Elsevier

Energy

Volume 87, 1 July 2015, Pages 481-489
Energy

Non-dimensional analysis for matching an impulse turbine to an OWC (oscillating water column) with an optimum energy transfer

https://doi.org/10.1016/j.energy.2015.05.018Get rights and content

Highlights

  • Method for matching a non-linear turbine and an OWC is proposed.

  • Size and speed of a turbine can be evaluated for a specific OWC and wave conditions.

  • Size and speed of different kind of turbines have been compared.

Abstract

OWC (Oscillating water column) wave power plants are widely used in ocean wave energy conversion. It is universally accepted that for a good efficiency of the plant, the turbine and the chamber should match each other according to the wave climate site. In this work an alternative methodology is presented for coupling the chamber and the turbine efficiently, carrying out a whole dimensional analysis of the OWC plant.

Basically, the wave data and the chamber geometry are the input data. The behaviour of the chamber is numerically simulated. From the numerical results, the optimum damping could be identified for every wave condition.

Once the optimum chamber damping is found, the objective is to determine which turbine matches this damping. Numerical results, based on the quasi-steady assumption, were used to simulate turbine performance under periodic conditions. The calculation of the diameter is based on the damping caused by the turbine on the OWC, whereas the rotational speed is fixed to maximize the turbine mean efficiency.

Furthermore, this methodology is worked out to compare the size and the rotational speed of different kinds of turbines. Finally, the influence of sea state changes on the parameters of the optimum turbine is also studied.

Introduction

Wave energy may have significant advantages due to the high concentration of energy. OWC (Oscillating water column) power plants are one of the devices most employed in wave energy conversion [1], [2]. This kind of plant has a partially submerged air chamber connected below the water surface to the open sea. The successive sea water waves come into contact with the system, compressing and decompressing the air within the chamber by the periodic motion of the oscillating free surface. This periodic motion creates a bidirectional periodic airflow which it is normally transformed into mechanical energy using a PTO (power take-off system), normally a turbine.

Global efficiency of an OWC plant is obtained as the product of the efficiencies of three energy transformation processes: transformation from wave energy to pneumatic energy, transformation of pneumatic energy into mechanical energy and conversion of mechanical energy into electrical energy. This work is focused on the two former transformations, from wave to mechanical energy.

One of the most important characteristics to consider when designing an OWC is the coupling between the OWC and the PTO. The movement of the water column is obviously affected by the external wave conditions, but also by the characteristics of the PTO. This is a key point when dealing with the coupling because the influence is reciprocal.

The PTO usually used in OWC devices is a self-rectifying turbine. Two different types of self-rectifying turbines are mostly used throughout the world [3]: Wells and impulse. Nevertheless, other types of self-rectifying turbine have made its appearance more recently: the Dennis-Auld turbine [4] or the biradial turbine presented in Ref. [5]. The effect made by the PTO over the OWC is characterized by the relation between the flow rate and the pressure difference across the PTO. This relation, which is linear in case of Wells turbines and non-linear in case of impulse turbines, is called “damping” and determines the effect of the PTO on the OWC. The damping made by the PTO is optimum when the wave energy extracted by the whole system is maximized.

Maximum energy transference from wave to mechanical energy involves that both the turbine and the OWC must work at maximum efficiency. Many studies have been conducted in this regard from a theoretical point of view [6], [7]. These works modelize the performance of the whole device to find the optimum relation between the OWC and the PTO in order to maximize the energy extraction. The results agreed fairly well with reality as it is shown in Ref. [8]. A further step is shown in Ref. [9] where a method is developed to ease the calculations to obtain enough information to tackle the time-modelling evolution, even of a PTO with non-linear characteristics as the authors point out despite of basing the work on linear wave theory. However, these works give useful information about the characteristics that the PTO must have, but do not define the design of the PTO itself.

