Airfoil profile coupling optimization method based on vortex generator flow control and profile optimization

Abstract

The invention relates to the technical field of aerodynamic optimization of wind turbine airfoils, and particularly discloses an airfoil coupling optimization method based on vortex generator flow control and molded line optimization, which comprises the following steps: S1, determining design variables and corresponding value ranges according to task requirements, and generating an initial sample point set; s2, generating airfoil geometry according to the initial sample point set; s3, performing CFD simulation on each airfoil geometry to obtain a training data set; step S4, constructing a Kriging agent model based on the training data set; s5, taking the Kriging agent model as a fitness evaluation function, and performing global optimization search in the budget design space by adopting a particle swarm optimization algorithm to obtain an optimal design parameter combination; s6, CFD verification is conducted on the optimal design parameter combination, and the optimal design parameter combination with the verification result meeting the preset precision and performance requirements serves as a final scheme to be output. According to the method, the limitation that airfoil optimization and VG flow control are mutually independent and a synergistic effect is not considered is solved.

Description

Technical Field

[0001] This invention relates to the field of wind turbine airfoil aerodynamic optimization technology, specifically to an airfoil coupling optimization method based on vortex generator flow control and profile optimization. Background Technology

[0002] As the core component for capturing wind energy, the aerodynamic performance of wind turbine blades directly determines the energy conversion efficiency of the wind turbine. Airfoil design is the foundation of blade design; a well-designed airfoil can significantly improve the blade's wind energy capture efficiency. Furthermore, under complex operating conditions, boundary layer separation often occurs on the blade surface, leading to a significant decrease in aerodynamic efficiency and affecting energy conversion efficiency. To mitigate this phenomenon, vortex generators, as a highly efficient passive flow control technology, are widely used.

[0003] Currently, scholars both domestically and internationally have made a series of advances in wind turbine airfoil optimization and vortex generator (VG) flow control. In current research, airfoil optimization and VG flow control are typically considered two independent design phases. Existing research either focuses on optimizing airfoil geometry through parametric methods or emphasizes the effect of VG parameters on suppressing flow separation, with few methods combining the two for coupled optimization. This design approach fails to consider the interaction between the airfoil profile and the VG device, making it difficult to achieve optimal global aerodynamic performance. Therefore, an integrated design method capable of synergistically optimizing airfoil profile and VG parameters is urgently needed to address the lack of coupled design in existing technologies. Considering that coupled optimization design is a multi-parameter, nonlinear problem, traditional optimization methods are insufficient to meet the coupling optimization conditions. Direct optimization methods couple the optimization algorithm directly with the CFD solver. Since each fitness assessment requires an expensive CFD calculation, the optimization process is time-consuming and computationally costly. Gradient optimization methods rely on the gradient information of the objective function with respect to design variables; for strongly nonlinear problems in this field, they are prone to getting trapped in local optima, and calculating the gradient itself requires multiple CFD calculations. Simple surrogate model methods use simple models such as polynomial response surfaces, which struggle to accurately fit the complex nonlinear flow field response of VGs coupled with the airfoil, resulting in low reliability of the optimization results. Therefore, there is an urgent need for an airfoil coupling method that combines a surrogate model with an optimization algorithm for surface flow control of a vortex generator and airfoil profile optimization. Summary of the Invention

[0004] To address the aforementioned problems, the purpose of this invention is to provide an airfoil coupling optimization method based on vortex generator flow control and profile optimization, overcoming the limitations of airfoil optimization and VG flow control being independent and failing to consider synergistic effects. This invention provides an airfoil coupling optimization method based on vortex generator flow control and profile optimization, comprising: Step S1: Obtain the task requirements, determine the design variables and their corresponding value ranges according to the task requirements, and generate an initial sample point set according to the design variables and their corresponding value ranges. Step S2: Generate airfoil geometry based on the initial sample point set; Step S3: Perform CFD simulation on each of the airfoil geometries to obtain a training dataset; the training dataset includes: lift coefficient and lift-to-drag ratio considering the vortex generator under the airfoil geometry; Step S4: Construct a Kriging proxy model based on the training dataset; Step S5: Using the Kriging surrogate model as the fitness evaluation function, the particle swarm optimization algorithm is used to perform a global optimization search in the budget design space to obtain the optimal combination of design parameters. Step S6: Perform CFD verification on the optimal design parameter combination, and output the optimal design parameter combination whose verification results meet the preset accuracy and performance requirements as the final solution.

