Vortex wave interference-based design method of super-transonic compressor blade

Abstract

The invention provides a design method of a super-transonic compressor blade based on vortex wave interference. The design method comprises the following steps: S1, carrying out geometric modeling on the compressor blade; s1.1, determining a blade modeling design range; s1.2, modeling parameters are determined; s1.3, determining the number m of control sections; s1.3. 1, obtaining a reference cross section number driven based on a geometric scale; s1.3. 2, obtaining the number of sections encrypted based on flow characteristics; s1.3. 3, obtaining a cross section lower limit of torsion change constraint drive; s1.3. 4, the number m of control sections is obtained; s1.4, determining a section control point number n; s1.4.1, obtaining the number of section control points encrypted based on geometric features; s1.4.2, acquiring an error constraint based on a curvature derivative, and correcting a section control point number; s1.5, performing geometric modeling and interpolation implementation on the blade by adopting radial basis function curved surface interpolation; s2, proxy modeling and global optimization are carried out; and S3, flow field optimization and blade design. The blade strength can be guaranteed, the overall performance of the gas compressor is remarkably improved, and the optimization effect which cannot be achieved through a traditional design method is achieved.

Description

Technical Field

[0001] This invention relates to the field of turbomachinery technology, and more particularly to a design method for supersonic compressor blades based on vortex interference. Background Technology

[0002] To improve the flow at the tip of transonic compressor blades, reduce aerodynamic losses caused by the interaction of leakage vortices and shock waves, and increase compressor efficiency and stall margin, researchers both domestically and internationally have proposed active control technologies such as plasma flow control and tip jetting, as well as passive control technologies such as tip grooves, tip winglets, slanted / swept blades, and bulges, from the perspectives of controlling tip leakage flow and channel shock waves. Active control technologies are highly effective in improving flow structure, but they typically rely on additional control units and energy inputs, leading to difficulties in implementation, high costs, and insufficient reliability, making them unsuitable for application in compact compressor systems operating in harsh environments. In contrast, passive control is more feasible in engineering practice due to its lack of external power, simple structure, and strong adaptability. Therefore, there is an urgent need for a novel smooth compressor blade design method capable of adaptively adjusting the spatial structure based on changes in wall flow parameters (such as shock wave incident position, shock wave intensity, or leakage vortex range) to meet the requirements for more precise and effective aerodynamic performance optimization under complex tip flow environments. Summary of the Invention

[0003] To address the aforementioned technical problems, a design method for transonic compressor blades based on vortex interference is provided.

[0004] The technical means employed in this invention are as follows: A design method for supersonic transonic compressor blades based on vortex wave interference includes the following steps: S1. Perform compressor blade geometry design; S1.1 Determine the scope of blade design: The scope of blade design mainly includes the tip region of the compressor blade, as well as local areas of the suction surface, pressure surface, and middle region of the blade. The scope of design can be appropriately modified according to the actual operating conditions and the specific structural characteristics of the blade. S1.2 Determine the design parameters; S1.3 Determine the number of control sections m ; S1.3.1 Obtain the number of reference sections driven by geometric scale based on shape parameters; S1.3.2 Obtain the number of cross sections based on flow characteristics based on shape parameters; S1.3.3 Obtain the lower limit of the cross section driven by torsional variation constraints based on the shape parameters; S1.3.4 Obtain the number of control sections based on S1.3.1, S1.3.2, and S1.3.3. m ; S1.4 Determine the number of section control points n ; S1.4.1 Obtain the number of cross-sectional control points encrypted based on geometric features; S1.4.2 Obtain error constraints based on curvature derivatives to correct the number of section control points in S1.4.1; S1.5 Based on S1.2, S1.3 and S1.4, radial basis function surface interpolation is used to perform geometric modeling and interpolation on the blade; and a control point system is constructed according to the number of control sections m determined in S1.3 and the number of control points n for each section determined in S1.4 to realize the parametric modeling of the blade. S2. Proxy Modeling and Global Optimization: Based on the geometric parameterization in S1, a proxy model is constructed using a limited number of numerical simulation samples. Global optimization is then performed on the proxy model and verified using a small number of samples to obtain a blade scheme that is superior in overall aerodynamic performance. S3. Flow field optimization and blade design: After completing proxy modeling and global optimization, high-fidelity CFD analysis is further combined to optimize the blade flow field in detail and modify the structure. Through multiple iterations of flow field analysis and geometric correction, the blade achieves optimal performance in key performance indicators such as aerodynamic efficiency, stability and stall margin.

