This work aims at investigating the impact of different tidal turbine locations on hydrodynamics in near-field and far-field flow; thus, three- and two-dimensional (3- & 2-D) models were exploited in combination and applied in a case study of Putuo-Hulu Islands’ tidal farm. We present a method for the simplification of tidal turbine which, based on the energy equation, determines turbine’s equivalent roughness by calculating resistance loss in flow passage. A 3-D turbine model of near-field flow in the frame of Computational Fluid Dynamics was constructed, and the flow velocity distributions in 7 combinations of “impeller rotating speed - inflow velocity” were simulated. Also a 2-D tidal model of far-field flow was established, and Finite Element Method was adopted to solve the 2-D shallow water circulation equations; thus, the impact of tidal turbine could be simulated by utilizing different location’s compositive roughness. The results show that the impact of turbine location on hydrodynamics is depending on the open degree of sea area, channel trend, and bathymetric and geographic features and that the farther distance from the turbine, the less impact on the flow field. Overall, the impact of turbine location on far-field flow is not significant, and the flow velocity varies below 8% relative to the velocity prior to turbine installation.
Tidal current power is a green and renewable energy, and the prospect of its development is considerable. Many countries with abundant marine resources are promoting the research on tidal current power generation technology and building up test field of tidal current generation.
In near-field hydrodynamic study of tidal turbine, Betz’ Law and Blade Element Momentum (BEM) theory were adopted to generalize the turbine. Bai et al. [
In far-field hydrodynamic study of tidal turbine, momentum method was used to generalize tidal turbine, that is, to add resistance loss item of turbine to the dynamic control equation. Couch and Bryden [
Although the study of tidal current power started late in China, the scientists also made some new breakthroughs in the research and development of energy-harvesting device, and the study of flow field also has a lot of achievements. For example, Xin et al. [
At home and abroad, studies on the effect of tidal turbine on hydrodynamic characteristics of large-scale far-fields which are combined with the integrated simulation of near-field hydrodynamic characteristics of turbine are few, especially in the aspects of turbine simplification and bottom friction determination. But in the previous studies, generalized bottom frictions were fixed values and did not change with the variation of flow velocity. Due to the large subjectivity of the existing research methods and the poor adaptability of the simplification method under different working conditions, the research methods could be developed in the direction of “near-field & far-field” integrated simulation. Therefore, in order to clarify the effect on flow field because of turbine installation, and then rationally arrange the berthages of tidal turbine in test field, “Putuo-Hulu Islands Tidal Power Demonstration Project” in Zhoushan City, China, was regarded as the study object. Firstly, we constructed a 3-D turbine model of near-field flow in the frame of CFD and simulated the flow velocity distributions in 7 combinations of “impeller rotating speed - inflow velocity”. Next, we presented a simplification method of tidal turbine, based on the energy equation, to determine turbine’s equivalent roughness by calculating resistance loss in flow passage. Then, we established a 2-D tidal model of far-field flow and applied Finite Element Method (FEM) in solving the 2-D shallow water circulation equations. Finally, the impact of tidal location on hydrodynamics could be simulated by utilizing different location’s compositive roughness. We combined 3-D turbine model and 2-D tidal model and simulated and analyzed the impact of turbine location on near-field and far-field hydrodynamics in tidal farm.
The site of project is located in the channel between Putuo Island and Hulu Island in Zhoushan City, China, and the geographical location of the tidal farm is shown in Figure
Geographical location of tidal farm.
Putuo Island and Hulu Island lie in a sea area where islands are numerous, and water depth changes complexly. In the sea area, the tidal current is characterized by the irregular semidiurnal tide, the fluctuation of tidal current is obviously affected by topography, and shallow sea effect is obvious. Velocity of tidal current between islands is relatively large, the mainly flow pattern is reciprocating flow, and the direction is roughly parallel to the channel. Meanwhile, the direction of tidal current is basically consistent with the tidal wave propagation [
Based on the compositive analysis of the bathymetric data, engineering geology, and tidal current resource conditions in this sea area, combining with the existing measured data, it is proposed to set the measuring points B1 to B5 as the berthages of the tidal turbine. The tidal turbine location in tidal farm is shown in Figure
Tidal turbine location.
There are two different carrier forms of tidal turbine with horizontal axis, variable pitch, and double impellers. One is for column type with single pile; that is, the structure is supported by a single pile and the impeller can be up and down according to the work needs. The other is for floating; the unit is supported by the floating platform, and the entire device is fixed by four anchor chains. Both the two carrier forms are double impellers with a rotary diameter (
The role of the carrier is ignored in the 3- and 2-D numerical simulation, and only the effect of the double impellers on the flow field is considered. The rotation direction of the impellers is opposite, the spacing between impellers is 3 m, and the hub diameter is 0.1
3-D turbine model.