[0005] In one possible implementation, the design variables include: airfoil geometry parameters and vortex generator parameters; The airfoil geometric parameters include: a class function parameter controlling the leading edge radius, a class function parameter controlling the trailing edge shape, and multiple control points; The parameters of the eddy current generator include: height, length, and position.

[0006] In one possible implementation, step S1 includes: An initial sample point set is generated based on the design variables and their corresponding value ranges, and the initial sample point set is generated using the Latin hypercube sampling method.

[0007] In one possible implementation, step S2 further includes: Based on the initial sample point set, the airfoil geometry is generated using the CST parameterization method.

[0008] In one possible implementation, the CST parameterization method includes: shape functions and class functions.

[0009] In one possible implementation, the shape function is expressed according to the following formula. : in, As control points, Let be the order of the curve fitting. For chord coordinates.

[0010] In one possible implementation, the class function is represented by the following formula. : in, For chord coordinates, To control the leading edge radius, a class of function parameters, Functional parameters for controlling the shape of the trailing edge.

[0011] In one possible implementation, step S4 includes: A Kriging proxy model to be validated is constructed based on the training dataset, and the accuracy of the Kriging proxy model to be validated is evaluated using cross-validation. When the accuracy assessment is passed, the Kriging proxy model to be verified that has passed the accuracy assessment will be used as the Kriging proxy model.

[0012] In one possible implementation, step S4 further includes: When the accuracy assessment fails, the airfoil geometry is regenerated based on the preset constraints of airfoil optimization and the initial sample point set.

[0013] In one possible implementation, step S6 includes: When the verification results do not meet the preset accuracy or performance requirements, the verification points and their calculation results are added to the training dataset to update the Kriging surrogate model, and a new optimal design parameter combination is obtained by performing a global optimization search in the budget design space.

[0014] This invention provides an airfoil coupling optimization method based on vortex generator flow control and profile optimization. It integrates airfoil surface parameters and VG parameters, generating an initial sample set using Latin hypercube sampling. The airfoil is then optimized using the CST parameterization method, adjusting surface features such as leading-edge radius and thickness distribution. A parameterized VG model is constructed using the momentum source term method, and computational fluid dynamics (CFD) simulations are performed to obtain lift coefficients and lift-to-drag ratios to build a training dataset. Based on this dataset, a Kriging surrogate model is constructed, and iterative optimization is performed using a particle swarm optimization algorithm. The results demonstrate that coupled optimization provides better aerodynamic performance and maintains good flow control compared to optimizing the airfoil alone or only optimizing the VG. This method has high applicability and can provide an effective technical approach for the collaborative design of various airfoils and VG devices. Attached Figure Description

[0015] Figure 1 A schematic flowchart of the airfoil coupling optimization method provided in an embodiment of the present invention; Figure 2 A comparison diagram of the aerodynamic shape before and after airfoil optimization is provided for embodiments of the present invention; Figures 3(a) and 3(b) are schematic diagrams of optimized airfoil mesh generation provided by an embodiment of the present invention; Figure 4(a) is a schematic diagram of parameter sensitivity analysis provided by an embodiment of the present invention; Figure 4(b) is a schematic diagram of the cumulative importance analysis provided by an embodiment of the present invention; Figure 5(a) is a schematic diagram of the determination coefficient R2 analysis provided by an embodiment of the present invention; Figure 5(b) is a schematic diagram of residual analysis provided by an embodiment of the present invention; Figure 6 A schematic diagram of coupled optimized lift coefficient for airfoil optimization considering VG flow control, provided for an embodiment of the present invention; Figure 7 A schematic diagram of coupled optimized lift-to-drag ratio considering VG flow control for airfoil optimization provided as an embodiment of the present invention; Figure 8 A comparative diagram of lift coefficients for various optimization schemes provided in embodiments of the present invention; Figure 9 A comparative diagram of the boost-to-drag ratio of various optimization schemes provided in the embodiments of the present invention; Figure 10(a) is a streamline diagram of the original airfoil with added vortex generator provided in an embodiment of the present invention; Figure 10(b) is a streamline diagram of the eddy current generator parameter optimization scheme provided by an embodiment of the present invention; Figure 10(c) is a streamline diagram of the airfoil parameter optimization scheme provided by an embodiment of the present invention; Figure 10(d) is a streamline diagram of the coupling optimization scheme provided in the embodiment of the present invention. Detailed Implementation

[0016] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. The following detailed description of the embodiments and the accompanying drawings are used to illustrate the principles of the present invention by way of example, but should not be used to limit the scope of the present invention. That is, the present invention is not limited to the described preferred embodiments, and the scope of the present invention is defined by the claims.

