Experimental analysis of the flow field around horizontal axis tidal turbines by use of scale mesh disk rotor simulators

ARTICLE IN PRESS Ocean Engineering 37 (2010) 218–227

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Experimental analysis of the flow field around horizontal axis tidal turbines by use of scale mesh disk rotor simulators L.E. Myers n,1, A.S. Bahaj Sustainable Energy Research Group, School of Civil Engineering and the Environment, University of Southampton, Southampton SO171BJ, UK

a r t i c l e in f o

a b s t r a c t

Article history: Received 10 June 2009 Accepted 17 November 2009 Available online 24 November 2009

Understanding the flow field around horizontal axis marine current turbines is important if this new energy generation technology is to advance. The aim of this work is to identify and provide an understanding of the principal parameters that govern the downstream wake structure and its recovery to the free-stream velocity profile. This will allow large farms or arrays of devices to be installed whilst maximising device and array efficiency. Wake characteristics of small-scale mesh disk rotor simulators have been measured in a 21 m tilting flume at the University of Southampton. The results indicate that wake velocities are reduced in the near wake region (close behind the rotor disk) for increasing levels of disk thrust. Further downstream all normalised wake velocity values converge, enforcing that, as for wind turbines, far wake recovery is a function of the ambient flow turbulence. Varying the disk proximity to the water surface/bed introduces differential mass flow rates above and below the rotor disk that can cause the wake to persist much further downstream. Finally, the introduction of increased sea bed roughness whilst increasing the depth-averaged ambient turbulence actually decreases downstream wake velocities. Results presented demonstrate that there are a number of interdependent variables that affect the rate of wake recovery and will have a significant impact on the spacing of marine current turbines within an array. & 2009 Elsevier Ltd. All rights reserved.

Keywords: Marine current turbine Wake Flow field ADV

1. Introduction Energy extraction from marine currents is poised to make the jump from conservative demonstrator-type devices to full-scale prototype machines in the near future with many companies currently working to develop devices in various forms that can tap the large marine current energy resource around the world. This energy tends to be concentrated at relatively compact sites where tidal flows are spatially constrained such as between islands, around headlands or estuarine-type inlets (Garrett and Cummins, 2004; Carbon Trust, 2005). If MCEC technology is to achieve electricity generation on any appreciable scale it will have to be installed in farms or arrays (see Fig. 1). Marine currents have many favourable characteristics that lend themselves to electricity generation, particularly over other renewable energy technologies. Tidal cycles are predictable with a time-varying flow speed and direction, which is beneficial for control of the electrical grid as generation can be accurately forecast ahead of time (Clarke et al., 2006). Many sites with strong

Abbreviations: ADV, acoustic Doppler velocimeter; MCEC, marine current energy converter n Corresponding author. Tel.: + 44 238059 3940; fax: + 44 238067 7519. E-mail addresses: [email protected], [email protected] (L.E. Myers). 1 www.energy.soton.ac.uk 0029-8018/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2009.11.004

tidal flows have bi-directional flow characteristics that could lead to more compact array or farm layouts compared with similar technologies such as wind. Peak flow speeds can exceed 8–10 knots (4–5 m/s) and when coupled with the high density of sea water result in large amounts of energy concentrated into what are relatively small areas (Myers and Bahaj, 2005; Blunden and Bahaj, 2007). However, marine current energy conversion is an emerging technology that whilst being able to benefit from some technology transfer from similar applications (such as wind energy) holds some unique problems that have yet to be addressed. The downstream flow field is of importance when determining inter-device spacing and layout of an array. Fluid passing through a horizontal axis MCEC experiences a reduction in velocity across the rotor plane. Downstream of the rotor this region of fluid moves at a lower velocity than the free stream fluid (that passed around the rotor) and hence must expand in order to conserve momentum. This takes the form of a gradually expanding coneshaped region downstream of the rotor, commonly known as the wake. Turbulent mixing in the boundary region between the wake and the faster moving free stream fluid serves to re-energise the wake, breaking it up and increasing the velocity. At a distance far downstream the wake will have almost completely dissipated and the flow field will closely resemble that which existed upstream of the rotor disk. Variables that may influence the wake structure

