Design approaches of performance-scaled rotor for wave basin model tests of floating wind turbines

Renewable Energy xxx (xxxx) xxx

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Design approaches of performance-scaled rotor for wave basin model tests of floating wind turbines Binrong Wen a, Xinliang Tian b, c, Xingjian Dong a, Zhanwei Li a, Zhike Peng a, *, Wenming Zhang a, Kexiang Wei d a

State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, 200240, China State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), China d Hunan Provincial Engineering Laboratory of Wind Power Operation, Maintenance and Testing, Hunan Institute of Engineering, Xiangtan, 411104, China b c

a r t i c l e i n f o

a b s t r a c t

Article history: Received 22 May 2019 Received in revised form 20 September 2019 Accepted 28 October 2019 Available online xxx

The Froude scaling law is usually utilized in the wave basin model tests of Floating Wind Turbines (FWTs). However, the Froude-Scaled Rotor (FSR) cannot generate desired aerodynamic loads due to the Reynolds-Number Scaling Effect (RNSE). To mitigate the adverse effects of RNSE, two approaches are proposed to design Performance-Scaled Rotors (PSRs) in this paper. Taking DTU 10 MW baseline wind turbine as an example, the SD2030 airfoil is selected to replace the original FFA-W3-xx airfoils. Maximum Lift Tracking (MLT) and Load Distribution Matching (LDM) algorithms are proposed to assign the chord lengths and twist angles. Herein, MLT leads all airfoils to operate at the optimal angle of attack that corresponds to the maximum lift coefficient and afterwards increasing the chord lengths. LDM simultaneously adjusts the chord length and twist angle, aiming to match the span-wise distribution of normal force at the design point. Results show that both approaches can generate desired rotor thrusts in a range of tip speed ratios, which seems to outperform prior PSRs in the existing publications. The blade mass and inertia can be preserved with careful manufacturing procedures. The redesigned PSRs are helpful to improve the accuracy and reliability of FWT model tests in the wave basin. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Floating wind turbine Model test Blade design Froude scaling Reynolds number

1. Introduction The Floating Wind Turbine (FWT) technology has gained more and more concerns in these years due to the particular superiority of offshore wind over other energy sources, such as great renewability and giant amount [1]. During the development of the FWT technology, the wave basin test in model scale plays an essential role. On the one hand, the wave basin model test is a necessary procedure during the design and development of FWT concepts. A mass of FWT concepts, especially novel floating platforms, have emerged in these years. To validate the feasibility of these concepts and to obtain the dynamic performances of the FWT systems, conducting model tests in the combined wind-wave conditions is among the most reliable approaches [2,3]. On the other hand, the

* Corresponding author. E-mail addresses: [email protected] (B. Wen), [email protected] (X. Tian), [email protected] (X. Dong), [email protected] (Z. Li), [email protected]. cn (Z. Peng), [email protected] (W. Zhang), [email protected] (K. Wei).

wave basin test plays an irreplaceable role in validating the numerical tools. As a novel integrated system combining a floating platform and a towering rotating rotor, the FWT will experience rather complicated external loads in the practical environmental conditions. The dynamics of the FWT system is governed by strong couplings among these loads. Until now, the coupling effects among environmental loads, couplings between FWT structure and external loads, as well as the couplings among FWT structures, have not been thoroughly reveled. Although several numerical codes such as FAST [4] and HAWC2 [5] have been developed to calculate the coupling dynamics of FWTs, the feasibility and reliability of these codes need further validations. In recent years, several wave basin tests of scaled FWTs have been performed. A review of these model tests is accessible in Refs. [3,6]. At the very beginning, the model tests were performed using Froude-Scaled Rotors (FSRs) and Froude-scaled environmental conditions [7]. However, it was reported that the results were not productive enough because the aerodynamic loads generated by the FSRs were far from the theoretically scaled values

https://doi.org/10.1016/j.renene.2019.10.147 0960-1481/© 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: B. Wen et al., Design approaches of performance-scaled rotor for wave basin model tests of floating wind turbines, Renewable Energy, https://doi.org/10.1016/j.renene.2019.10.147

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[8]. In addition, it seems impossible for FWT with FSR to correctly produce the unsteady aerodynamic performance or system fault responses that were revealed in numerical simulations [9e13]. These limitations are mainly caused the dramatically reduced Reynolds number experienced by the FSR in the Froude-scaled environmental conditions. This phenomenon is addressed as the Reynolds-Number Scaling Effect (RNSE). Experiments with an FSR may incorrectly estimate the motion response because a perfect reproduction of the structural responses can only be achieved with all external loads generated correctly. To mitigate the adverse effects of RNSE, different approaches have been proposed, among which redesigning the rotor is thought to be the most reliable alternative [3,8]. The concept of so-called Performance-Scaled Rotor (PSR) was proposed by Martin et al. [8] in 2014, that is, redesigning the model scaled rotor to match the desired aerodynamic loads, especially the rotor thrust. Dedicated concerns were paid to the rotor thrust because the rotor thrust most significantly impacts the motion response of the FWT system. In addition, the aerodynamic load is the most crucial additional excitation for FWTs compared with conventional floating platforms for the oil and gas industry. Following Martin et al. [8], different extensions have been conducted by researchers to improve PSR performance. Fowler et al. [14] with MARIN provided a thorough description of the numerical procedure to design a PSR. A Modified AG24 airfoil was utilized to design the PSR using an optimization algorithm. The redesigned PSR was manufactured with carbon fiber and was tested in front of a simple wind generation system. Results showed that the redesigned PSR markedly outperformed than the FSR. Besides, the redesigned PSR presented adequate thrust variation with blade pitch angle. Ridder et al. [15] with MARIN developed a new MARIN Stock Wind Turbine based on the NREL 5 MW wind turbine blade according to the performance-scaled principles. The AG04 airfoil was modified to pursue better thrust characteristics. Afterwards, a model rotor was manufactured and tested in the novel wind generation system at MARIN. The superiority of the PSR was further observed. Kimball et al. [16] tested MARIN Stock Wind Turbine at 1/ 130 scale at UMaine, and then tested it at 1/50 scale at MARIN. The power and thrust performances at different tip speed ratios, blade pitch angles, and Reynolds numbers were measured. Afterwards, the MARIN Stock Wind Turbine was installed on the DeepCwind semisubmersible platform to study the dynamics of the model FWT in the wind-wave conditions. Experimental results showed that the PSR could markedly outperform than the conventional FSRs. The MARIN Stock Wind Turbine was installed on an innovative TLP by Bozonnet et al. [17] to test the performance of a novel foundation for floating wind turbine. To more deeply investigate the performance of the model scaled rotors, Fernandes et al. [18] and Burmester et al. [19] conducted dedicated investigations. In addition to MARIN, redesigning PSR for FWT model test has also been applied by other institutes. In 2014, Hansen et al. [20] developed a 1/200 scaled rotor based on the Slig Donovan 7003 airfoil and dramatically increased blade chord to experimentally investigate the dynamics of a TLP-type FWT. In 2016, Du et al. [21] with Shanghai Jiao Tong University (SJTU) developed a PSR for the 1/50 scaled NREL 5 MW baseline wind turbine. The NACA 4412 airfoil was selected to redesign the model rotor. The lift and drag coefficients were derived from RANS simulations. A pattern search algorithm was developed to optimize the rotor design with the objectives of matching the rotor thrust while minimizing the total chord lengths. Afterwards, a model redesigned rotor was manufactured with carbon fiber and was tested [22]. Good correlations with the numerical calculation were obtained. In 2016, Bayati et al. [23] reported the aero-elastic design of the DTU 10 MW wind turbine blade for the LIFES50 þ wind tunnel scale model. The SD7032 airfoil was selected to redesign the rotor. An aero-elastic