[0017] In the description of this invention, it should be noted that, unless otherwise stated, "a plurality of" means two or more; the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance; those skilled in the art can understand the specific meaning of the above terms in this invention as appropriate.

[0018] This invention overcomes the limitations of existing technologies that design airfoil profile optimization and VG flow control independently, providing an airfoil-VG coupled design method based on a surrogate model and optimization algorithm. Compared with traditional methods that "optimize the airfoil first, then add VG" or "keep the original airfoil and only optimize VG," the coupled optimization method proposed in this invention has the following significant advantages: First, this invention achieves deep synergy between aerodynamic shape and flow control by simultaneously optimizing 23 design variables, including airfoil profile and VG. This coupled design method can effectively capture the nonlinear interaction between airfoil geometry and VG, overcoming the suboptimal solution problem caused by neglecting coupling effects in step-by-step optimization. Second, this method uses a Kriging surrogate model to replace computationally expensive CFD direct optimization, constructs a high-precision approximate model through intelligent sampling, and combines it with a particle swarm optimization algorithm for efficient global search. This technical approach further reduces computational costs while ensuring optimization accuracy, solving the computational bottleneck problem in multi-parameter coupled optimization.

[0019] Figure 1 A flowchart illustrating the airfoil coupling optimization method provided in an embodiment of the present invention is shown below. Figure 1 As shown, this invention provides an airfoil coupling optimization method based on vortex generator flow control and profile optimization, comprising: Step S1: Obtain the task requirements, determine the design variables and their corresponding value ranges based on the task requirements, and generate an initial sample point set based on the design variables and their corresponding value ranges. In one possible implementation, an initial sample point set is generated based on the design variables and their corresponding value ranges, using a Latin hypercube sampling method. This ensemble sampling strategy ensures a comprehensive exploration of the design space, laying the foundation for coupled optimization.

[0020] The design variables include: airfoil geometry parameters and vortex generator parameters; the airfoil geometry parameters include: function-like parameters controlling the leading edge radius, function-like parameters controlling the trailing edge shape, and multiple control points; the vortex generator parameters include: height, length, and position.

[0021] Step S2: Generate airfoil geometry based on the initial sample point set; In one possible implementation, the airfoil geometry is generated using the CST parameterization method based on an initial set of sample points. The CST parameterization method includes shape functions and class functions. The shape functions are based on Bernstein polynomials and accurately characterize the upper and lower surface profiles of the airfoil by adjusting the coefficients.

[0022] The airfoil surface features, including leading edge radius, thickness distribution, and trailing edge shape, are adjusted using shape functions and class functions, and optimized airfoil coordinate points are generated. The generated airfoil coordinate points are then imported into Pointwise software to complete the mesh generation of the airfoil, resulting in a .cas format mesh file. A hybrid meshing strategy is used, with a structured mesh in the airfoil boundary layer region and an unstructured mesh in the far field region to ensure computational accuracy and efficiency.

[0023] The shape function can be expressed by the following formula. Where, in the formula, and The parameters are as required. This process only optimizes the geometry of the airfoil, adjusting the leading edge radius, thickness distribution, and trailing edge shape while keeping the maximum thickness constant, generating the optimized airfoil, and then exporting the coordinate points of the generated airfoil.

[0024] The shape function can be expressed by the following formula. : in, As control points, Let be the order of the curve fitting. For chord coordinates.

[0025] The airfoil's upper surface profile is represented by the following formula: The lower surface profile of the airfoil can be represented by the following formula: In the formula, The upper surface of the airfoil This refers to the lower surface of the airfoil. Let be the y-coordinate of the trailing edge of the upper and lower surfaces. Let y be the y-coordinate of the trailing edge of the lower surface.

[0026] The class function is represented by the following formula. : in, For chord coordinates, To control the leading edge radius, a class of function parameters, Functional parameters for controlling the shape of the trailing edge.

[0027] Step S3: Perform CFD simulation on each airfoil geometry to obtain the training dataset; In one possible implementation, a parametric VG model is constructed using the momentum source term method, defining the VG's geometry and installation location in the form of momentum source terms. CFD calculations are performed using PHengLEI software, and the calculated lift coefficient and lift-to-drag ratio form the training dataset.

