Extended Abstracts for
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Extended Abstracts for
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Day 1 (29th March)
Session 1
11:10
11:35
12:00
12:25
The Influence of Vertical Velocity Shear on Tidal Turbine Performance
and Wake Recovery
Simon C. McIntosh (University of Oxford)
3
“From Vessel to Model”: Bridging the Gap between Real and Modelled
Flow Data
Paul Evans (Cardiff University)
5
Characterisation of the Coastal Hydrology of Oceans Using 3D
Computational Fluid Dynamics
Enayatollah Zangiabadi (Swansea University)
7
The Influence of Turbulence Model on Wake Structure of TSTs when
used with a Coupled BEM-CFD Model
Rami Malki (Swansea University)
9
Investigation of the influence of turbine to turbine interaction on their
performance using OpenFOAM
Gavin R. Tabor (University of Exeter)
11
Near-field flow downstream of a barrage: Experiments and 3-D
modelling
Penelope Jeffcoate (University of Manchester)
13
Sediment dynamics in the wake of a tidal current turbine
Lada Vybulkova (University of Glasgow)
15
A cross-flow device with an oval blade path: predictions and
measurements of blade forces
Peter B. Johnson (University College London)
17
Are Nearly all Tidal Stream Turbines Designs Wrong?
Stephen Salter (University of Edinburgh)
19
Experimental results from 1/20th scale model tests of the Transverse
Horizontal Axis Water Turbine
Ross A. McAdam (University of Oxford)
21
Session 2
14:00
14:25
14:50
Session 3
15:45
16:10
16:35
1
Day 2 (30th March)
Session 4
9:20
9:45
10:10
10:35
CFD Simulation of a 3-Bladed Horizontal Axis Tidal Stream Turbine
using RANS and LES
J. McNaughton (University of Manchester)
23
Computational Modelling of Unsteady Rotor Effects
Duncan M. McNae (Imperial College London)
25
Development of an Actuator Line Model for Tidal Turbine Simulations
Justine Schluntz (University of Oxford)
27
Modification of Open Channel Flow By Opposing Waves
A. Olczak (University of Manchester)
29
Prediction and Measurement of Time-Varying Thrust on Tidal Turbine
due to Mean and Oscillatory flow
E. Fernandez Rodriguez (University of Manchester)
31
Blade Element Momentum Theory for Tidal Turbine Simulation with
Wave Effects: A Validation Study
Hannah C. Buckland (Swansea University)
33
The Buhl High-Induction Correction for Blade Element Momentum
Theory Applied to Tidal Stream Turbines
Michael Togneri (Swansea University)
35
Session 5
11:30
11:55
12:20
12:45
Betz revisited
Guy T. Houlsby (University of Oxford)
Session 6
14:00
14:25
14:50
Numerical Analysis of Open-Centre Ducted Tidal Turbines
Clarissa S. K. Belloni (University of Oxford)
37
Evaluation of FVNS Solvers for Structures in Tidal Flow
Robert Stringer (University of Bath)
39
On the Garrett & Cummins limit
Thomas A.A. Adcock (University of Oxford)
41
Workshop Organisers:
Dr Richard H. J. Willden (University of Oxford)
Dr Takafumi Nishino (University of Oxford)
Prof. Guy T. Houlsby (University of Oxford)
Dr Tim Stallard (University of Manchester)
Sponsor:
Oxford Martin School, University of Oxford
2
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
The Influence of Vertical Velocity Shear on Tidal Turbine
Performance and Wake Recovery
Simon C. McIntosh*, Conor F. Fleming and Richard H. J. Willden
Department of Engineering Science, University of Oxford, OX1 3PJ, UK
Summary: The extent of vertical velocity shear expressed in tidal flows is highlighted with extracts of
field data taken from the Falls of Warness in the Pentland Firth. Resulting velocity profiles reveal
distinct divergences in shape for the same mean speed during flood and ebb tides with the ebb profile
observed to be much fuller than the low shear 1/7th power law used by the wind industry. A method of
applying a Log-law fit to the field data profiles is presented resulting in the calculation of ebb and
flood bed roughness heights of 0.015 and 0.127 m. The impact of operating turbines within the high
shear tidal environment is assessed computationally at approximately 1/30th geometric scale.
Two bed roughness cases are presented representative of the ebb and flood field data with mean
flow approx. 0.27 m/s. A uniform flow case is also simulated to provide a datum for evaluation of the
effect of sheared flow. High levels of vertical velocity shear commensurate with real tidal flows are
found to reduce overall power output by an applicable fraction compared to the uniform flow case.
The majority of this power decrease is attributed to flow field asymmetry at the rotor plane. Since
pitch angle is fixed, asymmetry of incident flow results in variation of relative velocity during each
revolution and so the blade operates at a lower lift to drag ratio for part of each revolution. Bed shear
and the associated higher turbulence levels are found to accelerate wake mixing resulting in a
downstream profile recovery much faster than the uniform flow case.
Introduction
Vertical velocity shear, the spatial variation of stream-wise velocity with distance from the seabed,
is highly pronounced for energetic tidal flows. Large spatial gradients result in significant variation of
flow variables across the swept area of a rotor. This in turn influences the distribution of loads acting
on the each blade and hence alters performance coefficients relative to the idealised case of uniform
flow.
Similar vertical velocity shears are observed to act across large wind turbines operating within the
atmospheric boundary layer. Indeed many of the analysis techniques developed for wind shear are
directly applicable to tidal flows. The exception for tidal flows is the vertical extent over which the
seabed boundary layer is able to expand. For atmospheric flows the boundary layer is effectively
unbounded where as for tidal flows the presence of a free surface limits the shear layer’s vertical
extent. In the case of shallow depth high velocity tidal flows this vertical constraint on shear layer
development produces significant gradients acting throughout the water column and across any tidal
device placed within the flow.
Methods
The magnitude of vertical velocity shear for real tidal flows is assessed via the analysis of six days
of tidal velocity measurements taken from the Falls of Warness in the Pentland Firth. The level of
vertical velocity shear is characterised for both the flood and ebb tides; with a large variation observed
between the ebb and flood profiles. Sheared flow simulations are then carried out to assess the impact
of a realistically sheared velocity profile on the loading, performance and wake recovery of a
horizontal axis tidal turbine.
*
Corresponding author.
Email address: simon.mcintosh@eng.ox.ac.uk
3
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Results
Figure 1 shows a highly sheared velocity profile abstracted from the field data for a mean flow
speed of 2 m/s during a flood tide. Also shown are associated 1/5th, 1/7th and log-law fits. The lowshear 1/7th power law, used extensively in the wind industry, is shown to significantly under predict
the level of shear present in the profile. A much better fit is obtained using a 1/5th power law with the
best performing model provided by a log-law fit employing a roughness height of 0.127m.
Profile height, ~ [y/H]
1
0.8
0.6
ADCP
th
1/7
th
1/5
log(law
0.4
0.2
0
1.5
2
Flow velocity, u [m/s]
2.5
Figure 1: An illustration of the time averaged velocity profile for the flood tide recorded at the Falls of Warness
with comparison to 1/5th, 1/7th and log-law velocity fits.
Computational simulations of a 1/30th scale horizontal axis turbine are carried out employing the
above log-law velocity inflow along with associated variations in turbulence intensity and dissipation
rate. Vertical velocity shear is found to reduce power output by an appreciable fraction compared to
operation in a uniform inflow. In addition, wake mixing is observed to occur much more rapidly for
the sheared flow case with a recovery of upstream profiles much faster than observed for the uniform
inflow case.
Conclusions
The level of vertical velocity shear observed at the Falls of Warness site is found to be much greater
than that predicted by typical 1/7th power law models adopted from the wind industry. A 1/5th power
law is shown to provide a more suitable fit to the field data. A log-law variation employing a terrain
roughness height of 0.127m provides a representative model of the vertical velocity shear. Compared
to uniform flow calculations, simulations of this highly sheared tidal environment predict a fall in
power coefficient by an appreciable fraction along with a reduction in the distance over which the
wake velocity recovers to the ambient profile.
Acknowledgements:
This study was completed as part of the PerAWaT project commissioned by the Energy Technologies
Institute (ETI).
4
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
“From Vessel to Model”: Bridging the Gap between Real and Modelled
Flow Data
Paul Evans* and Christopher Wooldridge
School of Earth and Ocean Sciences, Cardiff University, CF10 3AT, UK
Allan Mason-Jones, Tom O’Doherty and Daphne O’Doherty
School of Engineering, Cardiff University, CF24 3AA, UK
Simon Neill and Reza Hashemi
School of Ocean Sciences, Bangor University, LL59 5AB, UK
Rami Malki, Ian Masters and Enayatollah Zangiabadi
College of Engineering, Swansea University, SA2 8PP, UK
Summary: A shipboard acoustic Doppler current profiler (ADCP) has been used to obtain detailed
measurements of the tidal flow structure in an area off the Welsh coastline where tidal currents
typically peak at 3-4 ms-1 during spring tides. This paper describes the importance of such field data
for the calibration and validation of numerical models for tidal stream power generation.
Introduction
ADCP surveys have been undertaken within the Bishops and Clerks (including Ramsey Sound) off
the west coast of Wales, UK, which has a combined extractable power estimate of 541 GWh/y [1].
The principal objective of these surveys was to examine the region’s tidal stream resource potential, as
well as understanding the hydrodynamics of the region. Given its resource potential, this region has
been earmarked by the Welsh Government as a potential site for tidal stream energy generation, with
the first Welsh developer gaining consent in July 2011 to deploy a single device for a 12 month period
within Ramsey Sound. Previous work off the Welsh coast included a series of shipboard ADCP
surveys within a 1km2 area in the Bristol Channel to study power attenuation effects on turbine
performance [2].
The data was collected onboard Cardiff University’s 12 m RV Guiding Light as part of the Low
Carbon Research Institute (LCRI) Convergence Programme. This paper discusses the benefit of tidal
flow data for use within numerical models and demonstrates its importance for validation and
calibrations purposes to help bridge the gap between physical data collection and pure mathematical
modelling.
Methods
The ADCP data, which was collected during two major deployments in May and August 2011,
involved the completion of 260 vessel tracks (equating to over 200 nautical miles) over a range of tidal
states within the Bishops and Clerks. A 1.0 MHz shipboard ADCP with bottom-track capabilities was
mounted on a detachable mount on the side of RV Guiding Light for the ADCP surveys.
A series of numerical models have been employed as part of this research project to investigate
various elements of marine renewable energy generation, including a three-dimensional (3D)
unstructured oceanographic model (ADCIRC) of the Bishops and Clerks (inclusion of turbines in this
*
Corresponding author.
Email address: EvansPS3@cardiff.ac.uk
5
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
model follows a methodology developed in earlier work [3]), a standard finite volume CFD approach
with a k-ɛ turbulence model, a coupled Blade Element Momentum (BEM-CFD) model, and a transient
CFD model (which was used to examine the performance of a horizontal axis tidal turbine for a
similar project [4]) investigating power attenuation in an array of turbines.
Results
Vector plots of the hydrodynamic regime of the western-most point of mainland Wales have been
established. Scrutiny of these vector plots, in addition to on-site observations of phenomena such as
up-welling, eddies and vortices, has identified the significant flow characteristics of major tidal
channels. Preliminary results have revealed characteristics of the interrelationships between coastal
configuration and bathymetry and hydrodynamics of the areas. Although the tidal regime in this region
is well-established, the results indicate the extent to which smaller-scale features, such as geographical
salients, and point and linear features (Horse Rock and The Bitches) are significant in influencing the
principal tidal flow. Low pressure and areas of significant turbulence and vertical mixing form in the
wake of these features. The outcrops that form the Bishops and Clerks were originally thought to
channel tidal flow; however, at certain states of the tide local pressure fields build up to create a
further complex of back-tides and localised eddy systems. The results suggest that well-developed jet
streams exist in close proximity to narrow, deep channels and that the resultant chaotic system is
characterised by extreme turbulence, standing waves, well-defined vertical mixing, vortices, eddies
and locally significant flow anomalies.
Interpretation of the vectors using 2D and 3D visualisation techniques at different tidal states has
identified key hydrodynamic areas to quantify the flow structure and deviations from it. This
information is vital for the calibration, validation and ground-truthing of mathematical models. Future
work will explore the possibility of using a linear set of features, like the Bishops and Clerks rocks, as
an analogy for a tidal stream array and the effects downstream of such an array.
Conclusions
Results confirm that even small-scale variations in bathymetry and coastal configuration may have
a profound influence on the resultant flow regime. It has also been recognised that vectors change in
space and time to a far greater extent than expected.