design algorithm was proposed to define the blade thickness, chord length and twist angle. Wind tunnel tests showed that the PSR could well match the desired values in terms of aerodynamic loads and natural frequencies. In 2018, Schunemann et al. [24] with University of Rostock designed a PSR based on the DOWEC 6 MW wind turbine. The procedure of the blade design was demonstrated. The final design of the PSR was obtained by selecting lowReynolds-number airfoil SD2030, increasing the chord length by multiplying a factor of 1.3, and increasing twist angles at inboard sections while reducing them at outboard parts. Above PSRs can improve the rotor performance, especially the rotor thrust to a certain extent. However, it is hard to obtain satisfying similarity in other aspects such as power performance. In addition, the aerodynamic response of the PSR can be adversely altered due to the changed chord lengths. To effectively improve the PSR performance, dedicated airfoils were designed and multiple airfoils were assigned along the blade by Campagnolo et al. [25] and Martin et al. [26]. The chord lengths and inductions can be maintained in their designs. However, designing a PSR with multiple dedicated airfoils is rather complicated and challenging. It is believed that this method is more preferred in situations where unsteady aerodynamics is the primary concern, for example, in wind tunnel tests or tests dedicatedly for validation of advanced controller. In wave basin model test where the FWT motion performance is the first concern, accurately matching the aerodynamic load with single airfoil is reliable enough. Therefore, it is suggested to design the PSR with single low-Reynolds-number airfoil as most PSRs mentioned above did. Although the PSR concept has been extensively developed in recent years, there are still some shortcomings of the existing PSRs. Firstly, only one or two separated operating points where thrust coefficients of prototype and PSR intersect can be guaranteed. For other tip speed ratios, the rotor thrust of the PSR markedly deviates from the target value, which makes it a great challenge to reproduce the unsteady aerodynamic performance. Also, it poses a significant challenge to test controllers on the model FWT. The ideal situation is that the rotor thrust can be matched in a range of tip speed ratios, which is one of the main objectives of the present study. Secondly, a concise instruction or design procedure is demanded to lead the researchers to simply design a PSR for wave basin model tests. Thirdly, the main objective of the designs as mentioned earlier was to match the rotor thrust, while less focus was put on the mass control of the blade. As reported by Duan et al. [27], the mass of the PSR may be dramatically augmented than the FSR, which will adversely smear the FWT dynamic properties. To mitigate these drawbacks, we propose two approaches for PSR design dedicatedly for model tests of FWT in the wave basin. The development procedure of PSRs for the DTU 10 MW baseline wind turbine [28] is presented in detail to illustrate such approaches. The designed PSRs will be used to investigate the coupling dynamics of a novel FWT system in combined wind-wave conditions in the near further at the State Key Laboratory of Mechanical System and Vibration (SKL-MSV) and State Key Laboratory of Ocean Engineering (SKL-OE) at Shanghai Jiao Tong University (SJTU). The SD2030 airfoil is selected to replace the original FFAW3-xx airfoils to improve the aerodynamic performance. Two algorithms, i.e., Maximum Lift Tracking (MLT) and Load Distribution Match (LDM), are proposed to assign the twist angles and chord lengths. Concise design procedures are provided, which can be helpful for researchers to easily design a PSR for the FWT wave basin tests. In addition, analysis of the mass and inertia of the PSRs is also conducted, which indicates that the blade mass and inertia of the PSRs can also be well matched, not violating the Froude scaling law.