[0028] In one example, the exported airfoil coordinates are imported into Pointwise software for mesh generation. Pointwise's script recording function is used to record a script. Subsequent mesh generation after airfoil changes can be automated using the script. The mesh is a hybrid mesh: the airfoil boundary layer mesh is structured, and the far field mesh is unstructured. The exported mesh file is in .cas format. In PHengLEI software, code is added and compiled to add the vortex generator parameterized model to the Navier-Stokes equations using the source term method, defining the VG's geometry and mounting location as momentum source terms. CFD calculations are then performed to obtain the lift coefficient and lift-to-drag ratio for this airfoil considering vortex generator flow control, forming a training dataset.

[0029] The training dataset includes lift coefficient and lift-to-drag ratio considering vortex generators under airfoil geometry.

[0030] Step S4: Construct the Kriging agent model based on the training dataset; In one possible implementation, a Kriging surrogate model to be validated is constructed based on the training dataset, and a cross-validation method is used to evaluate the accuracy of the Kriging surrogate model to be validated. When the accuracy evaluation is passed, the Kriging surrogate model to be validated that passed the accuracy evaluation is used as the Kriging surrogate model. When the accuracy evaluation is failed, the airfoil geometry is regenerated based on the preset constraints of airfoil optimization and the initial sample point set.

[0031] In one possible implementation, the correlation coefficient matrix of the Kriging surrogate model is constructed using an anisotropic Gaussian correlation function, which takes the form: in, For the first The relevant parameters of each design variable are optimized using the maximum likelihood estimation method.

[0032] Step S5: Using the Kriging surrogate model as the fitness evaluation function, the particle swarm optimization algorithm is used to perform a global optimization search in the budget design space to obtain the optimal combination of design parameters. Step S6: Perform CFD verification on the optimal design parameter combination, and output the optimal design parameter combination whose verification results meet the preset accuracy and performance requirements as the final solution.

[0033] In one possible implementation, when the verification results do not meet the preset accuracy or performance requirements, the verification points and their calculation results are added to the training dataset to update the Kriging surrogate model, and a new optimal design parameter combination is obtained by performing a global optimization search in the budget design space.

[0034] Specifically, the Kriging model update adopts an adaptive sampling method based on the expectation boosting criterion. The process selects the most valuable sample points through iteration. In each iteration, the Kriging surrogate model is constructed and updated using existing CFD sample data, the expectation boosting function EI(x) is calculated, and the point xnew that maximizes EI(x) is found through an optimization algorithm. After performing CFD calculations on xnew, the new data is added to the training set to update the model. This process is repeated until convergence, thereby efficiently approximating the global optimum with minimal computational cost.

[0035] Example 1 This embodiment uses a wind turbine-specific airfoil (such as the DU97-W-300 airfoil) as the initial airfoil and applies the airfoil coupling optimization method of this invention. The optimization objective is to improve the lift-to-drag ratio of the airfoil while suppressing boundary layer separation. The specific steps are as follows: Design variables were determined and an initial sample point set was generated: airfoil geometry parameters included N1 and N2 for the suction and pressure surfaces, as well as 16 control points; vortex generator (VG) parameters included length, height, and position. A Latin hypercube sampling (LHS) method was used to generate a set of 200 initial sample points within the design space to ensure uniform coverage and avoid clustering. The sampling process was implemented using a Python script, generating a sample matrix containing all combinations of design variables.

[0036] The CST parameterization method is represented using the Python programming language. The shape function S(x) adopts Bernstein polynomial basis functions with an order of 7, and the coefficients Au and Al are adjusted using sample points. After running the code, an airfoil coordinate point file (in .dat format) is generated, containing the xy coordinate sequence of the airfoil profile. The comparison of the parameters before and after optimization for the 20 variables involved in airfoil optimization is shown in Table 1 below: Table 1 Figure 2 Table 1 shows a comparison of the aerodynamic shape of the airfoil before and after optimization. The horizontal axis represents the ratio of the airfoil's horizontal axis value to the chord length, and the vertical axis represents the ratio of the airfoil's vertical axis value to the chord length. The main parameter changes are shown in Table 1. The leading edge radius of the optimized airfoil is smaller than that before optimization, the maximum thickness of the airfoil remains unchanged, the curvature of the upper surface of the airfoil at the mid-to-rear position is smaller, the upper surface of the airfoil is more gentle, and the thickness and shape of the trailing edge of the airfoil remain basically unchanged.

