Unsteady aerofoil flows are often characterized by leading-edge vortex (LEV) shedding. While experiments and high-order computations have contributed to our understanding of these flows, fast low-order methods are needed for engineering tasks. Classical unsteady aerofoil theories are limited to small amplitudes and attached leading-edge flows. Discrete-vortex methods that model vortex shedding from leading edges assume continuous shedding, valid only for sharp leading edges, or shedding governed by ad-hoc criteria such as a critical angle of attack, valid only for a restricted set of kinematics. We present a criterion for intermittent vortex shedding from rounded leading edges that is governed by a maximum allowable leading-edge suction. We show that, when using unsteady thin aerofoil theory, this leading-edge suction parameter (LESP) is related to the A 0 term in the Fourier series representing the chordwise variation of bound vorticity. Furthermore, for any aerofoil and Reynolds number, there is a critical value of the LESP, which is independent of the motion kinematics. When the instantaneous LESP value exceeds the critical value, vortex shedding occurs at the leading edge. We have augmented a discrete-time, arbitrary-motion, unsteady thin aerofoil theory with discrete-vortex shedding from the leading edge governed by the instantaneous LESP. Thus, the use of a single empirical parameter, the critical-LESP value, allows us to determine the onset, growth, and termination of LEVs. We show, by comparison with experimental and computational results for several aerofoils, motions and Reynolds numbers, that this computationally inexpensive method is successful in predicting the complex flows and forces resulting from intermittent LEV shedding, thus validating the LESP concept.
Experimental studies of the flow topology, leading-edge vortex dynamics and unsteady force produced by pitching and plunging flat-plate aerofoils in forward flight at Reynolds numbers in the range 5000–20 000 are described. We consider the effects of varying frequency and plunge amplitude for the same effective angle-of-attack time history. The effective angle-of-attack history is a sinusoidal oscillation in the range $\ensuremath{-} 6$ to $2{2}^{\ensuremath{\circ} } $ with mean of ${8}^{\ensuremath{\circ} } $ and amplitude of $1{4}^{\ensuremath{\circ} } $. The reduced frequency is varied in the range 0.314–1.0 and the Strouhal number range is 0.10–0.48. Results show that for constant effective angle of attack, the flow evolution is independent of Strouhal number, and as the reduced frequency is increased the leading-edge vortex (LEV) separates later in phase during the downstroke. The LEV trajectory, circulation and area are reported. It is shown that the effective angle of attack and reduced frequency determine the flow evolution, and the Strouhal number is the main parameter determining the aerodynamic force acting on the aerofoil. At low Strouhal numbers, the lift coefficient is proportional to the effective angle of attack, indicating the validity of the quasi-steady approximation. Large values of force coefficients (${\ensuremath{\sim} }6$) are measured at high Strouhal number. The measurement results are compared with linear potential flow theory and found to be in reasonable agreement. During the downstroke, when the LEV is present, better agreement is found when the wake effect is ignored for both the lift and drag coefficients.
The flight maneuver of perching is abstracted as a linear pitch ramp, with and without a deceleration in the free-stream direction. We consider, first, experimental-computational comparison for flowfield and aerodynamic force coefficients for an SD7003 airfoil pitching from α = 0º to 45º; and second, an experimental survey of reduced frequency and pivot point for a range of flat plate pitching cases from 0º to 90º. The computational approach is 3D Large Eddy Simulation, and the experimental approach is by three degree of freedom electric motion-rig in a water tunnel. Accurate flowfield resolution in deep-stall is seen to require a large spanwise extent of computational domain. Meanwhile, experiment can be plagued with blockage, and dynamic blockage was seen to behave differently than static blockage. Even very low reduced frequencies of motion give lift overshoot beyond static stall, but comparatively large frequencies are necessary before the lift curve slope changes, either due to rate effects or acceleration effects. Moving the pitch pivot point further aft tends to attenuate both lift and drag production, and pitching about the three-quarter chord point cancels the rate-effect, in agreement with quasi-steady linear airfoil theory. Surprisingly, the aerodynamic coefficient history differs little between cases with and without streamwise deceleration, except towards the very end of the motion. The implication is that perching-type of ground tests or computations can be adequately conducted in a steady free-stream.
Direct force measurements and qualitative flow visualization were used to compare flow field evolution versus lift and drag for a nominally two-dimensional rigid flat plate executing smoothed linear pitch ramp manoeuvres in a water tunnel. Non-dimensional pitch rate was varied from 0.01 to 0.5, incidence angle from 0 to 90°, and pitch pivot point from the leading to the trailing edge. For low pitch rates, the main unsteady effect is delay of stall beyond the steady incidence angle. Shifting the time base to account for different pivot points leads to collapse of both lift/drag history and flow field history. For higher rates, a leading edge vortex forms; its history also depends on pitch pivot point, but linear shift in time base is not successful in collapsing lift/drag history. Instead, a phenomenological algebraic relation, valid at the higher pitch rates, accounts for lift and drag for different rates and pivot points, through at least 45° incidence angle.
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