# Experimental Determination of the Hydrodynamic Loading on Vertical-Axis Cross-flow Tidal Turbines with Blade Embedded Autonomous Sensors

Stefan Hoerner, Timo Bennecke, Wolf Iring Kösters, Karla Ruiz-Hussmann, Adhithiyan Jayaprakash, Shokoofeh Abbaszadeh, Jeffrey A. Tuhtan, Pierre-Luc Delafin, Cyrille Bonamy, Roberto Leidhold

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To cite this version:

Stefan Hoerner, Timo Bennecke, Wolf Iring Kösters, Karla Ruiz-Hussmann, Adhithiyan Jayaprakash, et al.. Experimental Determination of the Hydrodynamic Loading on Vertical-Axis Cross-flow Tidal Turbines with Blade Embedded Autonomous Sensors. 2025. hal-05197527v2

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Preprint submitted on 5 Oct 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Experimental Determination of the
Hydrodynamic Loading on Vertical-Axis
Cross-flow Tidal Turbines with Blade Embedded
Autonomous Sensors

Stefan Hoerner<fnref n="1" />,², Timo Bennecke², Wolf I. Kösters²,³ Karla

Ruiz-Hussmann<fnref n="1" />,², Adhithiyan Jayaprakash⁴, Shokoofeh Abbaszadeh⁴, Jeffrey

A. Tuhtan³, Pierre-Luc Delafin<fnref n="1" />, Cyrille Bonamy<fnref n="1" />, and Roberto Leidhold⁴

¹ Laboratoire des Écoulements Géophysiques et Industriels (LEGI), G-INP, CNRS, Université Grenoble-Alpes, Grenoble, France,

stefan.hoerner@universite-grenoble-alpes.fr,

² Institute of Fluid Dynamics and Thermodynamics, Otto-von-Guericke-University Magdeburg,
Germany

³ Department of Computer Systems, Tallinn University of Technology (TalTech), Tallinn, Estonia

⁴ Institute of Electrical Power Systems, Otto-von-Guericke University Magdeburg, Germany

**Abstract.** Hydrokinetic vertical-axis cross-flow turbines (CFTT) can efficiently harness tidal and ocean currents but are prone to vibrations and fatigue due to complex flow dynamics, especially at low rotational speeds where blade stall occurs. To study these effects, a lab-scale rotor was developed with strain gauges on the support structure and embedded miniaturized sensors in the blades. These sensors measure accelerations, rotational speed, pressure, and magnetic fields, capturing blade bending, torsion, and overall rotor motion. They can be calibrated in situ and can serve as a plug-and-play system for advanced rotor monitoring in future designs.

**Keywords:** Tidal energy, Vertical axis turbines, Cross-flow turbines, Experiments, Fluid-structure interactions, complex instrumentation

This preprint corresponds to the author version and has not undergone
peer review or any post-submission improvements or corrections.

# 1 Introduction

The first mature ecologically compatible technologies based on hydrokinetic energy converters are now available for tidal streams. In recent years, extensive field tests have been conducted successfully, and a first 17.5 MW pilot farm is currently being built in the English Channel<fnref n="1" />. However, the available sites remain limited [1],[4], and the power density and energy conversion efficiency of hydrokinetic turbines are generally low [11]. Vertical-axis cross-flow tidal turbines (CFTT) promise higher power density per

<footnote n="1">¹ for example see www.hydroquest.fr/en/flowatt-en/</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 1. (left) Analytical model of the angle of attack αb (black dashed). (right) Numerical 2D simulations (OpenFOAM, URANS, k-ω-SST model) ([8] CC BY 4.0)</figcaption></figure>

area than classic axial tidal turbines, which are often referred to as horizontal-axis turbines. For wind turbines, it has been shown numerically and experimentally that a higher power density can be achieved by an order of magnitude [5]. Due to fluid mechanical similarity laws, it can be assumed that this also applies to tidal turbines. However, CFTTs pose technical challenges as a result of their rotation axis being perpendicular to the flow. The rotor blades are subject to a continuous periodic change in the angle of attack αb [rad], as shown in Fig. 1 (left). An analysis using velocity triangles results in a non-sinusoidal periodic curve, which is given by (1). The values of αb depend on the operating point, which is expressed by the dimensionless tip speed ratio λr (2).

