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Moment loads acting on a blade of an ocean current turbine in shear flow
Ocean Engineering 172 (2019) 446–455
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Moment loads acting on a blade of an ocean current turbine in shear flow Kazuomi Yahagi, Ken Takagi
T
∗
Dept. of Ocean Technology, Policy, and Environment, The University of Tokyo, Kashiwa, Japan
ARTICLE INFO
ABSTRACT
Keywords: Current turbine Moment load Blade moment in the shear flow CFD of turbine blade
The Kuroshio flowing near Japan is one of the largest ocean currents and it is considered that this energy possibly be an important energy source for Japan. A full-scale generator with twin 40m turbine rotors is planned for at the rated flow speed of 1.5 m/s. Estimation of the blade loads are crucial for such big turbines. We focus on the effect of shear flow on an ocean current turbine and highlight the periodic fluctuation of moment loads at the blade root induced by the shear flow. Shear flow experiments and numerical computation with a commercial code were conducted for estimating the moment loads on a blade. The numerical computation was verified through the comparisons with the measured Cp and Ct in uniform flow. The numerical results of moment load in the shear flow are validated through the comparison with the experimental results. It is concluded that the moment loads are well estimated by the present CFD method. Using the same CFD method, some applications are shown.
1. Introduction The Kuroshio flowing near Japan is one of the largest ocean currents and it is considered that this energy possibly be an important energy source for Japan. The New Energy and Industrial Technology Development Organization (NEDO) and IHI corporation have developed a 100 kW class ocean current turbine system named “Kairyu” and successfully conducted a sea trial at the Tokara Islands in 2017 (IHI, 2017). Although the turbine diameter for 100 kW system is about 11m, it is expected that the diameter will be 40m for the 1 MW full scale generator at the rated flow speed of 1.5 m/s (Takagi et al., 2012). Estimation of the blade loads are crucial for the design of such big turbines. Especially the periodic fluctuation of the blade load is important for fatigue design. Blade load fluctuations are supposed to be induced by the turbulence, wave orbital motion and vertical profile of the inflow. In the case of tidal currents, a simple two-dimensional boundary layer shape based on the assumption of shallow water flow is often used to represent the vertical profile of flows (DNV, 2015). On the contrary, variation of profiles in the inflow for the ocean current turbine is supposed to be complex, since the water depth at the sea area where the current turbines will be deployed is deep. Thus, a simple two-dimensional boundary layer shape based on the assumption of shallow water flow may not be applicable. In addition, the influence of internal waves could be expected, though this is still under investigation. For example, Kodaira et al. (2014) investigated nonlinear internal waves in the Kuroshio. Kiyomatsu et al. (Kiyomatsu
∗
et al., 2014) measured the vertical profile of the Kuroshio near Miyake Island, and they reported that there is a strong shear flow near the free surface. Thus, we focus on the shear flow effect in this paper, and the periodic fluctuation of moment loads at the blade root induced by the shear flow is highlighted because the bending moment is one of the important parameters for the structural design of a blade. In the field of wind turbines, the National Renewable Energy Laboratory (NREL) summarized test results of the blade load due to the non-uniform wind (Hand et al., 2001), and NREL also provide a numerical model for estimation of blade loads (Jonkman and Buhl, 2005). Literatures on various numerical methods including the CFD are also available (for example (Hansen et al., 2006)) References in the literature dealing with non-uniform effects on tidal turbines also can be found. For example, Milne et al. (2013) measured blade loads in planar oscillatory flow and in spatially uniform unsteady flow (Milne et al., 2015). Faudota et al. (Faudota and Dahlhauga, 2012) conducted a wave loads measurements. Blackmore et al. (2016) and Mycek et al. (2014a) (Mycek et al., 2014b) studied effects of turbulence. Gaurier et al. (2013) measured a turbine blade strain under current and wave loading. On the other hand, numerical approaches are also found. Ahmed et al. (2017) made a comparison of CFD with field data on fluctuating loads due to velocity shear and turbulence. Parkinson et al. (Parkinson and Collier, 2016) conducted a field measurement and compared with results by a commercial software. O'Rourke et al. (O'Rourke et al., 2015) proposed a mathematical model for the Blade Element Method (BEM) to predict the hydrodynamic performance of a tidal turbine in non-uniform inflow conditions.
Corresponding author. E-mail address: [email protected] (K. Takagi).
https://doi.org/10.1016/j.oceaneng.2018.12.026 Received 24 March 2018; Received in revised form 5 December 2018; Accepted 5 December 2018 0029-8018/ © 2018 Elsevier Ltd. All rights reserved.
Ocean Engineering 172 (2019) 446–455
100.7
40
25.2
K. Yahagi, K. Takagi
r
390
60 unit : mm
Center of turbine rotor Turbine axis
y z x
Fig. 1. Plane view of the blade.
(a)
Table 1 Summary of the numerical method. Items
Methods
Solution Turbulence model Velocity-pressure coupling Gradient calculation Discretization
1st order implicit SST k-ω model SIMPLE method Least Squares Cell Based Momentum 2nd order upwind k 1st order upwind ω 1st order upwind
y x
Inlet
(b) Fig. 3. Detail of the mesh. (a) Meshing on the blade surface. (b) Meshing near the blade tip.
Outlet 65 152
Rotational region
unit: mm
390
900
z
4.0
2.0
8.0(m)
120
120
y
Stational region 0.0
W.L
550
x
6.0
390
Fig. 2. Overall computational domain. 570
In the present work, experiments in a circulating water channel, where a shear flow was created, and in an ocean engineering basin were conducted, and numerical estimations of the blade loads were also carried out by a commercial CFD code and compared with the experimental results.
Fig. 4. Principal dimensions of the turbine rotor.
where the definition of r is found in Fig. 1. It is noted that two blades are equipped as a turbine rotor because the Kairyu (IHI, 2017) uses two bladed turbines for better performance in the installation and the maintenance. It is also noted that, although the experimental model has a boss at the center of rotor, the boss is ignored for the numerical calculations to reduce the computational effort. It is noted that we focused on the blade moment load in this study as mentioned above. The moment about the turbine axis and an axis perpendicular to the r-axis and turbine axis are defined as Mx and My respectively. Non-dimensional forms of Mx and My are defined as
2. Numerical computation of the blade loads 2.1. Blades and hub Since the aim of this study is to reveal the effect of shear flow, a popular wing section is used, and the twisting angle is presented by a simple equation. The blade used in the present work is designed by referring to NMRI's blade (Chujo et al., 2017). NACA0012 is used for the wing section and the plan view of the blade is a trapezoid as shown in Fig. 1, where the size of the blade is the same as that of experimental model which will be mentioned in section 3. The twisting angle of the blade is represented as
= tan
1
450 11r
tan
1
1 11
CMx =
Mx 1 2
U 2 AR
, CMy =
My 1 2
U 2AR
(2)
where U is the inflow velocity at the turbine center, A is the projection area of the turbine rotor, R is the radius of the turbine rotor and is the water density.
(1) 447
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1.5m
0.8m
Screen×3
0.6m
Depth = 1.2m
0.6m
Inlet
Velocity meter
0.55m
0.55m
Velocity meter
0.55m
Length of test section=4.9m
Turbine 0.57m
Side view
1.5m Fig. 5. Arrangement of the experiment in a circulating water channel.
0.45
0.035
Velocity meter1 Velocity meter2
0.30
0.025 0.020
CMx
Z [m]
0.15 0.00
0.015
-0.15
0.010
-0.30
0.005 0.000
-0.45 0.30
0.35
0.40 0.45 0.50 Velocity [m/s]
0.55
3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 TSR
0.60
(a) Mx
Fig. 6. Time averaged vertical profile of the shear flow in a circulating water channel. The shear is created by three screens.
0.70 0.50
0.35
0.40
CMy
0.40
0.30 0.20
0.25
CMy
Circulating water channel Ocean Engineering Basin
0.60
0.30
0.10
0.20
0.00 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 TSR
0.15 0.10
(b) My
0.05
Fig. 8. Comparisons of time averaged (a) Mx and (b) My measured in the circulating water channel and in the ocean engineering basin.
