Self-propulsion of fishes-like undulating hydrofoil: A unified kinematics based unsteady hydrodynamics study

Abstract

Unsteady flow characteristics and propulsive performance during self-propulsion of various types of fishes-like undulating 2D NACA0012 hydrofoil are studied using a unified kinematic model. The model considers a range of non-dimensional wavelength of undulation λ∗ (0.8−∞), with the smaller value corresponding to body undulation of anguilliform fishes and the larger value corresponding to the caudal-fin pitching motion of carangiform fishes. The study is conducted at various frequency based Reynolds number Ref500−1750 at a constant maximum amplitude of undulation of 0.1. A level-set function based immersed interface method is used for the numerical simulations. Comparative analysis of dynamic-transient flow and propulsion characteristics of different types of fishes-like self-propulsion is presented. Time-wise varying dynamic-transient results are presented for flow patterns, propulsion velocity, net thrust force, and power input. After the onset of pitching or undulation, the vorticity patterns shows a dipole formation along with a jet formation based momentum excess behind the foil that leads to a net thrust force coefficient CTmnet. The dipole and the momentum excess disappears at the dynamic-steady state leading to zero CTmnet. It was found that the pitching as compared to the undulating foil accelerates faster and reaches a larger propulsion velocity. Further, the pitching based propulsion results in a fluctuating velocity and larger lateral force coefficient leading to instability. Furthermore, for the pitching motion, a smaller lateral force in the initial time period leading to maximum stability and a slightly larger propulsive efficiency is found during the initial as compared to later time periods. This work presents a detailed analysis of the dynamic-transient state leading to the dynamic-steady state for different types of fishes-like self-propulsion − which can be used for designing aquatic propulsion systems.