WO2007012200A1

WO2007012200A1 - Design system for composite wind towers

Info

Publication number: WO2007012200A1
Application number: PCT/CA2006/001266
Authority: WO
Inventors: Dimos Polyzois; Nibong Ungkurapinan
Original assignee: The University Of Manitoba
Priority date: 2005-07-25
Filing date: 2006-07-24
Publication date: 2007-02-01

Abstract

The present invention relates generally to design systems for composite fiber-reinforced polymer (FRP) wind tower systems. More particularly, the present invention relates to a method of designing a fiber-reinforced polymer wind tower including inputting design input data into a finite element analysis software system, the design input data selected from any one of or a combination of location specific data, power generator data, tower dimension data, and tower material properties; and, iteratively generating an output design based on the design input data until an optimum design is obtained.

Description

DESIGN SYSTEM FOR COMPOSITE WIND TOWERS

FIELD OF THE INVENTION

BACKGROUND OF THE INVENTION

Wind energy is the world's fastest growing energy source and is already a major source of energy across Europe. By the end of 2002, Europe was producing approximately 75% of the world's total wind energy, while Canada produced only 0.4% (Jacob, 2003). Technological advancements over the last 25 years have resulted in significant reduction in the cost of wind generated energy from 38 US cents (per kWh) in 1982 to between 4 and 6 US cents (per kWh) in 2001 (Jacob, 2003). According to Marsh (2001), this dramatic decrease is mainly due to the use of composite materials for the construction of lighter rotor blades. Indeed, composite materials are slowly finding their way into more and more applications in wind generator nacelles, cabins, fairings and parts of towers. Industry estimates suggest that 80,000 tons of finished composites will be required annually by 2005 for rotor blades alone.

Composite materials have the potential to decrease the total weight of the wind towers, leading to substantial saving in transportation and erection costs, making wind energy more affordable for remote and rural communities where the number of s required is usually small. In a white paper published by WindTower Composites (2003), it was reported that the cost of composite towers, based on a 2-unit wind farm, is 38 % less than the cost of steel towers. For a 25-unit wind farm, the cost of composite towers is 28% less than steel towers. Thus, even though the cost of composite materials per unit weight is higher than that of steel, the lower total weight of composite towers compared to steel, results in lower transportation and erection costs. Furthermore, the cost advantage for steel has been eroding over the last year as the price of steel in the world market has increased, while the cost of composite materials has been steadily decreasing. As a result, research in the development of composite wind towers has begun in earnest both in the United States and Europe (DOE, 2003; CORDIS, 2003).

The use of wind energy in rural communities will often provide significant economic advantages over conventional power generating systems. For example, Cambridge Bay, Nunavut is a community of about 1,200 people, located on the south shore of Victoria Island in the Canadian Arctic. Electrical power is provided by diesel shipped in from Hay River by barge in the summer. The results from an NRCan study, indicate that conversion to wind power would displace about 300,000 litres of fuel per year. At 1999 fuel prices, this translates to an annual saving of $258,000 in fuel costs.

The application of composite wind towers, however, is not limited to remote areas. As the cost of steel continues to rise and as towers become larger, high materials costs, coupled with high transportation and erection costs, makes composite materials more attractive for the construction of small wind farms.

As a result, there has been a need for fiber-reinforced polymer (FRP) wind tower systems and systems for designing such wind towers. In particular, there has been a need a design system that enables the input of design criteria and through finite element analysis provides an output design meeting the design criteria.

SUMMARY OF THE INVENTION

It is an object of the present invention to obviate or mitigate at least one disadvantage in the design of previous wind tower systems.

In a first aspect, the present invention provides a method of designing a fiber-reinforced polymer wind tower comprising the steps of: inputting design input data into a finite element analysis software system, the design input data selected from any one of or a combination of location specific data, power generator data, tower dimension data, and tower material properties; and, iteratively generating an output design based on the design input data until an optimum design is obtained. In further embodiments, the location specific data includes any one of or a combination of 50-year wind speed, live load due to snow, ice and rain, and live load due to earthquake, the power generator data includes any one of or a combination of weight of all components, nominal power, nominal wind speed, cut-in speed, cut-out speed, rotor speed, and rotor diameter, the tower dimensions data includes any one of or a combination of hub height, base diameter, top diameter, inner diameter, number of layers, layer thickness, fiber orientation and fiber volume and the tower material properties includes any one of or a combination of elastic modulus in the fiber direction, elastic modulus in transverse fiber direction, shear modulus, ultimate tensile in the fiber direction, ultimate compressive strength in the fiber direction, ultimate tensile strength in transverse fiber direction, ultimate compressive strength in the transverse fiber direction, ultimate shear strength, fiber density and Poison's ratio.

