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In-stream energy converters in a river – Effects on upstream hydropower station
Renewable Energy 36 (2011) 399e404
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Technical Note
In-stream energy converters in a river e Effects on upstream hydropower station Emilia Lalander*, Mats Leijon The Swedish Centre for Renewable Electric Energy Conversion, Division for Electricity, The Ångström Laboratory, Uppsala University, PO Box 534, SE-751 21 Uppsala, Sweden
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 September 2009 Accepted 30 May 2010 Available online 30 June 2010
The use of in-stream energy converters in rivers is an area of research that is still in its preliminary stages. The driving force of river flows is the potential energy the water gains when it precipitates on mountainsides, and this energy is traditionally converted by hydropower stations, where dams are used to create a larger head. Using an in-stream energy converter would be advantageous in areas restricted by regulation. In this paper the effects of using these converters on the upstream water level in a river are studied. This has been done both with an analytical model and with a numerical model. The analytical model described the water level increase due to energy capture to depend on how large fraction of the channel that is blocked by the turbine. It was also shown that as the converter induces drag on the flow, and as energy is lost in wake mixing, the total head loss will be a sum of energy capture and energy losses. The losses correspond to a considerable fraction of the total head drop. The numerical model was used to evaluate these results. The model used was the 3D numerical model MIKE from the DHI Group in Sweden. Turbines were modelled with an inbuilt function in the program. The results from the model did not correspond to the analytical results, as the energy capture was equal to the head drop in the program. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Numerical model In-stream energy converters Hydrokinetic energy Hydropower
1. Introduction In the field of hydrokinetic energy extraction, i.e. converting energy from water currents such as tides or in rivers, several models have been developed to study and understand the resource. One-dimensional analytical models have been used to study the effects on water level and velocity [1e3] whereas more advanced 2D and 3D models have been used to calculate the potential of tidal energy [4e6]. Some attempts have also combined analytical models with numerical ones to estimate the potential [7]. Using numerical models, an increased understanding of the nature of the flow is gained, but whether it is practically possible to construct the modelled turbines is yet to be seen. In one-dimensional models, turbine power can be related to a height drop along the channel [1]. The turbine power can be expressed as a variable dependant on the number of turbines and location along the channel [3], or as a fraction of the incoming kinetic energy flow [8]. For numerical simulations, the turbine power can be calculated using a power coefficient, Cp [6], but can also be calculated assuming the turbine imposes a force against the flow, which magnitude depends on a drag coefficient, CD [4]. Another way is to increase the bottom drag coefficient over a region where turbines
* Corresponding author. Tel.: þ46 (0) 18 471 58 12; fax: þ46 (0) 18 471 58 10. E-mail address: [email protected] (E. Lalander). URL: http://www.el.angstrom.uu.se/ 0960-1481/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2010.05.019
are present [5]. By including turbines in the numerical models the effects on the flow and surface elevation can be studied. All of the studies mentioned above are regarding tidal power. Extracting kinetic energy from river flows was recently discussed by Khan et al. [9]. The river concepts are similar to tidal ones, but differ in size, and are also subject to different flow regimes. Where tidal flows are periodic with a certain amplitude, hence predictable, and flow in two directions, river flows are less predictable, unidirectional and the velocity depends on the flow magnitude. There are of course differences in a regulated river and an unregulated one. In regulated rivers, i.e. controlled by hydropower, the flow varies on a daily, or even hourly, basis. In an unregulated river course, the flow variations depend on precipitation and, at snow fed areas, seasons (Fig. 1). These variations are on a weekly timescale or even seasonal time-scale. For both types of rivers, it is difficult to predict the annual flow variation and thus estimate the potential of a site. By analysing flow data over a longer time period it is however possible to estimate what flow intervals are likely to occur, and what flow the turbines should be constructed to handle at a specific site. The focus of this work has been to study how hydrokinetic energy converters influence the water level in a river. The studied site is in a regulated river channel one kilometre downstream from a hydropower station. The study aims to clarify effects on the upstream water level change from energy extraction, since the head of the hydropower station must not be affected significantly by the inclusion of kinetic energy converters.
400
E. Lalander, M. Leijon / Renewable Energy 36 (2011) 399e404 2500 Unregulated river Regulated river
3 flow / m /s
2000 1500 1000 500 0 1998
1999
2000
2001
2002
Fig. 1. Flow variation in a regulated (Lule river) and an unregulated (Kalix river) river course in Sweden from 1998 to 2002. Both rivers are among the largest in Sweden.