0.00 0.0
1.0
2.0
3.0
4.0
5.0
Time[s]
t
Fig. 7. Time history of My in the uniform flow. Measurement has been done in the ocean engineering basin.
xi
( ui ) = 0
xi
uj p u + [µ ( i + xi xi xi xi
( u i uj ) =
xj
(
ui uj )
2 3
ij
ui )] xi (4)
where, denotes the pressure, µ the viscosity, ij the Kronecker delta, ui the turbulent component and the over bar denotes the time average. The last term is obtained by using a turbulence model. In this paper, the SST k-ω turbulence model (Menter, 1993) is used. Other important information on the solver is shown in Table 1. The Reynolds number is 2.2×105 at the tip of the blade when the tip speed ratio (TSR) is 11.0 and the inflow velocity is 0.5 [ms−1]. Based on this value, the numerical mesh is constructed. Fig. 2 shows the size of overall computational domain.Where D denotes the diameter of rotor. It is noted that the sliding mesh is mainly used in the numerical computation. On the other hand, the Multiple Reference Frame (MRF)
ANSYS Fluent ver.18.0 is used for the numerical computation. Since the flow is incompressible, the conservation of mass is satisfied as
+
( ui ) +
+
2.2. Solver and mesh
t
Circulating water channel Ocean Engineering Basin
0.030
(3)
where, the Cartesian-coordinate system x i is used and ui denotes the fluid velocity. The Reynolds-averaged Navier-Stokes equations (RANS equations) is solved by the Fluent. The RANS equation is represented as 448
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0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
0.40 0.35
Cp
0.30 0.25 CMy
CFD -2 deg. (MRF) CFD 0 deg. (MRF) CFD -2 deg. (Sliding Mesh) Experiment -2 deg. Experiment 0 deg.
CFD(TSR7.2)
0.20
Experiment(TSR7.2)
0.15 0.10
3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 TSR
0.05
(a) Cp
0.00
1.20
0.0
1.0
2.0
1.00 0.80
4.0
5.0
(a) Time history
0.60 0.003
CFD -2 deg. (MRF) CFD 0 deg. (MRF) CFD -2deg. (Sliding Mesh) Experiment -2 deg. Experiment 0 deg.
0.40 0.20 0.00
CMy Periodogram [(N*m)2]/Hz
Ct
3.0 TIme[s]
3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 TSR (b) Ct Fig. 9. Measured and computed results of (a) Cp and (b) Ct in the uniform flow. Blade pitch angles are −2 and 0°.
model is used only for the uniform flow case and compared with the result of the sliding mesh computation. Fig. 3 shows the detail of meshing near the blade. Height of the wall cell is set to be smaller than y+ = 1. The time step is determined so that each time step corresponds to 1 degree of the turbine rotation. Total number of the mesh is 4,801,511 for the following calculations. In order to verify the convergence of results, a finer mesh calculation has also performed with 12,133,638 meshes. The difference of the power coefficient is 0.88% and 0.1% for the thrust coefficient. Thus, we assumed that the numerical results are converged with 4,801,511 meshes. It is noted that a linear variation in z-direction is used for a mathematical model of the shear flow at the inlet boundary in the shear flow computation. The coefficient of the linear equation is determined based on the measurement of shear flow in the circulating tank as
CFD Experiment
0.002 0.002 0.001 0.001 0.000 0.0
0.5
1.0
1.5 2.0 Frequency [Hz]
2.5
3.0
(b) Periodogram Fig. 10. An example of measured My in the circulating water channel for the blade pitch angle of −2°. (a) Time history and (b) Periodogram of the time history.
moments are measured by a moment load sensor which is located at the root of one blade. The experimental turbine rotor has a boss of 0.12m diameter and a sensor and a dummy sensor are fixed at both sides of the boss, while the numerical model ignores the boss and the censors. The thrust and moment of the turbine are also measured to check the power coefficient Cp and the thrust coefficient Ct. Xia and Takagi (Xia and Takagi, 2016) created a shear flow in the circulating water channel using screens. The screen is a lattice of 15 horizontal bars with diameter of 0.0272m and the bars are extended to the channel wall. The same screen is used for creating a shear flow in the circulating water channel. Fig. 5 shows the experimental arrangement of screens, velocity meters, and the turbine. The test section of the circulating water channel has dimensions of 4.9m (length) x 2.0m (width) x 1.2m (water depth). Three screens are used to create a shear flow with 10% gradient. An electro-magnetic velocity meter is installed
u= 0.416 + 0.045z [ms−1](5)
3. Experiment 3.1. Experimental set up Principal dimensions of the turbine is shown in Fig. 4. The shape and twisting angle are chosen so that the blade shape is represented by simple equations for the convenience of generating the numerical mesh as mentioned above. The diameter is chosen to guarantee the accuracy of the moment measurement. As a result, a free surface effect is observed that will be explained later. The rotation of the turbine rotor is controlled to keep the constant rate from TSR = 5 to 14. The blade
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0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
CMx average
Cp
K. Yahagi, K. Takagi
CFD Uniform Flow CFD Shear Flow Exp Uniform Flow Exp Shear Flow
0.045 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000
CFD Experiment
4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 TSR
3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 TSR
(a) Mx
(a) Cp
1.20 CMy average
1.00 0.80 Ct
0.60 CFD Uniform Flow
0.40
CFD Shear Flow Exp Uniform Flow
0.20
Exp Shear Flow
0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
CFD Experiment
4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 TSR
0.00 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 TSR
(b) My
(b) Ct
Fig. 12. Comparison between experimental results and computational results on the time average of Mx and My in the shear flow for the blade pitch angle of −2°.
Fig. 11. Measured and computed results of (a) Cp and (b) Ct in the uniform flow and in the sea flow. Blade pitch angle is −2°.
other hand, the free surface effect is more serious for the magnitude of fluctuations in the shear flow, because the amplitude of periodic fluctuation appearing in Fig. 7 has almost the same order as the fluctuation in the shear flow. Thus, the fluctuations of Mx and My in the shear flow are corrected by subtracting the fluctuation appeared in uniform flow. Fig. 8 shows comparisons of time averaged (a) Mx and (b) My measured in the circulating water channel and in the ocean engineering basin. Apparent blockage effect is observed. The measured value in the circulating tank is corrected using two values as the blockage effect correction. In addition to this, the free surface correction is made for the fluctuated part of the measured value in the shear flow as mentioned previously. The same blockage correction is made for Cp and Ct.
at the center line of the channel to measure the reference inflow velocity and another one is installed 0.35m off-center. Both meters are located 0.6m in front of the turbine. A measurement of vertical profile of the flow was conducted before installing the turbine. Fig. 6 shows the measured vertical profile of shear flow where the velocity is averaged in time. Although the vertical profile is not perfectly straight, the screens induce a linear shear flow with the gradient of 10.8%. We also measured the turbulence intensity, and it is found that the turbulence intensity for the shear flow is 4–5% while it is less than 2% for the uniform flow. 3.2. Blockage effects
4. Results and discussion
Since the width of the test section is only 2.0m, a blockage effect is expected. Thus, the same experiment is conducted in the ocean engineering basin of the University of Tokyo. The basin has dimensions of 50m (length) x 10m (width) x 5m (water depth). We used the same experimental set up, while the turbine was towed by a towing carriage. It is mentioned that, even in the ocean engineering tank, the free surface effect cannot be removed, though it is supposed to be smaller than the wall effect. Fig. 7 shows an example of time history of My which has a periodic fluctuation. It has the same period as the rotation of the turbine, and it is supposed to be a free surface effect. The amplitude of fluctuation is 2.5% of the average value. Therefore, the average value is supposed to have an inaccuracy of the same order due to the miller effect of the free surface. However, this inaccuracy is ignored in our experimental results since the inaccuracy is small. On the
4.1. Comparison of the CFD with the experiment In order to verify the numerical procedure, comparisons of Cp and Ct are performed. Fig. 9 shows the numerical results and the measured results of Cp and Ct. The numerical computations for the pitch angle of −2° are performed both by the MRF model and the sliding mesh model. The MRF results are almost identical to the sliding mesh results, and the MRF computation and the sliding mesh computation both show a fairly good agreement with experimental results. Thus, we concluded that the numerical procedure is appropriate, and the numerical results have enough accuracy for the further discussion, though the experimental value could have small errors due to the free surface effect as
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0.0
CFD
0.008
-10.0
Experiment
CMx phase
CMx amplitude
0.010
0.006 0.004 0.002
-20.0 -30.0 -40.0 -50.0 -70.0
0.000
4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 TSR
4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 TSR (a) Mx
0.020
(a) Mx
0.0
CFD
-10.0
Experiment
CMy phase
CMy amplitude
0.015
CFD Experiment
-60.0
0.010 0.005
-20.0 -30.0 -40.0 -50.0 CFD Experiment
-60.0
0.000
-70.0
4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 TSR
4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 TSR
(b) My
(b) My
Fig. 13. Comparison between experimental results and computational results on the amplitude of the first harmonic component in the time history of Mx and My in the shear flow for the blade pitch angle of −2°.
