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# OPTIDE - Technical Report

Stefan Hoerner, Roberto Leidhold, Pierre-Luc Delafin

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Stefan Hoerner, Roberto Leidhold, Pierre-Luc Delafin. OPTIDE - Technical Report. University Otto-von-Guericke Magdeburg. 2025. hal-05243683

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# OPTIDE FINAL TECHNICAL REPORT FOR DFG

– public version –

Stefan Hoerner (PI), Roberto Leidhold, Pierre-Luc Delafin

September 9, 2025

## 1 General Information

DFG reference number: TH 881/32-1, LE 2346/9-1

Project number: 457325924

Project title: OPTIDE – Performance increase and improvement of the fatigue strength of vertical axis water turbines through active blade adjustment

Name(s) of the applicant(s): Dominique Thévenin, Roberto Leidhold

Official address(es): Otto-von-Guericke Universität Magdeburg
Universitätsplatz 2, 39106 Magdeburg

Name(s) of the co-applicants: Stefan Hoerner (Project lead)

Name(s) of the cooperation partners: Christian-Toralf Weber
(University of Applied Sciences Magdeburg)
Pierre-Luc Delafin, Cyrille Bonamy
(LEGI, CNRS, G-INP University Grenoble-Alpes)

Reporting period: 15.02.2021 - 30.09.2024

## 2 Summary

Achieving Europe's 2050 renewable energy goals presents significant challenges, particularly in maintaining energy infrastructure stability due to the volatile nature of wind and solar power. Thermal power plants, which currently form the backbone of our energy infrastructure, require substantial cooling water and river mass flow, leading to thermal pollution and exacerbating issues due to climate change. Historically low water levels in rivers and lakes, as seen in 2022, 2023, and 2025, have forced power plants to reduce capacities during peak summer consumption. Classical hydropower is also increasingly affected. Ocean energy, particularly tidal streams, emerges as a resilient and sustainable energy source, largely unaffected by climate change and drought. Tidal streams are predictable and can provide base load power generation, contributing to grid stability and mitigating climate change effects. Research over the past two decades has focused on hydrokinetic turbine technologies that are less harmful to the environment. By 2025, extensive research had been conducted, with companies like Hydroquest installing tidal power prototype farms.

The OPTIDE project studied vertical axis, cross-flow tidal turbines (CFTT), which are more efficient in land use compared to classical axial turbines. These turbines, however, face complex unsteady flow dynamics, leading to fatigue, failure and decreased efficiency. The project aimed to optimize turbine efficiency and reduce structural loads through continuous blade pitching. Experimental optimization techniques were employed to achieve these goals, significantly reducing evaluation time compared to numerical simulations.

The project involved designing and instrumenting a flume-scaled turbine model, using a straight-bladed design with supports at the blade tips. The rotor design was based on preliminary simulations and computational fluid dynamics (CFD) analysis. An additional blade shape optimization considered various parameters, including blade thickness, rotor solidity, and Reynolds number.

A parallel pitch actuator development followed two paths: one using a commercial permanent magnet synchronous motor with a gearbox for the prototype, and another developing a direct-driven approach for future implementations. The direct-driven actuator, based on a limited angle torque motor (LATM), showed promising results in producing the required torque and precise angular position control.

The experimental optimization method developed in the project was a major achievement. It involved a genetic algorithm and an automated experimental setup, significantly reducing evaluation time. The optimization process successfully doubled the power coefficient and identified optimal pitch trajectories. The
results demonstrated the potential of experimental optimization methods in improving turbine efficiency and reducing structural loads.

In summary, the OPTIDE project highlighted the potential of experimental optimization techniques and show-cased their potential on tidal turbines, a resilient and sustainable energy source. The development of experimental optimization framework pave the way for future advancements in complex optimization tasks and tidal turbine technology.

