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Hydro- and aero-elastic phenomena are critical in the design and operation of aircraft, bridges, tall buildings, energy harvesters, and other flexible structures exposed to hydro- and aero-dynamic forces. Among these, flutter, buffeting, and vortex shedding are three distinct but interrelated dynamic responses that arise from fluid-structure interactions. Understanding the mechanisms behind each, their similarities, differences, and implications for structural integrity and control is vital for engineers and scientists working in aerospace, civil, and mechanical disciplines. This section provides a brief overview of each phenomenon, explains the conditions under which they occur, and presents a comparative analysis highlighting their interactions and implications.
Flutter is a hydro- or aero-elastic instability that occurs when the energy from aerodynamic forces is fed into a structure's natural mode of vibration, leading to potentially destructive oscillations. It is a dynamic instability that typically manifests as a self-excited vibration in flexible structures, such as aircraft wings or bridge decks.
Flutter arises when aerodynamic forces couple with the natural frequencies of a structure. For example, in aircraft wings, this interaction commonly involves the coupling of bending and torsional modes. If the airspeed reaches a certain critical value (flutter speed), the structure may enter sustained or even growing oscillations without any external periodic forcing. Flutter can be analyzed with mathematic eigenvalue analysis of the aeroelastic system's equations of motion, revealing when damping becomes negative due to aerodynamic feedback. The key parameters influencing flutter include mass distribution, stiffness, damping, and airflow characteristics.
Buffeting is a form of forced, broadband, and often stochastic oscillation that occurs due to turbulent wake flow impinging on a structure. Unlike flutter, buffeting is not a self-excited instability but rather a response to unsteady aerodynamic loading from turbulent eddies and vortices generated by upstream components or flow separations. Buffeting typically affects aircraft flying at high angles of attack, especially near stall conditions, or structures like tall buildings and towers subjected to gusty winds. It results in random, high-frequency vibrations that may cause fatigue and discomfort but do not typically lead to immediate catastrophic failure.
The analysis of buffeting involves both frequency-domain and time-domain simulations, utilizing wind tunnel testing or CFD simulations coupled with structural response models. While flutter is characterized by resonant coupling, buffeting is more akin to white noise excitation.
Vortex shedding is a fluid dynamic phenomenon where alternating low-pressure vortices are shed from the sides of a bluff body as fluid flows passes it. This periodic vortex formation induces fluctuating forces perpendicular to the flow direction, which can cause oscillations. The classic example is the Kármán vortex street formed behind a cylindrical structure. The vortex shedding is characterized by the Strouhal number (St), a dimensionless quantity that relates vortex shedding frequency f to fluid velocity and characteristic length:
where D is the characteristic length (e.g., the diameter of a cylinder of an energy harvester), and U is the velocity of the flow sufficiently far upstream of the bluff body. When the shedding frequency approaches a natural frequency of the body structure, resonance can occur, leading to large amplitude oscillations known as vortex-induced vibrations (VIV). Equipment generating energy from these VIV phenomena is conveniently called a VIV energy harvester, like the one developed in the H-Hope EU project. However, it is important to mention that vortex shedding is also relevant for its negative impact on the structural safety of tall chimneys, bridge cables, and underwater risers in marine technology and applications.
While flutter, buffeting, and vortex shedding all involve non-stationary hydraulic or aerodynamic forces acting on flexible bodies’ surfaces, their mechanisms of operation and structural responses are different and not always suitable for energy harvesting. Flutter is a self-excited dynamic instability, arising from the interaction of hydro- or aero-dynamic forces with the structure's natural modes of vibration and can lead to potentially catastrophic oscillations if not adequately controlled or mitigated, with possible safety risk for the energy harvester. Buffeting, on the other hand, externally driven by turbulent and unsteady aerodynamic loading, induces broadband frequency, and non-resonant responses that are often random in nature and can cause fatigue over time and reduce the operational lifespan of a energy harvester. Therefore, both are not suitable for energy extraction.