Fig. 14. Comparison between experimental results and computational results on the phase of the first harmonic component in the time history of Mx and My in the shear flow for the blade pitch angle of −2°.
mentioned above. We also confirmed that the MRF model gives good approximation for Cp and Ct and saves the computational time, though the model is mathematically not correct for the transient problem. It is mentioned that from here on out we discuss on the case of blade pitch angle of −2°, since Ct is larger than the case of 0°. Fig. 10-(a) shows an example of time history of My in the shear flow. Since the turbulent intensity of the inflow is about 4%, high frequency fluctuations are observed in the experimental time history. However, an apparent periodic variation is recognized and its frequency is equal to the rate of turbine rotation. On the contrary, the CFD result shows an apparent periodicity, since the inflow of the CFD does not have a turbulent component. In order to clarify this frequency, we obtained a periodogram of the time history which is shown in Fig. 10-(b). A sharp peek is appearing both for the experiment and the CFD at the frequency of 1.06 Hz which is equal to the rotation rate 1.06 rps of the turbine. Another small peak is also observed in the experiment at the frequency of 2.12 Hz which is supposed to be the second harmonic, while the CFD result has no second peek. It is concluded from these results that the first harmonic component of the Fourier series expansion is useful for the discussion on the fluctuations of the load acting on the blade, though the inflow contains a turbulent component and its influence is observed in the time history. Fig. 11 shows measured and computed results of Cp and Ct in the uniform flow and in the shear flow, where the sliding mesh is used for the computation. Since the generated shear in the circulating water channel is not strong, the difference between the uniform-flow case and
the shear-flow case is not apparent, though the forces in the shear flow is theoretically expected to be larger than it in the uniform flow. On the contrary, the CFD shows that Ct in the shear flow is slightly larger than it in the uniform flow, though this tendency is not clear in the case of large TSR. This tendency is not simple for Cp, since the shear flow case is larger only in the middle TSR. Thus, it is concluded that the influence of the shear flow is small if the shear is not strong, and the tendency depends on TSR. A large shear case will be shown and discussed in the next subsection as an example of the CFD application. Fig. 12 shows a comparison between experimental results and computational results on the time average of Mx and My, where the sliding mesh is used for numerical computation to represent the shear flow. The experimental results are corrected for blockage effects. The agreement between the experiment and the CFD is the same as that of Cp and Ct. However, the agreement for smaller TSR is not good. Especially Mx at TSR = 5, the discrepancy between the CFD and the experiment is big. The reason is supposed to be a separation of the flow on the blade. The influence of the separation is discussed in the next subsection. Fig. 13 shows the amplitude of the first harmonic component of fluctuation in the time history of (a) Mx and (b) My in the shear flow, and the phase is shown in Fig. 14. Where, the amplitude and phase are obtained as the first harmonic component of the Fourier expansion. The amplitude and the phase are corrected for the blockage effect and the free surface effect as mentioned above. It is apparent from these figures that the CFD results are in fairly good agreement with experimental
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0.450 0.425 CMx
0.400 Cp
0.375 0.350 Shear flow (40%) Shear flow (10%) Uniform flow
0.325 0.300 0.0
0.5
1.0
1.5 2.0 Time [s]
2.5
Shear flow (40 ) Shear flow (10%) Uniform flow
0.0
3.0
0.5
1.0
1.5 2.0 Time [s]
2.5
3.0
(a) Mx
(a) Cp 1.00 0.98 0.95 0.93 0.90 0.88 0.85 0.83 0.80
0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
Ct
CMy
Shear flow (40%) Shear flow (10%) Uniform flow
0.0
0.5
1.0
1.5 Time [s]
2.0
2.5
Shear flow (40%) Shear flow (10%) Uniform flow
0.0
3.0
0.5
1.0
1.5 2.0 Time [s]
2.5
3.0
(b) My
(b) Ct
Fig. 16. Time histories of (a) Mx and (b) My for the blade pitch angle of −2° and TSR = 7 (Period of turbine rotation = 0.81 s) in the shear flow.
Fig. 15. Instantaneous value of (a) Cp and (b) Ct for the blade pitch angle of −2° and TSR = 7 (Period of turbine rotation = 0.81 s) in the shear flow.
results, though the agreement is worse than that of averaged value. It is mentioned that the amplitude and the phase of Mx and My are not stationary in the experiment as seen in the time history shown in Fig. 10, since it is difficult to generate perfectly linear shear flow and the inlet flow contains turbulent component. It is also noted that Mx is more sensitive than My, since Mx is much smaller than My. The phase lag appearing in the small TSR case is observed both in the experiment and CFD. This is one of important characteristics of unsteady wing theory, though the phase lag is small. From these results, it is concluded that the CFD can predict the unsteady effects on the turbine blades in the shear flow expect for the case of small TSR where the separation is expected. It is noted that, although the CFD is a powerful tool to estimate the moment loads as mentioned above, it is too time consuming when we calculate the unsteady problem. Thus, in the simulation of the overall turbine system which includes the floating body and the mooring system, BEM is convenient for the estimation of blade force and moment (Takagi, 2012). The present results are utilized for improving a mathematical model which gives an unsteadiness correction to conventional BEM (O'Rourke et al., 2015).
CFD. Fig. 15 shows instantaneous value of the Cp and Ct, where the period of turbine rotation is 0.81 s. Crests in the time history Cp correspond to instants when the blade is vertical. On the contrary, valleys correspond to the horizontal position. It is apparent that in the large gradient case Cp has large fluctuations, while in the small gradient case the fluctuations are small. This tendency is explained by the attack angle of the local flow to the blade section. When the blade is vertical, the shear effect is added to the average inflow of the turbine. The additional inflow to the upper blade is positive while that to the lower blade is negative. Since the magnitude of the blade force is proportional to the square of the inflow speed, the summation of upper and lower blade-forces is slightly larger in the vertical position compared to the blade-force when the blade takes a horizontal position. The difference of the blade-force between the vertical position and the horizontal position is supposed to be proportional to the square of magnitude of the additional-inflow velocity. Thus, the fluctuation of the blade-force would be very small, if the attack angle of the flow does not change. However, the attack angle of the flow changes linearly according to the variation of inflow speed. On the other hand, if the attack angle increases Cp would increase and Ct would decrease. As a result, instantaneous Cp has the large fluctuation, while the fluctuation of Ct is small. This is the case for the large gradient of shear. When the gradient of shear is small, the same thing happens. However, since the influence of attack angle variation due to the shear is small compared to the attack angle without shear and the square of the magnitude of additional inflow is small, the fluctuations on both Cp
4.2. Application of the CFD Although the shear gradient in the experiment is 10.8%, a more severe gradient is reported in the measurement of the ocean current (Kiyomatsu et al., 2014). Thus, a comparison between the small gradient case (10%) and a large gradient case (40%) was carried out by the
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Table 2 Summary of amplitude for different TSRs in the shear flow. TSR = 6
Shear flow (10%) Shear flow (40%)
Cp amplitude
Ct amplitude
CMx amplitude
CMy amplitude
0.0003 0.0077
0.0002 0.0017
0.0022 0.0126
0.0092 0.0499
Cp amplitude
Ct amplitude
CMx amplitude
CMy amplitude
0.0002 0.0106
0.0001 0.0020
0.0021 0.0142
0.0100 0.0656
TSR = 7
Shear flow (10%) Shear flow (40%)
Shear gradient 10%
Shear gradient 40%
Uniform flow
0.60
0.45
0.30
0.15
0.00
Upper
Lower
Upper
Lower
Upper
Lower
(a) TSR=5.0
Shear gradient 10%
Shear gradient 40%
Uniform flow
0.60
0.45
0.30
0.15
0.00
Upper
Lower
Upper
Lower
Upper
Lower
(b) TSR=7.0 Fig. 17. Streamlines on the blade for the cases of (a) TSR = 5.0 and (b) TSR = 7.0 in different shear gradients of the flow. Blades are in the vertical position.
and Ct are very small. This is a qualitative explanation of this phenomenon. But, the quantitative estimation is difficult without the CFD, because the unsteady effect is supposed to be considered. Fig. 16 shows time histories of Mx and My in the shear flow. Time
histories apparently have a periodic fluctuation whose period is as the same as the period of turbine rotation. It is mentioned that the amplitude is not proportional to the shear gradient, and the ratio between amplitude and shear gradient depends on the TSR. The reason is 453
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Skin friction coefficient
Shear gradient 10%
Upper
Shear gradient 40%
Lower
Upper
Lower
Uniform flow
Upper
Lower
(a) TSR=5.0
Skin friction coefficient
Shear gradient 10%
Upper
Shear gradient 40%
Lower
Upper
Lower
Uniform flow
Upper
Lower
(b) TSR=7.0 Fig. 18. Distribution of the shear stress on the blade for the cases of (a) TSR = 5.0 and (b) TSR = 7.0 in different shear gradients of the flow. Blades are in the vertical position.
