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DOI: 10.1243/14750902JEME45

220: 1952006oceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment

N Barltrop, K S Varyani, A Grant, D Clelland and Xuan PhamWave-current interactions in marine current turbines

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SPECIAL ISSUE PAPER 195

Wave-current interactions in marine current turbinesN Barltrop1, K S Varyani1, A Grant2, D Clelland1, and Xuan Pham1*

1Department of Naval Architecture and Marine Engineering, Universities of Glasgow and Strathclyde, Glasgow, UK

2Department of Mechanical Engineering, University of Strathclyde, UK

The manuscript was received on 7 October 2005 and was accepted after revision for publication on 9 June 2006.

DOI: 10.1243/14750902JEME45

Abstract: The influence of waves on the dynamic properties of bending moments at the rootof blades of tidal stream vertical-axis rotors is reported. Blade element-momentum theory for

wind turbines is combined with linear wave theory and used to analyze this influence.Experiments were carried out with a 350 mm diameter rotor to validate the simulation and the

comparison shows the ability of the theoretical approach to predict the blade root bending moments. It can be concluded that, in steep waves, linear theory underestimates the dynamicbehaviour of bending moments. However, in long waves, linear theory works well. Bending moments at roots of rotor blades fluctuate with significant amplitudes (as much as 50 per centof mean value for out-of-plane bending moment and 100 per cent of mean value for in-planebending moment), which will be important for design of tidal stream rotors.

Keywords: tidal stream, current turbine, wave-current interaction, linear bladeelement-momentum theory

1 INTRODUCTION important consideration in determining limits for

device location and rotor operational envelopes. A substantial body of knowledge on wave loading Horizontal-axis wind turbines have achieved a

already exists, but not in this context. There is andominant position in the market and for tidal streamsurgent need for further research to determine thethe arguments in their favour are even more com-response and practical limitations posed by thepelling [1, 2]. Vertical-axis rotors are subject to cyclicassociated phenomena.loads even in uniform flow [3, 4], and in tidal streams

The main objectives of this study were, firstly, tothese will make the design more difficult in all butassess the limits imposed by waves on the perform-small machines. Reversing gravity loads, which areance of tidal stream rotors, to investigate ways invery important for horizontal-axis wind turbines,

which these limits might be relaxed by refinementsshould be much less important for tidal streamof rotor design and the control of operating con-turbines because buoyancy can be used to balanceditions, and to confirm that the concept is structurally the weight. For horizontal-axis machines, relatively and mechanically possible. In this paper, the authorslow levels of turbulence minimize stochastic structuralspecifically look into the dynamic property of bend-loads, but deterministic cyclic loading (from velocity ing moments acting about the roots of tidal streamshear and yaw error eff ects) may be comparatively rotors. Experiments are carried out and data arelarge. The eff ect of waves is likely to be important.used to validate simulation results based on aIt is desirable to locate rotors near the free surfacemathematical model, i.e. linear wave and bladeto make maximum use of the available cross-element-momentum theory. It is noticed that, in long sectional area and to intercept the highest stream

waves, the theory predicts very well the dynamicvelocities. The eff ect of waves will therefore be anresponse of these bending moments. However, in

* Corresponding author: Naval Architecture and Marine steep waves, probably due to the presence of highEngineering, University of Strathclyde, 100 Montrose Street, non-linearities, linear wave theory underestimates

these responses.Glasgow G4 0LZ, UK. email: [email protected]

JEME45 © IMechE 2006 Proc. IMechE Vol. 220 Part M: J. Engineering for the Maritime Environment








196 N Barltrop, K S Varyani, A Grant, D Clelland, and Xuan Pham

2 THEORY will increase incident flow velocity if they are in the

same direction, or decrease this velocity if they are

not in the same direction.The torque, thrust and bending moments induced

by stream flow are calculated based on blade Vertical wave particle velocity:

element-momentum theory [5]. Each blade of the

wind turbine is divided into a number of sections v=pH

T w

sinh[k w

((zr−ds)+d )]

cosh(k wd )

sinh(ww

) (3)