The channel was studied with both an analytical and a numerical model. For the study the numerical program MIKE was used, which was calibrated using current measurements. This is described in further details in Sections 3 and 4. The effects of turbines were calculated with the numerical model, and compared with the analytical model, and this is described in Sections 2 and 5. 2. Theory Turbines can be modelled as a section of a channel where energy is removed, i.e. causing a power loss. The effect of this energy capture can be analysed by simple analytical theories based on open channel flow theory by adding turbine energy capture to the total friction in the channel. This was done in Ref. [1] and is discussed in this section. The friction against the channel bed causes an along-channel head loss, Dhf, which is proportional to a stress term, sf, and the length of the considered channel, L:
Dhf ¼
L
rgRh
sf ;
(1)
where Rh is the hydraulic radius, r the density of water and g the gravitational constant. sf is proportional to the square of the velocity, V, and can be given in terms of the Darcy-Weisbach coefficient, f, as
sf ¼
fr 2 V : 8
(2)
When an in-stream energy converter is put in the channel, despite the energy being extracted, there exist several power losses connected to the turbine. The turbine caused head drop, Dht, is proportional to the total power, P, which in turn is the sum of the power being extracted and the power losses due to drag and to wake mixing:
Dht ¼
P
rgQ
:
(3)
The total head drop along the channel of a length L is then simply
Dhtot ¼ Dhf þ Dht 2.1. Analysis of power losses for in-stream turbines For a simple channel, a turbine can be modelled by calculating the pressure and velocity distribution in the channel using the Bernoulli equation, the continuity equation and the momentum equation. For a channel with constricting walls, the blockage effect can increase the power coefficient for a turbine. This was shown by
Garrett and Cummins [2,10]. The assumptions for the considered channel, seen in Fig. 2, were a frictionless flow, a flat channel bed and a small Froude number. Further assumptions are discussed in [10]. The force, F, exerted by a turbine with area At on the water in the considered channel is proportional to the pressure difference on either side of it, p1 p2, written as
F ¼ ðp1 p2 ÞAt :
(4)
This is the thrust of the turbine which can also be expressed by a non-dimensional coefficient, CD, as
F ¼
1 C rAt V12 : 2 D
(5)
where V1 is the velocity through the turbine. The power output from an ideal turbine, i.e. assuming no internal losses, is then
Pt ¼ FV1
(6)
For the constricted channel in the model described by Garrett and Cummins [10] the power output increases with blockage ratio, i.e. the fraction of the area that is occupied by the turbine. This is shown in Fig. 3 where Cp is plotted against the quotient of the wake velocity, V3, divided by the incoming velocity, V0, and also plotted against the CD-value. The increased power is a result of the higher pressure difference across the turbine as the turbine occupies a larger fraction of the channel area. The power captured by the turbine can be compared with the reference power, Pref, which is defined
Pref ¼ ðp0 p5 ÞAch V0
(7)
where p0 and V0 is the power and velocity in the undisturbed area, p5 the pressure after the wake mixing and Ach the channel cross sectional area. Pref is the total power consumed by a kinetic energy extractor in the channel. The height drop caused by the power extractor is calculated by a combination of Eqs. (3) and (7) is then
Dht ¼
Pref
rgQ
¼
ðp0 p5 Þ : rg
(8)
In Fig. 4 the head loss due to the presence of a hydrokinetic energy extractor is shown for V3/V0. When the drag coefficient is high, the wake velocity is small. The turbine is then not able to convert energy so the actual energy output is small. However, the total loss, Pref, increases with drag and is high for small V3. The turbine in the channel (Fig. 4) occupies 20% of the cross sectional area of the channel. Maximum turbine power capture occurs when V3/V0 ¼ 1/3. For this quotient Pref is more than double to Pt. When the fraction of the channel occupied by a turbine increases, Pref/Pt decreases. In this model, there is no limit to the depth and pressure at section 5 (p5), meaning the difference between the upstream depth, which is fixed, and the downstream depth shows a level drop. For a “real” channel, the water level would increase upstream, since the
Ach V0 p0
At V1 p1 p2
V4 V3 p4
V5
p4
p5
Fig. 2. View of a theoretical channel with a turbine in the middle. The flow is confined by the side walls.
E. Lalander, M. Leijon / Renewable Energy 36 (2011) 399e404
401
Fig. 3. Power coefficient Cp against V3/V0 (left) and CD (right). Percentage values show how large fraction of the channel area that is covered by the turbine.
turbine blocks the flow. This would lead to a velocity decrease, which in turn affects the total power in the flow. This effect is not covered by the model. The results are interesting in the sense that they show that the total power loss in the river stream can be more than twice the power captured by a kinetic energy converter. This means that at some occasions more power is lost in wake mixing and drag, than is captured by the turbine. This result is compared with results from a numerical model and is presented in Section 5. 3. Area and measurement description The studied site is located in a channel at 60 latitude in east Sweden situated downstream a hydropower plant (approximately 1 km downstream). The site is subject to turbulent flows and flow magnitude variations within half minute intervals. From the power station and about 600 m downstream, the channel is built of concrete and is almost rectangular in shape. Further downstream the natural shape of the channel has been modified together with the construction of the hydropower plant, formed to be smooth and evenly deep across the width. The lake, in which the river discharges, is also regulated. The elevation of the surface in the lake can depend on natural variations such as wind or atmospheric pressure, but is also a function of the operation of the downstream power plant (Fig. 5). The numerical model used to study turbine influence in the channel was calibrated with velocity measurements. Time-varying velocity together with time-varying depth change were measured with two ADCPs (Acoustic Doppler Current Profiler) from RD Instruments. The ADCPs, a 1200 kHz and a 600 kHz ADCP, were put downstream a bridge, in the same cross width positions, where the depths were 6 m and 4.5 m respectively, and the width 100 m. Both ADCPs had an in-mounted depth sensor, so time variations of
current velocity in three direction and depth could be measured simultaneously. An echo sounder (Eagle cuda) was utilized to measure depth. It was used in a grid with approximately 10 m wide cells over the section 150 m before the bridge and 100 m after the bridge. The two ADCPs were set to measure at 6 min interval (50 pings/ ensemble) for a period of 30 days. External factors changed the position of the 1200 kHz ADCP at two occasions, which caused bad measurement data for a short time period. Measurements from this period were cut out and are seen as a gap in Fig. 6. The water depth reading could be corrected for with the help of the 600 kHz ADCP, which had good readings for a period of 24 days. The measurement results are shown in Fig. 6. All water flowing through the channel passes through the hydropower station, owned by Vattenfall AB, upstream of the site. The measured velocity was compared with discharge data which was provided by the hydropower company. The yearly mean discharge in the channel is 300 m3/s and maximum flow exceeds 700 m3/s. The discharge varies on a daily basis, but is in general highest during winter and lowest during summer (Fig. 7). 4. Numerical simulation The numerical model was used to simulate water depth changes caused by energy extraction devices. The program used was the three-dimensional numerical program Mike3 Flow model FM (flexible mesh) which is a common tool for hydrodynamic studies. It was received from the DHI Group in Sweden.
