Abstract
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 Gharibet 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.
Highlights
In rowing athletes generate a propulsive force by means of a rowing oar blade
This causes a reaction force from the water at the other end of the oar, the oar blade, which together with the force at the handle generates the propulsive force at the oar lock, the pivot point on the boat
The cases h = 0 mm and h = 20 mm both show a symmetric wake of similar size, but the latter has a large amount of vorticity very close to the plate which, we conjecture, explains the maximum steady-phase drag CD found for this plate depth (h = 20 mm), see figure 4
Summary
In (competitive) rowing athletes generate a propulsive force by means of a rowing oar blade. During propulsion the oar blade is submerged close to the surface and the athlete exerts a force on the handle of the oar. To achieve this, understanding of the flow field around the oar blade during this propulsive phase is vital It appears that a rowing oar blade moves along a circular path during the drive phase, its motion is all but trivial. When observed from an Earth-bound reference frame the blade moves along a complex cycloid path and is subject to large accelerations and decelerations (Caplan, Coppel & Gardner 2010). This makes the flow around an oar blade highly dynamic and complex with the presence of a free surface possibly further complicating the flow dynamics
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