Wings In Steady Flow Research Articles

Normalized Lift: An Energy Interpretation of the Lift Coefficient Simplifies Comparisons of the Lifting Ability of Rotating and Flapping Surfaces

For a century, researchers have used the standard lift coefficient CL to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ½ρv 2, where v is the effective velocity of the wing. Because the lift coefficient was developed initially for fixed wings in steady flow, its application to other lifting systems requires either simplifying assumptions or complex adjustments as is the case for flapping wings and rotating cylinders.This paper interprets the standard lift coefficient of a fixed wing slightly differently, as the work exerted by the wing on the surrounding flow field (L/ρ·S), compared against the total kinetic energy required for generating said lift, ½v2. This reinterpreted coefficient, the normalized lift, is derived from the work-energy theorem and compares the lifting capabilities of dissimilar lift systems on a similar energy footing. The normalized lift is the same as the standard lift coefficient for fixed wings, but differs for wings with more complex motions; it also accounts for such complex motions explicitly and without complex modifications or adjustments. We compare the normalized lift with the previously-reported values of lift coefficient for a rotating cylinder in Magnus effect, a bat during hovering and forward flight, and a hovering dipteran.The maximum standard lift coefficient for a fixed wing without flaps in steady flow is around 1.5, yet for a rotating cylinder it may exceed 9.0, a value that implies that a rotating cylinder generates nearly 6 times the maximum lift of a wing. The maximum normalized lift for a rotating cylinder is 1.5. We suggest that the normalized lift can be used to evaluate propellers, rotors, flapping wings of animals and micro air vehicles, and underwater thrust-generating fins in the same way the lift coefficient is currently used to evaluate fixed wings.

The pitching delta wing

Delta wings in steady flow can provide high lift at large angles of attack and are therefore used on many highperformance aircrafts. However, the unsteady aerodynamic properties of a delta wing are practically unknown, although vital for operating and designing airplanes for poststall and other maneuvering. In this study, the flowfields around two pitching delta wings with apex angles of 90 and 60 deg were visualized in a towing tank at chord Reynolds numbers up to 3.5 xlO. The reduced frequency was varied in the range 0.05-3. The leadingedge separation vortex went through a growth-decay cycle with hysteresis during a pitching period. A distinct change of the separated flow was observed at a reduced frequency around ir.

An Automatic Adaptive Numerical Method for Lifting Surface Theories

For problems involving numerical lifting surface calculations, comparisons of the various approximate methods do not always yield satisfactory results. This paper presents a means of determining the accuracy of any approximate method without comparisons. Moreover, it enables the optimum ratio NS/NC (number of downwash chords/number of control points in the downwash chord) to be found automatically by just doing the necessary calculations to obtain any prescribed accuracy. For this purpose, a steepest descent method and an appropriate convergence theorem are used. Computations proceed along the direction of grad Igrad CL I in the NS-NC diagrams. Although this method is applied here mainly to vortex lattice methods (VLM) for wings in steady flow, it is a universal one applicable to any efficient unsteady VLMs or mode methods.

Force and pressure measurements on an airfoil oscillating through stall

Details of force, moment, and pressure distributions on a two dimensional, four foot chord, NACA 0012 airfoil, oscillating in pitch through stall, in a 7 ft. x 10 ft. low speed wind tunnel, are presented. Tests were run with the airfoil in a closed test section and also in a test section having four longitudinal slots in each sidewall set to provide minimum tunnel interference on the wing in steady flow. In unsteady flow, differences between the results for the closed and 2% open case are small. The dynamic stall process is not triggered by the bursting of a laminar separation bubble but rather by the separation of the turbulent boundary layer downstream of the bubble.