stability of tubular wind turbine tower

TO STUDY OF WIND RESISTANT STABILITY OF TUBULAR WIND TURBINE TOWER By Fahad jamil, Saad bin zia, Parvez ali abbasi, Moiz ansari NED University of Engineering & Technology MECHANICAL ENGINEERING Dec 5, 2012 NED UNIVERSITY OF ENGINEERING & TECHNOLOGY 1 ABSTRACT The work in this report represents how wind turbine towers are designed to give maximum stability in extreme conditions. Different stability criterion are explained and analyzed both analytically and numerically with the help of different standards (euro codes, AISC). For numerical analysis all task are performed on finite element package Abaqus. Two different tubular tower models are first analyzed and checked whether they satisfied stability criterions (deflection, local buckling). It was found that the both the towers are safe against the local buckling and stable under the extreme wind loading. The methodologies adopted in designing wind turbine tower to achieve an optimized result like, minimization of mass, maximization of natural frequency or maximization of stiffness at the end of the report is done. During optimization is observed that the 250kw tower model gives economical result if its design for the variable thickness i.e. less material required for manufacture which reduces its cost. 2 CHAPTER #1 1. INTRODUCTION 1.1. Introduction Owing to the rapidly increasing demand of energy, Energy generation providers recognized the importance of renewable energy. The use of wind to produce energy is one of the major forms of renewable energy. In fact, wind energy is the only renewable energy which grown faster than predicted. One major advantage of wind energy is that it is substantially economic way of producing energy. Renewable energy is energy which comes from natural resources such as sunlight, wind, rains, tides, waves & geothermal heat which are renewable (naturally replenished). About 16% of global final energy consumption comes from renewable, with 10% coming from traditional biomass, which is mainly used for heating, & 3.4% from hydroelectricity. To extract energy from wind, Wind turbines emerged as one of the most efficient ways of converting the kinetic energy in wind into mechanical power [13]. Many energy providers invested in research and development of wind turbines. Now a days wind turbines are installed in many countries. However, during the last decade many wind turbine damage occurs due to the structural failure of wind turbine towers. Majority of these failures are caused by the strong wind striking the structure or wind induced vibrations. Others are caused by high stresses and buckling loads. 3 Wind turbine towers are designed as thin-walled structure having thickness very less than the diameter. In order to reduce the weight of tower, the vertical dimensions of the tower is relatively large compared to its horizontal dimensions. This slender nature of wind turbine tower makes it more sensitive to wind loading. There are many different configurations in which wind turbine support structure is designed. It common practice to design wind turbine towers as taper tubular column since they are give more stability to tower against the wind loads and to save the material[11]. 1.2. Scope of project The scope of this research based project is to understand the stability against the wind loads and other structural design criterion (buckling, deflection, stress and natural frequency) to attain the maximum stability of wind turbine tower. It also includes finite element analysis and analytical analysis of two different wind turbine support structure. In addition, the report also includes a brief literature about the importance of foundation design in stability of wind turbine tower. CH I) contains brief introduction wind turbine system. CH II) contains the methodologies adopted in designing wind turbine tower. It discuss about the basic assumptions, design variables and pre-assigned variables. It also summarizes the two tower model on which calculations are performed latter. CH III) contain the design requirements of wind turbine towers. Buckling theories and design codes, stresses, Limitation on deflection and natural frequency. CH IV) summarizes about the wind loads. It contains wind data, wind profile shapes and formulation of wind loads. Ch V) contains finite element analysis of wind turbine tower. Ch VI) deals with the Dynamics (modal analysis) of wind turbine tower. CH VII) contains the numerical analysis of wind turbine tower. CH VIII) deals with the foundation design CH VIII) gives conclusions about the results obtained by finite element and numerical analysis. 4 1.3. Objective of project The objective of this project is simply to understand the basic design aspects of wind turbine towers and methodologies to achieve maximum stability by using different design criteria's and standard, and verifying these criterion with the help of finite element software. 1.4. Wind as renewable source The use of wind energy is increasing at an annual rate of 20%, with a worldwide installed capacity of 238,000 megawatts (MW) at the end of 2011, and is widely used in Europe, Asia, and the United States. The use of wind to produce energy is one of the major forms of renewable energy. In fact, wind energy is the only renewable energy which grown faster than predicted. One major advantage of wind energy is that it is substantially economic way of producing energy. 1.5. Working of wind turbines Wind power is the conversion of wind energy into a useful form of energy. A blade acts much like an airplane wing. When the wind blows; a pocket of low-pressure air forms on the downwind side of the blade. The low-pressure air pocket then pulls the blade toward it, causing the rotor to turn. This is called lift. The force of the lift is actually much stronger than the wind's force against the front side of the blade, which is called drag. The combination of lift and drag causes the rotor to spin like a propeller, and the turning shaft spins a generator to make electricity[13]. Wind turbines can be used as stand-alone applications, or they can be connected to a utility power grid or even combined with a photovoltaic (solar cell) system. For utility-scale sources of wind energy, a large number of wind turbines are usually built close together to form 5 awind plant. Several electricity providers today use wind plants to supply power to their customers. Stand-alone wind turbines are typically used for water pumping or communications. However, homeowners, farmers, and ranchers in windy areas can also use wind turbines as a way to cut their electric bills. Small wind systems also have potential as distributed energy resources. Distributed energy resources refer to a variety of small, modular power-generating technologies that can be combined to improve the operation of the electricity delivery system 1.6. History & Background of Wind Energy Wind power has been used as long as humans have put sails into the wind. Early in the twentieth century, windmills were commonly used across the Great Plains to pump water and to generate electricity. New ways of using the energy of the wind eventually spread around the world. By the 11th century, people in the Middle East were using windmills extensively for food production; returning merchants and crusaders carried this idea back to Europe. The Dutch refined the windmill and adapted it for draining lakes and marshes in the Rhine River Delta. When settlers took this technology to the New World in the late 19th century, they began using windmills to pump water for farms and ranches, and later, to generate electricity for homes and industry. Industrialization, first in Europe and later in America, led to a gradual decline in the use of windmills. The steam engine replaced European water-pumping windmills. In the 1930s, the Rural Electrification Administration’s programs brought inexpensive electric power to most rural areas in the United States. However, industrialization also sparked the development of larger windmills to generate electricity. Commonly called wind turbines, these machines appeared in Denmark as early as 1890. In the 1940s the largest wind turbine of the time began operating on a Vermont hilltop known as Grandpa’s Knob. This turbine, rated at 6 Fig1.1. Earlier Wind Mills in 19th Century 1.25 megawatts in winds of about 30 mph, fed electric power to the local utility network for several months during World War II. 1.7. Wind energy in Pakistan Pakistan is fortunate to have something many other countries do not, which are high wind speeds near major centers. Near Islamabad, the wind speed is anywhere from 6.2 to 7.4 meters per second (between 13.8 and 16.5 miles per hour). Near Karachi, the range is between 6.2 and 6.9 (between 13.8 and 15.4 miles per hour). In addition to high wind speeds near major centre’s as well as the Gharo and Keti Bandar corridor, Pakistan is also very fortunate to have many rivers and lakes. Wind turbines that are situated in or near water enjoy an uninterrupted flow of wind, which virtually guarantees that power will be available all the time Pakistan is developing wind power plants in Jhimpir, Gharo, Keti Bandar and Bin Qasim in Sindh. The government of Pakistan decided to develop wind power energy sources due to problems supplying energy to the southern coastal regions of Sindh and Balochistan, the project was undertaken with assistance from the government of China. 7 Fig.1.2 Wind Turbine Site at Jhampir http://maintainableworld.blogspot.com/2012/03/zorlu-plans-another-200-mw-windpower.html 1.8. Resource potential The wind map developed by National Renewable Energy Laboratory (NREL), USA in collaboration with USAID, has indicated a potential of 346,000 MW in Pakistan. The Gharo - Keti Bandar wind corridor spreading 60 KM along the coastline of Sind Province and more than 170 km deep towards the land alone has a potential of approximately 50,000 MW. 30% ~ 32% Capacity Factor estimated in Gharo -Keti Bandar area. Wind resource in Gharo - Keti Bandar wind corridor validated by RisO DTU National Laboratory, Denmark The govt. of Pakistan has targeted at least 5% of the total power generation from ARE sources by the year 2030. 8 Fig.1.3. Wind Farm (6MW) at Jhampir http;//www.aedb.org/main.htm 1.9. Wind map of Pakistan 9 Fig.1.4. Wind Map of Pakistan http://www.riazhaq.com/2011/02/pakistan-launches-wind-power-projects.html 1.10. Current Status of On-Grid Wind Power Generation Projects S.No Company Location of Land 1 Gharo New Park Energy Pvt Ltd 10 2 TenagaGenerasi Ltd. Kuttikun 3 Green Power (Pvt) Ltd, Kuttikun 4 Dawood Power Ltd. Bhambore 5 Master Wind Energy Ltd, Jhampir 6 Zephyr Power Ltd Bhambore 7 Beacon Energy Ltd. Kuttikun 8 HOM Energy (Private) Ltd, Jhampir 9 Sachal Energy Development Pvt Ltd, Jhampir 10 Fauji Fertilizer Company Ltd. Jhampir 11 Arabian Sea Wind Energy Pvt. Ltd. Lakha 12 Lucky Energy (Pvt) Ltd Jhampir 13 Metro Power Co. (Pvt) Jhampir 14 Gul Ahmed Energy Ltd, Jhampir 15 ZorluEnerji, Jhampir 16 Wind Eagle Ltd. (Technology Plc Ltd), Jhampir 17 Wind Eagle Ltd. (Technology Plc Ltd), Jhampir 18 Sapphire Wind Power Company (Pvt) Ltd, Jhampir 19 CWE Jhampir 20 Abbas Steel Group Bhambore 21 Abbas Steel Group Bhambore 11 1.11. Wind turbine Wind energy is the conversion of the kinetic energy of the wind, by the use of wind turbines, into mechanical energy which is then converted into electricity. Mechanical energy is simply created when the wind turbine blades spin and a generator is turned, thus producing electricity. 1.12. Components of wind turbine A wind turbine is made up of the following components: 1.12.1.Foundation In order to guarantee the stability of a wind turbine a pile or flat foundation is used, depending on the consistency of the underlying ground. 