supposed to be the same as the cases of Cp and Ct. However, since the influence of unsteadiness exists, again the quantitative estimation is difficult without the CFD. Table 2 shows a summary of amplitude for different TSRs. It seems that the larger gradient case experiences more sever fluctuations of the load than a linearly expected value from the 10% case. This is important information for the fatigue design of the blade. One of advantages of the CFD is that we can observe the detail of flow directly from visualized numerical results. Thus, two examples are shown here. The fist example is relevant to the separation of the flow on the blade which was mentioned in subsection 4.1. Figs. 12–14 show that the agreement between the CFD and the experiment is not good when TSR is small (TSR = 5.0), while the agreement is fairly good in the case of higher TSR. Since the local attack angle of the blade is large when TSR is small, it suggests that the separation on the blade happens. Fig. 17 shows stream lines on the blade in the cases of (a) TSR = 5.0
Fig. 19. Contour plot of magnitude of vorticity distribution on the center vertical plane for the 40% gradient, blade pitch angle = −2° and TSR = 7. 454
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and (b) TSR = 7.0. Since the Cp, which represents the efficiency of the turbine, is high in the case of TSR = 7, this case is considered to represent the normal operation-condition, while the case of TSR = 5.0 represents the torque-rich condition, i.e. low TSR. In the uniform flow, Fig. 17 shows that there are streamlines toward spanwise direction near the tip of the blade when TSR = 5.0. These stream lines suggest the flow separation for the case of low TSR. On the contrary, when TSR is high, streamlines toward the spanwise direction are not observed. This is confirmed in Fig. 18 which shows distributions of the skin friction coefficient. The skin friction coefficient is defined as
moment load are estimated with sufficient accuracy, though the agreement between the CFD and the experiment is worse than that of time averaged value. When TSR is small, the agreement between the CFD and the experiment on Mx and My is not good, the reason considered to be a separation happening on the blade. Flow visualizations of the CFD result confirm detail of the separation. Using the same CFD method, moment loads on a blade in the shear flow of 40% gradient were computed. It is found that the larger gradient case produces more severe fluctuations of the load than a linearly expected value, and the wake behind the turbine is not symmetric. These phenomena might be useful for the blade design as well as the design of a turbine array.
w 1 2
U2
(6)
Acknowledgements
where, w denotes the shear stress. It is apparent in Fig. 18 that the distribution of skin friction in uniform flow is not smooth when TSR is low, while it is smooth when TSR is high. These tendencies are basically the same in the cases of small and large shear gradient cases. However, when the shear gradient is large, directions of streamline are different from those in the case of uniform flow. The reason is supposed to be the unsteadiness of the flow, since the two-dimensional unsteady wing theory suggests that the separation does not happen even for the large attack angle if the flow is unsteady. But, the detail of flow is difficult to expect without the CFD. Although we do not give examples of three-dimensional visualization, it may be more informative. Another example is the wake flow behind the turbine which is very important for the design of the farm, since the wake affects the inflow of the turbine behind the front turbines. In addition, in the case of floating type ocean current turbine, the wake affects not only the efficiency but also the motion of floating devices in the second row. Fig. 19 shows a contour plot of magnitude of vorticity distribution on the center vertical plane in the shear flow. It is noted that the inflow passes through the center of the turbine, since the boss is ignored in the CFD computation. It is apparent that the wake after the turbine is not symmetry. The reason is supposed to be that the downwash induced by spiral trailing vortices is not uniform in a cylindrical region behind the turbine. Stronger trailing vortex at the upper half decelerate the fluid quicker than that in the lower half. As a result, the vertical velocity is induced. This effect might be important for the design of a turbine array.
This work is funded by the New Energy and Industrial Technology Development Organization, Japan (NEDO). The authors are grateful for their support. The authors are also appreciated Akishima Laboratory Inc. for their support to the experiment in the circulating water channel. References Ahmed, U., Apsley, D.D., Afgan, I., Stallard, T., Stansby, P.K., 2017. Fluctuating loads on a tidal turbine due to velocity shear and Fluctuating loads on a tidal turbine due to velocity shear and. Renew. Energy 112, 235–246. Blackmore, T., Myers, L.E., Bahaj, A.S., 2016. Effects of turbulence on tidal turbines: implications to performance, blade loads, and condition monitoring. Int. J. Mar. Energy 14, 1–26. Chujo, T., Matsui, R., Haneda, K., Nimura, T., Ishida, S., Inoue, S., 2017. Tank experiment of floating horizontal Axis current turbine with twin rotor for safety assessment. In: The 26th Ocean Engineering Symposium, Tokyo. DNV, G.L., 2015. STANDARD DNVGL-ST-0164 Tidal Turbines. DNV GL AS. Faudota, C., Dahlhauga, O.G., 2012. Prediction of wave loads on tidal turbine blades. Energy Procedia 20, 116–133. Gaurier, Z.B., Davies, P., Deuff, A., Germain, G., 2013. Flume tank Characterization of marine current turbine blade behaviour under current and wave loading. Renew. Energy 59, 1–12. Hand, M.M., Simms, D.A., Fingersh, L.J., JagerD, W., Cotrell, J.R., 2001. Unsteady Aerodynamics Experiment Phase V: Test Configuration and Available Data Campaigns. NREL/TP-500-29491. Hansen, M.O.L., Sørensen, J.N., Voutsinas, S., Sørensen, N., Madsen, H.A., 2006. State of the art in wind turbine aerodynamics and aeroelasticity. Prog. Aero. Sci. 42 (4), 285–330. Demonstration of the World's Largest Ocean Current Power Generation System, vol 57 Technical Report of IHI Corporation 4. Jonkman, Jason M., Buhl Jr., Marshall L., 2005. FAST User's Guide. Technical Report NREL/EL-500-38230. Kiyomatsu, k., Kodaira, T., Kadomoto, Y., Waseda, T., Takagi, K., 2014. ADCP measurements of ocean currents near Miyake Islands. J. Jpn. Soc. Nav. Archit. Ocean Eng. 20, 147–156. Kodaira, T., Waseda, T., Miyazawa, Y., 2014. Nonlinear internal waves generated and trapped upstream of islands in the Kuroshio. Geophys. Res. Lett. 41, 5091–5098. Menter, F.R., 1993. Zonal two equation k-ω turbulence models for aerodynamic flows. In: 23rd Fluid Dynamics, Plasmadynamics, and Lasers Conference , Orlando. Milne, I.A., Day, A.H., Sharma, R.N., Flay, R.G.J., 2013. Blade loads on tidal turbines in planar oscillatory flow. Ocean Eng. 60, 163–174. Milne, I.A., Day, A.H., Sharma, R.N., Flay, R.G.J., 2015. Blade loading on tidal turbines for uniform unsteady flow. Renew. Energy 77, 338–350. Mycek, P., Gaurier, B., Germain, G., Pinon, G., Rivoalen, E., 2014a. Experimental study of the turbulence intensity effects on marine current turbines behaviour. Part I: one single turbine. Renew. Energy 66, 729–746. Mycek, P., Gaurier, B., Germain, G., Pinon, G., Rivoalen, E., 2014b. Experimental study of the turbulence intensity effects on marine current turbines behaviour. Part II: two interacting turbines. Renew. Energy 68, 876–892. O'Rourke, F., Boyle, F., Reynolds, A., Kennedy, D.M., 2015. Hydrodynamic performance prediction of a tidal current turbine operating in non-uniform inflow conditions. Energy 93, 2483–2496. Parkinson, S.G., Collier, W.J., 2016. Model validation of hydrodynamic loads and performance of a full-scale tidal turbine using Tidal Bladed. Int. J. Mar. Energy 16, 279–297. Takagi, K., 2012. Motion analysis of floating type current turbines. In: 31th International Conference on Ocean. Offshore and Arctic Engineering OMAE2012, Rio de Janeiro. Takagi, K., Waseda, T., Nagaya, S., Niizeki, Y., Oda, Y., 2012. Development of a floating current turbine. In: OCEANS 2012, Virginia Beach. Xia, Y., Takagi, K., 2016. Effect of shear flow on a marine current turbine. In: Proc. of OCEANS, Shanghai, 2016.
