Far-field Modelling of the Hydro-environmental Impact of Tidal Stream Turbines Reza Ahmadian1 , Roger Falconer2 and Bettina Bockelmann- Evans 3 1
Corresponding Author: School of Engineering, Cardiff University, The Parade, Cardiff, CF24 3AA, U.K., email:
[email protected], Tel: +44 29 2087 5713, Fax: +44 29 2087 4939 2
3
School of Engineering, Cardiff University, The Parade, Cardiff, CF24 3AA, U.K., email:
[email protected] School of Engineering, Cardiff University, The Parade, Cardiff, CF24 3AA, U.K., email:
[email protected]
Abstract Interest in the marine renewable energy devices, and particularly tidal stream turbines, has increased significantly over the past decade and several devices such as vertical and horizontal axis turbines and reciprocating hydrofoils are now being designed around the world to harness tidal stream energy. While tidal stream turbines are being developed at a high rate and getting closer to commercialisation, it is important to acquire the right tools to assist planners and environmentalists, not only in finding a right location for the turbines, but also in identifying their potential impacts on the surrounding marine and coastal environment. In this study, a widely used open source depth integrated 2D hydro-environmental model, namely DIVAST, was modified to simulate the hydro-environmental impacts of the turbines in the coastal environment. The model predictions showed very good agreement with previously published 1D model results. Then, for demonstration purposes, the model was applied to an arbitrary array of tidal stream turbines in the Severn Estuary and Bristol Channel which has the third highest tidal range in the world. The model has shown promising potential in investigating the impacts of the array on water levels, tidal currents and sediment and faecal bacteria levels as well as the generated tidal power, which facilitates investigating the relative far-field impacts of the arrays under various climate change scenarios or different formations of the array.
1 Introduction Tidal energy extractors and, in particular, tidal stream turbines have attracted considerable interest in recent years, due to their modularity, minimal visual impact and their predictable energy generation. There are vast resources of tidal stream energy available around the world which can be exploited; for instance in the UK the tidal current energy resource technically available for extraction is estimated to be around 22 TWh/y, representing around 6% of UK electricity demand [1]. Likewise the tidal current energy resource technically available around Ireland is calculated to be 10.46 TWh/y [2].
In considering that tidal stream turbine technology is still in its infancy, these turbines have attracted significant interest from both academic and industrial researchers. This interest is reflected in the number of research studies being carried out on Computational Fluid Dynamics (CFD) and laboratory experimental modelling studies of turbine design and performance etc., including research studies being undertaken by: Myers and Bahaj [3], Bryden and Couch [4], Bahaj et al. [5], Batten et al. [6], O’doherty et al. [7] and Willis et al. [8] to mention but a few. These research studies have generally been complemented by trial scale and full-scale models, which have been installed and monitored in the real environment in the past few years, such as: the two turbines manufactured by Marine Current Turbines Ltd., UK, with 11m diameter single rotor, 300 KW, Sea?ow being installed off the North Devon coast, UK, and the grid connected double rotor SeaGen, which has been installed in Strangford Lough, Ireland [9, 10], and the 10m, 1MW OpenHydro turbine which has been installed in the Minas Passage of the Bay of Fundy, Canada, manufactured by Open-Hydro Ltd., Ireland [11]. Although every fixed tidal stream device has a small footprint, the overall impact of each installation can only be investigated by considering both the number and size of the devices installed around the coastline[12]. In addition, the environmental impact of energy extraction is not necessarily restricted to the immediate area around the turbine site[4]. The preceding facts show the importance of the far- field impact assessment studies, along with near- field impact studies. The current study mainly focuses on the far-field hydro-environmental impact assessment of tidal stream turbines. To undertake this assessment a 2-D hydro-environmental model, namely the DIVAST (Depth Averaged Velocity And Solute Transport) model, was modified so that the impacts of tidal stream turbines could be simulated by the model. Bearing in mind the lack of field measured data to validate the model, the developed model was set up for an idealised channel, as modelled by Bryden and Couch [4], with the predicted results in the current study being compared with the results published by Bryden and Couch. Then, for the purpose of demonstration, the model was applied to an arbitrary site along the Severn Estuary and Bristol Channel. The Severn Estuary has the third highest tidal range in the world, with the spring tidal range exceeding 14 m and the peak tidal currents being well in excess of 2m/s. These large currents have made the estuary very attractive from a renewable energy point of view and a number of tidal renewable energy schemes, including a 17 TWhr/year Severn Barrage, have been proposed to be sited in the estuary. To investigate all potential impacts of an array of stream turbine s in the selected site, the revised 2-D DIVAST model was linked to a 1-D hydroenvironmental model, namely FAS TER (Flow And Solute Transport in Estuaries and Rivers), and the impacts of the array on water levels, tidal currents, sediment transport and faecal bacteria concentrations have been investigated.
