Design and performance tests of a snake-like wave energy converter

Abstract

Research on renewable energy have become a focus in recent years. Ocean wave energy is a kind of renewable energy that exists widely in the world. This paper presents a snake-like ocean Wave Energy Converter (WEC) , which is more adaptive to the wave shape than some other WECs. In order to improve energy conversion efficiency, we designed and tested three types of magnetoelectric transducers for snake-like WEC, namely, axial magnetization transducer, radial magnetization transducer and Halbach permanent magnet array transducer. In order to enhance the power density of the WECs, a lumped parameter equivalent magnetic circuit model is proposed to optimize its magnetic structural parameter. Then the finite element analysis method is used to analyze models and verify theoretical results. Three 1:5 prototypes of the magnetoelectric transducers are fabricated for experimental verification. The experiments indicate that the prototype with the Halbach permanent magnets array transducer has an output power of 693.80 mW when WEC moves at a relative velocity of 0.1 m/s, the V _RMS value of induced voltage is 6.69 V. and this prototype has the highest volumetric Figure of Merit (FoM _v) of 1.67%. In conclusion, the Halbach permanent magnet array is more effective in energy conversion than the others, and it can effectively improve the energy harvesting performance for the snake-like WEC.

Keywords

WEC snake-like Halbach equivalent magnetic circuit model finite element analysis

1. Introduction

With the improvements of technology and living condition, people’s demand for energy consuming continues to increase. Traditional ore energy is not renewable and inefficient, furthermore, it brings a lot of pollution. The low-carbon and clean renewable energy technologies energy especially wave energy has become the focus of current researches [1]. Wave energy originates from offshore wind energy. It is a marine renewable energy with large reserves, wide distribution, no pollution, and high power density. Compared to some other renewable energy sources, the spatial distribution is more concentrated, and the resource density and distribution are more stable. To use WEC to generate wave energy for people who live on islands [2].

There are many kinds of wave energy converters (WECs), such as oscillating-body WEC (OWC) [3,4], float WEC [5,6], pendulum WEC [7], and etc. Various studies have achieved a lot of valuable results. Zhao etc. [8] proposed a novel system consisting of a front oscillating buoy type WEC and a rear fixed pontoon to improve the energy conversion performance of the original single pontoon breakwater-type WEC system. The experiments for both single pontoon system and two-pontoon system are conducted. Zheng etc. [9] proposed a novel hybrid WEC consisting of a floating OWC and several oscillating floats hinged around. Both water oscillation of the OWC and the wave-induced relative rotation of each float around the OWC are employed to extract wave power. The results reveal that the hybrid WEC holds a wider bandwidth of frequency response with a higher maximum power capture factor compared with those of the isolated OWC and hinged floats. Yu etc. [10] evaluated the rotational characteristics and capture efficiency of a novel variable guide vane WEC. It is observed that the device intermittently pauses when the velocity of the water particles at the height of the vane wheel is less than 0.211 m/s under no-generator conditions. Energy harvesting efficiency is approximately 7% because of the short time, lesser area, and small range of the device for harnessing the wave energy. An electrical load with a resistance varying in the range of 1–500 Ω is then connected to the generator, and the working performance of the WEC is investigated.

However, these kinds of WECs have common problems, including low energy conversion efficiency, poor adaptability, complicated structure, high cost, and short life. So it is lack of a simple and reliable structure which has wave energy harvest ability. Snake-like WEC is a new type of WEC which has higher efficiency and stronger applicability.

This study designed three types of magnetoelectric transducers for snake-like WEC. Lumped parameter equivalent magnetic circuit models of magnetoelectric transducers are proposed to optimize its magnetic structural parameter. Finite element analysis is utilized to analyze models. At last, the prototypes of the magnetoelectric transducers are manufactured and fabricated to do experiments.

Fig. 1.

Overall structure of snake-like WEC.

