Single-step versus coupled-aero-structure simulation of a wind turbine with bend-twist adaptive blades Alireza Maheri*, Siamak Noroozi, Chris Toomer, John Vinney University of the West of England, Bristol, BS16 1QY, UK *
[email protected]
Abstract: In wind turbines with bend-twist adaptive blades there is an interaction between the induced twist due to elastic coupling and the blade loading as the source load of induced twist. This interaction makes the simulation of these types of wind turbines a coupled aero-structure process that needs an internal correction loop. In each run of the correction loop a finite element analysis of the blade is necessary to find the induced twist and this makes the simulation process very time consuming and cumbersome. On the other hand, in wind turbines with stretchtwist adaptive blades the centrifugal force, as the source load, produces the induced twist but it is not affected by the induced twist directly. Therefore, a single-step simulation can be carried out with no need for a correction loop. A single step simulation is more time efficient than a coupled aero-structure one. This study compares the results of simulations of a modelled wind turbine with bend-twist adaptive blades both by a single step approach and by a coupled aero-structure approach. In this way the question of how accurate can be a single step simulation of a wind turbine with bend-twist adaptive blades, can be answered. Comparison of the results shows that even for small amounts of induced twist and low wind velocities a single step simulation approach gives unrealistic results and cannot be used for simulation of a wind turbine with bend-twist adaptive blades. Keywords: Wind turbine simulation, elastic coupling, induced twist, adaptive blades
1 Introduction Whenever a wind turbine blade twists, it directly affects the angle of attack, changing blade loading and therefore turbine power. This makes blade twist or pitch angle a key parameter in controlling wind turbine performance. Two methods are provided for the pitch control: classic active pitch control and passive pitch control. Passive control without any mechanical parts is a relatively new field in wind turbine
industry. This approach known as adaptive or smart blades employs the blade itself as the controller to sense the wind velocity and adjust its aerodynamic characteristics to affect the wind turbine performance. Adaptive blades are made of anisotropic composite materials with elastic coupling either in the form of bend–twist or in the form of stretch-twist. The concept of using elastic coupling in anisotropic composite materials as an advantage to make adaptive blades was introduced by Karaolis et al [1-2] and then progressed by other investigators. Research on adaptive blades is being carried out in several areas such as improving the annual energy capture [3-4], reducing the fatigue loading [5-6] and material configuration, design and manufacturing [7-10].
2 Simulation methods Twist angle of a blade is a combination of pretwist, pitch angle and the induced twist due to elastic coupling. Induced twist is a variable parameter which depends on the wind turbine run condition as well as the material and structural characteristics of the blade. In the other words the adaptive blades have dynamic topology that varies with the wind speed and rotor angular velocity. This fact makes the simulation of a wind turbine with adaptive blades different from the simulation of the wind turbines with ordinary blades. In the case of wind turbines with ordinary blades, knowing the wind turbine run condition and blade aerodynamic characteristics, an aerodynamic code can be employed as a wind turbine simulator to predict the wind turbine performance. The same wind turbine simulator can be used for simulation of a wind turbine with adaptive blades but since the induced twist must be known to have the blade aerodynamic characteristics, a structural analyser is also required to find the induced twist in different run conditions. Lack of a reliable analytical model for analysis of anisotropic composite shell structures makes the Finite Element Method the
first choice in analysis of these types of structure.
Blade material and structural characteristics Blade centrifugal load predictor
Source load
FEA of blade
Blade aerodynamic load predictor
Blade geometry and topology
Blade topology corrector
Induced twist
Wind turbine performance calculator
Wind turbine performance
Wind turbine run-condition Aerofoils Aerodynamic characteristics
Figure 1: Single-step simulation of a wind turbine with stretch-twist-coupled adaptive blades
Blade material and structural characteristics Wind turbine run-condition
Aerofoils aerodynamic characteristics
Wind turbine performance calculator
Blade aerodynamic load predictor
Source load
FEA of blade
Blade geometry and topology
Blade topology corrector
Induced twist
Wind turbine performance
Correction Loop
Figure 2: Coupled aero-structure simulation of a wind turbine with bend-twist-coupled adaptive blades
