Implementation of Tidal Stream Turbines and Tidal Barrage Structures in DG-SWEM

Abstract

There are two approaches to extracting power from tides – either turbines are placed in areas of strong flows or turbines are placed in barrages enabling the two sides of the barrage to be closed off and a head to build up across the barrage. Both of these energy extraction approaches will have a significant back effect on the flow, and it is vital that this is correctly modelled in any numerical simulation of tidal hydrodynamics. This paper presents the inclusion of both tidal stream turbines and tidal barrages in the depth-averaged shallow water equation model DG-SWEM. We represent the head loss due to tidal stream turbines as a line discontinuity – thus we consider the turbines, and the energy lost in local wake-mixing behind the turbines, to be a sub-grid scale processes. Our code allows the inclusion of turbine power and thrust coefficients which are dependent on Froude number, turbine blockage, and velocity, but can be obtained from analytical or numerical models as well as experimental data. The barrage model modifies the existing culvert 1Corresponding author: [email protected] model within the code, replacing the original cross-barrier pipe equations. At the location of this boundary, velocities through sluice gates are calculated according to the orifice equation. For simulating the turbines, a Hill Chart for low head bulb turbines provided by Andritz Hydro is used. We demonstrate the implementations on both idealised geometries where it is straightforward to compare against other models and numerical simulations of real candidate sites for tidal energy in Malaysia and the Bristol Channel. INTRODUCTION Tidal energy is a promising source of clean and predictable energy. To extract power from the tide the flow needs to pass through a turbine. This can either be a tidal stream turbine or a turbine in a barrage where the flow may be restrained to allow a head to build up. In the latter case it is obvious that there is a substantial interaction between energy extraction and the tidal hydrodynamics but even in the former case it is necessary to apply a force to the flow in order to generate power. Understanding 1 Copyright c © 2019 by ASME these interactions is crucial for evaluating the power output and environmental impact. To understand these interactions it is necessary to model the basin scale hydrodynamics. Placing tidal turbines or barrages in models at this scale is tricky because of the wide range of length scales involved (see Fig. 5 of [1]). Indeed, there may be some inherent inconsistency, since the flow through turbines is highly three-dimensional and this makes it difficult to conserve mass, momentum and energy fluxes correctly in a 2D or 3D model with a small number of sigma layers. In this paper we examine the inclusion of both tidal turbines and tidal barrages in DG-SWEM [2, 3]. This numerical model solves the shallow water equations which are generally used for modelling tidal hydrodynamics. The model is based on ADCIRC (ADvanced CIRCulation model) and solves the equations using a discontinuous Galerkin solver [4]. The first half of this paper presents the implementation of tidal stream turbines and presents a number of test cases. The second half does the same but for tidal barrages. TIDAL STREAM TURBINES Methodology Several approaches exist for implementing tidal stream turbines in large scale numerical models (see for instance [5]). One approach is to use enhanced bed friction to represent the thrust from the turbines. A disadvantage of this approach is that it creates ambiguities in terms of the length-scales of the process and exactly what thrust and energy are lost. An alternative approach was developed by Draper [6] who modelled the energy loss as a line sink within the model. Thus a head difference was introduced across the turbine row to represent the energy lost and thrust applied to the turbines. The model was found to be consistent with laboratory measurements [7]. Whilst this approach does reduce the turbine and the wake mixing to a subgrid scale process, it has the advantage of making it relatively easy to track where the energy is going and does not require very high mesh resolution in the turbine region. This approach was implemented in the discontinuous Galerkin version of ADCIRC by Serhadlıoğlu [8]. She used actuator disc theory to represent the turbines following [9]. Her model has been widely used (e.g. [10–12]). The present work takes the line-discontinuity approach and implements this in DG-SWEM. In contrast to Serhadlıoğlu’s turbine implementation, the one discussed in this paper is based on an input of power and thrust coefficient curves, which in turn can be obtained from any external analytical or numerical model as well as from experimental data. This leads to more flexibility in terms of turbine model selection. 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