(Fig. 1). Even though chord and pitch or twist anglevary along the blade, within each section, these will change the flow incidence angle and hencevalues are presumed constant to simplify the calcu- modify the lift and drag forces. The wave eff ects onlations. Lift and drag coefficients as functions of the rotor are periodical if the waves are regularincident angles are then calculated and adjusted waves. The wave eff ects on the rotor are also reducedappropriately to account for 3D eff ects. Velocities when the rotor is positioned at greater water depthof water flow passing the blade section are next because the wave kinematics decrease with depth.calculated taking into consideration the eff ects from The wave eff ects on the rotor can be ignored if wavecurrent and waves. As well as adding to the wave flow is small compared with tidal currents. The wavesparticle velocities, current changes the encountered are important if the waves flow speeds are a signifi-

wave frequency as follows. cant proportion of, or are greater than, those of the

tidal current. This generally happens in extreme

weather. To illustrate this comment, Table 1 shows f e= 1

T e

= 1T w

+U cLw

cos(hw

) (1)the dimension and a typical operating condition of

a full-scale marine current turbine, and Table 2 where U c

is the current velocity, T and L are waveshows the horizontal and vertical particle velocities

period and length, respectively. Subscript ‘e’ and ‘w’at the 0.7R position of the blade as it passes three

represent encountered and wave, respectively. h islocations, i.e. upright, down right, and horizontal,

the incident angle of current.respectively. As seen, the figures in this illustrative

The possible problems waves can cause to tidalexample reflects well the remark noted.stream water turbine are mainly embodied in change

of flow velocity field and pressure field around the

rotor. The former change will aff ect the fluid forcesTable 1 Dimensions and operating conditionson the rotor. The latter and former may trigger or

of rotor at full scale

depress the occurrence of cavitation.The eff ect of waves on the rotor depends on Diameter (m) 20.0Number of blades 3magnitude and direction of flow velocity that isRotation rate (rpm) 12.0

induced by waves. Horizontal wave particle velocity: Immersion of shaft (m) 20.0 Water depth (m) 40.0Current speed (kts) 5.0 (or 2.5 m/s)

u=pH

T w

cosh[k w

((zr−ds)+d )]

sinh(k wd )

cosh(ww

) (2) Maximum wave height (m) 9.0

Fig. 1 Co-ordinate system and velocity diagram in blade theory

JEME45 © IMechE 2006Proc. IMechE Vol. 220 Part M: J. Engineering for the Maritime Environment








197 Wave-current interactions in marine current turbines

Table 2 Horizontal and vertical particle velocities at 0.7R position

Wave period set at 12 seconds

Upright position Down right Horizontal

u (m/s) v (m/s) u (m/s) v (m/s) u (m/s) v (m/s)

H wave=8 m 1.99 1.02 1.64 0.46 1.78 0.73% current velocity 79.65% 40.99% 65.44% 18.38% 71.18% 29.13%H wave

=2 m 0.50 0.26 0.41 0.11 0.44 0.18% current velocity 19.91% 10.25% 16.36% 4.59% 17.79% 7.28%

Apart from velocity components due to waves and 3 ROTOR DESIGN AND MANUFACTURE

current, there are also velocity components due to

the rotation of the blade. All together, velocity of For the project, three rotor designs were produced,

water flow around each blade segment is calculated. with progressive refinement based on results of test-Directional components of this velocity consist of ing. The largest practical rotor diameter was used to

out-of-rotor-plane velocity, which is in the positive minimize scale eff ects.

x -axis direction, and in-rotor-plane velocity, which is The first model rotor [6] was essentially a windin the direction tangent to the positive y-z rotation turbine configuration, with a slight increase in blade(Fig. 1). From these findings, the out-of-plane (short chord and thickness for structural strength. The aero-for out-of-rotor-plane) lift–drag force and in-plane foil profile (NREL S814) was chosen for its good per-tangential lift–drag force on the blade section are formance at low Reynolds numbers, and its tolerancecalculated. Note that tip loss from the blade is also of surface imperfections. The rotor has three blades,introduced into momentum equations. The tip loss and an overall diameter of 350 mm. At the root, thecoefficient F is a function of distance r from root and blades taper down to a circular section to increaseangle of attack w and is expressed as the local strain and to facilitate the fitting of strain

gauges.

