Unsteady force generation and vortex dynamics of pitching and plunging aerofoils

Abstract

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.

Analysis of Flow Timescales on a Periodically Pitching/Surging Airfoil

“…Similar pitching experiments on a flat plate at a lower Reynolds number between Re 5 × 10 3 and 2 × 10 4 performed by Baik et al [16] showed that the instantaneous angle of attack and reduced frequency k determined flow evolution and that the LEV separation occurred later in the motion period, or at a higher angle of attack, with increased k, in agreement with the results of Rival et al [17]. They showed that leading-edge vortex circulation tended to increase linearly with the phase of the airfoil motion, with a faster growth corresponding to a lower reduced frequency k.…”

“…On pitching and plunging flat plates, Baik et al [16] showed that, for k ≤ 0.5, the LEV circulation increased linearly up until vortex separation, corresponding to this optimal formation time, whereas at k > 0.5, the vortex was pinched off prematurely due to the reversal of the airfoil motion. In experiments measuring various plunging motions at k 0.2-0.33, Rival et al [17] also found that the formation of the leading-edge vortex agreed with this optimal vortex formation time and suggested that, if the stroke motion could be altered such that the LEV saturated at the peak of the motion, the unsteady lift from LEV formation and dynamic stall could be used most effectively.…”

Unsteady dynamics of rapid perching manoeuvres

“…Recent studies (Ol et al 2009;Baik et al 2012;Pitt Ford & Babinsky 2013) have shown that classical potential flow theory from Theodorsen (1935), von Kármán & Sears (1938 and…”

On the aerodynamic forces on heaving and pitching airfoils at low Reynolds number

“…With the introduction of non-zero angle of attack, the airfoil may generate both thrust and lift. Heaving and pitching airfoils have also been studied extensively [Anderson et al, 1998, Ramamurti and Sandberg, 2001, Read et al, 2003, Ashraf et al, 2011, Baik et al, 2012, Widmann and Tropea, 2015. Pitching modifies the flow around the airfoil and can, for some combinations of the motion parameters, increase the net value of thrust and the propulsive efficiency.…”