[0005] Furthermore, in S1.2, the styling parameters include blade height. H String length c Blade tip gap g Initial shape leaf height position h 0, number of control sections m Control points for each section n suction and pressure surface arc length chord coordinates Cross-sectional position The local torsional angle function of the cross section is: θ ( h The curvature of the cross-sectional curve is k ( s ); The first and second derivatives of the local torsion angle function of the cross section represent spanwise load and gradient, respectively, and the first derivative of the curvature of the cross section curve represents the geometric undulation frequency.

[0006] Furthermore, in S1.3.1, the number of reference sections is based on geometric scale-driven calculations. Satisfy the following formula: ; In the formula, The spanwise average section spacing H For leaf height, h 0 represents the initial leaf height position; In S1.3.2, the number of cross sections encrypted based on flow characteristics. Satisfy the following formula: ; in, ; In the formula, For encryption height coefficient, For encryption height, To increase the spacing; In S1.3.3, the lower limit of the cross section driven by the torsional change constraint. The following formula: ; in, ; In the formula, This is for interpolation error. The second derivative of the local torsional angle function of the cross section; In S1.3.4, the number of control sections m Satisfy the following formula: .

[0007] Furthermore, in S1.4.1, the blade is divided into three segments along the chord length, including: the leading edge segment. Middle section and tail edge segment The middle section includes the shock wave section. ,in The location of the shock wave center Encrypt the half-width ratio of the shock wave region; Different control point counts were applied to the four segments to obtain the control point counts for the leading edge segment, trailing edge segment, mid-chord segment, and shock wave segment. Based on the number of control points in the leading edge segment, trailing edge segment, mid-chord segment, and shock wave segment, the number of cross-sectional control points encrypted based on geometric features is obtained.

[0008] Furthermore, the number of control points of the leading edge segment Satisfy the following formula: ; In the formula, The length of the leading edge segment. The spacing between control points on the leading edge segment; The number of control points on the trailing edge segment Satisfy the following formula: ; In the formula, The length of the trailing edge segment. The distance between control points on the trailing edge segment; The number of control points in the middle section Satisfy the following formula: ; In the formula, The spacing between control points in the middle section; The number of shock band control points Satisfy the following formula: ; In the formula, The spacing between control points in the shock wave band; The number of cross-sectional control points encrypted based on geometric features satisfies the following formula: .

[0009] Furthermore, in S1.4.2, the curvature derivative constraint method is used to limit the geometric reconstruction error, and the following requirements are set for each interpolation interval: ; in, The spacing between control points in each segment, including , , and ; It is the first derivative function of the curvature of the cross-section curve; To account for the allowable curvature discretization error, the minimum number of control points for each segment can be calculated in reverse, thereby correcting the number of section control points in S1.4.1.

[0010] Furthermore, in S1.5, the radial basis function interpolation satisfies the following formula: ; In the formula, It is the blade surface function to be interpolated. It is a radial basis function. It is the distance between the interpolation point and the control point. It is the weight of each control point. It is a polynomial term.