Please cite this article as: B. Wen et al., Design approaches of performance-scaled rotor for wave basin model tests of floating wind turbines, Renewable Energy, https://doi.org/10.1016/j.renene.2019.10.147

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2. Problem description

2.1. Scaling parameters To generate proper geometrical, kinematic, and dynamic performances at the model level, several significant non-dimensional parameters should be maintained. Firstly, the geometry of the scaled model should adequately match the full-scale prototype. To this end, a scaling ratio is generally selected at the very beginning, denoted as l. The geometrical length of the model is formulated as:

Lm ¼

Lf

l

(1)

where L is the geometry length of the structure; subscripts “m” and “f” represents the model and prototype, respectively. In most wave basin model tests, the performance of the inertia force with respect to the gravitational force should be well matched. To this end, the Froude number is defined, shown as follow:

U* Fr ¼ pffiffiffiffiffiffiffiffi gD*

(2)

where U* is the characteristic flow velocity; g is the gravitational acceleration and D* is the characteristic length scale. It is widely accepted that if the Froude number is preserved between the prototype and the model, the hydrodynamic characteristics, such as the floater motions and the wave loads, can be well matched. In addition to the inertia force, the viscous force is also of significance. The Reynolds number defined as the ratio of inertia forces to viscous forces should be considered:

Re ¼

cV

n

(3)

where n is the kinematic viscosity of the flow medium; V is the characteristic velocity of the flow (e.g., the relative velocity experienced by the blade section of the turbine); c is the characteristic length (e.g., chord length of the blade section). It is generally believed that if the Reynolds number is maintained, the flow over the model will act similarly to the prototype. It should be noted that the Reynolds number in the wave is thought to have a marginal impact on the tests and thus is not considered. The Reynolds number particularly refers to the aerodynamic perspective in FWT wave basin model tests. As for the model tests of wind turbines, the Tip Speed Ratio (tsr, or L) is one of the most important parameters to describe the rotor operating condition and thus should be maintained. It is defined as the speed at the blade tip to the free-stream velocity:

L¼

UR

(4)

V0

where U is the rotational speed of the rotor; R is the radius of the turbine rotor; V0 is the free-stream velocity. To conserve the frequency response between the prototype and the model systems, maintaining the tip speed ratio is one of the most basic constraints in FWT model tests. The flow geometry around the blade airfoils is thought to be preserved if the tip speed ratio and the blade geometry are properly scaled. In practice, the flows over the blade airfoil are markedly changed because the Reynolds number of the model rotor is dramatically reduced than the full-scale rotor. The mismatch in Reynolds number will be discussed in detail in Section 2.2. Despite the mismatch of the flow structure, the tip speed ratio should still be conserved to depict the frequency response of the model tests correctly. 2.2. Reynolds-Number Scaling Effect (RNSE) Applying proper scaling is an extreme challenge for wave basin tests for FWT because it requests correct depictions of both aerodynamic and hydrodynamic similarities. From Eq. (2) and Eq. (3), it is known that the Reynolds number for rotor and the Froude number for floater are incompatible. As suggested by Bredmose et al. [29], for FWT model test in the wave basin, the main objective is usually to reveal the global motion responses. Therefore, the Froude number should be firstly conserved, and the Reynolds similitude is treated as the secondary concern. Under Froude scaling law, the length and speed of the model structure will be reduced to l1 and l0.5 times, respectively. To preserve the tip speed ratio, the rotation speed of the model should be increased by l0.5 times. In this way, the tip speed ratio is compatible with the Froude number [see Eq. (4)]. However, it is impossible to maintain the Reynolds number in this case:

Rem ¼ l

1:5

Ref

(5)

It is shown that under the Froude scaling law, the Reynolds number of the rotor reduces dramatically, which is addressed as ReynoldsNumber Scaling Effect (RNSE). Eq. (5) indicates that the Reynolds number of the model is dramatically reduced than the full-scale prototype, which is further validated in Fig. 1. This remarkable reduction in Reynolds number will apparently smear the airfoil characteristics, as shown in Fig. 2. The lift coefficient CL of the model rotor is dramatically reduced while the drag coefficient CD is significantly increased. Both the decrease in CL and increase in CD are detrimental to the rotor

Full

Model

1.0E+08 1.0E+07 Re [-]

A successful model test should provide aerodynamics and hydrodynamics that well match the full-scale prototype. Experiences in the aerodynamic and hydrodynamic fields provide lots of valuable guides for the model tests of FWT in the wave basin. However, these experiences cannot be directly transplanted into the wave basin tests for FWTs because of its complicated structure and complex environmental conditions. Prior investigations have shown that the aerodynamic similitude and the hydrodynamic similitude cannot be conserved simultaneously [3,29]. In this section, the dominant scaling parameters and the so-called ReynoldsNumber Scaling Effect (RNSE) will be introduced.

3

1.0E+06 1.0E+05 1.0E+04 0

0.1

0.2

0.3

0.4

0.5 0.6 r/R [-]

0.7

0.8

0.9

1

Fig. 1. The Reynolds numbers along the blade for full-scaled and model-scaled rotors of DTU 10 MW baseline wind turbine.

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FFA-W3-301, Re = 10M

0.8

0.15

0.4

0.1

CD [-]

0.2

CD [-] CL [-]

2 1.2

0

200

-0.05 0 5 AOA [°]

10 0

100 0

0 -5

FFA-W3-301, Re = 30K

300

0.05

-0.4 1 -0.8 -5 -10

FFA-W3-241, Re = 30K

CL/CD [-]

FFA-W3-241, Re = 12M

-100 -10

-5 5 0 5 AOA [°] AOA [°]

10

10 -10

-5

0 5 AOA [°]

1015

Fig. 2. The airfoil characteristics of the full-scaled and model-scaled rotors for DTU 10 MW baseline wind turbine.

performance. If directly design the model scaled rotor with the Froude scaling law [noted as Froude-Scaled Rotor (FSR)], the aerodynamic performance will be far from the desired value. As depicted in Fig. 3, the rotor thrust of the FSR is much smaller than the full-scaled rotor: in the whole operating region, no thrust coefficient larger than 0.2 can be detected for the FSR. At the design point of tsr ¼ L ¼ 7.6, the thrust coefficient is CT ¼ 0.82 for the fullscaled rotor while only CT ¼ 0.14 is observed for the FSR. In addition, the span-wise distribution of the normal force FN at the design point is also compared and provided in the figure. The FSR cannot provide matched normal force. Worse still, it failed to generate the matched trend in the span-wise distribution. Generally speaking, the aerodynamic performance of the FSR, which is directly scaled down according to the Froude scaling law, significantly deviates from the desired values. Directly equipping an FSR during the FWT model test in the wave basin will generate incorrect floater motions. Therefore, appropriate modifications should be made to the FSR to obtain matched aerodynamic loads, which will be the main contents of the following sections.