[0037] Schematic diagram of the optimized airfoil mesh generation. The mesh is generated using the script recording function of Pointwise. A hybrid mesh is adopted during mesh generation, i.e., structured meshes are generated in the boundary layer region of the airfoil surface, and unstructured meshes are generated in the far-field region. The far-field extends 50 chord lengths in the front, back, up, and down directions. The height of the first layer of the mesh is 10^-5, and y+ is less than 1. Boundary conditions are set: the airfoil is a wall, and the far-field is a pressure far-field. The mesh file is exported in the.cas format.

[0038] Add and compile the code under the PHengLEI3vd0.sln file in the PHengLEI software. Add the vortex generator to the N-S equations using the momentum source term method, and convert the VG parameters (length, height, position) into source term parameters for input. The momentum source term is added to the equation in the form of body force as follows; Analyze a cylindrical region with length L and radius R. This region surrounds the VGs. The change in angular momentum is equal to the change in the angular momentum of the VGs, and the velocity distribution satisfies the velocity distribution of the Lamb-Oseen vortex leaving this region. For an annular region with inner radius r and radial thickness dr, the axial velocity of the fluid at the inlet is U, and the tangential velocity is zero. At the outlet, the axial velocity remains U unchanged, but the tangential velocity becomes Vθ. According to the angular momentum theorem, the torque acting on this annular region is equal to the change in the angular momentum of the fluid flowing through this region per unit time. Then the torque generated by the VGs is: Each term of the N-S momentum equation is a volume fraction. Divide the torque equation by the volume of this annular region, and the force is transformed into a volume integral form: Considering the flow resistance of the VG, the axial velocity changes, so an axial force is added to the source term. In this paper, it is assumed that the resistance of the VG satisfies a Gaussian distribution, so it is expressed as: In the formula, μ is the mean value; σ is the standard deviation. The properties of the Gaussian distribution function show that within the interval of the mean u±2σ, about 95% of the probability density is included, that is, most of the energy carried by the entire vortex structure and the induced drag it generates are highly concentrated in the inner region of the vortex core. It can be considered that the resistance is mainly concentrated in the region of [0, s0], which corresponds to [0, 2σ] of the Gaussian distribution, and the equation is obtained: The volume fraction of the axial force within the range of -L / 2 < x < L / 2 and r > 0 is equal to the resistance of the vortex generator acting on the flow field.

[0039] The influence of the airfoil wall on the vortex system generated by the vortex generator is addressed by adding mirror vortices. Considering the mirror vortices, the force equations acting on the vortex generator are as follows: In the PHengLEI software, import the .cas mesh file, execute the mesh transformation command to convert it into a .fts file suitable for PHengLEI, set the turbulence model to the kω-sst model, the incoming Mach number to 0.15, and the Reynolds number to 3×106, and perform steady-state CFD calculations. Obtain the lift coefficient and lift-to-drag ratio to form a training dataset.

[0040] To avoid dimensionality explosion and local optima in high-dimensional optimization problems, this invention conducts sensitivity analysis based on the training dataset, as shown in Figure 4. The sensitivity analysis uses the Random Forest algorithm to evaluate the influence of each design variable on the airfoil's lift-to-drag ratio, and determines key design parameters through feature importance ranking and cumulative contribution rate. Figure 4(a) shows the importance ranking results of each design variable. The horizontal axis represents the importance metric, and the vertical axis arranges all design variables by importance. The analysis shows that the VG parameters (h, p, l) have a significant impact on the lift-to-drag ratio, with their importance metrics all exceeding 0.05; while the upper airfoil parameter upN2, lower airfoil parameters lowN1, and lowN2 have lower contributions, with importance metrics all less than 0.01. This distribution characteristic conforms to the airfoil aerodynamic principles, i.e., the airfoil mid-section curvature parameters have a significant impact on aerodynamic performance. Figure 4(b) presents the cumulative importance curve. The results show that the cumulative importance of the first nine key variables has reached over 80%, and the cumulative importance of the first thirteen variables exceeds 90%. Two horizontal dashed lines mark the 80% and 90% cumulative importance thresholds, respectively, verifying the applicability of the Pareto principle in airfoil optimization problems, i.e., key parameters dominate the main response characteristics of the system. This analysis provides a quantitative basis for subsequent model dimensionality reduction, reducing the 24-dimensional design space to an 18-dimensional key parameter space while maintaining model accuracy, significantly improving optimization efficiency.