[0011] Furthermore, step S2 specifically includes the following steps: S2.1 Sample generation and size determination; Before establishing the proxy model, a certain number of design samples are generated to create a sample database. Latin hypercube sampling is used to ensure sample diversity and coverage. Since there is a coverage relationship between the number of samples and the dimension of variables, a lower limit for the sample size is set. ,in , Take 8~15; when d When the relationship is large or the geometric-aerodynamic relationship is strongly nonlinear, start with a smaller one. N The initial agent is trained and then dynamically expanded based on the error until the accuracy target is reached. To improve the effectiveness of the samples, geometric and physical feasibility filters are applied first to remove obviously infeasible points and avoid the training set being diluted by invalid samples. All design variables are uniformly linearly normalized to [0,1], and the output indicators can be logarithmically transformed as needed to improve the numerical condition number. S2.2, Agent model construction and accuracy verification; S2.2.1 After generating the sample database, a surrogate model is trained based on the sample data; a radial basis function neural network is used as the surrogate model. The input of the surrogate model is the geometric parameters of the compressor blades, and the output is the relevant aerodynamic performance indicators of the flow field, including the compressor's total pressure ratio, efficiency, and stall margin. S2.2.2 By mapping the input and output of the design samples, the relationship between the input and output is established using the RBFNN training algorithm; RBFNN accurately fits the complex relationship between aerodynamic performance and design variables through multi-layer nonlinear transformation; the trained neural network is validated, and the model is tested using partial sample data during the validation process; the accuracy is evaluated by calculating the prediction error of the model; if the accuracy is high, the model can be used in the global optimization process. S2.3, Global Optimization; Based on S2.2, global optimization is performed using genetic algorithms, NSGA-II, particle swarm optimization, or differential evolution. By continuously evaluating the aerodynamic performance under different design parameters and gradually adjusting the design parameters based on these results, the optimal solution is finally found. During the optimization process, representative designs are selected from the Pareto front or the best set of individuals every few generations, CFD is recalculated, and new data is added to the training set and the RBFNN is updated incrementally.

[0012] Furthermore, step S3 specifically includes the following steps: S3.1 Perform coupling control of shock wave and leakage vortex; In the blade tip region, the local expansion and compression effects are changed by fine-tuning the shape of the blade leading edge and mid-chord section to control the stability of the shock wave position. If the CFD prediction shows that the shock wave deviates significantly from the expected position, the surface curvature of the blade is further slightly changed to adjust the streamline shape. In the case of excessive leakage vortex intensity, the vortex entrainment is weakened by increasing the local curvature, thereby reducing the flow loss caused by the shock wave and leakage vortex. S3.2 Optimize the separation zone and stall margin; In the downstream section of the blade, the expansion of the separation zone is suppressed; boundary layer separation is delayed by adjusting the local trailing edge thickness or camber distribution to reduce the separation area; static pressure distribution and loss distribution are monitored by CFD, and if the flow stall occurs prematurely, the torsion angle distribution is optimized again to rematch the incoming flow angle of attack with the local aerodynamic load, improve the stall margin, and enhance the working stability of the compressor. S3.3 Numerical verification; After the local adjustments in S3.1 and S3.2 are completed, CFD verification is performed on each candidate geometry scheme. If the relative deviation between the simulation results and the surrogate model prediction is too large, the sample is used as a new benchmark to retrain the surrogate model, forming a closed-loop correction process. Some of the final designs are further verified in wind tunnel experiments to confirm the reliability of the numerical prediction.

[0013] Compared with the prior art, the present invention has the following advantages: 1. The design method for supersonic and transonic compressor blades based on vortex interference provided by this invention generates a stable pressure distribution on the blade surface by precisely adjusting the compressor blade geometry and utilizing the vortex interference effect, thereby reducing flow separation and shock wave phenomena and improving the aerodynamic efficiency of the blade. This method is particularly suitable for supersonic and transonic operating conditions, significantly improving the overall performance of the compressor while ensuring blade strength, achieving optimization effects that cannot be achieved by traditional design methods.

[0014] 2. The design method for supersonic and transonic compressor blades based on vortex interference provided by this invention combines radial basis function neural networks (RBFNN) with a surrogate model. By training the RBFNN model, the aerodynamic performance of the compressor blade's geometric parameters is predicted, achieving efficient and accurate flow field evaluation without traditional CFD simulation. This innovative method significantly shortens the design cycle and reduces computational costs, making it particularly suitable for high-dimensional optimization problems in the design of supersonic and transonic compressors.

