Multi-body interaction effect on the energy harvesting performance of a flapping hydrofoil
Introduction
Recently, a flapping hydrofoil has been widely studied as a novel method to extract energy from fluid flows. The flapping hydrofoil can perform without losing efficiency noticeably in unsteady flow environment. The hydrofoil is also better fitted for shallow water installation because of their rectangular sweeping area [[1], [2], [3]]. The idea of using the flapping hydrofoil was first introduced by McKinney and DeLaurier [4]. Motivated by their work, Jones and Platzer [5] showed that, for the hydrofoil of combined heaving and pitching motions, one could change from a propulsion regime to an energy harvesting regime if the pitching amplitude exceeds the heaving-based angle of attack.
The basic mechanism of efficient energy extraction from a flapping foil (from now on the “hydrofoil” is referred to as “foil” for simplicity) can be explained with vortices generated by the foil. The heaving motion of the foil with an appropriate angle of attack forms a strong leading-edge vortex near the surface of the foil and produces vertical force due to the low pressure region inside the vortex. However, as the leading-edge vortex separates and washes away from the surface, the vertical force decreases. To maintain large power generation, the foil should rotate and change its heaving direction to form another leading-edge vortex near the opposite surface of the foil [1,[6], [7], [8]].
Many studies on the energy harvesting foil have addressed the role of motion parameters and foil geometry on power generation. Among the earliest works is a numerical and experimental study conducted by Linsey [9] to determine the feasibility of energy extraction. Another comprehensive work was done by Dumas and Kinsey [10] and Kinsey and Dumas [7] in which they presented an efficiency map as a function of pitching amplitude and reduced frequency. Their map shows the efficiency as high as can be reached for a single foil and the best performance is around which is consistent with the analysis on optimal frequency for energy harvesting [8]. The foil shape is known to have minor impact on efficiency for thin foils [6,7]. It was also claimed that the increase in Reynolds number led to the better performance [7]. However, due to complication of turbulent flows, solid conclusion on the Reynolds number effect cannot be established, and it needs more investigation [1]. The studies on a foil with finite span reported that three-dimensional effects caused the reduction in efficiency, compared to its two-dimensional counterpart [6,11,12].
Several studies attempted non-sinusoidal pitching and heaving motions and achieved higher efficiency than that of sinusoidal motions for some specific conditions [13,14]. The flexible aero/hydrofoils motivated by the compliant propulsors of flying and swimming animals were also investigated, in which the flexible aero/hydrofoil showed efficiency improvement although the prescribed deformation of the aero/hydrofoil was considered instead of its passive deformation [15]. It is worth mentioning that the effect of a flexible foil on energy harvesting has not been fully understood, and in-depth research is required in this area [1].
Another bio-inspired idea to improve the harvesting performance is from multi-body interaction. This idea was motivated by aquatic animals and birds travelling as a group to benefit from the flow induced by their neighbors [[16], [17], [18]]. One of the earliest studies on multiple foils for energy harvesting is the work by Jones et al. [19], in which they experimentally investigated the efficiency of twin foils in a tandem configuration with small clearance and phase lag of between them. Since the idea of using tandem foils is to extract the remaining energy from the vortices generated by the front foil, both phase lag and relative distance between front and rear foils are important parameters to strongly determine the overall performance [13,20]. The tandem configuration seems disadvantageous because the rear foil positioned in the wake of the front foil is exposed to relatively lower flow velocity and fluid kinetic energy. Nevertheless, we are able to gain some benefit by properly positioning the rear foil for positive interaction with the vortices shed from the front foil [2]. Indeed, using the tandem configuration, higher efficiency can be achieved in some specific conditions (e.g., the phase lag of ) [[21], [22], [23]].
In addition to the tandem arrangement, the parallel foil arrangement was investigated experimentally or numerically for both in-phase and out-of-phase modes [[24], [25], [26]]. For the in-phase mode, the per foil efficiency decreases as the distance between the two foils decreases. However, for the out-of-phase mode, the reduction in the gap distance produces larger overall output.
Most, if not all, of previous works on multi-body effects focused on diverse arrangements of multiple foils with the same geometry. Instead of multiple foils, mutual interaction of an upstream bluff body and a downstream energy harvester is considered to improve the efficiency in our work. The stationary upstream body deflects uniform flow and increases the flow velocity encountered by the downstream energy harvester, which is able to contribute to larger power generation. This idea was applied to a vertical-axis rotary turbine with an upstream bluff body, and the increase in efficiency was reported [27,28]. In the application of this idea to the heaving and pitching foil, unsteady motion of the foil and its interaction with the vortex shed from an upstream body make flow dynamics too complicated to predict the overall effect based on available data reported in the literature. This difficulty motivates us to investigate the effect of an upstream body on the power generation of the downstream flapping foil and identify flow phenomena responsible for noticeable changes in power generation. We believe that this study will lead us to design an energy harvesting hydrofoil system with better performance.
The rest of paper is organized as follows. In Sec. 2, a foil model and variables investigated in this study are described. The method of numerical simulation and the validation of our numerical code are explained in Sec. 3. Sec. 4 discusses our results on heaving force/pitching moment generation and overall efficiency, based on the physical interpretation of vortex dynamics, which is followed by concluding remarks in Sec. 5.
Section snippets
Problem description
Our model consists of a pitching and heaving foil and a stationary upstream bluff body, a thin vertical plate, positioned upstream of the flapping foil (Fig. 1 (a)). As a foil model, we used the symmetric Joukowski foil mathematically described as [8]:where and are coordinates in and -planes respectively. The Joukowski foil is the mapping of a circle with radius from the -plane to the -plane. e and s are the parameters characterizing foil
Numerical method
Governing equations of a fluid domain are as follows for incompressible isothermal laminar flow:where ρ, ν, and p are fluid density, kinematic viscosity, and pressure, respectively, and is a velocity vector. The simulation of the flow around a flapping foil is numerically a challenging problem due to the large-amplitude motion of the foil. Several numerical approaches have been reported in literature including the panel method [9], the approach using moving meshes in
Physical principles of efficiency improvement with an upstream body
First, we describe the change in flow structure of a flapping foil with the presence of an upstream plate and address their effects on energy harvesting performance. In this section, we will consider only a single case of , , and (Fig. 4). This particular case was chosen because the foil was located at the region of higher power output than the single-foil case and the characteristics of flow structure and force/moment trends shown in this case can be generalized to other
Concluding remarks
In this study, we have numerically investigated the effect of an upstream bluff body on energy harvesting of an oscillating foil. Although we rely on two-dimensional simulation at the Reynolds number much lower than that of the actual application, we were able to find fluid-mechanical principles of improving the efficiency significantly by using a simple additional structure. The presence of the upstream body changes local flow structure around the foil in two ways. First, it deflects an
Acknowledgments
This study was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2015R1C1A1A02037111) and by a grant [KCG-01-2016-04] through the Disaster and Safety Management Institute funded by Korea Coast Guard of Korean government.
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