3.1. Potential alternatives to FSR To help search for alternatives to improve the scaled rotor performance, we conduct a brief analysis of the aerodynamic loads here. Let us take a blade section as the analysis object. The aerodynamic forces at the element are shown in Fig. 4. The normal force that mainly contributes to the rotor thrust is:

3. Solutions As demonstrated in Section 2, the Froude-Scaled rotor (FSR) cannot provide appropriate aerodynamic loads, which makes the model tests less reliable. In this section, potential alternatives to improve the performance of the model rotor will be discussed. Afterwards, two approaches are proposed to develop the Performance-Scaled Rotor (PSR).

FSR

Full

1.2

3

1

2.5

0.8

Fn [N/m]

CT [-]

Full

Fig. 4. The aerodynamic loads at the blade section.

0.6 0.4 0.2

FSR

2 1.5 1 0.5

0

0 5

6

7

8 tsr [-]

9

10

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 r/R [-]

1

Fig. 3. The thrust coefficient (left) and the span-wise normal force at the design point (right) of the full-scale rotor and the FSR for DTU 10 MW baseline wind turbine. l ¼ 64.

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FN ¼ L cos 4 þ D sin 4

(6)

where FN is the normal force acting on unit blade length; 4 is the inflow angle, shown as Eq. (9). L and D are the lift and drag forces on unit blade length, which is formulated as Eq. (7) and Eq. (8), respectively.

1 L ¼ rV 2 ,c,CL ðRe; aÞ 2

(7)

1 D ¼ rV 2 ,c,CD ðRe; aÞ 2

(8)

where r is the medium density; V is the relative wind speed experienced by the blade section; CL and CD are the lift and drag coefficients; a is the angle of attack (AOA), one of the most important factors to decide the lift and drag coefficient.

4 ¼ atan

V0 ð1  aÞ

Urð1 þ bÞ

¼ atan

1a Lmð1 þ bÞ

(9)

In Eq. (9), m denotes the position of the analyzed blade section, i.e., m ¼ r/R. a and b are the axial and tangential induction factors, respectively. Note that the drag force D is usually much smaller than the lift force L. To make a qualitative description, the normal force FN can be approximately treated as the lift force L. According to Eq. (7), to make the model-scaled rotor to generate enough thrust, alternatives that may work are concluded as follows: (1) Replacing the medium air (item r) by another medium with larger density. It is an effective alternative that can significantly increase rotor thrust. In the experimental tests of Kress et al. [30] and Sivalingam et al. [31], the scaled rotor was tested in the water tank. However, this method seems to be effective only for turbine performance analysis. As for the models of FWT in combined wind-wave conditions, it seems infeasible due to the constraints of the experimental apparatus. (2) Generating stronger wind (item V) than the Froude-scaled wind speed. This approach can effectively increase the rotor thrust and was applied in pioneering model tests. However, the increased velocity violates the Froude scaling law, and then the tip speed ratio cannot be maintained. As pointed out by Martin et al. [8], this method cannot provide appropriate load variation, and the modelling of blade pitch control will be a great challenge. (3) Increasing the chord length (item c). The aerodynamic loads increase linearly with the chord length. It is indicated in Fig. 3 that the thrust coefficient CT of the FSR is about 5e10 times smaller than the full-scaled. When other parameters are maintained, the chord length should be increased by 5e10 times to match the desired rotor thrust. However, this significantly increased chord length will dramatically increase the mass of the rotor, which will smear the model tests. The investigation of Schunemann et al. [24] showed that the desired thrust could not be properly reproduced even with the blade chord increased 3.3 times. (4) Changing the blade twist angle. It inherently changes the angle of attack (item a). This alternative can partly increase the lift force for the blade sections. However, as shown in Fig. 2, the lift coefficient CL at the model scaled is significantly reduced due to the RNSE. Redistributing the blade twist can partly improve the rotor thrust, but the desired values cannot be reached by only redesigning the blade twist, even when

5

leading all the blade sections to operate at the maximum lift coefficient. (5) Increasing the Reynolds number (item Re) by conducting the test in the high-pressure environment in dedicated wind tunnels. It is theoretically the best alternative to match the Reynolds number and the tip speed ratio. Miller et al. [32] have shown that this approach can realize the full dynamic similitudes (Reynolds number, Mach number, and tip speed ratio). However, such an experimental apparatus cannot be easily accessed. The operating section of a high-pressure wind tunnel is usually limited, which is challenging to conduct the tests. Besides, it is tough to deploy the wave tank near the high-pressure wind tunnel. This approach is more suitable to conduct experimental tests about the aerodynamics of model wind turbines. However, it is extremely challenging to conduct model tests for FWTs in combined wind-wave conditions. (6) Replacing the original blade airfoils with other airfoils that are suitable for the low Reynolds number conditions. This approach inherently changes the dependency of lift and drag coefficients on the angle of attack. It is thought to be the most promising alternatives and has attracted lots of implementations such as Refs. [21,23,24]. Based on the above discussion, approaches (3) (4) (6) are believed to be the most practical alternatives to improve the scaled rotor performance in the wave basin tests. To effectively match the desired rotor thrust and not destroy other similitudes, these three approaches are always utilized at the same time. In the following parts, PSRs will be designed for the DTU 10 MW baseline wind turbine by reasonably using strategies (3) (4) (6). Concise design procedure will be proposed, and the performance of the designed PSRs will be analyzed.

3.2. Baseline case: replacing the airfoils As discussed above, conventional strategies, such as redesigning the blade chord and twist, can only partly improve the rotor thrust but cannot perfectly address the thrust mismatch due to the poor performance of the original airfoils in the dramatically reduced Reynolds number conditions. Therefore, it is necessary to replace

Fig. 5. The geometries of SD2030 and the original FFA-W3-xx airfoils for DTU 10 MW baseline wind turbine.