2 Hydro-environmental Model Details The DIVAST model was modified to study the hydro-environmental impacts of tidal stream turbines. This model has been widely used in hydro-environmental modelling of the coastal environment [13-16] and was based on a finite-difference alternating direction implicit (ADI) solution of the depth integrated Navier-Stokes and solute transport equations [17, 18]. More recently, the model has been used in modelling the hydro-environmental studies of marine renewable energy devices [8, 19, 20]. The solute/sediment transport sub- model includes the effects of dispersion, diffusion, erosion and deposition, adsorption and desorption, as well as kinetic decay.
2.1 Governing Equations The 2D governing equations used in the model are briefly given in this section, but further information on the 2D and 1D model equations are given in Falconer [17] and Kashefipour [21]. The hydrodynamic equations used in the 2D model are based on the depth-integrated three-dimensional Reynolds averaged equations for incompressible and unsteady turbulent flows, in addition to the impacts of the other external forces such as: wind shear, bottom friction, and the earth’s rotation to give for the x-direction [22]: ∂ξ ∂q x ∂q y + + =0 ∂t ∂x ∂x
(1)
∂2 qx ∂2 qx ∂2 q y ∂q x ∂uq x ∂vqx ∂ξ τ xw τ xb + β + = fq y − gH + − + ε 2 2 + + ∂t ∂y ∂x ρ ρ ∂y 2 ∂x∂y ∂x ∂x
(2)
where qx, qy = discharges per unit width in the x, y directions (m2 s-1 ), ζ = water surface elevation above datum (m), H = total water depth (m), β = momentum correction factor for non-uniform vertical velocity profile (dimensionless), f = Coriolis parameter (rad s-1 ), g = gravitational acceleration(m s-2 ), τxw, τxb = surface and bed shear stress components respectively in the x-direction (N m-2 ), and ε = depth averaged eddy viscosity. The equation for the y-direction can be developed similarly to that given for the x direction (i.e. equation (2)).
The 2D advective-diffusion equation for predicting solute transport was acquired by integrating the 3D solute mass balance equation over the depth, giving:
∂φH ∂φq x ∂φq x ∂ ∂φ ∂φ + + − HD xx + HD xy ∂t ∂x ∂y ∂x ∂x ∂y ∂ ∂φ ∂φ − HD yx + HD yy = H ∑Φ ∂y ∂x ∂y
(3)
where φ = depth averaged concentration (unit/volume) or temperature (°C), Dxx, Dxy, Dyx, Dyy
= depth averaged dispersion-diffusion coefficients in the x, y directions respectively and ΣΦ = total depth average concentration of the source or sink solute. The sediment modelling includes both cohesive and non-cohesive sediment erosion and deposition processes, which are reflected in equation (3) through the source and sink term. For more information on sediment modelling see Falconer et al. [23]. The bacteria decay was modelled using a first order decay formulation according to the Chick's Law [24] and due to the importance of the sediment deposition and re-suspension on faecal bacteria level [25-29], bacteria and sediment interaction was incorporated in the model, with more details about the bacteria modelling being given in Yang et al. [30] and Ahmadian et al.[19].