In a further embodiment, the output design includes any one of or a combination of Tsai-Wu failure criterion values, ultimate stress and stress distributions, ultimate strain and strain distributions and deflections.

Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will now be described, by way of example only, with reference to the attached Figures, wherein:

Figure 1 is a schematic diagram of a typical (i) tubular steel and (ii) 8-cell FRP wind tower;

Figure 2 is a schematic diagram of the distribution of wind pressure acting on a wind tower;

Figure 3 is a schematic diagram of an example eight-node quadrilateral structural shell element utilized in accordance with the invention;

Figure 4 is an ANSYS model of a tubular steel wind tower;

Figure 5 is an ANSYS model of a CFRP wind tower;

Figure 6 is an ANSYS model showing the distribution of stresses in a tubular steel wind tower; Figure 7 is an ANSYS model showing the distribution of stresses in a GFRP tower;

Figure 8 is an ANSYS model showing the distribution of stresses in a CFRP tower;

Figure 9 is an ANSYS model showing values of Tsai-Wu failure criterion in a GFRP tower; and,

Figure 10 is an ANSYS model showing values of Tsai-Wu failure criterion in a CFRP tower.

DETAILED DESCRIPTION

Generally, the present invention relates to a system for designing fiber-reinforced polymer (FRP) wind tower structures as described in Applicant's copending application entitled "Composite Wind Towers Systems And Methods Of Manufacture" filed July 25, 2005 and incorporated herein by reference.

A design software package has been developed which incorporates structural analysis and design for wind towers. While the structural analysis model is described herein on the basis of the commercially available finite element ANSYS software program, it is understood that the model may be utilized using other finite element programs. It is also understood that within the context of this description that the design program combines the internationally recognized standard Germanischer Lloyd: Rules and Regulations, Part 1 - Wind Energy (1993) and the National Building Code of Canada (1995) but that other standards may be utilized.

Design Process Overview

Generally, the design process includes the steps of inputting the material properties of the components used in the fabrication of the wind tower, wind data, other client requirements, and iteratively generating an output design on the basis of an initially assumed set of fabrication parameters (dimensions of cells and fibre type and orientation) until an optimum design is obtained. The software program generates results that are checked against performance criteria set by national standard agencies and industry.

Large deflections and cross-section distortion are taken into account in the analysis and proper failure criteria are used in order to determine the ultimate load. This analytical model has been verified through comparison with experimental results.

The basic concept of a finite element technique is to use a finite number of defined elements whose displacement behaviour is described by a fixed number of degrees of freedom to predict the structural behaviour of structures. In this study, to model the composite tower, an eight-node quadrilateral layered shell element was used. This element, which is designated by ANSYS as SHELL 99, is a 100-layer shell structure. This element was chosen because of its ability to: a) handle unlimited number of layers with constant or variable thickness; b) account for large deflections; c) predict failure by the means of three different failure criteria; and, d) handle membrane stresses and strains in the process.

The Tsai-Wu failure criterion was adopted in the analysis to predict the ultimate capacity of the composite structures by using the stresses obtained from the finite element analysis and then comparing them to the material strengths. This failure criterion was chosen since it accounts for the interaction between different stress components. The Tsai-Wu coupling coefficient must be between -1.0 and 1.0. This requirement is necessary to ensure that the failure surface intercepts each stress axis and the shape of the surface is a closed one.

A fiber-reinforced polymer (FRP) structure experiences large deformations under lateral loading and, therefore, changes in its geometric configuration take place that cause the structure to respond in a nonlinear fashion. Thus, geometric nonlinearity must be taken into account in the analysis. Large deflections result in changes to the element orientation, and, consequently, changes in the element stiffness matrix. To deal with this problem in the current analysis, the element stiffness matrix is continuously updated using a Newton-Raphson iterative procedure. This method is based on the incremental procedure in which a series of successive linear iterations converge to the actual nonlinear solution.

