Unsteady pitching flat plates

Abstract

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.

Three-dimensional flow structures and unsteady forces on pitching and surging revolving flat plates

“…Following thin airfoil theory and integrating the sectional contribution over the span of the wing, the theoretical estimation of this circulatory force component is given as (Ellington 1984;Granlund et al 2013;Sane and Dickinson 2002): where φ is the angular velocity of the revolving motion, α is the angular velocity of the pitch-up motion and x 0 is the nondimensional distance of the pitching pivot point from the leading edge.…”

“…The delay is shown to be in accordance with the behavior of the spanwise flow which is affected by the interaction between the tip vortex and revolving dynamics. Further analysis shows that the enhanced force generation of the revolving-pitching wing during the pitch-up phase originates from: (1) increased magnitude and growth rate of the LEV circulation; (2) relatively favorable position and trajectory of the LEV and the starting vortex; and (3) generation of was studied by Granlund et al (2013). They showed the effects of the pitch rate and the pitch pivot point location on the time history of lift and drag in conjunction with the flow-field evolution.…”

Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows

“…High-fidelity simulations of moving and flexible airfoils to characterize unsteady phenomena at low Reynolds numbers have been performed by Visbal et al [70]. Garmann and Visbal [25] and Granlund et al [29] have investigated vortex structures on pitching flat plates in detail through computational and experimental methods, respectively. Pitt and Babinsky [55], Baik et al [3], and Rival et al [61] have studied the effects of leading edge vortices using experimental techniques.…”

Airfoil in a high amplitude oscillating stream

“…Other studies examine the pure pitch motion of airfoils. These investigations focus more on the load variations due to deep dynamic stall and the generation of a strong leading edge vortex (Granlund, Ol & Bernal 2013;Bross & Rockwell 2014). More recently, symmetric airfoils performing pure pitch motion in fully attached flow were numerically investigated and the influence of their thickness was compared to Theodorsen's theory (Motta, Guardone & Quaranta 2015).…”