[0015] 3. The design method for supersonic compressor blades based on vortex interference provided by this invention innovatively proposes a design strategy that shapes only the blade tip region to control the vortex interference effect in the blade tip region. By introducing radial basis function interpolation technology in this region for refined shaping, the pressure and velocity distribution of the airflow passing through the blade tip can be optimized to the greatest extent, significantly reducing aerodynamic losses and improving the overall efficiency of the compressor.

[0016] Based on the above reasons, this invention can be widely applied in fields such as supersonic and transonic compressors. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of the method of the present invention.

[0019] Figure 2 This is a schematic diagram of the research object in Embodiment 2 of the present invention.

[0020] Figure 3 This is a schematic diagram of the control section and control points in Embodiment 2 of the present invention.

[0021] Figure 4 This is a schematic diagram of the shaped blade in Embodiment 2 of the present invention.

[0022] Figure 5 This is a schematic diagram of the aerodynamic performance in Embodiment 2 of the present invention.

[0023] Figure 6 The tip static pressure coefficient cloud in Embodiment 2 of the present invention Figure 1 .

[0024] Figure 7 The tip static pressure coefficient cloud in Embodiment 2 of the present invention Figure 2 . Detailed Implementation

[0025] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0028] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0029] Example 1 In supersonic and transonic compressors, the complexity of the flow field increases significantly, especially in the blade tip region. The interaction between leakage vortices and shock waves, and their significant impact on the flow structure, severely limits the compressor's aerodynamic performance. The core of this problem lies in the nonlinear characteristics and multi-physics coupling phenomena of the flow field under supersonic and transonic conditions: leakage vortices, driven by the pressure difference at the blade tip clearance, carry high-energy airflow into the low-energy region, disrupting the flow field homogeneity in the mainstream region; simultaneously, the formation of shock waves under transonic conditions induces strong pressure gradient changes in the fluid locally, leading not only to sudden kinetic energy loss but also complex interference effects with the leakage vortex. This vortex-wave coupling further exacerbates the instability of the flow field and aerodynamic losses. Therefore, a new blade modification design method with intelligent structure generation capabilities, capable of handling high-dimensional nonlinear problems, and suitable for coupling flow field information is urgently needed to address the vortex-wave interference problem in supersonic and transonic compressors.

[0030] like Figure 1 As shown, this invention provides a design method for supersonic and transonic compressor blades based on vortex interference, which is an optimization design method for supersonic and transonic compressor blades based on vortex interference effects. This method uses radial basis function interpolation as the core to achieve blade geometric parameterization, focusing on refined modeling of the blade tip region to weaken the interaction between leakage vortices and shock waves. By setting control points and geometric constraints, combined with numerical simulation and experimental verification, the stability and efficiency of the blade in complex flow environments are ensured. Based on this, a surrogate model is used to construct the mapping relationship between geometric parameters and aerodynamic performance, and a global optimization algorithm is used to search for the optimal design scheme. Optimization objectives include reducing total pressure loss and vortex interference, increasing pressure ratio, and expanding stall margin. The entire design process is implemented in three stages, each stage including several specific steps, as follows: S1, First Stage: Compressor Blade Geometry S1.1 Determine the scope of blade design The geometry of compressor blades is a fundamental aspect of the entire design process, directly impacting the compressor's aerodynamic performance and operational stability. Under supersonic and transonic operating conditions, the flow at the compressor blade tip is the most complex, influenced by the coupling effects of leakage vortices and shock waves, creating an unstable flow region that significantly limits the compressor's aerodynamic performance. This invention employs radial basis function (RBF) interpolation technology to perform refined geometric modeling of the blade tip region of supersonic and transonic compressors. By precisely adjusting the geometry of the blade tip region, the interaction between shock waves and leakage vortices is weakened, thereby improving aerodynamic performance and enhancing compressor stability.

