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The impacts of partial confinement on the power extraction performance of a flapping foil generator at a Reynolds number of 1100 are numerically studied using an immersed boundary–lattice Boltzmann method. Four confinement levels are implemented with two thin plates of finite size symmetrically placed at the distance of 1.5, 2, 3, and 4 foil chord length from the neutral position of the flapping foil. Parametric studies on plate lengths varying from 10 to 50 foil chord lengths at the four confinement levels are conducted. The results show that the power-extraction efficiency increases nearly monotonically with the upstream plate lengths while the impact of the downstream plate lengths is much less significant, indicating that upstream confinement is the dominant factor influencing the power-extraction performance. Contrary to the performance improvement observed in studies on the effect of infinite walls, the efficiency decreases dramatically with the decrease in the distance from the plates to the foil. The reasons for the dramatically decreased performance due to confinement effects are found. First, the interactions between the boundary layer of the plates and leading edge vortices formed on the foil reduce the size of the low-pressure region on the suction surface of the foil, leading to reductions in lift forces and consequently to major reductions in the extracted power. In addition, large mass flow deficits between the finite plates are observed when the distance between the two plates is small, indicating substantial reductions in potential power that can be extracted from the inflow.

This paper presents a study on streamline penetration, velocity error, and consequences of a fluid–structure interaction (FSI) solver based on the feedback immersed boundary method (IBM). In the FSI solver, the fluid dynamics is solved by the lattice Boltzmann method; the solid structure deformation is solved by the finite difference method and the finite element method for two- and three-dimensional cases, respectively; and the feedback IBM is used to realize the interaction between the fluid and the structure. The IBM is implemented in non-iterative and iterative ways. For the non-iterative version, two types of integration are discussed: without and with velocity prediction step. Five benchmark cases are simulated to study the performance of the three implementations: a uniform flow over a cylinder, flow-induced vibration of a flexible plate attached behind a stationary cylinder in a channel, flow through a two-dimensional asymmetric stenosis, a one-sided collapsible channel, and a three-dimensional collapsible tube. Results show that both the IBM with prediction step, the iterative IBM, and one iteration IBM with proper feedback coefficients can suppress the spurious flow penetration on the solid wall. While the velocity error does not significantly affect the force production and structure deformation for external flows, reducing it significantly improves the prediction of the force distribution and structure deformation for internal flows. In addition, the iterative IBM with smaller feedback coefficient has better numerical stability. This work will provide an important guideline for the correct use of the feedback IBMs.