There are two types of adaptive blades depending on the type of designed elastic coupling in their structure. In the adaptive blades made of stretch-twist-coupled materials, the centrifugal force stretches the blade and as a result of that the elastic coupling produces an induced twist. In these blades the source load for the induced twist is centrifugal force which depends on the rotor angular velocity and blade mass distribution. In these blades the source load affects the induced twist but the induced twist does not affect the source load directly. Figure (1) shows a schematic diagram of a single-step simulation. By a single-step simulation approach, it is assumed that the induced twist has no significant effect on its source load. A structure code predicts the induced twist and after considering the required modifications applicable to the flow kinematics due to the presence of the induced twist, an aerodynamic code predicts the wind turbine performance. Having the Blade material and structural characteristics and the wind turbine run condition, a blade centrifugal load predictor gives the source load. By finite element analysis of the blade the induced twist becomes a known parameter. Applying the effect of the induced twist in the blade topology, the aerodynamic characteristics of the blade will be known. Now, the same simulator as used for the wind turbines with ordinary blades can be used to simulate the wind turbine with stretch-twist-coupled adaptive blades. Since in this approach each set of unknowns can be determined by a single-step calculation this approach has been called a single-step (SS) simulation. In the adaptive blades made of bend-twistcoupled materials, the flap bending in the blade due to the aerodynamic force bends the blade and as a result of that the elastic coupling produces an induced twist. In these blades the source load for the induced twist is aerodynamic force which depends on both the rotor angular velocity and wind velocity and also the blade topology and its aerodynamic characteristics. In these blades the source load affects the induced twist and the induced twist affects the source load. In the other words there is an interaction between the induced twist and the source load. This interaction makes the simulation of these types of wind turbines a coupled aero-structure (CAS) process that needs an internal correction loop. In a coupled aerostructure simulation, the effect of the induced twist on the initial loading situation is taken into account. Correcting the load, induced twist will
be re-calculated. This sequence repeats until a converged solution has been reached. A schematic description of a CAS simulation is shown in Figure (2). When trying to design, modify or optimise an adaptive blade, the entire process of simulation is embedded inside an iterative or trial and error algorithm. In the case of a bendtwist adaptive blade the simulation itself is an iterative (CAS) process. Convergence rate in the correction loop depends on the sensitivity of the source load to the induced twist. However, in design or optimisation procedures based on random-based methods like genetic algorithms, it is natural to expect fluctuating behaviour or even divergence in the correction loop. All these facts make CAS simulation of a wind turbine cumbersome and inefficient and bring the following question up. To avoid all the difficulties of a CAS simulation, can one use the SS simulation for a bend-twist-coupled adaptive blade? Or alternatively, how accurate could be simulation of a bend-twist adaptive blade through a SS simulation approach without involving the correction loop? To see how sensitive the source load to the variation of the induced twist is, the following section applies both SS and CAS simulation approaches to a single case and compare the results.
3 SS and CAS simulation of a bend-twist adaptive blade The simulated wind turbine is an approximation of a 2-blade AWT-27 wind turbine. Rotor radius, R Hub radius,
Rhub
13.757m 1.184m
No of blades, B Blades conning angle, δ Rotor angular velocity, Ω Pitch angle
2
53.333 rpm 1.2° TS
Rated power, Prated
300 KW
7°
Yaw 0 Tilt 0 Table 1: Blade and wind turbine specifications
Table (1) gives some specifications of the modelled blade and wind turbine. More details can be found in reference [11]. In the simulation, the same aerofoil data files as documented in the above reference have been used but it is assumed that the blade, structurally (and not aerodynamically) is made of two aerofoils of S814 and S809, distributed
Shell thickness, t Lay-up Fibre orientation, θ
10 mm mirror
E1 E 2 = E3 G12 = G13 G 23 ν 12 = ν 13
141.96 GPa
ν 23
0.42
20°
9.79 GPa 6.14 GPa 4.83 GPa 0.50
Table 2: Material properties of the blade
According to the ply angle of 20 degrees, this particular material lay-up generates an induced twist towards stall. CAS simulation of the modelled wind turbine has been carried out by using the computer code WTAB [12]. It is a coupled aero-structure code developed specially for simulating wind turbines with bend-twist adaptive blades. It consists of three linked programs as shown in Figure (3). WTAero is a BEMT based rotor aerodynamic code which calculates the blade loading and the wind turbine performance at the same time. ABMesh is a force-adaptive mesh generator that generates the mesh and defines the physical problem (nodal loading, locating boundary nodes and defining boundary conditions and defining elemental material properties). And finally TRIC is a finite element solver that predicts the induced twist due to elastic coupling.
blade and after that mesh generator and FE solver actuate to generate the mesh and analyse the blade to give the induced twist. Using the induced twist and correcting the initial topology of the blade, WTAero runs for the second and last time to give the wind turbine performance.
4 Results, discussion and conclusion Figure (4) and (5) show the curves presenting the relative differences between the results of SS and CAS simulations. Differences of the induced twist at the tip of the blade, power and power coefficient versus the wind velocity are shown in Figure (4) and differences of the induced twist, aerodynamic force and flap bending versus blade span location, associated to the wind velocity of 10 m/s, are shown in Figure (5). The relative differences have been calculated by the following equation
Diff =
Φ SS − Φ CAS × 100 Φ CAS
(1)
in which Φ stands for each of the above parameters. Percent difference between SS and CAS simulations
from hub to 0.55 of rotor radius R to the tip, respectively. The assumed material properties of the blade are given in Table (2).