Vortex shedding is driven by a regular, quasi-periodic aerodynamic phenomenon where vortices alternate from each side of a body, creating an oscillating lift force. If the frequency of vortex shedding matches the natural frequency of the structure, resonance occurs, resulting in potentially large amplitude vibrations known as vortex-induced vibrations. The phenomenon is highly dependent on the Reynolds and the Strouhal numbers and hence is quasi-predictable, leading to resonance and large oscillations at narrow frequency intervals. This makes it the most suitable phenomenon for energy harvesting.
To better explain the situation on vortex shedding, a scheme of the process is represented in Figure 1. The flow detaching from opposite sides of the cylinder is couloured differently to better highlight the alternate shedding of the vortices. Here follows a more detailed, but still simple-to-understand explanation of how the vortex shedding exerts forces, causing the cylinder motion in the vertical direction.
The incoming flow, arriving with free stream velocity U from the left, is turbulent. That means, that it is unstable in time and features small time fluctuations in velocity. As it flows around the cylinder, it is accelerated both on the upper and lower surface of the cylinder. Following the Bernoulli’s equation, in the absence of any work added or taken from the fluid, an increase in velocity is associated with a decrease in pressure and vice versa:
where p is the pressure, c is the water flow velocity of the fluid and 1 and 2 refer to two arbitrary positions.
As the flow travels, around the cylinder, it accelerates and reaches approximately the highest velocity at the extreme upper (A) and lower (B) points of the cylinder (Figure 1). Behind the cylinder (C) the flow slows down gradually. The immediate consequence of the Bernoulli Equation (2) is, that the pressure in the points (A) and (B) is lower than in the region behind the cylinder (C). The boundary layer adjacent to the cylinder is influenced by the adverse pressure gradient, pushing water within it from point (C) toward both points (A) and (B). Water flow within the thin boundary layer in the backward direction is possible only up to the point, where an adverse pressure gradient exists, that is between points A and C and B and C. At these locations, the water accumulates near points (A) and (B), and a boundary layer thickening occurs until the thick boundary layer is suddenly detached. This triggers the formation of the vortex, which propagates downstream. The propagation of the vortex downstream further changes the flow field around the cylinder, and now vortices start to detach (they are being shed) quasi-periodically. The reason for the periodic detachment of vortices one at a time from each side, can be at first explained by flow separation. When water flows around a cylinder, it follows the surface only up to a point. This happens because the fluid wants to stick to the surface—this is called the no-slip condition—but it slows down as it moves around the curved sides of the cylinder. As the fluid slows down near the surface (due to friction and pressure drop), it can’t maintain enough momentum to keep curving around the back at around point (C). At some point on each side, the fluid separates from the surface, making a chaotic flow—this is called the wake. Once separation occurs, it leads directly to vortex formation. The separation point depends on the Reynolds number (a measure of flow speed, diameter of the cylinder, and viscosity).
After separation, behind the cylinder, there are two shear layers—one from each side—where fast-moving outer fluid meets the slower fluid in the wake. These are highly unstable regions because the velocity difference creates shear, and small disturbances here grow quickly into large instabilities, which one can think of as being the vortices' starting point. These growing disturbances cause the shear layers to roll up into vortices.
It is important to highlight that the vortices do not form symmetrically on both sides simultaneously. To understand this, let’s say a vortex forms on the right side first. This pulls fluid toward itself (due to its low-pressure area), which deflects the wake toward that side. That leaves the left side with lower pressure, making it easier for the next vortex to form there. So, the next vortex forms on the left, then again on the right, and so on. It becomes a quasi-periodic, alternating cycle. The process then self-sustains through the alternating wake dynamics.
When a cylinder is placed in a horizontal flow — such as in Figure (1) — the fluid moves steadily from left to right. The cylinder is mounted so that it remains fixed in the horizontal direction but is free to oscillate vertically. As discussed in the previous section, the vortex-shedding process induces quasi-periodic pressure fluctuations. These pressure differences on the upper (A) and lower (B) surfaces of the cylinder generate a fluctuating lifting force F, which acts predominantly in the vertical direction. When the cylinder is mounted in a way that allows vertical movement while constraining horizontal displacement, the force F drives the up-and-down oscillatory motion of the cylinder, enabling energy harvesting in systems designed to exploit vortex-induced vibrations (VIV).