Alternatively, there are studies mainly focused on the PTO, which usually was a turbine as previously said. For instance, a technique to evaluate the performance of a Wells turbine once the behaviour of the OWC is known is shown in Ref. [10]. Later on [11], introduced an approximative equation to simulate the behaviour of the OWC as well, allowing the prediction of the performance of the whole system. Afterwards, it was successfully applied to evaluate the performance of different turbines under irregular wave conditions [12]. As reported by Refs. [13], this technique could be used to calculate the optimum rotational speed of a turbine once the wave conditions are known, but it does not allow to assess the optimal size of the turbine. A different methodology is proposed in Ref. [14] by using a stochastic model based on linear theory. Following this method, the diameter and rotational speed of a turbine can be evaluated for given wave conditions and chamber geometry. This technique, which was restricted to a PTO with linear characteristics in Refs. [14], was used afterwards in Ref. [15] to evaluate the diameter and rotational speed of a bi-radial turbine (non-linear PTO). However, since the technique requires a linear PTO, the performance of the bi-radial turbine had to be approximated by a linear relation between the flow rate and pressure drop. In Refs. [16], based on numerical and experimental results on the performance of Wells turbines (linear PTO), a selection diagram for Wells turbines was suggested.

In this work, the authors have confronted the same problem: to find a turbine that matches an OWC with an optimum energy transfer. The OWC chamber geometry comes from a previous study where an OWC converter was optimized for an intended site La Guardia Breakwater in northwest coast of Spain. The turbine selected to be installed is an impulse turbine (non-linear PTO), which leads to a complex problem because the authors mean not to simplify the turbine performance as a linear PTO. Finally, although the main aim of the work was to find the most adequate turbine for this installation, it was developed a general method for a quick assessment of the impulse turbine suitable for a specific OWC under different wave conditions.

Simulations in a numerical wave channel (see Ref. [17] for details) were used to determine the OWC performance for different PTO characteristics. Because of the idea of using an impulse turbine as a PTO, a set of slots was used to reproduce the effect of the PTO. This technique, used to simulate the PTO effect upon the OWC, was previously applied by Refs. [8], [18], [19] successfully. The advantage of using CFD numerical results for the OWC performance is to take into account viscous losses in the energy transfer made from the waves to the OWC. The chamber performance predicted by the numerical simulations is the input of the methodology developed here and it has been processed according to a dimensionless analysis to evaluate the turbines main characteristics for specific wave conditions.

Section snippets

Chamber

The input data to develop the analysis explained afterwards is the performance of the OWC chamber under different wave conditions. As previously said the performance of the OWC chamber was calculated by means of a numerical model previously validated in Ref. [17] from which pressure and flow rate in the OWC have been extracted. The simulations were developed assuming the incident wave to be regular. A 2D sketch of the OWC chamber can be seen in Fig. 1.

Applying classical dimensional analysis is

Results

The methodology presented above could be applied to every impulse turbine, both axial and radial. However, the latter presents a special feature which means that the statement regarding the damping is conditional on the design of the turbine. The flow in a radial impulse turbine is centrifugal/centripetal alternatively and because of this the flow pattern is completely different in each operation mode. This means that, to obtain a constant damping relation during the whole performance cycle,

Performance at off-design wave condition

In the methodology explained above, the turbine parameters are set to maximize the energy extraction in specific wave conditions. However, these conditions change frequently, which means that the ΨDopt of the OWC also changes (Fig. 4). It is common among inexperienced at OWC systems to think that working at off-design conditions can be easily negotiated introducing valves and modifying the rotational speed. The aim of this section is to illustrate the complexity of working at off-design

Conclusions

An alternative methodology to match a non-linear turbine to the characteristics of an OWC wave power plant for an optimal energy transfer has been described. The aim of this methodology is to find the basic turbine characteristics for given wave conditions and geometry of the OWC. This problem is usually faced by using approximative equations or neglecting the non-linearity. The main contribution of this work is, without neglecting the turbine non-linearity, to assess both of turbine

Acknowledgments

The authors wish to thank the Spanish International Cooperation Agency and JCyL (group GR57), for the support provided. This work was also partially funded by grant DPI2009-14546-C02-02 from the Spanish Ministry of Science and Innovation.

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