Aeroelastic Blade Optimization for an Urban Wind Turbine Ricardo Jorge Marques Penedo ´ UNIVERSIDADE TECNICA DE LISBOA ´ INSTITUTO SUPERIOR TECNICO Departamento de Engenharia Mecˆanica, Mecˆanica Aplicada e Aeroespacial

1

Introduction

Today, the challenges in the efficient use of resources is unparalleled. We begin to realize that the world needs a new energy paradigm, since the primary sources of energies used in the twentieth century, such as oil and natural gas are not sustainable alternatives in the near future [7]. Despite its flaws, like the irregularity of the weather, wind energy can have a significant contribute to a country’s electric energy. This can be achieve with big wind farms or with local small wind turbines. The main parameter to evaluate the economical efficiency of a power system is through its Overall Cost of Energy (COE) in a way that lower COE means better efficiency. Hence the need to optimize our wind turbine. The wind profile at a specific location is the most important parameter when analysing the annual power output of a wind turbine, a wind turbine optimized in a specific location will not have the same performance in other locations. On top of that, the aerodynamics of small wind turbine are slightly different from its bigger sisters, so that improvements can still be achieved. The main goal of this project is to investigate how wind turbine blades and operating regime can be optimized to minimize the COE, here defined as Overall Cost of Power , at a particular wind resource for a small urban wind turbine. A multidisciplinary approach was use in the analysis of the wind turbine. The Blade Element Momentum Theory (BEMT) was use in the aerodynamic analysis, the aerodynamic data of the airfoils were calculate with XFOIL and the optimization use the Simplex algorithm. This paper describes the multidisciplinary tools used in the analysis of a small urban wind turbine as well as three optimization problems, its results and conclusions.

2 2.1 2.1.1

Methodology Aerodynamic Analysis Blade Element Momentum Theory

The Blade Element Momentum Theory (BEM) method is well-known and widely used. The coded used was the one implemented in AeroDyn [12] and [28]. In practice, BEM theory is implemented by breaking the blades into many elements along the span. As these elements rotate in the rotor plane, they trace out annular regions, across which the momentum balance takes place. These annular regions are where the induced velocities from the wake change the local flow velocity at the rotor plane. In figure 1 the angle of the undisturbed flow is obtainned by adding the angle of pitch, beta, and the angle of attack, alpha. The angle of attack is function of the local velocity vector, which in turn is constrained by the local wind speed, the turbine’s rotation speed, the velocities in the blade element and the induced velocities. 0 The angle of the undisturbed flow is dependent on induced speed (a and a ) and the tip speed ratio of the blade (λr ) (equation (1)). tanφ =

1−a U∞ (1 − a) = . Ωr(1 + a0 ) (1 + a0 )λ

(1)

The induced velocities represented in equation (1) are function of the forces on the blades are calculated using BEMT. The distribution of thrust over a ring of width dr is given by equation (2) and torque by equation (3). 1

Figura 1: Velocities at blade section. Angle are with respect to the plane of the rotor

1 2 dT = B ρVtotal (Cl cosφ + Cd sinφ)cdr 2

(2)

1 2 dQ = B ρVtotal (Cl sinφ − Cd cosφ)crdr (3) 2 The Glaubert correction factor, as well as a Prandtl tip and hub loss correction factor are applied to the equations. The solution is obtainned using a predictor-corrector, the Adams-Bashforth in the first step and the Adams-Moulton in the next ones. The process is iterative and the solutions converge when it falls within a certain tolerance. 2.1.2

XFOIL

To obtain the 2D polar data from the different airfoils in study was used a program of 2D panels with a viscous formulation. The program used was the well known and documented XFOIL. The version used is 6.94 for Win32 optimized for Pentium 4 processors. The XFOIL is used to map the aerodynamic properties of the of the NACA 44XX family throughout the entire Reynolds range (figure 4).   Re − Renext (4) Cl = Clnext + (Clpreviously − Clnext ) Repreviously − Renext 2.1.3

Post-Stall Extrapolation of Coefficients

Wind turbine airfoils some times work in the post-stall regime. Therefore we must have access to aerodynamic data in the post-stall regime. We do this by blending the pre-stall with the post-stall data using the method of Selig & Du to the lift corrections and to the Eggar’s method to the drag [13]. These methods allow us having aerodynamic data ranging −180◦ to 180◦ . Equations (3.19) - (3.32) in [1] describe the application of this method.

