Flow Structure on a Rotating Wing: Effect of Radius of Gyration

Abstract The flow structure on a rotating wing (flat plate) is characterized over a range of Rossby number Ro = rg/C, in which rg and C are the radius of gyration and chord of the wing, as well as travel distance rgΦ/C, where Φ is the angle of rotation. Wings having low aspect ratio AR = 1, and moderate aspect ratio AR = 2 are considered. Stereoscopic particle image velocimetry (SPIV) is employed to determine the flow patterns on defined planes and, by means of reconstruction, throughout entire volumes. Images including Q-criterion, spanwise vorticity, spanwise velocity, downwash velocity, tangential velocity, vorticity flux and helical density are employed to represent the flow structure. These quantities are represented both with iso-surfaces, and on sectional slices along the span.The flow structure on a low aspect ratio wing is characterized for a range of radius of gyration rg/C, at a travel distance well after the onset of motion. When the radius of gyration is small, the leading-edge, tip and root vortices are highly coherent, with large dimensionless values of Q in the interior regions of all vortices, and large downwash between these components of the vortex system. For increasing radius of gyration, however, the vortex system rapidly degrades, accompanied by loss of large Q within its interior, and downstream displacement of the region of large downwash. These trends are accompanied by increased deflection of the leading-edge vorticity layer away from the surface of the wing, and decreased spanwise velocity and vorticity flux in the trailing region of the wing, which are associated with the degree of deflection of the tip vortex across the wake region. Radius of gyration also affects development of the sectional flow structure determined at the midspan of the wing. Combinations of large radius of gyration rg/C and travel distance rgΦ/C lead to separated flow patterns, similar to those observed on rectilinear translating wings at high angle of attack. In the extreme case, where the wing travels a distance corresponding to a number of revolutions, the highly coherent flow structure is generally preserved if the radius of gyration is small; it degrades substantially, however, at larger radius of gyration. The three-dimensional flow structure is also characterized on a moderate aspect ratio wing, at low and moderate radii of gyration, for a range of travel distance. Increase of the radius of gyration reduces the influence of rotation on the flow structure. At small radius of gyration, a coherent leading-edge vortex develops rapidly, then persists over a range of travel distance. At moderate radius of gyration, this leading-edge vortex is replaced by an arch vortex, which develops over a larger travel distance than the leading-edge vortex; it is eventually swept into the wake of the wing. The subsequent vortical structures on the wing are much less coherent, and these structures resemble a separated shear layer typical on a translating wing at high angle of attack α. The foregoing classes of vortical structures are associated with distinctive patterns of helical density, downwash, and tangential velocity. Taken together, the above results demonstrate the critical influence of radius of gyration on flow structure coherence for a range of wing aspect ratio. When the parameter rg is small, a coherent vortex system forms rapidly on a rotating wing, and this vortex system persists as the wing continues to rotate at constant angular velocity. When the parameter rg is increased to a moderate value, the flow structure development is not as rapid, and coherent vortical structures do not persist as the wing rotates at constant angular velocity.