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Fig.1. Artist’s impression of an MCEC array.

for a single rotor disk include the momentum drop across the rotor disk (rotor thrust), ambient and device generated turbulence, proximity to seabed/water surface and the nature of the vertical velocity profile. The length, width and persistence of the wake created by an MCEC will be most important for inter-device spacing within an array. Devices spaced too closely will suffer a decrease in performance whilst spacing devices too far apart will lead to a sub-optimal use of surface area within the region of strong tidal flow. First-generation tidal energy devices are expected to be installed relatively close to shore in water depths of 30–40 m that are suitable for conventional jack-up barges. With expected rotor diameters of 10–15 m it is clear that there is a high vertical blockage associated with the devices in the flow. Later generations of devices will most likely harness the stronger and much deeper flows such as those in the Pentland Firth, where depths can approach 100 m. Deep-water devices will require a greater level of technical experience gained from the installation and operation of initial device concepts. Despite the installation of several single device prototypes in the sea around the world there have been relatively few instances of comprehensive spatial and temporal flow measurement at sites with strong tidal flows. Historically there has been little need for detailed flow mapping of strong tidal flows; peak flow speeds and direction are of use for shipping but such areas are generally avoided by heavy shipping and marine civil works if possible. Thus data available tend to be of low resolution and a number of empirical/theoretical expressions have been developed to infer more detail. There are a number of different models or expressions that are used to simulate the vertical velocity profile in the sea using surface flow speed or depth-averaged data. One early method (UK Department of Energy, 1990) incorporated the sea bed roughness as a variable to more accurately define the velocity (and associated shear profile) in the lower part of the water column. The expression has been shown to be over-conservative when applied to a measured flow domain (Myers and Bahaj, 2008). A later relationship was proposed (European Commission, 1996) that suggested a simple power law from the sea bed to half depth, with the upper portion of the water column assigned a constant velocity. More recently some offshore survey work has been realized. Vertical velocity profiles have been measured in a few cases in UK waters, where reasonably strong tidal streams exist. Work in the Menai Strait in Wales (Rippeth et al., 2002) and measurements of the inflow velocity profile at a site near Lynmouth North Devon, where a 300 kW prototype device was installed in 2003 (UK Department of Trade and Industry, 2005). More recently data have been made available from the European Marine Energy Centre (Norris and Droniou, 2007), where an Acoustic Doppler

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Current Profiler (ADCP) was installed in the Falls of Warness tidal race in Orkney. Results showed that in waters 45 m deep, turbulence induced by wave motion had a significant effect on the upper 15 m close to the water turbulence generated from the sea bed also migrated towards the centre of the water column, reinforcing the view that the central third of the depth is most suitable for 1st-generation MCEC devices as it offers the most tranquil conditions. There is a distinct lack of ambient turbulence measurements at sites where strong tidal flows exist. This aspect of the flow field is important for wake mixing at distances greater than five rotor diameters downstream (Ainslie, 1985). A significant amount of work has been conducted (Dyer, 1971, 1980; Heathershaw and Langhorne, 1998) investigating turbulence and velocity profiles close to the seabed that serve to drive sediment transport under strong tidal flows. However, high frequency measurements were confined to regions close to the seabed and so are not very pertinent for quantifying flow conditions in the region where MCEC devices might operate. The paucity of flow measurements at tidal sites and the rapid development of technology highlight the very real need to understand the formation and nature of the wake region downstream of an MCEC. In addition, there is also a clear need of knowledge to quantify the relative influence of a number of device and physical environment parameters on this volume of flow. The experimental studies described in this paper attempt to provide an insight into such issues. Working at medium or large scale when investigating such a technology at basic research level is clearly unfeasible. Therefore this work has focused on small scale testing, which can be achieved at laboratory facilities. Modeling horizontal axis rotors becomes impractical at very small scale. Accurately scaling the channel flow properties whilst maintaining rotor thrust, power and tip speed is not possible without significantly altering aspects of the downstream flow field. For instance, accurate tip speed scaling would require a 100 mm diameter model rotor to have a rotational rate in excess of 1500 rpm in order to achieve a typical full-scale tip speed of 10 m/s. This is clearly impractical from a design point of view and would add a great deal of swirl and induce large pressure gradients in the wake. Since swirl and similar effects generally dissipate a short distance downstream of the rotor it is thought that accurate reproduction of the thrust exerted on the rotor is of principal importance. This thrust can be provided by static mesh disk rotor simulators that have the correct size for appropriate hydraulic scaling of the flow properties and have varying levels of thrust controlled through the level of porosity. The use of mesh disk simulators will not have the same influence on the flow as an energy extracting rotor. The principal differences are summarized below: i. energy extracted from the flow is converted to small-scale turbulence downstream of the disk as opposed to being extracted as mechanical motion; ii. vortices shed from the edges of the disk will differ from those of a rotating blade; iii. swirl angle of the flow from the mesh disk will be zero. All the effects highlighted above have been observed in previous studies of wind turbines as being exclusive to the near-wake region and have little bearing on general (far) wake recovery (Sforza et al., 1981; Connel and George, 1981). The longitudinal limit of the near wake is defined as the point at which the shear layer reaches the centerline turbine axis. This is generally observed to occur within 2–5 rotor diameters downstream for wind turbines (Vermeer et al., 2003). The extent of the near wake has been shown to be of a similar magnitude for

