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 study, 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 Reynolds number (Re = 255). The boundary conditions are 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 are discussed, and the critical or transitional values of the Strouhal (St) and normalized amplitude (A D) numbers are presented. It is shown that, at the fixed pitching amplitude, A D = 0.71, the 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 A D > 2. 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.

Linear and nonlinear perturbation analysis of the symmetry breaking in time-periodic propulsive wakes

“…used to describe this case : the Keulegan-Carpenter number KC = U/f D and the Reynolds number Re = U D/ν, where U is the maximum velocity of the cylinder, D is the cylinder diameter and ν is the fluid kinematic viscosity. We reproduce some results obtained experimentally by Dütsch et al [50] and numerically by Guilmineau et al [51] and Hosseinjani et al [52], at Re = 100 and KC = 5.…”

Investigations on vortex evolution and wake dynamics of bio-inspired pitching hydrofoils

“…Besides, the deflected wakes have great benefits to the production of the thrust. Hosseinjani and Ashrafizadeh 20 explained that the asymmetrical reverse Kármán vortex street can generate the side force, but its physics is still not understood well.

Figure 10.Spanwise vorticity at different k red . (a) 1.24; (b) 2.48; (c) 4.96.

…”

“…Besides, the deflected wakes have great benefits to the production of the thrust. Hosseinjani and Ashrafizadeh [21] explained that the asymmetrical reverse Kármán vortex street can generate the side force, but its physics is still not understood well. Reynolds number is also an important parameter to affect the performance and vortex evolution of the oscillating foils.…”