Comparative numerical analysis of the flow pattern and performance of a foil in flapping and undulating oscillations

Nature presents a variety of propulsion, maneuvering, and stabilization mechanisms which can be inspired to design and construction of manmade vehicles and the devices involved in them, such as stabilizers or control surfaces. This study aims to elucidate and compare the propulsive vortical signature and performance of a foil in two important natural mechanisms: flapping and undulation. Navier–Stokes equations are solved in an ALE framework domain containing a 2D NACA 0012 foil moving with prescribed kinematics. All simulations are carried out using a pressure-based finite volume method solver. The results of time-averaged inline force versus Strouhal number (St) show that in a given Reynolds number (Re), the flapping oscillations begin to produce thrust at a smaller St, and with a greater slope than undulatory oscillations. However, consumed power of the flapping foil versus St varies with considerably higher values and greater slope than undulating foil. In addition, efficiency graphs show similar ascending–descending behaviors versus St, with greater “peak propulsive efficiency” for the undulating foil. Furthermore, one of the most important differences between the vortical structures of flapping and undulatory oscillations is the distinguishable appearance of leading edge vortices in the wake of the flapping foil without observable ones in the wake of undulating foil. Finally, the formation and dissipation patterns of distinct vortices in the wakes of both oscillating foils vary with St.