1.12.2.Tower The tower construction doesn’t just carry the weight of the nacelle and the rotor blades, but must also absorb the huge static loads caused by the varying power of the wind. Generally, a tubular construction of concrete or steel is used. An alternative to this is the lattice tower form. 1.12.3.Nacelle The nacelle holds all the turbine machinery. Because it must be able to rotate to follow the wind direction, it is connected to the tower via bearings. The build-up of the nacelle shows how the manufacturer has decided to position the drive train components (rotor shaft with bearings, transmission, generator, coupling and brake) above this machine bearing. Fig.1.5. Wind Turbine Components 12 www.wwindea.org/technology/ch01/e n/1_2.html 1.12.4.Rotor blade The rotor is the component which, with the help of the rotor blades, converts the energy in the wind into rotary mechanical movement. Currently, the three-blade, horizontal axis rotor dominates. The rotor blades are mainly made of glass-fibre or carbon-fibre reinforced plastics (GRP, CFRP). The blade profile is similar to that of an aero-plane wing. They use the same principle of lift: on the lower side of the wing the passing air generates higher pressure, while the upper side generates a pull. These forces cause the rotor to move forwards, i.e. to rotate. 1.12.5.Hub A wind turbine hub, a fairly simple mechanism of the wind system, connects the motor with the blades using a gear to move the motor. 1.12.6.Transformer (this is not a part of the Wind Turbine) 1.13. Types of wind turbine tower The tower for wind turbine carries the rotor and the nacelle. Towers for large wind turbines may either tubular steel towers, lattice towers, or concrete towers[7]. 1.13.1.Guyed Tower Fig.1.6. Guyed tower 13 [7] A guyed tower is one which is held in place with guy wires. The tower itself is often just along steel pole which is 30 to 100 feet tall. There are usually three or four guy lines made of steel cable which run from the top of the tower to guy anchors on the ground which hold the tower in place. The anchors are usually set into a concrete base in the ground or held in place with augers that have been drilled into the ground. Guyed towers are often the least expensive type of wind tower and are often an excellent choice for a small residential scale wind turbine. The one thing you have to consider is that a guyed tower needs considerable space because the guy wires extend well beyond the base of the tower. Use of guy wires may bring down the initial cost of the tower as it would require less tower material. Many small wind turbines use guy wires for this reason; however the maintenance costs for the guy wires add more costs to the operation, thus should be avoided if possible. Additionally, the guy wires require a larger footprint and additional foundations. Therefore, it may present a problem with land accessibility and usage which may not be suitable in farm areas. 1.13.2. Lattice tower A lattice structure is made of struts which are assembled in a specific order to obtain a prescribed structural strength and stiffness with as little material as possible. In comparison with other tower concepts the lattice towers are less material consuming. The steel is used most effectively and the weight of the tower is less than the other comparable concepts. Quite tall towers can be built by means of lattice system. Since, the towers can be assembled on site no transport difficulties will be encounter. Lattice towers are manufactured using welded steel profiles. In general, the initial cost to build a lattice tower is less than the tubular tower because it requires less material for similar stiffness. Although the initial material cost may be lower for the lattice tower, the assembly and maintenance costs may be higher as each bolt needs to be tightened to a specification and checked periodically [14]. 14 Fig 1.7.Lattice Tower [14] 1.13.3.Tubular tower Most large wind turbines are delivered with tubular steel towers, which are manufactured in sections of 20-30 meters with flanges at either end, and bolted together on the site. The towers are conical (i.e. with their diameter increasing towards the base) in order to increase their strength and to save materials at the same time. This type of tower is constructed as a large tube often tapered at the base. On most of the larger towers of this type there is a ladder in the inside of the tube so that a worker can climb the tower to do repairs and maintenance on the turbine[7, 14]. The tubular tower has many advantages over the lattice tower. The enclosed area of the tubular tower cavity is useful. First, it provides a covered, protected area for climbing to access the wind turbine in bad weather conditions. Also, it provides a covered area that can house many electrical components. In a cold climate, wind wet area, this is an important feature. It provides a certain level of security by limiting the access to the turbine unlike the lattice tower. Additionally, it is more maintenance friendly. Although the initial material cost may be higher than the lattice tower, it does not rely on many bolted-connections which need to be torque and checked periodically. 15 Fig 1.8.Tubular Tower[14] Aesthetically, it is more appealing than the lattice tower. European countries have always favored tubular towers for aesthetic reasons. However, for very large wind turbines, transportation may be a challenge. The sections of the tubular towers are manufactured and then assembled on the wind turbine site. The current limitation of the tubular section size is 4.3 m in diameter[14]. 1.13.4. Hybrid concrete and tubular steel tower Hybrid tower used both concrete and tubular steel sections. The lower part is made up of concrete and the tubular section is mounted on the top of the concrete. The big advantage: transport and installation can be handled with conventional equipment. With a hub height of 100 meters, this makes a hybrid tower more cost-efficient than steel towers[14]. 16 Fig 1.9. Hybrid Concrete and Steel Tower[14] 1.13.5.Ferro-concrete tubular tower This types of concrete towers have are made of steel reinforcement bars. They have better dampening characteristics then those of other steel towers. These type of towers are cheaper but much heavier in weight than other towers[7]. There are two types of Ferro-Concrete towers: a) In-situ concrete tower: There constructed on site (in-situ), so they are free from transportation and fitting problems. b) Pre-cast concrete towers: Individual tubular section is pre-cast at pre-casting plant. These sections are transported to site and then placed over the foundation. These sections are then fastened together to form a unit with the steel cables running through the core of concrete tower wall. 17 CHAPTER #2 2. METHODOLOGIES A wind turbine tower is the main structure which supports rotor, power transmission and control systems, and elevates the rotating blades above the earth at a certain height.A successful structural design of the tower should ensure efficient, safe and economic design of the whole wind turbine system. It should provide easy access for maintenance of the rotor components and sub-components, and easy transportation and erection. Good designs ought to incorporate aesthetic features of the overall machine shape. 2.1. METHODOLOGIES In fact, there are no simple criteria for measuring the above set of objectives. However, it should be recognized that the success of tower structural design is judged by the extent to which the wind turbine main function is achieved. The different optimization methodologies considered. Each methodology differed, however, in selecting a criterion to be optimized [3]. 2.1.1 Minimization of the tower’s mass A minimum weight structural design is of paramount importance for successful and economic operation of a wind turbine. The reduction in structural weight is advantageous from the production and cost points of view. 2.1.2 Maximization of the tower’s stiffness The main tower structure must possess an adequate stiffness level. Maximization of the stiffness is essential to enhance the overall structural stability and decrease the possibility of fatigue failure. For a cantilevered tower, stiffness can reasonably be measured by the magnitude of a horizontal force applied at the free end and producing a maximum deflection of unity. 2.1.3 Maximization of the tower’s stiffness to mass ratio Maximization of the stiffness-to-mass ratio which is directly related to the physical realities of the design is a better and more straightforward design criterion than maximization of the stiffness alone or minimization of the structural mass alone. 18 2.1.4 Minimization of vibrations Minimization of the overall vibration level is one of the most cost-effective solutions for a successful wind turbine design. It fosters other important design goals, such as long fatigue life, high stability and low noise level. 2.1.5 Minimization of a performance index that measures the separation between the structure’s natural frequency and the turbine’s exciting frequency Reduction of vibration can be achieved by separating the natural frequencies of the structure from the exciting frequencies to avoid large amplitudes caused by resonance. 2.1.6. Maximization of the system natural frequency The phenomenon of resonance needs to be avoided to safeguard against the failures due to large amplitude responses, stresses and strains. The frequency of excitation cannot be changed as it is directly related to the operational requirements of wind turbine rotor. Hence the only way of avoid resonance is to control the natural frequency of the system. Another alternative for reducing vibrations is the direct maximization of the system natural frequencies. Higher natural frequencies are favorable for reducing both of the steady-state and transient responses of the tower. Different research studies were done in the past on these optimization techniques it was found that the maximization of tower natural frequency yields the most favorable results. 2.2. Method of increasing the natural frequency of the system There are two methods by which system natural frequency can be increased: a) By reducing the mass of the system b) By increasing the stiffness of the system The natural frequency of the system can be changed either by varying the mass or stiffness. However, reducing the mass of the tower is not feasible as it is governed by the structural requirement of the tower. Therefore, the stiffness of the system is the most prominent factor that is often changed to increase the natural frequency of the tower. 19 2.3. Basic Assumptions[3] 1) The basic structural model of the tower is represented by an equivalent long, slender cantilever beam built from segments (modules) having different but uniform crosssectional properties. The tower is cantilevered to the ground, and is carrying a concentrated mass at its free end approximating the inertia properties of the nacelle/rotor unit. This mass is assumed to be rigidly attached to the tower top. 2) Material of construction is linearly elastic, isotropic and homogeneous. The tower has a thin-walled circular cross-section. 3) The Euler-Bernoulli beam theory is used for predicting deflections. Secondary effects such as axial and shear deformations, and rotary inertia are neglected. 4) Distributed aerodynamic loads are restricted to profile drag forces. A two-dimensional (2D) steady flow model is assumed. 5) Nonstructural mass will not be optimized in the design process. Its distribution along the tower height will be taken equal to some fraction of the structural mass distribution. 6) Structural analysis is confined only to the case of flapping motion (i.e. bending perpendicular to the plane of rotor disk). 7) Under any load combination (including any load safety factors), the material of the load bearing structural elements of the tower should remain in the linear elastic region of its stress-strain diagram i.e. no plastic deformation has occurred. 