Energy generation from vortex induced vibrations report

Energy Generation from Vortex Induced Vibrations

1. Introduction

The issue of global climate change and the growing energy demand induce a need

for innovative energy harvesting devices. Geophysical flows represent a widely

available source of clean energy, useful to tackle the global energy demand using for

example wind turbines, marine turbines or wave energy converters. Yet, the energy

density in geophysical flows is small, and large systems are required in order to

harvest significant amount of energy.

The turbine generator is the most mature method for flow energy harvesting.

However, the efficiency of conventional turbines reduces with their sizes due to the

increased effect of friction losses in the bearings and the reduced surface area of the

blades. Furthermore, rotating components such as bearings suffer from fatigue and

wear, especially when miniaturised. These drawbacks of turbine generators urges

emergence of a new area in energy harvesting, i.e. energy harvesting from flow

induced vibration. The flow here includes both liquid flow and air flow. There are

three main types of energy harvester of this kind. They are energy harvesting from

vortex-induced vibration (VIV), flutter energy harvesters and energy harvesters with

Helmholtz resonators.

Flow-induced vibration, as a discipline, is very important in our daily life,

especially in mechanical engineering. Generally, scientists try to avoid flow-induced

vibration in buildings and structures to reduce possible damage. Recently, such

vibration has been investigated as an energy source that can be used to generate

electrical energy. Two types of flow-induced vibration are studied so far: vortex-

induced vibration and flutter

Dept of mechanical Engg. SJCET, Palai Page 1


2. Vortex Induced Vibrations

The non-linear resonance phenomenon known as Vortex-Induced Vibration (VIV)

has much relevance in several branches of mechanical engineering. For example, it

can be observed in civil structures, like slender chimneys stacks, tall buildings,

electric power lines or bridges, to name a few. It is also usual in offshore structures or

in the tubes of heat exchange devices. Because its practical and scientific interest,

VIV has lead to a large number of fundamental studies. Usually, VIV is considered as

an undesirable effect, as it may seriously affect the structural integrity or the

reliability of performance, but along this report we will see that if the vibration is

substantial, it can be used to extract useful energy from the surrounding flow

An original way to extract energy from these flows is to take advantage of flow-

induced vibrations, [2]. For instance, several devices based on fluid-elastic

instabilities like transverse galloping or flutter have already been introduced. [2–3].

Another kind of flow-induced oscillations that can be useful to harvest energy from a

flow is the vortex-induced vibrations (VIV) of a bluff body [1,2].The model is

presented and the generic case of energy extraction using VIV of an elastically-

mounted short rigid cylinder is analyzed.

3. Principle

When a fluid flows toward the leading edge of a bluff body, the pressure in the fluid

rises from the free steam pressure to the stagnation pressure. When the flow speed is

low, i.e. the Reynolds number is low, pressure on both sides of the bluff body remains

symmetric and no turbulence appears. When the flow speed is increased to a critical

value, pressure on both sides of the bluff body becomes unstable, which causes a

regular pattern of vortices, called vortex street or Kármán vortex street. Certain

transduction mechanisms can be employed where vortices happen and thus energy

can be extracted [3] . This method is suitable both air flow and liquid flow.



Figure 1 : Flow around a bluff body

3.1 Physics Theory

Vortex shedding is a widely occurring phenomenon applicable to nearly any

bluff (non streamlined) body submerged in a fluid flow. Since any real fluid flow is

viscous, there will be a significant boundary layer on the bodies’ surface for all but

the lowest Reynolds number flows. At some point along the bodies’ surface,

separation of the boundary layer will occur, depending on the exact surface geometry.

This separated layer, which bounds the wake and free stream, will tend to cause fluid

rotation, since its outer side, in contact with the free stream, moves faster than its

inner side, in contact with the wake. It is this rotation which then results in the

formation of individual vortices, which are then shed from the rear of the body and

travel down the wake. Typically, a pattern of periodic, alternating vortex shedding

will occur in the flow behind the body, which is referred to as a vortex street.