Acknowledgements:
The authors acknowledge the financial support of Welsh Assembly Government, the Higher Education
Funding Council for Wales, the Welsh European Funding Office and the European Regional
Development Fund Convergence Programme. The authors also acknowledge with grateful thanks the
collaboration and assistant of LCRI Marine partners, RNLI St David’s and St Justinian’s Boat Owners
Association. Navigational advice from David Chant based on his experience as an RNLI coxswain and
fisherman was invaluable for site-selection and general safety at sea.
References:
[1]
Fairley, I., Neill, S., Wrobelowski, T., Willis, M. and Masters, I. (2011). Potential array sites for tidal stream turbine electricity
generation off the Pembrokeshire coast. Proc. 9th European Wave and Tidal Energy Conference (EWTEC), Southampton, UK.
[2]
Willis, M., Masters, I., Thomas, S., Gallie, R., Loman, J., Cook, A., Ahmadian, R., Falconer, R., Lin, B., Gao, G., Cross, M., Croft,
N., Williams, A., Muhasilovic, M., Horsfall, I., Fidler, R., Wooldridge, C., Fryett, I., Evans, P., O’Doherty, T., O’Doherty, D. and
Mason-Jones, A. (2010) Tidal Turbine Deployment in the Bristol Channel – A Case Study, Proc. ICE Energy. 163 (3), 93 –105.
[3]
Neill, S., Jordan, J. and Couch, S. (2012). Impact of tidal energy converter (TEC) arrays on the dynamics of headland sand banks.
Renewable Energy, 37 (1), 387-397.
[4]
O’Doherty, T., Mason-Jones, A., O’Doherty, D., Evans, P., Wooldridge, C. and Fryett, I. (2010). Consideration of a Horizontal Axis
Tidal Turbine. Proc. ICE Energy. 163 (3), 1751-4223.
6
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Characterisation of the Coastal Hydrology of Oceans Using 3D
Computational Fluid Dynamics
Enayatollah Zangiabadi*, Ian Masters
College of Engineering, Swansea University, SA2 8PP, UK
Alison. J. Williams
College of Engineering, Swansea University, SA2 8PP, UK
Summary: Knowing the properties of the flow is required to set up a tidal stream turbine (TST).
Modelling of the flow in an estuary or a channel which has severe conditions depends on several
parameters such as the bed friction factor and topography of the seabed. Characterising the flow
profile and predicting the behaviour of the boundary layer in channels with different dimensions and
different flow conditions should be investigated in order to have an accurate model. It is also
necessary to study the effect of different friction coefficients on the velocity profile.
Introduction
Marine devices are used to harness hydrokinetic energy of tides, waves and currents in oceans,
rivers and streams. The developments of such devices are in preliminary stages but their significant
contribution to the future supply of clean energy is obvious in both the UK and also around the world.
Tidal energy has been developed more in comparison to other methods of marine renewable energies,
mainly because this kind of renewable energy is fully predictable. However, marine and estuarine
environments are characterised by roughness and irregularity in topography and three-dimensional
(3D) turbulent flows, which can hugely affect the performance of Tidal Stream Turbine (TST) and
should be investigated carefully [1].
Generally, when a fluid flows over a solid surface, the velocity of fluid relative to the surface is zero
and as we move away from the surface the velocity rapidly increases to the velocity of the main
stream and forms the boundary layer. Near the surface the shear stress is more effective and beyond
the boundary layer the effect of viscosity is negligible [2]. The boundary layer along with the main
stream flow determines the velocity profile of the flow above the surface. One of the important
parameters which affect the shape of the boundary layer is the roughness of the surface and the
velocity gradient is reformed with changing of the bed friction coefficient. Rocks, pinnacles and
severe changes in bathymetry can also affect the shape of the velocity profile and therefore affect the
overall performance of a TST.
Methods
A standard finite volume approach with a k-ɛ turbulence model has been used. For the transport of
any fluid the governing equations are the continuity equation and the momentum equation. This is a
two equation model, which means, it includes two extra transport equations to calculate the turbulent
kinetic energy, k, and the turbulent dissipation rate, ɛ.
The turbulence and the momentum equations are coupled through the dynamic viscosity which is a
sum of the laminar and turbulent values. In the current problem, as density of a fluid element does not
change during its motion we deal with incompressible flow. Besides that, there are no external source
terms.
*
Corresponding author:
Email address: 502830@swansea.ac.uk
7
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Another approach to determine the velocity gradient over the seabed is the logarithmic law of wall
formula [3]. The law of the wall states that the average velocity of a turbulent flow at a certain point is
proportional to the logarithm of the distance from that point to the "wall", or the boundary of the fluid
region [4]. The law of wall is theoretically appropriate to parts of the flow which are close to the wall
(<20% of the height of the flow), however with a good approximation it is acceptable for the entire
velocity profile of natural streams, especially in coastal flows, where the depth is small in comparison
to the horizontal dimensions [5].
Results
The model was run for smooth, intermediate and rough beds with uniform and power-law inlet
boundary conditions. A regular orthogonal mesh was used. The minimum cell length was 250 mm and
the domain length was 3200 m. It was decided to extract the velocity gradient close to the inlet (300
m) and near the outlet (3000 m) to investigate change of the velocity profile as the flow transport
along the length of the channel. The depth of the channel was 30 m and one value for velocity was
extracted for every meter of depth.
Conclusions
Both of the methods (law of wall and bed roughness) will be used in channels with variable
topography and then by comparing the results with real data, the best one will be selected to use for
future simulations.
The results validation will be done by applying the boundary conditions which will be based upon
flow data gathering by Acoustic Doppler Current Profiler (ADCP) survey in Operation Celtic Odyssey
IV late spring this year.
References:
[1] Seokkoo Kang, Iman Borazjani, Jonathan A. Colby, Fotis Sotiropoulos (2012). Numerical simulation of
3D flow past a real-life marine hydrokinetic turbine. Advances in Water Resources. 39:33-43.
[2] Bernard Massey. (1998). Boundary layer and wakes. In: John Ward-Smith Mechanics of Fluid.7th ed.
UK: Nelson Thornes Ltd. 312.
[3] Emmanuel Osalusi, Jonathan Side and Robert Harris (2009), Reynolds stress and turbulence estimates in
bottom boundarylayer of Fall of Warness,
[4] Th. v. Karman (1931), Mechanical Similitude and Turbulence,
[5] David Mohrig (2004), Conservation of Mass and Momentum. 12.110: Sedimentary Geology. MIT
OCW.
Fig. 1. Velocity profile of a flat channel for
uniform flow
Fig. 2. The Bathymetry of Ramsey Sounds while
looking towards northeast
(The graph has been generated by data acquired from
Seazone, Olex chart systems and the Royal Navy)
8
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
The Influence of Turbulence Model on Wake Structure of TSTs when used
with a Coupled BEM-CFD Model
Ian Masters, Rami Malki*, Alison Williams and Nick Croft
Marine Energy Research Group, Swansea University, SA2 8PP, UK
Summary: A coupled Blade Element Momentum - Computational Fluid Dynamics (BEM-CFD) model
is used to simulate tidal stream turbines. The simulations are conducted using three different
turbulence models, namely the k-ε, k-ε RNG and k-ω models. The significance of the choice of
turbulence model on wake hydrodynamics is evaluated.
Introduction
Errors in numerical simulations of tidal stream turbines using the coupled BEM-CFD method can
arise due to a number of reasons, such as the steady-state representation of an unsteady process,
discretisation of the blade, blockage effects and not accounting for the displacement of the water
surface. Another source of uncertainty in the results which is addressed in this study is the choice of
turbulence model. In this study, the coupled BEM-CFD model is applied with three different twoequation turbulence models to evaluate their significance on the flow structure downstream of the
turbine rotor.
Methods
A coupled BEM-CFD model [1] is used to simulate a tidal stream turbine in conjunction with three
different two-equation turbulence models, namely the standard k-ε, k-ε RNG and k-ω models. The
simulations are of a 0.5 m diameter rotor in a 1.4 m wide and 0.85 m deep flume based on the setup of
the experimental testing undertaken at the University of Liverpool [2].
Two tip speed ratios are considered: 4.0, which is the optimum value for the rotor used, and this is
compared to a non-optimum case of 6.0. The inflow velocity was set to 1.0 m s-1 which is within the
range of velocities implemented during the experimental investigation.
Results
Contours of velocity and turbulence intensity along vertical slices passing through the centre of the
rotor along the flow direction are presented in Fig. 1. Both sets of plots indicate subtle differences in
the flow structure downstream of the rotor. The lowest velocity region immediately downstream of the
nacelle was longest for the k- ε RNG model and shortest for the k-ω model. This can be related to
turbulence generation, at the nacelle surface which resulted in the highest turbulence intensities for the
k-ω model and the lowest for the k- ε RNG model.
Velocity and turbulence intensity profiles along the centreline through the rotor are presented in
Fig. 2. The velocity profiles indicate that flow recovery occurs over the shortest distance when using
the k-ω model and occurs over the longest distance when using the k- ε RNG model.
Downstream of the rotor circumference, turbulence intensity peak values were greatest for the k-ω
model, and the high turbulence intensity regions extended further downstream. For the k- ε RNG
model, turbulence intensity peak regions occurred further downstream along the wake.
*
Corresponding author.
Email address: r.malki@swansea.ac.uk
9
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Conclusions
The choice of turbulence model can have some influence on the wake structure downstream of a
tidal stream turbine. Quantifying the wake length based on a percentage value of the free-stream
velocity can yield significantly different predictions for the various models. More measured velocity
data within the wake region is required to evaluate the suitability of difference options.
The current model accounts for the influence of the blades within the momentum equations,
however future work will focus on including further source terms within the turbulence model
equations. This may improve the representation of large-scale turbulence breakdown into small scale
turbulence.
Acknowledgements:
This work was undertaken as part of the Low Carbon Research Institute Marine Consortium
(www.lcrimarine.org).
The Authors wish to acknowledge the financial support of the Welsh Assembly Government, the
Higher Education Funding Council for Wales, the Welsh European Funding Office, and the European
Regional Development Fund Convergence Programme.
References:
[1] Williams A.J., Croft T.N., Masters I., Bennet C.R., Patterson S.G. and Willis M.R. (2010). "A
combined BEM-CFD model for tidal stream turbines". 3rd International Conference on Ocean
Energy, Bilbao.
[2] Tedds S.C., Poole R.J., Owen I., Najafian G., Bode S.P., Mason-Jones A., Morris C., O'Doherty
T. and O'Doherty D.M. (2011). "Experimental Investigation of Horizontal Axis Tidal Stream
Turbines." EWTEC 2011, Southampton, UK.
Fig. 1 Velocity and Turbulence Intensity Contour Plots (U = 1.0 m s-1; TSR = 4.0)
Fig. 2 Velocity and Turbulence Profiles (U = 1.0 m s-1; TSR = 4.0 (solid), 6.0 (dashed))
10
Gavin R. Tabor*, Mulualem G. Gebreslassie, Michael R. Belmont
!
"
#
$ This paper presented the influence of turbine to turbine interaction on the performance of
%
(IBF). The results showed
individual turbines using a new CFD based model,
that a lateral proximity of turbines can improve the performance of individual turbines in a farm
compared to isolated devices due to a blockage effect. However, this might have a negative effect on
downstream turbines that can affect the overall power output of the farm, which opens the way for
further investigation using upstream and downstream turbines to obtain an optimized location of the
devices.
The study of turbine to turbine interaction is crucial to understand how energy shadowing of an
array of devices influences energy extraction from the individual devices. However, investigation of
these interactions using experiments could inflict significant cost especially with several devices in a
tidal stream farm. The best option to minimise this cost is therefore to use alternative methods such as
numerical simulations using computational fluid dynamics (CFD) software packages. In recent years,
CFD has been commonly used in modelling the flow features of tidal turbines and showed satisfactory
results.
The focus of this study was on a new class of tidal turbine, Momentum Reversal Lift (MRL),
designed by Aquascientific Ltd, which is currently in the prototype and testing phase [1]. The aim
being to investigate the turbine to turbine interaction of three devices configured laterally in a cross
flow using a simplified CFD based model called
%
.
Large-eddy simulation (LES) was utilized to simulate the MRL turbine using an open source CFD
code, OpenFOAM. The LES governing equation is a combination of the filtered Navier-Stokes (NS)
equations [2] and source terms as shown in Eq. (2). The LES governing equation can be defined as:
#
&#
$
.
0
Eq. 1
# &#
$
.
.
Eq. 2
where, U is the filtered velocity, p is the filtered pressure, µ is the dimensionless dynamic viscosity, Fs
is the surface tension, g is the gravitational acceleration. In this study, a new source term, forcing
function (Fb), was added to create a momentum change in the fluid flow. The forcing function was
used to represent the force applied by the immersed body (turbine) and can be defined as:
Eq. 3
This new source term is named as
%
and a code was developed considering drag
(FD) and lift (FL) forces. It is a compromise between at one extreme a full treatment using offset
meshing and/or sliding mesh techniques to describe the detailed internal blade motions and at the other
a highly simplified momentum extraction zone such as the porous disc method.