2. Snake-shape WEC design and optimization

The Snake-like WEC can convert wave energy into electrical energy directly, and it also can change the shape according to the working condition. Halbach permanent magnet array has the ability to enhance single-side strengthened magnetic fields [11], and Halbach permanent magnet array has been used in many fields [12,13]. The proposed magnetoelectric transducer with Halbach permanent magnet array is suitable for snake-like WEC. The snake-like WEC consists of some coil buoys and some permanent magnet buoys, and the two kinds of buoys alternately connected, as is shown in Fig. 1. Between a coil buoy and a permanent magnet buoy is the magnetoelectric transducer, which includes a transmission mechanism, a permanent magnet array and a coil winding. Figure 2 is installation diagram of snake-like WEC. One end of the WEC is fixed to the sea bed by a mooring line, and the other end of the WEC swings freely with the waves. The magnetoelectric regenerative WEC has many advantages, such as simple structure, fast response, light weight, etc., and the harvested power is easy to store and utilize. The linear generator type power generation structure can directly convert its vibration energy into electrical energy without using other transmissions, and has higher energy replacement efficiency [14].

Fig. 2.

Installation diagram of snake-like WEC.

Magnetoelectric transducer utilizes the power generation principle of the permanent magnet linear generators. There are three types of magnetoelectric transducers designed in this paper which are based on permanent magnet linear generator, as is shown in Fig. 3. Designed permanent magnet linear generator is part of magnetoelectric transducer. They are axial magnetization transducer, radial magnetization transducer and Halbach permanent magnet array transducer. The figure shows the coil winding, pole pieces and permanent magnets respectively. The magnetization direction of the permanent magnets are indicated by the arrows.

Fig. 3.

Magnetoelectric transducers: (a) axial magnetization; (b) radial magnetization; (c) Halbach permanent magnet array.

The theoretical analysis of the energy harvesting performances of the WEC with the above three magnetoelectric transducers is evaluated. Then verified the results of theoretical calculations by finite element analysis. It is possible to select an optimal type of magnetoelectric transducer in this process, as well as to optimize the designs of magnetoelectric transducer for specific wave types. The first need of the magnetic circuit design is to select a suitable permanent magnet material to increase its wave energy harvesting performance while ensuring the size within a reasonable range. Permanent magnets provide inner electromagnetic field of the WEC, the selection of the magnet material should mainly consider their coercivity, remanence, the maximum magnetic energy product and its operating temperature. Compared with other materials, NdFeB permanent magnet material has great advantages in terms of comprehensive performance. After making many comparisons and combining with practical application of the project, the NdFeB 42UH is selected as the permanent magnet material for the WEC.

The Halbach permanent magnet array transducer and its equivalent magnetic circuit model are constructed as shown in Fig. 4. In Fig. 4, the length of the permanent magnet array is τ, the thickness of the axial permanent magnet is τ_ma, the thickness of the radial permanent magnet is τ-τ_ma, the inner radius of the permanent magnet is r _mi, and the outer radius of the permanent magnet is r _mo. The inner radius of the coil winding is r _ci, and the outer radius of the coil winding is r _co.

Fig. 4.

Halbach permanent magnet array transducer and its equivalent magnetic circuit.

In this model, a pair of magnetic poles are selected for analysis. The stator casing also uses a high magnetic permeability material, ignoring the magnetic resistance R _c of the stator casing. It is assumed that the rotor guide has no magnetic leakage in the diameter direction, and can also be obtained by the Kirchhoff’s second law: $\begin{eqnarray}\displaystyle H_{cr}(r_{mo}-r_{mi})+H_{ca}{\tau}_{ma}=(R_{mr}+R_{ma}+2R_{g}){\Phi}_{g}. & & \displaystyle\end{eqnarray}$ (1)

H _c is the coercivity, B _r is the remanence, μ_r is the relative permeability of the permanent magnets and μ₀ is the vacuum permeability of the permanent magnet. Φ_g is the magnetic flux of the air gap at the position of the coil. R _m and R _g represent the reluctance of the permanent magnet and the air gap, respectively.

