Introduction:

Traditional energy harvesting methods use turbine-based devices with rotating blades. Due to their need for large size, light weight, and extremely fast rotational speeds these designs have inherent areas of structural weakness. They also have a high negative impact on the environment they are located in. Our research focuses on much more stable and less harmful forms of flow harvesting. In this section we investigate the concept of creating non-invasive flow energy harvesters. These harvesters would be located under water and use a simple flapping foil connected to an energy harvesting mechanism to extract energy from random movements of subsurface flows. In our studies we analyze the feasibility of creating two different types of flow harvesters. The first system works on a principle of mode-activation, where the system would actively oscillate at one mode state and the response to the other modes would generate power. The second system is a completely passive system that generates energy through strictly flow-induced movements. Both are explained in greater detail in the following two sections.

Modeling:

Mode-Activated (Active):

First we tested an active model that harvests energy… We modeled a two-dimensional foil mounted on a damper (c) in an incoming flow (U) as shown below. The fluid density is ρ. The foil was allowed to undergo a heaving motion and a pitching motion. Through an actuating system, a sinusoidal pitching motion was activated. The heaving motion was then generated. The net power input was the power required to create the actuating movements, while the power output was the power extracted through the damper.

Mode-Activated Harvester Model

The fluid flow was modeled based on the Navier-Stokes equations around the foil. These equations were then coupled with the hydrodynamic forces and moments in an iteration algorithm. Using this test different scenarios could be set up by changing specific parameters within the equations. This system was first demonstrated on a circular cylinder foil.

Flow-Induced (Passive):

We also tested a passive model that harvested energy through flow-induced responses. We investigated the feasibility of this device by clarifying the following: (1) through self-induced vibrations, is it possible to achieve predictable and controllable foil motions essential for stable energy production? (2) If so, within what range of geometric and mechanical parameters is this flapping pattern obtained? (3) What will be the energy harvesting performance of this device?

To answer these and other questions the passive system was modeled as a flapping foil with a rotational spring (kα) and a damper (c) as seen in the figure below. The idea behind this flow-induced energy harvester was that the flapping foil would respond to any unstable motions of the surrounding water by pitching and heaving motions. The damper worked as the generator extracting energy from the periodic motions.

Flow-Induced Harvester Model

In order to numerically analyze the system equations were set up according to the parameters shown for the heaving and pitching motions and there forces. A linear stability analysis suggested that when b is larger than −0.25 and kα is sufficiently small the system might become unstable, making it possible for flow energy harvesting. These new equations were then coupled with the Navier-Stokes equations and a boundary element analysis to achieve a full simulation of the fluid-structure interactions. After obtaining an equation for hydrodynamic force an iteration was done over time to test the effectiveness of this passive flow-induced energy harvester.

Tests & Results:

Mode-Activated (Active):

After running several fluid simulations it was found that the performance of the foil-based flow energy harvesting system depends on mechanical parameters such as the magnitude of the damping and the location of the pitching axis, as well as operational parameters such as the frequency and amplitude of the pitching motion. Positive net energy extraction (i.e., the energy extracted is larger than the energy spent) is possible only in small frequencies. Our results show that optimal performance is achieved when the pitching axis is close to the center of the hydrodynamic pressure so that the power input is minimized—in most cases a good choice is 0.2–0.5 chord length from the leading edge.

Vorticity control mechanisms, especially the interaction between the leading-edge vortices and the foil itself, play a critical role in the energy exchange between the foil and the surrounding flow field, and affect the performance of the system at large pitching angles. Specifically, we have identified an interaction mode in which part of the energy of the leading-edge vortices is recovered by the foil so that enhanced performance is obtained. To achieve this, two conditions have to be satisfied: (1) The energy recovery is obtained through the hydrodynamic moment induced by a LEV as it approaches the foil surface. This moment has to be in the same direction as the instantaneous pitching motion. (2) To maximize the moment it induces, the location of the vortex-foil encounter must be as far from the pitching axis as possible (ideally at the trailing edge).

Although our current model confirms that with the specific device the power harvesting capacity P cannot surpass Pm even if the mechanical design and the operational parameters are optimized, it is possible for further improvement through other measures. For example, our previous modeling based on potential flow shows that P can be significantly increased by utilizing ground effect, or by using two parallel foils in opposite phases of pitching. The inborn nonlinearity of the problem suggests that the dynamic behavior of the system might be different from what is illustrated in this study if the pitching motion is nonsinusoidal. This will bring in new parameters to be optimized. Indeed, nonsinusoidal pitching motions were applied in existing prototypes such as the Stingray as mentioned in the introduction. Clearly, further investigation in this issue is necessary.

Flow-Induced (Passive):

Through numerical calculations it was found that the system demonstrates four distinguishable behaviors depending on the location of the pitching axis and the stiffness of the rotational spring kα: (i) the foil remains stable in its initial position (α = 0 and h = 0); (ii) periodic pitching (around α = 0) and heaving motions are excited; (iii) the foil undergoes irregular motions characterized by switching between oscillations around two pitching angles; and (iv) the foil rotates to a position with an angle to the incoming flow and oscillates around it. Our simulations show that self-induced regular motions are possible only under a small range of parameters. In optimal conditions, an energy harvesting efficiency of 20% is achieved.

Although the flapping-foil flow energy harvester has clear advantages over traditional turbines with rotating blades in terms of environmental friendliness, its design and operation pose enormous challenges owing to the subtlety of the fluid-structure interaction problems involved. Indeed, as indicated by our current and previous studies, unless properly designed and operated, such a system is unable to achieve power extraction from an incoming flow.