[0031] S1.2 Determine the styling parameters Let the leaf height be H chord length isc The initial shape of the leaf height position is h 0. The number of control sections is m Control points for each section are n ;Action and pressure surface arc length chord coordinates Cross-sectional position The local torsional angle function of the cross section is: θ ( h Its first and second derivatives characterize spanwise loading and gradient, respectively, and the curvature of the cross-sectional curve is... k ( s Its first derivative characterizes the geometric fluctuation frequency.

[0032] S1.3 Determine the number of control sections m S1.3.1, Number of reference sections driven by geometric scale Let the spanwise average section spacing be Reference cross-section number driven by geometric scale for: ; It can be adjusted in real time according to the actual blade. The range should ensure that the second variation of torsion and thickness in the spanwise direction can be stably reproduced by radial basis function interpolation.

[0033] S1.3.2, Number of cross sections based on flow characteristics The region where the blade tip interacts with leakage vortices and shock waves requires additional cross-sections for further control of the flow field. Let the number of reinforced cross-sections be... The encryption height is The encryption spacing is The number of cross sections encrypted based on flow characteristics for: ; ; In the formula, This is the encryption height coefficient; Encryption height and encryption spacing The numerical values ​​are selected based on the characteristic scale of the leakage vortex and the thickness of the near-wall boundary layer.

[0034] S1.3.3 Lower limit of cross section driven by torsional variation constraint The spanwise interpolation error is required to be no more than There is an error estimate for piecewise cubic interpolation. Based on this, the upper limit of the spacing is given: ; ; In the formula, This is for interpolation error. The second derivative of the local torsional angle function of the cross section; Therefore, the number of control sections m for: .

[0035] S1.4 Determine the number of section control points n S1.4.1 Number of cross-sectional control points encrypted based on geometric features Divide the blade into three segments along the chord length: the leading edge segment Middle section and tail edge segment The middle section includes the shock wave region. , The location of the shock wave center Encrypt half-width for shock wave region.

[0036] Based on the actual situation, the four segments are encrypted with different numbers of points, that is... Number of control points in the leading edge segment : ; In the formula, The length of the leading edge segment. The spacing between control points on the leading edge segment; Number of control points on the trailing edge : ; In the formula, The length of the trailing edge segment. The distance between control points on the trailing edge segment; Number of control points in the middle section : ; In the formula, The spacing between control points in the middle section; Number of shock band control points : ; In the formula, The spacing between control points in the shock wave band; Finally, the number of cross-sectional control points encrypted based on geometric features is: .

[0037] S1.4.2 Error Constraints Based on Curvature Derivative To limit geometric reconstruction errors, the curvature derivative constraint method is used, with the following requirements for each interpolation interval: ; in, The spacing between control points in each segment, including , , and ; It is the first derivative function of the curvature of the cross-section curve; To account for the allowable curvature discretization error, the minimum number of control points for each segment can be calculated in reverse, thereby correcting the number of section control points in S1.4.1.

[0038] S1.5, Geometric Modeling and Interpolation Implementation Based on S1.2, S1.3, and S1.4, this invention employs RBF surface interpolation for blade shaping. First, it provides accurate geometric surface modeling, effectively avoiding discontinuities that may arise with traditional interpolation methods, ensuring the smoothness and continuity of the blade surface. Second, it allows for fine-tuning of key areas (such as the leading edge, trailing edge, and blade tip) without affecting the overall shape. Third, it constructs a control point system based on the number of control sections *m* and the number of control points *n* per section determined in S1.3 and S1.4, thereby achieving parametric blade shaping. Finally, it can flexibly adapt to different control point distributions, achieving precise geometric shaping in different regions of the blade to meet aerodynamic optimization requirements.

[0039] Radial basis function interpolation can be expressed in the following form:

[0040] in, It is the blade surface function to be interpolated. It is a radial basis function. It is the distance between the interpolation point and the control point. It is the weight of each control point. It is a polynomial term.