2.4. Description of the structure: As the name of the project suggest we have taken tubular tower in our study right throughout. We have model two different wind turbine towers one for 5kw and 250kw. They are designed as tapered tubular tower with increasing diameter towards the base. The thickness remains constant throughout the height of tower. The dimensions of 5kw tower are at base the outer diameter is 825mm and at the top the inner diameter is 250mm. the thickness of the tower is constant throughout and it is 6mm. The height of the tower is 12m. 20 The dimensions of 250kw tower are at the base the diameter is 2.5m and at the top the outer diameter is 1.5m. The thickness of the tower is constant and it is 15mm. The height of the tower is 35m. The tower dimensions are listed in a table below: Table 2.1.Tower Dimensions 5kw Tower Outer diameter 250kw tower 0.850m 2.5m 0.844m 2.485m 0.250m 1.5m 0.244m 1.485m Thickness 0.006m 0.015m Height 12m 35m at base Inner diameter at the base Outer diameter at the top Inner diameter at the top 2.5. Material used in wind turbine towers 2.5.1. ASTM 572 ASTM 572 is most commonly used material in wind turbine towers.ASTM A572 Grade 50 is considered a "workhorse" grade and is widely used in many applications. ASTM 572 is a high strength, low alloy steel that finds its best application where there is need for more strength per unit of weight. Less of this material is needed to fulfill given strength requirements than is necessary with regular carbon steels. In addition, ASTM A572 is noted for its increased resistance to atmospheric corrosion. Particularly Grade 50 contains more alloying elements than plain carbon steel and thus is 21 somewhat more difficult to form. Grade 50 is more difficult to cold work, but can be successfully bent or shaped but requires more force than plain carbon steel. It is commonly used in structural applications, heavy construction equipment, building structures, heavy duty anchoring systems, truck frames, poles, liners, conveyors, boom sections, structural steel shapes, and applications that require high strength per weight ratio. Fig. 2.1 Stress-strain curve for ASTM 572.[15] Material Composition Thickness Elastic Modulus Yield Stress Percentage Elongation (Gauge length= ) ASTM 572 0.18C, 1.2Mn, 0.44P, 0.05Si 25 200 350 25 Table 2.2.Material properties for ASTM 572 22 2.5.2. S355JR (equivalent to ASTM 572) S355 structural steel plate is a high-strength low-alloy European standard structural steel covering four of the six "Parts" within the EN 10025 – 2004 standard. With minimum yield of 350MPa, it meets requirements in chemistry and physical properties similar to ASTM A572 / 709. Careful attention should always be placed on the specific variation of S355 required if considering substitute material. S355 is used in almost every facet of structural fabrication. Typical applications include:      Structural steel-works: bridge components, components for offshore structures Power plants Mining and earth-moving equipment Load-handling equipment Wind tower components In our wind turbine tower design we have used ASTM 572 so our design and calculations are based on material properties of it. 23 CHAPTER #3 3. TOWER DESIGN The most obvious one is that it places the wind turbine at a certain elevation where desirable wind characteristics are found. It houses many electrical components, connections and the control protection systems and provides access area to the wind turbine. Most importantly, the wind turbine tower supports the wind turbine (a nacelle and a rotor) and carries the loads generated from the turbine. The structural properties of the wind turbine tower are very important as the property such as tower stiffness has a big influence on the performance and structural response of the wind turbine. Tubular towers can have either a round or a polygonal cross section. They can have an upwards (conically or stepwise) tapered geometry, which takes into consideration the smaller bending moment at the upper part. Modern wind turbine towers are tapered tubular tower; they have diameter increases towards the base. Generally, the idea is to increase the strength towards the base where high bending stresses are susceptible. Also, it saves the material and thereby reducing the cost of the tower[15]. Usually, the tubular of wind turbine tower has a large the ratio of height (H) to least horizontal dimension (D) that makes it a particularly more slender and wind sensitive than any other structures. On the other hand, the thickness is less than the radius of the tubular of shaft; hence the tower is more prone to buckling. 3.1. Height of the tower The height of the tower is a site-dependent parameter because it is upto the wind characteristics of the site. The design optimization for the least cost could favor tall towers in low wind areas and shorter towers in high wind areas. However, if there are obstacles such as trees or tall objects that may make the wind more turbulent, taller tower will be required. In addition, tall towers may prevent the turbine from the effect of wind shear if the site has frequent wind shear occurrence. 24 3.2. TOWER DESIGN REQUIREMMENTS The tower design is based primarily on types of load acting on the tower. These loads include[16]: a) Dead Load: loads acting from the rotor, nacelle and additional equipment at the top of the tower. b) Lateral Load: loads acting on the tower due to wind. This include wind shear which is may be uniform or linearly acting along the height of the tower or it may be varying by a cubic polynomial function. To counter these loads the tower must have adequate: i) Axial Strength: the critical load capacity of the tower in the axial direction must be greater than the applied axial loads by a factor of safety. ii) Flexural Strength: the flexural strength of the tower must be greater than the bending strength i.e. it can sustain moment generated by the wind force. Also it can sustain local buckling moment taking into account the slenderness of the tower. Certain limitations are also applied on the tower cross-sectional dimensions and on tower top deflection and rotation. A satisfactory tower design must meet all the above design requirements. 3.3. BUCKLING OF COLUMNS “Buckling is instability of equilibrium in structures that can occur from compressive load or stresses. A structure or its component may fail due to buckling at a load much smaller than the load which is produce material strength failure” [11]. Wind turbine towers are thin-walled structure which is made from thin-plates joined along their edges. The thickness of the plate is significantly small compared to other cross-sectional dimensions which are in turn small compared to the overall geometric dimensions. For a given column length and cross-sectional area, the designer can either avoid local buckling by using low b/t (width to thickness) ratios or avoid global buckling by using high b/t ratios. However, in the first case the global buckling load will be relatively small. 25 Thin-walled structures are susceptible to local buckling if in-plane stresses reach their critical values. Local buckling is manifested by localized deformations of the geometry of the structure. However, if a thin-walled column is made sufficiently long it may suffer global buckling before it experiences local buckling. This means that thin-walled structures must be designed against both local and global buckling. Theory and experiments show that the local and overall buckling phenomenon can interact and when this happens the buckling load can be depressed below the value of individual buckling loads. Practically buckling loads are as low as 30% of the theoretical load. This is due to the fact that: (a) Boundary conditions (b) Pre-buckling deformations (c) Geometric imperfections (d) Load eccentricities For axially compressed isotropic cylinders, small load eccentricities do not have a major influence on the buckling strength (Simitses, 1985 et al)[11]. The single dominant factor contributing to the discrepancy between theory and experiment for axially compressed isotropic cylinders is initial geometric imperfections. Now we discuss some major buckling theories we can use while designing a tower against buckling. We now examine each of the theory and determine which of these theory suits over stability criteria’s for tubular wind turbine towers. 3.3.1. EULER’S BUCKLING THEORY Euler, in 1744, determined the critical load for an elastic prismatic bar end-loaded as a column from [10] Pcr= ---------- (1) Where Pcr=critical load at which bar buckles, E=Modulus of elasticity, for steel, I=Moment of inertia of bar cross-section, L=column length of bar. 26 3.3.2. DRAWBACKS OF EULER’S THEORY One of the important assumptions of the Euler’s formula is that the column is initially straight and the load applied is truly axial. In reality, neither the column nor the load is truly axial. As we stated earlier that the small load eccentricities do not have a major influence on buckling strength but the initial imperfections of the columns significantly reduced the buckling load for the theoretically obtained values. 3.3.3. PERRY ROBERTSON EQUATION There are many formulas that are been derived which give more accurate or realistic result than the Euler’s formula. One of them is Perry Robertson formula σP=1/2[σyield+(η+1) σE] − σ η σ σ σ -- (2) Where η= CO y/ k2 CO is the initial out of straightness The formula is based on the assumption that the column is initially bent with the maximum offset of CO. 3.4. Local Buckling Of Tubular Structures We have already stated some of the most widely used buckling theories but, those theories are very much related to the overall or global buckling of columns. When we design structures with high slenderness ratio local buckling is much more prevalent than global buckling. In using steel tubes for structural members two considerations may be of importance. First, local buckling should be prevented at stresses below yield-strength, and second, a more severe restriction, is that the tendency to buckle locally should not reduce general buckling load of a tubular member. Local buckling stress of tubular structures with thin walls under uniform compression can be determined theoretically. Under ideal condition this stress is 27 σL=kE ---------- (3) Where r is the mean radius, t is the thickness, and k is 0.6. However, tests indicate that tubes can actually develop only a fraction of this stress because buckling of cylindrical tube is highly sensitive to initial imperfections [11]. Imperfections resulting from fabrication indentations, joint seams, and similar disturbances can greatly reduce the buckling stress. Even for seamless round tubes, a more realistic estimate of local buckling stress is obtained by using k=0.12. So, σL=0.12E ---------- (4) 3.5. Buckling Stress Criteria’s Apart from different buckling theories there are some other standards, codes and empirical relation for determining critical buckling loads. 3.5.1. According to brazier’s theory The value of critical local buckling stress of all tower sections must be higher than the yield stress of the tower material to prevent the occurrence of local buckling in the elastic region. σcr= 0.33E ---------- (5) According to brazier’s theory moment required for local buckling is less than the brazier moment [17]. Meq= ---------- (6) The local buckling moment can also be related to material stress failure by Meq= σ ---------- (7) 3.5.2. According to Eurocodes The design values of compression force (NED) must be less than the buckling resistance of compression member (Nb,Rd) [12]. ---------- (8) 28 For cross section with classes 1, 2, 3: Nb,Rd= ---------- (9) For cross section with class 4: Nb,Rd= ---------- (10) Where is the reduction factor = 1.0 = ---------- (11) = 0.5(1+α( -0.2)+ 2 ---------- (12) Where α is the imperfection factor is the non-dimensional slenderness 3.5.3. Allowable Buckling Stress Method: The allowable local buckling stress method involves (Burton, Sharpe, Jenkins, and Bossanyi)[2]: 1) Calculating the elastic critical buckling stress of a cylindrical steel tube, which has modulus of elasticity Es, wall thickness t, and mean radius rm, σcr elastic = 0.605Es --------- (13) 2) Calculating critical stress reduction coefficients for bending and axial loading αB =0.1887 + 0.8113 αo ---------- (14) αo= ---------- (15) , or 29 < 212 αo= ≥ 212 , ---------- (16) Where, αB is bending coefficient αo is axial loading coefficient 3) Putting these values along with the material’s yield strength fY to obtain the allowable local buckling stress. The maximum principal stress in the structure should not exceed this allowable local buckling stress value in order to avoid local buckling. σBuckling = Fy , α α > ---------- (16) or σBuckling= 0.75 3.6. α α , ≤ ---------- (17) Principal stresses To determine the principle stresses in tower the maximum distortion energy theory is used. The theory states that failure is predicted to order in a multiaxial state of stress when the distortion energy per unit volume becomes equal to or exceeds the