4 P P
t
2
Δh
t
[cm]
ref
3
1 0 0
0.2
0.4
0.6
0.8
1
V /V 3
0
Fig. 4. Total alteration of the water level due to the presence of a kinetic energy extractor, expressed as Pref, against V3/V0. Also shown is the water level change due to the actual power captured by a turbine (Pt). The turbine is assumed to occupy 20% of the channel cross section area.
Fig. 5. View of the channel with measurement locations marked out (for interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
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E. Lalander, M. Leijon / Renewable Energy 36 (2011) 399e404
Fig. 6. Measurement results for the 1200 kHz (black) and the 600 kHz (grey) ADCP. “Bad” data was cut off from the measurement series, and is shown as gaps.
The hydrodynamic module that was used in this work is based on the shallow water equations [11].
4.1. Setting model parameters The studied area was modelled with a flexible mesh system, allowing variable sized mesh where desired. The meshed domain includes 2518 nodes and 4652 elements. Bathymetry data was constructed using measurement data, maps and drawings for the area. Due to the bathymetry data being rather scarce, it is considered one of the greatest sources of errors for the simulation. Bottom friction is assumed to vary with the square of the velocity according to
! ! s f ¼ rCf V jVj:
(9)
The bottom friction coefficient, Cf (Eq. (9)), was set to 0.01. The simulations were run with two open boundaries shown in Fig. 8. These were defined as input discharge in the southern boundary (power station) and a varying water level at the northern boundary, where the channel discharges into the lake. Discharge data was received from the power station.
4.2. Calibrating the model In Fig. 8 the measured current speed is compared with the modelled data. There was an estimated 0.15 m/s difference between modelled and measured velocity. There could be various reasons for the errors, both in the measurements and in the model. For measurements, the error could be due to the position of the ADCP on the bottom, since the error increases with the tilting of the ADCP. Errors could also be due to the bathymetry data used as input data in the numerical model, which was prepared from drawings and measurements. Although it was difficult to assess errors in the measurements, the variations in the current speed data corresponded well to the variations in the discharge data (Fig. 8). For the purpose of this study, the validation was assumed good enough.
Fig. 7. Correlation plot between (left) velocity and water level (right) velocity and discharge.
5. Simulation results The effects of a power extraction device on the water level in a river site are studied here. As described in Section 2, the height drop along the channel is increased when energy is extracted. Main focus of this section is to study the magnitude of these effects and how they are altered when the water level at the downstream side of the channel varies. The turbine function which is inbuilt in MIKE was evaluated. In the numerical program, the turbines are described in a subgrid scale so that the turbines should be much smaller than the cell size. The turbines are assumed to exert a force on the flow which can be expressed using a drag coefficient according to Eq. (5). Since the turbines are modelled in a sub-grid scale, the cell size will affect the force calculations. For the considered channel, this meant that the force changed when the grid cell was altered, even maintaining the CD-value constant. Force and velocity through the turbine are the two output parameters for each turbine in MIKE. To calculate turbine power, Eq. (6) can then be used. However, the equation assumes the turbines are ideal and internal losses are not included. The actual energy capture would have to be multiplied with an efficiency constant. However, as Pref is compared with the turbine absorbed power Pt, this did not have to be considered. Turbines were modelled at two locations: by the downstream bridge and by the mid-channel bridge. The pattern was chosen due to logistical reasons. Due to the shallow depth at the outflow into the lake (4 m), large vessels are not likely to be able to enter the
Fig. 8. Input data for the model and results from the simulation. Measured data are shown in black and data from the simulation in grey.
E. Lalander, M. Leijon / Renewable Energy 36 (2011) 399e404
0.8 With turbines No turbines
0.6 Δ htot [m]
channel. Therefore turbines need to be deployed from the available bridges, namely the mid-channel and the downstream bridge. Although it could be possible to deploy turbines from the shore with large cranes, a first generation farm is likely to follow the pattern shown in Fig. 9. The simulations with turbines were done with a discharge of 500 m3/s. At this flow rate, the modelled velocity at the bridge is 1.2 m/s. Historical flow data show that the discharge only rarely exceeds 500 m3/s [12]. Thus this is close to the maximum value that the turbines will operate, and this is the reason this flow was chosen. The outflow boundary, i.e. the water level in the lake, was the reference level and unless otherwise stated it was kept constant at 0 m.
