Simulation Analysis and Experimental Study on Airfoil Optimization of Low-Velocity Turbine

Abstract

By combining computational fluid dynamics (CFD) and surrogate model method (SMM), the relationship between turbine performance and airfoil shape and flow characteristics at low flow rate is revealed. In this paper, the flow velocity tidal energy airfoil model is designed based on the Kriging model, and the original airfoil with a relative thickness of 12% and a relative curvature of 2.5% is obtained. The parameter optimization is carried out by setting the 4th CST equations through the surrogate model; the maximum lift-drag ratio is the optimization goal, the optimization design variable is 10, the maximum number of iterations is 100, and the maximum number of sub-optimization iterations is 200. The results show that the hydrodynamic performance of the airfoil with thinner thickness and more curvature is better, the maximum thickness part is shifted forward by 4.58%, and the lift-drag ratio is improved by 4.03%. The flow field and the efficiency are more stable, which provides an engineering reference for the optimal design of hydraulic turbine airfoils under low flow velocity. It supplements the research on the performance of turbine blades in low velocity.

1. Introduction

A hydraulic turbine is a machine that converts tidal energy into mechanical energy that is widely used in marine, renewable energy, and other fields. Hydraulic turbines are always divided into two categories: horizontal axis and vertical axis. At low flow velocities, horizontal axis turbines have high energy acquisition efficiency [1].

Airfoil optimization is mainly based on wind turbines, in terms of improving airfoil design. Fan et al. [2] modified the effect of the leading edge on turbine hydrodynamic characteristics and wake development characteristics, and the effect of the improved turbine on hydrodynamic performance and wake velocity distribution was investigated by using a channel test. Laurens et al. [3] designed a blade approaching the Bates limit on the basis of the blade momentum theory for wing sections. Gao et al. [4] investigated the performance of tidal current energy capture at low flow velocities by designing a composite blade, hoping to make better use of energy in low-velocity sea areas to solve the problems of startup. Bangga et al. [5] found that airfoil thickness is an important factor affecting the performance of rotors with high robustness. Yan et al. [6] studied the influence of swept design on the hydrodynamic function of airfoil blades. Jiao et al. [7] investigated the relationship between the positive and negative characteristics of the “S” type airfoil and the bi-directional pump through numerical calculations and experiments and found that a good airfoil shape can enhance the function of the blade and reduce energy loss. From the aspect of model algorithms, scholars have combined methods such as the surrogate model method (SMM), genetic algorithm (GA), and response surface method (RSM) with CFD to optimize the airfoil design. Du et al. [8] used a neural network combined with a surrogate model to design a fast reflective optimization framework that will be validated for the performance evaluation of airfoils. Tang et al. [9] combined SMM with GA to explore the non-stationary problem in the optimization of airfoil for cycloidal propellers (ACP). Sekar et al. [10] predicted the steady state field of incompressible laminar flow on an airfoil surface by a data-driven method based on a combination of deep convolutional neural network (CNN) and deep multilayer perceptron (MLP). Tao et al. [11] combined CFD with SMM, nested into GA, and achieved good results for robust optimization of airfoils. Raul et al. [12] accurately and efficiently retarded the adverse effects of airfoil power stall through aerodynamic shape optimization by proposing a surrogate-based model optimization technique. From the analysis of fluid flow in the vicinity of the airfoil, Liao et al. [13] summarized the relationship between the shape parameters of the blade and the aerodynamic performance using a multi-convolutional neural network with migration learning capability as a new surrogate model framework. Thuerey et al. [14] evaluated the accuracy of neural networks in calculating airfoil pressure and velocity distributions using a modernized U-net architecture. Chen et al. [15] numerically investigated the propeller-induced flow effect. Maalouly et al. [16] obtained that the transient response of the optimized turbine is faster and easier to control. Low flow velocity has a practical impact on the design and performance of a hydraulic turbine, and, at low flow velocity, the efficiency of turbine will be significantly reduced. Due to the decrease in flow velocity, the rotation speed of blades decreases, which leads to the decrease in turbine output power. Low flow rate may lead to unstable turbine operation. In some cases, the rotation of the turbine may be unstable, resulting in vibration or oscillation, which will not only reduce the performance of the turbine but also cause damage to it. These are closely related to the performance of hydraulic turbines.

