Coriolis effects enhance lift on revolving wings

At high angles of attack, an aircraft wing stalls. This dreaded event is characterized by the development of a leading edge vortex on the upper surface of the wing, followed by its shedding which causes a drastic drop in the aerodynamic lift. At similar angles of attack, the leading edge vortex on an insect wing or an autorotating seed membrane remains robustly attached, ensuring high sustained lift. What are the mechanisms responsible for both leading edge vortex attachment and high lift generation on revolving wings? We review the three main hypotheses that attempt to explain this specificity and, using direct numerical simulations of the Navier-Stokes equations, we show that the latter originates in Coriolis effects.

Figure 1

Illustration of the numerical setup. The fixed wing is modeled as a nonslip wall and embedded in a rotating (rigid body motion) flow. The latter is imposed via velocity Dirichlet conditions at the boundaries of the computational domain. The Navier-Stokes equations are directly solved in the fixed reference frame, taking into account additional centrifugal and/or Coriolis source terms.

Figure 2

Lift coefficient $C_L$ against distance $\delta$ traveled by the wing. $C_L$ is obtained for cases A $(\times )$, B $(\circ )$, C $(+)$, D $(\square )$, and $0 (-)$ by nondimensionalizing the lift force of the wing using the mean wing speed along the span $\widetilde{V_{\infty }}$.

Figure 3

Comparison of $Q>0$ criterion isosurfaces obtained for cases A (first column), B (second column), C (third column), and D (fourth column) at five distances of travel $\delta =0.8$ (first row), $1.6$ (second row), $2.4$ (third row), $3.2$ (fourth row), and 4 (fifth row).

Figure 4

Contours of streamwise (left column) and spanwise (right column) components of the Coriolis term obtained for case C at midspan. Contours are superimposed to $Q>0$ criterion isolines for three distances of travel $\delta =0.8$ (first row), $2.4$ (second row), and 4 (third row).