Freestream-turbulence decay and the sphere drag crisis predicted by the Langtry–Menter transition model

Reynolds-averaged Navier–Stokes prediction of the drag crisis of bluff bodies, such as sports balls and a swimmer’s head, requires a transition model whose predictions depend on the freestream turbulence intensity. However, two-equation models dissipate this turbulence before it reaches the body, and the consequence for the predicted crisis has not been quantified. This study mapped the drag crisis predicted by the Langtry–Menter transition model for a smooth sphere using 70 steady axisymmetric computations at Reynolds numbers of 1 × 10⁵–1.14 × 10⁶, with three inlet intensities and freestream decay uncontrolled or suppressed by sustaining terms. The computations were verified on three grids and validated against measurements. Uncontrolled decay lowered the intensity at the body increasingly with Reynolds number. The predicted crisis Reynolds number collapsed to within 7 % onto a single power law of the intensity at the body, for both decay treatments. At the experimental intensity, the predicted crisis Reynolds number was 26–60 % below the measured one: the drag fell before a separation bubble formed, and the steady wake recovered too much base pressure. Hence, the intensity reaching the body, not the inlet value, governs transition-model predictions near the drag crisis and should be controlled or reported.