Laminar flow past a spinning bullet-shaped body at moderate angular velocities

We present a numerical study of the flow past a spinning bullet-shaped body of length-to-diameter ratio L/D=2, focusing on the evolution of the forces and flow regimes that appear depending on the values of the two governing parameters, namely the Reynolds number, Re = ρ w ∞ D / μ , and the dimensionless angular velocity, Ω = ω D / ( 2 w ∞ ) , where ρ , μ and w ∞ are the free-stream density, viscosity and velocity, respectively, and ω is the angular velocity of the body. The parametric study covers the range 0 ≤ Ω ≤ 0.4 for Re < 450 , corresponding to laminar flow and moderate rotation velocities. It is shown that the ( Re , Ω ) parameter plane can be divided into four regions, corresponding to the destabilization of several instability modes. In the range 0 ≤ Ω ≲ 0.2 , three different flow regimes take place as Re increases keeping constant Ω : axisymmetric, frozen and spiral flow regimes respectively; the latter leading to a swirling configuration of vortices curling up around the axis, caused by a combination of the frozen mode and the vortex shedding. However, at Ω ≃ 0.2 , a new frozen spiral mode takes place for large enough values of Re, where two counter-rotating vortices spiral around the axis, as a result of a lock-in process of the vortex shedding associated to the unsteady spiral regime, being this mode the single unstable one existent for Ω ≥ 0.225 . An exhaustive study of the dependence of the drag and lift forces on Ω and Re is also presented.