The second rotor [7] also uses three blades. ItsF(w, r)=2

pacosGexpC−

1

2N

blades

(R−r)

(R|sin w|)DH (4)

diameter is increased to 400 mm to increase torque

and thrust, and blade chord is increased in anThe torque acting on the rotor is then the sum of attempt to combat the cavitation observed on thetorque acting on individual blade, which in turn isfirst rotor. The same aerofoil profile is used, but thethe sum of products of in-plane lift–drag forces andconfiguration at the blade root is changed: the bladesthe arm lengths from centres of blade sections to themerge into the hub without taper, and strain gaugesaxis of the rotor. Thrust on the rotor, similarly, is theare not fitted. However, blade angles can be adjustedsum of out-of-plane lift–drag forces on blade sectionsover a range of about 15 degrees.of all blades on the rotor.

In the third rotor [8], an attempt is made to pro-Bending moments acting around the root of eachduce a lightly loaded, high-solidity turbine with goodblade are calculated in the similar fashion. The out-resistance to cavitation and the eff ects of marineof-plane moment is the sum of products of out-of-growth. The blade number, diameter, and hub designplane lift–drag forces and the arm lengths fromare the same as for the second rotor. However, acentres of blade sections to the root of the blade. The

higher-lift aerofoil is used (NREL WA3-02) and bladein-plane moment is the sum of products of in-planechord is further increased.lift–drag forces and the arm lengths from centres of

In this paper, analysis focuses on the first modelblade sections to the root of the blade.rotor. The S814 is one of the series developed by The calculations are carried out for every time step.the National Renewable Energy Laboratory (NREL),The simulation modelling uses assumption of quasi-USA, for wind turbines. One particularly importantsteady flow and was coded in MathCAD by thecharacteristic of the S814 is the minimal sensitivity authors. The time step was selected based on theof its maximum lift coefficient to roughness eff ects,rotational speed of the rotor and the frequency of a critical property for stall-regulated wind turbines.the incident waves such that the amount of dataThe aerofoil has a very low drag coefficient and isobtained is sufficient to reflect the eff ects of both the

also not sensitive to change of angle of attack atrotational speed of the rotor and the encountered

frequency with the waves. around stalling angle. The profile shape is illustrated










in Fig. 2a; specific technical features of the NREL tests at Reynolds number of 3×106. In the simu-

lation, the three-dimensional eff ects on the liftS814 are detailed in [9]. The length of the blade

used for rotor 1 was 150 mm with maximum chord coefficient are considered and three-dimensional lift

coefficient is calculated based on two-dimensionalof 44 mm. Nominal chord length at the tip was

20 mm, but the tip was rounded to reduce shed lift coefficient using the following equation.

vortices. Chord and pitch distributions are shown

in Fig. 2b; an increase of about 5 degrees from CL3D=CL2D+DCL×3

Ac(r)

r B2

(5)the nominal pitch angle was found to give best

performance. where DCL

is the diff erence between CL

obtainedFigure 2c shows the two-dimensional character- from linear potential flow theory and the actual two-

istics of lift and drag coefficients based on tunnel dimensional lift coefficient CL2D

c(r) is the chord

length as the function of radial distance r from root.

The drag coefficient, on the other hand, is assumed

to be equal to the two-dimensional drag coefficient.

Curve-fit functions were developed based on these

lift and drag coefficients as function of angle of

attack. Intermediate coefficients can therefore be

estimated using these generic fuctions.

4 EXPERIMENT

Rotor performance (shaft torque, axial thrust, and

blade bending moments) was investigated in the

Universities of Glasgow and Strathclyde’s 77×4.6×

2.4 m-deep wave/towing tank. A two-dimensional

aerofoil section ‘boat’ made of glass fibre (Fig. 3a)

was used to house the motor, gearing, and torque

and thrust transducers. The rotor was supported in

front of the boat which itself was cantilevered down

from the towing tank carriage as in Fig. 3b.Strain gauges were used for the measurement of