The radial permanent magnet reluctance R _mr, the axial permanent magnet reluctance R _ma and the air gap reluctance R _g in Eq. (1) can be expressed as: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{mr}=\frac{r_{mo}-r_{mi}}{2{\pi}{\mu}_{r}{\mu}_{0}\left({\displaystyle \frac{r_{mo}+r_{mi}}{2}}\right)\left({\displaystyle \frac{{\tau}-{\tau}_{ma}}{2}}\right)}\end{eqnarray}$ (2) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{ma}=\frac{{\tau}_{ma}}{{\mu}_{r}{\mu}_{0}{\pi}({r_{mo}}^{2}-{r_{mi}}^{2})}\end{eqnarray}$ (3) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{g}=\frac{r_{co}-r_{mo}}{2{\pi}{\mu}_{0}\left({\displaystyle \frac{r_{co}+r_{mo}}{2}}\right)\left({\displaystyle \frac{{\tau}-{\tau}_{ma}}{2}}\right)}.\end{eqnarray}$ (4)

In this structure, the cross-sectional area of the magnetic flux passing through the radial permanent magnet is: $\begin{eqnarray}\displaystyle A_{mr}=\frac{{\pi}(r_{mo}+r_{mi})({\tau}-{\tau}_{ma})}{2}. & & \displaystyle\end{eqnarray}$ (5)

The cross-sectional area of the magnetic flux passing through the axial permanent magnet is: $\begin{eqnarray}\displaystyle A_{ma}={\pi}({r_{mo}}^{2}-{r_{mi}}^{2}). & & \displaystyle\end{eqnarray}$ (6)

The cylindrical surface area of the magnetic flux passing through the air gap: $\begin{eqnarray}\displaystyle A_{g}=\frac{{\pi}(r_{co}+r_{mo})({\tau}-{\tau}_{ma})}{2}. & & \displaystyle\end{eqnarray}$ (7)

Neglecting the magnetic flux leakage, the air gap flux density B _g can be approximated as: $\begin{eqnarray} \displaystyle B_{g}=\frac{B_{r}(r_{mo}-r_{mi}+{\tau}_{ma}){\mu}_{0}H_{c}}{2(r_{co}-r_{mo})B_{r}+(r_{mo}-r_{mi}+{\tau}_{ma}){\mu}_{0}H_{c}\left({\displaystyle \frac{A_{g}}{A_{mr}}}+\displaystyle\frac{A_{g}}{A_{ma}}\right)}. & & \displaystyle \end{eqnarray}$ (8)

The H _c and B _r can be obtained from the BH characteristic curve of the NdFeB permanent magnet.

With Eq. (1), Eq. (2), Eq. (3), Eq. (4), the magnetic flux of the air gap is: $\begin{eqnarray}\displaystyle {\Phi}_{g}=\frac{{\pi}B_{r}(r_{mo}-r_{mi}+{\tau}_{ma})}{{\displaystyle \frac{2(r_{mo}-r_{mi})}{(r_{mo}+r_{mi})({\tau}-{\tau}_{ma})}}+{\displaystyle \frac{{\tau}_{ma}}{{r_{mo}}^{2}-{r_{mi}}^{2}}}+{\displaystyle \frac{4{\mu}_{r}(r_{co}-r_{mo})}{(r_{co}+r_{mo})({\tau}-{\tau}_{ma})}}}. & & \displaystyle\end{eqnarray}$ (9)

Define the permanent magnet thickness ratio of the Halbach permanent magnet array to 𝛼_h: $\begin{eqnarray}\displaystyle {\alpha}_{h}=\frac{{\tau}-{\tau}_{ma}}{{\tau}}. & & \displaystyle\end{eqnarray}$ (10)

Calculate the magnetic fluxes of the air gap under various size parameter combinations as shown in Fig. 5.

Fig. 5.

Relationship between Φ_g and 𝛼_h under different size parameter combinations of Halbach permanent magnet array transducer.

It can be seen from Fig. 5 that the smaller r _co-r _mo is, the larger Φ_g is. When r _mo is increased, Φ_g is also increased. Φ_g increases with the increase of 𝛼_h. When 𝛼_h is small, the growth rate of Φ_g is larger, and when 𝛼_h is larger, the growth rate slows down. Since the Halbach permanent magnet array has the characteristics of unilateral reinforcement, the magnetic flux leakage is significantly less than that of the radial magnetization transducer. In addition, the side magnetic field enhanced by the Halbach permanent magnet array is sinusoidal, which is more conducive to improving the energy harvesting performance of the WEC. Therefore, in order to further theoretically analyze the Halbach permanent magnet array,𝛼_h = 0.7.