distortion energy per unit volume at the time of failure in a simple uniaxial state of stress test using the specimen of same material [2]. This theory is commonly used in engineering design because of its proven track record for predicting failure in ductile materials. Principal stresses σ1, σ2, and σ3are obtained at the critical points in the tower. In practice, an appropriate factor of safety, F s, is applied to reduce the material’s yield stress σy. (σ1 - σ2)2 + (σ2 – σ3)2 + (σ3 – σ1)2 = 2 30 σ ---------- (18) 3.7. AISC Design Criteria The American Institute of Steel and Construction (AISC), an organization that prepares specifications for structural steel design, has adopted the formulas for σ max proposed by structural stability steel council (SSRC) [10]. To obtain allowable stresses, the AISC specifies that the maximum stresses be divided by the following factor of safety: n1 = + , n2 = , ---------- (19) ---------- (20) The AISC formulas for allowable stresses are obtained by dividing the maximum stresses σmax by the appropriate factor of safety; thus, , , ---------- (21) ---------- (22) Where = The maximum value of specified as 200GPa. ---------- (23) permitted by AISC is 200; also the modulus of elasticity is 31 3.8. Tower Top Deflection Since we have assumed that the wind turbine tower behave as a cantilever beam, the tower top deflection is determine by applying uniform lateral load along the height of the tower. So, the maximum deflection δ at the free end is obtained by δ= ---------- (23) P is the applied lateral load is the height of tower I is the moment of inertia The obtained δ must be less than 1% of the total height of the tower[15]. That is δ< 0.01 3.9. Tower Top Rotation In order to avoid interference between the turbine blades and the tower, the maximum rotation at the tower top is limited to 5∘ . [2] The rotation Ɵ of the tower is determine by Ɵ ---------- (24) 32 CHAPTER #4 4. WIND LOADS AND WIND DATA Wind speed tends to increase with height in most locations, a phenomenon known as wind shear. The degree of wind shear depends mainly on two factors, atmospheric mixing and the roughness of the terrain. Terrain roughness also affects wind shear by determining how much the wind is slowed near the ground. In areas with a high degree of roughness, such as forests or cities, near- surface wind speeds tend to be low and wind shear high, whereas the converse is true in areas of low roughness such as flat, open fields. Wind shear may be greatly reduced or eliminated where there is an abrupt change in terrain height such as a sea cliff or mountain ridge. 4.1. Wind load formulation The wind velocity is varied along the tower height. The wind profile power lawrelationship is defined as[1, 8] ---------- (25) Where is the wind velocity at height Z, is the wind velocity at hub height, z is the height above ground, is the hub height and the power law exponent α is 0.2. The uniformly distributed wind load along the tower height Fd per unit length is directly proportional to the square of wind velocity at height z, V (z), as CdD(z) Fd = Where Cd is the drag co-efficient D(z) is the external diameter at the height z 33 ---------- (26) 4.2. Wind Data Of Coastal Areas of Pakistan Initially the entire coastal belt was considered to have suitable wind regime, however detailed analysis of the data recorded by Pakistan Meteorological Department revealed that there is significant difference in wind speeds between the coastal belt in hilly Balochistan and deserts of Sindh . Wind speeds in South Eastern zone thatmainly includes coastal belt in Sindh, inland areas adjoining to the coast, districts of Balochistan near to Karachi and desert areas of Sindh Province, have been recorded much higher than the wind speeds in South Western Zone that includes all along the coast of Balochistan province. A comparison of this data at a height of 30 meters is shown in Figurebelow [5,6]. Fig 4.1. Wind speed comparison of different sites of coastal areas of Pakistan [5] The map clearly indicates that the Gharo site is located within the vicinity of one of the best wind corridors in the country i.e. Gharo ~ Kati Bander Wind Corridor. 4.3. Comparison between Kati Bander and Gharo Amongst the two most suitable wind zones, Gharo and Kati Bandar reveal identical annual wind speeds. The meteorological data has further revealed that this zone has not received any cyclone with wind speeds dangerous for wind turbines since past 50 years and based on interviews from local residents this time is estimated to be around 80 years. However Kati Bandar is on the western edge of cyclone prone areas that hit coasts of Pakistan and India. So 34 now between gharo and katibander we have chosen gharo as the preferred site for the wind turbines [5]. Fig 4.2.Gharo-kati bander Wind speed comparison at hub height of 30m [5] 4.4. Terrain and Topographical Conditions of Gharo The terrain of the site is flat. There are no uphill and deep ditches; elevation with respect to sea level is same with minute rise. The contours are wide spread with equal levels in most parts of the area. The topography of the land is homogeneous and environment and habitat of the area are not much divergent. Vegetation cover in site is too less. Due to these facts, the land offers minimum shear and turbulence to the wind blowing from sea to inward land area. This represents excellent terrain and topographical conditions for installation of wind turbines. The terrain and topographical conditions of the site is shown in figure below. Fig 4.3.Geographical site location of Gharo [5] 35 4.5. Geographical Location of the Site Geographically, the site is located in such area where no developed infrastructure is available. However, site developments particularly required for wind farm projects can be done at site without disturbing the current site conditions. Moreover, population density is very rare, which minimizes all the expected negative impacts of wind power projects near to zero [5]. 4.6. Monthly Average Wind Speeds in Gharo The Monthly Average Wind Speeds (MAWS) of the area portrays true picture of potential available at the site for generation of power through wind energy. In accordance with the international standards set forth for grading of sites as per wind speeds, the site is graded as an excellent site. Monthly Wind Speed Variation At Gharo 12 10 8 6 4 2 0 Dec Nov Oct Sep Aug Jul Jun m50wind speed @ May Apr Mar Feb Jan m30wind speed @ Fig4.4.Monthly wind variation at Gharo At 30 meters height, we have averaged wind speed of greater than 5 m/s during 6-months of the year from April to September. Whereas, the maximum average wind speed of 9.14 m/s is during July. At 50 meters, we have the average wind speed of >5 m/s during 8-months from February to September and annual average is 6.6 m/s at this height. Wind data at 50 meters indicate that there is good wind power potential during at least eleven months of year when the wind speed is >4.5 m/s. 4.7. Wind Force And Pressure For Gharo 36 The velocity values given in the table are from the Meteorological department and contain average monthly wind speed data of Gharo. The Pressure profile is obtained by using the Eurocodes and using the values of tower height, wind speeds and air density as inputs. The wind force and pressure obtained at different height at Gharo is plotted in table below Table4.1. wind at 10m height Height=10 m Month Wind Speed (m/s) Wind Force (N) Pressure (N/m2) Jan 1.78 236.4045901 5.910114753 Feb 2.26 381.0945854 9.527364636 Mar 2.53 477.5918889 11.93979722 Apr 3.9 1134.867383 28.37168457 May 6.58 3230.484691 80.76211728 Jun 5.75 2466.900253 61.67250632 Jul 7.21 3878.702138 96.96755344 Aug 5.05 1902.824157 47.57060393 Sep 5.46 2224.34007 55.60850176 Oct 1.83 249.87228 6.246806999 Nov 1.51 170.1256489 4.253141222 Dec 1.78 236.4045901 5.910114753 37 Table4.2. wind at 30m height Height=30 m Month Wind Speed (m/s) Wind Force (N) Pressure (N/m2) Jan 3.52 3378.024392 28.15020327 Feb 4.08 4538.347854 37.81956545 Mar 4.17 4740.777405 39.50647837 Apr 5.96 9684.338783 80.70282319 May 9.14 22775.60099 189.7966749 Jun 7.79 16544.45135 137.8704279 Jul 9.91 26774.70924 223.122577 Aug 6.86 12829.97132 106.9164277 Sep 7.55 15540.72794 129.5060661 Oct 3.7 3732.337449 31.10281208 Nov 3.11 2636.927761 21.97439801 Dec 3.54 3416.520086 28.47100072 Table4.3. wind at 50m height Height=50 m Month Wind Speed (m/s) Wind Force (N) Pressure (N/m2) Jan 4.5 10017.70722 50.08853611 Feb 5.08 12766.46714 63.83233572 Mar 5.1 12867.18839 64.33594194 Apr 7.14 25219.68924 126.0984462 May 10.58 55375.1152 276.875576 Jun 8.95 39626.83421 198.1341711 Jul 11.34 63616.44795 318.0822397 Aug 7.9 30874.32631 154.3716315 Sep 8.75 37875.59058 189.3779529 Oct 4.73 11067.90923 55.33954615 Nov 3.96 7757.712473 38.78856237 Dec 4.47 9884.583024 49.42291512 38 4.8. Wind Data Of Keti-Bander at Different Heights Table4.4. wind at 10m height Keti-Bander Height=10 m Month Wind Speed (m/s) Wind Force (N) Pressure (N/m2) Jan 2.88 618.8720592 15.47180148 Feb 3.26 792.9596711 19.82399178 Mar 3.48 903.5961836 22.58990459 Apr 5.3 2095.885916 52.3971479 May 7.59 4298.327 107.458175 Jun 6.45 3104.097324 77.60243309 Jul 8.62 5544.092042 138.602301 Aug 5.76 2475.488237 61.88720592 Sep 5.66 2390.279916 59.75699791 Oct 2.7 543.9305208 13.59826302 Nov 2.07 319.7102728 7.992756819 Dec 2.8 584.9678028 14.62419507 Table4.5. wind at 30m height Keti-Bander Height=30 m Month Wind Speed (m/s) Wind Force (N) Pressure (N/m2) Jan 4.02 4405.848511 36.71540426 Feb 4.9 6545.903737 54.54919781 Mar 5.05 6952.807582 57.94006319 Apr 7.31 14568.41177 121.4034314 May 9.52 24708.78276 205.906523 Jun 8.09 17843.27207 148.6939339 Jul 10.41 29544.65434 246.2054529 Aug 6.93 13093.14337 109.1095281 Sep 7.05 13550.51147 112.9209289 Oct 4.27 4970.879144 41.42399287 Nov 3.56 3455.233886 28.79361572 Dec 4.03 4427.795419 36.89829516 39 Table4.6. wind at 50m height Keti-Bander Height=50 m Month Wind Speed (m/s) Wind Force (N) Pressure (N/m2) Jan 4.8 11397.92466 56.98962331 Feb 5.77 16470.05061 82.35025304 Mar 5.96 17572.59204 87.86296022 Apr 8.46 35406.58441 177.032922 May 10.58 55375.1152 276.875576 Jun 9.03 40338.41298 201.6920649 Jul 11.3 63168.44619 315.8422309 Aug 7.68 29178.68714 145.8934357 Sep 7.91 30952.53863 154.7626932 Oct 5.21 13428.22946 67.14114731 Nov 4.41 9621.006017 48.10503008 Dec 4.82 11493.10525 57.46552624 40 4.9. Wind data of Hawksbay at different heights Table4.7. wind at 10m height Hawksbay Height=10 m Month Wind Speed (m/s) Wind Force (N) Pressure (N/m2) Jan 2.9 627.4973497 15.68743374 Feb 3.3 812.5381853 20.31345463 Mar 4.1 1254.248567 31.35621418 Apr 5.3 2095.885916 52.3971479 May 5.7 2424.184173 60.60460432 Jun 5.7 2424.184173 60.60460432 Jul 5.7 2424.184173 60.60460432 Aug 5.1 1940.690377 48.51725941 Sep 4.3 1379.598811 34.48997026 Oct 2.6 504.3855035 12.60963759 Nov 2.1 329.0443891 8.226109727 Dec 2.7 543.9305208 13.59826302 Table4.8. wind at 30m height Hawksbay Height=30 m Month Wind Speed (m/s) Wind Force (N) Pressure (N/m2) Jan 3.6 3533.315803 29.44429836 Feb 4 4362.118275 36.35098563 Mar 4.9 6545.903737 54.54919781 Apr 6 9814.76612 81.78971766 May 6.5 11518.71857 95.98932142 Jun 6.4 11167.02278 93.05852321 Jul 6.5 11518.71857 95.98932142 Aug 5.8 9171.353674 76.42794728 Sep 5.1 7091.168521 59.09307101 Oct 3.3 2968.966751 24.74138959 Nov 2.8 2137.437955 17.81198296 Dec 3.5 3339.746805 27.83122337 41 Table4.9. wind at 50m height Hawksbay Height=50 m Month Wind Speed (m/s) Wind Force (N) Pressure (N/m2) Jan 4 7915.22546 39.5761273 Feb 4.4 9577.422806 47.88711403 Mar 5.4 14425.4984 72.127492 Apr 6.4 20262.97718 101.3148859 May 7.1 24937.90721 124.6895361 Jun 6.9 23552.74276 117.7637138 Jul 7.1 24937.90721 124.6895361 Aug 6.2 19016.32917 95.08164584 Sep 5.6 15513.8419 77.56920951 Oct 3.7 6772.464784 33.86232392 Nov 3.2 5065.744294 25.32872147 Dec 4 7915.22546 39.5761273 42 CHAPTER #5 5. FINITE ELEMENT ANALYSIS OF TOWER Different structural analysis of tubular wind turbine tower is performed on finite element software. Abaqus/CAE is used to obtain the finite element based results. Static, buckling and dynamic analysis (modal) all performed on Abaqus. This chapter deals with static and buckling analysis of tower. In static analysis the loads which are not varying with time is calculated which includes displacement analysis, principal stress and Von Mises stresses. In buckling analysis the eigenvalues and the buckling modes are obtained under the axial compressive load are other loads and gravity effects are ignored. 