Once a project location has been determined, the project design process requires a resource assessment with a much higher degree of scrutiny, including an under-standing and quantification of the effects of turbines on the hydrodynamics. These effects can be small scale, where turbines interact with one another directly (i.e., wake effects), or large scale, where the energy extraction from the turbines affects the estuarine scale tidal flows. Vennell et al. (2015) discuss the design process for arrays of tidal turbines and describe these different scales of processes as macro-and micro-effects. They also provide a list of the overall effects from arrays, par-tially reproduced here:
• Power extraction by an array reduces the free stream flow within a channel.
• Optimally tuned turbines in an array are not constrained by the Betz limit because they are not isolated turbines.
• Adding additional turbines to a single row may either increase or decrease the power depending on the channel characteristics.
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• Adding additional rows of turbines to a channel has diminishing returns of power.
As discussed by Vennell (2012), the difference between the behavior of turbines in an array versus in a free stream flow is best illustrated by looking at the source of the array’s energy. For a turbine in a free stream velocity, the optimal power is extracted when the flow through the turbines is reduced down to 1/3. However, for an array with significant flow blockage, the source of energy comes from the change in head induced by the flow blockage, therefore allowing the downstream velocity ratio to approach 1. In essence, the difference in behavior is attributed to the difference between extracting potential energy versus extracting kinetic energy.
Due to the complexity of tidal flows on the scale of an array, designing array layouts and performing the associated resource assessment require the use of numerical simulations of the array. Adcock et al. (2015) discuss the broad range of scales which must be resolved, beginning with turbine blade scales (O(cm)) ending with regional or estuary scales (O(100 km)). While it is not possible to resolve all these scales in a single model, it is necessary to resolve a broad range of scales, which is computationally challenging. Resource assessments utilized for siting considerations require a much higher model resolution than feasibility studies.
Typical grid resolutions are suggested by the IEC TS (2015) to be less than 50 m to capture the spatial variability of the flow. Adding to the difficulty is the fact that the model domain generally must include the full estuary and even extend out to the continental shelf; therefore, variable grid resolution is generally utilized. This may be accomplished using models with unstructured grids, such as the resource assessment for New Jersey by Tang et al. (2014) and for the Tacoma Narrows by Yang et al. (2014). Another study by Ramos et al. (2014) coupled several structured grids with varying grid resolutions in a relatively simple estuary. In another example, Bomminayuni et al. (2012) used a model with an unstructured grid and therefore higher resolution in the region of interest to simulate the flows in tidal channels near Rose Dhu Island, Georgia. Recently, Lewis et al. (2015) simulated the Irish Sea with a structured grid model and determined that model resolution had a significant effect on the local resource assessment. They demonstrated that higher model resolutions (with grid spacing less than 500 m) are required for siting considerations. The Kennebec River of the central Maine coast was found to contain narrow passages where mean tidal energy capacity is sufficient to meet the consumption needs of about 150 homes (Brooks2011).
For larger projects, in order to adequately address array effects, numerical simulations of the project site must include quantification of the effects of turbines on the flow field. The IEC TS (2015) puts the threshold for large projects at 10 MW, or 2% of the theoretical resource using the Garrett and Cummings (2005) method. This may be accomplished with high-order computational fluid dynamics (CFD) models resolving both the turbines and the fluid flow (e.g., Jo et al.2012; Shi et al.2013) or using actuator disk theory (e.g., Harrison et al.2010). However, due to the high computational demands and the necessity to include a large domain to capture the far-field effects, simplified approaches to resolving the effect of turbines Hydrokinetic Tidal Energy Resource Assessments Using Numerical… 107
are generally utilized. While there are several different options for incorporating the impacts of turbines on the flow field into models, they generally have similar approaches (e.g., Defne et al.2011; Work et al.2013; Yang et al. 2013).
One approach for modeling energy extraction incorporates an extra retarding force into the momentum equations. This force F⃗ may be written as
F⃗ =1
2ρCextjV⃗jV⃗ ð8Þ
where Cext is an extraction coefficient. It is possible to relate the extraction coef-ficient to specific turbine parameters including the losses related to the turbine structure as
Cext= Að cCs+ AsCtÞNt ð9Þ where Acis the cross-sectional area of the turbine support structure, Cs is the drag coefficient for the support structure, Asis the swept area, Ctis the thrust coefficient, and Ntis the number of turbines within the grid cell. After solving the momentum equations with the extra retarding force, the corresponding produced power is then found as
P =1
2ρCpAsjV⃗j3 ð10Þ
where Cp is the turbine power coefficient.