5. Conclusions We focus on the shear flow effect on an ocean current turbine. The periodic fluctuation of moment loads at a blade root induced by the shear flow is highlighted because the bending moment is one of important parameters for the structural design of the blade. Experiments in a circulating water channel and a towing tank were conducted, and numerical estimations of the blade loads were also carried out by a commercial CFD code and compared with the experimental results. A linear shear flow was created in the circulating water channel with three screens, and moment loads at the root of one blade was successfully measured in this shear flow. The blockage effect and influence of the free surface was removed from the measured data by utilizing experimental results obtained in the ocean engineering basin. ANSYS fluent was used for the computation and the numerical results were compared with the experiment. The meshing, size of computational domain, and the turbulence model are verified through the comparisons between the numerical result and the experiment for the power coefficient and the thrust coefficient in uniform flow. The numerical results of moment load in the shear flow are validated through the comparison with the experimental results of Mx and My. It is concluded that the time averaged values of Mx and My are estimated by the present CFD method very well, and the amplitude and phase of the periodic fluctuation of the
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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Moment loads acting on a blade of an ocean current turbine in shear flow Kazuomi Yahagi, Ken Takagi
T
∗
Dept. of Ocean Technology, Policy, and Environment, The University of Tokyo, Kashiwa, Japan
ARTICLE INFO
ABSTRACT
Keywords: Current turbine Moment load Blade moment in the shear flow CFD of turbine blade
The Kuroshio flowing near Japan is one of the largest ocean currents and it is considered that this energy possibly be an important energy source for Japan. A full-scale generator with twin 40m turbine rotors is planned for at the rated flow speed of 1.5 m/s. Estimation of the blade loads are crucial for such big turbines. We focus on the effect of shear flow on an ocean current turbine and highlight the periodic fluctuation of moment loads at the blade root induced by the shear flow. Shear flow experiments and numerical computation with a commercial code were conducted for estimating the moment loads on a blade. The numerical computation was verified through the comparisons with the measured Cp and Ct in uniform flow. The numerical results of moment load in the shear flow are validated through the comparison with the experimental results. It is concluded that the moment loads are well estimated by the present CFD method. Using the same CFD method, some applications are shown.
1. Introduction The Kuroshio flowing near Japan is one of the largest ocean currents and it is considered that this energy possibly be an important energy source for Japan. The New Energy and Industrial Technology Development Organization (NEDO) and IHI corporation have developed a 100 kW class ocean current turbine system named “Kairyu” and successfully conducted a sea trial at the Tokara Islands in 2017 (IHI, 2017). Although the turbine diameter for 100 kW system is about 11m, it is expected that the diameter will be 40m for the 1 MW full scale generator at the rated flow speed of 1.5 m/s (Takagi et al., 2012). Estimation of the blade loads are crucial for the design of such big turbines. Especially the periodic fluctuation of the blade load is important for fatigue design. Blade load fluctuations are supposed to be induced by the turbulence, wave orbital motion and vertical profile of the inflow. In the case of tidal currents, a simple two-dimensional boundary layer shape based on the assumption of shallow water flow is often used to represent the vertical profile of flows (DNV, 2015). On the contrary, variation of profiles in the inflow for the ocean current turbine is supposed to be complex, since the water depth at the sea area where the current turbines will be deployed is deep. Thus, a simple two-dimensional boundary layer shape based on the assumption of shallow water flow may not be applicable. In addition, the influence of internal waves could be expected, though this is still under investigation. For example, Kodaira et al. (2014) investigated nonlinear internal waves in the Kuroshio. Kiyomatsu et al. (Kiyomatsu
∗
et al., 2014) measured the vertical profile of the Kuroshio near Miyake Island, and they reported that there is a strong shear flow near the free surface. Thus, we focus on the shear flow effect in this paper, and the periodic fluctuation of moment loads at the blade root induced by the shear flow is highlighted because the bending moment is one of the important parameters for the structural design of a blade. In the field of wind turbines, the National Renewable Energy Laboratory (NREL) summarized test results of the blade load due to the non-uniform wind (Hand et al., 2001), and NREL also provide a numerical model for estimation of blade loads (Jonkman and Buhl, 2005). Literatures on various numerical methods including the CFD are also available (for example (Hansen et al., 2006)) References in the literature dealing with non-uniform effects on tidal turbines also can be found. For example, Milne et al. (2013) measured blade loads in planar oscillatory flow and in spatially uniform unsteady flow (Milne et al., 2015). Faudota et al. (Faudota and Dahlhauga, 2012) conducted a wave loads measurements. Blackmore et al. (2016) and Mycek et al. (2014a) (Mycek et al., 2014b) studied effects of turbulence. Gaurier et al. (2013) measured a turbine blade strain under current and wave loading. On the other hand, numerical approaches are also found. Ahmed et al. (2017) made a comparison of CFD with field data on fluctuating loads due to velocity shear and turbulence. Parkinson et al. (Parkinson and Collier, 2016) conducted a field measurement and compared with results by a commercial software. O'Rourke et al. (O'Rourke et al., 2015) proposed a mathematical model for the Blade Element Method (BEM) to predict the hydrodynamic performance of a tidal turbine in non-uniform inflow conditions.
Corresponding author. E-mail address: [email protected] (K. Takagi).
https://doi.org/10.1016/j.oceaneng.2018.12.026 Received 24 March 2018; Received in revised form 5 December 2018; Accepted 5 December 2018 0029-8018/ © 2018 Elsevier Ltd. All rights reserved.
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r
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60 unit : mm
Center of turbine rotor Turbine axis
y z x
Fig. 1. Plane view of the blade.
(a)
Table 1 Summary of the numerical method. Items
Methods
Solution Turbulence model Velocity-pressure coupling Gradient calculation Discretization
1st order implicit SST k-ω model SIMPLE method Least Squares Cell Based Momentum 2nd order upwind k 1st order upwind ω 1st order upwind
y x
Inlet
(b) Fig. 3. Detail of the mesh. (a) Meshing on the blade surface. (b) Meshing near the blade tip.
Outlet 65 152
Rotational region
unit: mm
390
900
z
4.0
2.0
8.0(m)
120
120
y
Stational region 0.0
W.L
550
x
6.0
390
Fig. 2. Overall computational domain. 570
In the present work, experiments in a circulating water channel, where a shear flow was created, and in an ocean engineering basin were conducted, and numerical estimations of the blade loads were also carried out by a commercial CFD code and compared with the experimental results.
Fig. 4. Principal dimensions of the turbine rotor.
where the definition of r is found in Fig. 1. It is noted that two blades are equipped as a turbine rotor because the Kairyu (IHI, 2017) uses two bladed turbines for better performance in the installation and the maintenance. It is also noted that, although the experimental model has a boss at the center of rotor, the boss is ignored for the numerical calculations to reduce the computational effort. It is noted that we focused on the blade moment load in this study as mentioned above. The moment about the turbine axis and an axis perpendicular to the r-axis and turbine axis are defined as Mx and My respectively. Non-dimensional forms of Mx and My are defined as
2. Numerical computation of the blade loads 2.1. Blades and hub Since the aim of this study is to reveal the effect of shear flow, a popular wing section is used, and the twisting angle is presented by a simple equation. The blade used in the present work is designed by referring to NMRI's blade (Chujo et al., 2017). NACA0012 is used for the wing section and the plan view of the blade is a trapezoid as shown in Fig. 1, where the size of the blade is the same as that of experimental model which will be mentioned in section 3. The twisting angle of the blade is represented as
= tan
1
450 11r
tan
1
1 11
CMx =
Mx 1 2
U 2 AR
, CMy =
My 1 2
U 2AR
(2)
where U is the inflow velocity at the turbine center, A is the projection area of the turbine rotor, R is the radius of the turbine rotor and is the water density.
(1) 447
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1.5m
0.8m
Screen×3
0.6m
Depth = 1.2m
0.6m
Inlet
Velocity meter
0.55m
0.55m
Velocity meter
0.55m
Length of test section=4.9m
Turbine 0.57m
Side view
1.5m Fig. 5. Arrangement of the experiment in a circulating water channel.
0.45
0.035
Velocity meter1 Velocity meter2
0.30
0.025 0.020
CMx
Z [m]
0.15 0.00
0.015
-0.15
0.010
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0.005 0.000
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0.35
0.40 0.45 0.50 Velocity [m/s]
0.55
3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 TSR
0.60
(a) Mx
Fig. 6. Time averaged vertical profile of the shear flow in a circulating water channel. The shear is created by three screens.
0.70 0.50
0.35
0.40
CMy
0.40
0.30 0.20
0.25
CMy
Circulating water channel Ocean Engineering Basin
0.60
0.30
0.10
0.20
0.00 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 TSR
0.15 0.10
(b) My
0.05
Fig. 8. Comparisons of time averaged (a) Mx and (b) My measured in the circulating water channel and in the ocean engineering basin.
