Elsevier

Ocean Engineering

Volume 204, 15 May 2020, 107273
Ocean Engineering

Analytical formula for estimation of surface wave power with application in the coastal ocean of Thailand

https://doi.org/10.1016/j.oceaneng.2020.107273Get rights and content

Highlights

  • Analytical formula based on parameterized wave spectrum for wave power estimation.

  • Accuracy and precision improving around 15% and 5% from traditional approach.

  • Synthetic tests showing applicability of the formula in intermediate to deep water.

  • Tests with reliable field datasets confirming the capability of the new formula.

  • Application of the new formula for its utility in evaluating wave power potential.

Abstract

Two common techniques in determining surface wave power include a full wave spectrum integration and a representative wave approach. Under the concept of spectral wave parameterization, a new estimation formula is introduced in this study to capitalize the advantages of both the numerical method and the closed-form solution. The formula was verified using synthetic wave data and its applicable condition is recommended to be in the upper-intermediate to deep water environment. Validation against reliable field wave data showed that the new solution can outperform the representative wave approach by allowing higher estimation performance around 5%–15% on average. The new formula was applied for a practical estimation of wave power in Thailand. While the resulting wave power was found to be relatively low around 0.3 to 1.5 kW/m, the utility of the new solution can be warranted according to its consistency with the full numerical technique. This encouraging outcome is achievable as the deviation of the resulting estimates is limited and symmetric about a neutral mean. In summary, the superiority of the new analytical formula can be attributed to its dependable replication of typical random wave field and its adaptability to irregular wave energy distribution in the nature.

Introduction

Alternative energy from the ocean contributes less than 0.1% of the renewable energy, with most of the present development projects found in European countries (Mofor et al., 2014, Sawin et al., 2015). Tidal power is to date the most advanced topic in the field since tides are deterministic and feature greatest magnitudes close to the shoreline, adding some reliability and practicality to the energy conversion (e.g. Defne et al., 2011, Lawless and Rodger, 2013, Work et al., 2013). The harvest of energy from irregular surface waves usually has to be performed in a harsh environment under some random conditions. State-of-the-art technologies have recently been developed to allow conversion of renewable energy from the waves which are induced everywhere in the ocean which covers more than 70% of the earth surface (e.g. Sørensen and Russell, 2006, Thomson et al., 2011).

Ocean wave energy is associated with relatively high spatial and temporal variations but, despite being a debatable topic, is more persistent than wind and solar energy (Falnes, 2007, Reikard, 2013). A feasibility study in a region always involves characterization and mapping of the available energy as initial tasks, allowing optimization for the energy converting scheme, and minimizing risk in the operation (Iglesias and Carballo, 2011). Magnitudes, time periods, and propagation directions of waves are the primary factors required in the estimation of wave energy flux and its total, non-directional quantity that represents the local wave power density (Jacobson et al., 2011). Advanced numerical models have also been introduced for predicting these parameters, mainly to overcome spatial limitation in launching field wave measurement campaigns (e.g. Arinaga and Cheung, 2012, Reikard et al., 2015).

A numerical solution can be executed to integrate energy fluxes contributed by random waves with different magnitudes and frequencies. This method is usually applied where wave energy spectra are available in the target area (e.g. van Nieuwkoop et al., 2013, Gonçalves et al., 2014). The other common implementation relies on the assumption of a narrow-banded wave field with some nominal leading waves (e.g. Hughes and Heap, 2010). This latter technique, commonly referred to as a representative wave approach, allows a simple closed-form equation for the computation of the total energy flux of the wave field. For deep water waves, the approach can further be simplified and only the nominal wave height and wave period are required in the estimation (e.g. Cornett et al., 2008, Fernández et al., 2015).

Scarcity of quality spectral wave data often leads to an application of the representative wave approach which offers an ease of use and practicality. Defne et al. (2009) performed a regression analysis and found that a reduction factor of 0.61 was appropriate in the estimation where the significant wave height and mean wave period were the nominal wave parameters. The adjustment may alternatively be achieved via an introduction of an adjusting sea state parameter derived from the zeroth and first negative moments of the frequency spectrum or the weighted average of the wave energy (e.g. Boronowski et al., 2010). Analyses based on field wave data, however, reveal that this conversion technique could lead to an underestimation of wave power by up to 18% since the wave power computed using the nominal wave does not match the actual energy spectrum in a random sea (Cahill and Lewis, 2014).

In the present study, the ultimate goal is to introduce a novel analytical formula for the estimation of wave power density. The derivation is first illustrated for the new solution which appears in closed form for practicality while considering incremental components of random wave energy similar to applying a numerical technique. Using reliable spectral wave data, the formula is verified and validated to assure its estimation capability, in comparison to the representative wave approach. An application of the new solution is subsequently demonstrated by estimating wave power potential along the coasts of Thailand. Beside the demonstration, an outlook of wave power potential can be obtained for feasible sites in the country where, to the authors’ knowledge, no characterizing or mapping of the local wave power has ever been attempted before. Based on all of the results, conclusions of the study are finally drawn to summarize underlying principles, estimation performance, and practical utilities of the new formula.

Section snippets

Estimation of wave energy flux and wave power density

The underlining physics of surface water waves and associated energy are reviewed briefly here since there are implications for estimation of wave power density. Several techniques commonly used in the estimation are reviewed as later on they will be compared to the new formula developed in the present research effort.

New analytical solution

Development of the new solution for estimation of wave power density based on the wave spectrum concept is described in this section. The keys in the problem formulation and the evaluation of the solution are illustrated for the first time below.

Verification of the new formula

The derivation of the new analytical formula introduced above involves a few assumptions and approximations. In this section, their implications are investigated focusing on behaviors of a few important terms and the final solution. First of all, the approximate wave dispersion relation in Eq. (19) needs to be investigated as it is applied throughout the formulation. Fig. 4 illustrates a non-dimensional wave number kok as a function of the relative water depth (kh), comparing the values

Validation

In the previous section, the new solution and associated terms are verified analytically and against synthetic data to explore its capability and applicable range. Here, the formula is to be validated using measured wave data from two reliable sources which will help disclose its performance and sensitivity under actual uncertainty and randomness of the wave field.

Practical application

The new formula is employed for practical use here for the estimation of wave power in the coastal ocean of Thailand. The attempt was achieved at 16 locations in the Gulf of Thailand and the Andaman Sea, respectively on the east and the west of the nation’s coastal ocean as shown in Fig. 11. Specific details including depths and coordinates of the locations can be found in Table 3.

The estimation was started by first modeling wind direction and speed over the entire region during May 2017 to

Conclusion and discussion

Ocean waves have recently been introduced as a promising source of alternative energy considering their abundance and reliability. For the estimation of wave power, two traditional methods are often applied including a full wave spectrum integration and a representative wave approach based on some nominal wave parameters. These two options are rather different in terms of implementation as the former relies on a numerical technique while the latter offers a simple closed-form analytical

CRediT authorship contribution statement

Chatchawin Srisuwan: Conceptualization, Methodology, Formal analysis, Validation, Writing - original draft, Writing - review & editing. Payom Rattanamanee: Resources, Investigation, Project administration. Winyu Rattanapitikon: Writing - review & editing, Supervision, Funding acquisition.

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.

Acknowledgments

This research project was supported by the Thailand Research Fund (TRF) and the Office of the Higher Education Commission (OHEC), Thailand as part of the research contract number MRG6180102. The authors are gratified by the kind assistance from all senior scholars and supporting staffs at the TRF and the OHEC agencies.

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