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SD2030 Re=30K

FFA-W3-241 Re=12M

FFA-W3-301 Re=10M

FFA-W3-361 Re=10M

FFA-W3-480 Re=10M

FFA-W3-600 Re=10M

Compared to the case of the FSR as shown in Fig. 3, the performance of “PSR, X1.0” has been significantly improved both in the magnitude of the normal force and the span-wise distribution trend. Based on the above comparison, it is concluded that substituting the original airfoils with SD2030 can improve thrust performance. However, the present thrust is still smaller than the desired values. According to the discussion in Section 3.1, the mismatched thrust can be addressed by carefully adjusting the blade chord lengths and twist angles. In the following sections, two methods to further improve the rotor thrust will be developed and introduced in detail.

2 1.5

CL [-]

1 0.5

3.3. Maximum Lift Tracking (MLT) approach

0 -0.5 -1 -10

-5

0

5 AOA [°]

10

15

20

Fig. 6. The airfoil characteristics of the SD2030 compared with original FFA-W3-xx airfoils.

the blade airfoils. In prior publications, AG 04 [15], AG 24 [14], NACA 6144 [21], SD 2073 [23], and SD 2030 [24] have been implemented. In the present study, SD2030 airfoil is selected to replace the original airfoils. The selection is based on the following considerations: firstly, SD 2030 airfoil has superior aerodynamic performance at low Reynolds numbers; secondly, the airfoil is relatively thin, which is a benefit for the mass control of the blade manufacturing because the chord lengths will be increased. The geometries of the SD2030 and the original FFA-W3-xx airfoils are compared in Fig. 5. The corresponding airfoil characteristics are compared in Fig. 6. Although the lift performance of SD 2030 airfoil is still relatively poorer than the original airfoils, marked improvements have been generated compared to the FSR (recall Fig. 2). By carefully assigning the chord length and twist angle, reliable match with the target thrust is promising to realize. To make a comparison, a baseline PSR, denoted as “PSR, X1.0”, is designed in this part. Only approach (6) in Section 3.1 is implemented, that is, replacing the original FFAW3-xx airfoils with SD2030 airfoil. The blade chord and the twist are maintained with the FSR. The thrust performance of the PSR is compared with the full-scaled rotor (denoted as “Full”), as shown in Fig. 7. The rotor thrust is markedly improved than the original FSR (recall Fig. 3).

a¼4  q  b

(10)

where q is the blade pitch angle, at the design point, it is assumed as q ¼ 0; b is the blade twist angle. The inflow angle 4 is formulated as Eq. (9). Substituting Eqs. (4) and (9) into Eq. (10), and assuming the optimal AOA which corresponds to the maximum lift coefficient is a*, the desired blade twist angle should be:

bðmÞ ¼ atan

PSR, X1.0

1a  a* Lmð1 þ bÞ

Full

1.2

3

1

2.5

0.8

2

FN [N/m]

CT [-]

Full

It is known that the lift coefficient of the airfoil increases with the angle of attack (AOA) before the stall angle. Once the stall angle is exceeded, the lift coefficient decreases with the further increasing of AOA. An intuitive idea to improve the thrust performance is to guide all the blade airfoils to operate at the maximum lift coefficient. This motivates the strategy of Maximum Lift Tracking (MLT) in the present study. It is realized by carefully designing the blade twist, or by changing the blade pitch angle through the blade pitch regulator. It should be noted that once the blade twist is assigned, the maximum lift coefficient can be reached only at one specific operating condition but cannot be maintained for other tip speed ratios. Note that the optimal tip speed ratio (corresponding to the maximum power coefficient) is the most frequently experienced operating condition. When the wind speed is lower than the rated wind speed, the variable speed controlled will lead the rotor to work at the optimal tip speed ratio. At high wind speeds, however, the blade pitch regulator will be actuated to limit the aerodynamic loads. In this case, the blade pitch can also be adjusted in the PSR to match the desired rotor thrust. Therefore, implementing the MLT at the design point (optimal tip speed ratio tsr ¼ L ¼ 7.6) seems to the most reasonable choice. As shown in Fig. 4, the AOA experienced by the blade airfoils is:

0.6 0.4 0.2

(11)

PSR, X1.0

1.5 1 0.5

0

0 5

6

7

8 tsr [-]

9

10

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 r/R [-]

1

Fig. 7. The thrust coefficient (left) and the normal force along the blade at the design point (right) of the baseline PSR compared with the full-scale rotor. Here, the chord length and blade twist of “PSR, X1.0” are maintained with the FSR.

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Fig. 8. The flow chart to design a PSR with MLT method.

According to experimental and numerical simulations, a* ¼ 8.5 is observed for SD2030 airfoil (see Fig. 6). Based on the experiences of the aerodynamic analysis, the axial induction factor is assumed as a ¼ 0.25, and the tangential induction factor b is neglected (in other words, b ¼ 0) in the present study. The design procedure with MLT is depicted in Fig. 8. Firstly, an FSR is designed to obtain the Froude-scaled blade chord and twist. Secondly, the alternative airfoil is selected, and the airfoil characteristics should be obtained through numerical or experimental methods. Then, a PSR is designed by replacing the original airfoils by the selected airfoil (SD2030 in the present study) while the chord and twist are maintained. Afterwards, the blade twist is reassigned based on the MLT requirement [Eq. (11)] at the design point (tsr ¼ L ¼ 7.6 in the present study). Finally, the blade chord is carefully changed to perfectly match the desired rotor thrust. To simply the design, this step can be conducted by multiplying a factor for all blade sections such as most prior publications did. To further improve the PSR performance and optimize the structure, the blade chord and twist are carefully polished, especially at the