*
Corresponding author.
: G.R.Tabor@exeter.ac.uk
11
The MRL turbine was simulated with a free surface on the top of the domain which requires
determining of the relative volume fraction of the two phases in a computational cell. A volume of
fluid method was used, which is an efficient method for treating free boundaries as described by [3].
The simulations were carried out using a small scale MRL model with a diameter of D = 0.20 m.
The results presented here are part of a wider investigation of turbine to turbine interactions in a
tidal stream farm. The influence of two turbines (2 and 3) configured side by side to a base turbine (1)
were considered for the analysis as shown in Fig. 1. The lateral spacing of the devices was at 2D (Fig.
1b) and 4D (Fig. 1c).
Figure 1: Velocity contours through the centreline of the turbine sliced in the XZ plane
The performance of turbine 1 in Fig. 1b was up by 1.6% while the same turbine in Fig. 1c was
increased by 0.75% compared with the performance of the isolated turbine (Fig. 1a). This result
showed that the influence of lateral turbines was positive and improved the performance of turbine 1
due to the blockage effect. The MRL turbine is designed to have high aspect ratio and this can create
blockage effect when stretches across a stream flow, which might eventually improve its performance.
Fig. 1b showed physically larger wake downstream of the turbines compared to Figs. 1a and 1c
which led to a net increase of the performance of turbine 1. However, there was a mixing of the wake
in Fig. 1b which could affect the performance of downstream turbines. The mixing was minimised by
increasing the lateral spacing (Fig. 1c) though the power output of turbine 1 was decreased compared
to the same turbine in Fig. 1b. This might give a better space for deployment of additional turbines in
staggered configuration and reduce the downstream length scale required in Fig. 1b to avoid wake
interaction. In this way the overall net power output of a farm can be optimized.
The results showed that the performance of individual turbines in a farm can be improved with a
small lateral spacing. However, due to the proximity of the turbines there was a mixing of the wake
produced by each turbine. This could inflict significant energy shadowing to other turbines located
downstream unless appropriate longitudinal spacing is used. An optimised location of the devices in a
tidal stream farm could be therefore obtained by adding upstream and downstream rows of turbines
which is currently under investigation.
$
[1] Janssen , A.P. and Belmont , M.R. (2009). Initial research phase of MRL turbine. Technical
report, Technical Report N0: MO 562L, 2009.
[2] Xie, Z. and Castro, I.P. (2006). LES and RANS for turbulent flow over arrays of wall-mounted
obstacles. '( ! ) # %#
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(
: 291-312.
[3] Hirt, C.W. and Nichols, B.D.. (1975). Volume of fluid (VOF) method for the dynamics of free
boundaries* 1. '(
*#
*
, ! " : 201-225.
12
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Near-field flow downstream of a barrage: Experiments and 3-D modelling
Penelope Jeffcoate*, Peter K. Stansby, David D. Apsley
Department of Mechanical, Aerospace and Civil Engineering, University of Manchester,
M13 9PL, UK
Summary: The effects of barrage implementation over large areas has been assessed using twodimensional modelling[1], however, in order to determine the effects of a barrage in the nearfield 3-D assessment is required[2]. Flume experiments, with three-component velocity
measurements, and 3-D CFD modelling were conducted to assess the velocity variations
throughout the flow downstream of a seven-duct barrage. The large velocity variations at
different depth locations in the experimental results show that within 20 duct diameters (20D)
of a barrage 3-D analysis is required. The CFD results also show flow variation across the
depth, however, more jet spreading occurs than in experiments.
Introduction
A key problem perceived to arise from tidal barrages is the detrimental environmental
impact; this may include changes in water levels, altered water turbidity and changes to
sediment drift patterns. Previously two-dimensional (depth-averaged) computational
modelling has been conducted to determine the effects of barrage implementation on an entire
estuary or coastline[1]; however the 3-D flow field close to the barrage requires analysis. In
order to assess the hydrodynamic effect of tidal barrage implementation, flume experiments
and 3-D computational modelling have been conducted.
Methods
A 1:143 scale model of a proposed Severn barrage[3] was fitted in an experimental flume,
with simplified cylindrical ducts and bulb turbines with fixed, angled stators. A Vectrino
ADV was used to record the three-component velocities at various depths and distances
downstream (Fig 1). A three-dimensional model of the upstream area, downstream area and
the barrage ducts was created using StarCCM+; the experimental inlet conditions were
applied to the model, including the upstream depth, downstream depths and inlet velocity.
The bulb turbine and resulting swirl velocity in the CFD modelling were represented by an inchannel blockage and body force respectively. The experimental flow field was analysed
using the velocity measurements and the effectiveness of 3-D computational modelling for
predicting flow effects of barrages was determined.
Results
The three-component velocities downstream at 1 duct diameter (1D), 2D, 5D, 10D and 20D
recorded in the experiments were analysed; the vertical and spanwise velocity vectors shown
at 1D (Fig. 2) indicate the large rotational element of the velocities downstream from the
ducts and the high variation of the velocity profiles throughout the depth. This variation
throughout the depth is evident up to 10D from the barrage; however, at 20D from the barrage
the velocity profiles are more uniform. This is most evident in the Uy and Uz components of
*
Corresponding author.
Email address: Penelope.jeffcoate@postgrad.manchester.ac.uk
13
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
the velocity, although, there are large variations in the Ux profiles within 2D of the barrage.
The StarCCM+ model produced similar velocity vectors, with high rotation close to the
barrage and variation in the velocities throughout the depth close to the barrage. The midheight velocity vectors produced are shown in Figure 3; these show the acceleration of the
flow through the ducts and past the turbine blockage. Both methods show a wake forming
directly downstream from the bulb body, with jets forming either side of the duct. The jets
can be seen to merge as distance from the ducts increases; however, the merging in the CFD
results is much higher than that shown in the experiments, so refinement of the CFD model is
required.
Conclusions
Within 20D of the barrage 3-D assessment is required in order to accurately determine the
flow field downstream from a barrage. Both experimental and computational assessments
showed high levels of swirl close to the barrage and flow circulation within 10D of the
barrage, but the overestimated jet merging of the 3-D CFD results should be improved. The
experimental results can be used for further analysis of the velocity profiles, swirl produced
by the stators and the close-to-bed velocities, and thus provide input into scour and sediment
transport modelling.
References:
[1] Burrows R. Walkington I.A. Yates N.C. Hedges T.S. Wolf J. Holt J. (2009a) The Tidal Range
Energy Potential of the West Coast of the United Kingdom. App Ocean Res 31(4), 229-238
[2] Jeffcoate P. Stansby P.K. Apsley D.D. (2011) Near-field modelling of a barrage: experiments, 3-D
CFD and depth-averaged modelling. Proc. of Conf. on Ocean, Offshore ad Arctic Eng. 5, 909-918
[3] Department of Energy (1981) Tidal Power from the Severn Estuary. DEP Energy Paper 46, 198
Fig. 1. Experimental barrage with Vectrino ADV
Fig. 3. StarCCM+ velocity vectors at duct mid-height
Fig. 2. Experimental vertical and span-wise velocity vectors at 1D downstream from barrage
14
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Sediment dynamics in the wake of a tidal current turbine
Lada Vybulkova1, Marco Vezza
School of Engineering, University of Glasgow, G12 8QQ,
United Kingdom
Harshinie Karunarathna
School of Engineering, Swansea University, SA2 8PP,
United Kingdom
Richard E. Brown
Department of Mechanical and Aerospace Engineering,
University of Strathclyde, G1 1XJ,
United Kingdom
Summary: One of the most important aspects of the environmental impact of tidal current turbines
(TCTs) is their effect on the dynamics of the suspended sediment load. High resolution computational
simulations of the hydrodynamics of a TCT have thus been conducted using the Vorticity Transport
Model (VTM) together with a model for the erosion of the seabed downstream from the turbine. The
present study shows that the high vortex-induced velocities in the wake of the turbine can cause
elevated local bed erosion.
Introduction
The environmental impact of devices designed to extract power from tidal currents has yet to be
thoroughly investigated. The interaction between the wake that is produced downstream of tidal
current turbines (TCTs) and the sediment on the seabed is of particular concern given the damage that
might be caused to the habitat of marine plants and animals that dwell on the ocean floor. High
resolution computational simulations of the hydrodynamics of a TCT and its wake have been
conducted using the Vorticity Transport Model (VTM) [1] together with a model for the uplift of
sediment from the seabed and its subsequent transport downstream of the turbine. These simulations
show the effect of the small-scale, highly intense vortical structures within the wake of the turbine in
creating patches of locally-elevated shear stress on the seabed in which sediment uplift is enhanced.
The effect of the turbine on the sediment near the seabed is shown to be strongly dependent on the
parameters of the device, such as the blade twist distribution, and corresponding power produced by
the turbine, but is also influenced by the natural instability within the wake that acts to destroy the
coherence of its fine-scale structure some distance downstream of the turbine. These findings suggest
that the design of TCTs for deployment in regions with significant sediment mobility needs to be
considered with some care regarding their impact on the seabed.
Methods
High-resolution computer simulations have been conducted using the Vorticity Transport Model
(VTM) for various blade twist distributions. The VTM provides a particularly accurate representation
of the vorticity dynamics within a rotor wake, and has been used to study the influence of the wake on
helicopter performance and, more recently, wind turbine efficiency, and can include the interactions of
the wake with a ground plane. The VTM calculates vorticity and velocity of an incompressible fluid,
solving the Vorticity Transport Equation [2]
1
PhD Candidate.
Email address: l.vybulkova.1@research.gla.ac.uk
15
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
where the vorticity field is defined as curl of the velocity field.
The vorticity source term in (1) represents the shed and trailed vorticity arising from the lifting
surfaces immersed within the flow. The effect of the ground on the wake in the VTM has been
modelled using the method of images [3].
A critical bed shear stress is used as the threshold condition for initiation of sediment motion. The
rate at which sediment moves into suspension (the erosion flux) is taken to depend linearly on the
excess bed shear stress
.
Results
Fig. 1. Slice through the wake vorticity field
The VTM simulations have predicted
qualitative differences between the wakes,
the scale of sediment pick-up rates and power
coefficients for a range of blade twist
distributions of a TCT. A slice through
the magnitude of the wake vorticity field Figure 1 shows instabilities in the wake.
The power coefficients of the chosen twist
distributions are given in Table 1.
Twist
TW1 TW2 TW3
Power coefficient
0.10 0.11 0.12
Table 1. Power coefficients
Fig. 2. Relative Excess Erosion Flux
The relative excess erosion flux evolution on Figure 2 represents an amount of sediment eroded from
the seabed relative to the amount of sediment eroded by a free stream.
Conclusions
A subtle change in the blade twist distribution can result in substantially different behavior of the
wake of a TCT. Further research is to be conducted to better understand the ways in which the details
of the design of a TCT can influence its impact on the ocean floor.
References:
[1] Brown, R.E., and Line, A.J. (2005). ``Efficient High-Resolution Wake Modelling
Using the Vortex Transport Equation,'' AIAA Journal, Vol.43, No.7, pp. 1434-1443.
[2] Line, A.J. (2004). Computational Modelling of Helicopter High-Frequency Dynamics,
PhD thesis, Glasgow University.
[3] Whitehouse, G.R and Brown, R.E. (2004) ``Modelling Rotor Wakes in Ground Effect'', Journal
of the American Helicopter Society, Vol.49 (3), pp. 238-249
16
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
A cross-flow device with an oval blade path:
predictions and measurements of blade forces
Peter B Johnson1,2, Adam Wojcik1, Kevin Drake1.
1. Department of Mechanical Engineering, University College London, WC1E 7JE, UK
2. School of Engineering, Nazarbayev University, Astana, Kazakhstan
Summary: A cross-flow device is proposed with an oval blade path (two straight lines joined by two
semi-circles). Unlike axial flow devices, the capacity of such a device is not limited by water depth.
Hydrodynamic performance of the device is predicted with a two-dimensional vortex model and
compared to two-axis blade force measurements from a lab-scale experimental device. There is some
encouraging agreement, and improvements to the numerical model are suggested.
Introduction
A cross-flow tidal stream energy device is proposed where the blades follow an oval path, in particular
the limiting case where the oval path consists of two straight lines joined by two semi-circles. The
motive is to develop a device with high hydrodynamic efficiencies and also the ability to be built on
very large scales because, unlike axial-flow rotors, the device can be made wider without needing an
increase in water depth. In the absence of a convenient acronym the device is named the ‘Moonraker’.
The focus of the present research is on the hydrodynamics of such a device, defined here as the forces
exerted by a flowing fluid on the blades during a representative revolution.
