Fish schooling, as one of the most exciting research fields, attract many attentions in recent years. Fishes may form a school because of various reasons, including mating, protecting and foraging. Numerous studies have shown that hydrodynamics is one of the most essential mechanisms governing the organization of fish schools. Wiehs, using a 2D model, demonstrated that fishes gained energetic benefits by forming a diamond pattern in collective swimming. In nature, however, there exit different kinds of spatial configurations (diamond, rectangular, and line). Thus, more specific researches about school patterns are needed to made to determine the optimal configuration. In the present study, parametric studies on two-dimensional spatial patterns, including rectangular and diamond shapes, are completed based on an integrated computational approach.

In this research, a flexible hydrofoil, NACA00XX, is chosen to denote the two-dimensional undulatory fish body at rest. At this time, the mid-line overlaps the mid-chord of the hydrofoil. By oscillating the mid-line in the transverse direction, the body propel itself at a certain speed . Here, a travelling wave kinematics which resemble to the observations of other carangiform or anguilliform swimming, is employed to drive the undulatory motion of the body. The wave motion is determined by several key parameters. After obtaining the kinematics of a single fish, the internal fish school will be formed by four fishes of this kind. Then, a sharp-interface immersed-boundary-method (IBM)-based incompressible flow solver is employed to implement the schooling simulations. In this in-house solver, the Navier-Stokes equations are discretized using a cell-centred, collocated arrangement of the primitive variables and are solved using a finite-difference-based Cartesian grid immersed boundary method.

In the present study, two categories of spatial patterns will be investigated: rectangle and diamond. For the rectangular configurations, with the assumption that fishes are evenly distributed in a huge fish school, we use three parameters, diameter *R*, position angle *β* and direction angle *θ* to define the minimal internal school which contains four fish and is confined in the given region, a circular area. Then, parametric studies will be done to determine the optimal rectangular internal structure. Compared with previous studies on rectangular patterns, the way of defining the rectangle makes the research thorough and complete. In addition, the diamond structure, the classical school pattern defined by long-axis *a* and short-axis *b*, will be investigated. The parametric studies are conducted on a wider range. Finally, the analysis of wake structures of different school patterns is made to support our results


Effect of Formation Pattern on Schooling Energetics in Fish-Like Swimming

Division / Sponsors: 
Heat Transfer Division (HTD), Fluids Engineering Division (FED)

Heat Transfer Summer Conference
Paper Proceedings: https://asmedigitalcollection.asme.org/HT/HT2020/volume/83709

18th International Conference on Nanochannels, Microchannels, and Minichannels
Paper Proceedings: https://asmedigitalcollection.asme.org/ICNMM/ICNMM2020/volume/83693

Fluids Engineering Division Summer Meeting
Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2020/volume/83716

HT-ICNMM2020 - Virtual Conference, SHTC - Virtual Conference, FEDSM2020 - Virtual Conference

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