The coil of WEC can reach the maximum damping coefficient (c) in the short-circuit state. The damping coefficient of the short-circuit state of the coil can be calculated. There are: $\begin{eqnarray}\displaystyle c=\frac{1}{{\rho}}\int _{{\Gamma}}{B_{g}}^{2}d{\Gamma}=\frac{2A_{g}(r_{co}-r_{ci}){B_{g}}^{2}}{{\rho}}. & & \displaystyle\end{eqnarray}$ (11)

𝛤 is the conductor volume, 𝜌 is the resistivity of the coil wire metal, and the resistivity 𝜌_Cu = 1.75 × 10⁻⁸ Ω ⋅ m.

Assuming τ is 0.1 m, τ_ma is 0.03 m, and r _mi is 0.01 m.

Define the permanent magnet-coil radial size ratio in the Halbach permanent magnet array transducer to 𝛽_h: $\begin{eqnarray}\displaystyle {\beta}_{h}=\frac{r_{mo}-r_{mi}}{r_{co}-r_{mi}}. & & \displaystyle\end{eqnarray}$ (12)

C of A single coil of the WEC under various dimensional parameter combinations can be calculated as shown in Fig. 6.

Fig. 6.

Relationship between c and 𝛽_h under different size parameter combinations of Halbach permanent magnet array transducer.

It can be seen from Fig. 5 that the larger r _co is, the larger c can be produced by a single coil. C is also closely related to 𝛽_h, and c increases slowly as 𝛽_h increases. The inflection point occurs when 𝛽_h is about 0.7, and then decreases rapidly as the 𝛽_h value increases. Therefore, in the design of the magnetic circuit, 𝛽_h = 0.7 is selected to be close to its maximum value.

N is the number of turns of the coil, and it can be approximated: $\begin{eqnarray}\displaystyle N=\frac{{\pi}}{2\sqrt{3}}\frac{A_{c}}{A_{w}}=\frac{2A_{c}}{\sqrt{3}{d_{w}}^{2}}. & & \displaystyle\end{eqnarray}$ (13)

A _c is the cross-sectional area of the coil, and A _w is the cross-sectional area of the wire. d _w is the diameter (d _w) of the wire.

R _{int, c} is the internal resistance of a single coil, and it can be approximated: $\begin{eqnarray}\displaystyle R_{int,c}={\rho}_{w}l_{c}/Aw={\rho}_{w}{\pi}DcN/Aw. & & \displaystyle\end{eqnarray}$ (14)

𝜌_w is the resistivity of the wire, 𝜌_Cu = 1.75 × 10⁻⁸ Ω ⋅ m, l _c is the length of the coil, and D _c is the diameter of the coil, the d _w of the coil is 1 mm (0. 0218 Ω ⋅ m).

Calculate the dimensional parameters of each structure separately under the requirement of maintaining the same size, in Table 1.

Table 1

Dimensions of the WECs (m)

Parameter	Axial magnetization transducer	Radial magnetization transducer	Halbach permanent magnet array transducer
r _mi (m)	0.02	0.02	0.02
r _mo (m)	0.124	0.1175	0.111
r _ci (m)	0.125	0.1185	0.112
r _co (m)	0.15	0.15	0.15
τ_mr (m)		0.2	0.14
τ_ma (m)	0.1		0.06
N	2500	3200	4000
R _{int, c} (Ω)	47.06	58.81	71.74

Four phases winding configuration is applied in the WEC, as in shown in Fig. 7.

Fig. 7.

Four phase winding configuration of the WEC.

For the coil winding, the Charging and rectifier circuit is designed, as shown in Fig. 8. In the magnetic circuit, the coils of opposite phases are respectively connected in forward and reverse directions into one winding, and the induced electromotive force of the coil is passed through a rectifying circuit composed of two rectifying bridge.

Fig. 8.

Charging and rectifier circuit.

Fig. 9.

Magnetic field distribution and the magnetic flux density in the Halbach permanent magnet array transducer.

Fig. 10.

Radial magnetic flux density of the coil.

Fig. 11.

Induced voltage of the windings of Halbach permanent magnet array transducer.

The finite element models of the WECs are built in COMSOL Multiphysics 5.4. The geometric model is built in a coordinate system about the z-axis in Fig. 9 because it could reduce the amount of calculation. Figure 9 is the finite element calculation result of the magnetic field distribution of the Halbach permanent magnet array transducer. The arrows indicate the magnitude and direction of the radial component of the magnetic flux density. Figure 10 shows the radial magnetic flux density at the center of the coil. Since the magnetic flux density is a vector in Fig. 9, its magnitude is shown in Fig. 10. The relative motion between the mover and the stator creates a regular induced voltage in the coil. Assume that the velocity of the mover in the stator is 0.1 m/s, and its induced voltage is as shown in Fig. 11.

