UC Berkeley

Part I: Vortical flows over spinning cones at angles of incidence

The aerodynamic performance of conically-shaped bodies are directly influenced by the flowsaround them. Flows over stationary cones develop symmetric trailing vortices near their leeward surface, where any induced lateral forces are neutralized; however, a cone spinning about its axis breaks the symmetry, resulting in unequal lateral forcing. To the author’s knowledge, there are no comprehensive experimental studies that characterize the asymmetric vortex systems behind spinning cones, a flow problem that has many implications on the trajectory and stability of spin-stabilized bodies. Moreover, the laminar-turbulent transition within the boundary layer has significant implications on skin friction and drag for incompressible flows; over spinning cones, transitions form as circular and spiral waves resulting from cross-flow and centrifugal instabilities. To date, the effects of large angles of incidence on the laminar-turbulent transition are not well-understood.

Vortical flows over spinning cones with half-angles 10 (deg) ≤ θc ≤ 45 (deg) at angles of incidence, 0 ≤ α ≤ 36 (deg), are visualized using a smoke-wire technique, and measurements of the flows are made using a planar particle image velocimetry technique. The Reynolds numbers for all cones are O(10,000) and the range of rotational speed ratios is 1 ≤ |S| ≤ 3. Symmetric vortex triads composed of primary, secondary, and tertiary vortices are aligned parallel with the leeward surface of nonspinning cones at sufficient angles of incidence, α ≳ θc. The triads grow in size and strength as they are continuously fed by the adjacent shear layer. Asymmetries in vortex systems over spinning cones are characterized by anti-cyclonic vortices in the counter-rotating meridian and cyclonic vortices in the co-rotating meridian. Generally, the anti-cyclonic vortices grow as they embrace the surface of the cone and are pushed in the direction of rotation. At sufficient distances from the vertex of the cone, the anticyclonic vortices burst and initiate turbulent events downstream. Contrarily, cyclonic vortices readily detach from the leeward surface and cease to grow as they are cut off from the vorticity supply; an increase in SD or α expedites the detachment of cyclonic vortices.

Distinct behaviours of the cyclonic and anti-cyclonic vortices arise for flows over the most slender cone, θc = 10 (deg). The distinction is attributed to vortex triads forming in closer vicinity to one another as the half-angle of the cone decreases. For θc = 10 (deg), cyclonic vortices are significantly influenced by the induced flows of the anti-cylonic vortices; they are pulled past the plane of symmetry into the counter-rotating meridian and smothered between the anti-cyclonic vortex triad and the surface of the cone, initiating detachment of anti-cyclonic vortices. Distinct flows are also observed over the largest half-angle cone corresponding to θc = 45 (deg). At nonzero angles of incidence, the stagnation point departs from the vertex of the cone and monotonically shifts along the windward surface. Low-speeds are measured near the vertex of the cone at zero incidence, resembling stagnation flows near the central axis of a disc. Regular vortex shedding events in the wake region are detected in the flow visualizations, a common characteristic of flows over discs and, more generally, bluff bodies.

Boundary layer instabilities are detected and studied in the smoke streakline images. Regularly spaced wave patterns and small-scale wavy rolls consistently mark streaklines near the surfaces of the cones. The rolls form near the leeward surface of spinning cones and in streaklines ingested deep within the rotating boundary layer; hence, they are likely signatures of centrifugal spiral wave instability. The rolls leave small-scale waves on detached portions of trailing vortices that deteriorate their coherency. Contrarily, angled wave patterns form on streaklines over the entire surface of the cones in both nonspinning and spinning cases; hence, they indicate signatures of cross-flow instabilities. The flow visualizations of boundary layer instabilities primarily serve as motivation for future, more comprehensive studies.

Part II: Vortical flows over a spinning disc at incidence

Flows normal to the surface of stationary discs exhibit periodic motions in their wakes attributed to vortex shedding events. The present study reveals and characterizes, for the first time, the origins of the shedding vortices near the upstream surface of a disc. Flows are studied over a disc at incidence angles between 0 and 36 (deg), both fixed and spinning with a rotational speed ratio of 2, and the Reynolds number of 27,000. A smoke-wire technique is used for flow visualization and planar particle image velocimetry for measurements near the plane of symmetry. Coherent vortical structures are observed near the upstream surface of the disc over the full range of the incidence angle. As the structures grow in size, they align themselves parallel to the surface of the disc and shed into the wake region. Two vortex shedding modes are observed. The first is dominant at low angles of incidence, up to ∼ 18 (deg). At the limiting case of normal flow, the vortical structures shed into the wake at the Strouhal number of about 0.2. At incidence beyond 18 (deg), a secondary mode becomes dominant that appears as a soliton on the vortical structures. It originates near the leading edge of the disc, traverses towards the trailing edge, and sheds into the wake region nearly twice as frequent as the first mode. The flows over spinning discs generally mimic the stationary disc flows; however, centrifugal forces affect the formation and decay of the vortical structures. Centrifugal effects leave cross-stream instability features on the vortical structures that are likely attributed to spiral wave instabilities within the boundary layer.