5.1 Model of wind turbine tower in Abaqus The tower is modeled as solid 3D tubular tapered tower as shown in figure. The tower is first created by two segment which can be separate along the vertical axis and then assembled together in assembly module. Fig 5.1.Tower Model in FEA 43 The tower is modeled in three-dimensional space, and a Cartesian coordinate system was chosen for the finite element modeling. 5.2. Material and Material Properties The tower is modeled as linear isotropic material and the ASTM 572 is used as a wind turbine tower material. The properties of the material are given as input to the Abaqus which are modulus of elasticity, E=200GPa and poisson'sratio,ν=0.3. It is important to note that the during analysis only elastic region of ASTM 572 is assumed. 5.3. Element Type The material of the tower is modeled as linear brick 8-node reduced integration element (C3D8R). This type of element is generally preferred for most cases because they are usually the more cost-effective of the elements that are provided inAbaqus. They are offered with first- and second order interpolation. In our analysis we have used first order interpolation. Since we have used first order reduced integration element there might be a few problems with it. One is associated with reduced integration and other with the order of element. 5.3.1 Full or Reduced Integration Reduced integration uses a lower-orderintegration to form the element stiffness. The mass matrix and distributed loadingsuse full integration. Reduced integration reduces running time, especially in three dimensions, while Full integration is time consuming. Hour-glassing can be a problem with first-order, reduced-integration elements (CPS4R, CAX4R, C3D8R, etc.) in stress/displacement analyses. Since the elements have only one integration point, it is possible for them to distort in such a way that the strains calculated at the integration point are all zero, which, in turn, leads to uncontrolled distortion of the mesh. To avoid this problem we have used finer mesh as possible in over analysis. According to Abaqus manual, make all elements as “well shaped” as possible to improve convergence andaccuracy. 5.4. Meshing the Model 44 To achieve high accuracy the meshing of the element should be fine as possible. The results are heavily depends upon the quality of mesh. As we mention earlier that problems like hourglassing can we avoid by using finer mesh. 5.4.1 Meshing of 5kw tower The meshing of 5kw tower is done by applying approximate global size of 0.07. The meshed model of 5kw tower is shown in figure below. Fig 5.2.Global seeds Fig.5.3.Meshing of 5KW tower 45 5.4.2. Meshing of 250kw tower The approximate global size used for the 250kw tower is 0.25. the mesh quality is shown in figure below. Fig.5.4.Meshing of 250KW tower 5.5. Boundary Conditions The supporting conditions of the tower are shown in the figure. It was assumed that the tower is rigidly attached to the ground, fixed-free boundary condition is applied i.e. tower is fixed from the base and free at the top. 5.6. Static Analysis In static analysis of wind turbine tower, displacement magnitudes, von mises stresses and principal stresses are obtained under static loads (not varying with time). 5.6.1. Static Analysis of 5kw Tower For 5kw tower the static load at the top of rotor/nacelle is applied whole at a concentrated load. 46 Wind load along tower is applied at an extreme wind conditions which is obtained at the hub height of 12m at extreme wind speed of 47.5 m/s. it is then converted into pressure according to the equation P= 1/2ρV2Cd ---------- (27) The pressure comes out be 4162 Pa which is assumed to be act uniformly along the height of the tower. Fig.5.6. Loading conditions in static analysis of 5KW tower 5.6.2. Static analysis of 250kw tower Similarly, for 250kw tower the static load at the top of rotor/nacelle is applied whole at a concentrated load. Wind load along tower is applied at an extreme wind conditions which is obtained at the hub height of 35m at extreme wind speed of 58.3 m/s. it is then converted into pressure according to the equation P= 1/2ρV2Cd 47 The pressure comes out be approx. 8300 Pa. but since the height of the tower is significantly large, the load acting along the tower is assumed to be linearly varying from 3000 Pa to 8500 Pa. The tower is assumed to be fixed rigidly attached to the ground (fixed boundary condition is applied at the base). Fig.5.7.Varying wind pressure along the height of 250KW tower 5.7. Buckling Analysis In buckling analysis of wind turbine tower eigenvalues are obtained under axial compression (static load of rotor/nacelle). All the other loads (wind load, gravity, etc) are neglected. As earlier stated that fixed boundary condition is applied at the base. 5.7.1. Buckling load for 5kw and 250kw tower The compressive load at the top of tower is applied as a concentrated load of rotor/nacelle. In case of 5kw tower the buckling load is 30000N while for the 250kw the load is 140.53KN. 48 Fig.5.8.Buckling Analysis loading conditions 5.8. Results for 5kw tower For 5kw tower, the maximum deflection in the direction of the wind comes out to be 68mm and von mises stresses comes out to be 91MPa. The prinicipal stresses are from 40MPa tensile stresses to the compressive stresses of 91MPa. All these stresses and deflection are well within the safe zone. The lowest eigenvalue of buckling analysis comes out to be 42.6 which means the critical load is well above the applied load. 49 Fig.5.9.Resultant deflection of 5kw tower 50 Fig.5.10. Deflection in the direction of wind 51 Fig.5.11. Von Mises Stress in 5KW Tower 52 Fig.5.12. Principal Stresses in 5KW Tower 53 Fig.5.13.Buckling Mode 1 of 5KW tower 54 Fig.5.14.Buckling Mode 2 of 5KW tower 55 Fig.5.15.Buckling Mode 3 of 5KW tower 56 5.9. Results of 250kw tower For 250kw tower, the maximum deflection in the direction of the wind comes out to be 177mm and von mises stresses comes out to be 101MPa. The principal stresses are from 99MPa tensile stresses to the compressive stresses of 102MPa. All these stresses and deflection are well within the safe zone. The lowest eigenvalue of buckling analysis comes out to be 139.66 which means the critical load is well above the applied load. Fig.5.16. Deflection in the Direction of Wind For 250kw Tower 57 Fig.5.17.Von Mises Stresses of 250KW Tower 58 Fig.5.18.Principal stresses of 250KW tower 59 Fig.5.19.Buckling mode 1 for 250KW tower 60 Fig.5.20.Buckling mode 2 for 250KW tower 61 CHAPTER #6 6. VIBRATION ANALYSIS OF WIND TURBINE TOWER The tower is as important for static stability of the turbine as it is for the dynamic behavior of the turbine. Regarding the structure of the tower, the dynamic behavior of the tower is determined by its natural frequency and excitation frequency of rotor and the blades. When designing a wind turbine tower a distinction is made between a soft and a stiff design. Stiff towers have excitation frequencies (rotor speed and blade frequency) lower than the natural frequency of the tower. For soft towers, the excitation frequencies for the turbine’s rated power are above the first natural frequency of the tower. On the basis of dynamics behavior the wind turbine towers are divided in 3 classes: i) Stiff-stiff tower A stiff-stiff tower is one in which natural frequency (fn) of tower is much higher than both the excitation frequency of rotor and blades i.e. (1p) and (N bp). These type of tower are very efficient in reducing the vibration but they are not cost effective. ii) Soft-stiff tower A soft-stiff tower is one in which natural frequency of tower is greater than rotor excitation frequency (fn> 1p) but lower then the blade passing frequency (Nbp>1p). iii) Soft-soft tower A soft-soft tower is one in which both the rotor and blade passing frequency are greater than first natural frequency of the tower. It will be an advantage to create a soft-soft support structure, because it uses less steel and is therefore cheaper, but the trends for both structure and excitation forces seem to converge to this soft area with a major risk of resonant behavior. The frequency of excitation at the startup and shut down need to passed in a very control way at resonance [1]. Small and medium-sized turbines have mainly stiff towers, whereas large turbines use a softsoft design in order to save material. 62 6.1. Natural Frequency of Tower The fundamental natural frequency of the tower with the concentrated mass of the nacelle and rotor mass at the top should be designed as the criterion of a stiff tower. In order to avoid resonance, the natural frequency of the wind turbine support structure must be sufficiently separated from the operating frequency of the turbine. The natural frequency of the wind turbine support structure must remain above the largest operating frequency of a particular turbine. Moreover, the turbine's excitation frequencies (the rotational frequency or the blade-passing frequency) should generally not be within 5% of tower natural frequency during prolonged operation. The tower natural frequency fn can be determined by equation[1, 9]. fn= ---------- (28) 6.2. Rotor frequency and the blade passing frequency The frequency, in Hertz (Hz), of a particular turbine is obtained by dividing the turbine angular speed in rotations per minute (rpm) by sixty[2]. frotor = ---------- (29) The blade passing frequency is determined by multiplying rotor frequency to the number of blades. Nbp= number of blades * frotor ---------- (30) For example, if the rotor has 3 blades then the balde passing frequency is, 3p= 3*frotor 63 ---------- (31) 6.3. FEA Based Vibration Analysis of Tubular Tower To obtain the natural frequency and its respective mode shape of tower, finite element analysis is performed on Abaqus. Abaqus performs eigenvalue extraction to calculate the natural frequency and its respective mode shape. The eigenvalue problem for the undamped finite element model is determined by: Mӱ+Ky=0 ---------- (32) Where M is the mass K is the stiffness And to keep the analysis simple the effect of damping is neglected. Abaqus have three different methods to extract the eigenvalues. They are lanczos, subspace and automatic multilevel substructuring (AMS). According to Abaqus manual theory the choice of method has very minimum effect on the extracted eigenvalue. So, in our analysis we have chosen the Lanczos criteria for obtaining the natural frequency of tower. All the applied loads and any other effect (gravity) all are ignored. Only concentrated load of rotor and nacelle is applied at the top of the tower. With fixed support boundary condition at the base is applied. Since the tower is designed to withstand the load of 5kw wind generator system, the axial compressive gravity forces which may destabilize the tower is not considered in case of this simulation but its effect is becomes significant for the large wind generator systems. 6.4. Natural frequencies and mode shapes of 5kw tower For 5kw tower the mass of rotor is applied at the top of tower as shown in fig 6.1. As stated earlier the fixed end boundary condition is applied at the bottom of the tower. The combined mass of rotor and nacelle is applied at the top of tower which is obtained by the equation provide: Y= 46.11*X+2757.1 ---------- (33) Where 64 Y is the mass of the rotor and X is the power output According to the equation the mass of tower at the top is 2987.65 Kg which approximated as 3000 kg. Fig 6.1. Mass of rotor and nacelle at the top of 5kw tower The first 3 modes of vibration and their respective eigenvalues are shown in the figures. 65 Fig 6.2. 1st mode of vibration of 5kw tower 66 Fig 6.3. 2nd mode of vibration of 5kw tower 67 Fig 6.4. 3rd mode of vibration of 5kw tower 68 6.5. Natural frequencies and mode shapes of 250kw tower. Similar type of analysis is performed on 250kw tower as in the case of 5kw. The combined mass of rotor and nacelle is applied at the top of tower which is obtained by the equation provide: Y= 46.11*X+2757.1 ---------- (34) Where Y is the mass of the rotor and X is the power output According to the equation the mass of tower at the top is 14286.8 Kg As shown in fig 6.5. the mass is applied as the inertia mass at the top of the top of tower in finite element analysis in Abaqus. Fig 6.5.Inertia mass of250kw rotor at the top of tower The modes shapes and eigenvalues obtained for the 250kW tower are shown in figures. 