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actuator disks replicating a tidal turbine in a shallow fluid flow (Bahaj et al., 2007). Whilst length scales and flow features shed from a tidal turbine support structure may differ from those of wind the fundamental issue of the far wake flow field mixing being driven by ambient turbulence is expected to remain. Key differences between wind and tide include potential flow acceleration above and below a tidal rotor and different turbulent length scales in both the ambient and wake regions. The structure of the near wake has little bearing on far wake properties. In this region the rate of wake expansion and dissipation is driven by ambient turbulence and proximity of bounding surfaces. For wind turbines longitudinal (downwind) spacing is in the order of 8–10 rotor diameters, comfortably within the far wake region. Previous experiments conducted by the authors (Myers et al., 2008a, 2008b) with a submerged actuator disk demonstrated that centerline velocity deficits are still appreciable at 10 diameters downstream and that downstream spacing could be in the order of 15–20 diameters. The close proximity of sea bed and water surface constrains vertical expansion of the wake and reduces flow entrainment on the underside of the wake as demonstrated in previous studies of tidal turbines in high blockage ratio environments (Strickland et al., 1979). This increases the wake length for a given ambient turbulence intensity compared with the relatively unconstrained case for wind turbines. Accurate representation of complex temporally and spatially varying flow of a full-scale tidal site is never going to be achievable at small scale in a laboratory setting. Indeed it has been stated that full scale wind turbine wake velocity deficits were smaller than wind tunnel experiments due to wake meandering caused by short time scale direction changes in the wind reducing time-averaged velocities downwind of the turbine (Ainslie, 1986). Another study (Barthelmie et al., 2005) measured this direction change downwind of a full-scale wind turbine and highlighted the overestimation of wake velocity arising from a numerical model. It remains to be seen if short term fluctuations in direction will occur at MCEC-suitable sites with strong tidal flows. Far wake characteristics are assumed to be similar to that of full-scale rotors due to parity between accurately scaled rotor thrust and channel flow properties (velocity profile, ambient turbulence, etc.). There is also evidence of previous investigations (Builtjes, 1978; Sforza et al., 1981; Myers and Bahaj, 2008) concerning the study of flow fields around horizontal axis rotors using mesh disk simulators. The overarching aim of this work is to investigate key variables that affect the flow field downstream of scale mesh disk rotor simulators in a vertically constrained flow field with vertical blockage ratios similar to that expected for first-generation tidal turbines. Far wake properties ( 45 diameters downstream) will be similar to an operational horizontal axis rotor and the identification and quantification of specific trends will guide the course of future research in this area. Work presented in this paper describes the experimental arrangement and results of investigation of the following parameters: varying rotor thrust, proximity of the rotor disk to the sea bed/surface and the effect of increasing sea bed roughness.

