Comparative Analysis of the Hydrodynamic Performance of Arc and Linear Flapping Hydrofoils

In order to improve the hydrodynamic performance of flapping hydrofoils and solve the problem of insufficient hydrodynamic force in plain river network areas, in this study, we consider the more realistic swing of fish tails and propose an arc flapping method, the coupled motion of which has three degrees of freedom: heave, pitch, and lateral displacement. Two flapping methods, positive arcs and negative arcs, were derived on the basis of the lateral displacement direction. By using the finite volume method (FVM) and overlapping grid technology, a numerical simulation was conducted to compare and analyze the pumping performance of three types of flapping hydrofoil, namely, linear, positive arcs, and negative arcs, in order to further provide guidance for the structural optimization of bionic pumping devices. The results showed that the wake vortex structures of the three flapping modes all had anti-Kármán vortex streets, but the wake vortex of linear flapping deflected upward, and the wake vortex of positive arc flapping tended to be further away in the flow field. In one cycle, thrust was always generated by the positive arc flapping hydrofoil and the linear flapping hydrofoil, but the thrust coefficient curve of the positive arc flapping hydrofoil was more stable than that of the linear flapping hydrofoil, and the peak value was reduced by 46.5%. In addition, under the conditions of a flow rate of 750 $\mathrm{L}·{\mathrm{s}}^{-1}$ and an average head of 0.006 m, the pumping efficiency of the positive arc flapping hydrofoil reached 35%, thus showing better pumping performance than the traditional linear flapping hydrofoil under conditions with ultra-low head.