$$ \alpha_b = \arctan \left( \frac{\sin \theta_r}{\lambda_r + \cos \theta_r} \right) \qquad (1) $$

where θr [rad] is the azimuth angle of the rotor (Fig. 1 (left) for the coordinate system).

$$ \lambda_r = \frac{\omega_r R}{v_\infty} \qquad (2) $$

where ωr is the angular velocity of the rotor in [rad/s] and R is the turbine radius in [m], whose vector product reflects the tangential velocity, and v∞ [m/s] is the velocity of the free flow. Tidal turbines are typically operated at λr ≈ 2, as they have relatively solid construction due to the high density of water compared to wind turbines. This requires a low λr value for the optimal operating point [14]. The low value λr in turn leads to very high αb values (30° for λ=2), which are significantly above the static stall angle of a common rotor blade profile. However, the rotor dynamics and the resulting high flow instabilities, expressed in high reduced frequencies, lead to an increase in the dynamic stall angle. In earlier work [8], this angle was shown to reach well over 20° in a common turbine design as presented in [9]. Therefore, simple turbine models based on static profile data and calculations allow for only a very rough estimate of the mechanics of such turbines, and the rotor dynamics are key for the turbine characteristics. Numerical models show high values for αb and dynamic blade separation in the upstream region of the rotor (Fig. 1 (right)), which are comparable to analytical predictions, while αb in the downstream region of the turbine is significantly
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** (left) Instrumentation of the turbine flume model. (middle) Experimental model in the lab flume. (right) Power uptake is realized with a velocity controlled servo drive.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Technical drawings and dimensions in mm of the microtag devices (from [15]) smaller due to the wake of the upstream region of the rotor in the flow field [6]. In summary, it can be said that the periodic angle change and flow separation generate alternating hydrodynamic loads that lead to vibrations and, in the worst case, to failure of the rotor structures. CFTTs have long been known for their vulnerability to fatigue failure [10]. However, fluid-structure interactions have been studied in less detail and most studies are numerical in nature [12]. Therefore, we have developed a flume-scale turbine model using extensive weak coupled fluid-structure interaction simulations by employing 2D CFD simulations mapped to 3D FEA [3] with suitable profile shapes [12] equipped with strain gauges [2] to assess hydraulic loads and experimentally analyse fluid-structure interactions. In this study, we present an autonomous microsensor system embedded in the blades of the flow channel model. The aim is to demonstrate a calibration process and the benefits and limitations of the current system, which represents a step forward in our development of a cost-effective measuring instrument for academic and industrial applications in the field of fluid-structure interaction.</figcaption></figure>

# 2 Methodology

## 2.1 General instrumentation setup

The instrumentation and measurement concept of the test setup is shown in Fig. 2. The turbine is a straight-bladed Darrieus CFTT with three blades and mountings at both blade tips. The design is based on an aluminum skeleton with 3D-printed fairings. The NACA0018 rotor blade profiles are slightly curved in
<table><caption>**Table 1.** Technical specifications microtags [15]. The sensor measures absolute pressure, 3D acceleration, angular velocities and magnetic fields.</caption><tr><td><strong>Pressure sensor</strong></td><td>MS5837-2BA (TE Connectivity)</td><td></td></tr><tr><td>pressure range</td><td>0-2000</td><td>mbar</td></tr><tr><td><strong>Inertial Measurement Unit (IMU)</strong></td><td>BMX160 (Bosch Sensortech)</td><td></td></tr><tr><td>linear acceleration range</td><td>16</td><td>g [9.81 m/s<sup>2</sup>]</td></tr><tr><td>linear acceleration accuracy</td><td>0.01</td><td>g [9.81 m/s<sup>2</sup>]</td></tr><tr><td>gyroscope data range</td><td>2000</td><td>deg/s</td></tr><tr><td>gyroscope data accuracy</td><td>+/-2</td><td>deg/s</td></tr><tr><td>magnetic field data range (x,y / z)</td><td>1300 / 2500</td><td>μT</td></tr><tr><td>magnetic field accuracy (x,y / z)</td><td>5 / 10</td><td>μT</td></tr><tr><td><strong>Overall weight &amp; dimensions</strong></td><td></td><td></td></tr><tr><td>weight</td><td>1.6</td><td>g</td></tr><tr><td>length x height x width</td><td>35 x 8.15 x 6.1</td><td>mm</td></tr><tr><td><strong>Data logging frequency</strong></td><td></td><td></td></tr><tr><td>logging rate</td><td>100</td><td>Hz</td></tr></table>

