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A generic kinematic model is presented for a unified hydrodynamics study covering the various types of motion found in real as well as hypothetical fish-like undulation. Undulating motion is presented here as a generic motion, considering chordwise forced flexibility—modelled by wavelength of undulation λ*—of a rigid NACA0012 hydrofoil in a free-stream flow. Using a level-set immersed boundary method-based in-house code, a non-dimensional study is presented for various wavelengths, λ* (0.8–8.0), and frequency of undulation, St (0.2–0.7), at a constant maximum amplitude of undulation of 0.1 and Reynolds number of 5000. A unified cause-and-effect-based analysis is presented with the help of flow patterns and propulsive performance parameters. Pressure contour demonstrates how the travelling wave distributes momentum in the streamwise direction and reduces the lateral force coefficient. Vorticity contours elucidate the mechanism of formation of reverse von Kármán vortex street and the secondary vortices. A correlation is proposed for thrust coefficient as a function of λ* and St. Good qualitative agreement is observed between the simulated results at smaller λ*-based undulating and larger λ*-based pitching foil and the published results for the anguilliform and thunniform fishes, respectively. The agreement with the real fishes is presented for the relative magnitude of thrust coefficient, propulsive efficiency, dynamic stabilization, and signal of the prey fish for the predator fish. Similar to propulsive performance of real fishes, larger (smaller) flexibility-based undulation (pitching) results in larger propulsive efficiency (thrust generation)—which can be used for the design of fish-like biomimetic propulsion system.

Summary Using a hybrid Lagrangian‐Eulerian approach, a level set function–based immersed interface method (LS‐IIM) is proposed for the interaction of a flexible body immersed in a fluid flow. The LS‐IIM involves finite volume method for the fluid solver, Galerkin finite element method for the structural solver, and a block‐iterative partitioned method–based fully implicit coupling between the two solvers. The novelty of the proposed method is a level set function–based direct implementation of fluid‐solid interface boundary conditions in both the solvers. Another novelty is the computation of the level set function from a geometric method instead of differential equations commonly used in level set methods—the novel geometric as compared to the traditional method is found to be more accurate and less time‐consuming. The LS‐IIM is demonstrated as second‐order accurate. Verification study is presented first separately for both the solvers and then together for four fluid‐structure interaction (FSI) problems, with different levels of complexity including lid‐driven flow, channel flow, and free‐stream flow. Benchmark solutions are presented for two class of FSI problems: first, easy to set up and less time‐consuming and, second, a reasonably challenging and complex FSI problem involving sharp edges and forced‐motion of the flexible structure. The benchmark solutions are proposed at steady state for the first problem, after a verification study with two open‐source solvers and, at periodic state, after a validation with published experimental results for the second problem. Our benchmark solutions may be useful for verification study in future.

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