Tidal current turbine power capture and impact inan idealised channel simulationKristen M. Thyng

Department of Oceanography, Texas A&M University3146 TAMU, College Station TX 77843-3146, USA

E-mail: kthyng@tamu.edu

Thomas RocDepartment of Marine Energy, IT Power Ltd.

29 Great George St., BS15QT. UKE-mail: thomas.roc@itpower.co.uk

Abstract—An idealised tidally-forced flat-bottomed channelwith a symmetric headland is modelled in ROMS with andwithout simulated turbines. The simulation is intended to ex-amine a common geometry to many areas of interest for tidalenergy development around the world. The turbine model isimplemented in ROMS with terms in the momentum equationsas well in the turbulence parameterisation. This model allowsfor a detailed investigation of turbine impacts due to its param-eterisation of several physical effects of turbines on a flow fieldand, additionally, can be implemented at a specific location in thewater column. Several methodologies for accurately calculatingthe power capture from two turbine array layouts are compared.A methodology which allows for accounting over the wholesystem leads to a more realistic result. Additionally, the impact ofthe turbines on the system is assessed hydrographically. Coherentstructures found in the speed, vorticity, and turbulent kineticenergy are disrupted near the headland tip due to the presenceof turbines, leading to a weakened system downstream. The pathof a large lee headland eddy is slightly altered, and all effectshave potentially significant impacts for a real system.

Index Terms—tidal energy, turbine model, ROMS, tidal cur-rent turbine, headland

I. INTRODUCTION

Tidal current turbines are currently being considered asa potential green, renewable source of energy for severalareas world-wide. Many areas of research contribute to theunderstanding necessary for development of tidal energy. Thefocus of this work is to connect ocean and turbine modelling inorder to better understand the effects of turbines on a realistic,though idealised, flow field.

Several groups are examining the existing flow fields inareas of interest for tidal current turbine (TCT) develop-ment using a numerical modeling approach [1]–[3]. This sitecharacterisation typically seeks to assess the potential poweravailable to hydrokinetic turbines and to understand flowfeatures that are pertinent to the extractability of the availablepower. However, it is also well-known that the presence ofturbines alters the flow fields, with implications both for theenvironment [4]–[7] and for power production. For example,given enough turbines, several studies have found a reductionin tidal range landward of the turbine array and an increasein tidal range seaward [6], [7]. From the power productionperspective, adding turbines to a system is coupled with theeffects on the system, making a numerical model with a turbinemodel all but necessary to understand the interplay between

the systems. As such, some oceanographic models seek tounderstand the effects of turbines on the system.

Garrett and Cummins developed a one-dimensional time-averaged model based on flow conservation where the pres-ence of the turbine array is simulated through a power-lawterm corresponding to the drag force associated with theturbines [8]. This simplistic approach gives a good preliminaryassessment of the upper bound on the available power ofconstricted flows but excludes numerous factors which turnout to be significant for realistic power assessment [8]. Anumber of studies improved this approach by simulating thehydrodynamic turbine effect on the flow via an increasedquadratic bottom shear stress [9]–[12]. In such an approach,instead of searching for the maximum extractable power, theextracted power is assumed equal to 10% of the total availableand accordingly dissipated as additional bottom shear stress.It should be highlighted that the previous models have beenbuilt on very restrictive assumptions.

The natural progression is to extend the scope of resolutionof numerical models to a second dimension. The first intuitivemethod for assessing tidal resources is to simulate a site andapply a tidal resource assessment on the model output withoutincorporating any TCT effects into the computation [13]–[15].Unfortunately, since the volume flux dynamics are essentialto properly estimate the potentially extractable energy [16],ignoring the device effects when assessing the tidal resourcefrom the natural flow can lead to significant discrepancies inrealistic cases [7]. Accordingly, a quadratic force was injectedin the right-hand side of the momentum balance in severalstudies [17]–[19]. This formulation of the turbine-inducedforce on the flow is also referred to as the actuator disc theory.