[0041] Based on the sensitivity analysis results, a Kriging surrogate model was constructed using Python's Scikit-learn library. The correlation coefficient matrix employed an anisotropic Gaussian correlation function. Wherein, θk represents the relevant parameters of the k-th variable, optimized using the maximum likelihood estimation method. Model accuracy is quantitatively evaluated using the coefficient of determination R² and root mean square error RMSE, with an accuracy standard set at R² > 0.9. The model validation results are shown in Figure 5. Figure 5(a) shows the comparison between predicted and actual values. It can be seen that the scatter points are closely distributed near the y=x reference line, and the coefficient of determination R² reaches 0.9853, indicating that the model has excellent prediction accuracy. Figure 5(b) is the residual analysis diagram. The residuals are randomly distributed around the zero line, without obvious trend distribution characteristics, further verifying the stability and reliability of the model. If the model accuracy does not meet the standard, the number of sample points will be increased by Latin hypercube sampling, and the airfoil parameter space will be adjusted for resampling. The surrogate model will be iteratively optimized until the preset accuracy requirements are met. This process effectively avoids overfitting and ensures the generalization ability of the surrogate model at unknown design points.

[0042] The validated Kriging surrogate model was used as the fitness function, and a particle swarm optimization (PSO) algorithm was employed for global optimization search within the design space. The PSO algorithm parameters were set as follows: population size 150, individual learning factor and social learning factor both 2.0, and maximum number of iterations 300 generations. Simultaneously, an aerodynamic performance constraint—the lift-to-drag ratio under medium angle-of-attack conditions should not be lower than the initial value—was introduced, and constraint violations were handled using a penalty function method. Through the swarm intelligence search mechanism of the PSO algorithm, the optimal parameter combination for coupled optimization was obtained.

[0043] The optimized coupled parameters are verified using CFD numerical methods, and the relative errors between the surrogate model predictions and the CFD calculations are compared. If the dual criteria of relative error < 5% and maximum lift-to-drag ratio improvement ≥ 10% are met, the final optimized scheme is output; otherwise, adaptive sampling based on the expected improvement criterion (EI) is adopted: the EI function EI(x) = E[max(0, f(x)] is calculated. fbest)], where fbest is the current optimal value; find the point that maximizes EI through particle swarm optimization, perform CFD calculation and add it to the training set to update the Kriging model. Repeat steps (5)-(7) until convergence.

[0044] like Figure 6 , Figure 7 A comparison of lift coefficient and lift-to-drag ratio results for coupling optimization and optimization of only VG parameters while maintaining the original airfoil. Figure 6 The horizontal axis represents the angle of attack, and the vertical axis represents the lift coefficient. In the legend, VG-C Cl represents the lift coefficient of the original airfoil with the vortex generator added, and Coupling-Opt Cl represents the lift coefficient considering the coupling optimization of this invention. Figure 7The horizontal axis represents the angle of attack, and the vertical axis represents the lift-to-drag ratio. In the legend, VG-C Cl / Cd represents the lift-to-drag ratio of the airfoil with the vortex generator added, while Coupling-Opt Cl / Cd represents the lift-to-drag ratio considering the coupling optimization of this invention. Within the angle of attack range of 6° to 20°, the lift coefficient and lift-to-drag ratio of the coupling-optimized scheme are significantly improved compared to the DU97W300 airfoil. The maximum lift-to-drag ratio of the Coupling-Opt scheme is achieved at approximately 12° of angle of attack, with the optimal lift-to-drag ratio angle of attack delayed by approximately 2°. In the small to medium angle of attack range, the lift coefficient of both schemes increases approximately linearly with increasing angle of attack, and the lift coefficient curve of the Coupling-Opt scheme remains above VG-C, indicating better lift generation capability. When α > 16°, the lift coefficient curves of the baseline schemes gradually flatten out, and the lift growth slows down. However, the lift coefficient of the Coupling-Opt scheme continues to increase up to 20° of angle of attack, indicating a further delay in the stall angle of attack. Meanwhile, the maximum lift coefficient is also higher than that of VG-C, with an increase of 31.1%, indicating that the coupling optimization scheme significantly improves its lift performance. Furthermore, throughout the entire angle of attack range, the lift-to-drag ratio curve of Coupling-Opt is generally higher than that of the benchmark scheme VG-C, reaching a peak value near α=12°, which is significantly higher than the corresponding value of VG-C. This indicates that coupling optimization not only improves the maximum lift-to-drag ratio and overall aerodynamic performance but also widens the efficient operating range, allowing the blades to maintain high efficiency over a larger angle of attack range. As the angle of attack increases, the lift-to-drag ratio of both schemes decreases, but the lift-to-drag ratio curve of the Coupling-Opt scheme decreases more gently at medium angles of attack, indicating its excellent performance under complex flow conditions.