# 3 Progress report

Achieving the European 2050 renewable energy goals and beyond bears an enormous challenge to maintain our energy infrastructure stability due to the volatile character of wind and solar power. In addition, thermal power plants which currently built the spine of our energy infrastructure require cooling water and sufficient mass flow in the rivers. This provides thermal pollution in the water bodies and will be increasingly problematic due to an expected loss of water and overheating of the rivers driven by climate change. This affects fossil, nuclear and biomass driven capacities. 2022 and 2023 provided us with historically low water levels in rivers and lakes worldwide [18]. 2025 already started with new negative records for the last five decades, e.g., for the Elbe River in Central Europe [1]. As a result, power plants regularly have to throttle down their capacities during the summerly energy consumption peaks. These effects will significantly increase in future [14]. Classical hydropower is also affected. European glaciers, our fresh water storage, are the most impacted worldwide, having lost more than 33% of their capacities in the past two decades [24]. Norway holds 50% of the hydropower reservoirs in EU. In 2022 they complained about significantly reduced hydropower capacities compared to the 20 years average [36]. Electrical energy supply was throttled down with significant impact to the European electricity market. In this scenario, ocean energy becomes a key element for a resilient energy generation and could serve as clean and sustainable energy source. This is particularly true for tidal streams which are mostly unaffected by climate change, glacier loss and drought. In addition, and in contrast to almost all other renewable energy sources, tidal streams are fully predictable as they depend on planetary and lunar motion.

When implemented at large scale, highly controllable tidal turbines can substantially contribute to solving the European grid stability problems and mitigate climate change consequences. The predictable and reliable nature of tidal and marine currents makes them ideal providers of base load power generation [22, 7, 33]. Moreover, like all hydropower technologies tidal turbines can be exploited as a demand side response, which is considered to be key for an improvement of the agility and resilience of the energy market and grid as a whole [48]. Following the sustainable development goals (SDGs) of the United Nations (SDG 14 aims to "conserve and sustainably use the oceans, seas and marine resources") there has been extensive research in the last two decades on hydrokinetic turbine technologies which do not require any dam installations and are in determined to be less harmful to their environment [20, 11, 13]. This has also been indicated by ethohydraulic lab experiments [32].

In 2025, the Tethys databases, a knowledge base with a unique data collection on marine energy technologies, listed 1408 publications on tidal energy converter technologies [3]. This shows that extensive research has been performed. Most studies focused on the turbines themselves, such as influence of the rotor geometry, e.g., blade shape [29, 15] or other design parameters [44, 17, 30, 19, 31, 38].

Today, it can be considered that general turbine design guidelines exist. Hydrokinetic turbines are in a mature state of technology for sustainable tidal energy exploitation. This is underlined by companies like Hydroquest (a spin-off of LEGI), which currently installs a tidal power prototype farm of 17 MW in the Channel [2]. The OPTIDE project has studied on so-called vertical axis tidal turbines, which are from turbomachinery point of view single stage, cross-flow type turbines without guiding apparatus. It has been shown numerically and experimentally that this turbine type features an order of magnitude better land-use in farm installations than classical axial turbines (often referred to horizontal axis turbines) [50]. This land-use can be considered to be a critical parameter as suitable spots for tidal energy farms are of limited supply due to flow conditions and concurrent use [8, 12]. Unfortunately, this turbine type rotates perpendicular to the flow. A very complex unsteady flow governs the rotor dynamics. The rotation creates alternating relative flow speeds on the blades and strong variations of the angle-of-attack on the blades a function of the azimuth angle of the rotor. The flow regime is thus dominated by periodical highly dynamic flow separation (stall) and reattachment at the blades, which leads to alternating vortex generation and shed. The dynamic
<figure><img src="image_3.png" /><figcaption>Figure 1: Weakly coupled FSI simulations top: 2D CFD simulations for load estimation (OpenFOAM, URANS, k-ω-SST turbulence model (azimuth angle 100°, 170°, 240°) [42]) bottom: 3D FEA model (Ansys mechanical) using mapped pressure loads to design the instrumentation and ensure structural strength of the flume model (azimuth angle 110°, 230°, 350°) deformations scaled up by factor 86 [9]</figcaption></figure>

stall provokes load variations which can lead to fatigue failure and decreased single turbine efficiency [34]. Past studies of our group concentrated on a blade-level flow control using passive morphing, a shape adaptation driven by the flow induced forces. For the experimental studies surrogate models of a single oscillating blade were employed [47]. We have characterized the fluid-structure interactions on the blades [21] and shown that such methods can significantly increase the turbine efficiency and lower the structural loads [46]. Morphing allows to increase the lifetime and reduce the material use [21].