Since 2D models are depth-integrated, this new force isuniform over the water column. Furthermore, its physicalmeaning can be equally regarded as a drag force [17] or anadditional shear stress [18], [19]. As a consequence, althoughthis type of representation allows a better understanding froma horizontal point of view, the vertical flow behaviours such asthe relation between water column height and correspondingdrag coefficient [16], vertical flow bypassing of the device ordistinction between bottom friction and energy extraction [20]are misrepresented and also poorly estimated. Another inducedhydrodynamic effect of turbines which cannot be neglectedin a large-scale turbine-farm yield-assessment is the induced

wake [7], [13], [21].Thanks to rapidly increasing computer-power development,

accurately understanding wake behaviours at a fine-scale im-plies a use of numerical models. These models allow for thesolving of the complete Navier-Stokes equations at fine enoughresolution to accurately simulate the local flow conditions.However, in the scope of large-scale array deployment and re-gional scale simulations, this approach carries one main issue:the prohibitively high requirements of computational time. Asa consequence, a 3D model based on relevant regional-scopehydrodynamic assumptions appears to be the most promisingalternative in developing a tool to treat the power and impactassessment of large-scale TCT array deployment in realisticenvironments. This is the approach followed in this work.

While potential tidal energy sites are varied in geometry,some common features can be found, allowing idealisednumerical domains to be relevant for site characterisation inother areas. In one study, Admiralty Inlet in Puget Sound,WA, is modelled for site characterisation, with an emphasison a headland in the system, Admiralty Head, as a dominantgeometric feature on the flow [1]. A study of AdmiraltyHead, idealised as tidal flow past a prominent headland, wasexamined previously from the perspective of tidal power andprovided energy metrics [3]. Prominent headlands and islandsare found to dominate the flow in other areas of interestfor tidal energy development as well. The Pentland Firth inScotland is being investigated for TCT placement, leading toa need for research to understand the flow dynamics in thearea [2], in particular, in relation to vortex-generation due toislands in the channel [22]. Recirculation areas due to vorticitydetaching from headlands are found in Minas Passage, inthe Bay of Fundy [23]. Additionally, an Ocean RenewablePower Company (ORPC) development in Cook Inlet is neara headland [24]. Furthering the understanding of the effectof turbines on flow features and site characterisation neara headland will aid in turbine placement in many regionsthroughout the world.

The methodology for this study is explained in Section II,with the turbine model introduced in Section II-A and thedomain and system setup in Section II-B. The differing effectsof two different array layouts are examined in Section III.Several approaches for calculating the power capture by theturbines are examined then applied to the simulation output.The effect of the turbines is examined from the perspective ofimpact on the flow field in Section IV. Included in the resultsand analysis is how the character of important flow featureschange in time due to the presence of the turbines, as well asthe overall effects to the system. Conclusions and future workare described in Section V.

II. METHODOLOGY

A. Numerical Model and Turbine Representation

To ensure the sustainability of commercial-scale TCTprojects, a balance between power extraction maximisationand impact minimisation must be found so that device layout

optimisation can take into account environmental consider-ations. The difficulty of this problem lies in the fact thatthe length scales required to fully understand viscous flowdynamics over a rotating turbine are much smaller than thelength scales required to fully understand the potential impactswhich might be generated by arrays of turbines at realistictidal sites [25]. Therefore, large-scale ocean circulation modelsappear to be the best suited for such investigation. Nonetheless,it has been shown that nonlinear sub-grid scale effects linkedto turbine-induced turbulence may have non-negligible impactson a large scale [1], [5], [26]. As TCT layout decision-makingrequires both accurate impact and resource assessments, itseems clear that the best approach is to inject a three-dimensional TCT representation coupled with a sub-grid scaleeffect parameterisation into an ocean circulation model inorder to address many involved issues.

Such requirements have been met through the adaptationof an existing ocean circulation model framework, RegionalOcean Modelling System (ROMS), by including a TCTrepresentation module [27]. ROMS is a 3D, split-explicit,free-surface, terrain-following, hydrostatic primitive equationoceanic model and has been widely used for a wide range ofstudies. The TCT representation method used is an innovativemethod treating each individual device as a 3D object andaccounting for the momentum capture as well as the sub-gridscale turbulence balance perturbations caused by discrete TCTdevices on flow hydrodynamics [28].

The turbine is modeled in ROMS by adding a force termto the momentum equations, representing the turbine in a gridcell. The form of this term is

F = −1

2ρAdCU

2d ,

where ρ is the fluid density, Ad is the rotor-disc area of theturbine, Ud is the flow velocity passing through the turbinegrid cells, and C is a function of the coefficient, Ct [28]:

C =1−√

1− Ct

1 +√

1− Ct

.