69 Fig 6.6.1st mode of vibration of 250kw Tower 70 Fig 6.7.2nd mode of vibration of 250kW tower 71 Fig 6.8.3nd mode of vibration of 250kW tower 72 6.6. Analytical Calculation Now we compare our finite element results with the analytical values. We can evaluate first natural frequency of tower (fn1). 6.6.1. For this first we perform calculations for 5kW tower fn= I= ---------- (35) t= *0.268*0.006=3.653*10-4 m4 ---------- (36) Where r is the mean radius The mass of the tower can be compute by multiplying density with the volume occupied by the tower. mtower = ρt* *D*t*L ---------- (37) where ρt=7850kg/m3 L=12m The mass of the tower comes out to be mtower=951.74 kg mrotor= 3000 kg E=200 GPa fn= fn≈1.03 cycles/sec One thing to noted that in both the calculations either finite element analysis or analytical, we have neglected the mass of the tower since it has very little effect on the tower natural frequency compared to the rotor mass. Also it is valid from the point of view that that tower mass is 951.74 kg when multiplied with 0.23 it becomes 219 kg which is much less than the rotor mass. 73 Even if we include the rotor mass the natural frequency comes out be approximately 1 cycles/sec. 6.6.2. For 250kW tower I= t= *1*0.015=0.0471 m4 ---------- (38) Where r is the mean radius The mass of the tower can be compute by multiplying density with the volume occupied by the tower, from Eq. 37: mtower = ρt* *D*t*L where ρt=7850kg/m3 L=35m The mass of the tower comes out to be mtower=25894.57 kg mrotor= 14286.8 kg E=200 GPa fn= fn≈.91 cycles/sec 74 6.7. Results Table 6.1.summarizes the results obtained from finite element analysis and analytical equations Table 6.1.Summary Of Result Obtained From Both Analytical And Finite Element Analysis. 5kw Tower 250kw Tower (Hz) (Hz) Mode 1 1.2405 1.18 Mode 2 1.2626 1.2160 Mode 3 17.218 15.504 From Analytical 1.03 0.91 equation(fn1) 6.8. Conclusion As we see from the obtained results that there is a difference between the finite element analysis and analytical results, this because of the approximation of diameter, that is we have taken mean dia throughout the calculation. Also it can be seen from the results that the natural frequency of 5kw tower is higher than the 250kw tower this mainly because of the mass at the top of the tower, and natural frequency is inversely proportional to the mass. The obtained result still be approximate results because in finite element analysis we have ignored the self-mass of tower, which will further reduce the natural frequency of the tower. As we earlier mention that it does not affect much in case of 5kw tower, But as for the 250kw tower, the mass is about 25894.57 kg which is greater than the rotor mass (14286.8 kg). That is why in analytical obtained natural frequency in which we include mass of tower is much less than the frequency obtained from the finite element analysis. 75 The 5kw tower is considered as a stiff tower because it has natural frequency of about 1.18 Hz. In general, small size wind turbine rotor rotates at about 15rpm to 20rpm. That has rotor excitation frequency of about 0.33 Hz which well below the tower natural frequency. The blade passing frequency of rotor, if it has three blades then it is 1 Hz, again it is within the safe zone. For 250kw tower since it natural frequency (of combined rotor and tower mass) is less than 1 Hz. It can be categorized as soft-stiff tower having rotor frequency below the natural frequency of the tower but blade passing frequency is higher than natural frequency. In such cases the resonance is to be passed in a very controlled way. i.e. by employing vibration isolators and dampers. 76 CHAPTER #7 7. ANALYTICAL CALCULATIONS 7.1. According to Eurocodes 7.1.1. For 5KW tower The dimensions of 5KW wind turbine tower are; Top diameter = 250mm Base diameter = 825mm Height = 12m Thickness = 6mm 50000 45000 40000 Rotor + Nacelle (kg) y = 46.118x + 2757.3 35000 30000 25000 20000 15000 10000 5000 0 0 100 200 300 400 500 600 Power (kW) Fig.7.1. mass of nacelle + rotor vs power output The relation to measure the mass of tower is; Y = 46.118X + 2757.3 ---------- (39) Where X = power of turbine in KW Y = mass of tower in Kg 77 700 800 For 5KW Turbine: Y = 46.118* (5) + 2757.3 Y = 2987.89 Kg For static load of tower; Pstatic= 2987.89 * 9.81 Pstatic= 29.31KN ( design load ) 1- Choose a section & determine the class €= ---------- (40) Where, Fy = yield strength of material = 350MPa €= € = 0.819 €² = 0.671 To find the class, we have to find the D/t ratio Where D = mean diameter D/t = D/t = 89.58 The D/t ratio calculated above is greater than the limit of class III which is 90€² so our class lies in class IV. The limit for each class is shown in figure below. 78 Fig7.2. Tubular section class determination [12] Now we follow the design procedure of class IV. As our tower is assumed as cantilevered beam, so its effective length is twice of its end length. Lcr = 24m 2- Calculate Elastic Buckling Load ( Ncr) Ncr= Where E = elastic modulus = 200GPa I = second moment of area = π*R³*t I = π * (0.2686)*(6e-3) I = 3.653e-4 m4 Ncr = Ncr = 1250.83KN 79 ---------- (41) 3- Calculate non-dimensional slenderness (ƛ) For class IV ƛ= ---------- (42) Where, Aeff = effective area = π*( Ro² - Ri² ) = = 0.01m² ƛ= ƛ = 1.674 4- Determine imperfection factor (α) Take α = 0.49 (for cold rolled sheets ) 5- Reduction Factor (x) = ---------- (43) where ϕ = 0.5 ---------- (44) ϕ = 2.262 Therefore, = = 0.2643 80 6- Calculate Buckling Resistance NB,RD= ---------- (45) NB,RD= NB,RD= 925.05KN For safe design, >1 According to Eurocodes #3 the design load for 5kw tower is below the critical load. 7.1.2. For 250KW tower The dimensions of 250KW wind turbine tower are; Top diameter = 1.5m Base diameter = 2.5m Height = 12m Thickness = 15mm 81 50000 45000 40000 Rotor + Nacelle (kg) y = 46.118x + 2757.3 35000 30000 25000 20000 15000 10000 5000 0 0 100 200 300 400 500 600 Power (kW) Fig.7.1. mass of nacelle + rotor vs power output The relation to measure the mass of tower from Eq. 39 is; Y = 46.118X + 2757.3 Where X = power of turbine in KW Y = mass of tower in Kg For 5kW Turbine: Y = 46.118* (5) + 2757.3 Y = 14286.8 Kg For static load of tower; Pstatic= 14286.8 * 9.81 Pstatic= 140.153KN ( design load ) 82 700 800 1- Choose a section & determine the class From Eq. 40 €= Where, Fy = yield strength of material = 350MPa €= € = 0.819 €² = 0.671 To find the class, we have to find the D/t ratio Where D = mean diameter D/t = D/t = 133.33 The D/t ratio calculated above is greater than the limit of class III which is 90€² so our class lies in class IV. The limit for each class is shown in figure below. Fig.7.2. Tubular section class determination [12] Now we follow the design procedure of class IV. 83 As our tower is assumed as cantilevered beam, so its effective length is twice of its end length. Lcr = 70m 2- Calculate Elastic Buckling Load ( Ncr) From Eq. 41 Ncr= Where E = elastic modulus = 200GPa I = second moment of area = π*R³*t I = π * (1)³*(15e-3) I = 0.0471 m4 Ncr = Ncr = 19e6 N 3- Calculate Non-Dimensional Slenderness (ƛ) For class IV , from Eq. 42 ƛ= Where, Aeff = effective area = π*( Ro² - Ri² ) = = 0.0935m² ƛ= ƛ = 1.3124 84 4- Determine Imperfection Factor (Α) Take α = 0.49 ( for cold rolled sheets ) 5- Reduction Factor (Χ) From Eq. 43 = where ϕ = 0.5 [From Eq. 44] ϕ = 1.634 therefore, = = 0.3836 6- Calculate Buckling Resistance From Eq. 45 NB,RD= NB,RD= NB,RD= 12.55e6 N For safe design, >1 85 7.2. Allowable Buckling Stress Method 7.2.1. For 5 kW Tower The dimensions of 5KW wind turbine tower are; Top diameter = 250mm Base diameter = 825mm Height = 12m Thickness = 6mm Mean radius = Rm = 0.26875m = ---------- (46) = 44.8 αo= αo= for for ≥ 212 < 212 ---------- (47) ---------- (48) = 44.8 < 212 As, Therefore αo = ---------- (49) αo = 0.7 αB = 0.1887 + 0.8113 αo αB = 0.1887 + 0.8113 * 0.7 αB= 0.75661 86 ELASTIC CRICTICAL LOAD σcr,elastic= 0.605*E* ---------- (50) σcr,elastic= 0.605* 200e9* ---------- (51) σcr,elastic= 2.7014 GPa Then, σbuckling = for αB*σcr> σbuckling= 0.75*αB*σcr ---- (52) for αB*σcr ≤ As, αB*σcr = 2.0217GPa &Fy/2 = 0.175e9 therefore, σbuckling = σbuckling= 299.616MPa 7.2.2. For 250 KW TOWER The dimensions of 250KW wind turbine tower are; Top diameter = 1.5m Base diameter = 2.5mm Height = 35m Thickness = 15mm Mean radius = Rm = 1m From Eq.47 = ---------- (53) = 66.72 87 From Eq. 47 αo= for < 212 From Eq. 48 αo= for ≥ 212 = 66.72< 212 As, Therefore , from Eq. 49 αo = αo = 0.643 αB = 0.1887 + 0.8113 αo αB = 0.1887 + 0.8113 * 0.643 αB= 0.7103 ELASTIC CRICTICAL LOAD From Eq. 50,σcr,elastic= 0.605*E* From Eq. 51,σcr,elastic= 0.605* 200e9* σcr,elastic= 1.815 GPa Then, from Eq. 52 σbuckling = for αB*σcr> σbuckling= 0.75*αB*σcr for αB*σcr ≤ As, αB*σcr = 1.3GPa &Fy/2 = 0.175e9 therefore, 88 σbuckling = σbuckling= 284MPa 7.3. AISC Design Criterion 7.3.1. FOR 5kW TOWER According to this criterion; , ---------- (54) , ---------- (55) Where, n1 = + , ---------- (56) and , n2 = ---------- (57) Where, = = ---------- (58) ---------- (59) 89 = 106.2 = = 89.3 < As Therefore, n1 = + , n1 = 1.38745 = 0.4659 allow = 163.07MPa 90 7.3.2. FOR 250kW TOWER According to this criterion: , , ---------- (60) Where, n1 = + n2 = , , ---------- (61) ---------- (62) Where, = = ---------- (63) ---------- (64) = 106.2 = = 70 As < 91 Therefore, n1 = + , n1 = 1.62747 = 0.48097 allow = 168.34MPa 92 7.4. Deflection Criterion As tower is fixed at base & free to move from top so it can assumed as cantilevered beam. Assume that Tower is subjected to uniform loading from base to top The equation of elastic deflection curve is given by; EI where, M = bending moment EI = flexural rigidity The bending moment at any point at a distance ‘x’ from Base is; M = Rax - Ma – Where, Ra= reaction atA = wl Ma= bending moment at A = = wlx - Eq (a) =>EI - ------- (1) Integrating above equation twice; EI = EIy = - - + C1 - + C1x + C2 Where, C1& C2 are constants of integration Applying boundary conditions; at x = 0 , y = 0 where y is deflection of tower in direction of loading at x = 0 , = 0 where is slope of curve Applying these conditions in above equations we get, C1 = 0 & C2 = 0 Then above eq. is => 93 =M ---------- (a) EIy = - - y= As maximum deflection occurs at top of tower, where x = L Therefore, ymax = - ( negative sign due to bending moment direction ) The slope of curve is given by; EI = - - For maximum slope, put x = L = _______________ (Eq. 7b) Now loading is increasing from bottom to top : Let w1is loading at base of tower & w2 is at top The equation of elastic deflection curve is given by; EI = M --------- (a) where, M = bending moment EI = flexural rigidity The bending moment at any point at a distance ‘x’ from Base is; M = Rax - Ma - - Where, Ra = reaction at base = 94 __________ (Eq. 7a) Ma = bending moment at base = Eq. (a) => EI = Integrating above eqn. twice, EI = EIy = Where, C1& C2 are constants of integration Applying boundary conditions; at x = 0 , y = 0 where y is deflection of tower in direction of loading at x = 0 , = 0 where is slope of curve Applying these conditions in above equations we get, C1 = 0 & C2 = 0 Then above eq. is, EIy = y= for maximum deflection, put x = L in above eqn. y=the slope of curve is given by, = For maximum slope, put x = L in above eqn. =- _____________ (Eq. 7.c) 95 7.4.1. Deflection for 5kW Tower For 5KW tower the pressure distribution is uniform so deflection due to wind pressure can be calculated as The wind velocity is 47.5 m/s at the hub height so the pressure can be calculated from the P=1/2*ρ*v2*Cd ---------- (65) Where ρ is air density = 1.23 kg/m3 Cd is the drag co-efficient = 3 (according to eurocode 1) so the pressure comes out is 4162 Pa The uniform force acting on the tower is 4162*0.250*12=12486 N The deflection can be calculated by Eq. 7.a = = 98.4mm The maximum deflection is still under 1% of the total height of tower.(deflection criteria is also satisfied). 