0.00 0.0
1.0
2.0
3.0
4.0
5.0
Time[s]
t
Fig. 7. Time history of My in the uniform flow. Measurement has been done in the ocean engineering basin.
xi
( ui ) = 0
xi
uj p u + [µ ( i + xi xi xi xi
( u i uj ) =
xj
(
ui uj )
2 3
ij
ui )] xi (4)
where, denotes the pressure, µ the viscosity, ij the Kronecker delta, ui the turbulent component and the over bar denotes the time average. The last term is obtained by using a turbulence model. In this paper, the SST k-ω turbulence model (Menter, 1993) is used. Other important information on the solver is shown in Table 1. The Reynolds number is 2.2×105 at the tip of the blade when the tip speed ratio (TSR) is 11.0 and the inflow velocity is 0.5 [ms−1]. Based on this value, the numerical mesh is constructed. Fig. 2 shows the size of overall computational domain.Where D denotes the diameter of rotor. It is noted that the sliding mesh is mainly used in the numerical computation. On the other hand, the Multiple Reference Frame (MRF)
ANSYS Fluent ver.18.0 is used for the numerical computation. Since the flow is incompressible, the conservation of mass is satisfied as
+
( ui ) +
+
2.2. Solver and mesh
t
Circulating water channel Ocean Engineering Basin
0.030
(3)
where, the Cartesian-coordinate system x i is used and ui denotes the fluid velocity. The Reynolds-averaged Navier-Stokes equations (RANS equations) is solved by the Fluent. The RANS equation is represented as 448
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0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
0.40 0.35
Cp
0.30 0.25 CMy
CFD -2 deg. (MRF) CFD 0 deg. (MRF) CFD -2 deg. (Sliding Mesh) Experiment -2 deg. Experiment 0 deg.
CFD(TSR7.2)
0.20
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0.05
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0.00
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1.00 0.80
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(a) Time history
0.60 0.003
CFD -2 deg. (MRF) CFD 0 deg. (MRF) CFD -2deg. (Sliding Mesh) Experiment -2 deg. Experiment 0 deg.
0.40 0.20 0.00
CMy Periodogram [(N*m)2]/Hz
Ct
3.0 TIme[s]
3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 TSR (b) Ct Fig. 9. Measured and computed results of (a) Cp and (b) Ct in the uniform flow. Blade pitch angles are −2 and 0°.
model is used only for the uniform flow case and compared with the result of the sliding mesh computation. Fig. 3 shows the detail of meshing near the blade. Height of the wall cell is set to be smaller than y+ = 1. The time step is determined so that each time step corresponds to 1 degree of the turbine rotation. Total number of the mesh is 4,801,511 for the following calculations. In order to verify the convergence of results, a finer mesh calculation has also performed with 12,133,638 meshes. The difference of the power coefficient is 0.88% and 0.1% for the thrust coefficient. Thus, we assumed that the numerical results are converged with 4,801,511 meshes. It is noted that a linear variation in z-direction is used for a mathematical model of the shear flow at the inlet boundary in the shear flow computation. The coefficient of the linear equation is determined based on the measurement of shear flow in the circulating tank as
CFD Experiment
0.002 0.002 0.001 0.001 0.000 0.0
0.5
1.0
1.5 2.0 Frequency [Hz]
2.5
3.0
(b) Periodogram Fig. 10. An example of measured My in the circulating water channel for the blade pitch angle of −2°. (a) Time history and (b) Periodogram of the time history.
moments are measured by a moment load sensor which is located at the root of one blade. The experimental turbine rotor has a boss of 0.12m diameter and a sensor and a dummy sensor are fixed at both sides of the boss, while the numerical model ignores the boss and the censors. The thrust and moment of the turbine are also measured to check the power coefficient Cp and the thrust coefficient Ct. Xia and Takagi (Xia and Takagi, 2016) created a shear flow in the circulating water channel using screens. The screen is a lattice of 15 horizontal bars with diameter of 0.0272m and the bars are extended to the channel wall. The same screen is used for creating a shear flow in the circulating water channel. Fig. 5 shows the experimental arrangement of screens, velocity meters, and the turbine. The test section of the circulating water channel has dimensions of 4.9m (length) x 2.0m (width) x 1.2m (water depth). Three screens are used to create a shear flow with 10% gradient. An electro-magnetic velocity meter is installed
u= 0.416 + 0.045z [ms−1](5)
3. Experiment 3.1. Experimental set up Principal dimensions of the turbine is shown in Fig. 4. The shape and twisting angle are chosen so that the blade shape is represented by simple equations for the convenience of generating the numerical mesh as mentioned above. The diameter is chosen to guarantee the accuracy of the moment measurement. As a result, a free surface effect is observed that will be explained later. The rotation of the turbine rotor is controlled to keep the constant rate from TSR = 5 to 14. The blade
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0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
CMx average
Cp
K. Yahagi, K. Takagi
CFD Uniform Flow CFD Shear Flow Exp Uniform Flow Exp Shear Flow
0.045 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000
CFD Experiment
4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 TSR
3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 TSR
(a) Mx
(a) Cp
1.20 CMy average
1.00 0.80 Ct
0.60 CFD Uniform Flow
0.40
CFD Shear Flow Exp Uniform Flow
0.20
Exp Shear Flow
0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
CFD Experiment
4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 TSR
0.00 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 TSR
(b) My
(b) Ct
Fig. 12. Comparison between experimental results and computational results on the time average of Mx and My in the shear flow for the blade pitch angle of −2°.
Fig. 11. Measured and computed results of (a) Cp and (b) Ct in the uniform flow and in the sea flow. Blade pitch angle is −2°.
other hand, the free surface effect is more serious for the magnitude of fluctuations in the shear flow, because the amplitude of periodic fluctuation appearing in Fig. 7 has almost the same order as the fluctuation in the shear flow. Thus, the fluctuations of Mx and My in the shear flow are corrected by subtracting the fluctuation appeared in uniform flow. Fig. 8 shows comparisons of time averaged (a) Mx and (b) My measured in the circulating water channel and in the ocean engineering basin. Apparent blockage effect is observed. The measured value in the circulating tank is corrected using two values as the blockage effect correction. In addition to this, the free surface correction is made for the fluctuated part of the measured value in the shear flow as mentioned previously. The same blockage correction is made for Cp and Ct.
at the center line of the channel to measure the reference inflow velocity and another one is installed 0.35m off-center. Both meters are located 0.6m in front of the turbine. A measurement of vertical profile of the flow was conducted before installing the turbine. Fig. 6 shows the measured vertical profile of shear flow where the velocity is averaged in time. Although the vertical profile is not perfectly straight, the screens induce a linear shear flow with the gradient of 10.8%. We also measured the turbulence intensity, and it is found that the turbulence intensity for the shear flow is 4–5% while it is less than 2% for the uniform flow. 3.2. Blockage effects
4. Results and discussion
Since the width of the test section is only 2.0m, a blockage effect is expected. Thus, the same experiment is conducted in the ocean engineering basin of the University of Tokyo. The basin has dimensions of 50m (length) x 10m (width) x 5m (water depth). We used the same experimental set up, while the turbine was towed by a towing carriage. It is mentioned that, even in the ocean engineering tank, the free surface effect cannot be removed, though it is supposed to be smaller than the wall effect. Fig. 7 shows an example of time history of My which has a periodic fluctuation. It has the same period as the rotation of the turbine, and it is supposed to be a free surface effect. The amplitude of fluctuation is 2.5% of the average value. Therefore, the average value is supposed to have an inaccuracy of the same order due to the miller effect of the free surface. However, this inaccuracy is ignored in our experimental results since the inaccuracy is small. On the
4.1. Comparison of the CFD with the experiment In order to verify the numerical procedure, comparisons of Cp and Ct are performed. Fig. 9 shows the numerical results and the measured results of Cp and Ct. The numerical computations for the pitch angle of −2° are performed both by the MRF model and the sliding mesh model. The MRF results are almost identical to the sliding mesh results, and the MRF computation and the sliding mesh computation both show a fairly good agreement with experimental results. Thus, we concluded that the numerical procedure is appropriate, and the numerical results have enough accuracy for the further discussion, though the experimental value could have small errors due to the free surface effect as
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4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 TSR
(b) My
(b) My
Fig. 13. Comparison between experimental results and computational results on the amplitude of the first harmonic component in the time history of Mx and My in the shear flow for the blade pitch angle of −2°.