Full

PSR, X1.0, MaxCL/CD

1.2 1.2 1 1 0.8 0.8

7

blade root region. The performance of the redesigned PSR with LMT is shown in Fig. 9. Firstly, the blade twists of the baseline PSR (“PSR, X1.0” in Section 3.2) are redesigned according to Eq. (11). The improved rotor is denoted as “PSR, X1.0, MLT”. Similar to the objective of the MLT method that tracks the maximum lift coefficient for the blade airfoils, Schunemann et al. [24] lead the blade airfoils to work at the angle of attack corresponding to the maximum lift-to-drag ratio. To make a comparison, a rotor redesigned with Schunemann et al.’s strategy is also presented and is denoted as PSR, X1.0, MaxCL/CD”. The thrust and power performance of the redesigned PSRs with MLT and MaxCL/CD are compared with the original DTU 10 MW rotor in Fig. 9. It seems that near the design point, the MLT slightly outperforms than the MaxCL/CD strategy. It should be noted that the MLT and MaxCL/CD strategies are almost the same, with only a constant difference in the blade twist assignment. The finally redesigned PSR is denoted as “PSR, X1.3, MLT”: all the blade chords are multiplied by a factor of 1.3. It is found that the PSR with MLT can well match the desired rotor thrust in a region near the design point. However, the power output cannot be satisfyingly matched. The span-wise load distributions of the PSR are shown in Fig. 10 and are compared with the full-scale rotor. It is depicted that the normal force can well match the desired value at the design point while the tangential force is less well performed, which is the underlying reason for the poorer performance of power coefficient than thrust coefficient as shown in Fig. 9. It is a general consensus that it is extremely challenging to simultaneously match the rotor thrust and the power output [8]. As for the model test to investigate the dynamics of the whole FWT system, the rotor thrust plays a more critical role. Therefore, matching the rotor thrust should be put in the first place. From this point of view, the redesigned PSR with LMT is productive. 3.4. Load Distribution Match (LDM) approach In addition to the LMT method as described in Section 3.3, another approach to theoretically match the rotor thrust is provided in this section. In the model test, the ideal condition is that the model rotor can not only depict the overall aerodynamic loads correctly but also can well model the load distribution along the blade length, especially the normal force which mainly contributes to the rotor thrust. Base on this motivation, the Load Distribution Match (LDM) method is proposed. According to Section 3.1, the rotor thrust is mainly contributed by lift force. Therefore, if the lift force can be matched satisfyingly, the normal force and the corresponding rotor thrust can also be

PSR, X1.0, MLT

PSR, X1.3, MLT

0.6

CP [-]

[-] CCTT [-]

0.5

0.6 0.6

0.4 0.3

0.4 0.4

0.2

0.2 0.2 00

0.1 0 55

6

7 6 8 tsr [-]

9

7 10

5 8 tsr [-]

6

7

9 8 tsr [-]

9

10 10

Fig. 9. The thrust coefficient (left) and power coefficient (right) of the PSRs with LMT.

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8

B. Wen et al. / Renewable Energy xxx (xxxx) xxx

Full

PSR, X1.0, MaxCL/CD

PSR, X1.0, MLT

PSR, X1.3, MLT

Fig. 10. The span-wise distributions of the normal force (left) and tangential force (right) at the design point for the PSRs with LMT.

as:

nearly matched. The basic motivation of LDM is depicted as:

Lf ¼ l2 ,Lm

(12)

According to Eq. (7), the lift force for unit blade length is formulated as:

8   1 2 > > < Lf ¼ 2 rV f ,cf ,CLf af ; Ref > > 1 : Lm ¼ rV 2m ,cm ,CLm ðam ; Rem Þ 2

Lf

:C

¼ Kf af þ C 0Lf

Lm

¼ Km am þ C 0Lm

(14)

where K represents the slope of the lift coefficient CL with respect to AOA; C 0L is the lift coefficient when a ¼ 0. According to the Froude scaling law, the following relations should be maintained:

pffiffiffi Vf ¼ Vm l

(18)

Substituting Eqs. (15) and (18) into Eq. (17), it yields:

(13)

It is known that at the design point, the blade sections are usually working at AOAs smaller than the stall angle to generate more power output. In other words, the airfoil works in the linear region:

8
8  dL 1 2 > > > da ¼ 2 rV f ,cf ,Kf < f   > > 1 > : dL ¼ rV 2 ,cm ,Km da m 2 m

(15)

Kf , cf ¼ l,Km ,cm

(19)

So far, based on the two constrains [Eqs. (12) and (17)], closed equations [Eqs. (16) and (19)] are deduced. Finally, the unknowns are solved:

8 1 Kf > > ,c c ¼ > > < m l Km f > > C0 C0 > > : bm ¼ bf  Lf þ Lm Kf Km

(20)

It is indicated in Eq. (20) that the LDM algorithm is closely related to the airfoil characteristics (K and C 0L ). A flow chart to implement the LDM is summarized in Fig. 11. A critical step of LDM is to obtain the values of K and C 0L for both original and alternative airfoils. An example of the procedure to get these values is depicted in Fig. 12. It is anticipated that the dependency of lift coefficient

Combining Eqs.(12)-(15), it is deduced:

h   i h i cf Kf 4f  qf  bf þ C 0Lf ¼ l,cm Km ð4m  qm  bm Þ þ C 0Lm (16) According to Eq. (9), the inflow angles of the prototype and the model can be conserved if the differences among inductions are neglected. That is, 4f ¼ 4m . Besides, as aforementioned, qf ¼ qm ¼ 0 at the design point. Until now, two unknowns, i.e., the blade chord c and twist b, should be decided. However, only one constraint has been found, i.e., Eq. (16). To close the equations, another constraint is proposed: in addition to the similitude between the lift, the deviation of lift to AOA should also be matched because the FWT usually experience significant unsteady aerodynamics:



   dL dL 2 ¼l , da f da m

(17)

The deviations of the prototype and the model are formulated

Fig. 11. The flow chart to design a PSR with LDM method.

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B. Wen et al. / Renewable Energy xxx (xxxx) xxx

SD2030 Re=30K

FFA-W3-241 Re=12M

Fit, SD2030 Re=30K

Fit, FFA-W3-241 Re=12M

values for both airfoils are very close. Therefore, a general multiplying factor of 1.5 is decided here. The aerodynamic performance of the redesigned PSR is shown in Fig. 13 and Fig. 14 along with the full-scale rotor. It is shown that in the region of tsr between 6 and 8, the thrust coefficient can well match with the prototype. Similar to the case of MLT shown in Fig. 9, the power coefficient cannot be well depicted. Fortunately, the aerodynamic torque has a relatively smaller influence on the motion performance of the FWT when compared with the rotor thrust. Generally, the redesigned PSR with LDM presents tremendous aerodynamic performance that matches satisfyingly with the full-scale prototype. In this section, two different algorithms to develop the PSR have been introduced. The PSRs decided with both methods exhibit excellent aerodynamic performance with respect to the full-scale prototype. However, merely focusing on aerodynamic performance is not enough to evaluate the redesigned PSRs. In the following section, other aspects such as the blade mass and the manufacturing of the PSRs will be discussed.

