Simulation of Magneto Static of Linear Generator Driven by Vortex Induced Vibration (Full Paper)

Simulation of Magneto static of Linear Generator Driven by Vortex Induced Vibration

Indra Ranu KUSUMA*1

1Department of Marine Engineering, Faculty of Marine Technology, ITS-Surabaya.*E-mail: [email protected]

Abstract

Vortex Induced Vibration (VIV) phenomenon that oscillate objects in the current has become one alternative energy in marine. Vortex resulting vibrations are usually avoided in various design structures, but on the linear generator system, the phenomenon of vibration can be used as energy to move the rotor of linear generator. The reciprocating motion of objects move the rotor of generator to across magnetic field that resulted by stator. Continuously movement of rotor, it results electric current. This paper concerns about investigation on magneto static of Linear Generator driven by VIV. The methodology of this research is done by drawing 3D (Three dimensions) model then converts it into the 3D finite element field simulator for electromagnetic and electromechanical software. Material properties, Loads and restraints, a multiple-turn winding of a conductor and force distributions are defined in the 3D finite element field simulator. Next, apply mesh control on the model and mesh model created. Finally, the result of magneto static analysis is Magnetic Flux density, magnetic field intensity, applied current density, eddy current density, and force distribution of the model of linear generator. .

Keywords: Linear generator; Vortex induced Vibration (VIV); Alternative Energy, Marine Current, Magneto static.

1. Introduction

Nowadays, the utilisation of fossil fuels in human life starts facing problem. The price of fossil fuels continues to rise due to the limitation of fossil fuel reserves and dependency on fossil fuel is still high. Next, the amounts of fossil fuels are limited and gradually decreased every year. It is because fossil fuel is non renewable energy and it takes hundreds of millions of years old to produce. Moreover, fossil fuels not only have problem in their availability but it also gives contribution to emission. Emissions of fossil fuels can be resulted from exhaust gas of vehicle. Therefore, the renewable energy or alternative energy is the most important for human being. Environmentally friendly energy resource is the next frontier.

One of prospect renewable energy resource is a marine. Marine energy is the world's largest energy savings. It is clean energy, renewable, and abundant. It comes in five forms, such as currents, waves, tides, thermal gradient, and salinity gradient. In this research, it focuses on the marine currents induced vortex vibration. Vortex power plant or called VIVACE (Vortex Induced Vibration for Aquatic Clean Energy) is one of the technologies in hydropower. Vortex in general result in vibration and an effect that is usually avoided in various design marine structures. But in this system, the vibrations are resulted generated which can be harnessed energy to generate electrical energy.

Recently, a new method has been proposed researcher extracted the marine energy from currents. This conversion tool produces kinetic energy from slow-moving water currents, where the principle of works is to take advantage of the natural instability phenomenon of Vortex Induced Vibration (VIV). The VIV occurs when current flows through stationary object. During this time, vortices will come out on the object caused the process of shedding. Then vortex shedding oscillates the object. The oscillation or vibration of object is avoided within most marine structure because it causes fatigue and damage on the structure. Although the phenomenon VIV should be eliminated, it can be used as energy to move rotor of linear generator produced electric energy.

Seminar Nasional Teori dan Aplikasi Teknologi Kelautan, 15 Desember 2011 X - 1

The novel of VIV has been proposed as shown in figure 1. It illustrates the structure of a flexible platform for vortex induced vibration power plant. It consists of oscillating part, linear generator, propulsor and base rig. The movement of oscillating part due to vortex produces electrical Energy. Then, it transmits to base rig. Function of base rig is for processing and transmitting the electric power for offshore to on shore. Rig base is as same as body of Ship SWATH. It can sail from one place to another place. The propulsor is placed at the stern of base rig. The advantage of the propelled base rig is for adjusting marine current in order to find appropriate place in order to oscillate object.

Figure.1. Flexible Platform for Vortex Induced Vibration

2. Terminology of Linear Generator

Basic theory of the emergence of electrical energy from the linear generator is the principle of Electromagnetic Induction. Electromagnetic Induction in which it can simply be interpreted as a the process of change in mechanical energy (kinetic energy) into electrical energy. Electromagnetic induction occurs in a coil if there is a change in the number of lines of magnetic force that covered at all times.