The German-French OPTIDE project, which is the base of the report at hand, has been co-funded from DFG and the French excellence initiative LabEx TEC21 at University Grenoble. The aim of the project was to determine the potential benefits from continuous blade pitching in order to control the angle-of-attack during each rotor turn (Group Hoerner/Thévenin), to develop the required control system and unconventional blade actuators (Group Leidhold).

The optimization objective was to minimize structural loads and to increase the turbine efficiency. The complex flow pattern in the rotor require costly unsteady flow simulations, the large design space and multiple optimization objectives cumulate to a very large number of potential design parameter combinations.

In consequence it has been decided to employ experimental optimization techniques (Exp-O) to reach the project goals. We have shown in prior publications that a cost or more precisely evaluation time reduction in the order of $10^5$ can be reached compared to numerical simulations. Exp-O bases on fully automatized experiments which are coupled with a governing optimization algorithm [4].

In the case at hand a flume scaled CFTT turbine model had been designed and instrumented. The project team opted for a straight-bladed turbine design with supports at the balde tips. This design has almost fully replaced the former commonly employed H-shape structure. The rotor design was based on preliminary weak-coupled (one way) simulations of the fluid-structure interactions [10]. 2D computational fluid dynamics (CFD) simulations of the CFTT have been carried out. The pressure (line) loads have been extruded along the blade span and mapped on a 3D finite-element analysis (FEA) of the structural response (see Fig.1). A
reduced order mechanical model has been developed and the FEA has been used to iteratively improve the
design of the turbine structure and to place targeted material weaknesses and solid hinges to achieve a load
decoupling and to allow for the instrumentation of the rotor structure with sets of strain gauges [9].

In a parallel process, suitable profile shapes for the blades have been investigated within a CFD based opti-
mization (CFD-O). It has been decided to embed the pitch actuators into the blades, with the aim to avoid
flow alterations. This has been the case for former experimental studies with external actuator e.g. [28].

The minimal diameter for an available drive was determined based on the expected working angle, as well
as the loads from inertia, added mass effects and flow induced forces, based on simulations [16] and pre-
liminary experiments based on a single oscillating hydrofoil surrogate system at LEGI labs [5]. The minimal
diameter of 12 mm for a conventional planet gear supported drive (Faulhaber 1226A024B 12/4) lead to signif-
icant constraints for the overall turbine size. A trade-off had to be made in between ratio of blade thickness
to chord length, rotor solidity (ratio of blade chord length to diameter), confinement in the flume (ratio of
cross-section to projected turbine surface) and blade related Reynolds number.

The blade shape optimization had to deal with a slightly thicker blade or a higher solidity compared to other
turbine rotors such as [29]. Finally a 13 mm thick blade with chord length of 69 mm with a rather unconven-
tional shape featuring a thick leading edge and a sharp angle on the suction side of the upstream rotor was
found to perform best along with a low fatigue risk. This foil is operating in a 400 mm turbine diameter at a
tip-speed ratio of 1.9 (not published yet). The optimization was based on 2D unsteady Reynolds-averaged
Navier-Stokes (URANS) simulations. Objectives were to provide the best performance (C<sub>P</sub>) and to minimize
the fatigue failure risk (C<sub>σ</sub>). The latter was calculated from stress with a low order mechanical model at the
most vulnerable position of the support. FEA simulations were performed to validate the model. The opti-
mization took roughly 200,000 CPUh on the LEGI cluster in about 5 months. The simulations were performed
using OpenFOAM, the method and the scripts for automation are published along with a method publica-
tion at several conferences [39, 40, 25] and in the community hosted open access journal . A second journal
article presenting the methods is currently under review [42]. A contribution which presents preliminary
results has been accepted for EWTEC 2025 conference [41]

In order to make progress in the already delayed project (we had to ask for a cost-neutral runtime extension) a standard NACA0018 profile with 70 mm chord length was employed for the experiments to fit the actuators. This choice led to an overall confinement of 20%, average blade based Reynolds numbers of 10⁵ and a radius based solidity of 1.05 (see Fig.2)

