1. Introduction
With rapid economic development and massive consumption of traditional fossil energy, tidal energy has gained a lot of attention due to its wide distribution, large reserves, renewability, and lack of contamination [
1,
2]. The tidal turbine, as a device for converting tidal energy into electrical energy, has been widely used. Its energy efficiency and hydrodynamic performance are determined by the blades. The foil, as a fundamental element of the tidal turbine blades, directly influences the hydrodynamic performance of the blades. Increasing the lift coefficient of the blade cross-sectional foil under conditions of equal inflow velocity and blade-swept area can effectively enhance the hydrodynamic performance of the blade. Over the years, various technological measures have been attempted to enhance foil performance, including leading-edge protuberances [
3], vortex generators [
4], and flaps [
5]. Among these, the Gurney flap has great potential for application due to its simple structural design.
The Gurney flap, initially used in racing car spoilers to enhance traction, is a small device installed perpendicular to the chord line on the pressure surface at the trailing edge of the blade to improve the foil’s performance [
6,
7,
8]. With advancing technology, Gurney flaps are now being applied to wind turbine blades to enhance their performance. Studies mainly investigate how Gurney flaps affect the performance of foils through numerical simulations and experiments.
Currently, researchers primarily concentrate on using numerical simulation studies to investigate the impact of the Gurney flap on the static performance of foils. Aramendia et al. [
9] developed an artificial neural network model based on the lift-to-drag ratio to predict the aerodynamic performance of foils, which could forecast the lift-to-drag ratio of foils with different heights of Gurney flaps. Mubassira et al. [
10] studied the effect of Gurney flap height on the aerodynamic performance of the NACA4312 foil. The research results indicated that, with an increase in height, both lift and drag increased, and a Gurney flap height of 1.5% chord length performed the best within the studied range. Sumaryada et al. [
11] examined the effects of different Gurney flap installation angles on the aerodynamic performance of the NACA4312 foil. After simulating the aerodynamic performance of the foil at different wind speeds, they found that, within the range of the installation angle studied, increasing the installation angle led to an increase in lift and a decrease in drag of the foil. Hao and Gao [
12] examined the influence of the shape of the Gurney flap on the aerodynamic performance of the S809 foil section of wind turbine blades. The results showed that the width of the rectangular Gurney flap had minimal impact on the foil’s performance, while the triangular flap was significantly more effective than the rectangular flap. Abdelrahman et al. [
13] investigated the effects of Gurney flaps of varying heights and quantities on the aerodynamic performance of the NACA0012 foil at different Reynolds numbers. The findings indicated that the Gurney flap enhanced the foil’s performance more at high Reynolds numbers, and double and triple flaps increased the lift-to-drag ratio at high angles of attack and low Reynolds numbers. Vadan and Srinivas [
14] investigated the impact of the length and installation position of the Gurney flap on the aerodynamic performance of the NACA 23112 airfoil. The study revealed that the Gurney flap can effectively enhance the performance of the airfoil, with the optimal configuration being a flap installed at the trailing edge of the airfoil with a height of 1% of the chord length. Tyagi et al. [
15] proposed an optimization framework for the Gurney flap on the NACA 0012 airfoil and significantly enhanced computational efficiency using the Radial Basis Function method. The results indicated that, within the range of their study, the optimal configuration for the Gurney flap was a height of 1.9% of the chord length with an installation angle of −58°. Besides static performance, some researchers have also explored the Gurney flap’s ability to improve the foil’s dynamic performance. Lee and Gerontakos [
16] examined the dynamic stall characteristics of a NACA0012 foil equipped with a Gurney flap, finding a beneficial impact of the Gurney flap on controlling the foil’s dynamic stall. Xie et al. [
17] studied the influence of the Gurney flap height on the energy capture performance of a flapping foil with Gurney flaps mounted on both surfaces of the NACA0012 foil. Research findings indicated that the lift and the maximum power coefficient increased as the height increased within the range of from 0 to 0.3 times the chord length. Masdari et al. [
18] examined how Gurney flap geometric parameters and foil oscillation parameters affect the aerodynamic performance during the pitching process of the NACA0012 foil. Numerical calculations revealed that the optimal height range was between 1% and 3.2% of the chord length. Furthermore, the lift coefficient to drag coefficient ratio was optimal when the Gurney flap was oriented at 90° to the chord direction, and increasing reduced frequency and oscillation amplitude led to an increase in the maximum lift coefficient. Zheng and Liu [
19] conducted a study employing an Improved Delayed Detached Eddy Simulation technique to assess the influence of serrated Gurney flaps on the aerodynamic characteristics of the NACA 0018 airfoil. The results elucidated that, at intermediate angles of attack, the serrated Gurney flaps exhibited a more significant enhancement in the airfoil’s aerodynamic efficiency.