Additionally, a term is added to each of the two k-ωturbulence closure scheme equations to simulate reduced tur-bulence length scales (Pk) and additional production of waketurbulence due to the turbine’s presence (Pω). The equationsare as follows

Dk

Dt=

∂

∂z

(KM

σk

∂k

∂z

)+ Ps + PB − ε+ Pk

Dω

Dt=

∂

∂z

(KM

σω

∂ω

∂z

)+ω

k(c1Ps + c2PB − c3εFwall + Pω) ,

where D/Dt represents the material derivative, k is theturbulent kinetic energy, KM is the vertical eddy viscosity,Ps is the shear production, PB is the buoyancy production, εis the turbulent dissipation rate, ω is the turbulent frequency,and Fwall is a wall function. Constants have the followingvalues: c1 = 0.555, c2 = 0.833, c3 = −0.6, σk = 2.0, and

Fig. 1. Simplified headland domain with overlaid magnified views of theregular (left) and staggered (right) array layout. Green dots represent the TCTlocation. After [3].

σω = 2.0. The added terms to represent the turbine are givenby

Pk = CpU3d

∆x− Cd

Udk

∆x

Pω = CωP 2s

ε,

where ∆x is the grid spacing of the porous disc, and param-eters Cp, Cd, and Cω are functions of the grid spacing andthe turbine blade chord length and pitch angle. See [28] forfurther details.

On the basis of grid and time resolution tests, thispower/impact assessment tool has been shown to be con-vergent and stable. The ability of the method to adequatelyreproduce features of the turbine wake, wake recovery, andwake interactions for TCTs of various thrust coefficientshas been validated against laboratory experiments involvingstandalone porous disc set-ups. In the absence of in-situ data,the scale applicability of the proposed model has been testedagainst analytical benchmarks and theoretical predictions. Thedetailed validation of this model can be found in [28].

B. Simulation Features

In this study, Admiralty Inlet has been represented as asymmetric headland with a flat-bottomed rectangular channel.This idealised case permits the effects due to the headlandto be isolated from the effects of complex bathymetry andthus a better understanding of the interaction between the TCTfarm and the vortices and other features occurring at the tipof the headland to be reached. The vortex propagation hasbeen shown to be the most significant hydrodynamic elementof this tidal flow [1], [25]. The headland model domain hasa length of 40 km, a width of 7 km, and a 100 meter deepflat bathymetry. The headland is symmetric and extends justover 2 km into the channel (Figure 1). Since the turbine modelrequires one grid cell in thickness and three grid cells across[28] and knowing that each simulated turbine has a diameterof 30 meters, the resolution employed for these simulations is30 meters in the x-direction and 10 meters in the y-directionwith 20 vertical layers.

The numerical channel domain has two open (west andeast) and two closed no-slip (north and south) boundaries.A semi-diurnal M2 tide is applied on both open boundariesusing the Chapman [29] and Flather [30] boundary condition

types and outward-moving baroclinic momentum is radiatedout of the system. The phase difference between the openboundaries is approximated using the shallow water wavespeed [1]. A linear density profile (from 1023 kg.m−3 at thesurface to 1025 kg.m−3 at the bottom, giving a buoyancyfrequency of N=0.01 s−1) is initially in place and is forced atthe open boundary. The bottom roughness is parameterisedby the ROMS quadratic bottom friction expression, whosedimensionless friction parameter is CD = 3 × 10−3. TheCoriolis force is included and the k-ω turbulence closurescheme is used [31]. The model was run for two tidal cyclesfor each case. The first tidal cycle is considered ramp-up andthe second tidal cycle is considered as suitable for analysis asthe ebb and flood flows are almost symmetrical. Simulationoutputs were recorded every 15 minutes.

Two turbine array layouts were studied, both composedof 10 turbines (Figure 1). The turbines have a 30 diameterrotor (which is on the large side but leads to a realisticblockage ratio), a thrust coefficient Ct = 0.86, and run bi-directionally. The turbine model rotor axis is aligned east-westand cannot yaw. The fact that the turbines cannot yaw in a flowregion where the bidirectionality can be an important factormeans that the power capture will not be optimum. The fixedorientation of the device, however, is inherent at this stage ofthe numerical platform development and will be improved inthe next stage of its development. In most real cases, turbinerotors would be placed outside of the surface and bottomlayers in order to avoid as much shear and wave strain aspossible, reducing additional loading and fatigue on the turbinestructures and blades to increase the device life time [32]. Inthe present case, due to the high blockage ratio (i.e., RotorDiameter/Water column height=1/3), the turbine hubs havebeen situated at mid-depth or 50 meters deep. The first layoutis referred to as “regular” and the second layout is referredto as “staggered”. Here the array layouts have been chosena priori and without performing row-by-row simulations andtherefore without considering the potential flow accelerationsor turbulence intensity increases which could be induced bythe wake interactions within the farm. The distances betweeneach device within the farm have been chosen to maintain aminimum spacing of 6 rotor-diameters between them (in bothx and y) so that none of the turbines are placed in the near-wake of an upstream device. The arrays were placed near theheadland tip in order to access the most energetic area in thedomain. It is worth noting that, although the blockage effectis not negligible, Ct corresponds to the thrust coefficient in anunconstrained flow. This is due to the fact that, in the presentmethod, the blockage effects are not accounted for throughan empirically increased Ct but through the set of momentumand turbulence source terms.