The reference case of a fixed pitch NACA0018 profile was characterized using high-speed 2D2C Particle-
Image Velocimetry (PIV) in the rotor region and 3C3D Acoustic-Doppler Velocimetry (ADV). The PIV was per-
formed with multiple overlapping measurement positions from 1 *D* (-400 mm) before the turbine to 2 *D*
(800 mm) behind the turbine using two 4 Mp high-speed cameras (Phantom VEO 640L) and covering 1000
(width) × 500 (streamwise) mm² per take. The processing of the data using automated blade masking based
on machine learning is part of an ongoing Master thesis. The sampling frequency was set to 1kHz. Complementing pointwise ADP measurements (along with total pressure at the point) were performed on a cross
section upstream of the rotor and with a 100 mm equidistant 3D grid of about 800 points from 2 *D* (800 mm)
to 7 *D* (2800 mm) behind the turbine (see Fig.3). This data has been exploited to generate a 3D wake classification which allows to assess turbulence intensity and time-averaged flow quantities with 3 components.
Fig.3 show the flow velocity components and dominant flow structures based on horizontal and vertical
slices in the mid planes of the flume. The analysis of the structures and the wake recovery is ongoing work.
A confinement correction for the characteristic curves has been applied based on the models of [23, 37, 35].
The structural loads have been gathered based on the five full bridges of strain gauges. A mechanical model
has been developed to separate the force components on a single blade. Details have been provided in
[10, 9]. The measurement of the isolated components of the blade loads allows to apply the same methods
developed for the numerical studies presented in [42].

In a parallel cooperation with partners from Taltech, Estonia, a miniaturized self-standing sensor device has
been embedded in one turbine blade. This FSI sensor, originally developed in a project for fish safety and
mounted on the dorsal fins of fish when passing turbines and hydraulic machinery [49] allows to measure
the FSI on blade level. It is equipped with an inertial measurement unit (IMU) and a pressure sensor. Thus
it is possible to measure the total pressure on a location of the blade and the linear accelerations as well as
angular speed in space (6-axis). The results show how the turbine deforms and provide data for pressure
based validation of 2D numerical simulations which are not biased by 3D effects as it is the case for force or
torque measurements. Conference contribution to ICOE in Chennai 2025 has been accepted for publication
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /><figcaption>Figure 2: OPTIDE CFTT rotor; (left) CAD render of the final flume model (Nottrodt 2025)(right) turbine model installed in the flume for subsequent optimization and PIV measurements (Hoerner 2025)</figcaption></figure>

[45].

The pitch actuator was developed in two parallel paths: 1) for the turbine prototype of the present project, and 2) as a new direct driven approach for future turbine implementations.

For path (1), a commercial small permanent magnet synchronous motor (PMSM) with a gearbox was used for the pitch drive, as mentioned above. This choice was taken because of the decisive size restrictions of the flume, requiring a very small blade profile and shorter time frame to be implemented. The objective is to control the pitch angle trajectory with the required dynamics and rejecting hydraulic load perturbations. The reference trajectory, i.e. the pitching law, gives the pitch angle as function of the azimuth angle. It is formed by a periodic spline function with four nodes. Each blade has embedded two motors with respective position sensors and gearboxes. Outside of the blade there are two MOSFET based inverters and a micro controller (Texas Instrument TMS320F28379D) implementing the control system for each blade. The control algorithm consists on an inner torque loop for each motor and a common cascaded angular speed and position loop for each blade. For improving the dynamic of trajectory tracking, a feed-forward branch has been added to the speed reference. The controllers have been adjusted for the fastest possible response but avoiding to excite oscillations due to the backlash nonlinearity of the gearboxes.

The actuating and control system described for each blade has been implemented three times. The three controllers are mounted in a rotating frame on the turbine and are linked by a CAN bus among them to implement the 120° shifted pitch law. One of the controllers is used as coordinator, for acquiring the azimuth angle, torque, strain gauges signals and communicating by WLAN with the governing PC, which implements the optimization algorithm, as shown in Fig. 4 (left). Details of this development was presented in [51], [52] and [26]. Friction, wear and gearbox backlash present in this actuator type introduces significant limitations for the implementation outside of the laboratory environment. Particularly gearbox backlash introduces control issues and increased wear by frequent reversals in pitch direction, occurring twice per revolution.