2.2

Aeroelastic Analysis

For the aero elastic coupling analysis the blade is treated as a flexible body. The deflection of the blade is obtainned by FAST with the summation Method of normal mode functions [15] The final mode shape is a linear combination of the first five modes of vibration. The modes of vibration for a given blade are calculated with the program BModes [16] that uses the Euler-Bernoulli beam approximation. To calculate the different modes are provided the geometrical and structural properties of the rotor. The aerodynamic forces are applied in the centre of each element with the shape of the blade defined by the mode shape calculate early.

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2.3 2.3.1

Optimization Optimization Algorithm

To solve the problem there are a wide variety of algorithms that can be used to perform design optimization of a small wind turbine. These algorithms fit into one of two main categories: gradient-based methods and gradient-free methods. Gradient-based methods include conjugate gradient method, the method of feasible descent and sequential quadratic programming [18]. The second group includes genetic algorithms, particle swarm [29] and the Simplex method ([18] - [21]). 2.3.2

Objective Function

In a wind turbine optimization the primary objective is to minimize the Overall Cost of Power (COE). By definition COE is the Total Cost divided by the Annual Energy Production (AEP) 5. Typically COE is expressed in cents/kWh. Cost (5) AEP Fingersh [35] and Fuglsang [24] have conducted a series of studies where they were able to correlate a series of characteristics of wind turbines with the total cost. However the lower end of this studies are for wind turbines with a spanwise of at least 20m, so we cannot use these results for our study, since we are aiming for small urban wind turbines with a maximum spanwise of 5m. The authors of [23] and [24] identify that the cost of a blade has a direct correlation to its weight and that the cost associated whit the manufacture of a blade for a small wind turbine is around 30% of the total. Therefore, if we assume a constant average density of the blade we can relate the cost with its volume. The volume for the entire blade is calculated section by section, in the same manner that a frustum in a pyramid [25]. Finally, the objective function used is presented in equation (6) and is called Overall Cost of Power. OverallCostof Energy(COE) =

OverallCostof P ower = 2.3.3

BladeV olume (1.00 − 0.30) + 0.30 InitialBladeV olume P20 P (i).F T i=1

(6)

Design Variables

In the optimization process five groups of design variables were used: chord, twist, airfoil thickness, blade radius and rotor speed. The chord distribution defines the overall shape of the blade. Twist angle, β in figure 1, is the angle of the blade relative to the blade plane of rotation. The variables were restricted by a lower and upper boundary and were defined only at a limited number of radial positions (along the span) to reduce the complexity of the problem. Linear interpolation was used for all the variable groups.

3

Wind velocity distribution

In the present project were used velocity wind distribution from three locations: two from Canada, a low to medium wind speeds at University of Toronto Institute for Aerospace Studies (UTIAS) [1], a medium to high wind speed from a wind farm in St. Lawrence, Newfoundland [1] and one from Portugal, with the lowest wind speeds, Alcochete [30]. The velocity wind distributions for the three locations are showed in figure 2. The histograms provides the percentage of time the wind blows at each speed. This allows a direct simulation of the total amount of mechanical power output as well as the ability to optimize designs to best match a specific location.

4

Results

To demonstrate all the potentiality of a local wind turbine optimization three problems are presented. In problem one was done a parametric study on how small changes in the design variable value 3

Figura 2: Wind velocity distribution data for the three locations will affect the overall performance of the wind turbine. In the second problem were performed three optimizations, one at each specific location, to determine the effect of the site-specific wind histograms on the optimized design, with the design being constraint by the maximum blade radius and maximum generator power. In the third problem the hypotheses are different from the second problem and the constraints were the minimum average power output to be achieved and again the maximum generator power.

