Aspect ratio effects on the leading-edge circulation and forces of rotating flat-plate wings

We investigate experimentally the effect of aspect ratio (AR) on the leading-edge vortex (LEV) circulation and lift force for flat-plate wings rotating from rest at 45° angle of attack. The objectives are to understand the influence of AR on the variation of LEV circulation with span and its scaling with kinematics, the tip vortex (TV) formation and its interaction with the LEV, as well as the lift force. Wings with AR = 1, 2, and 4 are tested, the tip Reynolds number (Re) is varied from 1,000 to 5,000, and the total stroke angles are either 120° or 360°. For Re_tip = 5, 000 and AR = 2 and 4, we use phase-locked, phase-averaged stereoscopic digital particle image velocimetry (S-DPIV) in multiple chordwise planes to reconstruct the time-varying, volumetric velocity and obtain circulation. The spanwise circulation of the total leading-edge (LE) flow, of the first LEV, and of a 25% chord square at the leading edge (LE) is computed, as well as the streamwise circulation of the TV; several scalings are tested. An increasing trend in the total circulation normalized by the tip velocity is found when plotted versus spanwise location, and the agreement is best for AR = 2 and 4 when the chord lengths traveled by the tip are matched. The trends of the circulation of the first LEV are similar to that of the total. Normalizing the circulation by the local velocity at a given spanwise location somewhat flattens the curves versus span away from the root and tip where, respectively, dividing by the small local velocities amplifies the data scatter, and tip-vortex effects are present. The AR = 4 curves are generally lower than AR = 2 inboard and higher outboard; the same trends are also observed for the first LEV. For the local-velocity-normalized circulation, there is a relatively good collapse of the data when plotted versus the angle of rotation or chord lengths traveled by the tip for multiple spanwise locations for a given AR. Considering the spanwise-averaged circulation, scaling by chord lengths traveled by the tip yields the best agreement in the averages between ARs for both the total and the first LEV circulation. After the initial growth the total circulation exhibits a gradual increase with chords traveled. However, the circulation of the first LEV for both ARs shows a plateau indicating an increased removal of spanwise vorticity at (s/c)_tip ≈ 3. When the independent variable is local chord lengths traveled, the circulation for both ARs agree early on then diverge, although all of the spanwise locations for both ARs, with the exception of 80% span, experience a circulation plateau before the end of their motion. For AR = 4, the breakdown process is evident in the circulation data for large angles and at spanwise locations greater than about 50% span; the breakdown is manifested as increased scatter in the AR = 4 circulation data. The trajectory of the LEV centroid and the spanwise flux of spanwise vorticity per unit area are both presented to illustrate significant factors that must be taken into account to properly characterize vortex strength in this type of highly three-dimensional flow. The effect of the TV and aft LEV tilt on the spanwise LEV circulation, which decreases near the tip, are discussed in the context of the TV circulation behavior and flow structures. The lift force is measured, and an invariance of lift coefficient is observed for a given AR and acceleration angle. Increasing AR has the effect of increasing the dimensional lift but decreasing the lift coefficient, suggesting that larger AR wings are less efficient in producing lift per unit area. The rate of lift coefficient increase after acceleration but before the constant-lift phase is shown to decrease with increasing AR. A lift impulse coefficient is computed from both the S-DPIV data and the force measurements for the case of Re = 5,000 and a rotation amplitude of 120° for both ARs, and compares favorably in slope which is directly related to the lift force.