Application Of Fictitious Domain Method In Biomimetic Hydrodynamics

Medusan propulsion and drag reduction of shark skin are two popular biomimetic fluid dynamic problems. In this paper, these two problems are numerically investigated using a fictitious domain method, and the propulsion and drag-reduction mechanisms are analyzed.For the propulsion of a 2D jellyfish, the effects of the non-dimensional control parameters on the propulsion velocity are examined. It is observed that:the propulsion velocity is a power function of flapping Reynolds number with different powers for two Reynolds number regimes. A theoretical model is proposed to explain the rationality of these two powers. The propulsion velocity of the jellyfish decays linearly with increasing shear modulus, and turns negative beyond a critical shear modulus. The swimming velocity descends and then ascends almost linearly with increasing flapping force, and the inflection point negatively relates to the duration time of the flapping force. The propulsion mechanism of jellyfish is also analyzed. The effects of the starting and stopping vortex rings on the medusan propulsion are respectively uncovered, and a plausible explanation is given to the backward motion of the jellyfish.Regarding the problem of the drag reduction by shark-skin-like riblets, the results of sawtooth-shaped riblets are validated by comparing to the previous results in literature. The mechanisms of the riblet-induced drag reduction are analyzed. The riblets have a fencing effect on the large-scale streamwise vortices, preventing the valley from the downwash flow and leading to low streamwise velocity in valley and thereby low shear wall stress. The spanwise motion of streamwise vortices and low-speed streaks are restrained, reducing the occurrence of coherent structures. The burst and generation of hairpin vortex are reduced, which reduces the negative effects of sweep on the drag force. The riblets with flat tips and valleys which are of more practical importance are also investigated. Similar drag-reduction performance is found, compared with sawtooth-shaped riblets.Investigations in this paper have improved the understandings towards mechanisms of medusan propulsion and drag reduction of shark skin, which may have some scientific and practical values.