Depending on the characteristics of the flow, mainly the Reynolds number, different

types of vortex streets may form, which will be discussed later in more detail. When

the pattern of shed vortices is not symmetrical about the body, which is the case in

any vortex street, an irregular pressure distribution is formed on the upper and lower

sides of the body, which results in a net lift force perpendicular to the flow direction.

Since the vortices are shed in a periodic manner, the resulting lift forces on the body

also vary periodically with time, and there for can induce oscillatory motion of the

body. This occurrence alone would qualify as vortex induced vibration; however,

there is a more interesting and important phenomenon, similar to linear resonance,

which can occur when the frequency of vortex shedding (fs) is close to the natural

frequency of the body in motion, (fn). In this phenomenon, referred to as “lock in”,

the vortex shedding frequency actually shifts to match the bodies’ natural frequency,

and as a result, much larger amplitudes of vibration can occur. It is this particular

aspect of vortex induced vibration, lock in, which has traditionally been of greatest



concern to structural engineers, since it poses the greatest risk of damage or failure.

Accordingly, the range of shedding frequencies which lock in can occur over is one of

the most important research areas within vortex induced vibration.

3.1.1 Vortex Shedding

Like many fluid flow phenomenon, vortex shedding has been observed to be directly

dependent on the Reynolds number of the flow, which is defined in Eq. 2-1.

Re = (U*D)/υ ........Eq. 2-1

U is the free stream velocity, D is the cylinder diameter, and υ is the kinematic

viscosity of the fluid. As a note, most studies in literature were in fact performed

using a submerged cylinder, which is the geometry later used in the experimental

methodology, so the correlation length of cylinder diameter used in Re is appropriate

and widely applicable, as many submerge structures are typically cylindrical in shape.

Figure 2 : Formation of vortices for various Reynolds number



3.1.2 Strouhal Number

An additional non-dimensional parameter has been established to relate the

frequency of vortex shedding (fs) to the flow conditions. This is given by the

Strouhal number S, and is defined in Eq. 2-2.

S = D *(fs) /U ........Eq. 2-2

Again, U is the free stream velocity, and D is the cylinder diameter. For a wide

range of Reynolds number, the Strouhal number varies very little, and can

essentially be taken as constant, as seen in Figure 3.

Figure 3 : Reynolds number and Strouhal number relationship

3.1.3 Lock In

As introduced earlier, lock in is a particular aspect of VIV which can result in

relatively large amplitudes of forced vibration. An analytical theory of lock in

based on first principles does not presently exist, and much of the research



encountered only gives descriptive or semi empirical evidence. As a result, the

present analysis only focuses on the key findings which are relevant to achieving

large amplitude vibrations, for the purpose of energy generation. Lock in is similar

to linear resonance in that the vibration amplitudes increase as the natural

frequency of the cylinder is approached by the vortex shedding frequency.

However, the analogy stops here, as lock in is a highly non-linear phenomenon,

affected by feedback loops referred to as fluid structure interaction. Additionally,

lock in does not result in the classic large amplitude spike at exactly the natural

frequency, as in linear resonance. Instead, lock in has been described as both a

self-limiting and self-governing occurrence, as the cylinder vibrations themselves

effect the vortex shedding process, and vice versa. It is self-limiting in the sense

that as the cylinder displacement increases, the vortex shedding is weakened, and

hence tends toreduce further motion.

3.1.4 Boundary Gap

Another modeling constraint affecting the oscillation of the cylinder is the

boundary gap ratio. The gap ratio is equal to the minimum distance between the

cylinder and lower flow surface boundary divided by the diameter of the cylinder.