III. ARRAY LAYOUT EFFECT ON POWER CAPTURE

A. Power Assessment Methodology

The power of a TCT is calculated as follows:

Power =1

2ρCpAdU

3 [Watt],

where Cp is the power coefficient. However, within an arrayof devices, U is impacted by the devices deployed upstream,affecting the power calculation. For that purpose, two newapproaches are considered to assess the power capture of thedifferent TCT farm layouts in the present document. Firstly,the power captured by a TCT deployed in a flow can be definedas the flow rate through the disc multiplied by the pressuredrop across the disc [33]:

Power Capture = AdUd(p+d − p−d ) [Watt]. (1)

Although Equation 1 does not account for any mechanical lossnor device yield, it should theoretically give a direct and accu-rate estimate of the power extracted by a TCT. According tomomentum theory, the expression of thrust force [34] and thedefinition of the induction factor (i.e., a = (U∞ − Ud)/U∞),the pressure drop across the disc can be expressed as follows:

(p+d − p−d ) = 2ρUd(U∞ − Ud),

Consequently, the power capture (Equation 1) can be rewrittenas follows:

Power Capture = 2ρAdU2d (U∞ − Ud). (2)

This formulation of the power capture is useful in this worksince, contrary to most existing methods for TCT representa-tion, the present method gives a direct estimate of the flowvelocity passing through the rotor disc, Ud. U∞ is oftendefined as the unperturbed flow velocity and/or the flowvelocity far upstream of a given device which, in the caseof a standalone device system, amounts to the same thing.In a multi-device system, defining U∞ turns out to be morecomplex. It is worth noting that the turbine Ct and Cp valueswere kept constant, regardless of the upstream flow velocity.The latter assumption implies some sort of artificial control atthe blade level, however, this simplification was necessary inorder to isolate the effects of turbine placement.

Yet, the present simulations are subjected to time varyingforcing. Therefore, the following adaptation of Equation 2must be made to obtain the power captured by each turbinewithin the farm:

Mean powerof one turbine

=1

T

n∑t

2ρAdU2dt

(U∞t− UdN,t

)×∆t,

where T is a full tidal cycle (43200 seconds), ∆t the time stepbetween each output (900 seconds), n = 50 and correspondsthe time-step index, U∞ the u-velocity component of theunperturbed flow simulations at the appropriate disc locationand Udt

is the u-velocity component from the simulationsincluding the turbine at the same disc location for a giventime index. By extension, in the case of a 10 device farm,the overall power capture of the farm is determined by thefollowing formula:

Powerof thefarm

=1

T

10∑N

n∑t

2ρAdU2dN,t

(U∞N,t− UdN,t

)×∆t. (3)

Here N is the index related to each turbine composing thefarm, U∞N

the u-velocity component of the unperturbed flowright at the disc location of the N th turbine and UdN,t

is theu-velocity component right at the disc location of the N thturbine for a given time index t.

A second approach based on simple energetic considerationsis also performed. The base statement is that the poweravailable for the devices equals the amount of kinetic energypresent in the flow without devices over a tidal cycle period:

AvailablePower

=

n∑t

∑i,j,k

1

2ρ‖v∞t,i,j,k

‖2 ×∆Vi,j,k ×∆t,

where i, j, k correspond respectively to the numerical indexalong the x, y, z directions, ‖v∞t,i,j,k

‖ is the unperturbed flowvelocity norm and ∆Vi,j,k represents the control volume ofthe (i, j, k)th cell composing the numerical mesh. In the samemanner, by computing the amount of kinetic energy presentin the flow with devices over a tidal cycle period, one canestimate the remaining power of the so-exploited tidal flow:

RemainingPower

=

n∑t

∑i,j,k

1

2ρ‖vt,i,j,k‖2 ×∆Vi,j,k ×∆t,

where ‖vt,i,j,k‖ is the flow velocity norm of the studied case.Therefore the amount of power dissipated by the present of theTCT farm can be assessed through the following expression:

Power Capture = Available Power− Remaining Power.(4)

These local (Equation 3) and global (Equation 4) approachespermit a complementary investigation of the power extractioninduced by the two-considered TCT farm layouts on the tidalsystem.