4.1

Problem 1 - Parametric study of the Design Variables

In this problem we try to answer which design variable will have the biggest impact in reducing the COE. The design variables in study were: chord, twist, airfoil thickness, blade radius and rotor rotation speed. The design variables range change from −20% to 20% in respect to a initial design (table 1). The study was conducted at three locations, Alcochete, St. Lawrence and UTIAS so that the site-specific effects could be incorporated and then decoupled for the final solution, an average of the three solutions.

Tabela 1: Initial geometry The results show the average COE of the three locations (figure 3), that allow us to decouple the site specific location.

Figura 3: COE average

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Figure 3 shows the average COE for the three locations. It demonstrates that with th exception of twist, who presents little variation, every other design variables have a big impact on how COE changes, with COE decreasing with the increase of the variables values. Physically this was expect since by definition (equation (5)), COE is inverse of power and by increasing the chord and blade radius we are increasing the blade area, and this way increasing the potential flow between the inner and the outer surfaces which will boost lift results in a bigger torque and, as a result, a higher power output. If we were analysing an aeroplane wing, the behaviour of twist was not expected since we will expect an increase of power with the increase of twist because of the higher potential flow, however, in an aeroplane wing we do not have the effect of constant rotation, which has a big influence in this case. As show in the figure 3, increase twist will result in a small increase of COE. This means that the initial design for twist is already in a local minimum, and if we decrease twist, we will decrease the potential flow and therefore less power, increasing COE. Increasing twist will result in flow separation and once again less power. Although rotor speed is not a geometrical variable its included in this study because of the impact it has on the overall performance and because it is perhaps one of the easiest way to implement through gearboxes or other methodologies. This variable is similar to chord in behaviour and in value. We concluded that the variable with the biggest impact in COE is the blade radius with a −30% decrease obtainned by increasing blade radius in 20%. If increase blade radius is not an option, the second variable with the biggest impact is chord with a −16% decrease in COE by increasing chord in 20%. As we said before if we were able to change rotor speed we can decrease COE by −13% increasing rotor speed in 20%. If we analyse the results near the initial design we conclude that changing the initial variable ±5% we can increase COE ±10% for blade radius and ±4% for chord. This results are important for fabrication because products are built within certain tolerances, and build system below the values will decrease performance.

4.2

Problem 2 - Site-Specific Optimization of a Small Urban Wind Turbine Constraint to Blade Radius of 2.5m

There are some scenarios in real life that limit the maximum blade radius that a wind turbine can have. In this problem we optimize a small urban wind turbine constrained to a blade radius of 2.5m based on the initial design given in table 1. The turbine were optimized for three different locations, Alcochete, St. Lawrence and UTIAS and the results are shown in figure 5. The design variables in study are chord, twist, airfoil thickness and rotor speed.

(a) Design Variables

(b) Constraints

Figura 4: Design variables and problem constraints for problem 2 Figure 5 demonstrates clearly the effect of the site-specific application, with the results for all design variables being very different from the baseline design. In the baseline design the chord distribution is very similar to those of bigger turbines, where the lower speeds in the sections closer to hub are compensated by the increase in chord and twist. However in the optimized blades the chord is reduced in the interior sections and increased in exterior ones. This results are not independent from the specific urban operation conditions of this turbines, with the low wind speeds and low Reynolds numbers driving the design. At the Reynolds numbers of operations, ranging from 4 × 104 to 9 × 105 , the flow is ruled by the big vortex and the drag is increased, so in order to achieve more lift an increased in area is needed. Since blade radius is constraint to 2.5m, the only way to achieve this is by increasing chord. The rotor speed, in the optimize site-specific solutions, is very similar throughout all the locations and 20% above the initial design. 5