2 1.5

y = 0.1222x + 0.5211

CL [-]

1 0.5 0

y = 0.0834x - 0.0207

-0.5 -1 -10

-8

-6

-4

-2

0 2 AOA [°]

4

6

8

10

Fig. 12. Schematic to obtain values of K and C 0L for the airfoil.

4. Results and discussion

over AOA has a great impact on the PSR’s aerodynamic performance. To mitigate the errors introduced by the elevation of K and C 0L , the values of (c, b) should be slightly corrected to further promote the PSR performance. It is shown in Eq. (20) that the multiplying factors deviate for different airfoils. However, it is known that most of the aerodynamic loads are generated by the outboard blade sections, i.e., FFA-W3-241 and FFA-W3-301 in the present study. The derived

The final geometries of the PSRs based on LMT and LDM algorithms are exhibited in Fig. 15. The chords of the PSRs with MLT and LDM are 1.3 times and 1.5 times of the FSR’s, respectively. Noting that the blade root region consists of cylinders that generate no lift force, the root regions are modified by reducing the chord lengths and adjusting the twist angles to promote the geometries. In addition, the mass and the rotational inertia of the redesigned PSR are validated. The rotor mass will impact the mass center of the FWT system and thus will markedly influence the motion response

PSR, LDM

Full

1.2

0.6

1

0.5

0.8

0.4

CP [-]

CT [-]

Full

9

0.6 0.4 0.2

PSR, LDM

0.3 0.2 0.1

0

0 5

6

7

8

9

10

5

6

7

tsr [-]

8

9

10

tsr [-]

Fig. 13. The thrust coefficient (left) and power coefficient (right) of the PSRs with LDM.

Full

PSR, LDM

Full

3

PSR, LDM

0.3

2

FT [N/m]

FN [N/m]

2.5 1.5 1

0.2 0.1

0.5 0

0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 r/R [-]

1

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 r/R [-]

1

Fig. 14. The span-wise distributions of the normal force (left) and tangential force (right) at the design point for the PSRs with LDM.

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Full

PSR, X1.3, MLT

PSR, LDM

Full

0.12

Twist [°]

Chord [m]

0.16

0.08 0.04 0

PSR, X1.3, MLT

PSR, LDM

30 25 20 15 10 5 0 -5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 r/R [-]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 r/R [-]

Fig. 15. The distributions of blade chord (left) and twist (right) of the PSRs and the prototype.

of the FWT. Experiments by Duan et al. [27] showed that the dynamic properties of FWTs with the FSR and a PSR were markedly different. One major cause is the different aerodynamic performance of both rotors. Besides, the markedly increased mass of the PSR in their experiment can be another potential reason for the differences. Therefore, the mass of the PSR is analyzed in this section. Afterwards, discussion about the MLT and LDM are conducted.

4.1. Blade mass analysis According to the Froude scaling law, the mass of the model blade is about 159.1 g at a scaling ratio of l ¼ 64. The mass of the blade can be formulated as:

M¼

N X

ci mi Dri

(21)

i¼1

where subscript i is the index of the blade section; mi is the relative mass of unit blade length of the airfoil; Dri is the length of blade section i; N is the number of the blade sections. Because the manufacturing procedure of the blade is unknown, the blade mass is represented by the surface area of the blade in the present study. The areas and perimeters for different airfoils for unit chord length are concluded in Table 1. It is shown that the area and perimeter of the alternative airfoil, i.e., SD2030, is relatively smaller than the original airfoils. This feature has been displayed in the airfoil geometries as shown in Fig. 5. Therefore, it can be inferred that although the chord lengths of the PSRs are increased, the mass of the PSR can be maintained or even reduced because of the significantly reduced SD2030 surface area. Based on the Froude scaling law, the required mass of individual blade is 159.1 g. According to our prior experience to manufacture a 1/50 scaled blade for the NREL 5 MW wind turbine [33], manufacturing a scaled blade (length of 1.26 m) with carbon fiber can control the blade mass around 140 g. Therefore, it is anticipated that manufacturing the PSRs with required mass can be realized with carbon fiber material. Furthermore, the blade inertia can be perfectly reproduced with a dedicated manufacturing procedure.

4.2. Discussion on MLT and LDM Actually, both MLT and LDM algorithms are the results of three approaches: replacing the original airfoils by a low-Reynoldsnumber airfoil, changing the blade twist, and increasing the chord length. The difference behind both methods is that the MLT decides the blade twist at first and afterwards changing the chord lengths to further match the desired rotor thrust, while the LDM assigning the chord length and twist angle at the same time by solving Eq. (20). Recall Eq. (11), when assigning the blade twist with MLT, the axial and tangential inductions are prescribed, and a general induction was utilized for different blade sections. This treatment may result in the errors when deciding the optimal blade twist in Eq. (11). Fortunately, the chord lengths can be later adjusted to improve the thrust performance. A potential alternative to improve the MLT algorithm is to assign the blade twists according to the actual inductions or to develop iterations between the twist assigning and the blade induction. To further guarantee the performance of the MLD-based PSR, a procedure with manually improving the chord and twist is provided at the end of the design procedure (recall Fig. 8). Besides, the maximum lift can only be maintained at the designed point (tsr ¼ 7.6 in the present study). The blade pitch angle should be regulated at other tip speed ratios to match the desired loads. During the deduction of the LDM algorithm in Section 3.4, it was assumed that the rotor thrust mainly consists of the lift while the drag force was neglected. This treatment can introduce some error to the assignments of blade chord and twist. In addition, the LDM algorithm possesses a significant dependency on the airfoil characteristics, especially the dependency of lift coefficient over AOA. Therefore, accurate estimation of the airfoil characteristics plays an essential role in LDM. Similar to MLT, the final blade chords and twists can be manually altered to mitigate the errors and thus promote the PSR performances. As shown in Figs. 9 and 13, both MLT and LDM can perfectly match the desired rotor thrust in a region around the design point (tip speed ratios from 7 to 9 for MLT and 6 to 8 for LDM). It seems that the PSR designs in the present study outperform than prior PSRs where only a few separated work points can be guaranteed.

