STUDY ON THE SCALING LAW OF FISH-LIKE BODY SELF-PROPULSION WITH CARANGIFORM UNDULATION

During the long history of evolution, carangiform swimmers have mastered an exquisite capacity to efficiently cruise in water by undulatory locomotion. Under the dynamic balance of the fluid forces, the carangiform swimmers show excellent ability to swim forward at a high speed and its performance is far superior to traditional artificial underwater vehicles. Hence, it is of great significance to discover the scaling law of hydrodynamic forces and cruising speeds for the self-propulsion of fish, and to develop formulas for the quick estimation of the forces and forward swimming velocity. Based on the open-source OpenFOAM platform, the simulation algorithm is implemented by utilizing the flexible body self-propulsion dynamics. The forward self-propulsion motions of the NACA0012 airfoil undulating in the carangiform mode are numerically simulated. Be inspired by our earlier study on thrust scaling law for the tethered models, the pressure forces and friction forces acting on the self-propelled fish-like body are analyzed. The results indicate that the pressure force coefficients, as well as the friction drag coefficients, obey the same form of scaling law in all cases under the condition of Reynolds number between 500 and 50 000, and then the quantitative prediction formulas of the forces are obtained according to the numerical results. Furthermore, the scaling law of the forward self-propulsion velocity can be derived from the equilibrium condition between pressure force and friction force, which makes it accessible to explicitly predict the cruising speed with the undulatory motion parameters of the fish body. Also, the influence of the thickness to chord ratio of fish body on the scaling laws for the hydrodynamic forces and propulsion velocity is discussed under conditions of Re = 500 and Re = 50000, the frequency f = 0.5 ~ 2 Hz and the undulatory amplitude A = 0.05L ~ 0.1L. The effect of different fish body shapes on the energy-utilization ratio is considered, it can be found that slenderer fish body tends to achieve optimal energy-utilization ratio as the Reynolds number increases.