2. Experimental set-up 2.1. Scaling parameters Scaling properties of an open channel can present problems at small scale due to the relationship between both Froude and

Reynolds numbers as follows: U Fr ¼ pffiffiffiffiffiffi gd

Re ¼

UL

n

ð1Þ

ð2Þ

where U is the flow velocity, g the acceleration due to gravity, d the water depth, L the characteristic length (generally taken as the depth for wide channels) and n the kinematic viscosity of the fluid. Linear scaling of these parameters cannot be achieved when the model/prototype ratio becomes too small. Froude scaling is important as there is a free surface in close proximity to the rotor and thus gravitational effects cannot be ignored. High Froude numbers can often occur in model systems that lead to unsteady water surface profiles; thus parity is generally maintained between prototype and model systems. In a large tidal channel, viscous forces dominate especially close to the sea bed; thus Reynolds scaling is important. Channel properties are used for this work (L represents the depth) as actuator disks do not rotate and for horizontal axis turbines (wind and tidal) Reynolds scaling is generally defined at the rotor blade surface. Discrepancy in Reynolds numbers between model and prototype is usually tolerated for the scaling of hydraulic channels if Froude similarity is maintained and both full-scale and model Reynolds numbers lie within the same turbulent classification. In terms of device scaling all physical distances are scaled in a linear manner. The principal device scaling parameter is the amount of thrust force exerted on the fluid by the rotor. This is generally expressed as a non-dimensionless parameter; the thrust coefficient is given by Ct ¼

Thrust ¼ 4að1aÞ 0:5rU02 Ad

ð3Þ

where r is the fluid density, U0 the free stream longitudinal flow velocity, Ad the area of the rotor and a the axial induction factor. The axial induction factor has a peak value of 1/3; hence the optimum value of Ct = 0.9. This equation is derived from actuator disk theory and is commonly found in wind turbine texts (Burton et al., 2001). It applies equally to horizontal axis MCECs, the only difference being the fluid density and typical operating flow speeds. Thrust values for marine turbines per unit area are approximately 50 times greater than wind turbines (at typical operating flow speeds) and 5 times greater for typical rotor swept areas.

2.2. Circulating flume Experiments were conducted at the 21 m tilting flume at the Chilworth research laboratory, University of Southampton. The flume is a conventional gravity fed flume with a working section 21 m in length, 1.35 m width and depths up to 0.4 m. Water is lifted from a large sump beneath the flume via 3 centrifugal pumps that convey fluid to a sump at the upstream end of the working section. Flow rates are controlled with butterfly valves on each feeder pipe and depth can be varied with an overflow tailgate situated at the downstream end of the working section. The vertical velocity profile in the flume is well developed (Fig. 2) and closely resembles a modified (1/7)th power law with a more uniform velocity close to the surface as measured at a full-scale tidal site (Carbon Trust, 2005). Adding artificial bed roughness reduces the velocity and increases shear in the bottom third of the water column.

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2.3. Mesh disk simulator rig

2.4. Flow mapping

Mesh disks were constructed of varying porosity to replicate changes in thrust force. Lower porosity disks were machined from thin sheet PVC plastic. Porosity (ratio of open to closed area) ranged from 0.48 to 0.35. Higher porosities were achieved by using wire mesh disks. The diameter of all disks was 100 mm. In order to accurately scale disk thrust coefficients from full scale to model scale in the Chilworth flume, actual disk thrust forces were in the order of 1 N. Disks were mounted in the flow via a stainless steel lever arm that was mounted on a rig that incorporated a variable point pivot arrangement to mechanically amplify the force. Measurements were taken with a regularly calibrated 10 N button load cell mounted at the top of the rig (Fig. 3 right), which was consistently excited to a fixed voltage for all runs. Output responses were measured over a length of time to ascertain mean disk thrust values using a Keithley 2700 multimeter/data acquisition system with 22-bit resolution.