According to the calculation needs, a cylinder flow field is designed, as shown in Figure
Computational domain and grids: (a) schematic of computational domain and (b) 3-D grids.
The density of grids in the range of 240 m from rotating domain to nonrotating domain in the cylinder flow field decreases gradually, and the maximum size of the grids increases from 0.1 m to 0.6 m. Moreover, there is no too large or too small size mutation. All these conform to the requirements of renormalization group (RNG) k-
This paper selects 3 points which are away from the impeller surface 50 m, 100 m, and 150 m on the axis of impeller in Condition 1 (inflow velocity is 1.843 m/s), and the three points are recorded as Point 1, 2, and 3, respectively. The changes of velocity of the 3 points under different numbers of grids are shown in Figure
Variations in velocity with grid numbers.
From Figure
Since the turbine model in this paper is constructed by imitating the shape of SeaGen impeller of tidal turbine, its radius
Relationship between impeller’s rotating speed and inflow velocity.
| | | | |
---|---|---|---|---|
| | |||
| | |||
0.614 | 0.4 | 3.82 | ||
| ||||
0.921 | 0.6 | 5.73 | ||
| ||||
1.229 | 0.8 | 7.64 | ||
| ||||
1.536 | 1.0 | 9.55 | ||
| ||||
1.843 | 1.2 | 11.46 | ||
| ||||
2.150 | 1.4 | 13.37 | ||
| ||||
2.457 | 1.6 | 15.28 | ||
The CFD software, Fluent, is applied in numerical simulation, and the specific setting of the CFD solver is as follows:
For the flow passage where the turbine is located, the flux of any flow section of this flow passage is equal when it is assumed that there is no flow crossing. According to the continuity equation, the acreage of flow sections of the downstream flow passage will be greater than the upstream because the flow velocity of the downstream of the turbine will decrease, as shown in Figure
Flow passage parameters.
The turbine causes partial energy loss of the water flow; it can be expressed by the frictional resistance loss
The cross section of the impeller is taken as the reference plane, two flow sections are taken in the upstream L1 and downstream L2, respectively, and the water body surrounded by the two flow sections and the side wall of the flow tube is studied. It is assumed that the average flow velocity of the flow section 1-1 at a certain time is
And then, (
According to Darcy Formula,
The approximate relationship between the resistance coefficient (
The relationship between
The equivalent roughness (
The wall shear stress formula is shown as
The shear stress
The compositive roughness of the turbine after it is placed is as shown in
The 3-D N-S equation is integrated along the depth direction (Z direction) to obtain the 2-D shallow water circulation equation, which is used as the governing equation. Meanwhile, the role of wind is ignored, as shown in the following:
In this paper, FEM is used to discretize the 2-D shallow water circulation equation. The computational area is divided by the uniform triangle grids, the number of unstructured grids is
Equation (
After the unit partition is determined, the number of the local unit nodes in whole coordinate is determined to form the whole matrix (increase the subscript
Equation (
The study area mainly includes the northeastern coast of Putuo Island and Hulu Island, the quadrilateral open sea facing the East China Sea. The study area is about 10 km from west to east, about 8 km from south to north, covering about 74 km2. The unstructured grids are used to divide the computational area in the model, and the density of the grids increases gradually from the open sea area to the island coastline. Finally, the number of unstructured grids’ nodes is 7,970 and the number of unstructured grids is 15,264. The grids generation of tidal model is shown in Figure
Grids generation of tidal model.
Submarine elevation contour.
Comparing Figures
The type of the open boundary of the model is the tide boundary; that is, the water level process of each grid node of the determined boundary is given along the open boundary. The water level process is obtained by harmonic analysis method and it is predicted by the global ocean tide model [
The marine hydrological data is obtained by the Second Institute of Oceanography of the State Oceanic Administration in August 2013, such as tide and tidal wave. The observation period was 10:00 on August 16th, 2013 to 17:00 on August 17th, 2013 (small tide), 14:00 on August 19th to 15:00 on August 19th (middle tide), and 10:00 on August 23th to 11:00 on August 24th (spring tide). In addition, the temporary tide level station of Hulu Island also provided the hourly tide level data from August 5th, 2013 to September 4th, 2013. The measuring points’ location is shown in Figure
Tidal model is validated by a long series pattern, and the model is calculated from 3:00 on August 16th, 2013 to 14:00 on August 24th, which lasted 204 hours. The measured data of the tidal level at the temporary test points on the western shore of Hulu Island are compared with the calculated results, as shown in Figure
Validation of tidal level.