Based on the above studies, the research on the utilization of tidal energy turbines is not common; the blade airfoils of turbines at low flow velocity with wide distribution are less often analyzed. In this paper, the low-flow tidal energy hydraulic turbine blade airfoils are studied, and new airfoils are proposed to be designed with thickness (t/c = 0–2.5%) and curvature (f/c = 10–15%) as independent variables. Through simulation calculations, in the range of flow velocity 0.5–0.8 m/s and incoming flow angle 0°–10°, the new 2D airfoil shape with lift-to-drag ratio as the objective function is determined. The relationship between airfoil shape and hydrodynamic performance is analyzed through experimental validation in order to find a better design range for the airfoil parameters. The purpose of this paper is to study the performance of turbine blades in low-velocity sea areas. By combining CFD with SMM, the relationship between blade shape, performance, and flow field in low-velocity sea areas is studied to improve the performance of turbines in low-velocity sea areas and increase the utilization of tidal energy.

2. Models and Meshes

2.1. Physical Model

The physical model of the blade is formed by the counterclockwise rotation of an asymmetric airfoil, with the airfoil thickness varying in the range t/c = 0–2.5%, the airfoil curvature varying in the range f/c = 10–15%, and the chord length is c. Thickness is the ratio of the maximum vertical diameter of the airfoil to the chord length c. Curvature is the ratio of the maximum tangent arc top height of the airfoil to the chord length c. The position of the blades in the turbine is shown in Figure 1. Figure 2 represents the geometry of the airfoil cross section as the thickness and curvature change.The length of rotation domain is r, and the length of the drainage basin is 15R. The grid generation adopts ICEM 2022R2. The grid type is a static domain structured grid, and the rotation domain is an unstructured grid. In the drawing, the outermost cylindrical surface and the upper and lower circular bottom surfaces are the interface where the rotation domain intersects with the static domain and where the hydraulic turbine is located. In order to help explain the grid diagram of the rotation domain, as shown in Figure 3, the number of grid units is 2,238,392, and the number of nodes is 407,312. The expansion option is smooth transition, and the transition ratio is 0.272.

Considering the efficiency of the turbine, the tip speed ratio ${\lambda }_0$ is taken as 3, the number of blades B is taken as 5, and the blades have good startability; the specific parameters are shown in

Table 1. Overall design parameters of the hydraulic turbine.

Power P/W	30.00	Tip speed ratio (${\lambda }_0$)	3.00
Blade number B	5.00	The radius of impeller R/m	0.32
Energy efficiency $C_P$	0.35	Wheel radius rhub/m	0.08
Fluid velocity V/m·s−1	0.50–0.80	Rotational speed n/r·min−1	150.00

. The airfoil chord length and torsion angle of the blade along the airfoil spread direction are optimized by the Wilson method [17], and the airfoil length is 0.32 m. The energy acquisition efficiency is related to the overall parameters as follows:

$$C_p=\frac{P}{0.5V^3\pi R^2}$$

(1)

$$C_t=\frac{T}{0.5V^2\pi R^2}$$

(2)

where $C_P$ is the energy acquisition efficiency, $C_t$ is the thrust coefficient, P is the rated power, T is the axial thrust, $\rho$ is the density, V is the incoming velocity, which is a constant, and R is the impeller radius.

2.2. Mathematical Model and Mesh Independence Verification

In this paper, ANSYS 21R2 is used for numerical simulation, and the flow field is set as a three-dimensional incompressible steady-state viscous turbulent field; the medium is water, the flow velocity is 0.5–0.8 m/s, the turbulence level is 5%, and the turbulent viscosity ratio is 10. 2D mesh division, as shown in Figure 4. Figure 5 shows the computational model of this paper with the blade placed in the rotation domain. The grid generation software for the two-dimensional grid is Pointwise, the field is 1m, and the grid structure is C-grid, C-grid. The grid can better fit the leading edge curvature of the airfoil without generating singular points. In addition, the C-grid is natural, and the encrypted trailing edge grid is beneficial to capture the wake shape. The far field behind the calculation domain is 20 times the chord length, and the far fields above, below, and in front are all 10 times the chord length, y += 1, and the grid growth rate of the boundary layer is 1.1.

The flow field is incompressible, and the coefficient of viscosity is constant. The continuity equation of the fluid is obtained as:

$$\frac{\partial u^i}{\partial x_t}=0$$

(3)

The momentum equation is:

$$\frac{\partial u_i}{\partial t}+\frac{\partial u_i{u}_j}{\partial x}=-\frac{1}{\rho }\frac{\partial \rho }{\partial x_i}+\upsilon \frac{\partial }{\partial x_j}(\frac{\partial u^i}{\partial x_j})$$

(4)

The solution is based on velocity and pressure coupling using the COUPLED algorithm, the discretization is in standard form, and the second-order windward is selected; the details are in

Table 2. Simulation settings.