For path (2), to overcome this limitations, a new pitch actuator type was developed in parallel for future turbine implementations. It is based on the concept of the limited angle torque motor (LATM), with the particular constrains for embedding them in turbine blades. The required slim and elongated profile is in
<figure><img src="image_6.png" /><figcaption>Figure 3: ADV wake measurements: (from top to bottom) Horizontal slice (mid plane) streamwise flow speed ($V_X$); transversal flow component ($V_Y$), Vertical slice (mid plane) streamwise flow component ($V_X$); (bottom) vertical velocity component ($V_Z$) (Bennecke 2025)</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Figure 4: Exp-O setup for the OPTIDE turbine: (left) The MCU at the rotating platform controls the automatized measurements and actuation. A WiFi connection allows to share the data with the governing optimizer on a stationary PC and to timestamp the data with external measurements such as the High-Speed PIV[43] (right). Fully instrumented model in the flume (Hoerner 2025).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 5: (left) Angle tracking capability of the proposed direct driven actuator at a pitching frequency of 1.5 Hz; (middle & right) Proposed direct driven pitch actuator: (middle) Cross section of the actuator. (right) Test bench for evaluating the actuator and control system.</figcaption></figure>

opposition to the state of the art in LATM which are characterized by a disk-like shape. The high torque allows to drive a blade directly without gearboxes.

Design criteria were elaborated and two proposals analyzed by means of the finite element method (FEM). It consists on an outer rotor, i.e. the pitching part of the blade, and an inner stator, i.e. the shaft of the blade fixed to the turbines' arms. The one proposal has windings on the inner stator and magnets on the outer rotor. The second proposal, which provided higher torque density, has magnets in the inner stator and windings in the outer rotor, as shown in Fig. 5 (middle). A prototype was built for the latter. For the sake of convenience it was constructed in a bigger size than the one of the flume turbine (threefold scale). A power electronic converter and a controller was designed and implemented. The inner control loop was designed specially tailored for the particular actuator, the outer control loops for angular speed and position are similar to those used for the gear-based actuator (1). The proposal could be validated, showing the capability to produce the required torque and precise angular position control (Fig. 5 (left)).

A paper with the results have been accepted for the European Wave and Tidal Energy Conference 2025 [27].

### 3.0.1 The experimental optimization method

The major achievement of the project was not the show case of a CFTT and the determination of an optimized pitching trajectory but the development of the experimental optimization method. It consists on an experimental optimization (Exp-O) framework based on the genetic algorithm and an automated experimental setup for evaluating the objective function. As aforementioned, Exp-O avoids extremely time consuming numerical simulations and can provide a gain in the evaluation time of a factor 10⁵ [6]. Such extreme cost reductions require a full automatization of the experiment which is able to evaluate one optimization individual (parameter set) in less than one minute.
<figure><img src="image_9.png" /><figcaption>Figure 6: (left) Power coefficient $C_P$ for each individual. The generation is identified by the color of the points. The circle identifies the unpitched reference trajectory ID0 and the star the trajectory ID217 with the highest $C_P$. (right) Power coefficient $C_P$ for each individual, ordered by increasing pitch angle span. The cross shows the individual ID273.</figcaption></figure>

The Exp-O process starts by the definition of a set of design parameters by the optimization algorithm. The pitch trajectories are determined by a spline function defined by four nodes. The genetic algorithm defines an initial set of variations of the design variables (the four nodes) subsequently called individuals. In order to cover the entire design space, an equidistant pseudo-randomizing algorithm (Sobol function) generates the variations. Such a group of individuals, called population, is sequentially evaluated by calling a calculation and communication script which translates the individual parameter set into a trajectory and sends the position set point list (2000 points) to a micro-controller (MCU). During the runtime, the runner torque, the runner position, the angular position of the blades, blade actuation current and the signals from the strain gauges and the embedded FSI sensor are captured. The MCU provides signal feedback for the sensors which are subsequently processed and provided to the optimizer. Based on the results, the best fitting individuals are used to generate a new generation by crossover of the design parameters. This ensures a fast convergence of the results, while a parallel performed random mutation of some design parameters will provide a good coverage of the design space. The system was considered to be converged if the best value for the objective function could not be improved over two generations.