In order to visualise the flow field around the mesh disk rotor simulators, a large number of point measurements were taken within the channel. A Nortek ADV device was used for high frequency velocity sampling. The uptake of such devices has been swift due to affordability and ease of use. The functionality and the general accuracy of ADV devices have been addressed elsewhere (Lohrmann et al., 1994); Voulgaris and Trowbridge, 1998; Rusello et al., 2006; Blanckaert and Lemmin, 2006). The Vectrino ADV used for this work incorporated advanced firmware and was set to sample at 50 Hz with a sample volume of 0.15 cm3. The inflow profile was measured upstream of the disk and a comprehensive set of downstream points were measured. Offset distances from the disk centre-axis were expressed in terms of disk diameters (D). Downstream measurements in the longitudinal axis generally extended from 3 to 20D and laterally (cross flume) up to 4D. For all tests presented, the water depth was equal to 0.3 m or 3D, which is the ratio for prototype and 1st generation devices. Vertical measurement distance intervals were taken as 0.1d where d = total water depth. Each flow map consisted of 250–350 downstream point measurements depending on the function of the experiment. Sample periods ranged from 90 to 180 s depending on the flow conditions at any particular point (generally a function of observed turbulence intensity).

3. Data reduction and accuracy 3.1. Flow conditions and data filtering

Fig. 2. Chilworth flume velocity profile comparison.

The flow characteristics of the Chilworth flume are quite stable considering the large volume of water in the system. Table 1 illustrates the variation in mean flow velocity at a single point over a range of sample periods. Generally the mean flow speed can be ascertained to within 71% over a period of 90 s. Note that sample #10 in Table 1 can be discounted according to Chauvenet’s criterion (Taylor, 1982). Due to the high concentration of suspended solids in the Chilworth flume, no doubt arising from being located in a hard water area, ADV acoustic signal strengths and device correlation

Fig. 3. Experimental set-up at Chilworth flume (left) and close-up of mesh disk pivot unit (right).

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Table 1 U-component velocity variation in Chilworth flume. Sample number 1 2 3 4 5 6 7 8 9 10 11 12

Sample duration (s)

Mean U-component velocity (m/s)

Difference from 600-s sample (%)

90 90 90 90 90 90 90 90 90 90 300 600

0.2472 0.2516 0.2497 0.2502 0.2488 0.2506 0.2504 0.2517 0.2498 0.2430 0.2478 0.2487

 0.63 1.16 0.38 0.60 0.04 0.75 0.66 1.21 0.45  2.31  0.36 0.00

sound pulse has been emitted, reflected and is returning to the probe when it intercepts the following emitted pulse within the sample volume. This event depends primarily on the height of the measurement volume above the bed coupled to the ADV velocity range. All experiments conducted in the Chilworth flume measurements close to 90 mm above the bed often suffered from such reflection errors. The vertical extent of the weak spot depends on the composition of the bed material and the firmware of the ADV device (Nortek website (unpublished), 2006). Measurements taken in such weak spots were characterised by greater energy levels (than regions of flow immediately adjacent to the sample volume) and increased data spiking was prevalent. A velocity cross-correlation filter was applied to such data sets (Cea et al., 2007). This method applies the filter and removes all erroneous data before replacement data such as those from a tailored algorithm does not re-introduce data spikes. Other filter methods are available and a simple minimum/maximum filter was generally applied to most data sets where a smaller number of spikes were present. Fig. 5 shows raw data at one of the sample points taken where ADV reflection errors occurred. Data are presented in velocity correlation space. As with the phase-space filter (Goring and Nikora, 2002) good quality data are assumed to lie within the bounds of an ellipsoid. In many instances dead spots were identified from the ADV velocity trace and the probe submersion depth adjusted to avoid this phenomenon. 3.2. Data presentation Horizontal axis rotor wake recovery can be defined in terms of velocity deficit, which is a non-dimensional number relative to the free-stream flow speed at hub height (U0) and the wake velocity (UW): Udeficit ¼ 1

Iffi scores were consistently high. The correlation coefficient (R2) can be expressed in terms of the dimensionless spectral width (fr): 2 f2 r

ð5Þ

Turbulence intensity is commonly defined as

Fig. 4. ADV correlation values for a typical 180-s sample.