bending moments about the root of the blade in the

case of rotor 1. The strain gauges were made water-

tight using M-Line J-Coat. The shaft to which the

rotor was attached was hollow. The cables of the strain

gauges were accommodated through the inside of

the shaft and the signals were transferred through

slip rings. Provision was made for amplifying the

signals before passing them through the slip rings,

but slip ring tests and the final results demonstrated

remarkably good performance without the need

for amplifiers on the rotating shaft. The shaft wassupported by linear bearings to allow rotation and

axial movement. To allow precise speed control, a

motor/generator with gearbox and tachometer was

used with closed loop control. The motor/generator

could provide power (at low current speeds) or

absorb power (at the higher current speeds). The

shaft extended in front of the boat bow sufficiently

for minimal interference between the boat and theFig. 2 (a) Sectional profile of NREL S814 blade.rotor. A grease box prevented the entry of water(b) Chord and pitch distribution along blade.around the shaft. The boat was clamped and bolted(c) Lift and drag coefficients based on tunnel

tests at Rn=3×106 by steel beams to a rail-mounted moving carriage










Fig. 3 (a) Arrangement of rotor and devices. (b) Profile and cross-section views of theexperiments

over the tank. The carriage moved the boat along the (0.0−1.6 m/s), wave heights and frequencies, and

depths of immersion whilst the rotational speed istank at steady speed to simulate tidal currents. A

flap type wave generator produced waves of a set at about 200 rpm. The aims were to investigate

the magnitude and variation of thrust, torque, andknown wavelength and period. These are of course

encountered at a higher frequency than the generated bending moment at the root of the blade in the case

of rotor 1 and thrust, torque, and rpm in the case of wave frequency when the rotor is moving towards

the waves. (Note that, within the limitations of poten- rotor 2. The results were then compared with calcu-

lations. This paper presents the dynamic property of tial flow theory, the model was a precise Froude-

scaled representation of the real case of a fixed rotor bending moments acting about the roots of blades

of rotor 1 in waves of 150 mm height (model scale),encountering waves of the generated length on the

current.) two frequencies, i.e. 0.5 Hz and 1.0 Hz, and towing speed 0.0−1.6 m/s. For a 10-m diameter, full scaleExperiments were carried out to test the perform-

ance of the tidal stream rotors for diff erent con- turbine, these frequencies would correspond to 10.69

and 5.35 second periods, and to towing speedditions. The most important parameters were the

dynamic properties of the rotor under diff erent 0–8.55 m/s. The upper currents are clearly much

higher than would be found in practice, but are wave heights, wave frequencies, and current speeds.

Only the first rotor was strain gauged because the useful for testing the theory. Reflection from the tank

side walls are assumed to be insignificant as therequirements for high stresses in the root under

the towing test conditions were not compatible waves travel straight down the tank and there is a

clearance of 2.1 m on either side of the turbine from with the need to load the rotor more highly to obtain

a high Reynolds number in the cavitation tests. the tank wall. For tests at low velocities, the starting

position of the testing is set at approximately oneThe experiments covered a range of towing speeds










third of the tank length from the beach so that (at model scale), respectively. The maximum wave

slope is approximately 8 degrees. The corresponding reflected waves from the beach would not reach the

turbine by the end of the test run. tip–speed ratios are 12.22 and 3.77, respectively.

Sim_Mx and Sim_My represent the simulation resultsIt should also be noted that, in these tests, the

Reynolds number varies in the range of 4.32×103 to of out-of-plane and in-plane bending moments,

respectively, whilst Exp_Mx and Exp_My refer to6.0×104, which is lower than the range of 0.75×106

to 1.5×106 for S814 data. A low Reynolds number their corresponding experimental results. As canbe seen, in long waves, blade element with linearcan degrade the dynamical properties of the airfoil

and can be a source of discrepancy between the test wave theory can predict the dynamic response of

both out-of-plane and in-plane bending moments.data and the simulation data.