B. Results

For most of the tidal cycle, except near slack tide, thedevices’ wakes are overlapping in the case of the staggeredlayout. The velocity deficit, Udef = U∞(1 − a), demon-strates this and is shown in Figure 2. Oppositely, in thecase of the regular layout, the device wakes surge into thedevice inter-space without overlapping over the next row.This counter-intuitive feature is due to the headland geometry,which aligns the staggered array turbines as the flow movesparallel to the headland. In this regard, the regular layoutappears regular from an east-west direction consideration butappears as staggered from a wake consideration, and vice-versa for the staggered array layout. This observation tendsto suggest that the regular layout farm should extract moreenergy out of the tidal flow than the staggered layout farm.Interestingly, the local approach for power extraction findsthat the energy extraction difference between the layouts isnegligible, whereas the global approach for power extraction(Equation 4) confirms the hypothesis. Indeed, by applying thelocal approach for power extraction over a full tidal cycle,the regular layout farm extracts 6.008 MW while the stag-gered layout farm extracts 6.051 MW. However, consideringthe energy budget over the entire domain and over a full

tidal cycle by using the global power capture approach, thepower extraction assessment for the regular layout farm equals7.5348 MW and for the staggered layout farm is 6.1845 MW.Consequently, the global approach reveals a 18% differencein terms of power capture between the two farm layouts andthus confirms the hypothesis made on the wake over-lappingobserations. The local approach seems to exclude potentialflow acceleration within the farm and thus underestimates thereal power extraction.

The turbulence intensity, I =√

2/3k/U , is shown in Figure3. The overall farm-induced turbulence does not differ muchbetween the layouts either in magnitude or spatial spreading.In addition, by performing a TKE budget over the entiredomain for the two layout cases (Equation 5) and subtractingthem, the difference in TKE is a thousand times smaller, andtherefore negligible, than the difference in power extractionbetween the two cases. The TKE budget is

TKE Budget =

n∑t

∑i,j,k

ρ× kt,i,j,k ×∆Vi,j,k ×∆t, (5)

where k is the turbulent kinetic energy. Consequently, we canapproximate that all of the 18% of power extraction differencebetween the two farm layouts is due to actual power captureimprovement rather than an increase in turbulent dissipation.Additionally, Figure 3 shows that, for the staggered layout,the turbulence intensities are higher in front of the turbineslocated in the farms wake than they are for the regular layout.Accordingly, one could expect more turbulence-related loadingon the turbine blades and structures for the staggered layoutthan for the regular layout.

To conclude, although a priori staggered layouts tend to bemore adequate for tidal flows in straight channels, the previoussection showed that the optimum farm layout cannot befound on a-priori considerations but solely by accounting forsite-specificities, namely channel geometry and farm-inducedturbulence in this case.

C. Analysis

Based on the previous simulation results, a rule of thumb forassessing the power capture might be worked out. Knowing thepower capture of the entire farm thanks to the global approach(Equation 4), one could postulate that this quantity can beexpressed as a function of the velocities taken at a similardistance upstream of each turbine composing the farm:

Farm power capture =1

T

10∑N

n∑t

1

2ρAdU

3udN,t

×∆t, (6)

where Uud is the velocity at some particular upstream distance.If such rule of thumb exists and could be applied to any kind ofarray layout, the power capture assessment would be heavilysimplified. In order to find the upstream distance, velocitiesat different distance upstream of each device constituting theregular layout farm were recorded over a full tidal cycle. Thesevelocities were then used in Equation 6. The power extractionestimations obtained were normalised by the power extraction

Fig. 4. Normalised power extraction versus distance upstream of the devices.The dashed line represents the aimed value and the solid line represents theestimations from the regular array layout simulation

estimation obtained via the global approach (7.5348 MW), andare shown plotted against the distance upstream of the devicesin Figure 4.