(a) Chord

(b) Twist

(c) Thickness

(d) Rotor Speed

Figura 5: Design variable comparison of optimization results The effect of site-specific optimization is clearly demonstrate in figure 7 where the power output profile for the three location is very different. The low wind potential site, Alcochete, tries to maximize the power output at a low range of velocities, from 4m/s to 6m/s. The price to pay for this behaviour is shown at velocities above 12m/s with a big decrease in the power curve. The high wind potential site, St. Lawrence, maximizes the power output at higher velocities, being the only location where the maximum generator power output of 10Kw is reached, for 16m/s. Figure 8 demonstrates the full potential of a urban site-specific optimization with all final solutions improving COE by no less than −40%. This is very impressive since blade radius were fixed at 2.5m for both designs. If we had to choose only one location to install our urban wind turbine we would pick St. Lawrence where the absolute COE is the lowest. Since we were able to improve and optimize the overall cost of energy for all the three locations, the designs found were the best for the specific locations.

4.3

Problem 3 - Site-Specific Optimization of a Small Urban Wind Turbine constrained to Minimum Power Output

We have an isolated site with an average power need of 1.5KW and we want to supply all its energy needs with a wind turbine and auxiliary batteries. Therefore, we need to optimize a wind turbine constraint by an average power output of 1.5KW and a maximum generator power input of 25KW. The design variables are chord, twist, airfoil thickness, blade radius and rotor speed. The locations optimized were Alcochete, St. Lawrence and UTIAS. The initial designs were no longer the one used in previous problems but instead were provided by the designer so that it would meet the requirements 6

(a) Alcochete

(b) St. Lawrence

(c) UTIAS

Figura 6: Final blade geometry for the three locations by comparison with initial geometry (red)

Figura 7: Power profile of the final results for problem 2 3. (a) variaveis

(b) constrangimentos

Tabela 2: Design variables and problem constraints for problem 3

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Figura 8: COE for the initial and final designs of problem 2

Tabela 3: Initial design for problem 3

(a) chord

(b) Twist

(c) Thickness

(d) Rotor Speed

Figura 9: Design variable comparison of optimization results The final designs are very similar between each other and with the initial design. In relation to the initial design, blade radius, who was been identified in problem 1 as the one with the most influence

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over COE, changed only 6% i Alcochete, 3.5% in St. Lawrence and 6.2% UTIAS. Chord distribution is slightly different from initial design, with the lower potential sites, ALcochete and UTIAS, presenting the biggest changes. Twist distribution is the variable where the final designs are more different from the initial, with twist increased in the sections closer to hub, to take advantage of the flow at lower speeds, and sections closer to the tip have twist values inferior to the baseline because of the higher flow speeds. Rotor speeds are also very similar to the baseline. In all locations the optimizer tried to maximize power output by increasing the blade area. However for the location with the biggest wind distribution, St. Lawrence, and since the constraint for minimum power average was easily satisfied, the optimizer tried to reduce blade volume because it has a direct impact on COE, so, the chord distribution and blade radius are inferior to the values in the other locations.

Figura 10: Power profile of the final results for problem 3 Despite the values of the three curves being very close together, the advantages of a site-specific optimization are still present in the power profile (figure 10) adjust himself to the site wind distribution. For this specific problem, the final design for Alcochete tried to maximize power output in the middle region of the wind profile, but once again, the differences to the other locations were very small.

(a) Power

(b) COE

Figura 11: Average power output and COE variation for problem 3 The justification for the results being so close is related with the specific conditions and constraints of this problem, where the initial design is the same for the three locations. However, the power achieved in the most energetic location is more than 200% of the power in the lowest sites, so that by forcing the same initial design for all the locations, and with this design being so close to a minimum, we constraint the final solutions. Despite a good initial design we were able to improve COE by −22% in Alcochete, −9.97% in St. Lawrence and finally −3.98% in UTIAS. This shows the increase that may be expected for a cost-constrained turbine blade optimization problem.

