Numerical Simulation of the Wake Structure and Thrust/Lift Generation of a Pitching Airfoil at Low Reynolds number via an Immersed Boundary Method

Abstract

In this paper, an accurate computational algorithm in the context of immersed boundary methods is developed and used to analyze an incompressible flow around a pitching symmetric airfoil at Re=225. The boundary condition can be accurately implemented by an iterative procedure applied at each time step and the pressure is also updated simultaneously. Flow phenomena, observed at different oscillation frequencies and amplitudes, are numerically modeled and the physics behind the associated vortex dynamics is explained. It is shown that there are four flow regimes associated with four wake structures. These include three symmetric flow regimes, with adverse, favorable and no vortex effects, and an asymmetric flow regime. The phenomena associated with these flow regimes and the critical or transition Strouhal (St) and normalized amplitude (numbers are discussed. It is shown that at the fixed pitching amplitude,  , Transition from adverse (drag generation) to favorable (thrust generation) symmetric flow regime occurs at St=0.23. Moreover, at this particular amplitude, transition from symmetric to asymmetric regime occurs at St=0.48. It is also shown that at St=0.22, the wake is always deflected and the flow is asymmetric for large-enough amplitudes ().  The dipole vortices and lift generation are two characteristics of asymmetric vortex street. This numerical study also reveals that the initial phase angle has a dominant effect on the appearance of dipole vortices and vortex sheet deflection direction.  Numerical results are in good agreement with the available experimental data.