The input requirements for the computer analysis and design of the composite towers are listed in Table 1.

Table 1- Typical Input Parameters for Structural Analysis and Design Input Parameters

Location Specific

50-year wind speed at a reference height of 10-m, v_1/50 Live load due to snow, ice and rain Live load due to earthquake Wind Turbine

Weights of all components Nominal power, P_d Nominal wind speed, v_r Cut-in speed, Cut-out speed, Rotor speed, n Rotor diameter, R

Nacelle/Rotor Dimensions Tower Dimensions (initial values are required)

Hub height, H Diameter at the base, d_b Diameter at the top, d, Inner diameter, ά_{ Number of layers Layer thickness Fiber orientation Fiber volume

Material Properties

Elastic modulus in the fiber direction, Ei

Elastic modulus in transverse fiber direction, E₂

Shear modulus, G^

Ultimate tensile in the fiber direction, Fi¹"

Ultimate compressive strength in the fiber direction, Fj⁰"

Ultimate tensile strength in transverse fiber direction, F₂"¹

Ultimate compressive strength in the transverse fiber direction, F₂ ^CU

Ultimate shear strength, F^su

Fiber density

Poison's ratio

DESIGN LOADS

There are two types of loads that are taken into account: loads acting on the tower and loads transferred from the wind turbine to the top of the tower. The wind tower should be designed to resist these loads and their combination.

Load Acting on the Tower a) Dead load

Dead loads are computed on the basis of the unit weight of the materials. Dead loads consist of the particular self-weight of the shell, linings, ladders, and any permanent equipment. b) Live load due to snow, ice and rain

Live loads are determined according to National Building Code of Canada (1995). c) Live load due to wind

The wind turbine tower is designed for all loads and/or deflections caused by wind on the tower calculated in accordance to the National Building Code of Canada (1995). d) Live load due to earthquake

The wind turbine towers were also designed to withstand the minimum lateral seismic forces. Loads Transferred from the Wind Turbine to Tower According to the Germanischer Lloyd: Rules and Regulations, Part 1 - Wind Energy (1993), wind turbine towers should be designed to resist not only the following load cases, but also their combinations when they exist:

Dead loads (Dead load is due to the mechanical system stored at the top of the tower.

There are three main weight components, which should be included in the calculations: the blades, the nacelle, and the rotor)

Normal operating loads

Extreme operating loads

Annual wind (10 minutes)

Annual gust (5 seconds)

50-year wind (10 minutes)

50-year gust (5 seconds)

Generator short circuit (blackout)

Rotor eccentricity

Load Combinations

The combinations of the above load cases are given in Table 2.

Table 2 - Load combinations

The first load combination is referred to as a normal operating condition, which combines dead loads, loads due to normal operation, loads due to eccentricity caused during installation of the rotor, and the earthquake loads. The second load combination is referred to as an extreme operating condition and does not combine the loads due to earthquake. Under this condition, the wind turbine works under a wind speed very close to the cut-out speed.

The third load combination is referred to as an operating condition under annual wind over a period of 10 minutes. In this scenario, forces caused by a generator short circuit (blackout) are included.

The fourth load combination is referred to as an operating condition under annual gust over a period of 5 seconds. Since the wind frequency is very small, it is extremely rare to combine it with other load cases caused by fault condition.

The fifth load combination is referred to as an operation condition under 50-year wind over a period of 10 minutes. Similarly to the third load combination, loads due to blackout are included.

The last load combination is referred to as an operating condition under 50-year gust over a period of 5 seconds. Similarly to the fourth load combination, other loads due to fault condition are not included.

In order to form the load combinations, the appropriate load factors, which are given in Table 3, are applied to the various loads components according to the load case group (Germanischer

Lloyd: Rules and Regulations, Part 1 - Wind Energy, 1993).

Table 3 - Safety factors for loads

OUTPUT

The output results from structural analysis and design software consist of the following parameters in tabular or graphical form:

Tsai-Wu failure criterion value

Ultimate stress and stress distributions

Ultimate strain and strain distributions Deflections

EXAMPLE

An example of a structural analysis and design for a 750KW Wind Tower is discussed.

