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.
Highlights
Birds, insects and marine creatures use, and benefit from, the phenomena associated with flapping wings, tails and fins
The Kármán vortex street (KVS) regime generates drag; the Aligned Vortex Street (AVS) is a neutral regime with no net momentum transfer to the main flow; the reverse Kármán vortex street (RKVS) is a thrust producing regime; and the asymmetric reverse Kármán vortex street regime (ARKVS) is a thrust and lift generating flow regime
For the particular symmetric airfoil used in this study, two groups of flapping scenarios are studied at a fixed Reynolds number (Re = 255)
Summary
Insects and marine creatures use, and benefit from, the phenomena associated with flapping wings, tails and fins. Numerical Simulation of the Wake Structure and Thrust/Lift Generation of a Pitching Airfoil at Low Reynolds Number Via an Immersed Boundary Method 335 amplitude and flapping mode on the lift/thrust generation and momentum loss. He et al (2012) have studied transition and symmetry-breaking in the wake of a flapping airfoil by an immersed boundary method (IBM) They have presented results that show flow patterns from the KVS regime to the RKVS one. The physics behind the wake structure, the transition from one flow regime to another and the thrust/lift performance of a sinusoidally flapping symmetric airfoil over a wide range of Strouhal numbers and oscillation amplitudes is studied. Non-physical velocities are assigned to the Eulerian grid points outside of the flow domain These numerical results are some by-products of the IBM computations. Where: n is the number of grid points; φ is the velocity component
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