The application of this type of approach can vary depending on the model resolution. For relatively coarse grid resolution, each grid point where the retarding force is applied may represent multiple turbines and therefore the extraction coef-ficient can become quite large. A drawback of course is that the turbines within each grid cell cannot be individually tuned, and therefore, the optimal turbine array layout cannot be determined. However, this approach can be beneficial for ana-lyzing far-field effects within the full estuary or bay. Alternatively, for simulations with relatively high grid resolution, a single turbine may be resolved within a grid cell. Obviously, this would be the preferred approach for optimizing the array layout. For 3D model applications in deeper tidal straits, the retarding force may also have a depth dependence where the vertical position of the turbine is resolved, further improving the accuracy of the localized effect of energy extraction.
In addition to the turbines exerting a retarding force on the flow, turbines and their associated structure will have a pronounced effect on the turbulent charac-teristics of the flowfield. In order to account for the change in turbulence produced by tidal turbines, Roc et al. (2013) incorporated modifications to the turbulence closure scheme. One modification includes an added turbulent kinetic energy source term for the grid cells with turbines. Another addition is to include a term accounting for the transfer of large-scale turbulence to smaller-scale turbulence, a short circuiting of the turbulent cascade induced by the interaction of existing
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turbulence with the turbine structure. Finally, a term is included to model reduction in the spectrum of the turbulent length scales due to the partial generation of turbulence from the fluid structure interactions.
There have been numerous tidal power assessments performed with the effects of tidal power extraction around the world. The maximum tidal power potential of Johnstone Strait, British Columbia, Canada, was studied by Sutherland et al. (2007) using a 2D finite element model and the maximum extractable power in north-western Johnstone Strait was estimated. Also, using a 2D model, Polagye et al.
(2009) studied and characterized the in-stream tidal energy potential of Puget Sound, Washington, and quantified the far-field, barotropic effects of the energy extraction. The available tidal power from in-stream turbines placed in the Minas Passage of the Bay of Fundy and the Passamaquoddy–Cobscook Bay located near the entrance to the Bay of Fundy has also been examined using 2D models (Karsten et al. 2008, Walters et al. 2013). Recently, Funke et al. (2014) have applied an adjoint method with a 2D shallow water hydrodynamic model for designing tidal turbine layouts. This approach allows for quicker convergence to the optimized turbine array layout, thereby requiring much less computational resources than using a large suite of traditional forward model simulations alone.
Three-dimensional models have also been utilized for simulating the impacts of energy extraction. Tidal stream energy resources in northwest Spain were modeled numerically and the impacts of tidal stream energy were assessed (Ramos et al.
2014). Yang et al. (2013,2014) used a 3D model applied for an idealized case and for the Tacoma Narrows and showed significant volume flux impacts between the 1D/2D and the 3D simulations. Yang and Wang (2015) evaluated the effect of energy extraction on stratification in an idealized estuary. Hasegawa et al. (2011) applied a model looking at far-field effects from tidal energy extraction in the Bay of Fundy and the Gulf of Maine. Shapiro (2011) used a 3D model to demonstrate a significant decrease in the extractable energy for a given turbine capacity compared to 1D estimates due to flow bypassing the turbine array. Rao et al. (2016) used a 3D model of the Western Passage in Passamaquoddy Bay to optimize the turbine array layout. Hakim et al. (2013) modeled the Muskeget Channel and found modest impacts on the underlying hydrodynamics. Pacheco and Ferreira (2016) designed the optimal location of a turbine array on the coast of Scotland and examined the effect on the hydrodynamics.
When performing resource assessments using numerical models for tidal energy projects, validation of the model is an essential component of the process. The IEC TS for tidal energy resource assessments (IEC2015) provides guidelines for per-forming the calibration and validation of the numerical model. Model calibration is the procedure by which model parameters (e.g., bottom friction, turbulence parameters) are adjusted to provide the most accurate match to measured data.
The TS recommends comparing the model and measured tidal height data on the basis of harmonic constituents, both the amplitudes and the phases, and adjusting the model parameters as necessary. For calibrating the currents, the TS suggests comparing the model results with mobile current observations that capture spatial Hydrokinetic Tidal Energy Resource Assessments Using Numerical… 109
and temporal variability to ensure that the model is able to capture the strongly advective flows as well as refining the grid sufficiently to ensure grid convergence.
Validation is the procedure which is used to ensure that the model simulations have sufficiently low uncertainty for providing reasonable resource assessments.
The TS recommends that the AEP be calculated using both direct measurements as well as the model simulations for at least one proposed turbine location. The recommendation is for the uncertainty in the AEP to be less than circa 15%. This comparison can only be accomplished for observations prior to turbine deployments and therefore model simulations in which energy extraction is not included. For large projects in which energy extraction needs to be included in the model for the final resource assessment, the validation of the model is done without energy extraction, because it is not possible to obtain data prior to turbine deployment. The only exception would be if a pilot study in which a small number of turbines are deployed at the project location was done prior to the resource assessment for the full-scale project, then a modeling study including the energy extraction for the pilot study could be used to validate the model.