Fig. 14. Comparison between experimental results and computational results on the phase of the first harmonic component in the time history of Mx and My in the shear flow for the blade pitch angle of −2°.
mentioned above. We also confirmed that the MRF model gives good approximation for Cp and Ct and saves the computational time, though the model is mathematically not correct for the transient problem. It is mentioned that from here on out we discuss on the case of blade pitch angle of −2°, since Ct is larger than the case of 0°. Fig. 10-(a) shows an example of time history of My in the shear flow. Since the turbulent intensity of the inflow is about 4%, high frequency fluctuations are observed in the experimental time history. However, an apparent periodic variation is recognized and its frequency is equal to the rate of turbine rotation. On the contrary, the CFD result shows an apparent periodicity, since the inflow of the CFD does not have a turbulent component. In order to clarify this frequency, we obtained a periodogram of the time history which is shown in Fig. 10-(b). A sharp peek is appearing both for the experiment and the CFD at the frequency of 1.06 Hz which is equal to the rotation rate 1.06 rps of the turbine. Another small peak is also observed in the experiment at the frequency of 2.12 Hz which is supposed to be the second harmonic, while the CFD result has no second peek. It is concluded from these results that the first harmonic component of the Fourier series expansion is useful for the discussion on the fluctuations of the load acting on the blade, though the inflow contains a turbulent component and its influence is observed in the time history. Fig. 11 shows measured and computed results of Cp and Ct in the uniform flow and in the shear flow, where the sliding mesh is used for the computation. Since the generated shear in the circulating water channel is not strong, the difference between the uniform-flow case and
the shear-flow case is not apparent, though the forces in the shear flow is theoretically expected to be larger than it in the uniform flow. On the contrary, the CFD shows that Ct in the shear flow is slightly larger than it in the uniform flow, though this tendency is not clear in the case of large TSR. This tendency is not simple for Cp, since the shear flow case is larger only in the middle TSR. Thus, it is concluded that the influence of the shear flow is small if the shear is not strong, and the tendency depends on TSR. A large shear case will be shown and discussed in the next subsection as an example of the CFD application. Fig. 12 shows a comparison between experimental results and computational results on the time average of Mx and My, where the sliding mesh is used for numerical computation to represent the shear flow. The experimental results are corrected for blockage effects. The agreement between the experiment and the CFD is the same as that of Cp and Ct. However, the agreement for smaller TSR is not good. Especially Mx at TSR = 5, the discrepancy between the CFD and the experiment is big. The reason is supposed to be a separation of the flow on the blade. The influence of the separation is discussed in the next subsection. Fig. 13 shows the amplitude of the first harmonic component of fluctuation in the time history of (a) Mx and (b) My in the shear flow, and the phase is shown in Fig. 14. Where, the amplitude and phase are obtained as the first harmonic component of the Fourier expansion. The amplitude and the phase are corrected for the blockage effect and the free surface effect as mentioned above. It is apparent from these figures that the CFD results are in fairly good agreement with experimental
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0.450 0.425 CMx
0.400 Cp
0.375 0.350 Shear flow (40%) Shear flow (10%) Uniform flow
0.325 0.300 0.0
0.5
1.0
1.5 2.0 Time [s]
2.5
Shear flow (40 ) Shear flow (10%) Uniform flow
0.0
3.0
0.5
1.0
1.5 2.0 Time [s]
2.5
3.0
(a) Mx
(a) Cp 1.00 0.98 0.95 0.93 0.90 0.88 0.85 0.83 0.80
0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
Ct
CMy
Shear flow (40%) Shear flow (10%) Uniform flow
0.0
0.5
1.0
1.5 Time [s]
2.0
2.5
Shear flow (40%) Shear flow (10%) Uniform flow
0.0
3.0
0.5
1.0
1.5 2.0 Time [s]
2.5
3.0
(b) My
(b) Ct
Fig. 16. Time histories of (a) Mx and (b) My for the blade pitch angle of −2° and TSR = 7 (Period of turbine rotation = 0.81 s) in the shear flow.
Fig. 15. Instantaneous value of (a) Cp and (b) Ct for the blade pitch angle of −2° and TSR = 7 (Period of turbine rotation = 0.81 s) in the shear flow.
results, though the agreement is worse than that of averaged value. It is mentioned that the amplitude and the phase of Mx and My are not stationary in the experiment as seen in the time history shown in Fig. 10, since it is difficult to generate perfectly linear shear flow and the inlet flow contains turbulent component. It is also noted that Mx is more sensitive than My, since Mx is much smaller than My. The phase lag appearing in the small TSR case is observed both in the experiment and CFD. This is one of important characteristics of unsteady wing theory, though the phase lag is small. From these results, it is concluded that the CFD can predict the unsteady effects on the turbine blades in the shear flow expect for the case of small TSR where the separation is expected. It is noted that, although the CFD is a powerful tool to estimate the moment loads as mentioned above, it is too time consuming when we calculate the unsteady problem. Thus, in the simulation of the overall turbine system which includes the floating body and the mooring system, BEM is convenient for the estimation of blade force and moment (Takagi, 2012). The present results are utilized for improving a mathematical model which gives an unsteadiness correction to conventional BEM (O'Rourke et al., 2015).
CFD. Fig. 15 shows instantaneous value of the Cp and Ct, where the period of turbine rotation is 0.81 s. Crests in the time history Cp correspond to instants when the blade is vertical. On the contrary, valleys correspond to the horizontal position. It is apparent that in the large gradient case Cp has large fluctuations, while in the small gradient case the fluctuations are small. This tendency is explained by the attack angle of the local flow to the blade section. When the blade is vertical, the shear effect is added to the average inflow of the turbine. The additional inflow to the upper blade is positive while that to the lower blade is negative. Since the magnitude of the blade force is proportional to the square of the inflow speed, the summation of upper and lower blade-forces is slightly larger in the vertical position compared to the blade-force when the blade takes a horizontal position. The difference of the blade-force between the vertical position and the horizontal position is supposed to be proportional to the square of magnitude of the additional-inflow velocity. Thus, the fluctuation of the blade-force would be very small, if the attack angle of the flow does not change. However, the attack angle of the flow changes linearly according to the variation of inflow speed. On the other hand, if the attack angle increases Cp would increase and Ct would decrease. As a result, instantaneous Cp has the large fluctuation, while the fluctuation of Ct is small. This is the case for the large gradient of shear. When the gradient of shear is small, the same thing happens. However, since the influence of attack angle variation due to the shear is small compared to the attack angle without shear and the square of the magnitude of additional inflow is small, the fluctuations on both Cp
4.2. Application of the CFD Although the shear gradient in the experiment is 10.8%, a more severe gradient is reported in the measurement of the ocean current (Kiyomatsu et al., 2014). Thus, a comparison between the small gradient case (10%) and a large gradient case (40%) was carried out by the
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Table 2 Summary of amplitude for different TSRs in the shear flow. TSR = 6
Shear flow (10%) Shear flow (40%)
Cp amplitude
Ct amplitude
CMx amplitude
CMy amplitude
0.0003 0.0077
0.0002 0.0017
0.0022 0.0126
0.0092 0.0499
Cp amplitude
Ct amplitude
CMx amplitude
CMy amplitude
0.0002 0.0106
0.0001 0.0020
0.0021 0.0142
0.0100 0.0656
TSR = 7
Shear flow (10%) Shear flow (40%)
Shear gradient 10%
Shear gradient 40%
Uniform flow
0.60
0.45
0.30
0.15
0.00
Upper
Lower
Upper
Lower
Upper
Lower
(a) TSR=5.0
Shear gradient 10%
Shear gradient 40%
Uniform flow
0.60
0.45
0.30
0.15
0.00
Upper
Lower
Upper
Lower
Upper
Lower
(b) TSR=7.0 Fig. 17. Streamlines on the blade for the cases of (a) TSR = 5.0 and (b) TSR = 7.0 in different shear gradients of the flow. Blades are in the vertical position.
and Ct are very small. This is a qualitative explanation of this phenomenon. But, the quantitative estimation is difficult without the CFD, because the unsteady effect is supposed to be considered. Fig. 16 shows time histories of Mx and My in the shear flow. Time
histories apparently have a periodic fluctuation whose period is as the same as the period of turbine rotation. It is mentioned that the amplitude is not proportional to the shear gradient, and the ratio between amplitude and shear gradient depends on the TSR. The reason is 453
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Skin friction coefficient
Shear gradient 10%
Upper
Shear gradient 40%
Lower
Upper
Lower
Uniform flow
Upper
Lower
(a) TSR=5.0
Skin friction coefficient
Shear gradient 10%
Upper
Shear gradient 40%
Lower
Upper
Lower
Uniform flow
Upper
Lower
(b) TSR=7.0 Fig. 18. Distribution of the shear stress on the blade for the cases of (a) TSR = 5.0 and (b) TSR = 7.0 in different shear gradients of the flow. Blades are in the vertical position.
