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=ρw∞D/μRe=ρw∞D/μ, and the dimensionless angular velocity, Ω=ωD/(2w∞)Ω=ωD/(2w∞), where ρρ, μμ and w∞w∞ are the free-stream density, viscosity and velocity, respectively, and ωω is the angular velocity of the body. The parametric study covers the range 0≤Ω≤0.40≤Ω≤0.4 for Re<450Re<450, corresponding to laminar flow and moderate rotation velocities. It is shown that the (Re,Ω)(Re,Ω) parameter plane can be divided into four regions, corresponding to the destabilization of several instability modes. In the range 0≤Ω≲0.20≤Ω≲0.2, three different flow regimes take place as Re increases keeping constant ΩΩ: 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≃0.2Ω≃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≥0.225Ω≥0.225. An exhaustive study of the dependence of the drag and lift forces on ΩΩ and Re is also presented.