The coefficient of viscous drag and lift coefficient were directly related to the gap

ratio. As the gap ratio increases, viscous drag decreases and lift increases. This is

due to the effect of the gap ratio on vortex shedding. When the cylinder is in close

proximity to the flow surface boundary, flow over the cylinder is uneven. Normal

vortex shedding patterns are weakened or disrupted completely. It was found that,

for a boundary gap value of about 3.0 or greater, the effect of the boundary gap on

vortex shedding was negligible. To calculate an appropriate gap distance for a

1.25” diameter cylinder, as will be used in the test apparatus, multiply the cylinder

diameter by three: 3*1.25” = 3.75”. This yields a gap ratio of 3, rendering the

effects of the boundary on vortex shedding negligible.

4. Energy Harvesting In Liquid Flow

The energy harvester based on Kármán vortex street is shown in the

“Electromagnetic energy harvesting from vibrations induced by Karman vortex street

“ (Dung-An Wang , Chun-Yuan Chiu, Huy-Tuan Pham)[3]. One approach to harvest



energy is to convert mechanical energy of ambient vibration into electrical energy by

electromagnetic induction. Electromagnetic harvesters have been proposed and

investigated by many researchers. Electromagnetic energy-harvesting device based on

vibration induced by Karman vortex Street is illustrated in figure 4(a), a flow channel

with a flexible diaphragm is connected to a flow source. A permanent magnet is glued

to a bulge on top of the diaphragm and a coil is placed above the magnet. The

pressure fluctuation due to vortex shedding from a bluff body drives the diaphragm

into vibration. As shown in Fig 4(b). the increase of the pressure causes the

diaphragm to deflect in the upward direction. As the pressure increases to the

maximum, the diaphragm reaches its highest position. When the pressure drops, the

diaphragm moves downward shown in Fig 4(c). As the pressure decreases to the

minimum, the diaphragm reaches its lowest position .Thus, by connecting the energy

harvester to a flow source, the oscillating movement of the diaphragm with an

attached magnet under a coil makes the energy harvesting possible.



Figure 4: Flutter energy harvesting

5. Vortex Induced Vibration Aquatic Clean Energy (VIVACE)

The Vortex Induced Vibration Aquatic Clean Energy converter design was

patented in 2008 by Professor Michael Bernitsas of the University of Michigan. The

converter harnesses energy from water flow using vortex induced vibrations. The

VIVACE system is composed of a cylinder secured horizontally in a stationary frame

and allowed to oscillate transverse to the direction of water flow. The cylinder is

connected to the frame at the ends of the cylinder, where magnetic sliders move up

and down over a rail containing a coil. The motion of the magnet over the coil creates

a DC current, which can be stored or converted to AC to be sent into the grid. This

technology is superior to dam technology in several ways. It is capable of producing

energy from fluid flow without altering the local environment, posing any danger to

nearby residents, changing the landscape in any visible way, or interfering with water

traffic in any slow moving waterway (0.5-5 knots). Energy generation from VIV has

significant potential for coastal areas as well. Energy demand in coastal regions is

much larger than demand inland. Scalability and versatility are two of the greatest

strengths of this technology. Modules can range in size from single-cylinder arrays to

thousand-cylinder, mega-watt producing power plants. In their initial report, Bernitsas

et al. outline array specifications for 1kW to 1000MW cylinder arrays. Areas of



potential power production include ocean water bodies and rivers. Flow in the prime

production speeds required for this technology is significantly lower than for other

turbine based hydrokinetic technologies.

According to Bernitsas, VIVACE has superior energy density compared with

other nonturbine ocean energy technologies. As of August 2010, Bernitsas’ start-up

company, Vortex Hydro Energy, has begun open water tests in the St. Clair River in

Port Huron, MI

Figure 5: Cylinder arrangement in VIVACE



5.1. Physical Model

A simple schematic of a single module of the VIVACE Converter considered

in this paper is depicted in Figure 6. The elements of this module are: a circular rigid

cylinder of diameter D and length L, two supporting linear springs each of stiffness

k/2, system damping system, one or more generators, generator damping,

transmission damping , and the energy generating damping . The cylinder is placed

with its axis in the z direction perpendicular to the flow velocity U, which is in

direction x. The cylinder oscillates in the y direction, which is perpendicular to its axis

in z and the flow velocity in x. As discussed in Section V, the VIVACE Converter

design is modular, scalable, and flexible in the sense of geometry and configuration.

