Numerical simulation of the self-propulsive motion of a fishlike swimming foil using the δ^+-SPH model

The present work is dedicated to the application of the recently developed （δ＋ -SPH） scheme to the self-propulsive fishlike swimming hydrodynamics. In the numerical method, a particle shifting technique （PST） is implemented in the framework of δ-SPH, combining with an adaptive particle refinement （APR） which is a numerical technique adopted to refine the particle resolution in the local region and de-refine particles outside that region. This comes into being the so-called δ＋- SPH scheme which contributes to higher numerical accuracy and efficiency. In the fishlike swimming modeling, a NACA0012 profile is controlled to perform a wavy motion mimicking the fish swimming in water. Thanks to the mesh-free characteristic of SPH method, the NACA0012 profile can undergo a wavy motion with large amplitude and move forward freely, avoiding the problem of mesh distortion. A parallel staggered algorithm is adopted to perform the fluidstructure interaction between the foil and the surrounding fluid. Two different approaches are adopted for the fishlike swimming problem. In Approach 1, the foil is fixed and flaps in a free stream and in Approach 2, the wavy foil can move forward under the self-driving force. The numerical results clearly demonstrate the capability of the δ＋ -SPH scheme in modeling such kind of self-propulsive fishlike swimming problems.

Using spanwise flexibility of caudal fin to improve swimming performance for small fishlike robots

This paper examines the beneficial effects of the spanwise flexibility of the caudal fin for the improvement of the swimming performance for small fishlike robots. A virtual swimmer is adopted for controlled numerical experiments by varying the spanwise flexible trajectories and the spanwise flexible size of the caudal fin while keeping the body kinematics fixed. 3-D Navier-Stokes equations are used to compute the viscous flow over the robot. Elliptical, parabolic and hyperbola trajectories are chosen to describe the spanwise flexible profile of the caudal fin. According to the sign（positive or negative） of the phase difference of the swinging motion, the spanwise flexibility can be divided into the fin surface of ＂bow＂ and the fin surface of ＂scoop＂. It is observed that for both the fin surface of ＂bow＂ and the fin surface of ＂scoop＂, the spanwise elliptical trajectory has the optimal swimming velocity, thrust, lateral force, and efficiency. With comparisons, using the flexible caudal fin with the fin surface of ＂bow＂, the lateral force and the power consumption can be reduced effectively and the swimming stability can be increased while reducing little the swimming velocity and thrust. Meanwhile, using the flexible caudal fin with the fin surface of ＂scoop＂ can greatly improve the swimming velocity, thrust, and efficiency while increasing part of the lateral force and the power consumption. Three-dimensional flow structures clearly indicate the evolution process around the swimming robot. It is suggested that the fish, the dolphin, and other aquatic animals may benefit their hydrodynamic performance by the spanwise flexibility of the caudal fin.

Effect of head swing motion on hydrodynamic performance of fishlike robot propulsion

This paper studies the effect of the head swing motion on the fishlike robot swimming performance numerically. Two critical parameters are employed in describing the kinematics of the head swing： the leading edge amplitude of the head and the trailing edge amplitude of the head. Three-dimensional Navier-Stokes equations are used to compute the viscous flow over the robot. The user-defined functions and the dynamic mesh technology are used to simulate the fishlike swimming with the head swing motion The results reveal that it is of great benefit for the fish to improve the thrust and also the propulsive efficiency by increasing the two amplitudes properly. Superior hydrodynamic performance can be achieved at the leading edge amplitudes of 0.05L （ L is the fish length） and the trailing edge amplitudes of 0.08L. The unsteady flow fields clearly indicate the evolution process of the flow structures along the swimming fish. Thrust-indicative flow structures with two pairs of pressure cores in a uniform mode are generated in the superior performance case with an appropriate head swing, rather than with one pair of pressure cores in the case of no head swing. The findings suggest that the swimming biological device design may improve its hydrodynamic performance through the head swing motion.