• Energy Research

Abstract A new white-light volumetric flow measurement technique is presented that can be used in large-scale facilities. The technique enables large volumes to be measured with high temporal and spatial resolution and without the need for a class-4 laser. This LED-based Lagrangian particle tracking velocimetry is demonstrated by measuring the tip vortex formation and the near wake of a 1.2 m diameter tidal turbine in a 25 m diameter, 2 m deep tank. Seven streamwise-distributed volumes of interest are combined, each 334 mm long, 244 mm wide and 140 mm deep, reaching up to one diameter downstream of the turbine. The system does not require re-calibration when moved. By assuming a periodic flow field, a phase-averaged flow field was reconstructed with a temporal resolution of 3.9 ms and a spatial resolution of 5.4 mm. The large volume and high time and spatial resolution could enable key research questions to be addressed on high-Reynolds-number flows and could provide valuable benchmark data for numerical model development and code validation. Graphical abstract

Model-scale testing might suffer from blockage effects due to the finite dimensions of the test section. Measurements must be corrected to predict the forces that would have been measured in unconfined conditions. Blockage corrections are well-established for streamlined and bluff bodies, while more data is needed to develop corrections for bodies that generate both high lift and large wakes. In this work, towing tank and water tunnel tests of two-dimensional circular arcs are employed to develop a correction for a blockage ratio, i.e. the ratio of the frontal area of the geometry to the cross-sectional area of the test section, up to 0.2477. Experiments are conducted at positive incidences between the ideal angle of attack and deep-stall at transitional Reynolds numbers from 53 530 to 218 000. The results show that a linear blockage correction can be devised for the whole range of tested blockage ratios. Furthermore, the critical angle of attack and Reynolds number at which the force crisis occurs is independent of the blockage ratio. These results may allow extending the range of model sizes that can be tested in water and wind tunnels and may contribute to the accurate accounting of blockage effects at transitional Reynolds number conditions.

Detached eddy simulation is employed to investigate the wake development downstream of the rotor of an axial-flow turbine and its dependence on the tip speed ratio. In this study, we found that the trend of the momentum deficit as a function of the rotational speed shows opposite directions in the near wake and further downstream. While the momentum deficit in the near wake increases with the rotational speed, it decreases further downstream. For instance, we found that at six diameters downstream of the rotor the streamwise velocity in its wake recovered to about 30% of its free-stream value at the lowest simulated tip speed ratio of 4, while its recovery was equal to about 65% at the largest tip speed ratio of 10. This is due to the earlier breakdown of the tip vortices. The results of the computations demonstrate indeed that mutual inductance phenomena between tip vortices, promoting pairing events and the eventual instability of the helical structures, occur at shorter downstream distances for higher values of tip speed ratio. Wake instability enhances the process of wake recovery, especially due to radial advection. Therefore, higher rotational speeds do not promote wake recovery through more intense tip vortices, but through their greater instability. Implications are important, affecting the optimal distance between rows of axial-flow turbines in array configurations: the operation at higher rotational speeds allows for smaller distances between turbines, decreasing the cost and environmental impact of farms consisting of several devices.

Abstract Tidal turbines operate in a highly unsteady environment, which causes large-amplitude load fluctuations to the rotor. This can result in dynamic and fatigue failures. Hence, it is critical that the unsteady loads are accurately predicted. A rotor's blade can experience stall delay, load hysteresis and dynamic stall. Yet, the significance of these effects for a full-scale axial-flow turbine are unclear. To investigate, we develop a simple model for the unsteady hydrodynamics of the rotor and consider field measurements of the onset flow. We find that when the rotor operates in large, yet realistic wave conditions, that the load cycle is governed by the waves, and the power and blade bending moments oscillate by half of their mean values. While the flow remains attached near the blade tip, dynamic stall occurs near the blade root, resulting in a twofold overshoot of the local lift coefficient compared to the static value. At the optimal tip-speed ratio, the difference between the unsteady loads computed with our model and a simple quasi-steady approximation is small. However, below the optimal tip-speed ratio, dynamic stall may occur over most of the blade, and the maximum peak loads can be twice those predicted with a quasi-steady approximation.