As can be seen from the Fig. 10 and Fig. 11, the waveform of radial magnetic flux density and waveform of induced voltage are approximately the same. This is due to the working principle of the magnetoelectric transducer. The peak value of the induced voltage of the Halbach permanent magnet array transducer is 106.6 V. Analyze axial magnetized transducer and radial magnetized transducer in the same way. The volume of three types of the WECs stay same. According to the results of the finite element calculation of axial magnetization transducer and radial magnetized transducer, their induced voltages are as shown in Fig. 12 and Fig. 13. The voltage waveforms of the three transducers are different, which is caused by the difference in the magnet arrays of the three transducers. Eventually, in the same excitation environment, the peak induced voltages of the axial magnetized transducer and radial magnetized transducer are 45.3 V and 56.6 V, respectively. It can be concluded that the Halbach permanent magnet array transducer has the best energy harvesting capability. Then calculate the induced voltages of the three structures at different velocities range of 0.01 to 0.1 m/s, in Fig. 14.

Fig. 12.

Induced voltage of the windings of axial magnetization transducer.

Fig. 13.

Peak value of the induced voltage of the windings of radial magnetization transducer.

Fig. 14.

Induced voltage of different velocities.

Pure resistance is used as a load of WEC under experimental conditions, and the load equivalent circuit is shown in Fig. 15. E is coil windings induced voltage, R _int is internal resistance of coil windings, R _load is the load, and L is inductance of coil windings. The power consumed on R _load is considered as the energy harvesting power.

Fig. 15.

Load equivalent circuit.

Under experimental conditions, there is inductance of coil windings in WEC, and force of inductance is also related to the voltage frequency. L of a single winding can be calculated using the approximate calculation formula: $\begin{eqnarray}\displaystyle L=\frac{10{\pi}{\mu}_{0}N_{c}N^{2}r^{2}}{9r+10w_{c}}. & & \displaystyle\end{eqnarray}$ (15)

N is the number of turns of the coil, N _c is the number of coils contained in a single winding, r is the average radius of the coil, and w _c is the axial thickness of the coil.

The F _{d, single} generated by a single winding can be approximated: $\begin{eqnarray}\displaystyle F_{d,single}=\frac{EI\cos {\varphi}}{v}\cos \left(\frac{{\pi}vt}{{\tau}}+{\theta}\right). & & \displaystyle\end{eqnarray}$ (16)

I is the amplitude of current, φ is phase difference between induced electromotive force and current, and it can be approximated $\begin{eqnarray}\displaystyle {\varphi}=\arctan \left(\frac{{\omega}L}{R_{int}}\right). & & \displaystyle\end{eqnarray}$ (17)

The phase difference between the two groups of winding is 90°, so the damping force (F _d) can be approximated as: $\begin{eqnarray}\displaystyle F_{d}=\frac{\sqrt{2}EI\cos {\varphi}}{v}\cos \left(\frac{{\pi}vt}{{\tau}}+{\theta}\right). & & \displaystyle\end{eqnarray}$ (18)

3. Experimental study

The prototypes of the WEC are manufactured and fabricated, as is shown in Fig. 16. The scaled WEC models with different magnets arrangements shown in Table 2 are designed according to the geometric ratio of 1:5. The test system for the WECs is shown in Fig. 17. The test system consists of a prototype of the WEC, a Hall current sensor, a NI CompactRIO embedded system, a vibration test bench (Su Shi DL-300-40), and an oscilloscope (Tectronic TDS 2012). The d _w of the coil is 0.3 mm (0.24 Ω ⋅ m).

Fig. 16.

The prototype of the WEC.

Fig. 17.

Test system for the WEC.

Fig. 18.

The peak value of the induced voltage of the prototypes.

Fig. 19.

The V _RMS value of the induced voltage of the prototypes.

