitching moments and negative aerodynamic damping caused by helicopter rotor blade dynamic stall was studied by means of computational fluid dynamics. A discrete vortex method was used for the simulations. The model geometry was a NACA 0012 airfoil oscillating in an α(t) = 15 deg + 10 deg sin(ωt) motion at the reduced frequency of k = 0.173. The freestream flow conditions were of M = 0.117 and Re = 1.463296 x 10 6 . The flap actuation was a brief pulse signal of a sinusoidal shape

Fins improve the swimming performance of fish sperm: a hydrodynamic analysis of the siberian sturgeon Acipenser baerii

The flagella of sturgeon sperm have an ultrastructure comprising paddle‐like fins extending along most of their length. These fins are seen in several other marine and freshwater fish. The sperm of these fish are fast swimmers and are relatively short lived: it is therefore tempting to think of these fins as having evolved for hydrodynamic advantage, but the actual advantage they impart, at such a small length scale and slow speed, is unclear. The phrase “the fins improve hydrodynamic efficiency” is commonly found in biological literature, yet little hydrodynamic analysis has previously been used to support such conjectures. In this paper, we examine various hydrodynamic models of sturgeon sperm and investigate both swimming velocity and energy expenditure. All of the models indicate a modest hydrodynamic advantage of finned sperm, in both straight line swimming speed and a hydrodynamic efficiency measure. We find a hydrodynamic advantage for a flagellum with fins, over one without fins, of the order of 15–20% in straight line propulsive velocity and 10–15% in a hydrodynamic efficiency measure.

The flow field around a rotor in axial descent

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.

ALLEVIATION OF ROTOR BLADE DYNAMIC STALL VIA TRAILING EDGE FLAP FLOW CONTROL

A trailing-edge flap flow control for the mitigation of large negative pitching moments and the associated negative damping during helicopter rotor blade dynamic stall was studied by means of CFD. A discrete vortex method was used for the simulations. The model geometry was a NACA 0012 airfoil, oscillating in a fi(t) = 15o + 10osin(!t) motion at the reduced frequency of k=0.173. The freestream flow conditions were M=0.117 and Re=1,463,296. The flap actuation was a brief pulse signal and it was shown that for optimum results upward flap deflection for the duration of about the 1/3 of the oscillation time period should be employed. The pulse signal should start in the 3rd quarter of the azimuth. Detailed analysis of the flowfield showed that the trailing-edge vortex (TEV), induced by the downstream convecting dynamic stall vortex (DSV), is responsible for the occurence of large negative pitching moments and negative damping. The flap flow control technique proved to be successful in mitigating these eects by displacing the TEV to a higher location where the DSV could only push it o the trailing edge, thus eliminating its eect. The method was shown to be promising for other cases from the helicopter flight envelope as well.