[0041] S2, Second Phase: Agent Modeling and Global Optimization This stage, building upon the geometric parameterization of the first stage, constructs a surrogate model using a limited number of numerical simulation samples to approximate the repeated evaluations in CFD. Global optimization is then performed on the surrogate model, and the results are verified using a small number of samples. The aim is to obtain a blade design that offers overall superior aerodynamic performance while maintaining sufficient fitting accuracy to the geometric-aerodynamic nonlinear relationship, significantly reducing computational load.

[0042] S2.1 Sample Generation and Size Determination Before establishing the surrogate model, a certain number of design samples need to be generated. To ensure the diversity and coverage of the samples, this invention uses the Latin Hypercube Sampling (LHS) method. Since there is a coverage relationship between the number of samples and the dimension of the variables, a lower limit for the sample size is set. ,in , Take 8~15. When d When the relationship is large or the geometric-aerodynamic relationship is strongly nonlinear, a smaller value can be used first. N The initial agent is trained and then dynamically expanded based on the error until the target accuracy is achieved. To improve sample effectiveness, geometric and physical feasibility filters (such as leading edge thickness, leading edge radius, trailing edge thickness, etc.) are applied first to remove obviously infeasible points, preventing the training set from being diluted by invalid samples. All design variables are uniformly linearly normalized to [0,1], and the output indicators can be logarithmically transformed as needed to improve the numerical condition number.

[0043] S2.2, Proxy Model Construction and Accuracy Verification After generating the sample database, the next step is to train a surrogate model based on this sample data. In this invention, a radial basis function neural network (RBFNN) is chosen as the surrogate model. The input to the surrogate model is the geometric parameters of the compressor blades. The output is the relevant aerodynamic performance indicators of the flow field (such as the compressor's total pressure ratio, efficiency, stall margin, etc.).

[0044] By mapping the inputs and outputs of the design samples, the relationship between the inputs and outputs is established using RBFNN training algorithms (such as least squares and gradient descent). RBFNN, through multi-layer nonlinear transformations, can accurately fit the complex relationship between aerodynamic performance and design variables. After training, the neural network needs to be validated. Validation involves testing the model using a subset of sample data (usually a cross-validation set). The model's accuracy is evaluated by calculating its prediction error. If the accuracy is high, the model can be used in the global optimization process.

[0045] S2.3, Global Optimization The core idea of ​​global optimization algorithms is to continuously evaluate the aerodynamic performance under different design parameters and gradually adjust the design parameters based on these results to ultimately find the optimal solution. In this invention, genetic algorithms (GA), as well as NSGA-II (multi-objective), particle swarm optimization (PSO), and differential evolution (DE) can be used. To ensure the search breadth matches the dimensionality, the population size and number of iterations can be selected according to requirements.

[0046] To improve the quality of the agent and optimization, representative designs are selected from the Pareto front or the best set of individuals every few generations during the optimization process, CFD is recalculated, new data is added to the training set, and RBFNN is incrementally updated.

[0047] S3, Third Stage: Flow Field Optimization and Blade Design After completing the surrogate modeling and global optimization, further high-fidelity CFD analysis is needed to optimize the blade flow field in detail and correct its structure. The goal of this stage is to match the optimal geometric solution obtained from the surrogate model with the actual complex flow phenomena, paying particular attention to the impact of vortex interference on shock wave incident position, shock wave intensity, leakage vortex range, leakage vortex intensity, and separation zone range under supersonic and transonic conditions. Through multiple iterations of flow field analysis and geometric correction, the blades are ensured to achieve optimal performance in key indicators such as aerodynamic efficiency, stability, and stall margin.

[0048] S3.1 Coupling control of shock wave and leakage vortex The blade tip region is a key area for flow field optimization in supersonic and transonic compressors. In this region, the stability of the shock wave position can be controlled by fine-tuning the shape of the blade leading edge and mid-chord section to alter local expansion and compression effects. If CFD predictions indicate that the shock wave deviates significantly from the expected position, further minor adjustments to the blade surface curvature and streamline morphology are necessary. For cases with excessively strong leakage vortices, increasing local camber can reduce vortex entrainment, aiming to minimize flow losses caused by the shock wave and leakage vortices.