Methods
A two-dimensional point vortex model
was implemented in Matlab according to
the method of [1] and modified to
accommodate an oval blade path. The
circulation about the blades is
determined from empirical data ([2] at
large scale and [3] for lab-scale) and the
Kutta-Joukouski relation.
A dynamic stall model has not been
implemented, though this should be
included in future models as per [1].
Ideally a three-dimensional model (also
introduced by [1]) would be used,
however while its implementation is
incomplete the best remedy for this is to
correct blade forces for the effects of tip
vortices. The vortex model predicts that
at large scale the Moonraker can achieve
high power coefficients (see Fig. 1).
A lab-scale prototype of the
Moonraker was constructed (see Fig. 2)
and tested in the towing tanks at UCL
and at QinetiQ (where blockage was
1.5%). One blade was instrumented with
a two-axis load cell which was built inhouse at UCL. The blade, which is
Fig. 1. Power coef., CP vs blade speed ratio, Λ from vortex model of large
scale Moonraker. The Betz limit is exceeded by using two rows of blades.
(o) Infinite blade length (x) AR = span/chord = 20
Fig. 2. Prototype Moonraker in the UCL towing tank
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Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
hollow carbon fibre, was split in two at the centre and re-joined with a stainless steel beam; a pair of
straing gauges was attached to each of the four sides of the rectangular cross-section of the beam.
Results
Figure 3 shows an example of
experimental
results
from
QinetiQ, showing the component
of force on the blade normal to
its motion, as compared to
predictions. There is good
agreement except for the aspects
annotated on the figure. The
clipping is due to the nonsymmetric range of the load cell
(as a result of stray resistance in
the circuit). There are some
oscillations about the mean on
the downstream side, potentially
due to turbulence created by the
structure.
Tangential forces showed high
power coefficients in some cases,
though this component of force
measurement has a higher
uncertainty. Agre-ement with the
vortex model for tangential
forces was poor, probably due to
the difficulty of predicting drag
at low Reynolds number, which
ranged from 40,000 to 120,000.
Fig. 3. Dimensionless normal forces on a blade over one revolution, plotted
against normalised azimuth,Θ (upstream pass on the left, downstream pass on the
right, with grey areas indicating regions where blades follow a curved path).
(-) Fourier averaged measurements from two independent towing experiments
(o) vortex model,
Conclusions
The hydrodynamics of a cross-flow device with an oval blade path have been investigated.
Predictions of blade forces using a point-vortex model were compared to experimental measurements
on a lab-scale prototype using an instrumented blade to measure two-axis forces. Results show some
good agreement in terms of the force normal to the blade’s motion, while agreement is not good for
the tangential force. In future the vortex model should be extended to three-dimensions and should
include a dynamic stall model. Further, experiments at a higher Reynolds number would be valuable.
Acknowledgements:
This work was funded by EPSRC and NESTA. Thanks to Sinan Hasan for his help with experiments.
References:
[1] Strickland, J.H., Smith, T. and Sun, K. (1981), A Vortex Model of the Darrieus Turbine: An
Analytical and Experimental Study. Report No. SAND81-7017. Sandia National Laboratories
[2] Sheldahl, R. E., Klimas, P. C. and Feltz, L. V. (1980) Aerodynamic characteristics of seven
symmetrical airfoil sections through 180-degree angle of attack for use in aerodynamic analysis
of vertical axis wind turbines. Report No. SAND80-2114. Sandia National Laboratories
[3] Althaus, D. (1980). Profilpolaren fur den Modellflug. Neckar-Verlag
18
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Are Nearly all Tidal Stream Turbines Designs Wrong?
Stephen Salter
Institute for Energy Systems, School of Engineering, University of Edinburgh EH9 3JL.
Summary: There were many possible options for onshore wind turbines but the three-bladed axialflow horizontal-axis design with a mono-tube tower is now universal. It is therefore not surprising
that nearly all of the proposals for tidal-stream turbines use horizontal-axis axial-flow. The widely
separated rotors are the equivalent of leaky pipes in a hydro-electric scheme. This paper attempts to
show that, despite its widespread popularity, the transfer from wind technology is wrong and that a
cross-flow design [1] with rotation about a vertical axis [2] is better.
Introduction
Calculating the forces on a turbine blade needs information about the angle of incidence of the flow
which changes steadily along the span of an axial-flow machine. Many of the papers (eg. [3] [4]) at
the 2011 EWTEC conference concerned turbulence in the turbine wakes. Flow is blocked around the
hub and accelerated in the region outside the tips. Conventional machines must be placed a long
distance downstream to avoid the problem.
A vertical cross-flow design
Flow conditions can be made the same everywhere with the vertical-axis, cross-flow configuration
using close-packed rotors fitted with variable-pitch blades. Rectangles can fill a higher fraction of the
channel cross-section than circles. A high blockage-ratio allows them to exceed the Betz limit in the
high impedance flows that are found in long channels with rough seabeds.
Very large downstream forces are transmitted to the sea bed with a tri-link mechanism which is
free in pitch, roll and heave, which suffers no bending moments and which allows self-installation and
electrical connection to pre-placed attachment points with a post-tensioned rock interface on the
seabed. The links are made from post-tensioned concrete which is highly resistant to fatigue. Link
buoyancy can be adjusted to make links float or just sink. The tri-link arrangement requires the rotor
diameter to be at least twice the channel depth but allows the use of a large fraction of that depth. It
gives swept rotor areas of 7000 square metres and peak power ratings of 70 MW in the Pentland Firth.
The lines of action of the links are in planes passing through the centre of pressure so that the
downstream force does not induce pitch or roll. The large diameter makes the system stable in these
degrees of freedom but the rotor is able to follow tidal rise and fall. Hydraulic rams at the lower ends
of the tri-links assist connection and disconnection, reduce extreme wave loads and even allow some
power generation from waves which can be compared favourably with that from some nameless wave
energy devices.
Rim power take-off at the full rotor diameter keeps the velocity into the power-conversion system
as high as allowed by cavitation. High velocity means lower force. Digital hydraulic technology with
poppet-valve control of displacement gives correct tip-speed ratio combined with true synchronousgeneration, energy storage and a zero-stiffness rotor coupling. The full-diameter ring-cam pump will
act as a geometrically-tolerant bearing. The vertical axis allows the use of a non-contacting gutter
seal providing dry, clean operating conditions and shirtsleeve access to generating plant, even while
on load. A large number (60 plus) of variable-pitch blades will each be shorter than the typical eddy
size. Blades have a constant cross-section, no twist and a chord small enough to be moved in an ISO
sea-container. They will be supported at both ends by stream-lined rings which suppress tip vortices
and provide plenty of space for the pitch-changing mechanism. Most of the components can be used
in a rotor of any diameter and in water depths from 10 to 50 metres.
19
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Support of the blades at both ends reduces bending stress by a factor of four compared with
conventional cantilevered designs. Maximum bending stress is at mid-span, well away from maximum
shear at the two ends. There is no levering up of bearing loads as in axial-flow machines. The blades
stay at the same depth so there is no fatigue due to variations in hydrostatic pressure. Measurement of
the blade pitch-torque and relative water velocity provides all the information needed for control. The
blades can present the correct pitch-angles for flow from any direction and are not affected by vertical
velocity-shear. Changing pitch angle can limit fluid-loading forces, clip unwanted power peaks with
instant torque removal, present an extremely low drag during installation and give high bollard pull
and high agility when the rotor is used as a propeller during installation. A line of contra-rotating
units can leave a wake which is less turbulent than the incoming water flow so that further banks of
rotors can be close, the size of the resource can be maximised and the lengths of cable connections
minimized. A way to calculate the angles needed to present a constant pressure across the front of a
turbine was given by Salter [5]. Results are shown below.
Figure 1. The downstream force for the required even pressure across the rotor is used to get the contribution for
each turbine blade, the lift force perpendicular to the resultant velocity and so the blade pitch-angle.
Conclusion
The answer to the question in the title is yes.
References:
[1] McAdam RA., Houlsby GT., Oldfield MLG. Structural and Hydrodynamic Model Testing of the
Transverse Horizontal Axis Water Turbine. EWTEC Southampton, September 2011.
[2] Salter S. Taylor JRM,. Vertical-Axis Tidal-Current Generators and the Pentland Firth.
Proc.I.Mech.E. vol. 221 Part A. Journal of Power and Energy Special Issue paper pp.181-195.
[3] Stallard T., Collings R., Feng T., Whelan JI. Interactions Between Tidal Turbine Wakes:
Experimental Study of a Group of 3-Bladed Rotors. EWTEC Southampton, September 2011.
[4] O’Doherty DM., Mason-Jones A., Morris C., O’Doherty T., Byrne C, Prickett PW. Grosvenor RI.
Interaction of Marine Turbines in Close Proximity. EWTEC Southampton, September 2011
[5] Salter SH. Pitch-Control for Vertical-Axis, Marine-Current Generators.
World Renewable Energy Conference Aberdeen May 2005.
20
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Experimental results from 1/20th scale model tests of the Transverse
Horizontal Axis Water Turbine
Ross A. McAdam*, Guy T. Houlsby, Martin L.G. Oldfield
Department of Engineering Science, University of Oxford, OX1 3PJ, UK
Summary: In December 2010 and January 2011 a series of tests were carried out on 1/20th scale, 0.5m
diameter, configurations of the Transverse Horizontal Axis Water Turbine (THAWT) in the combined
wind, wave and current tank at Newcastle University. Measurements were made of the hydrodynamic
and structural performance of the turbines, over a range of flow conditions. As well as producing
conventional power and thrust curves for the experimental tests, the variation of blade loading is
explored in order to understand and improve the fatigue resistance of the device.
Introduction
The THAWT device is a variant of a Darrieus turbine and has been proposed as an alternative
design of tidal energy convertor, which can be more easily scaled by stretching the device across a
channel. The turbine is configured with the rotation axis horizontal and perpendicular to the flow. The
key feature of the turbine is that the blades are angled and connected to form a structurally stiff truss,
which allows long stretches of multi-bay rotors to be constructed (Fig. 1(a)).
In December 2010 and January 2011 a series of tests were carried out on 0.5m diameter,
configurations of the THAWT device in the combined wind, wave and current tank at Newcastle
University. These tests were carried out to provide further verification of the hydrodynamic
performance of the turbine and to provide detailed information on blade hydrodynamic loading, to
allow structural design of a full scale turbine.
Test regime
Truss and parallel-bladed configurations of the THAWT device, each 0.5 m mean diameter and 1.5
m total length, were tested in the Newcastle flume (see Fig. 1), in Froude number flows between 0.10
and 0.18. The basic configuration for each device consisted of six blades and a rotor solidity of 0.25.
The effect of blockage ratio on performance is investigated with experiments in flow depths of 0.8 m
and 1.0 m. The variation of performance with both rotor solidity (number of blades), and blade fixed
pitch angle has also been investigated for the parallel-blade configuration.
The speed of the turbine was steadily ramped in a quasi-steady fashion using a motor-generator
with speed control, while the power produced was measured using a torque and speed sensor. The
blade loads were measured in the truss and parallel configurations of the rotor using strain gauges at
various locations along a blade, the signals from which were transmitted wirelessly from the rotating
device (see Fig. 1(b)). Further details of the experimental setup and test regime can be found in [1].
Results
Due to the quasi-steady ramping of the rotor speed the power coefficient for each test can be
calculated over the entire power curve as shown in Fig. 2(a). This power curve exhibits the usual bell
curve shape. However, both configurations of rotor achieved power coefficients greater than the
Lanchester-Betz limit, as a result of blockage effects [2]. Curves are also presented for the thrust
coefficient of the device, which is necessary to understand the effect that the device has on the flow in
future local and macro-scale modelling.
*
Corresponding author.
Email address: ross.mcadam@eng.ox.ac.uk
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Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Based on the measurements of bending moment along the blades, the distributed hydrodynamic
load normal to the blade minor axis can be calculated during a rotation of the device, as shown in Fig.
2(b). The calculated blade loadings demonstrate that by utilising a high blockage, the flow through
the device is significantly deflected and does not produce the symmetric loading that would be
expected from a cross-flow device experiencing uniform flow. The significant metric in the blade
loading is the range of the loading normal to the blade minor axis, which is the main driver of fatigue
in the rotor and is anticipated to be the most likely failure mechanism.
Conclusions
The results from the experimental tests should allow a parameterised model of the THAWT device
to be created, in which the power, thrust and blade loadings can be predicted at a specified set of
device configuration, flow characteristics and tip speed ratio.
References:
[1] McAdam, R. A., Houlsby G. T., Oldfield M. L. G. (2011). Structural and Hydrodynamic Model
Testing of the Transverse Horizontal Axis Water Turbine, 9th European Wave and Tidal Energy
Conference, Southampton.
[2] Houlsby, G. T., Draper, S., Oldfield, M. L. G. (2008). Application of linear momentum actuator
disc theory to open channel flow. Report No. OUEL 2296/08, Department of Engineering
Science, University of Oxford.