supposed to be the same as the cases of Cp and Ct. However, since the influence of unsteadiness exists, again the quantitative estimation is difficult without the CFD. Table 2 shows a summary of amplitude for different TSRs. It seems that the larger gradient case experiences more sever fluctuations of the load than a linearly expected value from the 10% case. This is important information for the fatigue design of the blade. One of advantages of the CFD is that we can observe the detail of flow directly from visualized numerical results. Thus, two examples are shown here. The fist example is relevant to the separation of the flow on the blade which was mentioned in subsection 4.1. Figs. 12–14 show that the agreement between the CFD and the experiment is not good when TSR is small (TSR = 5.0), while the agreement is fairly good in the case of higher TSR. Since the local attack angle of the blade is large when TSR is small, it suggests that the separation on the blade happens. Fig. 17 shows stream lines on the blade in the cases of (a) TSR = 5.0
Fig. 19. Contour plot of magnitude of vorticity distribution on the center vertical plane for the 40% gradient, blade pitch angle = −2° and TSR = 7. 454
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and (b) TSR = 7.0. Since the Cp, which represents the efficiency of the turbine, is high in the case of TSR = 7, this case is considered to represent the normal operation-condition, while the case of TSR = 5.0 represents the torque-rich condition, i.e. low TSR. In the uniform flow, Fig. 17 shows that there are streamlines toward spanwise direction near the tip of the blade when TSR = 5.0. These stream lines suggest the flow separation for the case of low TSR. On the contrary, when TSR is high, streamlines toward the spanwise direction are not observed. This is confirmed in Fig. 18 which shows distributions of the skin friction coefficient. The skin friction coefficient is defined as
moment load are estimated with sufficient accuracy, though the agreement between the CFD and the experiment is worse than that of time averaged value. When TSR is small, the agreement between the CFD and the experiment on Mx and My is not good, the reason considered to be a separation happening on the blade. Flow visualizations of the CFD result confirm detail of the separation. Using the same CFD method, moment loads on a blade in the shear flow of 40% gradient were computed. It is found that the larger gradient case produces more severe fluctuations of the load than a linearly expected value, and the wake behind the turbine is not symmetric. These phenomena might be useful for the blade design as well as the design of a turbine array.
w 1 2
U2
(6)
Acknowledgements
where, w denotes the shear stress. It is apparent in Fig. 18 that the distribution of skin friction in uniform flow is not smooth when TSR is low, while it is smooth when TSR is high. These tendencies are basically the same in the cases of small and large shear gradient cases. However, when the shear gradient is large, directions of streamline are different from those in the case of uniform flow. The reason is supposed to be the unsteadiness of the flow, since the two-dimensional unsteady wing theory suggests that the separation does not happen even for the large attack angle if the flow is unsteady. But, the detail of flow is difficult to expect without the CFD. Although we do not give examples of three-dimensional visualization, it may be more informative. Another example is the wake flow behind the turbine which is very important for the design of the farm, since the wake affects the inflow of the turbine behind the front turbines. In addition, in the case of floating type ocean current turbine, the wake affects not only the efficiency but also the motion of floating devices in the second row. Fig. 19 shows a contour plot of magnitude of vorticity distribution on the center vertical plane in the shear flow. It is noted that the inflow passes through the center of the turbine, since the boss is ignored in the CFD computation. It is apparent that the wake after the turbine is not symmetry. The reason is supposed to be that the downwash induced by spiral trailing vortices is not uniform in a cylindrical region behind the turbine. Stronger trailing vortex at the upper half decelerate the fluid quicker than that in the lower half. As a result, the vertical velocity is induced. This effect might be important for the design of a turbine array.
This work is funded by the New Energy and Industrial Technology Development Organization, Japan (NEDO). The authors are grateful for their support. The authors are also appreciated Akishima Laboratory Inc. for their support to the experiment in the circulating water channel. References Ahmed, U., Apsley, D.D., Afgan, I., Stallard, T., Stansby, P.K., 2017. Fluctuating loads on a tidal turbine due to velocity shear and Fluctuating loads on a tidal turbine due to velocity shear and. Renew. Energy 112, 235–246. Blackmore, T., Myers, L.E., Bahaj, A.S., 2016. Effects of turbulence on tidal turbines: implications to performance, blade loads, and condition monitoring. Int. J. Mar. Energy 14, 1–26. Chujo, T., Matsui, R., Haneda, K., Nimura, T., Ishida, S., Inoue, S., 2017. Tank experiment of floating horizontal Axis current turbine with twin rotor for safety assessment. In: The 26th Ocean Engineering Symposium, Tokyo. DNV, G.L., 2015. STANDARD DNVGL-ST-0164 Tidal Turbines. DNV GL AS. Faudota, C., Dahlhauga, O.G., 2012. Prediction of wave loads on tidal turbine blades. Energy Procedia 20, 116–133. Gaurier, Z.B., Davies, P., Deuff, A., Germain, G., 2013. Flume tank Characterization of marine current turbine blade behaviour under current and wave loading. Renew. Energy 59, 1–12. Hand, M.M., Simms, D.A., Fingersh, L.J., JagerD, W., Cotrell, J.R., 2001. Unsteady Aerodynamics Experiment Phase V: Test Configuration and Available Data Campaigns. NREL/TP-500-29491. Hansen, M.O.L., Sørensen, J.N., Voutsinas, S., Sørensen, N., Madsen, H.A., 2006. State of the art in wind turbine aerodynamics and aeroelasticity. Prog. Aero. Sci. 42 (4), 285–330. Demonstration of the World's Largest Ocean Current Power Generation System, vol 57 Technical Report of IHI Corporation 4. Jonkman, Jason M., Buhl Jr., Marshall L., 2005. FAST User's Guide. Technical Report NREL/EL-500-38230. Kiyomatsu, k., Kodaira, T., Kadomoto, Y., Waseda, T., Takagi, K., 2014. ADCP measurements of ocean currents near Miyake Islands. J. Jpn. Soc. Nav. Archit. Ocean Eng. 20, 147–156. Kodaira, T., Waseda, T., Miyazawa, Y., 2014. Nonlinear internal waves generated and trapped upstream of islands in the Kuroshio. Geophys. Res. Lett. 41, 5091–5098. Menter, F.R., 1993. Zonal two equation k-ω turbulence models for aerodynamic flows. In: 23rd Fluid Dynamics, Plasmadynamics, and Lasers Conference , Orlando. Milne, I.A., Day, A.H., Sharma, R.N., Flay, R.G.J., 2013. Blade loads on tidal turbines in planar oscillatory flow. Ocean Eng. 60, 163–174. Milne, I.A., Day, A.H., Sharma, R.N., Flay, R.G.J., 2015. Blade loading on tidal turbines for uniform unsteady flow. Renew. Energy 77, 338–350. Mycek, P., Gaurier, B., Germain, G., Pinon, G., Rivoalen, E., 2014a. Experimental study of the turbulence intensity effects on marine current turbines behaviour. Part I: one single turbine. Renew. Energy 66, 729–746. Mycek, P., Gaurier, B., Germain, G., Pinon, G., Rivoalen, E., 2014b. Experimental study of the turbulence intensity effects on marine current turbines behaviour. Part II: two interacting turbines. Renew. Energy 68, 876–892. O'Rourke, F., Boyle, F., Reynolds, A., Kennedy, D.M., 2015. Hydrodynamic performance prediction of a tidal current turbine operating in non-uniform inflow conditions. Energy 93, 2483–2496. Parkinson, S.G., Collier, W.J., 2016. Model validation of hydrodynamic loads and performance of a full-scale tidal turbine using Tidal Bladed. Int. J. Mar. Energy 16, 279–297. Takagi, K., 2012. Motion analysis of floating type current turbines. In: 31th International Conference on Ocean. Offshore and Arctic Engineering OMAE2012, Rio de Janeiro. Takagi, K., Waseda, T., Nagaya, S., Niizeki, Y., Oda, Y., 2012. Development of a floating current turbine. In: OCEANS 2012, Virginia Beach. Xia, Y., Takagi, K., 2016. Effect of shear flow on a marine current turbine. In: Proc. of OCEANS, Shanghai, 2016.
5. Conclusions We focus on the shear flow effect on an ocean current turbine. The periodic fluctuation of moment loads at a blade root induced by the shear flow is highlighted because the bending moment is one of important parameters for the structural design of the blade. Experiments in a circulating water channel and a towing tank were conducted, and numerical estimations of the blade loads were also carried out by a commercial CFD code and compared with the experimental results. A linear shear flow was created in the circulating water channel with three screens, and moment loads at the root of one blade was successfully measured in this shear flow. The blockage effect and influence of the free surface was removed from the measured data by utilizing experimental results obtained in the ocean engineering basin. ANSYS fluent was used for the computation and the numerical results were compared with the experiment. The meshing, size of computational domain, and the turbulence model are verified through the comparisons between the numerical result and the experiment for the power coefficient and the thrust coefficient in uniform flow. The numerical results of moment load in the shear flow are validated through the comparison with the experimental results of Mx and My. It is concluded that the time averaged values of Mx and My are estimated by the present CFD method very well, and the amplitude and phase of the periodic fluctuation of the
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