General Information

The technical data of a 750 kW wind turbine (NM48/750) are listed in Tables 4 and 5. This technical information was provided by NEG Micon (2002). For this example, it was assumed that the wind turbine tower is located in Churchill, Manitoba, Canada. Three types of towers were designed to support the 750 kW wind turbine. The first tower was assumed to be made of steel while the other two towers were assumed to be made of advanced composite materials, namely glass fiber reinforced polymers (GFRP), and carbon fiber reinforced polymer (CFRP). The composite towers were comprised of eight cells as described in Applicant's copending application. The towers analyzed in this example, shown in Figure 1, have the following characteristic parameters: a height of 50-m, a diameter at the base of 3.5m, and a diameter at the top of 2.5-m. The composite towers have a constant inner diameter of 2m.

Table 4- Wind Tower Parameters

Table 5 - Wind turbine mass distribution

The Young's modulus for the steel tower material of 200,000 MPa and the yield strength of 350 MPa were assumed. For composite towers, a fiber volume ratio of 0.60 was assumed. The material elastic properties and the ultimate strength of GFRP and CFRP used are given in Table 6.

Table 6 - Material elastic properties and the ultimate strength of GFRP and CFRP

Where, Ei and E₂ are the elastic modulus in the fiber direction, transverse fiber direction, respectively; G,₂ is the shear modulus; Fi¹" and Fi^cu are the ultimate tensile and compressive strength in the fiber direction, respectively; F₂ ^m and F₂ ⁰" are the ultimate tensile and compressive strength in the transverse fiber direction, respectively; and F^su is the ultimate shear strength.

Loads on the Wind Turbine Tower

The typical distribution of wind pressure acting on the tower is shown in Figure 2. The summarized lateral wind pressure and factored lateral wind pressure, calculated according to the National Building Code of Canada (1995), as mentioned in the previous section, are given in Table 7. The loads transferred from the wind turbine to the tower were determined according to the Germanischer Lloyd: Rules and Regulations, Part 1 - Wind Energy (1993) and the summarized factored loads and their combination are given in Tables 8 and 9.

Table 7- Wind pressure acting on the tower

Table 8-Summarized factored loads acting at the top of the tower

Table 9- Summarized load combinations

Load Factored loads combinations F_x Fy F₁ M_x M_y M₁

(kN) (kN) (WV) (kN-m) (kN-m) (kN-m)

In Table 9, the additional moment due to an eccentricity between the center of gravity of the nacelle and the tip of the tower of 1.125 meters has been added to the moment M_y . The additional moment is, therefore, equal to M_y = 1.125F- . The load combinations and wind pressures given in Table 9 were used in the finite element analysis described below.

Finite Element Modeling

The finite element technique uses a finite number of elements whose displacement behaviour is described by a fixed number of degrees of freedom to predict the structural behaviour of structures. Modeling of the tubular steel and the composite wind turbine towers was carried out using the ANSYS finite element software and the theoretical model described earlier.

a) Modeling of the tubular steel wind turbine tower

To model the tubular steel wind turbine tower, an eight-node quadrilateral structural shell element was selected, as shown in Figure 3. This element is designated by ANSYS as SHELL93. The element is particularly well suited to model curved shells. The element has six degrees of freedom at each node: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z-axes. The deformation shapes are quadratic in both in-plane directions. The element has plasticity, stress stiffening, large deflection, and large strain capabilities. The material properties used in the analysis are described in Table 6.

The discretization of the tubular steel tower is shown in Figure 4. The base of the tower is perfectly fixed. The loads, as described in Table 9, were applied at the tip of the tower in 500 N increments to the maximum loads, in order to obtain a load-time response of the model. The tower was designed to meet both strength and serviceability criteria.

b) Modeling of the composite wind turbine towers The geometry of both the GFRP and the CFRP wind turbine towers were built in ANSYS as shown in Figure 5. To model both the GFRP and the CFRP wind turbine towers, an eight-node quadrilateral layered shell element was selected. This element is designated by ANSYS as SHELL99 and allowed the user to model up to 250 layers. The element has six degrees of freedom at each node: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z-axes. This element was chosen mainly because of its ability to be meshed over an area. Material properties for both the GFRP and the CFRP towers used in the analysis are given in Table 6.