2.2 Turbine Representation The turbines have been integrated into the model by adding the reaction of axial thrust and drag force induced by turbines as external forces in the shallow water momentum equations (i.e. equation 2). Consequently, the momentum equation in the x-direction was revised as given below; with the y-direction equation being written in a similar manner:
∂q x ∂uq x ∂vqx ∂ξ τ xw τ xb + β + = fq y − gH + − + ∂t ∂y ∂x ρ ρ ∂x 2 ∂ 2q ∂ 2 q x ∂ q y FTx FDx ε 2 2x + + + + ∂x∂y ρ ρ ∂y 2 ∂x
(4)
where FTx = reaction of axial thrust induced by the turbines on the flow; based on the Newton’s third law of motion, this reaction is equal to the thrust in the opposite direction and FDx = drag force induced by the pile of a turbine per unit area normal to the flow in the xdirection, respectively. Assuming that the angle which the axis of the turbine makes with the positive y-direction is θ (as illustrated in Figure 1), then each component of the reaction of the axial thrust induced by the turbines on the flow can be written as:
FTx = FT × Sin(θ ) × sign( u)
(5)
FTy = − FT × Cos(θ ) × sign(v )
(6)
where FT, FTx and FTy = total, x and y components of the reaction of the axial thrust induced by the turbines on the flow per unit area, respectively, u and v = velocity components in the x- and y- directions, respectively and sign(x) = sign function which returns +1 when x is positive and -1 when x is negative.
θ
U
Turbine plane
φ
u
v
∆y ψ
Turbine axis
y x
∆x
Figure 1 Turbine and velocity direction schematic
The total reaction of the axial thrust per unit area is calculated by dividing the axial thrust by the area of the cell, giving: FT =
T 1 1 = × CT ρ AU eff 2 ∆x × ∆y 2 ∆x × ∆y
(7)
where CT= thrust coefficient whic h can found from the literature by knowing the Tip Speed Ratio (TSR), hub pitch and related velocities [5] and it is considered to be constant in this study; Ueff = effective flow velocity, which is the velocity normal to the turbine or parallel to the turbine axis. Turbines can be designed, either to rotate freely to be perpendicular to the flow or to rotate only 180° to face the ebb and flood flow. When the turbine can rotate freely, the turbine is always normal to the flow and subsequently the effective velocity is equal to the flow velocity. When the turbine is designed to rotate through only 180°, as illustrated in Figure 1, the turbine is not normal to the flow all the time during the tidal cycle. The velocity component in the x- and y-directions can be written as: u = U × Sin (φ )
(8)
v = U × Cos (φ )
(9)
where U = speed (m s-1 ) and φ = angle that the flow makes with the positive y direction (degrees). Then the effective velocity can be calculated using:
U eff = v × Cosθ + u × Sinθ
(10)
Using equations 8, 9 and 10, the effective velocity can be rewritten relative to the velocity and the turbine axis direction, to give:
U eff = U × Cos(θ − φ )
(11)
As the piles are fixed, the components of the drag force induced by the pile of a turbine on the flow are influenced by the flow direction, giving:
FDx = FD × Sin (θ ) × sign( u)
(12)
FDy = FD × Cos (θ ) × sign (u )
(13)
where FD, FDx and FDy = total, x and y components, respectively, of the drag force induced by the pile of turbine per unit area. Total drag force per unit area can be calculated in a similar manner to the drag force induced by any other object giving: 1 1 FD = × CD ρ AcU 2 2 ∆x × ∆y
(14)
where CD = the drag coefficient, and Ac = the cross-sectional area perpendicular to the flow. The energy flux available for a turbine is [4]: P=
1 3 C p ρAU eff 2
(15)
where P = energy flux (W m-2 ), and Cp = power coefficient.
3 Model Application 3.1 Idealised Channel Bryden and Couch [4] modelled the energy extraction process in a rectangular 1000 m wide and 4000 m long channel using a 1-D model. The refined 2-D model was setup for an analogous channel with a 100 m × 100 m grid. Similarly, upstream and downstream boundaries were set to water level and flow boundaries respectively. The model was first run for the original channel without any artificial energy extraction. The only difference between the two models was the bed roughness, which was used as a calibration parameter, to reproduce the initial conditions without any energy extraction. Bryden and Couch [4] used a Manning’s number of 0.035, while the Manning’s number used in this study was 0.037. Figures 2 and 3 illustrate a comparison between the predicted water levels and velocities during this study and the values published by Bryden and Couch [4]. As shown, both results match well and show that the channel used in the study carried out by Bryden and Couch was well reproduced in the current 2-D model.