By contrast, the calculated results are in good agreement with the measured results, the phase of the calculated results are consistent with the measured results, and the relative error of the tidal height is less than 10%, which indicates that the model is satisfactory for the verification of tide level and can simulate the change of tide level in the sea area more accurately. Taking the middle tide process for example, the validation results of flow velocity and flow direction of each measuring point are shown in Figure
Validation of flow velocity and direction: (a), (c), (e), (g) and (i) are validation results of flow velocity; (b), (d), (f), (h) and (j) are validation results of flow direction.
On the whole, the variation trend of flow velocity and flow direction of measuring points is basically the same as measured value. From the point of time corresponding to flow peak and the change of flow direction, the two are also relatively close. Relative error between the simulated value and the calculated value of flow velocity is less than 10%, and the error can be controlled within 18% in addition to some special moments.
From the foregoing, the velocity distribution of the tidal farm in the computational area is reasonable, the calculated results of flow velocity and flow direction are consistent with the measured data, and the variation trend is also similar, which shows that the mathematical model of the tidal current is basically reliable and can be used in the hydrodynamic study of the tidal farm.
Based on CFD results, velocity distributions in center plane of double impellers in each combination are shown in Table
Velocity distributions on impellers’ center planes in different combinations.
| | |||
---|---|---|---|---|
① | Inflow Velocity | 0.614 | | |
(m/s) | ||||
Angular Speed | 0.4 | |||
(rad/s) | ||||
| ||||
② | Inflow Velocity | 0.921 | | |
(m/s) | ||||
Angular Speed | 0.6 | |||
(rad/s) | ||||
| ||||
③ | Inflow Velocity | 1.229 | | |
(m/s) | ||||
Angular Speed | 0.8 | |||
(rad/s) | ||||
| ||||
④ | Inflow Velocity | 1.536 | | |
(m/s) | ||||
Angular Speed | 1.0 | |||
(rad/s) | ||||
| ||||
⑤ | Inflow Velocity | 1.843 | | |
(m/s) | ||||
Angular Speed | 1.2 | |||
(rad/s) | ||||
| ||||
⑥ | Inflow Velocity | 2.150 | | |
(m/s) | ||||
Angular Speed | 1.4 | |||
(rad/s) | ||||
| ||||
⑦ | Inflow Velocity | 2.457 | | |
(m/s) | ||||
Angular Speed | 1.6 | |||
(rad/s) |
Flow velocity profiles of each
With different
The flow velocity of the wake at the impeller axis in these 7 combinations has been restored to 96.9%, 94.1%, 94.0%, 91.1%, 91.2%, 88.3%, and 88.3% of their inflow velocity, respectively. In this paper, we take the investigation of Yang as a criterion to determine whether the computational range is normal enough; that is, when the flow velocity is restored to 80% ~ 90% of the inlet velocity, it is determined that it meets the energy generation efficiency and the work needs [
Equivalent roughness is calculated according to (
Simulated results in different combinations.
Combinations | Pressure | Pressure | Energy Loss | Resistance Coefficient | Chézy Coefficient C | Equivalent Roughness | Compositive Roughness | ||
---|---|---|---|---|---|---|---|---|---|
No. | | | |||||||
(m/s) | (rad/s) | ||||||||
1 | 0.614 | 0.4 | 101097 | 101079 | 0.015 | 1.598 | 7.005 | 0.274 | 0.275 |
2 | 0.921 | 0.6 | 100777 | 100737 | 0.036 | 1.687 | 6.817 | 0.282 | 0.283 |
3 | 1.229 | 0.8 | 100301 | 100228 | 0.068 | 1.760 | 6.674 | 0.288 | 0.289 |
4 | 1.536 | 1.0 | 99664 | 99551 | 0.109 | 1.809 | 6.583 | 0.292 | 0.293 |
5 | 1.843 | 1.2 | 98854 | 98693 | 0.160 | 1.848 | 6.514 | 0.295 | 0.296 |
6 | 2.15 | 1.4 | 97836 | 97616 | 0.222 | 1.887 | 6.445 | 0.298 | 0.299 |
7 | 2.457 | 1.6 | 96593 | 96304 | 0.296 | 1.923 | 6.385 | 0.301 | 0.302 |
Figure
Relationship between inflow velocity and compositive roughness.
Compositive roughness of turbine increases logarithmically with the increasing of inflow velocity.
Equation (
In this paper, 5 different installation locations of the tidal turbine are considered, and the comparison of the flow field before and after the installation is simulated in the process of spring tide under the 5 conditions. Taking the center of the double impeller as the center of the circle, the radius 100 m, 200 m and 300 m is taken as the exploratory circumference to count and compare the changes of flow field. Take the B4 berthage as an example, and the exploratory circumference as shown in Figure
Exploratory circumference schematic.