Electromagnetic induction was first studied and discovered by Michael Faraday in 1831. Electromagnetic induction or electric impact is the generation of electrical energy from the magnetic field, so that the energy change is closely related to the concept of magnetic flux. Electromagnetic Induction and to understand, then we begin by studying the Magnetic Flux and Faraday's Law.

2.1. Magnetic Flux

Magnetic flux is defined as the product between the components of magnetic induction with a wide field. As the equation below: Φ=Bcosθ A (1)

Where: Φ = Magnetic flux (weber)B = Magnetic induction (tesla)A = Area of Field (m2)Θ = The angle between the normal line to the magnetic field


Oscilating Part

Base Rig

VIV Linear Generator

Propulsor

2.2. Faraday’s LawIt said that if there is a change on the amount of magnetic flux when entering the coil, then the ends of the coil has become induced emf. Then, the amount of induced emf will depend on the rate of flux differences and the number of windings. The equation of induced emf is as follows:

ε=−N ∆Φ∆ t

(2)

Dimana :ε = GGL Induksi (Volt)N = Jumlah LilitanΔΦ/Δt = Laju perubahan fluks magnetic.Tanda (-) = Sesuai Hukum Lenz

2.3. Lenz’s LawLenz's law is "the direction of induced currents is such that the resulting magnetic field opposite to the direction of magnetic field that causes induced currents." Based on Figure 2, it shows that the movement of the magnet inside the coil causes the galvanometer needle to deviate. If the magnetic north pole is moved close to the coil, the galvanometer needle deviated to the right. If the magnet is stationary in the coil, if the magnetic north pole is moved away from the coil, the galvanometer needle deviated to the left. Deviations galvanometer needle showed that at both ends of the coil there is an electric current. An event such as the emergence of electric current is called electromagnetic induction. The potential difference arising at the end of the coil is called electromotive force (emf) induction.

Figure.2. Working principle of induced emf

The occurrence of induced emf can be explained as follows: If the magnetic north pole brought near to the coil. The number of magnetic field entering the coil increases. Changes in the number of magnetic field that causes the deviation needle galvanometer. The same thing will happen if the magnet is moved out of the coil. However, the deviation of the galvanometer needle as opposed to the original deviation. Thus, it can be concluded that the induced emf causes changing in the magnetic of field enclosed by the coil. According to Faraday, a large induced emf at both ends of the coil is proportional to the rate of change of magnetic flux enclosed coil. That is, the faster the change of magnetic flux, the greater the induced emf arising.

2.4. Component of Linear generator

Linear generator consists of two main parts, namely Rotor & Strator. The stator is part of the generator that unable to move (static). Its Components is a stator core and stator. Stator laminations made from iron aims to reduce eddy current losses. Stator coil is formed of a coil of wire, where the number of coils is determined according to need. The rotor is one of the main components of a generator that can move in a linear motion. Permanent magnet generator and non permanent magnet such as copper coils is used as rotor. In design applications that have made, the basis of Linear Generator design as well as its formulation is to use the principle of induction of permanent magnets with the composition as shown figure 3.a. Two (2) pieces of magnets with different arrangements poles north (N) - South (S) and south (S) - north (N) will cut


NS

NS

NS

NS

NS

two pieces of the stator coils on different locations but with in the same core and one coil will be

awakened induced emf due to changes in the magnetic field in the same time. For the design of the stator by using copper wire (Copper Wire), it is wrapped around the iron core will be designed like a figure 3.b

2.5. Magnetostatic Equation of Linear Generator

Magnetostatic or so called DC Magnetic Field analysis belongs to the low-frequency electromagnetic domain or regime; i.e. displacement currents are neglected. In addition, the fields depend on position only and do not depend on time. Furthermore, the size of the object is much smaller than the wavelength. The Magnetostatic Analysis, linear and non-linear, calculates the magnetic fields produced by one the following: Permanent magnet and steady DC electric current.Maxwell’s equations relevant to magnetostatic analysis fields are:

∀×H=J s (3)∀ ∙B=0 (4)

where H is the magnetic field, Js is the source current density, and B is the magnetic flux density. The constitutive relation connects B and H:

B=μ(H+H c) (5)where m is the magnetic permeability, in general a function of H. Hc is the coercive force or coercivity. Thus the Magnetostatic Analysis solves the above two Maxwell’s equations. This type of analysis does not consider time-dependent effects such as eddy currents. It has many applications, including: DC machines; Permanent magnets; Motors; Generators; Actuators; Magnetic recording.The Magnetostatic analysis solves for the magnetic field inside the model. Once a solution is obtained, the following additional quantities are computed: Magnetic field distribution, Magnetic flux density distribution, applied current density, Nodal force distribution, rigid body force,and Inductance matrix. The magnetic field, the magnetic flux density, the nodal force, and the current density distributions are displayed on the model at nodes.