Parameters	Model
Turbulence model	Realizable k-$\epsilon$
Solution method	Coupled
Spatial discrete gradient	Least squares cell-based
Spatial discrete pressure	Second order
Discrete momentum in space	Second-order upwind
Spatial discrete turbulent kinetic energy	Second-order upwind
Spatial dispersion ratio dissipation rate	Second-order upwind
Convergence criterion	1 $\times {10}^{-6}$

.

Compared with the general model, the realizable k-$ϵ$ model provides higher precision and accuracy in simulating complex flow and separated flow. At low velocity, it can better deal with the boundary layer and separation region and better simulate the flow characteristics near the wall. The COUPLED algorithm is used to solve Navier–Stokes equations simultaneously. Because of the implicit scheme, the calculation accuracy and convergence are better than the explicit method. The algorithm can solve the whole velocity range, that is, from low-speed flow to high-speed flow. This makes it more flexible and adaptable when dealing with flows in different speed ranges. The least squares cell-based gradient calculation method reconstructs the accurate value of the linear function at the node from the central value of the surrounding cells on any unstructured grid by solving the constraint minimization problem, and it maintains the second-order spatial accuracy. The accuracy of this method is higher than that of gradient based on element, and, at low flow rate, the flow may become very complicated, including separation, turbulence, and other phenomena. The second-order upwind scheme can better deal with these complex flow characteristics and provide more accurate simulation results.

The k-equation is:

$$\frac{\partial \left(\rho K\right)}{\partial t}+\frac{\partial \left(\rho {\overline{u}}_{j}K\right)}{\partial x_j}=\frac{\partial }{\partial x_j}[(\mu +\frac{{\mu }_t}{P_{\tau K}})\frac{\partial K}{\partial x_j}]+P_K+G_b-\rho \epsilon -Y_M$$

(5)

The $\epsilon$-equation is:

$$\frac{\partial \left(\rho \epsilon \right)}{\partial t}+\frac{\partial \left(\rho {\overline{u}}_j\epsilon \right)}{\partial x_j}=\frac{\partial }{\partial x_j}[(\mu +\frac{{\mu }_t}{P_{\tau \epsilon }})\frac{\partial \epsilon }{\partial x_j}]+\rho C_1\overline{S}\epsilon -G_2\rho \frac{{\epsilon }^2}{K+\sqrt{\nu \epsilon }}+C_{\epsilon 1}\frac{\epsilon }{K}{C}_{\epsilon 3}{G}_b$$

(6)

In the general design range, the original airfoil is designed according to the combination of initial airfoil thickness and curvature [18]. We set the boundary condition type of the fluid inlet as velocity inlet, with the size of 0.5–0.8 m/s, and the medium is water. The outlet boundary condition type is pressure outlet, and the relative atmospheric pressure is 0 Pa. Blades and hub are set as non-slip boundary conditions, and the side boundary condition type of static domain is a wall boundary. The interface boundary condition is set between rotating domain and stationary domain. The flow rates are 0.5 m/s, 0.6 m/s, 0.7 m/s, and 0.8 m/s, respectively, and the y += 1; the estimated wall distance is $3.9\times {10}^{-5}$ m, $3.3\times {10}^{-5}$ m, $2.9\times {10}^{-5}$ m, and $2.5\times {10}^{-5}$ m.

As shown in

Table 3. Effect of mesh on ($C_P$) and P.

Mesh	QUADS	CP	P
D1	1,790,713	0.34259	29.9205
D2	2,238,392	0.34301	29.9311
D3	2,686,070	0.33951	29.7943

, three sets of grids, D1, D2, and D3, are used to validate the grids, the maximum difference in the energy acquisition efficiency is at 1.021%, and the maximum difference in the power is at 0.457%, which verifies the grid independence and indicates the reliability of the calculation results.

