Implementation and validation of a strongly coupled numerical model of a fully passive flapping foil turbine

https://doi.org/10.1016/j.jfluidstructs.2021.103248Get rights and content

Abstract

This paper presents the implementation and validation of a strongly coupled numerical model of a fully passive flapping foil turbine operating at a high Reynolds number. Thanks to a strong fluid–solid coupling strategy, the well known added-mass instability is mitigated while simulating a lightweight flapping foil. The numerical results are first validated in the case of a fixed foil undergoing static stall. The model is then validated with respect to numerical results available in the literature for a heavy flapping foil turbine. Finally, the numerical results of the strongly coupled model are compared to experimental data of a lightweight turbine prototype tested in a confined channel. The numerical results have shown to be in good agreement with the experimental measurements. Indeed, the kinematics and harvesting performances of the turbine prototype have been accurately reproduced by the numerical simulations. Besides, the leading edge vortex shedding observed in the experiments has also been precisely reproduced by the numerical results. The strongly coupled model implemented and validated in the present paper constitutes a useful tool for expanding the parameter space in the search for an optimised design of the fully passive flapping foil turbine.

Introduction

Micro and pico hydropower technologies have shown to be a promising solution in the present energy transition scenario, whose primary goal is to move towards a more sustainable and eco-friendly development. Among those technologies, oscillating foils are innovative devices capable of efficiently harvesting diffuse hydrokinetic energy to produce electricity on a small and local scale. Besides contributing to the development of the hydropower potential of low current sites (with average flow velocities of about 1ms−1), such turbines have a limited environmental impact and thus ensure a better ecological continuity (Xiao and Zhu, 2014).

McKinney and DeLaurier (1981) first introduced the idea of using a two degree of freedom (DOF) oscillating foil as an energy harvesting device. They showed that a foil performing a translational motion – heaving – and a rotational motion – pitching – in the cross-section of a flow is capable of harvesting its kinetic energy. Originally, the first concept studied is that of an active flapping foil, in which the two DOF are kinematically constrained. Since then, many numerical and experimental studies have been carried out and successfully proved the feasibility of the concept (Xiao and Zhu, 2014, Young et al., 2014, Wu et al., 2020).

Despite the high hydraulic efficiencies of about 40% achieved by the active flapping foil (Kinsey et al., 2011), this first concept has the disadvantage of requiring very complex and costly constraining mechanisms. An alternative solution introduced by Shimizu et al. (2008) and Zhu et al. (2009) consisted of constraining only the pitching motion and leaving the heaving motion free. The so called semi-passive flapping foil would have the advantage of being less complex from a technological point of view, while proving to be as efficient as the fully activated devices. However, reports from the first full scale prototype of a semi-passive flapping foil turbine (Stingray, 2002) highlighted prohibitively high maintenance costs related to the pitching activation system.

Finally, Peng and Zhu (2009) suggested the much simpler concept of a fully passive flapping foil turbine. Through a numerical study, they showed that an elastically mounted 2-DOF foil could perform self-sustained oscillations in a suitable way for energy harvesting purposes. In this configuration, the foil undergoes deep dynamic stall and shed a leading edge vortex (LEV) twice during one period of oscillation, preventing the system from a chaotic behaviour and giving raise to limit cycle oscillations instead.

Later, Zhu (2012) and Wang et al. (2017) refined the numerical findings of Peng and Zhu (2009) under more realistic conditions. Very recently, those results where experimentally validated by Duarte et al. (2019). They provided conditions on the structural parameters of the system in order for its dynamic behaviour to be suitable for energy harvesting.

An extensive numerical optimisation of the structural parameters of a fully passive flapping foil turbine has been performed by Veilleux and Dumas (2017). Varying the mass–spring–damper properties for both DOF of a NACA15 foil with a fixed pitching axis located at one third of the chord length from the leading edge, they found an optimised configuration with a hydraulic efficiency of 33.6%. However, their numerical model was implemented with a weak fluid–solid coupling strategy. The parameter space for the numerical optimisation conducted by Veilleux and Dumas (2017) was then constrained by a lower limitation of the foil mass, otherwise their simulations would diverge due to the well known added-mass instability (Causin et al., 2005, Förster et al., 2006).

Those promising numerical results were later verified by Boudreau (2019), who performed the very first experimental study on the subject. He also conducted a numerical study on a new oscillatory behaviour of a fully passive flapping foil. His findings suggested that a high inertia system could operate without undergoing deep dynamic stall – and thus without shedding LEV – leading to substantially higher efficiencies. The feasibility of such a heavy flapping foil turbine has yet to be verified experimentally.

In summary, great advances have been achieved both numerically and experimentally on the development of the fully passive flapping foil turbine. Yet relatively little is known about the performances of the system equipped with a lightweight foil. Aside from the very recent experimental study carried out by Duarte (2019), no numerical model has yet been implemented to that end.

In such context, this paper presents the implementation and the validation of a numerical model capable of simulating a lightweight fully passive flapping foil. Thanks to a strong fluid–solid coupling strategy, the model will constitute a useful tool for expanding the parameter space in the search for an optimised design of the turbine. In what follows, Section 2 starts by introducing the physical parameters and equations that govern the dynamics of a fully passive flapping foil turbine; the implementation of the numerical model in order to solve the governing equations is then presented. Finally, the results of the different steps of validation of the numerical model are discussed in Section 3.

Section snippets

Problem statement

Let x be the direction of a uniform flow of free stream velocity U. A fully passive flapping foil turbine interacting with that flow can be modelled by a rigid blade performing a 2-DOF oscillatory motion: the heaving motion in the y direction, and the pitching motion about the axis (P,z). A 2D model of the system on the plane (P,x,y) is proposed in Fig. 1.

A symmetric foil of chord length c is elastically mounted with springs and dampers for each DOF. The viscous damping coefficient and

Results and discussion

The results of the validation of the strongly coupled numerical model of a fully passive flapping foil turbine are presented and discussed in this section. First, the numerical results are validated in the well documented case of a fixed foil undergoing static stall followed by vortex shedding. Second, the accuracy of the model is validated in the simulation of the optimised design of a heavy flapping foil turbine proposed by Veilleux and Dumas (2017). Finally, the validity of the present model

Conclusion

Fully passive flapping foil turbines are a promising solution in terms of small and local scale electricity production. They can contribute to the environmentally friendly exploitation of the diffuse hydrokinetic energy from low current sites. Deprived of technologically complex activation and constraining mechanisms, their behaviour are fully induced by the fluid–structure interactions with the flow. Therefore, the design of a fully passive flapping foil turbine requires an extensive knowledge

CRediT authorship contribution statement

Leandro Duarte: Methodology, Formal analysis, Investigation, Writing - original draft. Guilhem Dellinger: Methodology, Writing - review & editing. Nicolas Dellinger: Conceptualization, Validation. Abdellah Ghenaim: Resources, Project administration. Abdelali Terfous: Validation, Supervision.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research project is supported by University of Strasbourg, France, ICube laboratory, France and INSA Strasbourg, France . The authors would like to show their gratitude to the colleagues from the lab who provided insight and expertise that greatly assisted the research.

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