Surface texture, boundary-layer transition, and drag on a swimmer’s head: a computational study across the sphere drag crisis

Abstract

A competitive swimmer’s head, approximated as a sphere, travels at 1.6-2.2 m/s (Re = 3.2-4.4 × 10⁵), spanning the sphere drag crisis. Ridged caps are marketed as tripping the boundary layer to trigger the crisis at lower velocity. Whether they do is unknown: towing experiments cannot isolate the head, and, to our knowledge, no computational study has examined a cap surface. This study performed the first controlled computational comparison of a smooth sphere and an idealized crown-textured cap, using unsteady Langtry–Menter transition-model simulations at four velocities with identical meshing parameters and a fixed time step. At 1.6-2.0 m/s, no drag difference was resolved; at 1.8 and 2.0 m/s, differences above 2.5 % were excluded. At 2.2 m/s, near sprint pace, the cap’s drag was 31 ± 21 % (k = 2) higher, owing to intermittent high-drag, high-lateral-force episodes absent on the sphere. Pressure drag exceeded 92 % of the total. In the model’s first assessment against the sphere drag crisis, both boundary layers remained laminar yet separated at 102-105°, the turbulent value measured above the crisis, not at the expected laminar 79-82°. The drag difference thus arose in the wake, not through boundary-layer transition. These results suggest that effective cap relief would need to alter the separation or the wake rather than merely reduce skin friction; for simulation practice, the intermittency field, not the separation angle, shows whether transition is predicted. Agreement in separation angle alone can therefore give a false impression that the drag-crisis physics has been captured.