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5

Conclusions

This paper presents a multidisciplinary framework for the site-specific design optimization of small urban wind turbine rotors. Aerodynamic modelling is achieved through a blade element momentum theory method extended with the summation modes method to give aeroelastic solutions. A Simplex optimizer was used to perform the design optimization of the turbine blades and performance. The core of the FAST program, with a custom MATLABr interface, was used in the Aerodynamic analysis and the optimization algorithm were implemented in MATLABr . In the test studies the main objective was to minimize the cost of overall energy (COE) by changing the turbine blades and operation conditions. In this project COE is function of blade volume and power output. The direct production costs of a blade were made dimensionless and the new costs are related to the initial design through blade volume. The design variables were: chord, twist, airfoil thickness, blade radius and rotor speed. The constraints were the maximum generator power input, the maximum blade radius in problem two and the minimum average power output in problem three. We conclude from problem one that the design variable with the biggest influence on COE performance is blade radius, where an increase of 20% in the variable value, relative to the baseline, will result in −20% decrease in COE. The second variable is chord where the same change, in percentage, relative to the baseline, will result in a −16% decrease in COE. We conclude that rotor speed presents the same behaviour and values as those in the chord variable. In problem two we clearly demonstrate the benefits of a urban site-specific optimization. The constraints were the generator power input of 10Kw and the maximum blade radius of 2.5m. The results show the adaptation of the power curve to the site wind distribution, resulting in a decrease in COE never inferior to −40%. The chord distribution captured the physics of the problem and was very different from the baseline, with the low Reynolds number and the big vortex prevailing over the flow, and the optimized solution has a bigger platform area than the baseline, in order to increase lift. Problem three presents a different approach to the problem. Here we try to obtain a wind turbine optimized to a specific location with the constraint that it should be able to deliver at least 1.5Kw of average wind power. The generator power input was constraint to 25Kw. Despite the final design being very similar to the initial design, the improvements in COE were −22% in Alcochete, −9.97% in St. Lawrence and −3.98% in UTIAS. The main objective of the project was to develop a multidisciplinary frame work that could be used to calculate/optimize a site-specific small urban wind turbine, not by rescaling an existing design, but by focusing and analysing the specific problems of a urban site, with special focus on aerodynamics. The advantages of that approach were a better overall cost of energy for all the studied locations.

6

Future Work

The results presented in this work do not fully exploit the potential of the framework developed, so improvements can still be made in many areas. The framework is modular and that new modules can be easily incorporated. One of the main limitations of the results was the aerodynamic data used because we have very low Reynolds numbers in most of the operation regimes and accurate data for that regimes is hard to find. A future improvement would be using more accurate aerodynamic data through wind tunnel test or equivalent. Other limitation of the final results is the airfoil shape definition. In the current program airfoil shape control was made by a single thickness parameter, the airfoil thickness in the NACA 44XX family. A module can be incorporate that defines at each iteration the mode shape. With this approach we can no longer map the Reynolds number a priori but we need to recalculate the aerodynamic properties at each iteration, which will increase the CPU time. Noise is of great importance in a urban environment. The design turbines should not have problems with that since they have very low rotor speed. However their study can be easily incorporated in the framework, because FAST program has already a noise module, and its results should be use in the constraint part of the optimization.

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This study only used an aeroelastic formulation of the problem. To have more realistic results, the structural part should also be included and coupled with the aeroelastic analyses. Fatigue problems are very important in wind turbines since they are machines exposed to cyclic loads which can reduce significantly the life cycle. Fatigue analyses can easily be incorporated in the framework since FAST program has a module to treat this problem. Air flow around urban buildings is a very complex matter. In this project we simplified the analyses by considering the flow steady, perfectly aligned and by neglecting turbulence. In reality the flow is highly turbulent and shear tension must be considered. So in future work a more realistic wind model should be included.

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