In a single objective optimization (maximizing the performance) it was possible two almost double the power coefficient $C_P$. The optimum was reached within five generations with hundred individuals each. They were tested and referred to as ID1 to ID499. An imposed reference trajectory (ID1) with a constant pitch angle $\beta = 0$ (unpitched) was evaluated first and used as reference subsequently.

In Table 1 the results of the experimental optimization are summarized. The trajectory ID1 is the unpitched case used as reference. The four trajectories providing the highest $C_P$ are shown subsequently.

<table><caption>Table 1: Result with the highest $C_P$</caption><thead><tr><th>ID</th><th>C<sub>P</sub></th><th>C<sub>P</sub><br>relative to unpitched</th><th>pitch span<br>degrees</th><th>pitch power<br>relative to generator's power</th><th>stress<br>relative to unpitched</th></tr></thead><tbody><tr><td>1 (unpitched)</td><td>0.158</td><td>1</td><td>0</td><td>0</td><td>1</td></tr><tr><td>217</td><td>0.311</td><td>1.97</td><td>20</td><td>0.025</td><td>1.18</td></tr><tr><td>164</td><td>0.303</td><td>1.92</td><td>18</td><td>0.026</td><td>1.11</td></tr><tr><td>30</td><td>0.299</td><td>1.90</td><td>22</td><td>0.034</td><td>0.92</td></tr><tr><td>204</td><td>0.299</td><td>1.89</td><td>25</td><td>0.029</td><td>1.39</td></tr></tbody></table>

Figures 6 to 9 show the results of the optimization process. Figure 6 (left) shows that the optimal pitch law is already found in the third generation (ID217, $C_P$ improvement by factor 1.97). The trajectory for ID217 is
<figure><img src="image_10.png" /><figcaption>Figure 7: (left) Angle of attack for the unpitched blade α, for the pitched blade α', and the pitch angle β as function of the azimuth angle for the $C_p$-optimal trajectory ID217. (right) Angle of attack for the unpitched blade α, for the pitched blade α', and the pitch angle β as function of the azimuth angle for the trajectory ID273.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 8: (left) Power coefficient $C_p$ for each individual, ordered by increasing pitch power. The cross shows the individual ID342. (right) Angle of attack for the unpitched blade α, for the pitched blade α', and the pitch angle β as function of the azimuth angle for the trajectory ID342.</figcaption></figure>

shown in Fig. 7 (left). All later individuals performed less.

Even though the optimization was performed for the power coefficient as the sole objective function, the individuals were also ordered by increasing actuation angle span in Fig. 6 (right). When accounting for the pitch angle, ID273 can become an interesting alternative to use ID217 for an industrial application as it performs already very good ($C_p$ increased by factor 1.62) but requires only a small actuation angle and thus allows for a reduction of the hardware costs when using LATM and exploitation of the very limited pitch angle.

By comparison of both trajectories in Fig. 7, a general similarity can be observed, which is also present in all other better performing trajectories (not shown here). While the effective angle of attack $\alpha'$ is decreased in the upstream part of the rotor (azimuth angle $\phi$ 0-180°) it is kept constant or increased at roughly 180° and then again slightly decreased starting from 270°. The upstream pitch characteristics can be explained by velocity triangles which predict high angles-of-attack for the given operation point. As the stall point is reached a reduction of $\alpha'$ seems reasonable. However, in the downstream part the velocity triangles predict very high negative angles for $\alpha'$. The strongly simplified physics do not account for the wake of the upstream rotor region. In consequence $\alpha$ is over-predicted. The high turbulent wake region has significant lower flow velocities and thus smaller $\alpha$. In consequence, the optimizer tends to increase $\beta$ in order to reach higher angles for $\alpha'$.

Figure 8 shows the optimization results again for all generations while the primary objective ($\max(C_p)$) is
plotted over the actuation effort (electrical power). In this case, ID342 becomes very interesting as it features a significant lower consumption as the optimum ID217. It allows to reduce the actuation costs by factor 1.6 compared to the optimum (ID217) featuring a suboptimal but very high $C_P$ improvement of factor 1.82 compared to the reference (ID1).