R2 ¼ e2p

UW U0

ð4Þ

The dimensionless spectral width is the product of the received signal width and the sample time interval. Higher correlation values are commonly associated with greater measurement accuracy. A value of correlation greater than 70% is recommended by Nortek for measurement of turbulent velocities. During experimental work typical device signal to noise (SNR) ratios were above 22 and correlation 490%. However these are not definitive measurements of sample accuracy and can be used only as a crude guide for ADV performance. This is illustrated in Fig. 4, where the correlation scores of U-direction velocity of a 3-min sample taken in low turbulence flow is presented. It can be seen that whilst filtering out data with correlation scores 490% removes the largest velocity spikes other data values that might be removed using other filtering methods are missed. Sample size is reduced by 27% in this example for filter criteria of correlation 490%; thus an amount of good quality data is lost. In general ADV data sets were composed of good quality samples. Flow downstream of the disks contained no entrained air within the water column and turbulence levels were not excessive with any instances of large eddies or reversing flows. The most adverse measurements occurred when the ADV suffered reflection errors. The down-looking or vertical ADV probe can suffer from a number of weak or dead spots. This occurs when a

s U

ð6Þ

where s is the root-mean square of the turbulent velocity fluctuations and U the mean velocity. Contour plots of turbulence levels and mean velocity illustrate a vertical slice of the mesh disk and associated flow field running down the centre plane of the flume as shown in the left part of Fig. 6. Line graphs show the centreline data running in a downstream direction along the centreline of the disk and flume as shown in the right of Fig. 6.

4. Results and discussion 4.1. Varying disk thrust The value of MCEC rotor disk thrust and hence thrust coefficient (Ct) will vary over the range of operational inflow speeds in a similar manner to wind turbines. Whilst an optimum value of Ct will be close to 0.9 (according to momentum theory) there will be periods of flow speed less or greater than the rated flow speed of the MCEC device, where values of Ct might be lower than the value of 0.9.Thus it is clear that MCEC devices may operate over a range of Ct during standard operation. Fig. 7 shows some of the centre plane velocity deficit profiles from a set of experiments with varying disk thrust. The near wake region o5 diameters downstream is most affected with stronger initial deficits occurring for greater disk thrust. However, beyond 7 diameters downstream the velocity deficits are broadly identical for all disks tested.

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Fig. 5. Raw velocity data shown in velocity correlation space. Sample subject to beam reflection error.

Fig. 6. Regions of flow mapped in the Results section of this report. Centre plane vertical slice (left) and centreline (right).

Fig. 7. Centre plane velocity deficits for varying rotor disk thrust coefficient. Ct = 0.61 (top), 0.86 (centre) and 0.94 (bottom).

Fig. 8 shows centreline data that reinforce this observation. Initial velocity deficits close to the disk are not a true function of disk porosity as one might expect. Hole size and frequency also influence thrust characteristics. This was assumed to be due to increasing orifice type losses associated with reducing hole diameter. Thus for disks with equal porosity, smaller and more numerous holes would result in a higher disk thrust than a disk

with fewer larger holes. Ambient turbulence has a significant effect on wake mixing and recovery in the far wake region and so the convergence of the velocity deficit profiles for varying disk thrust is somewhat expected. At distances greater than 10 diameters downstream all velocity deficit profiles are virtually identical as the effects of varying thrust coefficient, which primarily increase the initial momentum drop across the disk,

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have dissipated. It is expected that a reduction in velocity of 10% or less would most likely be tolerated for placing an MCEC downstream of another device. As the kinetic energy flux is proportional to the cube of velocity this would still yield a reasonable reduction in power output for a downstream device. From these results it would seem unlikely that longitudinal spacing of MCEC devices will be much less than 10 diameters (possibly 15) unless downstream devices are offset laterally from those operating upstream. Access for installation and maintenance vessels may also drive MCEC device layout within an array precluding tighter spacing. A further area worthy of consideration is the differing amounts of turbulence added to the near wake region by the MCEC device structure. With a wide range of prototype forms presently in development, predicting the flow field in the near wake may prove quite difficult. The support stem used for the mesh disk experiments in this work was deliberately made as narrow as possible to minimise any added turbulence in the near wake and to isolate the disk/flow properties as the principal experimental variables.