2.6. Power Equation of Linear Generator

GGL Induction equations below are used to determine the value of the output power of the Linear Generator System:

E=ωΨ pm N (6)

Where:

ω = angular frequency (rad / s) =ω=2πvw p

ψ pm =induction of permanent magnet flux per pole

wp = distance between the poles (m) ρ = Kaawat copper resistance (ohm / meter) l = Wire length (m) A = Wire cross-sectional area (m2)Φ = Fluks Magnetik (weber)B = Induksi Magnetik (tesla)A = Luas Bidang, dimana dalam hal ini


Figure 3.a Permanent Magnet Linear Generator Figure 3.b Non Permanent Magnet LG

Ψ pm=∅2

=B× A silinder

2 (weber)

N = number of coils in the coil =N=N poleN turns v = rate of the velocity of the magnet (m / s)

magnet berbentuk Silinder (m2)

3. Simulation and Analysis

Simulation of magnetostatic is reached a study by performing the following steps. Firstly, it draw linear generator in 3D (Three Dimension) modeling. By using finite element method which solves the physical equations directly without any simplifications or assumptions, it defines material properties for each body, Specifies restraints and loads. Specify restraints such as Flux is Normal for magnetic studies. For electric studies, specify voltages or charges. Then, Mesh the model where it divides the model into many small pieces called elements.

3.1. 3D (Three Dimension) Modeling of Linear Generator

VIV Linear Generator is designed in three dimensions as shown in figure 4. Its rotor is attached at ocilating part. Because of vortex, the objects move reciprocating carried the generator’s rotor. The rotor contains copper coil that cross a long stator’s and cut off magnet field of rotor.

Figure.4. 3D Modeling of Linear Generator

3.2. FEA ( Finite Element Analysis)Finite Element Analysis (FEA) provides a reliable numerical technique for analyzing engineering designs. The process starts with the creation of a geometric model. Then, the program subdivides the model into small pieces of simple shapes (elements) connected at common points (nodes). Finite element analysis programs look at the model as a network of discrete interconnected elements.The Finite Element Method (FEM) predicts the behavior of the model by combining the information obtained from all elements making up the model. Meshing is a very crucial step in design analysis. Mesh control lets you specify different sizes of elements for components and faces. FEA estimates a global element size for the model taking into consideration its volume, surface area, and other geometric details. The size of the generated mesh (number of nodes and elements) depends on the geometry and dimensions of the model, element size, mesh tolerance, and mesh control. In the early stages of design analysis where approximate results may suffice, you can specify a


inzet

larger element size for a faster solution. For a more accurate solution, a smaller element size may be required, as shown in figure 5..

Tabel 1. Mesh Information

No.Of Nodes

No.Of Elements

Element Size (m)

Tolerance (m)

56832 282423 0.093299 0.004665

3.2.1. Material

Define all the necessary material properties required by the corresponding analysis type. For example, the permeability is required for Magnetostatic, AC Magnetic, and Transient Magnetic studies, while the permittivity is needed for Electrostatic studies. Definition of material properties at any time before running the analysis, as listed in table 2.

Table 2. Material InformationNo. Part Name Material Name Permeability Type1 air gap-1-Body 1 (Extrude1) Air Isotropic

