Numerical Analyses of the Flow Past a Short Rotating Cylinder

This work studies the three-dimensional flow dynamics around a rotating circular cylinder of finite length, whose axis is positioned perpendicular to the streamwise direction. Direct numerical simulations and global stability analyses are performed within a parameter range of Reynolds number Re=DU infinity/nu<500 (based on cylinder diameter D, uniform incoming flow velocity U infinity), length-to-diameter ratio AR=L/D <= 2 and dimensionless rotation rate alpha=D Omega/2U(infinity)<= 2 (where Omega is rotation rate). By solving Nav\-ier--Sto\-kes equations, we investigated the wake patterns and explored the phase diagrams of the lift and drag coefficients. For a cylinder with AR=1, we found that when the rotation effect is weak (0 <=alpha less than or similar to 0.3), the wake pattern is similar to the unsteady wake past the non-rotating finite-length cylinder, but with a new linear unstable mode competing to dominate the saturation state of the wake. The flow becomes stable for 0.3 less than or similar to alpha less than or similar to 0.9 when Re<360. When the rotation effect is strong (alpha greater than or similar to 0.9), new low-frequency wake patterns with stronger oscillations emerge. Furthermore, the stability analyses based on the time-averaged flows and on the steady solutions demonstrate the existence of multiple unstable modes undergoing Hopf bifurcation, greatly influenced by the rotation effect. The shapes of these global eigenmodes are presented and compared, as well as their structural sensitivity, visualising the flow region important for the disturbance development with rotation. This research contributes to our understanding of the complex bluff-body wake dynamics past this critical configuration.