96 7.4.2. Deflection for 250kWTower The wind pressure varies linear along the tower height. The wind velocity at the hub height of the tower is 58 m/s. This can be calculated with the reference extreme wind speed of 55m/s at the height of 25m then by using power-law wind profile relation ---------- (66) comes out to be 58m/s at the hub height of 35m Now again calculating the pressure at the hub height from Eq. 65, P=1/2*ρ*v2*Cd Cd= 4 v=58m/s P=8300 Pa we have taken that the pressure from 3000pa at the base to the 8300pa at the top of tower [15]. w1= 3000*35*1.5= 157500 N (uniform load) w2= (8300-3000)*1.5*35+288750 N (triangular distributed load) I=0.0471 m4 then from Eq. 7.c =- ---------- (67) = 207.4mm Thus, the calculated deflection is under 1% of the total height of tower, deflection criteria are also satisfied. 97 CHAPTER #8 8. EVALUATION In previous chapters we analyzed tower design in finite element analysis and analytically as well and conclude that tower design is under safe limits. In this chapter we try to optimize the tower design by changing its dimensions. In chapter two, we already states some optimization methods, but here we are interested in evaluating critical buckling load and allowable local buckling stress behavior by changing the thickness or diameter of the tower. We know that tapered tubular towers are designed as long slender members and d/t ratio plays a significant role in the overall stability of the tower. Since the cross-section of the tower is continuously changing, so first we evaluate the critical buckling load and local buckling stress at different diameter along the height of the tower. 8.1. Buckling Load at Different Cross-Section Along The Tower Height By Varying Diameter In our actual design, we have chosen constant thickness for both the towers. so here we calculated the critical buckling load at different cross-section by varying diameter. For 250kw tower as we can see that the critical buckling load (according to Eurocodes standard) is linearly increasing as the diameter of the tower increases. At the top of the tower where the diameter is minimum,the critical buckling load is well within safe zone. Buckling Load at Different Dia At (15mm) Thickness Buckling load 20000000 18.3E+6 15.3E+6 15000000 12.5E+6 10000000 9.9E+6 7.5E+6 5000000 0 1.5 1.75 2 2.25 Mean dia (m) Fig. 8.1. Effect of varying diameter for 250kw tower 98 2.5 Since the calculation is performed on taking mean diameter and our actual design is tapered tubular tower (increasing dia towards the base) we evaluate buckling load at different crosssection, by observing the above graph in fig8.1.it show that we can reduce the base diameter (let say from 2.5m to 2m) to save the material of the tower. Now the mean diameter changes from 2m to 1.75m (top dia is still 1.5m). Now we repeat the same procedure for allowable local buckling stress, by keeping the thickness constant and varying the diameter of the tower. allowable local buckling stress Allowable Local Buckling Stress At 15mm Thickness 3.00E+08 2.96E+08 2.95E+08 2.90E+08 2.90E+08 2.85E+08 2.84E+08 2.80E+08 2.78E+08 2.75E+08 2.73E+08 2.70E+08 2.65E+08 2.60E+08 1.5 1.75 2 mean dia (m) 2.25 2.5 Fig.8.2. Allowable Local Buckling Stress at 15mm Thickness Note that the local buckling stress method is based on the r/t ratio not on d/t ratio It is interesting to note that the allowable local buckling stress decreases as the d/t or r/t ratio increases. From the fig.8.2.it shows that in our actual design when base diameter is 2.5m and the mean dia in that case is 2m the critical buckling load is 284MPa. However, when we reduced the base diameter from 2.5 to 2m the critical buckling load also increases. As shown in the fig.8.2.when base diameter is 2m the mean diameter is 1.75m, the critical buckling load is290MPa. From here we conclude that in order to have safe design against the local buckling the d/t ratio should be minimum. 8.2. Buckling Load and Allowable Buckling Stress by Varying Thickness 99 Previously we conclude that the local buckling behavior by varying the diameter. However, local buckling is not only depending upon the diameter, it’s a function of d/t ratio. So now we evaluate the effect of varying the thickness of the tower. First we keep our initial outer diameter for both top and base. i.e. 1.5m and 2.5m, and the mean diameter is 2m. We obtained the allowable local buckling stress at different thickness as shown in fig.8.3. From the Fig.8.3. It is clear as the thickness decreases the d/t ratio increases and the allowable local buckling stress decreases. Allowable Local Buckling Stress At Different Thickness With Mean Daimeter (2m) 2.90E+08 buckling stress 2.85E+08 2.80E+08 2.84E+08 2.81E+08 2.75E+08 2.77E+08 2.70E+08 2.73E+08 2.65E+08 2.60E+08 2.68E+08 2.62E+08 2.55E+08 2.50E+08 0.01 0.011 0.012 0.013 0.014 0.015 thickness (m) Fig.8.3. Allowable Local Buckling Stress at Different Thickness With Mean Diameter (2m) At 12mm thickness the allowable buckling stress is still well above our induced stresses in tower which is about 101MPa. So we reduce our tower thickness from 15mm to 12mm, from fig.8.4. It is clear that the critical buckling load is well above the design load, so now we move one step ahead to check the allowable local buckling stress. 100 Buckling Load At Different Thickness ( Mean Diameter) 14000000 12.5E+6 12000000 11.7E+6 10.9E+6 Buckling load 10000000 10E+6 9.2E+6 8.4E+6 8000000 6000000 4000000 2000000 0 0.01 0.011 0.012 0.013 0.014 0.015 Thickness (m) Fig.8.4.buckling load at different thickness (mean diameter 2m ) As shown in fig.8.5. at 12mm thickness we obtained allowable local buckling stress at different cross-section along the height of the tower. Now we again model the tower in finite element analysis of thickness 12mm. The result obtained at this model is shown in fig.8.6. and fig8.7. Allowable Local Buckling Stress At 12mm Thickness allowable local buckling stress 2.90E+08 2.87E+08 2.85E+08 2.80E+08 2.80E+08 2.73E+08 2.75E+08 2.66E+08 2.70E+08 2.65E+08 2.60E+08 2.60E+08 2.55E+08 2.50E+08 2.45E+08 1.5 1.75 2 2.25 2.5 mean diameter (m) Fig.8.5. Allowable Local Buckling Stress at 12mm Thickness 101 Fig.8.6. Von Mises stress of 250kW tower at 12mm thickness 102 Fig.8.7. Deflection of 250kW tower at 12mm thickness The result shows that the tower deflection and stresses are increased significantly. 103 8.3. Variable Thickness Model of 250kW Tower Also from different stress analysis up till now we can see that the maximum stress occurs at the base of the tower. This leads to another possible model that has variable thickness along the tower height. The thickness of the tower increases towards the base to give maximum strength at the base. Now we reduce tower thickness from 15mm at the base to 10mm at the top. This configuration leads to the optimization technique of minimization of mass, which is to have more mass at high stressed areas then the low stress areas of the tower. By performing finite element analysis, with same boundary and loading condition as in case of actual model we obtained following stresses and deflection and buckling load. Fig8.8. Von Mises Stress in Variable Thickness Tower 104 Fig.8.9. Deflection in variable thickness tower 105 Fig.8.10. 1st Buckling mode of variable thickness tower By observing the von-mises stresses in fig.8.8 it’s clear that the stress are almost equal to the initial 15mm constant tubular tower. And in comparison with constant 12mm thickness tower the stress are appreciably reduced. As with the deflectionits less than the case of 12mm constant thickness towerwhich another decisive factor. In the buckling analysis, the eigenvalue obtained is 125, which mean the critical buckling load is well above the design load and hence the tower is safe. This variable thickness tower is best suited to replace the initial constant thickness tower since its gives same characteristics and analytical values with less material. 106 8.4. Buckling Load at Different Diameter for 5kW Tower Similar analysis is performed for the 5kw tower and the critical buckling and allowable local buckling stress values obtained are shown in fig.8.11. and fig.8.12. Buckling Load At Different Diameter 3000000 2.8E+06 Buckling load (N) 2500000 2.1E+06 2000000 1500000 1.5E+06 1000000 9.8E+06 576.7E+03 500000 110.7E+03 0 0.25 287.8E+03 0.35 0.45 0.55 0.65 0.75 0.85 diameter(m) Fig.8.11. buckling load at different diameter for 5kw tower Allowable Buckling Stress At Different Diameter 3.30E+08 local buckling stress 3.20E+08 3.10E+08 3.19E+08 3.12E+08 3.00E+08 3.05E+08 2.99E+08 2.90E+08 2.93E+08 2.80E+08 2.87E+08 2.81E+08 2.70E+08 2.60E+08 0.25 0.35 0.45 0.55 0.65 0.75 0.85 diameter (m) Fig.8.12. allowable buckling stress at different diameter for 5kw tower From Fig.8.11. It can be observed at the lowest cross-sectional area which is at the top of tower the critical buckling load is very small a slight reduction in diameter or thickness brings critical load very close to the design values. So in 5kw tower we left the tower as it is, because it has not much room for optimization. 107 CHAPTER #9 9. CONCLUSION In this work we model different tower design (constant thickness or variable), the major design factor is based on the buckling load and buckling stresses under the constraints of deflection. Specific conclusions from this work include: 1) Shape of the Tower The tapered tubular tower with constant thickness is better than the constant diameter tubular tower, since its safe tower material and reduces cost. 2) D/t Ratio The tower becomes more prone to local buckling as the d/t ratio increases. In order to design the tower against local buckling the d/t ratio should be minimum as possible. However, it should be kept in mind that at smaller cross-section the critical buckling load reduced significantly. So, d/t ratio should be chosen with respect to both critical buckling load and allowable buckling stress. 3) Natural Frequency Of Tower Small or medium size wind turbine tower can be designed as stiff tower whichhave highnatural frequency than the operating frequency of rotor. This makes tower safe against the resonance which leads to the structural failure of wind turbine tower. 4) Maximum Stresses Occur at the Base of the Tower While designing a wind turbinetower it should be kept in mind that the maximum stresses occur at the base of the tower (fixed support end). So tower should have high strength at the base. 5) Variable Thickness Along the Tower Height We earlier conclude that tapered tubular tower have high strength at the base. It is also possible to have variable thickness tower; thicker at the base and as we move up along the tower heightthickness gradually decreases. We know that the maximum stresses occur at the base and as we move up the stress magnitude decreases, so the tapered tubular with variable thickness is also an economical option which reduces both material and cost. 108 Even though this work is limited only to the design and stability of towers in static conditions this work can be extend if one takes wind velocity as a function of time and similar effects like vortex shading or wind induced vibrations i.e. dynamics analysis. Also the effect of tower connections, bolts and weld can be taken into to account to give more sophisticated design of tower. Similarly, a wind turbine tower is designed for a particular rotor which operates at a certain speed and frequency. The effect of rotor and blade forces, especially the rotor thrust becomes significant as the size and weight of wind turbine increases. 109 APPENDIX A 110 FOUNDATION OF WIND TURBINES “The most successful structures stay still. That’s the goal of the exercise.” Introduction The foundation’s only task is to ensure the stability for the wind turbine, and to do so over its life time. This is done by transferring and spreading the loads acting on the foundation to the ground. Onshore wind turbines are usually supported by either a slab foundation or a pile foundation. Soil conditions at the specific site usually govern whether a slab foundation or a pile foundation is chosen. A slab foundation is normally preferred when the top soil is strong enough to support the loads from the wind turbine, while a pile supported foundation is attractive when the top soil is of a softer quality and the loads need to be transferred to larger depths where stronger soils are present to absorb the loads. When assessing whether the top soil is strong enough to carry the foundation loads, it is important to consider how far below the foundation base the water table is located. Usually load acts on foundation are of two types.   