(a) Truss configured device on frame
(b) Parallel configured device in flume
150
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Rising
Falling
0
1
2
3
4
5
Tip speed ratio
Distributed blade load (N/m)
Cp
Fig. 1. Photographs of the two main configurations of rotor tested at Newcastle
100
50
0
0
90
180
270
-50
-100
Rotational position (degrees)
(a) Power coefficient versus tip speed ratio
(b) Distributed blade loading at peak power
Fig. 2. Performance of the truss bladed device in 1m flow at a Fr = 0.172 and blockage ratio of 0.5
22
360
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
CFD Simulation of a 3-Bladed Horizontal Axis Tidal Stream Turbine using
RANS and LES
J. McNaughton*, I. Afgan, D.D. Apsley, S. Rolfo, T. Stallard, P.K. Stansby
Modelling and Simulation Centre, School of MACE, The University of Manchester
Summary: Detailed 3D modelling of a tidal stream turbine (TST) is performed using a new slidingmesh method implemented in EDF’s open-source Computational Fluid Dynamics (CFD) solver,
Code_Saturne. A two-equation transient Reynolds Averaged Navier Stokes (RANS) k– Shear Stress
Transport (SST) model is used to study the flow-field for a range of tip-speed-ratios (TSR). The
results are validated against the thrust and power coefficients of a laboratory scale experiment. Results
are compared to a wall resolved Large Eddy Simulation (LES) which is carried out by other members
of the research group.
Introduction
Full scale experimental measurements of TSTs and their wakes are both costly and extremely
difficult to carry out which hinders the development and design process. The use of CFD allows for
such tests to be carried out without these problems. The aims of this work is to investigate the
possibility of using advance CFD to understand the flow physics and predict the behaviour of a TST
under different operating conditions.
Methods
The flow around a three-bladed 0.8m diameter (D) TST with nacelle and mast has been numerically
simulated using the k– SST model shown in Fig 1. The geometry matches the laboratory scale
experiments carried out in a towing tank at the University of Southampton [2]. Wall-functions are
used and so a near-wall cell spacing is used so that y+ is in the range 20 – 100 at the blades. Several
levels of mesh refinement are investigated with a final grid of 2.84 million cells. Calculations are
performed using Code_Saturne, an open-source CFD code developed by EDF R&D [1].
Code_Saturne is a finite volume discretization with a co-located arrangement, able to deal with
unstructured meshes. A new sliding-mesh method is implemented within Code_Saturne to allow for
rotation of the TST within an outer domain. The simulation is first-order in time with 1.5 of rotation
per time-step. The LES is, however, wall resolved (y+ < 10 and mesh size 7 million) and uses a timestep around 100 times smaller owing to the mesh characteristics and second-order time-scheme.
Fig. 1. Flow-field for the k– SST simulations. Left: Iso-surfaces of vorticity coloured by velocity
magnitude. Right: Velocity plane through the domain.
*
Corresponding author.
Email address: j.mcnaughton@live.co.uk
23
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Fig. 2. Force coefficients at range of TSR for experimental, RANS and LES.
Results
Thrust, CT, and power, CP, coefficients are compared with the experiments of [2] for a range of TSR
in Fig 2. The k– SST model under-predicts the force coefficients by around 10%. The LES
calculations match the experimental values by around 3% throughout, except for the lower end of the
TSR scale. No wake data is given from experimental measurements by [2] or numerical simulations of
the same geometry by [3] and so comparison is drawn between the present RANS and LES predictions.
CFX simulations are presented in [3] using the same turbulence model. These give closer prediction of
CP than the present work but over-predict CT at the optimal TSR 6. However, their analysis employs
a coarse mesh which will not necessarily represent the flow physics accurately.
Conclusions
A sliding-mesh method is implemented in the open-source software, Code_Saturne. The k– SST
model correctly predicts the force-coefficient curves. However, under-predicts the experimental values.
An LES carried out as part of the project shows to increase accuracy of the results. This could be
because of the difference in higher order time-scheme although this would require a significantly
lower time-step.
Acknowledgements:
This research was performed as part of the Reliable Data Acquisition Platform for Tidal (ReDAPT)
project commissioned and funded by the Energy Technologies Institute (ETI). The authors are highly
grateful to EDF for additional funding and access to its High Performance Computing (HPC) facilities.
References:
[1] Archambeau, F., Mechitoua, N., Sakiz, M. (2004). Code_Saturne: a finite volume code for the
computation of turbulent incompressible flows-industrial applications. International Journal on
Finite Volumes, 1(1):1–62.
[2] Bahaj, A. S., Batten, W.M.J., Molland, A.F., Chaplin, J.R. (2005). Experimental investigation
into the effect of rotor blade sweep on the performance of the Marine Current Turbines.
Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy,
215(5):611–622.
[3] Mcsherry, R., Grimwade, J., Jones, I., Mathias, S., Wells, A., Mateus, A., Ferguson House, E
(2011). 3D CFD modelling of tidal turbine performance with validation against laboratory
experiments. 2011.
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Computational Modelling of Unsteady Rotor Effects
Duncan M. McNae1, J. Michael R. Graham
Department of Aeronautics, Imperial College London, SW7 2AZ, UK
Summary: Motivated by the importance of understanding the loads on tidal-stream turbine blades, the
rotor response due to unsteady flow is analysed using numerical methods. The unsteady effect of
particular interest is that of dynamic inflow, which is where changes in rotor state, results in changes
in wake strength, which takes time to develop into a steady condition.
An implementation of the Vortex Lattice Method has been developed in order to determine the
importance of this effect. Various test scenarios are modelled and the difference in transient induced
velocity observed in each case is discussed.
Introduction
Tidal-stream turbines operate in a harsh marine environment, and can be subjected to significant
flow fluctuations due to turbulence. Additionally, the requirements of suitable sites will often
necessitate that the rotor is positioned near to the free surface, and hence will be subjected to velocity
fluctuations as a result of passing waves [1]. These flow oscillations result in two characteristic turbine
phenomena, that of dynamic inflow and added mass. Having an understanding of these dynamic
effects is especially valuable for the fatigue design of the rotor blades, and also for control system
models. Additionally, dynamic inflow becomes an important design factor when considering extreme
events, due to the overshoot in loads that result.
It has been shown in some cases, such as in oscillatory flow, that dynamic inflow does not pay a
major role in the loads, which are predominantly in phase with velocity [2]. However in cases such as
step changes in pitch or flow velocity, dynamic inflow has been shown to have a large effect [3]. The
aim of this research is to gain an understanding of what causes this difference.
This study aims to interpret numerical simulations of unsteady flow situations, in order to further the
understanding of dynamic inflow, and the effect it has on rotor loads in differing load cases. A Vortex
Lattice Method has been used, which when compared to other numerical techniques, has the advantage
that the solution attempts to find both the wake strength and shape, and hence also the the wake
induced velocity. Additionally, the method requires less computational effort than CFD. The research
demonstrates the relevance of the Vortex Lattice Method when considering dynamic effects in tidalstream turbines.
Methods
A Vortex Lattice Method for rotor modelling has been realised in a computer simulation. The
Vortex Lattice Method is an inviscid potential flow solver, with the blades represented at the camber
surface. This method is validated against Theodorsen’s Theory and Blade Element Momentum
Method codes. A pictorial representation of the Vortex Lattice Method simulation is provided in
Figure 1, where the shading is a function of circulation strength.
Various test cases are run on a rotor design that matches the experimental setup implemented by
Whelan et al. [2]. A step change in blade pitch angle was compared with an equivalent step in change
in flow velocity, representing a coherent gust. From the simulation, various quantities such as wake
induced velocity on the rotor disk can be determined. Through the analysis of these factors, the effect
of dynamic inflow can be observed.
The numerical analysis will be augmented with comparable experimental work, undertaken in a
recirculating water flume equipped with a towing carriage.
1
Corresponding author.
Email address: d.mcnae09@imperial.ac.uk
25
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Results
Different authors have shown that step changes in blade pitch angle produce a much greater
dynamic inflow effect, and therefore much larger load overshoots [3]. This is what was observed with
the application of the Vortex Lattice Method, as the load overshoot for step increase in flow velocity is
noticeably smaller.
Conclusions
The differences in dynamic inflow effect that are predicted by previous studies have been
qualitatively realised in the numerical computations. Additionally, the added mass effect appears to by
small, agreeing with the much of the literature on rotors in unsteady flow.
References:
[1] Carbon Trust (2005). UK tidal stream resource assessment (Phase II). Black and Veatch Ltd,
[2] Whelan, J. I., Graham, J. M. R., Peiró, J. (2009). Inertia Effects on Horizontal Axis Tidal-Stream
Turbines, In: Proc. 8th European Wave and Tidal Energy Conference.
[3] Snel, H., Schepers, J. G. (1992). Engineering moles for dynamic inflow phenomena, Journal of
Wind Engineering and Industrial Aerodynamics. 39, 267-281.
Figure 1. 3D representation of vortex lattice solver, one blade and its wake removed for clarity,
shading is a function of circulation.
26
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Development of an Actuator Line Model for Tidal Turbine Simulations
Justine Schluntz*, Richard H. J. Willden
Department of Engineering Science, University of Oxford, OX1 3PJ, UK
Summary: The paper presents a RANS embedded actuator line model for the simulation of tidal
turbine rotor flows. The method enables time resolved flow simulations at considerably less expense
than blade resolved simulations, whilst enabling modelling of discrete blade effects. The method is
developed for use on unstructured grids, thus permitting simulation of ancillary turbine geometries,
e.g. nacelles. Further, the method is developed to allow for arbitrary blade motion and turbine type.
Introduction
Various rotor modelling techniques exist in which the rotor can be modelled in a time averaged
sense using either an actuator disk or a Blade Element Momentum (BEM) representation.
Alternatively, time resolved models are available through either complete modelling of the blade
resolved flow field or through the use of an actuator line method. In the actuator line method the rotor
blades are approximated by point forces applied at the quarter-chord and distributed along the span of
each blade (Figure 1). The actuator lines move in time, enabling an unsteady flow solution. Actuator
line models allow for the effects on the flow due to the presence of discrete blades to be modelled
without requiring the discretisation of the blade boundary layer, thereby increasing the speed of the
computation as compared to blade-resolved models. Unlike RANS embedded actuator disc and BEM
models, the time-dependent influences of the blades are directly included in actuator line simulations.
Sorensen and Shen [1] developed an actuator line model for use in horizontal-axis wind turbine
simulations. Churchfield et al. [2] used a similar model in an investigation of tidal turbine arrays.
These simulations, however, have been restricted to rotors in structured local polar grids. This type of
grid is unsuitable for including the presence of stationary turbine components such as the shaft and
nacelle. The objective of the present work is to develop a model that is adapted for unstructured grids,
thus enabling arbitrary blade motion and the capacity to model a range of rotor types. Additionally the
use of an unstructured grid enables the stationary turbine geometry to be explicitly meshed.
Methods
An actuator line model has been embedded in a commercial CFD solver, ANSYS FLUENT. The
actuator line model may be viewed as an unsteady adaptation of BEM. As in BEM models, each rotor
blade is split into spanwise segments and blade element theory is used to calculate the aerodynamic
forces on each segment. Rather than average the influence of the blades over a revolution, however,
the forces in an actuator line model are applied to the flow only along the blade quarter chords at the
rotor’s current position. The rotor position is then updated at the beginning of the following time step.
In each time-step, the forces on each segment of each actuator line are calculated using the local
velocity at the segment’s collocation point, the local angle of attack, and tabulated data for the
aerodynamic coefficients. The force at the collocation point is then distributed to surrounding cell
centroids in the finite volume fluid stencil. The Navier-Stokes equations are then solved taking
account of the presence of the blades through the imposed forces along the actuator lines. The fluid
and loading solution is then iterated until convergence before proceeding to the next time step.
Results
The concept of approximating a lifting surface using an actuator line was verified using a 3D elliptic
wing. Computational results for the spanwise circulation distribution for a stationary elliptic wing
*
Corresponding author.
Email address: justine.schluntz@eng.ox.ac.uk
27
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
were plotted against the analytical potential flow solution for both symmetric (Figure 2) and cambered
wings over a range of angles of attack. The results compared favourably with the analytical solution
for structured as well as unstructured grids. Initial results showed that the circulation near the wing
tips was not as accurately reproduced as the circulation near the blade midspan, but this was improved
upon by concentrating more collocation points in the vicinity of the tips. The test cases were run on
both structured and unstructured grids.
Further work will include model validation against the NREL Phase VI wind tunnel test results.
Representative simulations of rotating rotors will be presented at the workshop.
