Numerical Study On Undulatory Propulsion

In this paper,the hydrodynamics,the flow characteristics and the wake structure of the undulatory swimming fish are numerically investigated.The three-dimension undulatory plates are also studied preliminarily.The main work and some conclusions are as follows:A novel adaptive control dynamic-grids generation method based on two-dimensional body fitted grids is developed,which offers a solution to the application of high-precision structured grids in the complicated moving and deforming boundary flow fields.The adaptive control method manages to generate updated high-precision body fitted structured grids in each time step according to the movement and deformation of flow field boundaries.With this new method,advantages of structured grids in the accuracy and rate of generation,and the applicability of turbulence models,could be made full use of.The NACA0010 wing is taken as the two-dimensional body of fish,and the simulated body undulates actively in unbounded oncoming flow.The analysis of hydrodynamic coefficients reveals that the propulsive efficiency?_P of undulatory propulsion ranges between 40%and 60%in the laminar flow.But in the turbulent flow,?_P is about 80%.The undulation results in a significantly increase of frictional force at the laminar flow(Re<10~4).However,the undulation has an adverse effect on friction when fish is swimming at the turbulence flow(Re>10~6).The turbulence kinetic energy and the turbulent viscosity ratio both become smaller under the undulation,which implies that the turbulence strength is reduced by the undulatory motion.The wake of an undulatory swimmer will be different patterns if the kinematic parameters vary including the amplitude a,the wave number 2?b,the phase velocity Sp and the swimming frequency f(f=b×Sp).The positions of vortices in y direction are mainly influenced by the amplitude a.When the wave number 2?b increases,the wake structure changes from a single row of vortices to a double row.The reverse von Karman Street occurs when the phase velocity are increased to 2.0.When the swimming frequency f is smaller than 0.5,there is no wake vortices street existing.As it comes to about 1.0,the wake vortices structure appears as the single row which is aslo be called as“zigzagging vortex chain pattern”.When f is bigger than 1.5,the typical reverse von Karman Street is formed.Thus,it can be concluded that the swimming frequency f is the key parameter for the wake structure.The hydrodynamics of two three-dimension undulating plates in different shapes is investigated numerically.It is found that both of the frictional force and the pressure difference force of the trapezoidal plate are larger than that of the rectangular plate.It should be noticed that the increment of the pressure difference force are much more than that of the frictional force.So the trapezoidal plate is a better choice than the rectangular plate used in undulatory propulsion.