[0045] Figure 8 This is a diagram comparing the lift coefficients of various optimization schemes. Figure 8The horizontal axis represents the angle of attack, and the vertical axis represents the lift coefficient. In the legend, VG-C Cl represents the lift coefficient of the original airfoil with a vortex generator added but without parameter optimization; VG-D Cl represents the lift coefficient of the airfoil with only optimized vortex generator parameters; Ailfoil-Opt Cl represents the lift coefficient of the airfoil with only optimized airfoil parameters; and Coupling-Opt Cl represents the lift coefficient of the coupled optimization scheme. The lift coefficient curve of the Coupling-Opt scheme remains superior across the entire angle of attack range, with the most significant lift advantage in the medium-to-high angle of attack range of 12°–20°. This indicates that the coupled optimization scheme not only improves the aerodynamic performance of the airfoil but also further delays the stall angle of attack. The lift coefficient curve of the Airfoil-Opt design is relatively close to that of the Coupling-Opt design at small and medium angles of attack, indicating that optimizing airfoil parameters alone can achieve good results at low and medium angles of attack. However, as the angle of attack increases further, the lift curve gradually flattens out, and at a 20° angle of attack, its lift coefficient is significantly lower than that of the Coupling-Opt design. The VG-C and VG-D curves are generally low, indicating that relying solely on the original vortex generator arrangement or optimizing only the vortex generator parameters has a limited effect on improving lift characteristics.

[0046] Figure 9 This diagram illustrates the comparison of the lift-to-drag ratios of various optimization schemes. Figure 9 The horizontal axis represents the angle of attack, and the vertical axis represents the lift-to-drag ratio. In the legend, VG-C Cl / Cd represents the lift-to-drag ratio of the original airfoil with a vortex generator added but without parameter optimization; VG-D Cl / Cd represents the lift-to-drag ratio of the scheme with only vortex generator parameter optimization; Ailfoil-Opt Cl / Cd represents the lift-to-drag ratio of the scheme with only airfoil parameter optimization; and Coupling-Opt Cl / Cd represents the lift-to-drag ratio of the coupled optimization scheme. The lift-to-drag ratio curve of the Coupling-Opt scheme is at its highest position in most angles of attack ranges, with its peak value corresponding to angles of attack of approximately 10°–14°, and is significantly higher than other schemes, indicating that this scheme has a greater advantage in improving aerodynamic efficiency. The lift-to-drag ratio of the Airfoil-Opt scheme is not significantly different from that of the Coupling-Opt scheme at small angles of attack, but decreases more significantly as the angle of attack increases, further illustrating the synergistic enhancement effect of coupled optimization in flow separation control. The lift-to-drag ratio curves of VG-C and VG-D have always been at a low level, indicating that simply adding or optimizing vortex generators without airfoil synergistic optimization is insufficient to achieve a significant improvement in aerodynamic performance.

[0047] Figures 10(a), 10(b), 10(c), and 10(d) show the streamlines of the original airfoil with added vortex generators, optimized vortex generator parameters only, optimized airfoil parameters only, and the coupled optimization scheme, respectively, at a 20° angle of attack. At a 20° angle of attack, the VG-C scheme in Figure 10(a) and the VG-D scheme in Figure 10(b) exhibit large flow separation regions, generating large separation vortices and showing significant flow separation. The Airfoil-Opt scheme in Figure 10(c) shows small-scale flow separation in the trailing edge region. In contrast, the Coupling-Opt scheme in Figure 10(d) has a smaller flow separation region and generates the smallest separation vortex, demonstrating that the Coupling-Opt scheme has a superior ability to suppress flow separation compared to other schemes at a 20° angle of attack. In summary, the coupled optimization method for airfoil optimization considering VG flow control in this invention can not only effectively improve its aerodynamic performance but also maintain good flow control capabilities.

[0048] Compared to individual designs that optimize only the airfoil or only the VG, the embodiments of the present invention achieve a more comprehensive improvement in aerodynamic performance within the range of 6°-20° angle of attack, with a lift-to-drag ratio improvement of 17.36% at a 10° angle of attack, and still maintain excellent flow control performance under high angle of attack conditions.