Conclusions
The actuator line method has been developed for use in an unsteady 3D simulation of one or more
tidal turbines. The model has been adapted for use on an unstructured grid, allowing for stationary
turbine geometry such as the nacelle and shaft to be explicitly included in the mesh.
Acknowledgements:
JS would like to thank the Rhodes Trust for supporting her doctoral research.
References:
[1] Sorensen, J. N. And Shen, W. Z. (2002). Numerical modelling of wind turbine wakes. J. Fluid
Mech. 124, 393-399.
[2] Churchfield, M. J., Li, Y., Moriarty, P. J. (2011). A large-eddy simulation study of wake
propagation and power production in an array of tidal-current turbines. In: Proc. 9th European
Wave and Tidal Energy Conf, Southampton.
Fig. 1. Actuator line representation of a blade.
Fig. 2. Circulation distribution for a symmetric wing at varying angles of attack (structured grid).
28
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Modification of Open Channel Flow By Opposing Waves
A. Olczak* and T. Stallard
School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester, M13 9PL
Summary: An experimental study is presented of the effect of waves on both the depth variation of mean
velocity and turbulence characteristics of flow in a wide channel. The scale conditions considered represent a
full-scale site of approximately 30 m depth with mean speed 3.8 m/s and wave periods of 8 - 16 s. Turbulence
intensity and length scale are obtained representing fluctuations that are both turbulent and wave-induced.
Preliminary comparison is drawn to full scale data from the European Marine Energy Centre tidal site [1], [2].
Background
To maximise energy extraction from tidal stream sites it is likely that turbines will be installed in arrays
with devices at close proximity. Most of the potential sites are at exposed locations and waves and current
coexist so it is important to understand the influence of waves on turbine and array design. Waves of long
period such as swell waves influence flow velocity across the water column and so are expected to effect
loading, power output, wake generation and the rate of wake expansion and recovery.
Methodology
A water depth of h = 0.5 m and mean flow speed U = 0.46 m/s is developed in a 5 m wide channel.
Time varying velocities (ux (t), uy (t) and uz (t)) are sampled at 200 Hz using a NORTEK Acoustic Doppler
Velocimeter (ADV) Vectrino+. Flow is measured without waves and with the addition opposing regular
waves of frequency 0.5Hz, 0.8Hz and 1Hz. A depth profile is recorded 6 m from the inlet on the centreline
of the flume. For the flow only cases, samples of 5 min duration are recorded at 1 mm increments over the
range 0.08 < z/h < 0.92. For flow with opposing waves, samples of 1 min duration are recorded at seven
depth increments. Mean velocity, U, turbulence intensity, T Ii = ui /Ux , and turbulence spectra (Figures 1 - 3)
are obtained where ui is time-average of all fluctuations including wave induced. Length scales are obtained
for each sample by auto correlation (Equation (1)) of each time-varying sample and, at mid-depth, by cross
correlation of samples measured simultaneously at a range of increments.
Li = U x
Z ∞
0
Ri (t)dt
Ri (t) =
where
< ui (t)ui (t + dt) >
< u2 >
(1)
Flow Characteristics
The stream wise velocity profile is found to exhibit a power law profile, Ux (z) = Ux,max (z/h)1/n , with
n = 10.6 (Figure 1(a)). This is a similar profile to full scale flow speeds of 0 - 0.4m/s. The depth averaged
streamwise turbulence was found to be 12%, a similar magnitude to the turbulence reported at the EMEC
tidal site ( [2]). Anisotropy is also similar: ratio of 1:0.67:0.5 reported by [2] compared to 1:0.65:0.55.
Streamwise turbulence length scale by Equation 1 was found to be 0.28 m at mid-depth but increases towards
bed. This approach is sensitive to sample length but is in reasonable agreement with 0.245 m (∼ 0.54h) by
cross correlation at mid depth. Lateral and vertical length scales are Ly = 0.16 and Lz = 0.07 m by Equation
1 and Ly = 0.15 m and Lz =0.12 m by cross correlation. Smaller streamwise length scale of order of 11-14 m
(∼ h/4) are reported by [2].
Opposing Waves
As expected co-generation of flow and opposing surface waves results in minimal change to the mean
velocity profile. Both Ux and Uz are within the experimental scatter. A reduction in the lateral velocity Uy
is also observed indicating that waves reduce the transverse circulation that develops within a wide channel.
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Oxford Tidal Energy Workshop
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1
1
1
1
1
0.8
0.8
0.8
0.8
0.8
0.8
0.6
0.6
0.6
0.6
0.6
0.6
0.4
0.4
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
0.2
0.2
Z/H
Z/H
1
0
0
0.5
U
1
0
−0.05
x
0
U
0.05
0
−0.04
y
−0.02
U
0
0
0
0.5
TIx
z
1
0
0.5
0
TIy
(a) Mean velocity
1
0
0
0.5
TIz
(b) Turbulence intensity
1
0.8Hz
0
10
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
−2
Z/H
TKE
10
0
0
0.5
Lx
1
0
0
0.2
Ly
0.4
0
−4
10
−6
10
−2
0
0.1
Lz
10
0.2
(c) Length scale
0
10
Frequency (Hz)
2
10
(d) Kinetic energy spectra
Figure 1: Depth profiles of (a) mean velocity, (b) turbulence intensity and (c) length scale, Equation 1, for uniform
flow only (×) and with opposing waves of 1 Hz (◦), 0.8 Hz (•) and 0.5 Hz (*). Green markers by cross correlation.
Kinetic energy spectrum also shown (d) for z/h = 0.5 without and with waves of 0.8 Hz.
Wave induced kinematics appear as higher turbulence intensity, particularly close to the surface. Length
scale is generally reduced reflecting the magnitude of wave induced oscillation.
Conclusion
Measurements are reported of turbulence characteristics in a wide channel and modification by opposing
waves. Waves of 0.5 Hz increase the turbulence intensity throughout the water depth but only the upper
third of the depth is influenced by higher wave frequencies. Integral length scales are modified throughout
the water column but the Auto correlation method employed is found to be sensitive to sample length.
Turbulence characteristics reported represent all flow- and wave-induced fluctuations. Analysis of turbulence
fluctuations only is ongoing.
References
[1] G. McCann, M. Thomson, and S. Hitchcock. Implications of Site-Specific Conditions on the Prediction
of Loading and Power Performance of a Tidal Stream Device. In 2nd International Conference on Ocean
Energy (ICOE 2008), October 2008.
[2] I.A. Milne, R.N. Sharma, R.G.J Flay, and S. Bickerton. Characteristics of the Onset Flow Turbulence at
a Tidal-Stream Power Site. Proceedings 9th EWTEC, Southampton, UK. 5-9th September, 2011.
30
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Prediction and Measurement of Time-Varying Thrust on Tidal Turbine
due to Mean and Oscillatory flow
Fernandez Rodriguez, E., Stallard, T. and Stansby, P.K.
School of Mechanical, Aerospace and Civil Engineering, University of Manchester, M13 9PL
Summary: The suitability of a blade element momentum method for predicting time-varying thrust due
to both steady flow and opposing waves is assessed by comparison to experimental measurements
obtained at small geometric scale. A blade element model is developed and validated for steady flow
against published data for both a 0.8 m diameter rotor [1] and a 0.27 m diameter rotor [2]. Timevariation of angular speed, thrust and power are obtained for uniform flow only and flow combined
with opposing waves. Comparison is drawn between measured time-varying thrust and predicted timevarying thrust based on flow velocity measured at hub height and assumed quasi-steady over intervals
up to one-tenth of a wave period.
Blade Element Momentum Theory
Blade Element Momentum (BEM) Theory is widely used to obtain the variation of power coefficient
(CP) and axial thrust coefficient (CT) with turbine’s rotational speed (TSR). A turbine power curve is
obtained by relating the lift and drag curves for each section of a blade to the net thrust and power
developed by the rotor. Design software such as GH Bladed is widely used for both wind- and tidal
stream turbine design. This approach has been shown to be suitable for prediction of performance of
mean performance of tidal stream turbines [1, 2] although corrections for blockage may be required.
There is less published information available concerning the suitability of this approach for prediction
of time-varying thrust and power. This is particularly important for flows comprising both uniform
flow and current for which there is uncertainty on the transient loads effects on the rotor. This research
employs the BEM theory to predict in a quasi-steady state the turbine’s unsteady behaviour.
Experimental Approach
The experimental arrangement is as described in [2]. A rotor of diameter =0.27 m is supported on a
strain gauged support structure and assisting or retarding torque applied by a custom dynamometer.
Angular speed is obtained from an optical encoder. Torque is held constant in time at values of
[0.0039-0.0156] N-m to attain tip-speed ratios over the range 4-6.5 in steady flow. The rotor is located
at mid-depth and mid-span of a 5 m wide flume with water depth 0.45 m. The incident flow velocity,
, is measured at hub height using a Nortek Vectrino+ ADV prior to rotor installation. All
parameters are sampled at 200 Hz. The influence of oscillatory flow on the rotor performance is
investigated by development of regular waves of 2 cm amplitude and frequency of 0.5 Hz opposing
the mean flow. Mean axial velocity in the absence of waves is = 0.462 m/s. Axial velocity with
waves varies from 0.66 to 0.23 m/s with a mean of uc+w = 0.442 m/s.
Predicted and Measured Thrust
Accuracy of the present BEM implementation is demonstrated by comparison to published predictions
from [1] and [2] and to measurements due to steady flow (Figure 1). Comparison is drawn between
measured and predicted thrust (F x,m and F x,p) assuming steady flow (averaged over dt = 120 s) and for
time-varying flow (averaged over dt = 0.1 s). To facilitate comparison and because velocity
measurements are not synchronized with thrust, the time-varying tip speed ratio (TSR) and thrust
coefficient are normalized to the steady flow mean velocity for both measurements and predictions.
From measurements:
Eq.1
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Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
A fitted curve on the experimental average thrust coefficient graph at 20 Hz (Figure 2b) is employed
in the model´s prediction to obtain improved synchronized velocity and time varying thrust
coefficients.
0.6
1.2
1
0.4
0.8
CP
0.3
CT
Published
BEM
Experiments
0.8
0.7
0.6
CT
0.5
0.9
Theory 15°
Theory 20°
Theory 25°
Theory 27°
0.5
0.6
CP
0.4
0.2
0.4
0.1
0.2
0.3
0.2
0.1
0
0
2
4
6
8
0
0
10
2
4
6
8
10
0
0
1
2
3
4
5
6
7
TSR
TSR
TSR
Figure 1: BEM predictions of thrust and power curves compared with published data [2] for range of pitch
angles and (b) to published predictions [1] and experimental measurements.
2
12
1.8
1.6
10
1.4
8
CT
N
1.2
6
1
0.8
0.6
4
0.4
2
0.2
3
4
s
5
6
0
0
1
2
3
4
5
TSR
6
7
8
9
10
Figure 2: Example of time varying thrust force (a) during one minute sample with waves opposing mean flow and
(b) the variation of thrust coefficient over each 0.1 s interval obtained from measurement and prediction. Both
measurement and prediction normalised to mean flow of uc = 0.462 m/s.
Conclusions
A BEM numerical code has been written and employed to predict time-varying thrust and power
from a tidal stream rotor due to oscillatory flow developed by mean flow and opposing waves.
Implementation has been verified against previous publications of two tidal stream turbines [1, 2] and
additional experiments. The measured thrust coefficient is lower than predicted based on steady
assumptions for low TSR and greater than predicted for high TSR. When averaged over a two-minute
sample the average measured thrust coefficient is found to be greater than steady predictions by
around 8-9 %. Ongoing work addresses the case of forced oscillation in steady flow to improve
understanding of the effect of oscillating loads on performance.
References:
[1] Batten, W. M. J., A. S. Bahaj, et al. (2008). "The prediction of the hydrodynamic
performance of marine current turbines." Renewable Energy 33(5): 1085-1096
[2] Whelan, J. and T. Stallard (2011). Arguments for modifying the geometry of a scale model rotor.
9th European Wave and Tidal Energy Conference, . Southampton. 5-9 ,September 2011.
32
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Blade Element Momentum Theory for Tidal Turbine Simulation with
Wave Effects: A Validation Study
Hannah C. Buckland*, Ian Masters
College of Engineering, Swansea University, SA2 8PP, UK
James A. C. Orme
Swanturbines Ltd, Digital Technium, Singleton Park, Swansea, UK
Summary: The non-linear and three-dimensional effects of a regular wave and tidal dynamic inflow on
a tidal stream turbine are important for performance optimisation and to determine survivability. A
reactive coupling between Blade Element Momentum Theory (BEMT) and Chaplin’s stream function
wave theory is used as a simulation tool to determine turbine performance in dynamic inflow. The
simulation is validated against a unique data set by Barltrop et al. [1] of a towed turbine in a wave
climate. The comparison considers axial force and torque, providing validation of the BEMT scheme,
the wave model and the wave frequency coupling between them.
