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.
identified for the Portsmouth Naval Shipyard located on Seavey’s Island. The grid refinement capability showed significant advantage over the original simulation results given its relatively low computational expense and high accuracy for the regions with the refined resolution. Of particular interest is the channel on the north side of Seavey’s Island (labeled in Fig.2b), which the parent grid did not resolve.
Fig. 1 Bathymetry from the parent grid (blue outline) and child grid (red outline) for the feasibility study of the Piscataqua River
Fig. 2 Color contours of the magnitude for the mean depth average currents for a the feasibility study of the Piscataqua River (Defne et al.2012), serving as the parent grid and b the child grid (Yang and Haas2015)
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For a small deployment with little impact on the currents, the technical resource assessment for an individual turbine requires computing the velocity probability distribution shown in Fig.3a. Using Eq. (4) with the power curve shown in Fig.3b and taking the swept area to be 20 m2, the power probability distribution is com-puted and shown in Fig.3c. The peak power is under 100 kW, well under the maximum estimated for the full estuary. Finally, the AEP is computed using Eq. (5) as 186 MWhr for this location.
For larger-scale projects which will extract a significant portion of the kinetic energy in the flow, the resource assessment requires the model simulation to include the effect of the turbines on the flowfield. Therefore, two new sets of simulations were completed where turbines are modeled using Eq. (8) for grid points in a transect spanning the width of the channel north of Seavey’s Island. The coefficient Cextwas set equal to 0.05 and 0.2 for the two simulations. The extraction coefficient is formulated using Eq. (9), and the drag and thrust coefficient along with the area associated with each individual turbine stays constant; therefore, the higher extraction coefficient is indicative of a factor-four increase in the number of turbines within the cell.
The tidal constituents were computed from the 32-day simulations and used to compute one-year times series of the velocity for each grid point across the transect.
Figure4shows the probability distributions for velocity in the center grid cell in the transect for the three cases: Cext equal to 0, 0.05, and 0.2. The effect of energy extraction on the flowfield is quickly apparent as the peak velocity weakens and the distribution becomes more narrow. An even clearer example of the effect of energy extraction is shown in Fig.5 as the spatial distribution of the mean velocity dif-ference between the energy extraction case and the original non-extraction case.
The reduction of velocity (negative values) in the channel is more significant, 0.3 versus 0.1 m/s, for the larger extraction cases in Fig.5b. There is a corresponding
Fig. 3 aVelocity probability distribution for a location north of Seavey’s Island (43.0841oN 70.7384oW). b Example power curve used for computing AEP. c Probability distribution of the power for an array of devices with a total capture area of 20 m2
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increase in velocity (0.1–0.2 m/s), although not as pronounced, in the main channel south of Seavey’s Island. Clearly, the added resistance of the turbines in the north channel is diverting some of the flow to the south channel.
Tidal turbines have backwater effects where the increased dissipation causes the water level to increase behind the turbine which is reflected through the changes in mean water level shown in Fig.6. In thisfigure, it is clear that the turbines cause an increase in mean water level on the order of several cm in the north channel.
Because of the bidirectionality of the flow, the mean water level increases on both sides of the turbine arrays. There is also a small increase (<1 cm) in water level further upstream in the estuary and a minimal decrease (<0.5 cm) in the south channel.
Fig. 4 Mean velocity probability distributions for the center grid cell in the transect north of Seavey’s Island (43.0841oN 70.7384oW) for a no energy extraction b Cext equal to 0.05 and c Cextequal to 0.2
Fig. 5 Color contours of the difference of the depth-averaged velocity magnitude between the energy extraction and original non-extraction cases for a Cextequal to 0.05 and b Cextequal to 0.2.
The magenta dot shows the location of energy extraction
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The dissipated power (Pdiss) by the turbines is computed as
Pdiss= Cext
1
2ρV3dA ð11Þ
where dA is the horizontal surface area of the grid cell with the turbines. Note that this is subtly different than the vertical face generally used for the swept area in Eq. (4). As indicated in Eq. (9), this is the total power dissipated which includes losses from the support structure as well as usable power captured by the turbines.
In addition to calculating the power dissipated by the turbines, it is beneficial to compute both the kinetic and potential energy flux (or power) through the transect and to evaluate how much this changes with the energy extraction. The kinetic energy flux, Pkinetic, is computed as the sum of I grid cells across the transect written as
Pkinetic= ∑I
i = 1
1
2ρjVij3hiwi ð12Þ
where hiand wiare the water depth and width of each cell across the channel,jVij is the depth-averaged velocity for each grid cell. Similarly, the potential energy flux is computed as
Ppotential= ∑I
i = 1
ρgjVijηihiwi ð13Þ
whereηi is the sea level fluctuation away from the mean water level.
Figure7 shows time series of the power dissipated as well as the kinetic and potential energy fluxes both before and after extraction. It is apparent that the Fig. 6 Color contours of the difference of the mean water level (MWL) between the energy extraction and original non-extraction cases for a Cextequal to 0.05 and b Cextequal to 0.2. The magenta dot shows the location of energy extraction
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potential energy flux is much larger than the kinetic energy flux, close to an order of magnitude difference. The energy extraction has the effect of decreasing both the kinetic and potential energy flux; therefore, it is clear that it is theoretically possible to extract more than 100% of the original kinetic energy flux. For the two cases shown here, the 1-year-averaged original undisturbed kinetic energy flux is 0.43 MW and the mean power dissipated is 0.14 and 0.22 MW which is 33% and 53% of the mean kinetic energy flux, respectively. Because this is a small branch for the estuary, this power is significantly less than the maximum available power according to the Garrett and Cummings estimate of 21 MW. The residual kinetic energy flux is decreased for both cases down to 0.26 and 0.11 MW, respectively.
For this site, the total energy flux reduction from both the kinetic and potential energy flux is greater than the rate of dissipation because a portion of the flow is diverted to the southern side of the island. It is also apparent that the loss for both the potential and kinetic energy flux is far greater for the second case with a smaller proportional increase in energy dissipation, indicating less efficient energy extrac-tion for this case.
Finally, the velocity probability distributions are used to produce the corre-sponding power probability distributions as shown in Fig.8. The two cases have similar shape for the probability distribution, although the higher extraction case has higher rates of occurrences and higher peak power. The AEP for both cases is calculated using annual probability distributions and Eq. (5) and is found to be 1220 and 1925 MWhr per year, respectively.
This resource assessment is sufficient to provide a general idea of the available power and what could be generated along with the potential channel and estuary scale effects. However, in order to do a full site design including turbine layouts within the array, an even higher grid resolution such that each turbine location is individually resolved would be required. Although the action of the turbines Fig. 7 Time series of the extracted power, the original and residual kinetic power, and the original and residual potential power for the transect on the north side of Seavey’s Island (43.0841oN 70.7384oW) for a Cext equal to 0.05 and b Cextequal to 0.2
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themselves do not necessarily need to be resolved, having the model resolve each turbine location would permit the ability of the model to account for the turbine interactions and permit a sensitivity test for the turbine locations. In addition, for a full hydrokinetic tidal power project design, power intermittency will have to be considered as well; its relative significance depends on individual project needs and available energy storage resources.