A suitable mathematical model is used to optimize the airfoil instead of the real objective function, which is called the surrogate model method. The Kriging model adopted in this paper often deals with nonlinear problems in engineering [18]. To construct the surrogate model, the sample space is sampled, and, in this paper, Latin hypercube sampling [19] is chosen, which can obtain more comprehensive spatial information with fewer points. The addition is performed according to the LCB addition criterion, using a 4th CST parameterization [20] to optimize 10 design variables, a maximum number of iterations of 100, and a maximum number of sub-optimization iterations of 200. The CST method is used to represent the geometric coordinates of the airfoil, and the upper surface equations are:

$$y_u=C_x·S_{u\left(x\right)}+x·y_{TEu}$$

(7)

The lower surface equations are:

$$y_l=C_x·S_{l\left(x\right)}+x·y_{TEl}$$

(8)

where $y_{TEu}$ and $y_{TEl}$ denote the y-coordinates of the trailing edges of the upper and lower surfaces, respectively. The type function $C_{\left(x\right)}$ is defined as follows:

$$C_{\left(x\right)}=x^{N1}·{(1-x)}^{N2}$$

(9)

The function $S_{\left(x\right)}$ is defined as follows:

$$S_u\left(x\right)={\sum }_{i=0}^N{A}_{ui}·S_i\left(x\right)$$

(10)

$$S_l\left(x\right)={\sum }_{i=0}^N{A}_{li}·S_i\left(x\right)$$

(11)

$$S_i\left(x\right)=\frac{N!}{i!(N-i)!}{x}^i{(1-x)}^{N-i}$$

(12)

Generally, the airfoils N1 and N2 are taken as 0.5 and 1.0, respectively, in equation; $A_{ui}$ and $A_{li}$ are the coefficients to be determined, and $S_i\left(x\right)$ is the Burstein polynomial. From the above defining equation, it is seen that the geometry of the airfoil is determined by determining the coefficients $A_{ui}$ and $A_{li}$, where $n_{up}$ and $n_{low}$ represent the number of coordinates of the upper and lower surfaces of the airfoil. The term $A_0$, as the first term of the undetermined coefficient, affects the leading edge radius of airfoil, so that $A_{u0}=-A_{lo}$ makes the upper and lower surface radii of the airfoil at the leading edge the same. The Kriging model can be expressed in the following mathematical form:

$$S_l\left(x\right)={\sum }_{i=0}^N{A}_{li}·S_i\left(x\right)$$

(13)

An expression for the weighting factor $\omega$ needs to be given to obtain the predicted values in the design space. Consider the unknown function as a Gaussian static random process defined as:

$$Y\left(x\right)={\beta }_0+Z\left(x\right)$$

(14)

where ${\beta }_0$ is the unknown constant, also referred to as the global trend model, which denotes the mathematical expectation of Y(x). Additionally, $Z(•)$ signifies a static stochastic process with zero mean and variance ${\sigma }^2$(${\sigma }^2$(x) = ${\sigma }^2$, ∀ x).

This covariance can be expressed as follows:

$$Cov[Z\left(x\right),Z\left(x^{\prime }\right)]={\sigma }^{2}R(x,x^{\prime })$$

(15)

The correlation function, R(x,x′), exhibits a value of 1 at a distance of 0 and approaches 0 as the distance approaches infinity. Additionally, x displays a decrease in correlation as the distance increases. The 2D airfoil is the optimization object. The maximum lift–drag ratio is the objective function, and the maximum thickness, camber, and leading edge radius of the airfoil are constrained. The fourth-order CST parameterization is adopted, and the optimal number of design variables is 10. The maximum number of iterations is 100, and the maximum number of sub-optimization iterations is 200. In the optimization process, the initial sample points are extracted by the Latin hypercube method. According to the LCB plus-point criterion, the adopted proxy model is a Kriging proxy model without gradient as the approximate model of high-precision CFD performance analysis. The design space is sampled experimentally and simulated to obtain the response value, and the initial model is established. Under the LCB plus-point criterion, the corresponding sub-optimization questions are solved to obtain the predicted optimal solution, and new data are added to the existing dataset until the sample point sequence converges to the local or global optimal solution.

3. Results And Discussion

3.1. Airfoil Hydrodynamic Simulation Results and Experimental Verification

The Kriging model is used to optimize the airfoil, and the optimized 2D airfoil is shown in Figure 6. Through the simulation of the optimized airfoil, the change rules of the pressure field and velocity field on the surface of the airfoil are investigated, and the lift–drag ratio and lift force of the optimized airfoil are analyzed at the same time.