403
+0.2
0.4 0.2
−0.2 0 0
100
200
Position of mid-channel bridge 300
400
Distance from power station [m] Fig. 10. Surface elevation along a 400 m section for different surface levels at the lake (indicated by numbers). The mid-channel bridge with the added turbines is located at 400 m and the large height drop from 0 to 200 m occurs due to a constriction in the channel at 200 m.
5.1. Modelling turbines For the turbines at the downstream bridge, the CD-value was chosen so that the total power loss caused by turbines became 5e10 kW for each turbine at a flow of 500 m3/s, calculated with Eq. (6). Each turbine had a cross sectional area of 25 m2 (5 5) centred at 3 m depth. At the mid-channel bridge, the velocity is higher and the cross section larger. Each turbine here was modelled to cause a power loss of 15e20 kW at the same flow, and their cross sectional area was 49 m2 (7 7) centred at 5 m depth. The reference water level in the lake was first assumed fixed at 0 m. However, measurements from the ADCP indicated the variations due to downstream regulation and wind conditions in the lake can cause a deviation of the surface level of more than 0.4 m. Due to this, the downstream water level was changed to correspond to these variations, i.e. 0.2 m. This was applied in the downstream boundary, while all other parameters have been kept constant, and the deviation of the water level upstream was calculated. Thereafter turbines were included in the model. The model was run with three turbines in the mid-channel bridge and four turbines by the downstream bridge. Using output force and velocity, the total power consumed was calculated with
Eq. (6). When the water level was at the reference level 0 m, the total power consumed by the turbines, Pt, was 95 kW. However, when the downstream level was changed, so did the total power consumption, since the velocity in the channel was changed. The results of this are shown in Fig. 10. For a downstream level of þ0.2 m, the total turbine power was simulated to 85 kW. For a downstream level of 0.2 m, the turbine power became 100 kW. 5.2. Head loss calculation In Fig. 10, the along-channel head drop is shown. Assuming no turbines in the channel, only frictional losses cause a head drop, Dhf. This is seen in Fig. 10 as a solid line. When turbines are included, modelled to cause a power loss of 85e100 kW, the total head drop, Dhtot, is the sum of Dhf and Dht, shown as a dashed line. Due to the narrow channel and large discharge magnitude, the head loss due to friction is relatively high and corresponds to 95% of Dhtot for the modelled case. Dht modelled by MIKE has a value of 2 cm when the water level is þ0.2 m in the downstream lake. It is interesting to note that when calculating Pref according to Eq. (8), i.e. the total power loss including wake losses, using a head loss of 2 cm it should be 100 kW. However, when calculating the Pt with the output data of force and velocity V1 obtained from MIKE, the same result of power is achieved, i.e. 100 kW. As was shown in Section 2.1, Pt should in fact be much smaller than Pref, due to e.g. wake losses. A conclusion from this is that the turbine function in MIKE does not account for the losses in the wake. For resource estimations, it is important that the total loss can be accurately calculated. Otherwise, using this program, the total resource would be overestimated. Also, even though kinetic energy extractor has a small influence in the channel, it is a large effect for the hydropower station, since a regular hydropower station would be able to convert the head at a higher efficiency. 6. Conclusion
Fig. 9. Turbine set-up along the channel.
In this work the effects upstream on the water level has been studied. A special focus on river sites has been applied although the results are equally valid on any channel. Two main conclusions can be drawn from this work. The first is that a kinetic energy extractor causes a head loss upstream at an upstream power plant. The total head loss is the sum of the head loss caused by the energy being captured, the head loss caused by internal losses, and losses in wake mixing.
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E. Lalander, M. Leijon / Renewable Energy 36 (2011) 399e404
This is important since it shows that a converter that is able to convert the total head loss would be much more efficient than an in-stream converter. For the specific case study, the use of water current turbines should not be implemented because the power lost by the main hydropower plant would be greater than the power generated by the in-stream turbines. These turbines would instead be suitable at sites that are restricted from the use of dams, and thus where regular hydropower is absent. The second conclusion was that the turbine function in the numerical program MIKE did not account for the power loss connected with in-stream energy converters. This leads to an overestimation of the power captured by the turbine. The turbine function in MIKE was also shown to be difficult to handle since the CD-value, which is the variable defining turbine performance, has to be chosen carefully. The force and velocity output varied with both the CD-value chosen, and on the grid size.
Acknowledgements The numerical program Mike21 was used with permission from Stefan Ahlman at the DHI Group in Sweden (www.dhi.se). The flow data was provided by Vattenfall AB (www.vattenfall.se). The authors acknowledge the financial support from The Swedish Energy Agency (STEM) and Östkrafts Environmental Fund.