5.2 Steep waves of 150 mm height and 1.0 Hz

frequency 5 VALIDATION

Figures 5a and 5b, and 5c and 5d, show the dynamic5.1 Long waves of 150 mm height and 0.5 Hz

properties of bending moments about roots of rotorfrequency

blades in steep waves of 1.0 Hz frequency and 150 mm

height at current speeds of 0.3 m/s and 1.0 m/s,Figures 4a and 4b, and 4c and 4d, show dynamic

properties of bending moments about roots of rotor respectively. The corresponding tip–speed ratios aretherefore 12.22 and 3.77, respectively. The maximumblades in waves of 0.5 Hz frequency and 150 mm

height at current speeds of 0.3 m/s and 1.0 m/s wave slope is approximately 29.5 degrees. It can be

Fig. 4 (a) Out-of-plane bending moment in waves of 150 mm height and 0.5 Hz frequency andcurrent speed of 0.3 m/s at model scale. (b) In-plane bending moment in waves of 150 mmheight and 0.5 Hz frequency and current speed of 0.3 m/s at model scale. (c) Out-of-planebending moment in waves of 150 mm height and 0.5 Hz frequency and current speed of 1.0 m/s at model scale. (d) In-plane bending moment in waves of 150 mm height and0.5 Hz frequency and current speed of 1.0 m/s at model scale










Fig. 5 (a) Out-of-plane bending moment in waves of 150 mm height and 1.0 Hz frequency andcurrent speed of 0.3 m/s at model scale (b) In-plane bending moment in waves of 150 mmheight and 1.0 Hz frequency and current speed of 0.3 m/s at model scale (c) Out-of-planebending moment in waves of 150 mm height and 1.0 Hz frequency and current speed of

1.0 m/s at model scale (d) In-plane bending moment in waves of 150 mm height and1.0 Hz frequency and current speed of 1.0 m/s at model scale

seen that blade element with linear wave theory can wave has been synchronized with the measured wave

(Fig. 5b). (It is interesting that in these relatively steeppredict relatively well the fluctuation of in-plane

bending moment (My) both in low and high current waves the diff erence between the linear wavelength

and the non-linear wavelength results in a loss of speed ranges. However, for out-of-plane bending

moment, the fluctuation predicted is less than that synchronization between rotor position and wave

phase in just a few wave cycles. This is significantmeasured. This highlights the significance of high

non-linearities associated with steep waves. Figures when comparing predictions with measurements,

but is not important for design.)4a and 4c show that the amplitude of bending

moment variation recorded during the test is of the

order of two times that predicted. 6 CASE STUDY USING LINEAR BLADE

SIMULATION MODEL5.3 General discussion

A general observation on the dynamic characteristics6.1 Eff ects of flow incidence angle

of bending moments at the root of a rotor blade

is that it sees that the main oscillation at the Of theoretical interest is the eff ect of the vertical

component of wave particle velocity, which mainly encountered wave frequency. The rotor frequency

shows in the smaller superimposed oscillation in the aff ects the flow incidence angle onto the aerofoil

(Fig. 6). The numerical calculations show a smallin-plane bending moment and is mainly the self-

weight eff ect. The numerical model is clearly giving eff ect at the main peaks of the wave loads (because

these correspond to peaks in the horizontal velocity reasonable results, especially in the middle of the

short segment of time history where the numerical where the vertical wave velocity is zero). Also










Fig. 6 Out-of-plane bending moment with and withoutvertical wave velocity

numerically it has been possible to consider cases

where wave and current are in diff erent directions.

Figure 7 shows firstly a case with the current and

wave normal to the rotor plane and secondly a case

with the wave direction at 45 degrees to the rotor

plane. The highest total and fluctuating wave loadsoccur with the wave propagating normal to the

rotor plane.

6.2 Eff ects of waves on bending moments

Figure 8a and 8b show the influence of waves on out-

of-plane and in-plane bending moments, respectively.

It appears that within the practical wave frequency

range, steeper waves impose less bending moments Fig. 8 (a) Out-of-plane bending moment in diff erentin both directions about the roots of the rotor blade. conditions (b) In-plane bending moment in

diff erent conditionsIn steady water condition, i.e. without waves, the

out-of-plane bending moment is steady but thein-plane bending moment varies harmonically with to that in steady water condition. The fluctuation of the frequency of rotor due to the gravity bending My is significant in long waves, as seen in Fig. 8b.moment component. The amplitude of the out-of-

plane bending moment fluctuation is more than 6.3 Full-scale case study halved as wave frequency increases from 0.5 Hz

