We present results on the drag on, and the flow field around, a submerged rectangular normal flat plate, which is uniformly accelerated to a constant target velocity along a straight path. The plate aspect ratio is chosen to be $AR=2$ to resemble an oar blade in (competitive) rowing, the sport which inspired this study. The plate depth, i.e. the distance from the top of the plate to the air–water interface, the plate acceleration and the plate target velocity are varied, resulting in a plate width based Reynolds number of $4\times 10^{4}\lesssim Re\lesssim 8\times 10^{4}$. In our analysis we distinguish three phases; (i) the acceleration phase during which the plate drag is enhanced, (ii) the transition phase during which the plate drag decreases to a constant steady value upon which (iii) the steady phase is reached. The plate drag force is measured as function of time which showed that the steady-phase plate drag at a depth of $1/5$ plate height (20 mm depth for a plate height of 100 mm) increased by 45 % compared to the plate top at the surface (0 mm). Also, it is shown that the drag force during acceleration of the plate increases over time and is not captured by a single added mass coefficient for prolonged accelerations. Instead, an entrainment rate is defined that captures this behaviour. The formation of starting vortices and the wake development during the time of acceleration and transition towards a steady wake are studied using hydrogen bubble flow visualisations and particle image velocimetry. The formation time, as proposed by Gharib et al. (J. Fluid Mech., vol. 360, 1998, pp. 121–140), appears to be a universal time scale for the vortex formation during the transition phase.

Abstract

The effect of finger spread on overall drag on a swimmer's hand is relatively small, but could be relevant for elite swimmers. There are many sensitivities in measuring this effect. A comparison between numerical simulations, experiments and theory is urgently required to observe whether the effect is significant. In this study, the beneficial effect of a small finger spread in swimming is confirmed using three different but complementary methods. For the first time numerical simulations and laboratory experiments are conducted on the exact same 3D model of the hand with attached forearm. The virtual version of the hand with forearm was implemented in a numerical code by means of an immersed boundary method and the 3D printed physical version was studied in a wind tunnel experiment. An enhancement of the drag coefficient of 2% and 5% compared to the case with closed fingers was found for the numerical simulation and experiment, respectively. A 5% and 8% favorable effect on the (dimensionless) force moment at an optimal finger spreading of 10° was found, which indicates that the difference is more outspoken in the force moment. Moreover, an analytical model is proposed, using scaling arguments similar to the Betz actuator disk model, to explain the drag coefficient as a function of finger spacing.

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