Figure 2 Comparison of depths in the channel without artificial energy extraction. Magenta line: predicted values. Blue dots: values reported by Bryden and Couch [4]
Figure 3 Comparison of velocities in the channel without artificial energy extraction. Magenta line: predicted values. Blue dots: values reported by Bryden and Couch [4]
Figures 4 and 5 illustrate a comparison between the water levels and velocities predicted by the current model and the results reported by Bryden and Couch[4]. There is good correlation between the predicted and published results and the comparisons show that the refined method integrated in the model to extract energy performs appropriately.
Figure 4 Comparison of depths in the channel with artificial energy extraction. Magenta line: predicted values. Blue dots: values reported by Bryden and Couch [4]
Figure 5 Comparison of velocities in the channel with artificial energy extraction. Magenta line: predicted values. Blue dots: values reported by Bryden and Couch [4]
3.2 Severn Estuary and Bristol Channel The 1D-2D linked model of the Severn Estuary and Bristol Channel was set up from the outer Bristol Channel to the River Severn tidal limit, located close to Gloucester (Figure 6). The
simulation was carried out for 300 hr including a spring and neap tidal cycle. The 1D model was from Gloucester to the Severn Bridge and the 2D model was set up from the old Severn crossing (M48 bridge) to an imaginary line between Milford Haven and Hartland Head. The upstream 1D model boundary condition at Gloucester was set as a flow rate varying between 60 and 106 m3 /s (i.e. the normal River Severn condition) while the downstream boundary located in the proximity of the Severn Bridge was set as a water level boundary condition, where values for this boundary were dynamically derived from the 2D model. The time step for the 1D model was 420 s. This model consisted of 351 cross-sections with an average distance of 240 m between two consecutive cross-sections. These cross-sections have shaped four reaches connecting to each other with two junctions. The inflows for all major inputs to the River Severn in the 1D model domain, including the River Wye, were treated as lateral inflows. The bed elevations required for the 2D model were acquired by interpolation of the bathymetric data digitised from the Admiralty charts 1179, 1166, 1165 and 1152 at the centre of the cells. The 2D model was based on a coarse (600 m) and fine (200 m) grid, with a maximum time step of 105 and 35 s for the coarse and fine grids, respectively. The model predictions for the different grid sizes were compared and it was found that the model was not over sensitive to the mesh size [19]. In all 17 river and stream discharge s were included into the Severn Estuary and Bristol Channel 2D model domain, with these rivers and streams including the Taff, Ely, Parrett and Avon discharge locations, and with all sources including both flow and water quality point source inputs. Moreover, flow and enterococci inputs for all the main wastewater treatment works along the estuary and rivers were also included in the model [30].
Figure 6 Model domain extent and validation sites: A, Southerndown, B, Minehead [30]
The downstream boundary of the 2D model was specified as a water level boundary condition and the boundary values for the simulation period were obtained from the Proudman Oceanographic Laboratory (POL) Irish Sea model [31]. Since this boundary was so far seawards of the region of interest, the concentrations of faecal indicators and suspended sediments were set to zero along the downstream boundary. The upstream boundary of the 2D model was set as a flow boundary condition and the flow and water quality indicators at this location were acquired from the 1D model. The models were then calibrated using Admiralty Chart data and were then validated against different sets of field data collected at two sites illustrated in Figure 6 by Stapleton et al. [32]. The model predictions and field measurements showed good agreement, with typical comparisons between predicted water elevations and depth-averaged current speeds and measured data being shown in Figures 7 and 8 respectively. More information on the model details and model calibration can be found in Ahmadian et al. [19].