Table 2

Dimensions of the prototypes (cm)

Parameter	Axial magnetization transducer	Radial magnetization transducer	Halbach permanent magnet array transducer
r _mi (cm)	0.5	0.5	0.5
r _mo (cm)	2.5	2.375	2.25
r _ci (cm)	2.6	2.475	2.35
r _co (cm)	3	3	3
τ_mr (cm)		4	2.8
τ_ma (cm)	2		1.2
N	1000	1300	1600
R _{int, c} (Ω)	84.40	107.28	129.02

The peak values and the voltage RMS (V _RMS) values of induced voltage of the prototypes at velocities range of 0.01 to 0.1 m/s is shown in Fig. 18 and Fig. 19. It can be seen that the peak value of induced voltage of the Halbach permanent magnet array transducer at a velocity of 0.1 m/s is 8.18 V, and V _RMS value is 6.69 V. The peak value and V _RMS value of induced voltage of the axial magnetization transducer is 3.13 V and 2.65 V. The peak value and V _RMS value of induced voltage of the radial magnetization transducer is 4.72 V and 3.33 V. It could discover that the Halbach permanent magnet array transducer has the best energy harvesting performance in the three types of transducer in same volume.

In Fig. 18 and Fig. 19, it can be seen that the results of peak value and V _RMS value of induced voltage are basically consistent with the calculation results of finite element models. The value increases as the velocity of the WEC movement increases. Under the requirement of maintaining the same size, it can find that the energy harvesting performance of WEC with the Halbach permanent magnet array is the best of three kinds of WEC. If the three structures have the same harvesting power and the same velocity, the volume of the Halbach permanent magnet array transducer will be the smallest.

Table 3 shows the performace of the three transducers, it is found that the best matching load of WEC depends on coil internal resistance and coil inductance. The coil inductance is usually small, so the best matching load resistance takes the value of the coil internal resistance. Therefore, the best matching load resistances for the three prototypes in this experiment are different, respectively 84.40 Ω, 107.28 Ω, 129.02 Ω. The experiments also indicate that a winding could harvest vibration power of 41.60 mW, 51.58 mW and 173.45 mW when WECs at a relative velocity of 0.1 m/s. Each prototype has four windings. So the output power of prototypes are 83.20 mW, 103.16 mW and 346.88 mW.

We introduce the volumetric Figure of Merit (FoM _v) [15], which aims it compare the performance of devices as a function of their overall size. $\begin{eqnarray}\displaystyle FoM_{v}=\frac{P_{out}}{{\displaystyle \frac{1}{16}}Y_{0}{\rho}_{ave}Vol^{\frac{4}{3}}{\omega}^{3}}. & & \displaystyle \nonumber\end{eqnarray}$

P _out is the output power of prototype; Y ₀ is the displacement amplitude of the prototype; ω is the angular frequency; 𝜌_ave and Vol are the average density and volume of the prototype.

Table 3

Performances of the three vibration energy harvester prototypes

Parameter	Axial magnetization transducer	Radial magnetization transducer	Halbach permanent magnet array transducer
Load∕Ω	42.2	53.64	64.51
Vol∕cm³	452.16	452.16	452.16
P _in∕mW	166.40	206.32	693.80
P _out∕mW	83.20	103.16	346.88
FoM _v∕%	0.41	0.50	1.67

The Halbach permanent magnets array transducer prototype has a higher FoM _v of 1.67%.

4. Conclusion

This paper proposed three types of magnetoelectric transducers to adapt the snake-like WEC that can harvest wave energy. In order to increase the power of WEC, lumped parameter equivalent magnetic circuit model of three types of magnetoelectric transducers is proposed. The static magnetic field modeling and construction parameter optimization are performed on this theoretical foundation. After calculating the optimal size ratio, finite element analysis is used to verify the lumped parameter equivalent magnetic circuit model, and the open circuit voltages are obtained. Finally, three prototypes are made in 1:5 ratio for experimentation. The experiments indicated that prototype with the Halbach permanent magnets array transducer could harvest vibration power of 693.80 mW when WEC at a relative velocity of 0.1 m/s, and P _out is 346.88 mW. The Halbach permanent magnets array transducer prototype has a higher FoM _v of 1.67%. The result of this experiment is superior to other two types. This type of WEC can be used in the ocean environment, and it also provides ideas for the snake-like WEC research.

Footnotes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant NO. 51675265), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). The authors gratefully acknowledge these supports and reviewers who given valuable suggestions.

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