Abstract The ability to accurately predict the forces on an aerofoil in real-time when large flow variations occur is important for a wide range of applications such as, for example, for improving the manoeuvrability and control of small aerial and underwater vehicles. Closed-form analytical formulations are only available for small flow fluctuations, which limits their applicability to gentle manoeuvres. Here we investigate large-amplitude, asymmetric pitching motions of a NACA 0018 aerofoil at a Reynolds number of $$3.2 \times 10^4$$ 3.2 × 10 4 using time-resolved force and velocity field measurements. We adapt the linear theory of Theodorsen and unsteady thin-aerofoil theory to accurately predict the lift on the aerofoil even when the flow is massively separated and the kinematics is non-sinusoidal. The accuracy of the models is remarkably good, including when large leading-edge vortices are present, but decreases when the leading and trailing edge vortices have a strong interaction. In such scenarios, however, discrepancies between the theoretically predicted and the measured lift are shown to be due to vortex lift that is calculated using the impulse theory. Based on these results, we propose a new limiting criterion for Theodorsen’s theory for a pitching aerofoil: when a coherent trailing-edge vortex is formed and it advects at a significantly slower streamwise velocity than the freestream velocity. This result is important because it extends significantly the conditions where the forces can be confidently predicted with Theodorsen’s formulation, and paves the way to the development of low-order models for high-amplitude manoeuvres characterised by massive separation. Graphic abstract

Mitigating the impact of variable inflow conditions is critical for a wide range of engineering systems such as drones or wind and tidal turbines. Passive control systems are of increasing interest for their inherent reliability, but a mathematical framework to aid the design of such systems is currently lacking. To this end, in this paper a two-dimensional rigid foil that passively pitches in response to changes in the flow velocity is considered. Both an analytical quasi-steady model and a dynamic low-order model are developed to investigate the pivot point position that maximizes unsteady load mitigation. The paper focuses on streamwise gusts, but the proposed methodology would apply equally to any change in the inflow velocity (speed and/or direction). The quasi-steady model shows that the force component in any arbitrary direction can be kept constant if the pivot lies on a particular line, and that the line coordinates depend on the gust and the foil characteristics. The dynamic model reveals that the optimum distance of the pivot location from the foil increases with decreasing inertia. For a foil at small angles of incidence, the optimum pivot point is along the extended chord line. This knowledge provides a methodology to design optimum passively pitching systems for a plethora of applications, including flying and swimming robotic vehicles, and provides new insights into the underlying physics of gust mitigation.

There are a wide range of applications in which it is desirable to mitigate unsteady load fluctuations while preserving mean loading. This is often achieved with active control systems, but passive systems are sometimes more desirable for enhancing reliability. This is the case, for example, for wind and tidal turbines, where unsteady loading limits the fatigue life of the turbine and results in power peaks at the generator. Here, we consider the unsteady load mitigation that can be achieved through a foil with a trailing-edge flap that is connected to the foil via a torsional spring. We develop a theoretical model and show that the preload can be tuned to preserve the mean foil loading. The spring moment that maximises the unsteady load mitigation is approximately constant, and the load fluctuation reduction is linearly proportional to the ratio of the flap to the full chord of the foil. We verify this relationship through water tunnel tests of a foil with a hinge at 25% of the chord from the trailing edge. As theoretically predicted, we measure unsteady load mitigation of up to 25%, without any variation in the mean load. In highly unsteady flow conditions, when boundary layer separation occurs, the unsteady load reduction decreases. Overall we conclude that passive trailing-edge flaps are effective in alleviating unsteady load fluctuations and their effectiveness depends on their size relative to the foil.