4.2. Proximity to bounding surfaces There are a number of device concepts for harnessing energy from marine currents. Whilst the use of a horizontal axis rotor is emerging as the most common form of prime mover the means of supporting the rotor structure varies considerably. This gives rise to devices potentially operating at various points down through the water column. Fig. 9 shows the effect of variation of the vertical position of the disk in the water column. There is a significant increase in wake velocity deficit when the disk is placed within close proximity of the bed. Fig. 10 reinforces this observation, showing greater centerline velocity deficit for the lowest disk position persisting far downstream. Observation of Reynolds stresses with increasing downstream distance (Fig. 11) for the deeper disk immersion highlights the lack of vertical symmetry that can result for a disk in a vertically constrained flow. This gradually dissipates with downstream distance until at 20D downstream the shear stress profile approaches that of the inflow condition, where the Reynolds stress is more constant with depth. This observed lack of vertical symmetry for mean velocity and higher order flow characteristics effect has implications for numerical simulation of the flow field downstream of MCECs (Myers et al., 2008a, 2008b). A more indepth approach for modeling the flow field will be required, removing the assumption that the wake is axi-symmetric at all distances downstream (Fig. 12). Turbulent kinetic energy (TKE) energy can be expressed as TKE ¼

Fig. 8. Centreline velocity deficits for varying disk Ct.

 1  02 u þv02 þ w02 2

ð7Þ

The term is actually expressed per unit mass of fluid, where u0 is the varying component of the flow equal to the instantaneous velocity minus the mean velocity. The over bar denotes the time-averaged parameter. For the deep immersion disk (centred at 0.33d) a normalised representation of the TKE reveals no flow acceleration beneath the disk and a much higher mass flow rate above the disk. This would suggest that the mean pressure difference between the disk and bed reduces inversely with distance and that there is very little mass flow; hence flow re-energisation occurs beneath the disk

Fig. 9. Centre plane velocity deficits for varying disk submersion depths. Disk centre at 0.75d (top), 0.66d (centre) and 0.33d (bottom).

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of the wake with free stream fluid and ultimately serve to reduce wake velocity deficits downstream. Increased TKE levels beneath the disk persist downstream for disks centred at 0.5d and 0.66d. The increased TKE levels above the deep immersion disk serve to prevent large vertical expansion of the wake. Fig. 9 shows the symmetry of the wake around the centreline and the band of fast moving flow bounding the upper part of the wake. It seems as if reducing the disk/bed distance ultimately causes the disk to act hydraulically as a submerged obstruction. Seabed mounted MCEC devices may need to ensure that rotors do not sweep too close to the slower moving fluid close to the sea bed if compact array layouts are to be realised. Second-generation devices may well be installed in much deeper flows (relative to rotor diameter) and hence wake expansion will be altered from the length scaling employed in this work. Previous work by the authors has demonstrated that wake lengths could increase in very deep (almost unconstrained) flows [Myers et al. 2008a, 2008b) Fig. 10. Centreline velocity deficits for varying disk submersion.

Fig. 11. Centre plane vertical slices of Reynolds stress of a disk with increasing downstream distance (disk vertically centred at 0.33d from bed).

Fig. 12. Centre plane vertical slices of normalised TKE at 4D downstream for disk at varying depths.

and the underside of the downstream wake. As the distance between the disk and bed is increased there is evidence of increased TKE levels (in excess of inflow levels), which aid mixing