Figure 7 Comparison of predicted and measured water elevations at Southerdown (site A)
Figure 8 Comparison of predicted and measured current speeds at Southerdown (site A)
There are many protocols required for a site selected for deployment of an array of turbines, such as: high currents and a minimum depth at low spring tide, distance from the navigation channels, proximity to the national grid connections and support infrastructure, and finally not causing any significant damage to the environment and marine habitat which cannot be easily mitigated against [8]. Since the main focus of this study was to investigate the hydroenvironmental impact of tidal stream turbines, the site used in this study was solely selected for the model demonstration purposes and none of the required considerations for selecting the site, apart from relatively high flow velocity and minimum depth, have been taken into consideration. Finally, 10 m diameter turbines were used in this study, which is a relatively small size of turbine in comparison to some of the more recent commercial horizontal axis turbines, to fulfil the minimum turbine depth requirements. To investigate the potential far- field impacts of turbines, the model was set up for an array of 2000 × 10 m diameter turbines in an area of 7.2 km2 . This means that the turbines would be 50 m (i.e. 5 x turbine diameter) away from the closest turbine in each direction. The array and the point for whic h results have been presented in this paper are illustrated in Figure 9.
Figure 9 Array formation for 2000 turbines
Figure 10 shows the water levels for a spring tide, at point P1. Moreover, Figure 11 illustrates the differences in the water level across the estuary with the turbine array included and excluded in the model, at mean ebb tide at Barry (red dot). This figure shows that the changes in water levels are less than 10 centimetres in the vicinity of the array. Considering the mean depth of water, which is more than 20 m in the area, it can be concluded that the array does not make a significant change in the water levels.
Figure 10 Water levels at P1 for a spring tide without and with the turbine array
Figure 11 Changes in water levels across the estuary at high water at Barry (red dot) after including the array of turbines
Figure 12 illustrates the velocities for a spring tide at P1. This figure shows that the velocities predicted by the model after including the array of turbines was lower at P1 (located inside
the array) than the predicted velocities for the existing situation. Figure 13 illustrates typical differences in the velocities across the estuary after including the array of turbines in the model to the no turbine condition, at mean ebb tide at Barry (red dot). This figure shows that the velocities reduce inside the array, and both upstream and downstream of the array.
Figure 12 Current speeds at P1 for a spring tide without and with the turbine array
Figure 13 Changes in the velocities across the estuary at mean ebb at Barry (red dot) after including the array of turbines- vectors show the actual velocities
To study the sensitivity of the model to power extraction, the model was run for a number of scenarios with the power coefficient (C p ) changing from 0.25 to 0.45. It was found that the model was not over sensitive to power extraction. Typical water levels and velocities predicted during a spring tide at P1 for a number of these cases are shown in Figures 14 and 15, respectively.
Figure 14 Comparison of water levels at P1 for a spring tide without and with the turbine array with different power coefficient
Figure 15 Comparison of velocities at P1 for a spring tide without and with the turbine array with different power coefficients
Figure 16 shows the suspended sediment (SS) concentrations during a spring tide at P1, without and with the turbine array. The figure shows that the SS concentrations are slightly lower inside the array. Moreover, Figure 17 illustrates typical differences in the SS concentrations between with the array and the existing situation across the estuary, at mean ebb at Barry (red dot). It was found that the SS concentrations were changed around 15 km away from the array when they were compared to the existing situation. It was found that the SS levels reduced both upstream and downstream of the array and increased to the side of the array.
Figure 16 Suspended sediment levels at P1 for a spring tide without and with the turbine array
Figure 17 Changes in suspended sediment levels across the estuary at mean ebb tide at Barry (red dot) after including the array of turbines
Figure 18 illustrates the concentrations of faecal enterococci during a spring tide at P1. It can be seen that, as for the SS concentrations, the faecal bacteria concentrations are slightly lower inside the arrays. Figure 19 illustrates the typical differences in faecal enterococci concentrations across the estuary with the turbine array included and excluded in the model, at mean ebb at Barry (red dot). The results show that changes in the faecal enterococci concentrations are following the same trends as the changes in the SS concentrations and changes in the faecal bacteria levels occur up to typically 15 km away from the array. These changes are thought to be a direct consequence of changes in the ability of the flow to transport water quality constituents and an indirect consequence of changes in the SS concentrations, which affects the transport of bacteria attached to the sediments and the decay rate. However, to acquire a better understanding of the impacts of the tidal stream turbines on faecal bacteria concentrations, more comprehensive studies are required.