Another aspect of investigating the influence of the Gurney flap on foil performance is through experimental research. Liebeck [
8] conducted the first experimental research on Gurney flaps and found that those within the range of from 1% to 2% of the chord length increased lift. The best lift enhancement was observed at a height of 1.25% of the chord length. Maughmer et al. [
20] conducted low-speed wind tunnel experiments on the S903 foil to investigate the impact of Gurney flaps’ height on foil performance. They discovered that a Gurney flap with a height of 2% chord length significantly increased the maximum lift coefficient of the foil. Chandrasekhara et al. [
21] conducted experimental analysis on foils using a combination of Gurney flap and leading-edge droop. They observed that employing a Gurney flap with a height of 1% chord length not only increased the lift of the foil but also resulted in a decrease in drag, thereby enhancing the aerodynamic performance of the foil. Cole et al. [
22] conducted wind tunnel experiments on five different foils, and the results indicated that the influence of the Gurney flap on aerodynamic performance is coupled, to some extent, with the geometric shape of the foil. Zhang et al. [
23] conducted wind tunnel experiments on wind turbine foils to investigate the lift enhancement effects of Gurney flaps of different heights. The results showed that a Gurney flap with a height of 1.5% chord length could provide the foil with a higher lift-to-drag ratio. Yang et al. [
24] also studied the effects of the height and width of Gurney flaps on aerodynamic performance, particularly under high turbulence intensity. They found that the height of the Gurney flap significantly affected aerodynamic performance, while the thickness had a small impact. Additionally, under extremely high turbulence levels, the influence of the Gurney flap on aerodynamic performance was minimal. Chandra et al. [
25] investigated the impact of Gurney flaps and vortex generators on the aerodynamic performance of the Eppler 423 foil. Their experimental results showed that a height of 2% chord length performed the best, but the simultaneous installation of Gurney flaps and vortex generators decreased the lift-to-drag ratio of the foil. Avivoli and Singh [
26] explored the aerodynamic effects of Gurney flaps on three different low-aspect-ratio wings through experimental studies. Their findings revealed that Gurney flaps effectively increase the maximum lift coefficient and stall angle by augmenting the pressure difference between the wing’s upper and lower surfaces, thereby enhancing the aerodynamic performance. Ivanković et al. [
27] conducted an experimental investigation into the influence of Gurney flaps and vortex generators on the aerodynamic characteristics of the NACA 0021 airfoil. The experimental results demonstrated that both Gurney flaps and vortex generators enhance the aerodynamic performance of the airfoil by increasing the maximum lift coefficient and reducing hysteresis, with larger Gurney flaps showing a more pronounced improvement.
In summary, the current research on Gurney flaps has mainly focused on the wind power field. There is relatively limited research on the optimized design of Gurney flaps considering the dynamic performance of the hydrofoil. Therefore, this study focuses on the S809 hydrofoil and combines multi-objective optimization algorithms with CFD numerical simulation technology to establish a multi-objective optimization design platform by quantifying the dynamic performance of hydrofoil. The aim is to optimize the structure of the hydrofoil with a Gurney flap to improve its dynamic performance by addressing the optimization challenge with a genetic algorithm and providing a reference for the optimization of tidal turbine performance.