Numerical Studies on the Hydrodynamic Patterns and Energy-Saving Advantages of Fish Swimming in Vortical Flows of an Upstream Cylinder

Abstract

Fish in nature can extract the vortex energies from the environment to enhance their swimming performance. This paper numerically investigated the hydrodynamic characteristics and the energy-saving advantages of an undulating fish-like body behind the vortical flows generated by an upstream cylinder. The numerical model was based on a robust ghost cell immersed boundary method for the solution of incompressible flows around arbitrary complex flexible boundaries. We examined the dynamic characteristics, the swimming performance, and the wake structures of the downstream fish under different locations and diameters of the cylinder in a wide range of Strouhal numbers. It was found that the average drag coefficient was significantly reduced in the presence of the upstream cylinder, while the RMS (root mean square) lift coefficients were very close for different locations and diameters of the cylinder as well as in the fish-only case. Therefore, the downstream fish gain efficiency and thrust enhancement by capturing energies from the vortex flows, which are more significant for smaller Strouhal numbers (St). However, the swimming efficiency converges to near 0.12 at St = 1.2 for different locations and diameters of the upstream cylinder, just slightly higher than that of the fish-only case. The fish can experience the thrust in not only the von-Kármán vortex street, but also the reversed one. In addition, the fish can be situated in the extended shear layer region and the fully developed wake region dependent on the position and diameter of the upstream cylinder, leading to abundant wake modes such as the splitting, coalescing, and competing of vortices.