Finite Element Results and Discussion

A summary of the analysis results from the finite element analysis of the 50-m tower supporting a 750 kW wind turbine is given in Table 10. The results include the tip deflection, the maximum stress, the failure criterion, and the total mass of the tower. In the analysis, the geometric non- linearity was taken into account since the large deflections were expected to occur in those towers.

Table 10- Summary of the analysis results of 750 kW tower wind turbine tower

The analysis shows that a shell thickness of 23-mm is required for the tubular steel wind turbine tower, resulting in a total mass of 85.1 tons. The tip deflection of the steel tower is 560.45 mm, which is less than the serviceability limit for lateral deflection of 1 m. The serviceability limit for lateral deflection is defined as the distance between a rotor blade and a tower. The maximum stress of 219.01-MPa occurred near the base of the tower, as shown in Figure 6. This stress is less than the limit design strength of 3ϊ5-M?Α (0.9F_y).

For the 8-cell GFRP wind turbine tower, each cell was made up of 16 equal thickness layers of 1.25-mm. The fiber orientations were (90, 0β, 90)₂. When individual cells were assembled to form a complete tower, 28 additional layers, with the following fiber orientation: (0₂₇, 90), were added to make the tower stiffer and to provide confinement to the cells. The total mass of the GFRP tower was 78.4 tons. The tip deflection of the GFRP tower is 967.74 mm, which is less than the serviceability limit for lateral deflection of 1 m. The maximum stress of 71.39-MPa occurred at the stiffener near the base of the tower as shown in Figure 7.

For the 8-cell CFRP wind turbine tower, each cell was made up of 20 equal thickness layers of 1.25-mm. The fiber orientations were (90, 0₈, 90)₂. When individual cells were assembled to form the complete tower, one additional circumferential layer was added to provide confinement. The total mass of the CFRP tower was 47.8 tons. The tip deflection of the CFRP tower is 627.74 mm, which is less than the serviceability limit for lateral deflection of 1 m. Figure 8 shows the stress distribution in the CFRP tower. The maximum stress of 152.29-MPa occurred at the stiffener near the base of the tower.

Figures 9 and 10 show values of the Tsai-Wu failure criterion along the GFRP and the CFRP tower and the failure criteria were 0.39 and 0.18, respectively. These values were less than unity, which indicates that both composite towers are safe to resist the factored loads. Although, both composite towers can resist a greater load, the serviceability limit for lateral deflection is the controlling factor in the design. The GFRP and the CFRP towers are approximately 8 and 44 percent lighter than the tubular steel tower respectively.

The above-described embodiments of the present invention are intended to be examples only. Alterations, modifications and variations may be effected to the particular embodiments by those of skill in the art without departing from the scope of the invention, which is defined solely by the claims appended hereto.

Claims

CLAIMS:

1. A method of designing a fiber-reinforced polymer wind tower comprising the steps of: inputting design input data into a finite element analysis software system, the design input data selected from any one of or a combination of location specific data, power generator data, tower dimension data, and tower material properties; and, iteratively generating an output design based on the design input data until an optimum design is obtained.

2. A method as in claim 1 wherein the location specific data includes any one of or a combination of 50-year wind speed, live load due to snow, ice and rain, and live load due to earthquake.

3. A method as in claim 1 or claim 2 wherein the power generator data includes any one of or a combination of weight of all components, nominal power, nominal wind speed, cut-in speed, cutout speed, rotor speed, and rotor diameter.

4. A method as in any one of claims 1-3 wherein the tower dimensions include any one of or a combination of hub height, base diameter, top diameter, inner diameter, number of layers, layer thickness, fiber orientation and fiber volume.

5. A method as in any one of claims 1-4 wherein material properties includes any one of or a combination of elastic modulus in the fiber direction, elastic modulus in transverse fiber direction, shear modulus, ultimate tensile in the fiber direction, ultimate compressive strength in the fiber direction, ultimate tensile strength in transverse fiber direction, ultimate compressive strength in the transverse fiber direction, ultimate shear strength, fiber density and Poison's ratio.

6. A method as in any one of claims 1-5 wherein the output design includes any one of or a combination of Tsai-Wu failure criterion values, ultimate stress and stress distributions, ultimate strain and strain distributions and deflections.

7. A method as in any one of claims 1-6 wherein tower dimension data is an output.