Thus, converters of various sizes can be developed by assembling modules of various

sizes and properties in a variety of configurations.

Figure 6 : Simple Schematic of a VIVACE Module with Coordinate System

Figure 7 shows artist’s rendition of a small array of VIVACE Converter for an

offshore power plant. The supporting piles, which house all the transmission and

electricity generating components, are hydrodynamically faired to prevent their own



VIV. The oscillating cylinders are attached by small pins to sliding bearings on a steel

rod with springs and damping to provide an elastic support to achieve VIV of the

cylinders. The PTO system presently used in the VIVACE Converter lab models

consists of a gear-belt transmission system and an off-the-shelf rotary generator.

Alternatives such as a hydraulic system or a linear generator are possible.

Figure 7 : VIVACE setup

There is use of a hydraulic system to connect multiple VIVACE modules to

one generator. Direct transmission to mechanical energy through hydraulics to pump

water for irrigation or raise pressure for water desalination is being studied as well. In

addition to the quantities used to define a module, for a VIVACE Converter assembly,

the following geometric variables need to be defined as shown in Figure 8: h = water

depth, d = draft of the VIVACE Converter assembly, t = vertical distance between

centers of cylinders, p = horizontal distance between centers of cylinders.



Figure 8 : Arrangement of cylinders

5.2. Benchmarking

Two benchmarking methods are used in this section. First, VIVACE is

compared to traditional and alternative energy resources based on data [4].The

comparison results are shown in Figure 9 in terms of $/kWh. The assumptions behind

these calculations are summarized in Tables 1, 2, 3. Table 5 shows the fuel cost per

BTU; Tables 2 and 3show the assumptions for conventional and alternative energy

generation, respectively. The assumptions behind the VIVACE Converter are

summarized in Table 4..

Table 1:Fuel cost assumptions



Figure 9 : Comparison of energy sources

Table 2:Assumption of cost estimate of conventional energy source



Table 3:Assumption of cost estimation of alternate energy source



Table 4 : Data regarding 100 MW VIVACE converter



6. Vortex Shedding Vertical Axis Turbine (VOSTURB)

Current hydro-turbines aim to capture the immense energy available in tidal

movements, however commonly applied technologies rely on principles more

applicable in hydroelectric dams. Tidal stream currentsin some areas are not strong

enough to make such turbines both efficient and economically viable. A new low-

energy vortex shedding vertical axis turbine (VOSTURB) to combat the inefficiencies

and challenges of hydro-turbines in low velocity free tidal streams is available. Some

of the energy in tidal streams is extracted naturally from vortex shedding; as water

streams past a bluff body, such as pier, low pressure vortices form alternatively on

each side, inducing a rhythm of pressure differentials on the bluff body and anything

in its wake. VOSTURB aims to capture this energy of the vortices by installing a

hydrofoil subsequent to the bluff body. This foil, free to oscillate, translates the vortex

energy into oscillatory motion, which can be converted into a form of potential

energy. It aims to harvest such foil motion, or the ability of VOSTURB to capture

vortex energy, and begin to use the amount of tidal energy that can be theoretically

harnessed. A small scale model of VOSTURB, a cylindrical bluff body with a

hammer shaped hydrofoils shown below. Ultimately it was found that the frequency

of the VOSTURB foil oscillations corresponded highly with the theoretical frequency

of vortex shedding for all moderate to high flow speeds [6]. Low speeds were found

to produce inconsistent and intermittent small oscillations. This signifies at moderate

to high flow speeds, VOSTURB was able to transform some vortical energy into

kinetic. The maximum average power obtained 8.4 mW corresponded to the highest

flow velocity 0.27 m/s [6]. Scaled to prototype conditions this represented 50 W at a

flow velocity of 0.95m/s, the maximum available . Although it was ascertained that