References [1] Bryden IG, Grinsted T, Melville GT. Assessing the potential of a simple tidal channel to deliver useful energy. Applied Ocean Research 2004;26 (5):198e204. [2] Garrett C, Cummins P. Generating power from tidal currents. Journal of Waterway, Port, Coastal and Ocean Engineering 2004;30(3):114e8. [3] Garrett C, Cummins P. The power potential of tidal currents in channels. Proceedings of the Royal Society A 2005;461:2563e72. [4] Blunden LS, Bahaj AS. Effects of tidal energy extraction at Portland Bill, southern UK, predicted from a numerical model, in: Proceedings of the 7th European wave and tidal energy conference, EWTEC07, Porto, Portugal, 2007, pp. 1e10. [5] Sutherland G, Foreman M, Garrett C. Tidal current energy assessment for Johnstone Strait, Vancouver Island. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 2007;221:147e57. [6] Carballo R, Iglesias G, Castro A. Numerical model evaluation of tidal stream energy resources in the Ría de Muros (NW Spain). Renewable Energy 2009;34 (6):1517e24. [7] Blanchfield J, Garrett C, Rowe A, Wild P. Tidal stream power resource assessment for Masset Sound, Haida Gwaii. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 2008;222 (5):485e92. [8] Bryden IG, Couch SJ, Owen A, Melville G. Tidal current resource assessment. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 2007;221:125e35. [9] Khan MJ, Iqbal MT, Quaicoe JE. River current energy conversion system: progress, prospects and challenges. Renewable and Sustainable Energy Reviews 2008;12:2177e93. [10] Garrett C, Cummins P. The efficiency of a turbine in a tidal channel. Journal of Fluid Mechanics 2007;588:243e51. [11] Mike 21 and Mike 3 flow model FM, hydrodynamic and transport module, scientific documentation. DHI; 2008. [12] Grabbe M, Yuen K, Goude A, Lalander E, Leijon M. Design of experimental setup for hydro-kinetic energy conversion. International Journal on Hydropower and dams 2009;15(5):112e6.
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Technical Note
In-stream energy converters in a river e Effects on upstream hydropower station Emilia Lalander*, Mats Leijon The Swedish Centre for Renewable Electric Energy Conversion, Division for Electricity, The Ångström Laboratory, Uppsala University, PO Box 534, SE-751 21 Uppsala, Sweden
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 September 2009 Accepted 30 May 2010 Available online 30 June 2010
The use of in-stream energy converters in rivers is an area of research that is still in its preliminary stages. The driving force of river flows is the potential energy the water gains when it precipitates on mountainsides, and this energy is traditionally converted by hydropower stations, where dams are used to create a larger head. Using an in-stream energy converter would be advantageous in areas restricted by regulation. In this paper the effects of using these converters on the upstream water level in a river are studied. This has been done both with an analytical model and with a numerical model. The analytical model described the water level increase due to energy capture to depend on how large fraction of the channel that is blocked by the turbine. It was also shown that as the converter induces drag on the flow, and as energy is lost in wake mixing, the total head loss will be a sum of energy capture and energy losses. The losses correspond to a considerable fraction of the total head drop. The numerical model was used to evaluate these results. The model used was the 3D numerical model MIKE from the DHI Group in Sweden. Turbines were modelled with an inbuilt function in the program. The results from the model did not correspond to the analytical results, as the energy capture was equal to the head drop in the program. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Numerical model In-stream energy converters Hydrokinetic energy Hydropower
1. Introduction In the field of hydrokinetic energy extraction, i.e. converting energy from water currents such as tides or in rivers, several models have been developed to study and understand the resource. One-dimensional analytical models have been used to study the effects on water level and velocity [1e3] whereas more advanced 2D and 3D models have been used to calculate the potential of tidal energy [4e6]. Some attempts have also combined analytical models with numerical ones to estimate the potential [7]. Using numerical models, an increased understanding of the nature of the flow is gained, but whether it is practically possible to construct the modelled turbines is yet to be seen. In one-dimensional models, turbine power can be related to a height drop along the channel [1]. The turbine power can be expressed as a variable dependant on the number of turbines and location along the channel [3], or as a fraction of the incoming kinetic energy flow [8]. For numerical simulations, the turbine power can be calculated using a power coefficient, Cp [6], but can also be calculated assuming the turbine imposes a force against the flow, which magnitude depends on a drag coefficient, CD [4]. Another way is to increase the bottom drag coefficient over a region where turbines
* Corresponding author. Tel.: þ46 (0) 18 471 58 12; fax: þ46 (0) 18 471 58 10. E-mail address: [email protected] (E. Lalander). URL: http://www.el.angstrom.uu.se/ 0960-1481/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2010.05.019
are present [5]. By including turbines in the numerical models the effects on the flow and surface elevation can be studied. All of the studies mentioned above are regarding tidal power. Extracting kinetic energy from river flows was recently discussed by Khan et al. [9]. The river concepts are similar to tidal ones, but differ in size, and are also subject to different flow regimes. Where tidal flows are periodic with a certain amplitude, hence predictable, and flow in two directions, river flows are less predictable, unidirectional and the velocity depends on the flow magnitude. There are of course differences in a regulated river and an unregulated one. In regulated rivers, i.e. controlled by hydropower, the flow varies on a daily, or even hourly, basis. In an unregulated river course, the flow variations depend on precipitation and, at snow fed areas, seasons (Fig. 1). These variations are on a weekly timescale or even seasonal time-scale. For both types of rivers, it is difficult to predict the annual flow variation and thus estimate the potential of a site. By analysing flow data over a longer time period it is however possible to estimate what flow intervals are likely to occur, and what flow the turbines should be constructed to handle at a specific site. The focus of this work has been to study how hydrokinetic energy converters influence the water level in a river. The studied site is in a regulated river channel one kilometre downstream from a hydropower station. The study aims to clarify effects on the upstream water level change from energy extraction, since the head of the hydropower station must not be affected significantly by the inclusion of kinetic energy converters.
