Numerical investigation of hydrodynamic characteristics of fish-like undulation using the adaptive dynamic-grid method

To investigate the hydrodynamics of undulatory swimming, a key issue in numerical analysis is to determine the correlation between undulatory locomotion and the flow characteristics. In this study, a novel dynamic-grid generation method, the adaptive control method, is implemented to deal with the moving and morphing boundaries in an unsteady flow field at all Reynolds numbers. This method, based on structured grids, can ensure the orthogonality and absolute controllability of the grids and is performed to precisely simulate the wake and the boundary layer. The NACA0010 wing is employed as a two-dimensional (2D) body model of a fish in the simulations. To maintain the calculation stability, the increase stage of the amplitude is defined as a smooth transitional stage. Analysis of hydrodynamic coefficients reveals that undulation results in a significant increase of frictional force in laminar flow (Re <= 104). However, the undulation also results in a reduction of the frictional force when the fish swims in turbulent flow (Re >= 106). The vorticity distribution and the Q-criterion are both used to accurately capture the shedding vortexes in the wake. Furthermore, these vortex pairs have a substantial impact on the turbulence and the wake, in which the turbulent kinetic energy and the turbulent viscosity ratio both decrease at Re >= 106. The wake of an undulatory fish presents different vortex patterns with various kinematic parameters. When the phase velocity is greater than the incoming velocity and the wave number is sufficiently large, thrust is yielded, accompanying the distinct reverse Karman Street in the wake.