accordance with the circumference of the turbine to take into account the flow curvature resulting from rotation [9]. The diameter and height (blade length) of the turbine are 400 mm, and the blade chord length is 72.5 mm.

All relevant parameters, such as torque, azimuth angle and blade support load, are recorded via microcontrollers on a rotating platform and transmitted by WiFi from a Raspberry Pi 3A + [13] to a desktop computer. The strain measurement system, consisting of five full bridges with strain gauges, enables the determination of individual blade load components. This system records loads synchronously with flow fields, which are currently measured using high-speed particle image velocimetry (PIV). Details were presented in [2]. The turbine scaling was a trade off in between flow similarity (Reynolds number) and confinement (currently 20%). The blade based Reynolds number varies from 50,000 to 100,000 depending on the operation point.

## 2.2 Embedded FSI sensors

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Coordinate system and Z-axis data (gravity) after bias removal and calibration</figcaption></figure>

ing modes or deformation.

The sensors provide linear acceleration, angular velocity and the magnetic field flux density. In addition, a temperature-compensated sensor measures the total

In addition, autonomous embedded FSI microsensors (microtag) were installed in one blade. Technical specifications and drawings are shown in Fig. 3 & Tab. 1. Sensor was installed 11 mm toward the leading edge from the quarter chord of the hydrofoil. Vertical distance from upper blade tip is 150 mm. The opening for the pressure transducer diaphragm has a 2 mm diameter. A silicone tube connects the pressure transducer to blade surface. The cavity for the sensor is filled with ultra-soft silicone to fix the position. The blade stiffness is assured using a metal rod (stainless steel) as reinforcement. Thus it is hypothesised that the modification has negligible influence to the structural characteristics, such as bending
surrounding pressure. The data was streamed via the microUSB connection to the Raspberry Pi on the rotating platform and time-stamped to synchronize the microtag with the other data collected on the turbine.

## 2.3 Bias removal and calibration

The sensor is embedded into the blade and cannot be removed easily. Therefore it is not possible to calibrate the sensor using standard methods such as [7]. As a consequence, the bias from the sensor tilt is removed and the sensor is calibrated based on a reference measurement in the installed position. A series of measurements (N = 2997 samples) without any motion and without water (in air) is performed. The aim of the bias removal is to reorient the coordinate system of the data from the tilted installation towards the rotating reference X, Y, Z (Z is aligned with gravity, origin is the sensor, see Fig. 4). The tilt is determined with linear acceleration. (3) allow to determine the time-averaged values for the tilt angles, pitch $\bar{\rho}_s$, roll $\bar{\phi}_s$, and yaw/azimuth $\bar{\theta}_s$.

$$ 
\begin{align} 
\bar{\rho}_s &= \frac{1}{N} \sum_{i=0}^{N} \left( \tan^{-1} \left( \frac{a_{s,x}}{\sqrt{a_{s,y}^2 + a_{s,z}^2}} \right) \right) \nonumber \\
\bar{\phi}_s &= \frac{1}{N} \sum_{i=0}^{N} \left( \tan^{-1} \left( \frac{a_{s,y}}{\sqrt{a_{s,x}^2 + a_{s,z}^2}} \right) \right) \tag{3} \\
\bar{\theta}_s &= \frac{1}{N} \sum_{i=0}^{N} \left( \tan^{-1} \left( \frac{\sqrt{a_{s,x}^2 + a_{s,y}^2}}{a_z} \right) \right) \nonumber 
\end{align} 
$$

where $\mathbf{a}_s$ is the tilted and raw linear acceleration. $x, y, z$ are the space axes in the reference frame of the tilted sensor. After determination of the tilt angles a 3×3, 3D rotation matrix with Euler angles $\mathbf{R}$ is applied to entire data. Finally the acceleration is calculated using (4) with the time-averaged acceleration magnitude