4.3. Increasing seabed roughness Persistence and intensity of the rotor wake should be reduced as ambient turbulence levels increase. This has been found to be true with measurements from wind turbines (Baker et al., 1985). To test this hypothesis for a constrained flow artificial seabed roughness was introduced to increase the turbulence intensity in the bed region. The bed roughness was 4 m in length (40D) beginning far upstream of the disks to ensure that the flow regime was stable across the region of measurement. It was found that a new boundary layer profile was fully developed and stable 1.8 m downstream of the leading edge of the roughened bed. Particle roughness length was between 6.7 and 10 mm, scaled to represent a rocky seabed that would have the greatest effect on added turbulence in the bed region. The increased shear in the vertical velocity profile is shown in Fig. 2. Fig. 13 shows the Udirection turbulence intensity downstream of 2 disks placed at varying distance from the rough seabed. The band of turbulence generated by the bed roughness can be clearly observed. It is encouraging to note that in the absence of the disk the bedgenerated turbulence migrates approximately (1/3)rd of the total water depth up from the bed in close agreement with observations from the EMEC tidal berth (Norris and Droniou, 2007). With the disk located at half depth the added diskgenerated turbulence remains separated from the ambient bed turbulence. Placing the disk closer to the bed causes these regions to merge and persist far downstream. Increased turbulent mixing would suggest a shortened wake but conversely the close proximity of the bed-generated turbulence increases the wake velocity deficit downstream of the rotor disk. As with the deepimmersed disk (with a smooth bed) the low mean velocity close to the bed allows little mass flow beneath the disk to re-energise the underside of the wake. Despite the large increase in turbulence intensity in this region the downstream velocity remains very low as shown in Fig. 14. This reduces the shear motion (and hence rate of wake recovery) that occurs when the flow velocity between the wake and free stream fluid is larger. Therefore the higher turbulence intensities do not enhance wake recovery in this instance; in fact it highlights the problem of expressing turbulence intensities at low mean flow speeds. Fig. 15 shows the centreline downstream velocity deficits. In both cases velocity deficits are greater than similar smooth-bed experiments. The far wake velocity deficit of the deeper immersed disk is clearly greater. Tidal energy sites with a rocky seabed may therefore be less attractive for the installation of MCEC technology. The more pronounced velocity shear in the lower part of the water column

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Fig. 13. Centre plane turbulence intensity for varying disk depth over a roughened bed. Disk centre at 0.5d (top) and 0.33d (bottom).

Fig. 14. Downstream centreplane velocity for an actuator disk placed within close proximity of a roughened bed. (Disk centre at 0.33d).

Fig. 15. Centreline velocity deficits for varying disk depth over an artificially roughened bed.

will result in a slow-moving turbulent flow that will reduce wake recovery and increase structural loading on device rotor blades. Devices installed at sites with these characteristics should avoid extracting energy in the lower third of the water column.

5. Conclusions The results of studies investigating the flow field around 100 mm diameter mesh disk rotor simulators at the University of Southampton Chilworth hydraulics laboratory has highlighted some interesting results that will serve to shape on-going research in this area.

Variation in the rotor disk thrust yielded the expected result that there is little effect on the wake structure greater than six disk diameters downstream. In the far wake region velocity deficits converged for all values of disk thrust, reinforcing the theory that this region of wake recovery is principally driven by turbulent mixing of the wake with the ambient flow. For full-scale MCEC devices it is unlikely that changes in rotor disk thrust and the effect on the downstream flow will be a significant driver for array design. Reducing the distance between disk and seabed serves to increase the persistence of the wake. It is postulated that this is caused by a restriction of mass flow rate beneath the disk leading to a stagnant slow-moving region of flow on the underside of the wake. Higher shear forces act on the upper surface of the wake as free stream flow velocity is only slightly retarded but still the active surface area of the wake where re-energisation can occur is much reduced. Increasing the distance between the rotor disk and the bed allows increased flow beneath the disk and an increase in the centerline rate of wake recovery. Full-scale MCECs operating close to the sea bed may therefore require more generous longitudinal inter-device spacing if individual device yields are not to be compromised. Added turbulence in the form of increased sea bed roughness acted to reduce the amount of wake mixing when the rotor disk was in close proximity to the bed. The slow-moving highly turbulent layer of fluid generated from the roughened bed mixed with the underside of the wake but tended to stagnate, reducing the mixing rate between wake and free stream fluid in this region. When the disk was placed higher up in the water column, interaction with the bed-generated turbulence was reduced and wake velocity deficits approached those of similar experiments with a smooth bed. Thus no reduction of wake persistence could be realised by increasing ambient turbulence in the bed region. The increased velocity shear associated with seabed roughness should encourage device developers to avoid flow interaction in this region, at least in the short term.

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