400
E. Lalander, M. Leijon / Renewable Energy 36 (2011) 399e404 2500 Unregulated river Regulated river
3 flow / m /s
2000 1500 1000 500 0 1998
1999
2000
2001
2002
Fig. 1. Flow variation in a regulated (Lule river) and an unregulated (Kalix river) river course in Sweden from 1998 to 2002. Both rivers are among the largest in Sweden.
The channel was studied with both an analytical and a numerical model. For the study the numerical program MIKE was used, which was calibrated using current measurements. This is described in further details in Sections 3 and 4. The effects of turbines were calculated with the numerical model, and compared with the analytical model, and this is described in Sections 2 and 5. 2. Theory Turbines can be modelled as a section of a channel where energy is removed, i.e. causing a power loss. The effect of this energy capture can be analysed by simple analytical theories based on open channel flow theory by adding turbine energy capture to the total friction in the channel. This was done in Ref. [1] and is discussed in this section. The friction against the channel bed causes an along-channel head loss, Dhf, which is proportional to a stress term, sf, and the length of the considered channel, L:
Dhf ¼
L
rgRh
sf ;
(1)
where Rh is the hydraulic radius, r the density of water and g the gravitational constant. sf is proportional to the square of the velocity, V, and can be given in terms of the Darcy-Weisbach coefficient, f, as
sf ¼
fr 2 V : 8
(2)
When an in-stream energy converter is put in the channel, despite the energy being extracted, there exist several power losses connected to the turbine. The turbine caused head drop, Dht, is proportional to the total power, P, which in turn is the sum of the power being extracted and the power losses due to drag and to wake mixing:
Dht ¼
P
rgQ
:
(3)
The total head drop along the channel of a length L is then simply
Dhtot ¼ Dhf þ Dht 2.1. Analysis of power losses for in-stream turbines For a simple channel, a turbine can be modelled by calculating the pressure and velocity distribution in the channel using the Bernoulli equation, the continuity equation and the momentum equation. For a channel with constricting walls, the blockage effect can increase the power coefficient for a turbine. This was shown by
Garrett and Cummins [2,10]. The assumptions for the considered channel, seen in Fig. 2, were a frictionless flow, a flat channel bed and a small Froude number. Further assumptions are discussed in [10]. The force, F, exerted by a turbine with area At on the water in the considered channel is proportional to the pressure difference on either side of it, p1 p2, written as
F ¼ ðp1 p2 ÞAt :
(4)
This is the thrust of the turbine which can also be expressed by a non-dimensional coefficient, CD, as
F ¼
1 C rAt V12 : 2 D
(5)
where V1 is the velocity through the turbine. The power output from an ideal turbine, i.e. assuming no internal losses, is then
Pt ¼ FV1
(6)
For the constricted channel in the model described by Garrett and Cummins [10] the power output increases with blockage ratio, i.e. the fraction of the area that is occupied by the turbine. This is shown in Fig. 3 where Cp is plotted against the quotient of the wake velocity, V3, divided by the incoming velocity, V0, and also plotted against the CD-value. The increased power is a result of the higher pressure difference across the turbine as the turbine occupies a larger fraction of the channel area. The power captured by the turbine can be compared with the reference power, Pref, which is defined
Pref ¼ ðp0 p5 ÞAch V0
(7)
where p0 and V0 is the power and velocity in the undisturbed area, p5 the pressure after the wake mixing and Ach the channel cross sectional area. Pref is the total power consumed by a kinetic energy extractor in the channel. The height drop caused by the power extractor is calculated by a combination of Eqs. (3) and (7) is then
Dht ¼
Pref
rgQ
¼
ðp0 p5 Þ : rg
(8)
In Fig. 4 the head loss due to the presence of a hydrokinetic energy extractor is shown for V3/V0. When the drag coefficient is high, the wake velocity is small. The turbine is then not able to convert energy so the actual energy output is small. However, the total loss, Pref, increases with drag and is high for small V3. The turbine in the channel (Fig. 4) occupies 20% of the cross sectional area of the channel. Maximum turbine power capture occurs when V3/V0 ¼ 1/3. For this quotient Pref is more than double to Pt. When the fraction of the channel occupied by a turbine increases, Pref/Pt decreases. In this model, there is no limit to the depth and pressure at section 5 (p5), meaning the difference between the upstream depth, which is fixed, and the downstream depth shows a level drop. For a “real” channel, the water level would increase upstream, since the
Ach V0 p0
At V1 p1 p2
V4 V3 p4
V5
p4
p5
Fig. 2. View of a theoretical channel with a turbine in the middle. The flow is confined by the side walls.
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401
Fig. 3. Power coefficient Cp against V3/V0 (left) and CD (right). Percentage values show how large fraction of the channel area that is covered by the turbine.