Dead Loadsare the weight of the tower materials and the soil surrounding the foundations. Live Loadsinclude the wind. Wind may be a vertical force downward, a horizontal force, or an uplift force. A live load may also be exerted by water in the soil around the foundations. Wet soil exerts much more force than dry soil. Frozen soil exerts much more force than wet soil Direction of load The weight of objects is caused by gravity and results in a vertical downward load. Wind can be in any direction, as mentioned earlier. The soil exerts forces in all directions, but foundations usually see the horizontal thrust of the soil on the outside of the foundation . 111 Wind turbine foundation types Gravity base The most common type of wind turbine foundation, the gravity base provides a great deal of stability. The weight of the concrete base and overlying soil prevents the turbine from tipping over. Resembling an inverted mushroom, the foundation spreads out in a cemented octagon shape with thickness tapering out toward the edges of the platform. The size of the main portion of the octagonal base varies depending on the soil reaction pressure. According to the Southeastern University and College Coalition for Engineering Education, the total reinforcing power of a gravity base ranges from 40,000 to 100,000 pounds. Rock-anchored Rock-anchored wind turbine foundations work best in areas where bedrock lies within 8 feet of the surface, according to the Southeastern University and College Coalition for Engineering Education. Similar to a gravity base, a rock-anchored foundation utilizes a spread-footing foundation that sits on the surface of the soil but includes anchors that extend down through the bedrock and hold a turbine upright. Overall, this foundation type is less expensive than the gravity base although it calls for the existence of surface rock formations that can hold anchors in place. Spread foundation A spread foundation (or a slab foundation) is a foundation which consists of a big plate that makes use of the big area for spreading the loads to the ground. The geometry is often 112 cylindrical or a square prism and the construction material is almost exclusively reinforced concrete. The bigger bottom area there is the smaller pressure on the ground. This is limiting the area of the foundation so that the ground pressure doesn’t exceed the maximum allowed pressure for the soil. Besides the ground pressure, the width of the plate has to be sufficient big to prevent the tower from turning over. The settlements must not be too large, but the most essential is that the differential settlements are kept low to remain the tower vertical. This type of foundation is suitable for strong and stiff soils that don’t give large settlements. That is the reason why this type of foundation mostly is used on friction soils with high friction angle, salty clays, fillings, organic soils or other soils with low modulus of elasticity and/or strength. Piles Piles are typically used instead of footings where the soil quality is poor. They are, generally speaking, more expensive to install and have to be driven into the ground with specialized equipment. They can work one of two ways: 1. Piles can be driven down to a point where they bear on bedrock or other sound substrate. 2. Piles can be driven into soil far enough that the friction of the soil against the sides of the pile is enough to resist any downward movement. 113 If the soil properties are not sufficient to foot the foundation on the ground it can be a good solution to install piles to conduct load to better soil at a greater depth in the ground. Due to the big bending moment from the wind, piles might be exposed to tensional loads which have to be considered. The connection between the piles and the plate is important for the load distribution. The two extreme cases is a clamped connection which does not allow any rotation, and a hinged connection with no rotational stiffness. The clamped case will introduce a big bending moment in the pile top, and the second one will not. The actual case is neither the clamped one, nor the hinged but an intermediate of these two. If the latter one is the one that match the actual connection best the horizontal force acting on the foundation (from the wind load) must be handled in another way. Generally the plate is footed at some depth in the ground having soil surrounding it, and the soil along the perimeter of the foundation can resist the horizontal forces. 114 The design of any foundation consists of two parts   Stability analysis Structural design of foundation Design criteria The essential criteria’s for wind turbine design are:- 1. Stiffness The far most important serviceability criterion and the most common foundation design specification provide by the manufacture other than the loads, is the minimum foundation rotational stiffness. In order to avoid excessive motion at the tower top and to provide the require damping, the final foundation design must satisfy minimum rotational and horizontal stiffness values provided by the turbine manufacturer. 2. Strength Withstand factored loads and fatigue loads 3. Stability Resist excessive translational and rotational movement under extreme loads. Design for stability compares un-factored overturning moments and horizontal forces with resisting moments and sliding resistance. For both sliding and overturning stability, convention among geotechnical designers is that the FoS must be greater than or equal to 1.5. This minimum is established to preserve safety while allowing for minimal amounts of soil backfill and concrete dead weight (resistance mechanism). 4. Stability Analysis To ensure that a construction is not turning over, the eccentricity of the load must be within the perimeter of the foundation. E= < (1-a) Where 115 M is the bending moment acting at the bottom of the structure V is the vertical load on the structure including the weight of the construction B is the width of the construction (or diameter if it is a circular construction) In general a stronger design criterion than equation (1-a) should be used because of the high pressure this will generate on the soil and the big second order moment that will occur due to the rotation of the construction. Failure – Due to Instability This mode of failure is apparent when the load forces the pile to buckle. The lateral support of the soil will prevent the pile to buckle, therefore the stronger soil the less risk for buckling. In addition the slenderness of the element is significant. There is a calculation method for how to calculate the critical load and the critical length, which take into account the lateral support from the soil. The method assumes a sinusoidal deflection curve of both the initial deflection and the deflection from the loading. Pcr = 2 ---------- (68) Lcr = π* --------- (69) Where Pcr = critical or buckling load Kd = design value for sub-grade reaction d = transverse dimension of pile Ed = young modulus of pile material I = moment of inertia of pile Lcr = critical length of pile Bearing Capacity of Soil Bearing capacity of soil is the ability of soil to safely carry the pressure placed on soil from any engineer structure without undergoing a shear failure with accompanying large settlements Qu = qu*B*W 116 ---------- (70) Where Qu= bearing capacity of soil qu = ultimate bearing capacity of soil B = foundation width W = lateral length of foundation The ultimate bearing capacity of soil is the critical bearing capacity at the verge of failure. It depends on soil cohesion & other bearing factors. Check for Bearing Capacity The pressure exerted by structure & moment that wind created at base is less than the bearing capacity of soil for save design. The soil exerted on pressure is, P= + ---------- (71) Where P = pressure on soil ( toe pressure ) W = vertical down thrust including weight of foundation B = foundation width M = moment at the base Z = section modulus For safe design, the above pressure should not exceed the ultimate bearing capacity of soil 117 CALCULATIONS For 5 kW tower (square foundations) M = mr + mt + mf ---------- (72) M = total mass of structure mr = mass of rotor &nascalle = 2987.89kg mt = mass of tower = ρ*π*d*t*l mf = mass of foundation = 2*(mt+ mr) --------- ( assumed ) where ρ = density of material = 7850 kg/m3 d = mean diameter = 537.5mm t = thickness = 6mm l = length of tower = 12m mt = (7850)*π*0.5375*6e-3*12 mt = 954.4kg therefore, total vertical load on soil is, W = M * 9.81 W = 11826.87*9.81 W = 116.0197 KN Therefore toe pressure is, from Eq.71 is: P= + ---------- (73) M = pressure exerted by wind on tower * area * half length M = 4400*0.5375*12*6 M = 170.28 kNm Z= ( for square foundation ) Assume dimension of square foundation is 4 by 4 m Z =10.667 m3 P= + P = 23.214KPa 118 ---------- (74) Assume ultimate bearing capacity of soil is 63 KPa The allowable bearing capacity of soil is, Qa = Factor of safety is, FS = FS = 2.714 Check for Over-turning E= < E= < E = 1.4678 < 2 So our design is safe…. 119 For 250 kW tower (For square foundations) From Eq. 72: M = mr + mt + mf M = total mass of structure mr = mass of rotor & nacelle = 14286.8 kg mt = mass of tower = ρ*π*d*t*l mf = mass of foundation = 4*(mt+ mr) …… ( assumed ) where ρ = density of material = 7850 kg/m3 d = mean diameter = 537.5mm t = thickness = 6mm l = length of tower = 12m mt = (7850)*π*2*15e-3*35 mt = 25894.577kg therefore, total vertical load on soil is, W = M*9.81 W = 200906.218 kg * 9.81 W = 1970.89 KN Therefore toe pressure is, from Eq. 73 is: P= + M = pressure exerted by wind on tower * area * half length M = 8300*2*35*17.5 M = 10167.5 KNm Z= ( for square foundation ) Assume dimension of square foundation is 12 by 12 m Z =288 m3 P= + P = 49 KPa Assume ultimate bearing capacity of soil is 100 KPa 120 [From Eq. 74] The allowable bearing capacity of soil is, Qa = Factor of safety is, FS = FS = 2.041 Check for over turning E= < E= < E = 5.1588 < 6 So our design is safe…. 121 REFERENCES [1] Preliminary Design of 1.5-MW Modular Wind Turbine Tower. ChawinChantharasenawong*, PattaramonJongpradist and SasarajLaoharatchapruek Department of Mechanical Engineering, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand. [2] Design of wind turbine tower and foundation systems: optimization approach John Corbett Nicholson University of Iowa [3] Structural design optimization of wind turbine towers Hani M. Negma, Karam Y. Maalawib,* a Aerospace Engineering Department, Cairo University, Cairo, Egypt b Mechanical Engineering Department, National Research Center, Cairo, Egypt [4] A STUDY OF WIND-RESISTANT SAFETY DESIGN OF WIND TURBINES TOWER SYSTEM Ching-Wen Chien, Jing-Jong Jang Ph.D. Candidate, Department of Harbor and River Engineering, National Taiwan Ocean University/ E&C Engineering Corporation Keelung, Taiwan. [5] WIND FARM AT GHARO, PAKISTAN: BASIS FOR SITE SELECTION. IrfanAfzalMirza, Prof Dr. Shahid Khalil, Brig DrNasim A. 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[15] Wind resistant stability of tubular wind turbine towers Dr.Muhammadkashifkhan , Muhammad inam. (SUPARCO). 122 [16] Optimization of thin wall cylindrical shell by Mathews A. Dawson 2004 [17] Wind turbine design and implementation Worcester polytechnic institute 2010 REFERENCESFOR FOUNDATION [18] DNV, Rules for the Design, Construction and Inspection of Offshore Structures, DetNorskeVeritas, Høvik, Norway, 1977.(Reprint 1978) [19] DNV, Foundations, Classification Notes, No.30.4, Det Norske Veritas, Høvik, Norway,1992. [20] DNV, Rules for Classification of Fixed Offshore Installations” Det Norske Veritas,Høvik, Norway, 1998. [21] Det Norske Veritas (DNV), Design of offshore wind turbine structures, Offshore Standard DNV-OS-J101, October 2007 [22]European Committee for Standardization (ECS), Eurocode 7 – Geotechnical design – Part 1:General rules, Swedish Edition SS-EN1997-1, Swedish Standards Institute (SIS), Stockholm2008 [23] European Committee for Standardization (ECS), Eurocode 7 – Geotechnical design – Part 2:Ground investigation and testing, Standard EN1997-2, ComitéEuropéen de normalisation (CEN), Brussels 2007 123