[0049] The optimization design method of this invention provides a new approach to simultaneously considering vortex generator flow control and airfoil optimization. Compared with the traditional step-by-step design mode of "optimizing the airfoil first and then adding VG", the coupled optimization method proposed in this invention has the following significant advantages: First, this invention achieves deep synergy between aerodynamic shape and flow control by simultaneously optimizing 23 design variables, including airfoil profile and VG. This coupled design method can effectively capture the nonlinear interaction between airfoil geometry and VG, overcoming the suboptimal solution problem caused by neglecting coupling effects in step-by-step optimization. Second, this method uses a Kriging surrogate model to replace computationally expensive CFD direct optimization, constructs a high-precision approximate model through intelligent sampling, and combines it with particle swarm optimization algorithm for efficient global search. This technical route further reduces computational costs while ensuring optimization accuracy, solving the computational bottleneck problem in multi-parameter coupled optimization. At the same time, this method is not dependent on specific airfoil or VG types, providing a universal technical solution for the collaborative design of various airfoils and flow control devices, and has significant engineering application value.

[0050] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. An airfoil coupling optimization method based on vortex generator flow control and profile optimization, characterized in that, include: Step S1: Obtain the task requirements, determine the design variables and their corresponding value ranges according to the task requirements, and generate an initial sample point set according to the design variables and their corresponding value ranges. Step S2: Generate airfoil geometry based on the initial sample point set; Step S3: Perform CFD simulation on each of the airfoil geometries to obtain a training dataset; The training dataset includes: lift coefficient and lift-to-drag ratio considering vortex generators under airfoil geometry; Step S4: Construct a Kriging proxy model based on the training dataset; Step S5: Using the Kriging surrogate model as the fitness evaluation function, the particle swarm optimization algorithm is used to perform a global optimization search in the budget design space to obtain the optimal combination of design parameters. Step S6: Perform CFD verification on the optimal design parameter combination, and output the optimal design parameter combination whose verification results meet the preset accuracy and performance requirements as the final solution.

2. The airfoil coupling optimization method based on vortex generator flow control and profile optimization according to claim 1, characterized in that, The design variables include: airfoil geometry parameters and vortex generator parameters; The airfoil geometric parameters include: a class function parameter controlling the leading edge radius, a class function parameter controlling the trailing edge shape, and multiple control points; The parameters of the eddy current generator include: height, length, and position.

3. The airfoil coupling optimization method based on vortex generator flow control and profile optimization according to claim 1, characterized in that, Step S1 includes: An initial sample point set is generated based on the design variables and their corresponding value ranges, and the initial sample point set is generated using the Latin hypercube sampling method.

4. The airfoil coupling optimization method based on vortex generator flow control and profile optimization according to claim 1, characterized in that, Step S2 further includes: Based on the initial sample point set, the airfoil geometry is generated using the CST parameterization method.

5. The airfoil coupling optimization method based on vortex generator flow control and profile optimization according to claim 4, characterized in that, The CST parameterization method includes: shape functions and class functions.

6. The airfoil coupling optimization method based on vortex generator flow control and profile optimization according to claim 5, characterized in that, Also includes: The shape function can be expressed by the following formula. : in, As control points, Let be the order of the curve fitting. For chord coordinates.

7. The airfoil coupling optimization method based on vortex generator flow control and profile optimization according to claim 5, characterized in that, Also includes: The class function is represented by the following formula. : in, For chord coordinates, To control the leading edge radius, a class of function parameters, Functional parameters for controlling the shape of the trailing edge.

8. The airfoil coupling optimization method based on vortex generator flow control and profile optimization according to claim 1, characterized in that, Step S4 includes: A Kriging proxy model to be validated is constructed based on the training dataset, and the accuracy of the Kriging proxy model to be validated is evaluated using cross-validation. When the accuracy assessment is passed, the Kriging proxy model to be verified that has passed the accuracy assessment will be used as the Kriging proxy model.

9. The airfoil coupling optimization method based on vortex generator flow control and profile optimization according to claim 7, characterized in that, Step S4 further includes: When the accuracy assessment fails, the airfoil geometry is regenerated based on the preset constraints of airfoil optimization and the initial sample point set.

10. The airfoil coupling optimization method based on vortex generator flow control and profile optimization according to claim 1, characterized in that, Step S6 includes: When the verification results do not meet the preset accuracy or performance requirements, the verification points and their calculation results are added to the training dataset to update the Kriging surrogate model, and a new optimal design parameter combination is obtained by performing a global optimization search in the budget design space.

Images