turbine blocks the flow. This would lead to a velocity decrease, which in turn affects the total power in the flow. This effect is not covered by the model. The results are interesting in the sense that they show that the total power loss in the river stream can be more than twice the power captured by a kinetic energy converter. This means that at some occasions more power is lost in wake mixing and drag, than is captured by the turbine. This result is compared with results from a numerical model and is presented in Section 5. 3. Area and measurement description The studied site is located in a channel at 60 latitude in east Sweden situated downstream a hydropower plant (approximately 1 km downstream). The site is subject to turbulent flows and flow magnitude variations within half minute intervals. From the power station and about 600 m downstream, the channel is built of concrete and is almost rectangular in shape. Further downstream the natural shape of the channel has been modified together with the construction of the hydropower plant, formed to be smooth and evenly deep across the width. The lake, in which the river discharges, is also regulated. The elevation of the surface in the lake can depend on natural variations such as wind or atmospheric pressure, but is also a function of the operation of the downstream power plant (Fig. 5). The numerical model used to study turbine influence in the channel was calibrated with velocity measurements. Time-varying velocity together with time-varying depth change were measured with two ADCPs (Acoustic Doppler Current Profiler) from RD Instruments. The ADCPs, a 1200 kHz and a 600 kHz ADCP, were put downstream a bridge, in the same cross width positions, where the depths were 6 m and 4.5 m respectively, and the width 100 m. Both ADCPs had an in-mounted depth sensor, so time variations of
current velocity in three direction and depth could be measured simultaneously. An echo sounder (Eagle cuda) was utilized to measure depth. It was used in a grid with approximately 10 m wide cells over the section 150 m before the bridge and 100 m after the bridge. The two ADCPs were set to measure at 6 min interval (50 pings/ ensemble) for a period of 30 days. External factors changed the position of the 1200 kHz ADCP at two occasions, which caused bad measurement data for a short time period. Measurements from this period were cut out and are seen as a gap in Fig. 6. The water depth reading could be corrected for with the help of the 600 kHz ADCP, which had good readings for a period of 24 days. The measurement results are shown in Fig. 6. All water flowing through the channel passes through the hydropower station, owned by Vattenfall AB, upstream of the site. The measured velocity was compared with discharge data which was provided by the hydropower company. The yearly mean discharge in the channel is 300 m3/s and maximum flow exceeds 700 m3/s. The discharge varies on a daily basis, but is in general highest during winter and lowest during summer (Fig. 7). 4. Numerical simulation The numerical model was used to simulate water depth changes caused by energy extraction devices. The program used was the three-dimensional numerical program Mike3 Flow model FM (flexible mesh) which is a common tool for hydrodynamic studies. It was received from the DHI Group in Sweden.
4 P P
t
2
Δh
t
[cm]
ref
3
1 0 0
0.2
0.4
0.6
0.8
1
V /V 3
0
Fig. 4. Total alteration of the water level due to the presence of a kinetic energy extractor, expressed as Pref, against V3/V0. Also shown is the water level change due to the actual power captured by a turbine (Pt). The turbine is assumed to occupy 20% of the channel cross section area.
Fig. 5. View of the channel with measurement locations marked out (for interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
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Fig. 6. Measurement results for the 1200 kHz (black) and the 600 kHz (grey) ADCP. “Bad” data was cut off from the measurement series, and is shown as gaps.
The hydrodynamic module that was used in this work is based on the shallow water equations [11].
4.1. Setting model parameters The studied area was modelled with a flexible mesh system, allowing variable sized mesh where desired. The meshed domain includes 2518 nodes and 4652 elements. Bathymetry data was constructed using measurement data, maps and drawings for the area. Due to the bathymetry data being rather scarce, it is considered one of the greatest sources of errors for the simulation. Bottom friction is assumed to vary with the square of the velocity according to
! ! s f ¼ rCf V jVj:
(9)
The bottom friction coefficient, Cf (Eq. (9)), was set to 0.01. The simulations were run with two open boundaries shown in Fig. 8. These were defined as input discharge in the southern boundary (power station) and a varying water level at the northern boundary, where the channel discharges into the lake. Discharge data was received from the power station.
4.2. Calibrating the model In Fig. 8 the measured current speed is compared with the modelled data. There was an estimated 0.15 m/s difference between modelled and measured velocity. There could be various reasons for the errors, both in the measurements and in the model. For measurements, the error could be due to the position of the ADCP on the bottom, since the error increases with the tilting of the ADCP. Errors could also be due to the bathymetry data used as input data in the numerical model, which was prepared from drawings and measurements. Although it was difficult to assess errors in the measurements, the variations in the current speed data corresponded well to the variations in the discharge data (Fig. 8). For the purpose of this study, the validation was assumed good enough.
Fig. 7. Correlation plot between (left) velocity and water level (right) velocity and discharge.
5. Simulation results The effects of a power extraction device on the water level in a river site are studied here. As described in Section 2, the height drop along the channel is increased when energy is extracted. Main focus of this section is to study the magnitude of these effects and how they are altered when the water level at the downstream side of the channel varies. The turbine function which is inbuilt in MIKE was evaluated. In the numerical program, the turbines are described in a subgrid scale so that the turbines should be much smaller than the cell size. The turbines are assumed to exert a force on the flow which can be expressed using a drag coefficient according to Eq. (5). Since the turbines are modelled in a sub-grid scale, the cell size will affect the force calculations. For the considered channel, this meant that the force changed when the grid cell was altered, even maintaining the CD-value constant. Force and velocity through the turbine are the two output parameters for each turbine in MIKE. To calculate turbine power, Eq. (6) can then be used. However, the equation assumes the turbines are ideal and internal losses are not included. The actual energy capture would have to be multiplied with an efficiency constant. However, as Pref is compared with the turbine absorbed power Pt, this did not have to be considered. Turbines were modelled at two locations: by the downstream bridge and by the mid-channel bridge. The pattern was chosen due to logistical reasons. Due to the shallow depth at the outflow into the lake (4 m), large vessels are not likely to be able to enter the
Fig. 8. Input data for the model and results from the simulation. Measured data are shown in black and data from the simulation in grey.