In Figure 4, the dashed line, representing proper repre-sentation of the normalised power capture, meets the solidline, representing the estimated power capture obtained viaEquation 6, at 2 diameters upstream of the device. Onecould therefore postulate that by applying the velocities at 2diameters upstream of each device to Equation 6, an accurateestimation of the real power capture could be obtained. To val-idate this hypothesis, we apply this calculation to the staggeredlayout case and compare this power capture estimation to theestimation obtained thanks to the global approach (Equation4) for the same case. Unfortunately, by doing so, the powercapture estimation is 26% lower than the estimation obtainedvia the global approach for the staggered layout case. Thisobservation tends to show that, as the optimum farm layout,precise power capture assessments of TCT arrays cannot bemade on a priori considerations but solely by accounting forsite flow-specificities.

IV. ARRAY HYDRODYNAMIC IMPACTS

A. Results

This section focuses on the unaltered initial case with noturbines, and the regular array layout. The staggered turbinearray layout generally affects the flow field less than theregular turbine array. This is probably due to the fact that withthe angle of the flow past the tip of the headland, the staggeredarray layout causes the turbine wakes to align, having lesseffect on the flow field, whereas in the regular layout, thewakes are staggered. The staggered array can be assumed tohave an effect on the flow field that is less extreme than theregular array.

The results are discussed in terms of changes to significantflow features, both in time and in overall changes to thepertinent fields, and changes to a tidal energy metric. Resultsare shown at a hub height of 50 meters (mid-water column),but effects from the turbine array are found throughout thewater column.

(a) Staggered array: ebb (b) Staggered array: flood

(c) Regular array: ebb (d) Regular array: flood

Fig. 2. Velocity deficit, Udef , for both turbine farm layouts at the peak speeds of both ebb and flood.

Even this idealised headland channel flow has many compli-cated flow features that are realistic in their scope. The effectsof tidally-generated headland eddies dominate the flow field,directly and indirectly. See the left-hand column of subplotsin Figure 5 for snapshots at a single time during ebb tide inthe initial case with no turbines. Vorticity is generated alongthe stoss side of the headland and detaches at the headlandtip (Figure 5(c)). The vorticity rolls up and separates intomultiple small vortices, lee of the headland tip, which coalescetogether into a larger eddy with a much lower vortex strength.This behavior is reflected in the magnitude of the horizontalvelocity, or speed, which is largest moving past the headlandand around the outside of the large eddy (Figure 5(a)). Theturbulent kinetic energy is strong both near the headland tip,as seen in an organised structure streaming from the tip, andaround the outside of the large lee eddy (Figure 5(e)).

Plots from the simulation with a regular array layout areshown in the right-hand column in Figure 5. The presence ofthe turbines is clear in all of the plots. In the top plot, Figure5(b), the turbines reduce the speed in very localised areas attheir location and in their wakes. Additionally, they affect thespeeds further downstream: while a thin jet of strong currentsextends beyond the headland tip in the initial case, the currentspushing past the headland in the regular array case do not haveas large of maximum values and are spread out over a largerarea. A coherent structure can be seen in all of the fields in theinitial case near the headland tip, but this structure is mostlydisrupted by the presence of the turbines in the regular array

case. The far-field TKE, as seen in the outside of the largeeddy, is weaker and less prominent in the case with turbines.

The behavior in all of the fields in the regular array casefollows directly from the turbine model. The turbines locallyextract momentum and increase turbulence, which in the near-field decreases the speed and increases the TKE. The increasedenergy dissipation near the turbines leads to decreased speedand TKE in the far-field. The presence of the turbines right atthe headland tip, where vorticity that is being generated alongthe stoss side of the headland is to detach to form structuresdownstream, disrupts the processes and leads to a less coherentfeature, as seen in the vorticity and TKE.

Several aspects of the bulk flow field effects of the turbinesare summarised in Figure 6. Maximum speed is used as aproxy of the location of the large lee eddy and other areas ofstrong currents. The speed is significant to power productionsince power is proportional to the speed cubed. The differencein the maximum speed values at each (x, y) location betweenthe initial and turbine array cases are shown in Figure 6(a).Areas where the initial case has larger speeds are positive(red), and areas where the turbine case has larger speeds arenegative (grey). The effect of the turbines on the speed field isto shift the main areas of strong currents (mainly in the largeeddy field and streaming from the headland tip on both tidaldirections) outward, across the channel from the headland, andto weaken it. The line to the outside left of the plot showsthe along-channel average of the difference in maximums,indicating a shift of the speed field across-channel from the