2 part osilating ems-1-Body 1 (Extrude8) Aluminium Isotropic

3 Part stator 2-1-Body 1 (Fillet1) Copper Isotropic

4 Part stator 2-2-Body 1 (Fillet1) Copper Isotropic

5 part stator ems-1-Body 1 (Extrude4) Aluminium Isotropic

6 Partair-1-Body 1 (Extrude1) Air Isotropic

7 rotor lg-1/gen rotor 1-1-Body 1 (Extrude3) Silicon Iron Isotropic

8 rotor lg-1/gen rotor 2-1-Body 1 (Extrude4) FR-4 EG 150 Isotropic

9 rotor lg-1/gen rotor 3-1-Body 1 (Fillet1) Copper Isotropic

10 rotor lg-2/gen rotor 1-1-Body 1 (Extrude3) Silicon Iron Isotropic

11 rotor lg-2/gen rotor 2-1-Body 1 (Extrude4) FR-4 EG 150 Isotropic

12 rotor lg-2/gen rotor 3-1-Body 1 (Fillet1) Copper Isotropic

3.2.2. Load/Restrain

Loads and restraints are necessary to define the electric and magnetic environment of the model. The results of analysis directly depend on the specified loads and restraints. Loads and restraints are applied to geometric entities as features that are fully associative to geometry and automatically adjust to geometric changes.For example, if you apply a voltage to a face; all the nodes of that face are assigned the applied voltage. If you modify the geometry such that the area of the face is changed, then again all the nodes of that face are assigned that same applied voltage. Nevertheless, remeshing the model is required after any change in geometry to update loads and restraints.

Tabel 3. Load/Restrain

Figure 6. Load / Restrain3.2.3. Coil

A coil literally means a multiple-turn winding of a conductor such as copper wire wound around a bobbin. When the conducting windings carry current, a magnetic field is produced. In the context of FEA, it can also mean a solid or a volume conductor carrying a current that produces a magnetic field.


Figure 5. Meshing Model

Figure 7. Wound Coils

3.3. Results

Magnetic Flux Density (Tesla) shows that the rotor part has induction of magnetic field between 3.104 sampai dengan 7.104 tesla. It is huge number of flux density. Although only 30 A applied to the coils, The rotor has become non permanent magnet with huge magnetic flux density. In the rotor, It is still no magnet because there is no current applied to this part. However, when the rotor move reciprocating with fast frequency, the coils in the stator has Electric Induction.

Figure 8. Magnetic Flux DensityThen, the result has been shown in figure 8 supported the nest results. It can be seen in figure 9. The Magnetic Field Intensity results. It has similar result the rotor has become good magnet dan has intensinty 4 107 – 6 107 Amp/m.


Figure 9. Magnetic Field Intensity

Figure 10. Applied Curent Density

However, the using of current will result current density, as shown in figure 10. So it can result eddy current. Eddy current phenomenon can be reduced using lamination iron in the rotor part and statator. Or the design cooling system will help to the system.

4. SummaryThe flexible structure for linear generator driven by VIV has been proposed. In the point of magnetic view, this system can be apllied well. The magnetic static can be resulted from the coil current. Although, the stability of this structure is not in the discussion. The result of magneto static analysis has been got as follows: Magnetic Flux density is high approximately more than 5.104tesla, magnetic field intensity is less than 6. 107 Amp/m, applied current density or eddy current density is still high approximately 3 10 10 Amp/m2. Finally, Linear Generator VIV can be candidat and has prospect as renewable energy resource in Indonesia. It is clean energy, renewable, and abundant.


Reference 1. Pontes, M.T., and Falcão, A., (2001), “Ocean Energies: Resources and Utilization”,

Proceedings of 18th World Energy Council Congress, Buenos Aires, October 2001.2. Sarpkaya, T., 2004, “A Critical Review of the Intrinsic Nature of Vortex Induced

Vibrations,” Journal of Fluids and Structures, Vol. 19(4), pp 389-447.3. Bernitsas, M. M., Ben-Simon, Y., Raghavan, K., Garcia, E. M.H., 2006, “VIVACE

(Vortex Induced Vibrations Aquatic Clean Energy): A New Concept in Generation of Clean and Renewable Energy from Fluid Flow,” 25th International OMAE Conference, 2006.

4. Bernitsas, M., MacBain, J. "VIVACE (Vortex Induced Vibration Aquatic Clean Energy): A New Concept In Generation Of Clean And Renewable Energy From Fluid Flow" PowerPoint Presentation 7 June 2006.

5. Hulbert, 2008. Final Report Design of a Power Take Off System for the VIVACE Generator. Naval Architecture and Marine Engineering in The University of Michigan. Michigan.

6. Elizabeth Maloney, Hahn Garcia. “Prediction by Energy Phenomenology for Harnessing Hydrokinetic Energy Using Vortex-Induced Vibrations”. Naval Architecture and Marine Engineering University of Michigan, 2008

7. Raghavan, Kamaldev. “Energy Extraction from a Steady Flow Using Vortex Induced Vibration”. Naval Architecture and Marine Engineering University of Michigan, 2007


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Simulation of Magneto Static of Linear Generator Driven by Vortex Induced Vibration (Full Paper)