Table 1 Area and perimeter of the airfoil with unit chord length. Airfoils 2

Airfoil surface area [m ] Perimeter [m]

FFA-W3-241

FFA-W3-301

FFA-W3-360

FFA-W3-480

FFA-W3-600

Cylinder

SD2030

0.1401 2.1107

0.1812 2.1652

0.2232 2.2317

0.2976 2.3587

0.3720 2.5006

0.7854 3.1416

0.0605 2.0242

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With the rotor thrust matched in a range of tip speed ratios rather than few separated points, it is possible to conduct a reliable modelling of unsteady aerodynamics where the tip speed ratio is time-varying, such as the cases with floater oscillations. Besides, investigating the blade pitch control on the model FWT may be possible. It seems that the LDM is able to provide preferable dynamic performance than MLT because one of the constraints in LDM is to maintain the dynamic characteristics, as shown in Eq. (17). On the other hand, the advantage of MLT is presented by its smaller blade chord lengths. As indicated in Fig. 15, the chord length of MLTbased PSR is 13.3% smaller than that of LDM-based PSR. Correspondingly, the MLT-based PSR is relatively more lightweight, preserving larger weight margin for deploying sensors on the blade for loading monitoring, such as Fiber Bragg Grating sensors. A flaw of the present PSRs is that the aerodynamic torque is relatively smaller than the full-scaled rotors. This drawback may generate incorrect yaw motion of the floater because the aerodynamic torque and the resultant gyroscopic moment are among the essential excitations on the rotational motions. Therefore, to more accurately model the dynamic performance of the FWT system, the matching of the aerodynamic torque should also be improved in the future. 5. Conclusions When conducting wave basin model tests for the Floating Wind Turbine (FWT), scaling requirements in the Froude number for hydrodynamics and the Reynolds number for aerodynamics are naturally incompatible. Note that the primary purpose of the model test for FWT in the wave basin usually locates in investigating the motion performance of the FWT system. Consequently, the Froude number similarity is put in the first place. When applying the Froude scaling law, the Reynolds number for the rotor dramatically reduces, which significantly reduces the aerodynamic loads of the model rotor. To match the appropriate aerodynamic loads especially the rotor thrust, two algorithms are proposed in the present study to develop Performance-Scaled Rotors (PSRs). The proposed approaches are used to design PSRs for the DTU 10 MW baseline wind turbine dedicatedly for the wave basin model tests. According to the analysis and discussion in the foregoing sections, the following conclusions are drawn: (1) When applying Froude Scaling Law in the wave basin for FWT model tests, the aerodynamic loads of the model rotor markedly reduces due to the dramatical reduction of the Reynolds number, which is addressed as the ReynoldsNumber Scaling Effect (RNSE). (2) To mitigate the adverse effects of RNSE, replacing the original airfoils with low-Reynolds-number airfoil is the most effective approach. In addition, increasing the blade chord and reassigning the blade twist can also partly increase the aerodynamic performance of the model-scale rotor. (3) Maximum Lift Tracking (MLT) and Load Distribution Match (LDM) algorithms are productive to optimize the blade chord and twist assignment. The former lead all blade sections to work at the maximum lift coefficient at the design point. The latter aims to approximately match the span-wise normal force at the design point. Both MLT and LDM algorithms are shown to present satisfying thrust performance. (4) PSRs designed with MLT and LDM algorithms can generate desired rotor thrust in a region near the design point (the optimal tip speed ratio), which makes it possible to test unsteady aerodynamics with such PSRs in the wave basin model tests. Besides, the mass and inertia of the blade can be well matched by optimizing the manufacturing procedure.

11

The PSRs designed in the present study will be manufactured by carbon fiber in the near future and will be experimentally investigated in the dedicated wind generation system developed by SJTU. Afterwards, the PSR will be installed on a novel floating platform developed by the SKL-OE and SKL-MSV at SJTU. Acknowledgements This work is financially supported by the National Natural Science Foundation of China (Grant No.11632011, 11572189 and 11872243) and Natural Science Foundation of Shanghai (Grant no.19ZR1426300). Nomenclature a b c CD CL C 0L CT D D* FN Fr FN g K L m M r R Re U* V V0

a a* b q l L

m n r

4

U

Axial induction factor Tangential induction factor Characteristic length; Chord length Drag coefficient Lift coefficient Lift coefficient at null AOA Thrust coefficient Drag force Characteristic length scale Normal force Froude number Tangential force Gravitational acceleration Slope of lift coefficient Lift force Relative mass of unit blade length Normalized mass Radial distance from the rotor axis Rotor radius Reynolds Number Characteristic flow velocity Characteristic velocity; Relative wind speed Free-stream velocity Angle of attack Angle of attack at the maximum lift coefficient Blade twist angle Blade pitch angle Scaling ratio Tip speed ratio Normalized blade station Kinematic viscosity Flow density Inflow angle Rotational speed

Abbreviations AOA Angle of Attack DTU Technical University of Denmark “f” Full scale FSR Froude-Scaled Rotor FWT Floating Wind Turbine LDM Load Distribution Matching “m” Model scale MLT Maximum Lift Tracking PSR Performance-Scaled Rotor RNSE Reynolds-Number Scaling Effect SKL-MSV State Key Laboratory of Mechanical System and Vibration SKL-OE State Key Laboratory of Ocean Engineering

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12

SJTU tsr

B. Wen et al. / Renewable Energy xxx (xxxx) xxx

Shanghai Jiao Tong University Tip speed ratio

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