Balaenid whales, as continuous ram filter feeders, can efficiently separate prey from water by baleen. The feeding process of balaenid whales is extremely complex, in which the flow distribution and pressure drop in the oral cavity play a significant role. In this paper, a theoretical model coupled with oral cavity velocity and pressure in balaenid whales is established based on mass conservation, momentum conservation and pressure drop equations, considering both the inertial and the friction terms. A discrete method with section-by-section calculation is adopted to solve the theoretical model. The effects of four crucial parameters, i.e. the ratio of filtration area to inlet area (S), the Reynolds number of entrance (Re in ), the ratio of thickness to permeability of the porous media formed by the fringe layer (φ) and the width ratio of the anteroposterior canal within the mouth along the tongue (APT channel) to that along the lip (APL channel) (H) are discussed. The results show that, for a given case, the flow distribution and the pressure drop both show increasing trends with the flow direction. For different cases, when S is small, Re in is small and φ is large, a good flow pattern emerges with a smoother flow speed near the oropharynx, better drainage, better shunting and filtration, and higher energy efficiency. However, for smaller values of H, some energy efficiency is sacrificed to achieve additional average transverse flow in order to produce better shunting and filtration. The research in this paper provides a reference for the design of high-efficiency bionic filters.

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Natural fish have evolved with an excellent swimming performance after millions of years. Based on the flexible features of the pectoral fin, this paper focuses on the kinematics and hydrodynamics of the fin when fish are swimming stably in still water in labriform mode. The locomotion mechanism based on the morphology of the pectoral fin is applied to establish a kinematic model composed of five rays and membranes, which is adopted to control the pectoral fin to reach deformation in approximately the same way as the labriform mode. A semi-empirical theoretical model based on the kinematics is proposed to calculate the hydrodynamic force. In order to study the flow field, the numerical simulation of fluid-structure interaction is carried out and the results are validated by the present semi-empirical model, which also verifies the feasibility of the semi-empirical theoretical model for describing the dynamics of the pectoral fin under a complex water environment. In addition, the relationship between propulsion performance and locomotion parameters (e.g. frequency of motion, amplitude of flapping and rowing angle, and phase lag between flapping and rowing) of the multi-degree of freedom flexible pectoral fin is also revealed. It is found that the frequency and amplitude of the flapping angle have a significant influence on the hydrodynamic thrust, while the rowing angle and phase lag have little effect. The established models and the results provide effective tools and significant reference for the design of bionic pectoral fins.

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Balaenid whales are giant filter feeders that feed on the dense aggregations of prey. Through their unique oral filters, they can effectively filter water out and leave prey in their mouths. In this study, a theoretical model is established to analyze the hydrodynamic filtering system in the balaenid whales suspension feeding. First, the appropriate velocity profiles in the anteroposterior and mediolateral directions are adopted to approximate the flow field in the anteroposterior channel along the tongue (APT channel). Then, a four-stage Runge–Kutta method is used to calculate the particle trajectories and predict the corresponding filter cake profile by solving the particle motion equations. Finally, the effects of three crucial parameters, i.e. the APT channel width D T , the fringe layer permeability K, and the food particle diameter d p, are discussed. The results show that the particle trajectories consist of a series of backward-outward arcs and the food particles tend to accumulate in the posterior region of the oral cavity. The growing parabolic filter cake profiles are formed except for the case of extremely low permeability. A small D T and large K make the tendency of particle posterior aggregation obviously. So squeezing the tongue and having larger fringe layer permeability are both conducive to the swallowing process. But the change in d p has less influence on this tendency. The proposed theoretical analysis method is a fast and low-cost calculation method. The study on the balaenid whales’ filter feeding biomechanics and hydrodynamics is helpful to guide the design of the high-efficiency bionic filters.