VOSTURB could consistently capture some of the vortical energy; the percentage of

which could not be calculated with certainty. Thus, the average kinetic power

assessments of the foil were compared to the available power of the mean flow for

each flow speed calculated by two methods: (1) over the foil's swept area; (2) the area

of fluid displaced by the bluff body immediately in front of the foil. The maximum

efficiency of the foil, found for the fastest flow speed was at 18% and 45%

respectively. It was found that both average foil power, available flow power, and

efficiency all decreased with a decrease in flow velocity. This study can serve as only

a preliminary study for the effectiveness of VOSTURB as a hydro-turbine for tidal



power. In the experiments, the foil was allowed to oscillate freely with little

resistance. Future testing of VOSTURB needs to observe whether the vortex energy

can overcome the resistive torque introduced by a generator to induce oscillatory

motion as well as further optimize the foil design.

Figure 10: Schematic of VOSTURB capturing kinetic energy from vortex shedding



7. Energy harvesting in air flow

One method of energy harvesting based on Kármán vortex street, called

flapping-leaf. The flapping-leaf energy harvester had the same principle as the

‘energy harvesting eel’ while it was only designed to work in airflow. The device

consisted of a PVDF cantilever with one end clamped on a bluff body and the other

end connected to a triangular plastic leaf. When the airflow passed the bluff body, the

vortices produced , fluctuated the leaf and thus the PVDF cantilever to produce

electrical energy. The energy harvester generated a maximum output power of 17µW

under the wind of 6.5m/s [5]. It consists of a flexible plate with piezoelectric

laminates which was placed behind a bluff body. It was excited by a uniform axial

flow field in a manner analogous to a flapping flag such that the system delivered

power to an electrical impedance load. Experimental results showed that a RMS

output power of 2.5 mW can be derived under a wind of 27m/s. The generator was

estimated to have an efficiency of 17%. The plate had dimensions of 310 mm × 101

mm × 0.39 mm and the bluff body has a length of 550 mm.Dimensions of the

piezoelectric laminate were 25.4 mm × 20.3 mm × 0.25 mm. Jung and Lee (2011)

recently presented a similar electromagnetic energy harvester as VIVACE. Instead of

operating under water, this device was designed to work under air flow. In addition,

this device had a fixed cylinder bluff body in front of the mobile cylinder. These two

cylinders had the same dimensions. It was found that the displacement of the mobile

cylinder largely depends on the distance between the two cylinders and the maximum

displacement can be achieved when this distance was between three and six times of

the cylinder diameter. In the experiments, a prototype device can produce an average

output power of 50-370 mW under wind of 2.5-4.5 m/s. Both cylinders had a diameter

of 5cm and a length of 0.85 m. Zhu et al(2010c) presented a novel miniature wind

generator for wireless sensing applications. The generator consisted of a wing that

was attached to a cantilever spring made of beryllium copper. The airflow over the

wing caused the cantilever to bend upwards, the degree of bending being a function of

the lift force from the wing and the spring constant. As the cantilever deflects

downwards, the flow of air is reduced by the bluff body and the lift force reduced

causing the cantilever to spring back upwards. This exposes it to the full airflow again

and the cycle is repeated. When the frequency of this movement approaches the

resonant frequency of the structure, the wing has the maximum displacement. A



permanent magnet was fixed on the wing while a coil was attached to the base of the

generator. The movement of the wing caused the magnetic flux cutting the coil to

change, which generated electrical power. The proposed device has dimensions of

12cm × 8cm × 6.5cm. It can start working at a wind speed as low as 2.5m/s when the

generator produced an output power of 470 µW. This is sufficient for periodic sensing

and wireless transmission. When the wind speed was 5 m/s , the output power reached