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0.8 With turbines No turbines
0.6 Δ htot [m]
channel. Therefore turbines need to be deployed from the available bridges, namely the mid-channel and the downstream bridge. Although it could be possible to deploy turbines from the shore with large cranes, a first generation farm is likely to follow the pattern shown in Fig. 9. The simulations with turbines were done with a discharge of 500 m3/s. At this flow rate, the modelled velocity at the bridge is 1.2 m/s. Historical flow data show that the discharge only rarely exceeds 500 m3/s [12]. Thus this is close to the maximum value that the turbines will operate, and this is the reason this flow was chosen. The outflow boundary, i.e. the water level in the lake, was the reference level and unless otherwise stated it was kept constant at 0 m.
403
+0.2
0.4 0.2
−0.2 0 0
100
200
Position of mid-channel bridge 300
400
Distance from power station [m] Fig. 10. Surface elevation along a 400 m section for different surface levels at the lake (indicated by numbers). The mid-channel bridge with the added turbines is located at 400 m and the large height drop from 0 to 200 m occurs due to a constriction in the channel at 200 m.
5.1. Modelling turbines For the turbines at the downstream bridge, the CD-value was chosen so that the total power loss caused by turbines became 5e10 kW for each turbine at a flow of 500 m3/s, calculated with Eq. (6). Each turbine had a cross sectional area of 25 m2 (5 5) centred at 3 m depth. At the mid-channel bridge, the velocity is higher and the cross section larger. Each turbine here was modelled to cause a power loss of 15e20 kW at the same flow, and their cross sectional area was 49 m2 (7 7) centred at 5 m depth. The reference water level in the lake was first assumed fixed at 0 m. However, measurements from the ADCP indicated the variations due to downstream regulation and wind conditions in the lake can cause a deviation of the surface level of more than 0.4 m. Due to this, the downstream water level was changed to correspond to these variations, i.e. 0.2 m. This was applied in the downstream boundary, while all other parameters have been kept constant, and the deviation of the water level upstream was calculated. Thereafter turbines were included in the model. The model was run with three turbines in the mid-channel bridge and four turbines by the downstream bridge. Using output force and velocity, the total power consumed was calculated with
Eq. (6). When the water level was at the reference level 0 m, the total power consumed by the turbines, Pt, was 95 kW. However, when the downstream level was changed, so did the total power consumption, since the velocity in the channel was changed. The results of this are shown in Fig. 10. For a downstream level of þ0.2 m, the total turbine power was simulated to 85 kW. For a downstream level of 0.2 m, the turbine power became 100 kW. 5.2. Head loss calculation In Fig. 10, the along-channel head drop is shown. Assuming no turbines in the channel, only frictional losses cause a head drop, Dhf. This is seen in Fig. 10 as a solid line. When turbines are included, modelled to cause a power loss of 85e100 kW, the total head drop, Dhtot, is the sum of Dhf and Dht, shown as a dashed line. Due to the narrow channel and large discharge magnitude, the head loss due to friction is relatively high and corresponds to 95% of Dhtot for the modelled case. Dht modelled by MIKE has a value of 2 cm when the water level is þ0.2 m in the downstream lake. It is interesting to note that when calculating Pref according to Eq. (8), i.e. the total power loss including wake losses, using a head loss of 2 cm it should be 100 kW. However, when calculating the Pt with the output data of force and velocity V1 obtained from MIKE, the same result of power is achieved, i.e. 100 kW. As was shown in Section 2.1, Pt should in fact be much smaller than Pref, due to e.g. wake losses. A conclusion from this is that the turbine function in MIKE does not account for the losses in the wake. For resource estimations, it is important that the total loss can be accurately calculated. Otherwise, using this program, the total resource would be overestimated. Also, even though kinetic energy extractor has a small influence in the channel, it is a large effect for the hydropower station, since a regular hydropower station would be able to convert the head at a higher efficiency. 6. Conclusion
Fig. 9. Turbine set-up along the channel.
In this work the effects upstream on the water level has been studied. A special focus on river sites has been applied although the results are equally valid on any channel. Two main conclusions can be drawn from this work. The first is that a kinetic energy extractor causes a head loss upstream at an upstream power plant. The total head loss is the sum of the head loss caused by the energy being captured, the head loss caused by internal losses, and losses in wake mixing.
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This is important since it shows that a converter that is able to convert the total head loss would be much more efficient than an in-stream converter. For the specific case study, the use of water current turbines should not be implemented because the power lost by the main hydropower plant would be greater than the power generated by the in-stream turbines. These turbines would instead be suitable at sites that are restricted from the use of dams, and thus where regular hydropower is absent. The second conclusion was that the turbine function in the numerical program MIKE did not account for the power loss connected with in-stream energy converters. This leads to an overestimation of the power captured by the turbine. The turbine function in MIKE was also shown to be difficult to handle since the CD-value, which is the variable defining turbine performance, has to be chosen carefully. The force and velocity output varied with both the CD-value chosen, and on the grid size.
Acknowledgements The numerical program Mike21 was used with permission from Stefan Ahlman at the DHI Group in Sweden (www.dhi.se). The flow data was provided by Vattenfall AB (www.vattenfall.se). The authors acknowledge the financial support from The Swedish Energy Agency (STEM) and Östkrafts Environmental Fund.
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