Difference of flow velocity is the velocity after installation minus the velocity before installation at the same time, and maximum difference of flow velocity represents maximum value of deceleration in flow velocity at a certain time. Distribution of maximum difference of flow velocity near turbine was shown in Figure
Distribution of maximum difference of flow velocity in (a) B1 location; (b) B2 location; (c) B3 location; (d) B4 location; and (e) B5 location.
It can be seen from Figure
Hourly changing process of extreme value of deceleration and relative difference of flow velocity in different exploratory circumference with radius of 100 m, 200 m, and 300 m are respectively shown in Figures
Variations in flow velocity of circumference with radius of 100 m: (a) and (b) represent B1 location; (c) and (d) represent B2 location; (e) and (f) represent B3 location; (g) and (h) represent B4 location; and (i) and (j) represent B5 location.
Variations in flow velocity of circumference with radius of 200 m: (a) and (b) represent B1 location; (c) and (d) represent B2 location; (e) and (f) represent B3 location; (g) and (h) represent B4 location; and (i) and (j) represent B5 location.
Variations in flow velocity of circumference with radius of 300 m: (a) and (b) represent B1 location; (c) and (d) represent B2 location; (e) and (f) represent B3 location; (g) and (h) represent B4 location; and (i) and (j) represent B5 location.
As can be seen from these figures, the extremal curves of deceleration at each berthage show a certain periodicity, which is the result of the periodicity of the tidal current. The curves of B2 berthage are special, and the curve patterns of other berthages are similar. Most of the deceleration minimum curves of all circumferences are located above the horizontal axis and most of the deceleration maximum curves are below the horizontal axis. This shows that there is a certain degree of deceleration and growth of flow velocity appearing near the turbine, which is also consistent with the results of the 3-D near-field simulation. The peak value of the deceleration maximum curves of each turbine generally decreases with the increase of the circumferential radius, which means that the farther away from the turbine, the smaller the effect of the turbine on the flow field. From the curves of relative difference of flow velocity, the effect of the turbine on the far-field of flow field is smaller as a whole, and the maximum change in flow velocity does not exceed 8% of the flow velocity before the installation of the turbine. The degree of deceleration and growth of all berthages were compared as shown in Table
Comparison of deceleration and growth degree.
| | |
---|---|---|
100 m | B4> B3> B1> B5> B2 | B3> B2> B1> B5> B4 |
200 m | B4> B3> B1> B5> B2 | B3> B2> B1> B4> B5 |
300 m | B4> B3> B1> B5> B2 | B4> B2> B3> B1> B5 |
As can be seen from Table
Extremum of flow velocity variation.
| | | | ||||||
---|---|---|---|---|---|---|---|---|---|
Deceleration | Growth | Relative Difference | Deceleration | Growth | Relative Difference | Deceleration | Growth | Relative Difference | |
(m/s) | (m/s) | (%) | (m/s) | (m/s) | (%) | (m/s) | (m/s) | (%) | |
B1 | -0.023 | 0.006 | 1.758 | -0.022 | 0.007 | 1.754 | -0.016 | 0.006 | 1.391 |
B2 | -0.001 | 0.017 | 0.419 | -0.001 | 0.011 | 0.226 | -0.003 | 0.009 | 0.281 |
B3 | -0.064 | 0.034 | 4.754 | -0.043 | 0.024 | 3.354 | -0.034 | 0.007 | 3.147 |
B4 | -0.091 | 0.002 | 7.461 | -0.088 | 0.01 | 6.877 | -0.053 | 0.024 | 3.947 |
B5 | -0.019 | 0.002 | 1.503 | -0.012 | 0.003 | 0.953 | -0.009 | 0.003 | 0.714 |
It can be seen from Table
To sum up, for the installation of tidal turbine in tidal farm, the following conclusions can be obtained by combining the consideration of the bathymetric data and the tidal resource in the engineering sea area:
The data supporting this article is confidential. Tianjin University requires that these data cannot be released.
The authors declare no conflicts of interest.
Hongqiang Zhang assisted in setting up the two models, processed and analyzed the data, and drafted the manuscript. Daming Li established the conceptual framework of this paper and set up the two models. Yanqing Li and Ting Yang assisted in setting up the two models and revised the manuscript. Shan Luo, Shunfa Tian, and Shilong Bu assisted in processing the data and revised the manuscript. All authors provided completion in their field.
This research was financially supported by the National Natural Science Foundation of China (Grant No. 51079095) and the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51021004). This work was supported by the State Key Laboratory of Hydraulic Engineering Simulation and Safety of Tianjin University.