Figure 18 Faecal bacteria levels at P1 for a spring tide, without and with turbine array
Figure 19 Changes in faecal bacteria levels across the estuary at mean ebb tide at Barry (red dot) after including the array of turbines
Finally, Table 1 shows the amount of total, mean and maximum available power for extraction by the turbine array over the phase when the turbines were activated during the simulation period (287.6 hr). In modelling the turbine impacts, the turbines were not active during the first tidal cycle to avoid any instability which could be caused by the initial condition. Subsequently, the electricity generation phase was equal to the simulation period (300 hr), deduced by the first tide duration (12.4 hr). The available energy to each turbine at
each time step was calculated using Equation 15 and total available energy was calculated by adding up the available energy for all turbines during the simulation period. Table 1 Total, mean and maximum available power to the array Mean available Power (MW)
Max. available Power (MW)
Total available Energy * (MWhr)
31.4
245.5
9019
*
in 287.8 hours
The potential annual output of the turbine array can be calculated using the mean generated power. Subsequently, the estimated annual output of the turbine array would be 275 GWhr. The average value of the velocity magnitude at P1, which is inside the array, over the simulation period was 0.947 ms -1 . Using this value as the effective velocity for all turbines, the mean generated power of the array using Equation 15 was equal to 26.72 MW. This value was 85% of the mean generated power predicted by the model. The proximity of this value to the model predicted mean power output confirms the model power predictions. Besides, as the mean generated power predicted by the model was larger tha n the value calculated by using the average velocity at P1, it can be concluded that the average value of the velocity magnitude for all the turbines were higher than the average value of the velocity magnitude at P1. Although the output values are discouraging in the first instance, it is worth recalling that at the beginning of this section it was stated that the array with 10 m diameter turbines was not practical at this site and was only selected to demonstrate the model abilities.
4 Conclusion A 2D depth integrated hydro-environmental model has been modified to simulate the impacts of tidal stream turbines on water levels, tidal currents and water quality constituent predictions in marine and coastal water bodies. This modification was carried out by calculating the thrust and drag applied on each turbine and including the corresponding additional terms in the refined momentum equations as external force terms. In the absence of any real data published in the literature, the refined model was tested against published 1-D modelling results in the first instance. After it was found that the model results were close to the published results, the model was used to model the potential far field impacts and power generated of an arbitrary array of turbines in the Severn Estuary and Bristol Channel for demonstration purposes. The hydroenvironmental impacts of the turbine array were investigated, as well as the array potential power output. It was found that the impacts of the turbine arrays on the water levels were not significant. The velocities were reduced inside and both upstream and downstream of the array, this reduction was more than 25% in some places inside the array. Conversely, the velocities were increased along the sides of the array, with these flow patterns indicating that the flow resistance of the turbine array was encouraging flow, and increasing currents, around the array as expected. Furthermore, the model predictions have shown that the suspended
sediment concentrations changed noticeably within 15 km from the turbine array. The suspended sediment levels decreased upstream, downstream and inside the array while there were predicted to increase less significantly along the sides of the array. Since large populations of bacteria living in estuarine waters are attached to sediments, the interaction of bacteria and suspended sediments was included in the model for faecal bacteria flux predictions. The faecal bacteria concentrations predicted by the model indicated that the changes in the faecal bacteria concentrations were very similar to the predicted changes in the suspended sediment levels. This was thought to be due to the complex processes involved in faecal bacteria transport, which were affected by the changes in the bacteria attached to the suspended sediments as well as bacteria advection, diffusion and decay etc. This study has shown that the refined hydro-environmental modelling tool developed as a part of this research programme can be used in predicting the potential hydro-environmental impacts in marine and coastal water bodies, along with the power output of tidal stream turbine arrays particularly for such cases where the relative impacts and output of the arrays under various boundary conditions and array configurations are required.
5 ACKNOWLEDGMENTS The study is carried out as a part of MAREN project, which is part funded by the European Regional Development Fund (ERDF) through the Atlantic Area Transnational Programme (INTERREG IV).
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