Introduction
As the marine energy industry evolves from device design to deployment, fast and robust turbine
computer simulations are needed to predict performance and survivability in varied fluid flow
conditions. Within the MatLab computing environment, this scheme can successfully simulate tidal
turbine performance with low computational time when compared to a more traditional CFD
approach. The inclusion of loss corrections and wave theory adapts BEMT to model the performance
of a real turbine and the scheme can be validated against experimental data.
Computational Methods
BEMT models the performance of a turbine by combining one-dimensional momentum theory with
rotational momentum and blade element theory. In both cases, two sets of equations are obtained for
the turbine axial force and torque. The system is resolved by using the least squares method for the
difference between the complementing theories thus converging on an agreed solution. A complete
derivation of these equations and verification of the model is given in [2].
The stream function wave theory describes a 2D periodic wave of permanent form in irrotational
and incompressible flow. The frame of reference moves with wave speed reducing the problem to one
of constant flow. The problem is defined in the same way as finite depth linear wave theory and
similar boundary and flow conditions apply. Wave velocities are summed with the tidal velocities to
give a combined flow velocity, stored in a velocity matrix. This can then be used to interpolate the
incident flow velocity at the blade element position in blade element theory and the upstream flow
velocity for momentum theory. The accelerative terms calculated from stream function wave theory
are retained as they produce hydrodynamic force on the turbines which is calculated from Morison's
equation, [3].
BEMT assumes a fully developed wake, steady state, at each iteration therefore the number of
iterations is kept high. Wave and tidal flows do not act independently of each other. This model cannot
capture the rotation of flow which may occur and the effect of the current velocity on the dispersion of
the waves, [2]. An improved wave and tidal coupling theory is an active research area for the Marine
Energy Research Group (MERG).
*
Corresponding author.
Email address: 513924@swansea.ac.uk
33
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Results
Barltrop et al. [1] investigate the axial force and torque for a 0.4m diameter turbine in a wave tank.
The figure compares the experimental against computational results respectively with 90rpm rotational
frequency, 0.7ms-1 current, in the presence of waves with frequency 0.833Hz and specified wave
heights. The turbine was towed along the length towards a prescribed wave which was induced
throughout the towing tank therefore realistic coupling between tides and waves is not captured.
However, the apparent wave celerity will increase as the wave frequency seen by the turbine increases.
A good agreement is observed between experimental data and the proposed scheme, with greater
agreement in larger wave heights. This is due to a flow disturbance creating turbulent inflow, the
effect of which is seen in the experimental results for no waves, in particular for torque. This
disturbance is periodic and has a frequency of 9 per rev, implying that the 3 blades may be passing
structures in turn. This blade pass disturbance becomes less significant with increasing wave height as
the wave period begins to dominate the inflow velocities and accelerations.
Conclusions
An increased inflow velocity, with a fixed turbine rotational speed, always gives a decrease in TSR.
The turbine reaction to this depends on the operating conditions and TSR. Therefore wave effects are
dependent on the shape of the performance coefficient TSR curves around the operating condition of
the turbine. Pitch, twist, chord length and aerofoil shape all impact on these TSR curve profiles. It is
important that wave effects do not periodically stall the turbine and maximum axial force conditions
are considered. The coupled BEMT scheme is proven to be a quick, simple and robust engineering
tool suitable for predicting performance characteristics of real tidal turbines and is validated against
experimental data. This extends the established BEMT turbine model to complex inflow problems and
provides confirmation that steady state BEMT is still valid for dynamic flow conditions.
References:
[1] Barltrop, N., Varyani, K. S., Grant, A., Clelland, D., Pham, X. P. (2007) Investigation into WaveCurrent Interactions in Marine Current Turbines. J. Power and Energy. 221, 233-242.
[2] Masters, I., Orme, J. A. C., Willis, M., Chapman, J. (2010) A Robust Blade Element Momentum
Theory Model for Tidal Stream Turbines including Tip and Hub Loss Corrections. In: Proc. Institute
of Marine Engineering, Science and Technology, J. Marine engineering and technology. 10, 25-35.
[3] Orme, J. A. C. (2006) Dynamic Performance Modelling of Tidal Stream Turbines in Ocean
Waves. PhD Thesis, Civil and Computational Engineering, Swansea University.
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Oxford Tidal Energy Workshop
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The Buhl High-Induction Correction for Blade Element Momentum
Theory Applied to Tidal Stream Turbines
Ian Masters, Michael Togneri*
College of Engineering, Swansea University, SA2 8PP, UK
Summary: Blade element momentum theory (BEMT) is an extremely useful tool for simulation of
turbines extracting power from a flow of fluid, but it is known to have difficulty making satisfactory
predictions for turbines operating in significantly non-optimum conditions. One such case is that of the
high-induction condition, wherein the axial momentum extracted from the fluid flow as it passes
through the rotor disc exceeds some threshold. Several semi-empirical corrections have been proposed
that attempt to rectify the BEMT treatment of this operating condition; in this work we examine a
refinement of the Buhl correction, and validate results against experimental measurements [1] of a
scale model turbine.
Outline
BEMT allows much more rapid simulation of tidal stream turbines (TSTs) than is possible with
conventional CFD modelling. This rapidity is achieved by making several simplifying assumptions,
not of all which are perfectly satisfied for all possible TST operating conditions. Two of these
assumptions interact with one another to make the high-induction condition problematic: firstly, we
imagine the fluid passing through the rotor disc as flowing through an enclosed streamtube. The
second of these assumptions is made in the treatment of axial momentum flux through the rotor disc.
The extraction of kinetic energy from a fluid flow by a turbine decelerates the flow. In deriving the
BEMT model we assume that this deceleration can be characterised by a single parameter a(r), the
‘axial induction factor’, which varies with radial position r on the rotor disc. a relates the flow velocity
in the far upstream (U∞) to the velocity at the disc (U) and the velocity in the far wake (U1) through the
following equations:
Clearly, if a exceeds 0.5, we have a reversal of flow in the far wake; equally clearly, this reversal is
prohibited by continuity, since we have assumed a closed streamtube bounding the flow. A highinduction correction attempts to overcome the difficulties associated with these assumptions by
adjusting the relationship between a and the axial thrust on the rotor disc. The Buhl correction
assumes a quadratic relation between a and the axial force coefficient, CFa , above some critical value
of a, conventionally 0.4; a more complete derivation of the theory is available in Chapman et al. [2].
This relationship is fully described by three parameters, obtained by matching the value and gradient
of the corrected and uncorrected CFa -a curves at the critical value of a and by specifying the value of
CFa at
. The relationship between axial thrust coefficient and axial induction factor for classical
BEMT, the Glauert high-induction correction and other correction scheme by Spera and Glauert is
illustrated in figure 1.
Results
We have found that a BEMT model with a Buhl high-induction correction is able to satisfactorily
predict the power output of a turbine by validation against experimental results. Predictions of axial
*
Corresponding author.
Email address: M.Togneri@swansea.ac.uk
35
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
thrust, however, are less satisfactory, with the numerical model overpredicting thrust compared to
measurements. Results from several simulations and from experimental work are shown in figure 2;
more in-depth discussion of these results can be found in [2].
Acknowledgements:
This work was undertaken as part of the Low Carbon Research Institute Marine Consortium
(www.lcrimarine.org). The Authors wish to acknowledge the financial support of the Welsh Assembly
Government, the Higher Education Funding Council for Wales, the Welsh European Funding Office,
and the European Regional Development Fund Convergence Programme.
References:
[1] Tedds, S.C. et al (2011). Experimental Investigation of Horizontal Axis Tidal Stream Turbines.
In: Proc. of 9th EWTEC Conference. Southampton, UK
[2] Chapman, J.C.; Masters, I.; Togneri, M.; Orme, J.A.C. (2012). The Buhl correction factor applied
to high induction conditions for tidal stream turbines. Submitted to Renewable Energy
2.5
BEMT CFa-a curve
Spera-corrected C Fa-a curve
Glauert-corrected C Fa-a curve
2
Buhl
CFa
1.5
1
0.5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
a
Figure 1: Relationship between axial induction factor and thrust coefficient for classical BEMT and a selection
of high-induction correction schemes. Combined tip-hub loss factor of F = 0.8
0.4
0.3
Cp
0.2
0.1
0
-0.1
5.5
Without high induction correction
High induction correction, C Fa1 = 2
High induction correction, C Fa1 = 1.816
High induction correction, C Fa1 = 1.6
High induction correction, C Fa1 = 1.3
Uncorrected flume data
Blockage-corrected flume data
6
6.5
7
7.5
8
7
7.5
8
TSR
0.9
CFa
0.8
0.7
0.6
0.5
5.5
6
6.5
TSR
Figure 2: Comparison of numerical and experimental CP and CFa values for a scale model of a TST operated in
the high-induction regime.
36
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Numerical Analysis of Open-Centre Ducted Tidal Turbines
Clarissa S. K. Belloni*, Richard H. J. Willden & Guy T. Houlsby
Department of Engineering Science, University of Oxford, OX1 3PJ, UK
Summary: A computational study of open-centre tidal turbines using three-dimensional Reynolds
Averaged Navier-Stokes simulations is presented. We investigate turbine performance, power and
thrust, and relate these to the flow characteristics through the open-centre turbine. A substantial
decrease in power is found relative to a bare turbine of the same external diameter. We also analyse
the open-centre turbine in yawed flow. For yawed flow we observe an increase in power coefficient
compared to the unyawed open-centre turbine which we attribute to increased effective blockage. The
yawed open-centre turbine performs significantly poorer in terms of basin efficiency.
Introduction
One of the many concepts being pursued by the tidal stream energy industry is the open-centre
ducted turbine featuring an aperture at the centre of the turbine disc. Manufacturers claim a
performance benefit due to a speed-up effect generated by the duct as well as the jet flow through the
turbine aperture [1, 2]. In this study we analyse the flow field and the efficiency of this type of device
and compare it to that of an equivalent bare turbine [3].
Methods
We model the outer ducts as solid bodies and use porous discs to represent the turbine rotors, a
simplification that greatly reduces computational complexity while capturing energy extraction and
the primary interaction of the disc with the flow through and around the duct. The computational
approach has been validated for bare turbines by comparison to Linear Momentum Actuator Disc
Theory for turbines in arbitrarily blocked flows [3]. The topology of the open-centre turbine
investigated is shown in figure 1. The channel dimensions were 75m x 75m x 290m, the turbine
dimensions were D = 16m, resulting in an overall blockage of B = 0.035. Symmetry conditions were
used for the upper, lower and lateral boundary conditions in the case of unyawed flow. And in the case
of yawed flow periodic conditions were used on the lateral surfaces.
Results
We observe jetting flows through the opening at the centre of the turbine. We investigate the
influence of aperture and observe an increase in pressure drop and flow velocity through the turbine
disc with increasing aperture size, see figure 2. However, these increases, which increase the power
generated per unit area of disc, are offset by the decrease in turbine disc area due to the increase in
aperture size, thus resulting in an overall reduction in turbine performance with increasing aperture
size, see figure 3.
For the open-centre turbine in yawed flow an increase in power coefficient is visible relative to that
in unyawed flow. This increase in power coefficient can be attributed to the increased effective
blockage of the device; the device is longer than its diameter and hence the projected area normal to
the yawed flow direction is greater. Further the basin efficiency, defined as the ratio of useful power
generated to total power removed from the flow field, of the yawed open-centre turbine is significantly
lower than for the unyawed case due to large scale flow separations on the outer duct wall.
*
Corresponding author.
Email address: clarissa.belloni@eng.ox.ac.uk
37
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Conclusions
For the open-centre turbine we present flow simulations and analyses for varying central aperture
sizes. In all cases we find a flow jetting effect through the centre of the turbine. The effect of this
jetting is outweighed by the decrease in rotor area, leading to a reduction in overall turbine
performance with aperture size. Yawed flow is found to increase performance due to increased
effective blockage, but at the expense of decreased basin efficiency.
Acknowledgements:
The authors would like to express their gratitude to the Engineering and Physical Sciences Research
Council (EPSRC), Research Councils UK (RCUK), the German Academic Exchange Service
(DAAD), and the Oxford Martin School which have partially funded this work.
References:
[1] Clean Current Power Systems Incorporated. http://www.cleancurrent.com/index.htm, cited on 20
March, 2012
[2] OpenHydro Group Ltd. http://www.openhydro.com/home.html, cited on 20 March, 2012.
[3] C.S.K. Belloni, RH.J. Willden (2011): “Flow Field and Performance Analysis of Bidirectional
and Open-centre Ducted Tidal Turbines”. In Proc. 9th European Wave and Tidal Energy
Conference, Southampton, UK.