The intensity of the vertical force F also affects the energy harvester performance and design, To understand this, it is necessary to highlight that this force depends on the pressure p acting on the cylinder according to the following equation:
where A is the surface, on which the pressure p acts. A larger surface area A leads to a greater force for the same pressure variation. In the context of energy harvesting, this has direct design implications: increasing the diameter of the cylinder increases the area exposed to pressure fluctuations, thereby amplifying the lift force generated during vortex shedding. Consequently, whenever the dimensions of the water channel or stream permit, it is highly advantageous to use a cylinder with the largest height. This maximizes the energy extraction potential of the system and enhances the overall efficiency of the harvester.
While the vortex shedding primarily results in forces perpendicular to the flow direction (i.e., vertical forces that cause the cylinder to oscillate up and down), it also has implications for the forces acting along the flow direction. The dominant horizontal force acting on the cylinder is the drag force. This arises because of the pressure distribution around the cylinder in the horizontal direction: the flow slows down and builds pressure on the upstream side of the cylinder, while on the downstream side, the flow separates from the surface, creating a low-pressure wake. This imbalance generates a net force that pushes the cylinder downstream in the direction of the flow. This force is generally steady and is referred to as form drag or pressure drag. Since the cylinder is constrained from moving horizontally, the mounting structure or support must provide a reaction force to counteract the horizontal forces generated by the flow. This includes both the steady drag and any fluctuating components. The support effectively holds the cylinder in place, preventing it from being swept away by the flow.
Importantly, while these horizontal forces act continuously on the cylinder, they do not contribute directly to the vertical motion that is characteristic of vortex-induced vibrations. However, proper consideration of the horizontal forces is crucial, particularly when designing energy harvesters, as they influence the overall stability, structural stress, and energy transfer within the system.
When the cylinder oscillates vertically due to the unsteady lift forces F from vortex shedding, it moves against a restoring force (usually from springs) and may also work against damping forces, which can be mechanical or electrical (e.g., from an induction generator). The extracted power P hence comes from these oscillations. This power can be estimated in the most simplified (among others assuming the movement of the cylinder is purely sinusoidal) form according to the following equation:
where F is the instantaneous vertical force acting on the cylinder, A is the amplitude of the movement of the cylinder and ω is the frequency of the sinusoidal motion.
If properly implemented, the power P can be extracted using a linear or rotating induction generator, making a design an energy harvester. Based on this simplified equation, it is possible to derive some additional conclusions. Work done per cycle increases linearly with amplitude A if force is constant. If the force also increases with amplitude (as is common near resonance), then the work scales with 𝐴². The maximum power output typically occurs when the system is in resonance condition, i.e. when the vortex shedding frequency matches the natural frequency of the cylinder-spring system. The final design of the H-Hope energy harvester will include the most appropriate amplitude, at which it should operate so as to maximize the power. The VIV energy harvester featuring 2x the amplitude of the original energy harvester would provide 4x the amount of work of the harvester operating at low amplitude.
The VIV energy harvester features the length b in the direction perpendicular to the flow, along the surface of the channel or stream. The power available for extraction is linearly proportional to the length. That means, the VIV energy harvester having twice the length, will produce twice the power of the original design.
Scaling laws can be implemented also for the power P of the incoming flow, let’s consider the case the flow has velocity U. The power of the flow scales with U³, meaning the flow with 2x higher velocity will provide an opportunity for extraction of 8x the power of the original flow with low velocity, provided that in both cases the VIV energy harvester would ideally operate in lock-in condition.