<figure><img src="image_12.png" /><figcaption>Figure 9: (left) Power coefficient $C_P$ for each individual, ordered by increasing tangential stress in one arm. The rms value of the AC component (in V) of the amplified strain gauge signal is given. The cross shows the individual ID431. (right) Angle of attack for the unpitched blade $\alpha$ for the pitched blade $\alpha'$, and the pitch angle $\beta$ as function of the azimuth angle for the trajectory ID431.</figcaption></figure>

Finally, Fig. 9 shows the optimization objective plotted over the amplitude of the stress variation (rms value of the amplified strain signal) for the tangential force component. This value is proportional to the stress from the torque ripple in the supporting arms and thus an indicator for the fatigue risk (the smaller the better) following the approach of the well known S-N curves, also known as Wöhler lines. With this second objective, ID431 performs very well as a tradeoff in between maximizing power and minimizing cyclic loads. While $C_P$ is increased by a factor 1.86 compared to ID1, the stress is significantly reduced compared to both ID1 and ID217, with only small differences in the performance improvement.

In Table 2 the results of the experimental optimization are summarized. As provided in Table 1, the reference and the optimum ID217 are provided, while the remaining rows are showing trajectories for a good tradeoff between $C_P$ and: pitch angle span (ID273), pitch power (ID342) and stress (ID431), respectively.

<table><caption>Table 2: Summarized results of the experimental optimization.</caption><thead><tr><th>ID</th><th>C<sub>P</sub></th><th>C<sub>P</sub><br>improvement<br>relative to<br>unpitched</th><th>pitch span<br>degrees</th><th>pitch power<br>relative to generator's power</th><th>stress<br>relative to unpitched</th></tr></thead><tbody><tr><td>1 (unpitched)</td><td>0.158</td><td>1</td><td>0</td><td>0</td><td>1</td></tr><tr><td>217</td><td>0.311</td><td><strong>1.97</strong></td><td>20</td><td>0.025</td><td>1.18</td></tr><tr><td>273</td><td>0.256</td><td>1.62</td><td><strong>6</strong></td><td>0.008</td><td>0.96</td></tr><tr><td>342</td><td>0.288</td><td>1.82</td><td>14</td><td><strong>0.016</strong></td><td>1.01</td></tr><tr><td>431</td><td>0.294</td><td>1.86</td><td>25</td><td>0.036</td><td><strong>0.80</strong></td></tr></tbody></table>

This preliminary analyze of the results clearly shows the potential of Exp-O even though the full data set has not yet been fully exploited. The hence unpublished results are currently processed and will be published (first authors Leidhold & Hoerner) along with the Exp-O framework. Further articles from PhD students involved in the project (Ruiz & Bennecke) are currently in preparation.
## 3.1 Conclusion & Outlook

An experimental platform, involving the flume, the pitch-controlled and instrumented turbine prototype, the data acquisition and processing system, the test benches for pitch actuators and multiple numerical models with about 3000 simulations have been developed and performed during the project.

Preliminary results of the experimental pitch law optimization show the enormous potential of both the method and the application which allowed to double the performance of the flume model. This impressive improvements are obviously only possible on a small scaled turbine (Re 100,000 in average). Full scaled turbines will be constraint by the physical limits for a hydrokinetic turbine similar to the Betz limit, which is not fully applicable as it does not account for free surface effects. The already promising power coefficients allow for an improvement of 50-75% when accounting for current power coefficients of 0.35 to 0.40 as starting point.

The method itself has proven to be very efficient and robust for exploration and optimization of a very complex problem with a multidimensional design space (five parameter) in less than 6 hours with 500 individuals (evaluated parameter sets).

Future work shall make use of the platform and perform further exploration and optimization studies with varying constraints and objectives. An in depth characterization of the turbine, including characteristic curves for different conditions, flow field and hydrodynamic load measurement will also be performed.

## References

(Publications with involvement of the project PI's are printed in **bold**)

[1] Undine network. water level and flow rates for German rivers. URL: https://undine.bafg.de/elbe/pegel/elbe_pegel_magdeburg_strombr.html.

[2] Energies de la mer - flowatt project, 2025. URL: https://www.energiesdelamer.eu/2021/06/08/hydroquest-qair/.

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