$\bar{a}_{s,i} = \frac{1}{N} \sum_{j=0}^{N} (a_{s,i,j})$ to obtain the gain factor $q$:

$$ q_a = \frac{\sqrt{\bar{a}_{s,X}^2 + \bar{a}_{s,Y}^2 + \bar{a}_{s,Z}^2}}{g} \quad (4) $$

In a final step, the remaining offset is removed to achieve zero acceleration in X, Y and gravity g in Z. Previously calculated tilt angles (3) are used to reorient the angular velocities ($\omega_s$) from the gyroscope. After reorientation, the rotational velocity n (sec. 2.5) is used to determine the gain $q_\omega$ using (5).

$$ q_{\omega} = \frac{\frac{n}{60s} \cdot 360^{\circ}}{\bar{\omega}_{s,Z}} \quad (5) $$

with n the rotational speed (30 rpm) of the turbine. The gyroscope offset is calculated from the calibration data set, as it has no motion and it is known that $\omega_{b,i}=0$. The total bias removal and calibration method is given by eq. 6.
$$ 
\begin{aligned}
\mathbf{a} &= \underline{\underline{\mathbf{R}}} \times \mathbf{a}_s \cdot q_a - \mathbf{o}_a \\
\omega_b &= \underline{\underline{\mathbf{R}}} \times \omega_s \cdot q_\omega - \mathbf{o}_\omega
\end{aligned} 
\qquad (6) 
$$

Fig. 4 shows the new reference system and sensor accuracy for acceleration Z (to- wards gravity). Maximal deviation (including outliers) from gravity is of ±0.04 m/s² (relative deviation ±0.42%, standard deviation 0.012 m/s², relative stan- dard deviation 0.12%). This corresponds to the manufacturer's technical data sheet values (tab. 1) and shows the very high accuracy of the sensor system.

## 2.4 Pressure data

The microtag's pressure sensor measures the total pressure, which is of limited use for the current application as it includes the static pressure. To remove this effect, the static pressure was calculated and subtracted from the data to obtain only the remaining dynamic pressure share, as shown in eq. 7.

$$ p_{\text{dyn}} = p_{\text{total}} - (p_{\text{ambient}} + \rho_{\text{water}}gh) \qquad (7) $$

with water density $\rho_{\text{water}}=1000 \text{ kg/m}^3$ and averaged vertical distance from wa- ter level at flume inlet to sensor $h=300 \text{ mm}$. This hydrostatic share is $p_{\text{hydro}}= 2452.5 \text{ Pa}$. Ambient pressure ($p_{\text{ambient}}=106401.66 \text{ Pa}$) is the ensemble average from calibration data. It includes the offset. Other terms for time-varying pres- sure inducing quantities like velocity gradients and added mass are neglected.

## 2.5 Measurement set up

A series of measurements has been carried out at $n=30 \text{ rpm}$ to demonstrate the usefulness of the system. This corresponds to $\lambda_r=1.01$ with a power coefficient $C_P=0.0516$ for a flume velocity $v_\infty=0.62 \text{ m/s}$. The operating point was cho- sen arbitrarily. However, at 30 rpm, a large angle of attack of the rotor blades and massive flow separation with strong fluid-structure interactions are likely to occur during each revolution. This was considered advantageous for the demon- stration of the sensors. Additional rotor velocities will be considered in future. Turbine best point is at $\lambda_r=2.02$ with $C_P=0.22$. The period for one rotation is 2 s (200 samples). Data was captured for 90 s leading to $N=9004$ samples (microtag captures at 100Hz) and $N=90040$ (rotating platform at 1 kHz). The microtag data is interpolated to 1kHz and synchronized. Finally 34 full rotor revolutions are assessed.