The efficiency of a Vortex-Induced Vibration (VIV) energy harvester is closely tied to the underlying physics of vortex shedding and the subsequent dissipation of vortex energy. The fluctuating vertical forces acting on the cylinder arise due to the periodic formation and shedding of turbulent vortices on either side of the cylinder. These vortices originate directly at the surface of the cylinder and are typically generated at a relatively large scale, as illustrated in Figure 1.
Once shed, these large-scale vortices travel downstream, carrying with them a significant amount of kinetic energy. However, the energy of these vortices is not immediately dissipated. Instead, it undergoes a process known as the cascade of turbulent energy dissipation. In this process, energy is transferred from large vortices to progressively smaller ones through interactions that occur only between vortices of similar size. As the cascade progresses, vortices continue to break down into smaller and smaller structures.
Eventually, when the vortices reach a characteristic scale comparable to that of molecular motion, their identity as coherent structures is lost. At this point, their kinetic energy is no longer distinguishable from random thermal motion and is irreversibly converted into heat. This final stage marks the end of the cascade of turbulent energy dissipation, and all the energy initially carried by the large vortices is dissipated.
The VIV energy harvesting underlying physics therefore sets serious physical limitations to the energy harvesting process.
For the vortex shedding process to function effectively and for a VIV energy harvester to generate usable power, turbulent vortices must be continuously formed and shed from the cylinder. This process initiates the transfer of turbulent kinetic energy, which ultimately is always dissipated. It is this dynamic interaction that gives rise to periodic pressure variations and the resulting fluctuating lift forces perpendicular to the main flow—forces that drive the energy harvesting mechanism. However, the very requirement for generating and dissipating turbulent vortices inherently limits the overall efficiency of the energy conversion process. A significant portion of the flow kinetic energy is inevitably lost as heat during turbulence dissipation, rather than being captured and converted into electrical energy.
Although turbulence dissipation represents the most fundamental and limiting factor in the operation of VIV energy harvesters, it is difficult to quantify it precisely. The complexity arises from the dynamic nature of vortex formation and dissipation, the unsteady flow patterns, and the interaction between the moving cylinder and the surrounding fluid. As a result, accurately measuring or modelling the exact amount of kinetic energy lost or retained in the outflow remains a significant challenge in both theoretical and experimental studies.
The VIV energy harvester is also subject to an additional fundamental limit in energy conversion, which arises from the conservation of mass and energy within the control volume. Specifically, the water that flows into the harvester—carrying kinetic energy—must also exit the system. To better understand this constraint, consider the kinetic energy of the water both entering and leaving the control volume of the VIV energy harvesting device.
The incoming water possesses kinetic energy, which serves as the primary energy source for the energy harvester. However, because the flow must continue downstream, a portion of that kinetic energy is retained in the outgoing water. The kinetic energy Wk is dependent on the mass m of the water in the control volume having velocity U of the water is directly related to its mass m and velocity U, according to the classical expression.
This implies that a VIV energy harvester will be capable of extracting more energy in situations where the flow velocity in the stream or channel is high.
However, due to the necessity for water to continue flowing out of the harvester's control volume, the amount of energy available for extraction is limited to the difference between the incoming and outgoing kinetic energy. The optimal scenario for energy extraction occurs when the velocity of the incoming water is high while the velocity of the outgoing water is significantly reduced.
This energy conversion constraint is not unique to VIV energy harvesting systems. Similar limitations are found in other renewable energy technologies. A well-known example is the Betz limit in wind energy, which states that no more than approximately 59% of the kinetic energy in the wind can be converted into useful power under ideal conditions. This principle reflects the fundamental physical constraint that some energy must remain in the moving fluid to allow continuous flow through the system.
Understanding this process is crucial for energy harvesting, as it highlights a key opportunity: rather than allowing all vortex energy to be lost as heat, VIV energy harvesters can intercept part of it by converting the induced motion of the cylinder into electrical energy. The more efficiently this conversion occurs—by optimizing device design, tuning the resonance between vortex shedding frequency and cylinder oscillation, and minimizing mechanical losses—the more effectively the harvester can tap into this natural flow phenomenon.