The pressure nephograms of the optimized airfoil and the multi-point optimized airfoil are shown in Figure 7 and Figure 8. Comparatively speaking, the negative pressure area on the upper surface of the optimized airfoil is obviously smaller than that of the original airfoil, which also leads to a larger lift coefficient of the optimized airfoil and a smoother pressure gradient at the trailing edge of the optimized airfoil. It reflects that the optimized airfoil leading edge surface is attached to the flow without separation, and the trailing edge trailing edge region of the airfoil is extremely thin. From Figure 9, it can be concluded that, after optimization, the lift–drag ratio of the airfoil is significantly improved because the pressure difference between upper and lower is more obvious.

Figure 10 and Figure 11 show that the flow velocity above within the wake region is reduced by the separation effect, the flow velocity on the upper surface decreases slightly, and the guidance of the fluid on the upper surface is weakened. The intensity of turbulence increases below the wake region, and the flow velocity on the lower surface increases. As a result, the pressure difference between the upper and lower surfaces of the airfoil increases. The lift also increases. From Figure 12, it can be concluded that, after optimization, the lift of the airfoil is significantly improved because of the more obvious difference between the upper and lower speeds.

Figure 13 shows the comparison of lift–drag ratio between the original airfoil and optimized airfoil in the low-flow range, which shows that the best lift–drag ratio of the original airfoil is 109.39. The best lift–drag ratio of the optimized airfoil is 113.80, which is an improvement of 4.03%, and the optimized airfoil has a significantly better lift–drag ratio than that of the original airfoil.

As shown in Figure 14, in the comparison between the lift of the original airfoil and the optimized airfoil in the low flow range, the maximum lift of the original airfoil is 308.38 N. The maximum lift of the optimized airfoil is 419.97 N, and the average lift is 26%. The maximum lift of the optimized airfoil is 419.97 N, with an average increase of 26.54%. The lift of the optimized airfoil is significantly better than that of the original airfoil, reflecting that the optimized airfoil can provide more lift and less drag.

In addition, this paper carries out the experimental verification of the lift force. An experimental platform was built, as shown in Figure 15a, using a 60CST-M00630 asynchronous motor (Okoda, Changzhou, China) and a XDS100v2 simulator (Ickey, Shanghai, China), controlling the flow rate of the water tank at 0.5–0.8 m/s, printing the 0.1 m airfoils, fixtures, and part of the structural parts with an ANYCUBIC PHOTON MONO X 3D printer (ANYCUBIC, Shenzhen, China), and curing them with a light curing machine. The lift force was measured by a tensiometer, the flow rate was measured by an LS300A flow meter (JINSHUI HUAYU, Weifang, China), the printing material was transparent resin, and the experimental process is shown in Figure 15b. Compared with the simulation results, the average error is 4.076%, and the data comparison is shown in Figure 16, which illustrates the reliability of the simulation results. The average error observed in the experimental verification may be related to the experimental conditions, the limitation of the number of samples, and other reasons. Optimization of the experimental equipment, an increase in the number of samples, and comparative analysis and other methods can help us evaluate the performance of turbine airfoil design more accurately.

3.2. Blade Hydrodynamic Performance

The airfoil lift with bending and thickness is shown in Figure 17a; a numerical simulation of the optimized blade after twisting by the Wilson method shows that the blade varies with the wingspan chord length and twist angle, as shown in Figure 17b. Lift shows a tendency to increase and then decrease with increasing thickness; the maximum lift is 30.259% higher than the average lift, lift increases with increasing curvature, and the maximum lift is 21.491% higher than the average lift. When the thickness is more than t/c = 12%, lift begins to decrease, mainly due to the trailing edge separation effect of the airfoil. The overall hydrodynamic performance of the turbine is improved by optimizing the lift–drag ratio and lift of the airfoil.

The pressure field, velocity field, and streamline of the blade are reflected in Figure 18, Figure 19, Figure 20 and Figure 21. The figures show that the pressure at the blade tip is higher than that at the blade root, and the speed near the blade tip is faster. In the 3D simulation, the moving reference system model is used in the area around the turbine rotor, and the the calculations were stationary. The rotating speed of the blades is 150 r/min; the tip speed ratio is 3.