# 3 Results & discussion

Tab. 2 shows the resulting measurement data. A cumulative phase lag of 2.2°

<table><caption>**Table 2.** Measurement data for 30 rpm, $\lambda = 1.1$, $C_P = 0.05$; if not expressed otherwise, the median value for 34 rotations is shown.</caption><thead><tr><th></th><th>Symbol</th><th>Unit</th><th>X</th><th>Y</th><th>Z</th></tr></thead><tbody><tr><td>acceleration</td><td>a</td><td>[m/s<sup>2</sup>]</td><td>-1.833</td><td>0.010</td><td>9.623</td></tr><tr><td>rotational speed</td><td>ω</td><td>[°/s]</td><td>-16.71</td><td>12.53</td><td>-179.30</td></tr><tr><td>dyn. pressure</td><td>p</td><td>[Pa]</td><td>-1809.51 (min)</td><td>-547.03 (median)</td><td>405.09 (max)</td></tr></tbody></table>

per rotation is found for the microtag compared to the rotating platform. A simple adjustment method by adding the 2.2° for each revolution is applied for
<figure><img src="image_7.png" /><figcaption>Fig. 5. Linear acceleration in radial direction (X-axis) which corresponds to the centrifugal load. The acceleration shows repeatable pattern of the three blades.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6. Angular speed of the Z-axis of the sensor. The gyroscope data shows the rotational speed of the rotor which median is -179.30°/s which is equivalent to 29.88 rpm.</figcaption></figure>

compensation. It is hypothesised that this phase lag as well as other inaccuracies origin from misalignment of the sensor (Z) compared to the rotor rotation axis. This leads to a tumbling motion compared to the rotor rotation for each rotation comparable to the obliquity of the earth ecliptic. For some of the parameters, a reference value is known. For the gyroscope in Z ($\omega_{b,Z}$) a median of 179.3° is measured ($\bar{n}$=29.88 rpm). The drive system encoder (power take off) provides a rotational velocity $\bar{n}$=30.17 rpm. This leads to an absolute difference to the reference of -0.29°/s (-0.96% relative). Centrifugal acceleration ($a_X$) can be calculated for the distance of the sensor to the rotation axis $R$=0.19 m. The reference value is $a_X$=1.90 m/s². Measured median is 1.833 m/s² (absolute difference 0.067 m/s² = 6.4%). Finally $a_Z$ has a reference of 9.81 m/s². The measured median is of 9.623 m/s² (absolute difference -0.187 m/s², -1.91%).

Fig. 5 shows the centrifugal acceleration (X-axis). A repeatable pattern is visible for each 120°. It includes not only the tumbling from misalignment but also blade bending due to hydrodynamic loads. However it should be noted that only one blade is shown. Measured data shows that alternating loads from the two other blades impact also the one with embedded sensors. The difference in the magnitudes of the three load alternation phases reflects this effect.

Angular velocity from the gyroscope is shown in fig. 6. This velocity is equivalent to $n$=29.88 rpm or $\omega_{b,Z}$=179.3°/s (see difference from expected value above).

The pattern of the three blades becomes visible again while the rotational speed at the shaft ($\omega_r$) remains almost at constant speed. This means that the torque
<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Pressure over the azimuth angle for one turn (orange) and 34 turns (blue). ripple translates into a torsion of the runner which quantifies in the variation of the angular blade speed in Z. Pressure curves (fig. 7) show a significant decrease on the suction side for the first 55° and subsequent stalling of the profile with chaotic variations per turn. The curve stabilizes at 100° and forms a plateau for 150°. It finally increases from 250° to the maximum amplitude at 0° (pressure side). The slope is very useful for validation of 2D CFD simulations of such turbines as pressure is largely uninfluenced by 3D effects.</figcaption></figure>

# 4 Conclusions & outlook

An embedded microsensor to capture the hydraulic loading and blade kinematics is placed in a flume scaled model of a CFFT. It measures pressure, accelerations and angular velocities in space.

A case adapted sensor calibration method is proposed and validated on a show-case dataset. Results show that the sensors provide insights in turbine deformation (torsion, bending) and show well-known load ripple from alternating loads. Pressure curves are from great interest for a better understanding of the FSI. Future work will investigate the data in more depth by using spectral and time-series analysis and by investigation of FSI effects on blade level for an entire characteristic curve. The spatial resolved free surface level in the rotor region will also be accounted when calculating dynamic pressure in future. This will lead to very important data for validation of 2D simulations for such turbine types. Pressure data combined with accelerations and angular velocities provide a rich database for the FSI characterization of such machines.

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