(a) Staggered array: ebb (b) Staggered array: flood

(c) Regular array: ebb (d) Regular array: flood

Fig. 3. Turbulence intensity for both turbine farm layouts at the peak speeds of both ebb and flood.

headland in the turbine case, relative to the initial case.This shift is probably due to the decrease in energy in the

system moving past the headland tip. This decrease in energy,combined with the disrupted vorticity past the headland, leadsto the strong currents tending slightly more straight beyond theheadland with less curvature into the eddy when comparedwith the initial case. The main positive, red areas indicatewhere the initial case has stronger currents than the turbinecase, due to extraction by the turbines, whereas the southernnegative grey areas are where the currents have shifted to inthe regular turbine array case.

Figure 6(b) shows the difference in maximum TKE betweenthe initial and regular array simulations. There is a distinctionin relative behavior in the cases in the near- and far-field.Very near to the turbines and in their wake, the TKE isstronger in the turbine case, which is expected given thatseveral terms have been added to the turbulence equations inorder to model the increased turbulence caused by the turbines.Further downstream, the initial case TKE is larger than theturbine case, probably due to the near-field dissipation due tothe turbines in the regular array case which leaves less energyto be dissipated downstream. These trends are reflected in theacross-channel average shown below the plot: the initial casetends to be larger except near the turbines themselves.

The mean kinetic power density, shown in Figure 7, gives

a measure of the potentially extractable resource present in asystem. Like in the plot of the difference of maximum speeds(Figure 6(a)), this plot shows a large-scale shift away fromthe headland tip of the resource. In the near-field area to theturbines, which is the area of largest resource, the field iscompletely altered by the turbines. In fact, the area of largestresource has decreased substantially, as seen in the differencebetween the corresponding filled and black line contours.

B. Discussion

The far-field disruption by the turbines to the structure set uplee of the headland tip (seen in all fields) could have significantimpacts in a real-life situation. The path and characteristics ofthe large lee eddy change slightly in the turbine case. Whilein reality the eddy pattern would be much more complicatedthan in this idealised case (due to bathymetry, complicatedcoastline, and a more complex tidal forcing, among otherthings), a small shift in the eddy trend could have a bulk effecton the system. In Admiralty Inlet, for example, the lee eddiesfrom Admiralty Head dominate the flow over a large area.

It is clear in Figures 5(e), 5(f), and 6(b) that the far-fieldTKE is weaker when the turbines are in place. Turbulencealters mixing in a system, and this shift in where the mixingoccurs due to the turbines may be significant.

In the near-field, the change in the structure of speed,vorticity, and TKE streaming from the headland tip is limited

(a) Initial case: speed (b) Regular array: speed

(c) Initial case: vertical vorticity (d) Regular array: vertical vorticity

(e) Initial case: turbulence kinetic energy (f) Regular array: turbulent kinetic energy

Fig. 5. Initial simulation on the left and regular array on the right with properties shown at hub height. Overlaid arrows are velocity vectors at hub height,overlaid signal shows time position in tidal cycle (free surface), and inset plot shows headland tip area, magnified. All snapshots are taken at the same timeon ebb tide.

in distance from the headland tip, but could have significantimpacts in that small area, besides the impacts on the far-field.The change in the eddy locations and rate could affect bottomsediment transport, which could affect the bathymetry in thearea [1], [35].

All of these effects are somewhat minor in scope on theirown, but could have major implications, especially giventhat only ten turbines were being modelled in this case. Animportant follow up to this work is to move the location ofthe turbine array to an area with a good available resource,but with a less important location hydrographically (that is,not right at the headland tip where vorticity is being shed), inan attempt to limit impact on the system.

V. CONCLUSIONS AND FUTURE WORK

Several power assessment methodologies have been usedand compared in order to calculate the power capture of twodifferent layouts of 10 device arrays. The first assessment

method is based on the flow velocity passing at the positionof each device for each time step (Equation 3, the “localapproach”). The second calculation estimates the amount ofpower dissipated by the turbines over a tidal cycle (Equation4, the “global approach”). A third assessment method is afunction of the velocities taken at a similar distance upstreamof each turbine composing the array (Equation 6). Comparisonbetween the results has demonstrated the global approach tobe most realistic methodology. Additionally, in Equation 3,U∞ should not represent the unperturbed flow velocity butthe flow velocity perturbed by the upstream devices withoutthe presence of the considered device. Written as it is, thelocal approach (that is, Equation 3) is equivalent to the classicapproach (i.e., P = − 1