Combined with the above characteristics of low velocity flow field, it can be seen that the pressure change trends are basically the same, and the impeller blades also have a certain positive and negative pressure difference. The pressure difference of the optimized impeller is greater than that before optimization, so the output power is also greater. As for the velocity, the incoming velocity begins to decrease at the upstream of the impeller, but the decreasing gradient is small. Due to the rotation of the blades, the water velocity behind the impeller drops sharply, and the velocity loss behind the blades is obvious. The speed at the blade root is slow, and the speed outside the blade tip is affected by the obstruction effect, even exceeding the speed when it comes. At the same time, it is suggested that the existence of vortex will reduce the instantaneous torque near the blade tip. The tip vortex will gradually fall off during the rotation, which will affect the internal flow field of the turbine. Due to the influence of tip vortex in the blade deployment direction, the flow separation near the upstream tip will be weakened during the rotation process.

4. Conclusions

Based on the results above, optimizing the airfoil shape is critical for turbine blade performance enhancement, which is of great research significance. In this paper, using the airfoil at the maximum lift as the optimization object, through the simulation and analysis of two-dimensional and three-dimensional blade airfoil velocity and pressure fields, the influence of the airfoil thickness of 10–15% and the curvature of 0–2.5% on the hydrodynamic performance of the turbine as well as the energy efficiency was investigated, and the following conclusions are obtained:

(1) The thinner and more curved airfoils provide greater lift, the maximum lift of the airfoil with 12% thickness is 30.259% higher than the average lift, and the maximum lift of the airfoil with 2.5% curvature is 21.491% higher than the average lift. As the thickness of the airfoil increases (t/c > 12%), the thicker radius of the leading edge of the airfoil does not result in leading edge separation, and the trailing edge of the airfoil has a separation effect, resulting in a decrease in the lift, whereas with the increase in the curvature of the airfoil (f/c = 10–15%), the lift of the airfoil increases. After increasing the radius of the leading edge, decreasing the thickness, and increasing the curvature, the velocity difference between the upper and lower surfaces increases. According to Bernoulli’s principle, the pressure difference between the upper and lower surfaces increases, which in turn improves the lift and the maximum lift–drag ratio.

(2) After the optimization of the airfoil, the leading edge radius increased, the maximum thickness point was moved forward, the lift-to-drag ratio increased by 4.03%, and the lift increased by 26.54% on average. This indicates that the optimized airfoil has a higher lift-to-drag ratio and more lift, while the pressure distribution on the upper and lower surfaces is more uniform.

(3) With the optimized airfoil, the flow field of the turbine is stable, the speed loss at the rear of the blade is obvious, the speed at the root of the blade is small, and the speed at the outside of the blade tip is increased due to the blocking effect, even exceeding the incoming flow speed. With the increase in speed, the tip vortex gradually falls off, which affects the internal flow field of the turbine, resulting in the weakening of the flow separation near the upstream tip during the rotation process. The optimized airfoil has no obvious vortex shedding, which reduces the impact on the downstream flow field environment. Less vortex shedding makes the impeller absorb more energy from the flow.

In this paper, under the relatively small approach angle, the relatively thin airfoil with large leading edge radius and high bending degree is optimized, and excellent hydrodynamic performance can be obtained. The results show that the optimized airfoil can provide larger lift and lift–drag ratio in the conventional angle range, and the flow field is more stable, reducing the impact on the downstream flow field environment. The efficiency of the turbine and the stability of obtaining energy in the low speed range are improved. The stability of flow field directly affects the performance of the turbine. Under the condition of low flow rate, the change of velocity and pressure is more intense, which leads to the instability of the flow field. This instability may lead to vibration, excessive wear, and even fracture of turbine blades, thus reducing the efficiency and reliability of the turbine. Therefore, optimizing the flow field is very important. In addition, the later flow field optimization is not only a fine-tuning of the existing design, but also an iterative and feedback process. By testing the turbine under actual working conditions, we can continuously obtain new data and experience, and we can further adjust and optimize the flow field. In the future, designing new shapes and adopting new materials at the tip can reduce the stress concentration and friction resistance at the tip, thus reducing the generation of tip vortex. Active flow control or passive flow control can also be used to effectively restrain or guide the generation of tip vortex, thus improving the efficiency of turbine. This paper also has limitations. The experimental conditions may not fully simulate the real marine environment, which may affect the accuracy of the results. In addition, the performance evaluation and stability analysis of long-term operation also need further study. Although this research has some limitations, it has important practical significance for the design and operation of tidal energy turbines, and it also has certain universal applicability to other types of turbines.

In addition, the performance evaluation and stability analysis of long-term operation also need further study. In the future, the parameters such as overlap ratio can be further optimized for turbines in low-speed sea areas, and the shapes of different parts such as blade tips can be designed to further improve the optimization effect of turbines.