1
0.8
Bare
Open(centre, full disc
Open(centre D
=3m
hole
Open(centre Dhole=6m
Open(centre D
=9m
hole
CP
0.6
0.4
0.2
0
0
0.2
0.4
~
0.6
0.8
1
basin
Fig. 1. The open-centre turbine.
Fig. 3. Performance of the open-centre turbine.
Fig. 2. Velocity and pressure jump profiles plotted against the radial position for the open-centre turbine with varying
opening diameters at the maximum power point for each device.
38
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Evaluation of FVNS Solvers for Structures in Tidal Flow
Robert Stringer*, Jun Zang
Department of Architecture & Civil Engineering, University of Bath, BA2 7AY, UK
Summary: In an attempt to accurately predict the von Kármán vortex shedding and associated forces
of a cylindrical structure subject to tidal flow, a numerical environment is proposed and tested using
two prominent Finite Volume Navier-Stokes (FVNS) solvers. The methodology has been developed
through extensive literary exploration and iterative testing with the aim of generating an accessible
means of analysis and to compare the solvers by closely matching the setup environments. A second
study on cross-flow tidal turbine performance is also ongoing; although this is not discussed here,
presentation of preliminary results at the workshop is intended.
Introduction
Over a full tidal cycle, realistic cylindrical supporting structures for marine energy applications,
such as monopoles, can experience flows equivalent to Reynolds numbers (Re) from zero up to
supercritical values. At the majority of flow speeds, undesirable fluctuating lift and drag forces are
generated often referred to as Vortex Induced Vibrations (VIV). Accurate capture of the effects of
VIV can aid both structural and turbine performance optimisation. Therefore, the study here aims to
develop an effective testing methodology, comparing the solvers ANSYS® CFX-13.0 and
OpenFOAM® 1.7.1 at test points throughout the full range of tidal conditions, from a Reynolds
number of 40 up to 106.
The study of flow around circular cylinders has been popular amongst academics with notable
contributions from Roshko [1] and Achenbach and Heinecke [2] providing crucial experimental data.
Numerical efforts often focus on specific Reynolds values, with effective turbulence modelling central
to the success of the studies. Although many papers are considered, Tutar and Holdø [3] and Benim
et al [4] are examples containing valuable results regarding geometry, meshing resolution and
turbulence model selection. The literature analysis provided sufficient data to devise a proposed
optimum scheme that is applied to all turbulent cylinder cases.
Computational Method
Due to the high Re values in the study requiring prohibitively large grids, 2D meshes were used
throughout. An Unsteady Reynolds-Averaged Navier-Stokes (URANS) model is chosen over LES
due to the applicability of LES being questionable in 2D and evidence of only marginal improvement
over two-equation turbulence models. Turbulence was modelled using the Shear Stress Transport
(SST) two equation model [5], chosen due to a proven accuracy in predicting heavily separated flows.
This was combined with a robust Low-Re boundary meshing strategy, body fitted near wall cells and
aspect ratio control. More specifically, the meshes were iteratively derived such that a y+ < 1.5 was
guaranteed, allowing the SST model to predict flux gradients within the boundary layer as opposed to
the standard logarithmic wall model. In practice this was achieved differently between the two codes;
CFX employs a Low-Re formulation whereby the k-equation is artificially set to zero and the
momentum flux is directly computed from velocity profile, shear stress includes a function of viscous
and logarithmic values and ω is calculated by an algebraic expression. Conversely, OpenFOAM does
not include such a formulation in the distribution being tested, therefore a continuous wall model by
Spalding is applied where a single function is iteratively solved which describes a “universal” velocity
profile from laminar to logarithmic layer; interestingly the Spalding wall model is the default method
provided by OpenFOAM for LES computations where a wall model is desired.
*
Corresponding author.
Email address: r.m.stringer@bath.ac.uk
39
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
Results
Results were extracted for key parameters including lift and drag components, Strouhal number,
boundary layer thickness, pressure and velocity distribution, wake dimensions and more. An example
result is presented in Fig. 1. depicting the drag coefficient versus Re for a smooth cylinder; data
includes experimental values from Zdravkovich [6] and Massey [7] and computed from CFX and
OpenFOAM. Although only drag coefficient is displayed here, it is representative of the quality of the
results more generally; low and subcritical Re values are modelled with high success by OpenFOAM,
while force terms in upper critical and supercritical flows are better predicted by CFX.
Zdravkovich
Massey
CFX
OpenFOAM
10
CD
1
0.1
1
10
100
1000
Re
10000
100000
1000000 10000000
Fig. 1. Graph of flow Reynolds number vs. Coefficient of Drag
Conclusions
The modelling of an essentially 3D problem in 2D is a common simplification in an effort to reduce
run times and increase productivity. The results of the 2D URANS method developed here show some
significant achievements particularly up to the higher subcritical region Re < 10000, this may be
extended up to Re = 105 with further testing with results being suitable for engineering purposes.
Further study of the results may also shed light on the discrepancy between the solvers despite efforts
to closely match the numerical environments such as common meshes and governing parameters.
References:
[1]
[2]
[3]
[4]
[5]
[6]
[7]
Roshko, A., On the Wake and Drag of Bluff Bodies. Journal of the Aeronautical Sciences, 1955. 22(2):
p. 124-132.
Achenbach, E. and E. Heinecke, On Vortex Shedding from Smooth and Rough Cylinders in the Range
of Reynolds-Numbers 6x103 to 5x106. Journal of Fluid Mechanics, 1981. 109(Aug): p. 239-251.
Tutar, M. and A.E. Holdo, Computational modelling of flow around a circular cylinder in sub-critical
flow regime with various turbulence models. International Journal for Numerical Methods in Fluids,
2001. 35(7): p. 763-784.
Benim, A.C., et al., RANS predictions of turbulent flow past a circular cylinder over the critical regime.
Proceedings of the 5th Iasme/Wseas International Conference on Fluid Mechanics and Aerodynamics
(Fma '07), 2007: p. 235-240.
Menter, F.R., 2-Equation Eddy-Viscosity Turbulence Models for Engineering Applications. Aiaa
Journal, 1994. 32(8): p. 1598-1605.
Zdravkovich, M.M., Conceptual Overview of Laminar and Turbulent Flows Past Smooth and Rough
Circular-Cylinders. Journal of Wind Engineering and Industrial Aerodynamics, 1990. 33: p. 53-62.
Massey, B.S., Mechanics of fluids. 6th ed. ed. 1989: Van Nostrand Reinhold. [608]p.
40
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
On the Garrett & Cummins limit
Thomas A.A. Adcock
Department of Engineering Science, University of Oxford, OX1 3PJ, UK
Summary: Garrett & Cummins derived a limit to the energy that may be extracted from an idealised
tidal channel. In this note we show that this limit may be exceeded if the drag coefficient of a turbine
is allowed to vary with time. We also consider how the limiting energy may be practically extracted
using actuator disc theory and again find increased energy is available than previously reported.
Introduction
Garrett & Cummins [1] used a simple model for the flow in a tidal channel connecting two basins.
Whilst the model involves a major simplification of the tidal dynamics of a real channel, it is
nevertheless valuable for gaining understanding of the problem of extracting energy from a tidal
stream. The model assumes a tidal channel linking two bodies of water whose water levels are
independent of the flow in the channel. The flow in the channel is then dependent on the difference in
the water level (assumed sinusoidal), the drag in the channel due to bed friction and turbines, and the
inertia of the water. After non-dimensionalisation (see [1]) this gives the equation
dQ'
= cos (t ') ! ( !0 + !1 ) Q' Q'
dt '
(1)
where Q` is the non-dimensional flow rate, t` non-dimensional time, and λ0 and λ1 the non-dimensional
drag components due to the channel friction and the presence of turbines. Realistic values for λ0 are
roughly between 0.4 and 4. Garrett & Cummins found the limit for the maximum power that may be
extracted from such a channel to be remarkably insensitive to the channel properties (λ0), when the
power output was normalised by density, driving amplitude, the naturally occurring peak flow rate,
and gravitational acceleration (all results in this note are presented normalised by these variables). The
Garrett & Cummins limit represents the maximum power that may be extracted by a channel. In
reality, the amount of power that can be utilised for useful work is rather smaller than the limiting
value due to mixing behind the turbine, viscous turbine losses, generator losses, etc. The mixing losses
may be captured using an actuator disc model, with the wake induction factor “tuned” so that
maximum useful work is extracted [2].
Power extracted from the flow
The Garrett & Cummins analysis assumed that the drag coefficient, and hence λ1 was constant. In
practice, this could vary as, say, a turbine is operated at different tip-speed-ratios. We therefore allow
λ1 to vary with time. As the model is periodic we assume that the optimum form of λ1 can be
decomposed into harmonics of the driving frequency allowing us to write
N
!1 (t ') = " ! n cos ( nt '+ !n )
(2)
n=0
where Λ and ϕ are unknown coefficients and N the number of components used in the analysis. We
search for the values of these which will give maximum power extraction using an optimisation
routine, imposing the condition that at all times λ1 must be positive (i.e. the turbines cannot be
switched to act as a pump). Equation 1 is solved using a 4th order Runge-Kutta time-stepping scheme.
Due to the symmetric nature of the flow, odd harmonics in Equation 2 do not lead to an increase in the
maximum power output. However, even harmonics do lead to an increase in the available power. This
is small for channels where λ0 is large — the analysis of these is quasi-steady and so introducing a
time varying component would not be expected to yield increased energy. However, for channels with
small λ0 a substantial increase in power extracted is possible. This is shown in Figure 1 for different
41
Oxford Tidal Energy Workshop
29-30 March 2012, Oxford, UK
numbers of harmonics. It can be seen that the solution appears to be converging as more components
are used.
Normalised power
0.4
N=0
N=2
N=4
N=6
0.35
0.3
0.25
0.2
Limit derived by Garrett & Cummins
0
0.5
1
1.5
2
2.5
⁄0
3
3.5
4
Figure 1 Energy that may be extracted from a channel with different numbers of components.
Useful energy available
An upper limit for the useful energy available may be derived by using an actuator disc model in the
channel to calculate λ1 and the power output. To maximise power output, the wake induction factor of
the turbines needs to be “tuned” [2]. In this analysis we use the turbine model of Garrett & Cummins
[3]. Whilst this is valid only for small Froude number, for realistic channels we find negligibly
different results when the finite Froude number model [4] is used. We assume the optimum wake
induction factor has sinusoidal components in the same manner as Equation 2 and a routine is run to
find these. We consider only one row of turbines — multiple rows may be accounted for by dividing
λ0 by the number of rows. Figure 2 shows the available power for two different blockage ratios. N=0
corresponds to the analysis of Vennel (see his Fig. 7b).
Conclusions
We have shown that it is possible to extract more power from an idealised channel than the limit
introduced by Garrett & Cummins and also that more of this may be utilised than given in the anlaysis
by Vennel.
References:
[1] Garrett, C., Cummins, P. (2005). The power potential of tidal currents. Proc. R. Soc. A. 461
2563-2572
[2] Vennel, R. (2010) Tuning turbines in a tidal channel . J. Fluid Mech. 663, 253-267.
[3] Garrett, C., Cummins, P. (2007). The efficiency of a turbine in a tidal channel. J. Fluid Mech.
588, 243–251.
[4] Houlsby, G. T., Draper, S., Oldfield, M. L. G. (2008). Application of linear momentum actuator
disc theory to open channel flow. Report No. OUEL 2296/08, Department of Engineering
Science, University of Oxford.
(a)
(b)
0.12
Normalised power
Normalised power
0.3
0.1
0.08
0.06
0.04
0.25
0.2
0.15
0
0.5
1
1.5
2
⁄0
2.5
3
3.5
4
0
0.5
1
1.5
2
⁄
2.5
3
3.5
0
Figure 2 Useful power available. (a) blockage=0.4; (b) blockage=0.8. Thick line — N=0; dash —
N=2; dots — N=4
42
4
Workshop Attendees
Adcock, Thomas
Belloni, Clarissa
Buckland, Hannah
Cheong, Sei Him
Drake, Kevin
Evans, Paul
Fernandez Rodriguez, Emmanuel
Ferrer, Esteban
Fleming, Conor
Graham, Michael
Houlsby, Guy
Hunter, William
Jeffcoate, Penelope
Johnson, Peter
Malki, Rami
Mason‐Jones, Allan
Masters, Ian
McAdam, Ross
McIntosh, Simon
McNae, Duncan
McNaughton, James
Nishino, Takafumi
Olczak, Alex
Salter, Stephen
Schluntz, Justine
Serhadlioglu, Sena
Stallard, Tim
Stansby, Peter
Stringer, Robert
Tabor, Gavin
Taylor, Paul
Togneri, Michael
Vogel, Christopher
Vybulkova, Lada
Willden, Richard
Zang, Jun
Zangiabadi, Enayatollah
43
University of Oxford
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Imperial College London
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Swansea University
Cardiff University
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Imperial College London
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