Figure 9 presents simulation results of bending to 1.0 Hz. In steep waves, Fig. 8b shows that themoments acting on a hypothetical full-scale rotor of fluctuation of bending moment (My) is mainly due20 m diameter rotating at 7 rpm in waves of 3.0 mto the gravity component as the in-plane bending height and 10.0 s period on top of current speed of moment in the steep waves is more or less equivalent

Fig. 7 Out-of-plane bending moment corresponding Fig. 9 Bending moments about root of blades of ato wave normal to rotor plane and wave at 45

degrees to rotor plane hypothetical full-scale rotor










2.0 m/s. The tip–speed ratio (ratio between tangential REFERENCES

speed of tip of the blade by the current speed) is then1 Pham, X., Liu, Y., Varyani, K., and Barltrop, N.equivalent to 3.6, which corresponds to the current

Report on tidal stream rotor tests. Universities of speed of 1.0 m/s at model scale. The water depth isGlasgow and Strathclyde, 2004.set at 40.0 m and the clearance between still water

2 Myers, L. and Bahaj, A. S. Basic operational para-surface and highest point of blade tip is 10.0 m. The

meters of a horizontal axis marine current turbine.hub radius of the rotor is 1.4 m and root radius is In Proceedings of Eighth World Renewable Energy 0.3 m. As a result, the mean thrust acting on the rotor Congress, Denver, USA, 2004.is 0.124 MN and mean torque is 0.142 MNm. The 3 Sutherland, H. J. Fatigue case study and loading

spectra for wind turbines, IEA Fatigue Expertscorresponding mean power generated is 0.104 MW.Meeting, pp. 77–87, April 1994. As can be seen in Fig. 9, the variation of bending

4 Smith, K., Randall, G., and Malcolm, D. Evaluationmoments acting about the root of the rotor blades isof wind shear patterns at Midwest Wind Energy

very significant. The range of fluctuation of out-of-Facilities, American Wind Energy Association (AWEA)

plane bending moment is approximately 0.78 MNm WINDPOWER 2002, Portland, Oregon, June 2002.about the mean value of 0.38 MNm. The in-plane 5 Eggleston, D. M. and Stoddard, F. S. Wind turbine bending moment is smaller, but its dynamic property engineering design, 1978 (Van Nostrand Reinhold,

New York).is equally significant, with the range of fluctuation6 Wang, D., Atlar, M., and Paterson, I. Performanceapproximately 0.24 MNm about the mean of about

tests of the first tidal stream rotor. Report No. MT-0.1 MNm. 2003-016 , School of Marine Science and Technology,University of Newcastle upon Tyne, October 2003.

7 Wang, D., Atlar, M., and Paterson, I. Performancetests of the second tidal stream rotor. Report No. MT-

7 CONCLUSION 2004-027 , School of Marine Science and Technology,University of Newcastle upon Tyne, December 2004.

The paper has briefly introduced blade element- 8 Wang, D., Atlar, M., and Paterson, I. Performancemomentum theory, which includes wave eff ects in tests of the third tidal stream rotor. Report No. MT-

2005-002 , School of Marine Science and Technology,analyzing dynamic properties of bending momentsUniversity of Newcastle upon Tyne, January 2005.acting at roots of rotor blades of a tidal stream rotor.

9 Tangler, J. L. and Somers, D. N. NREL airfoil familiesExperiments were also described in the validation of for HAWTs. http://wind.nrel.gov/, 1995.simulation results. Based on what has been obtained,

the following conclusions are drawn.

$ In-plane and out-of-plane bending moments both APPENDIX

fluctuate significantly and this is worse in steep

waves. In long wave condition, the fluctuation of Notation

these bending moments can be predicted well by

linear wave theory with blade element-momentum d water depth

theory. However, in steep waves, due possibly to ds rotor axis depthhigh non-linearities involved, the out-of-plane H wave heightbending moment fluctuates significantly more k

w wave number

than that predicted (by about two times in this T w

wave periodcase). zr instantaneous vertical position of centroid

$ Waves approaching along the normal to the rotor of blade section with respect to rotor axisplane lead to the largest bending moments on

the blades. w w

angle of attack







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