60 50 40 30
Tip induced twist
20
Power
10 0 -10 -20 5
10
15 20 Wind Velocity (m/s)
25
Figure 4: Percent difference between SS and CAS simulations versus wind velocity
aerodynamic code WTAero
Mesh generator ABMesh
FE solver TRIC
Correction loop Figure 3: WTAB, a coupled aero-structure code for CAS analysis of wind turbines with adaptive blades
SS simulation of the modelled wind turbine has been also carried out by using WTAB code while the correction loop runs only once. In SS simulation the code starts with actuating WTAero to find the aerodynamic load on the
Figure (4) shows that two different simulation approaches give different predicted tip induced twist with a difference of about 4% to 52%. For the case of the modelled wind turbine, SS simulation over predicts the tip induced twist. Since in this case study the induced twist is towards feather, using CAS simulation the calculated induced twist in each run of the correction loop reduces and as a result of that the aerodynamic loading of the blade increases until the convergence is achieved. The over-prediction of induced twist is the reason for under prediction of the power by SS simulation. According to these figures the curves can be divided into two parts. In the first parts, (low
Percent difference between SS and CAS simulations
60 40 20 0 -20 -40
Induced twist Aerodynamic force Flap bending
-60 -80 1
3
5 7 9 Radial Location, r (m)
11
13 Tip
Figure 5: Percent difference between SS and CAS simulations versus blade span
Figure (6) shows the predicted tip induced twist versus the wind velocity obtained by a CAS simulation. It also shows the number of iterations in CAS simulation and the percent difference between the SS and CAS simulations results for tip induced twist. Difference curve for the tip induced twist is drawn again in this figure. The trend of the difference curve
associated to the tip induced twist shows an oscillatory behaviour. This means that there is not an obvious relation between the wind velocity (or the magnitude of the tip induced twist) and the level of difference. Therefore there is no way to introduce a correction procedure to be applicable to the predicted tip induced twist by a SS simulation to have more accurate results. Figure (6) also shows that the number of iterations in CAS simulation and the percent difference between the SS and CAS simulations results for tip induced twist increases as the tip induced twist decreases in lower wind velocities. It means that the results of SS simulation have even larger amounts of errors for low and medium wind velocities (small tip induced twists).
10
50
9
40
8 7
30
6
20
5 4
10
3 2
Percent difference between SS and CAS results
60
11 Tip Ind.Twist(deg)/ No of iterations
and medium wind velocities), the percent differences do not follow the wind velocity through a predictable relation while in the second parts, (higher wind velocities), the percent differences decrease as the wind velocity increases. A higher wind velocity results more parts of the blade experience the deep stall situation, where a few degrees variations in the angle of attack due to different values of predicted induced twist by SS and CAS simulations, only affects the blade performance slightly. On the other hand, in the low and medium wind velocities the blade performance is very sensitive to the amount of predicted induced twist. According to Figure (5), SS simulation under predicts the span-wise distributions of the aerodynamic force and flap bending. The maximum force under predictions of about 65% happens at the tip of the blade. Since flap bending has been obtained by integration of the aerodynamic force, the trend of the difference curve associated to the flap bending is smoother than the trend of the difference curve associated to aerodynamic force. The difference curve associated to the induced twist in Figure (5) is almost a constant line of about 40% which is the same as the difference in the tip induced twist, shown in Figure (4), at a wind velocity of 10 m/s. This curve shows that the span wise distribution of the induced twist is almost the same in both SS and CAS simulations. In the other words only the magnitude of the induced twist is a function of the blade loading and the trend of the induced twist is independent of that.
0 5
10
15 20 Wind Velocity (m/s)
25
Tip induced twist No of iterations Percent difference betw een SS and CAS results for tip induced tw ist
Figure 6: Higher No of iterations in a CAS simulation and larger errors in SS simulation in lower wind velocities and smaller induced twists
In conclusion, referring to the above discussion, it is evident that in the case of wind turbines with bend-twist-coupled adaptive blades a single-step simulation has an inherent source of error and gives unrealistic results. No matter how accurate blade loading and induced twist calculations are, the SS simulation cannot be used for prediction of the wind turbine performance with bend-twist adaptive blades.
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[9] Locke J, Hidalgo I C. The Implementation of Braided Composite Materials in the Design of a Bend-Twist Coupled Blade. Sandia National Laboratories, Report SAND20022425, August 2002. [10] Locke J, Valencia U. Design Studies for Twist-Coupled Wind Turbine Blades. Sandia National Laboratories, Report SAND20040522, June 2004. [11] NWTC Design Codes, (WT_Perf Version 3.1 by Marshall Buhl). http://wind.nrel.gov/designcodes/simulators/wtp erf/. Last modified 17-December-2004; accessed 10-January-2005. [12] Maheri A, Noroozi S, Toomer C A, Vinney J. WTAB, a Computer Program for Predicting the Performance of Horizontal Axis Wind Turbines with Adaptive Blades. Accepted for publication in the Journal of Renewable Energy.
