Abstract
The thrust generated by heaving airfoil in incompressible flow is studied both numerically and theoretically. It is found that the behaviors of leading-edge vortex (LEV) under different airfoil’s transverse velocities have an important influence on the thrust. When this velocity is small, the LEV is advected downstream regularly; however, as transverse velocity increases, the LEV can be pushed back to the leading edge again and pass over it to the opposite side of the airfoil. In cases with the LEV passing over the leading edge, the maximum transient thrust can be enhanced by several times compared with that in the single-stroke motion. The reason and critical condition for the occurrence of passing-over leading-edge vortex (PO-LEV) are found. Based on the source of the pressure Poisson equation, a near-field force theory is developed and used together with the boundary vorticity flux (BVF) theory to clarify the thrust enhancement mechanisms.
Highlights
When an airfoil flaps at a relatively large amplitude, the boundary layer around its head would separate and roll into a concentrated leading-edge vortex (LEV)
This vortex pair has different behavior compared with one single LEV, and it departs from the airfoil more quickly, making the newly formed LEV in it unable to pass over the leading edge again in most situations
The behavior of leading-edge vortex (LEV) in heaving motion and its role in thrust generation are numerically investigated, of which the underlying physical root is analyzed by a weighted pressure-source theory combined with the boundary vorticity flux (BVF) theory
Summary
When an airfoil flaps at a relatively large amplitude, the boundary layer around its head would separate and roll into a concentrated leading-edge vortex (LEV). Due to the strong links between the wake and the force experienced by a body, the vortical wake is named the “footprint” of the flapping wing by Zhang.22 This wake view is important, when the heaving frequency is high, the symmetry between upstroke and downstroke is broken and wake flow may be chaotic, making it impossible to identify regular vortex street. For unsteady flow, the well-known impulse theory (along with the unsteady vortex-force theory29,30) involves some vorticity-moment integrals, of which the objectivity (the independence of the calculated forces on the choice of the origin in taking moments) has to be ensured by the vanishing total vorticity in the integration domain This property makes it difficult to focus only on the force caused by an individual local vortical structure of particular interest, such as the LEV. A near-field theory based on the source of the pressure Poisson equation that belongs to the velocity-pressure formulation is developed and used together with boundary vorticity flux (BVF) theory to uncover the thrust-enhancing mechanisms by the PO-LEV
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