1.6 mW

Figure 11: Principle of energy harvesting in air flow

7.1 Piezoelectric Energy Harvesting

Piezoelectric transducers have been used in several designs for fluid flow

energy harvesting. Their goal is to generate power, on the scale of microwatts and

milliwatts, for small electronic devices such as remote sensors. There have been flag-

like devices built, one of which is a piezoelectric eel , which is an underwater sheet of

piezoelectric polymer that oscillates in the wake of a bluff body. Operating in air,

other devices are based on more conventional rotating turbine designs that implement

piezoelectrics driven by cam systems .In the category of wheat-like generators is an

oscillating blade generator, which uses a piezoelectric transducer to connect a steel

leaf spring to leaf-like ears. The device utilized a vertical rigid sail, fixed to a



vertically cantilevered piezoelectric transducer. These devices would oscillate in a

fixed direction when introduced to wind

A photograph of one of the devices is shown in Figure 5. The assembly would

be placed in a moving air stream, such that the plane of the sail and the piezo buzzer

was perpendicular to the flow. The sail would oscillate forwards and backward

relative to the flow, causing the piezo to bend back and forth. This, through the direct

piezoelectric effect, would cause the piezo to generate a current through any electric

load connected to it.

Figure 12 : Photograph of a piezoelectric device

7.2 Remote Sensing Application

Operating on the micro and milliwatt scale, devices of this type are not

necessarily designed to be alternatives to large scale energy generation. Instead, most

of these devices, including ours, are designed for applications where batteries or long

power cords can be eliminated. In the right application, this can lead to a savings in

capital, maintenance, or labour costs.



One application that is a prime candidate for using energy harvesting devices

is remote sensing. Environmental and structural sensors are often used in locations

where providing power and data connections is not cost effective. Instead, sensors

transmit data wirelessly, and power is provided at the individual sensor. To limit

power requirements needed for data transmission, sensor networks are often designed

where each sensor operates as a node, relaying data along from other sensors. Power

often comes from a battery, but there the capacity of the battery must be able to

handle the drain from the device long enough that it does not become too time and

labor intensive to periodically replace. This situation can be alleviated by generating

energy onsite, which is where energy harvesting devices become an option. Through

these devices, power is either continuously provided to the sensor electronics, or more

often, it is stored in a small battery or capacitor to provide more continuous power.

This is a viable solution as long as the average power output of the energy harvester is

more than the average consumption of the sensor, over periods of time for which the

intermediate storage can provide power.

Figure 13: Possible remote sensing application



8. Conclusion

A vibration energy harvester is an energy harvesting device that couples a

certain transduction mechanism to ambient vibration and converts mechanical energy

to electrical energy. Ambient vibration includes machinery vibration, human

movement and flow induced vibration. For energy harvesting from machinery

vibration, the most common solution is to design a linear generator that converts

kinetic energy to electrical energy using certain transduction mechanisms, such as

electromagnetic, piezoelectric and electrostatic transducers. Electromagnetic energy

harvesters have the highest power density among the three transducers. However,

performance of electromagnetic vibration energy harvesters reduces a lot in micro

scale, which makes it not suitable for Magneto-electromagnetic System (MEMS)

applications.

Energy harvesters from flow-induced vibration, as an alternative to turbine

generators, have drawn more and more attention. Useful amount of energy has been

generated by existing devices and the start flow speed has been reduced to as low as

2.5 m/s. However, most reported devices that produce useful energy are too large in

volume compared to other vibration energy harvesters. Thus, it is difficult to integrate

these devices into wireless sensor nodes or other wireless electronic systems. Future

work should focus on miniaturise these energy harvesters while maintain current

power level. In addition, researches should be done to further reduce the start flow

speed to allow this technology wider application.



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