2ρAdCpU3∞) as it does not account for

fluid surging into the row gaps nor the upstream wake velocityyet it does not require any power coefficients. Nonetheless,the global approach can be considered as unbiased only whenthe open boundaries of the simulation are not directly subject

(a) Speed

(b) Turbulence kinetic energy

Fig. 6. Difference in maximum speed and TKE between the initial, no turbinecase and the regular turbine array case. Positive (red) values indicate areas inwhich the initial case has larger maximum values and negative (grey) valuesindicate areas in which the turbine array case has larger values. Line plotsto the left (bottom) of the main plot area show the along- (across-) channelaverage of the plot values, with coloring indicating position greater than (red)or less than (grey) zero.

Fig. 7. Mean kinetic power density. The values for the initial simulationare shown in colored, filled contours and corresponding values for the regulararray simulation are overlaid in black contours and labeled.

to the blockage effects, such as flow increase, caused by thepresence of TCT arrays. Therefore, simulation domains haveto be sufficiently larger than the TCT footprint in order tosafely apply this methodology.

Emphasis has been placed on using the appropriate approachfor power assessment as well as the necessity to accountfor site specificities in the optimization process. Under thisfocus, an 18% increase in power capture was achieved throughfarm layout optimisation based on the domain geometry.

Allowing for device yawing and blade design adaptation andcontrol would also improve the turbine model, and will beimplemented in future versions of the model. Furthermore, ithas previously been suggested that natural flows intrinsicallypossess both potential and kinetic energy and the energy ex-traction is partly balanced between these two components [10].Consequently, integrating the potential energy variations andtransfers in the power capture assessment approach might haveto be considered and raises the question of the relevance ofassessing the potential of a site only on kinetic considerations[36].

The power output assessment could be even more realisticby taking into account cut-in speed and rated power speed. Thecut-in speed is the flow velocity below which the turbine doesnot produce power and turbine rotor stays still. On the otherhand, the rated power is the maximum power that a turbine canproduce. This maximum of power production coincides with athreshold flow velocity above which pitch-control mechanismreduces angle of attack of the blades and thus maintains apower output close to the rated power [37]. This thresholdaids in avoiding failure and dismantling of the turbine structureand blades due to extreme loadings [37]. Along with a morerealistic blade control of the device power production, anestimate of electrical and mechanical losses involved in theprocess would ameliorate the power extraction assessment.

In terms of impact of turbines on the system, it was shownthat even a relatively small number of turbines, placed inthe area of strongest resource near the headland tip, havea noticeable impact of the system. Near the headland, thecoherent structure in the speed, vorticity, and TKE that wasseen in the initial simulation with no turbines was disrupted bythe presence of the turbines. The local vorticity and TKE wereincreased and the speed was decreased by the presence of theturbines. The upstream increase in dissipation by the turbinesled to less turbulence in the far-field. Additionally, there wasa slight shift in the area of strong currents across the channelfrom the headland, probably due to weakened momentum andvorticity in the system.

The effects of the turbines could be significant for a real sys-tem. Each of these changes could affect the location, timing,and rate of mixing and transport. This in turn could affectmany processes in the area, including sediment transport.Future work will examine the impacts of turbines at otherlocations in the system, in an attempt to mitigate the effectof the turbines on the system while maximising the powerproduction.

ACKNOWLEDGMENT

This material is based upon work supported by the Depart-ment of Energy under Award Number DE-FG36-08GO18179and by the University of Washington PACCAR Professorship.The authors would like to thank the International Network onOffshore Renewable Energy (INORE; www.inore.org) for theInternational Collaboration Incentive Scheme (ICIS) and ITPower Ltd. for having made this collaboration possible.

DISCLAIMER

This report was prepared a an account of work sponsoredby an agency of the United States Government. Neither theUnited States Government nor any agency thereof, nor any oftheir employees, makes any warranty, expressed or implied, orassumes any legal liability or responsibility for the accuracy,completeness, or usefulness of any information, apparatus,product, or process disclosed, or represents that is use wouldnot infringe privately owned rights. Reference herein to anyspecific commercial product, process, or service by tradename, trademark, manufacturer, or otherwise does not nec-essarily constitute or imply its endorsement, recommendation,or favoring by the United States Government or any agencythereof. Their views and opinions of the authors expressedherein do not necessarily state or reflect those of the UnitedStates Government or any agency thereof.

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