[0049] S3.2 Optimization of Separation Zone and Stall Margin In the downstream section of the blade, it is crucial to suppress the expansion of the separation zone. By adjusting the local trailing edge thickness or camber distribution, boundary layer separation can be delayed to reduce the separation area. CFD monitoring of static pressure distribution and loss distribution reveals that premature flow stall occurs; therefore, secondary optimization of the torsion angle distribution is necessary to re-match the incoming flow angle of attack with the local aerodynamic load, thereby improving the stall margin and enhancing the compressor's operational stability.

[0050] S3.3 Numerical Verification After local adjustments are completed, CFD verification is performed on each candidate geometry scheme. If the relative deviation between the simulation results and the surrogate model predictions is too large, the sample is used as a new benchmark to retrain the surrogate model, forming a closed-loop correction process. Some final designs can be further verified in wind tunnel experiments to confirm the reliability of the numerical predictions.

[0051] Example 2 The study focuses on the planar blade cascade of a transonic compressor.

[0052] 1. Research Subjects Taking a certain type of transonic compressor as the research object, a schematic diagram of the research object is shown below. Figure 2 .

[0053] 2. Selection of control sections and control points, such as... Figure 3 As shown.

[0054] 3. Shaped leaves, such as Figure 4 As shown.

[0055] 4. Sample collection and database construction Within the aforementioned parameter space, a sample database was constructed using Latin Hypercube Sampling (LHS). Three-dimensional high-fidelity CFD calculations were performed on each sample group, recording the total pressure loss coefficient and static pressure rise performance indicators to form the initial database.

[0056] 5. Optimization Results 5.1 Aerodynamic performance Figure 5 This diagram illustrates the aerodynamic performance of the prototype and the optimized design. Compared to the prototype, the optimized design reduces the total pressure loss coefficient by approximately 4%.

[0057] 5.2 Flow Field Analysis Figure 6 and Figure 7 This is a contour plot of the static pressure coefficient at the blade tip of the cascade. From... Figure 6 As can be seen from the prototype, the static pressure sloping groove (short black dashed line) that represents the trajectory of the leakage vortex clearly appears. The optimized shape significantly reduces the distribution range of the low-pressure core region of the blade cascade along the axial direction on the suction side. The starting position and area of ​​the low-pressure core region are delayed and reduced by more than 40% compared with the prototype.

[0058] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A design method for supersonic transonic compressor blades based on vortex wave interference, characterized in that, Includes the following steps: S1. Perform compressor blade geometry design; S1.1 Determine the scope of blade design: The scope of blade design mainly includes the tip region of the compressor blade; S1.2 Determine the design parameters; S1.3 Determine the number of control sections m ; S1.3.1 Obtain the number of reference sections driven by geometric scale based on shape parameters; S1.3.2 Obtain the number of cross sections based on flow characteristics based on shape parameters; S1.3.3 Obtain the lower limit of the cross section driven by torsional variation constraints based on the shape parameters; S1.3.4 Obtain the number of control sections based on S1.3.1, S1.3.2, and S1.3.

3. m ; S1.4 Determine the number of section control points n ; S1.4.1 Obtain the number of cross-sectional control points encrypted based on geometric features; S1.4.2 Obtain error constraints based on curvature derivatives to correct the number of section control points in S1.4.1; S1.5 Based on S1.2, S1.3 and S1.4, radial basis function surface interpolation is used to perform geometric modeling and interpolation on the blade; and a control point system is constructed according to the number of control sections m determined in S1.3 and the number of control points n for each section determined in S1.4 to realize the parametric modeling of the blade. S2. Proxy Modeling and Global Optimization: Based on the geometric parameterization in S1, a proxy model is constructed using a limited number of numerical simulation samples. Global optimization is then performed on the proxy model and verified using a small number of samples to obtain a blade scheme that is superior in overall aerodynamic performance. S3. Flow field optimization and blade design: After completing proxy modeling and global optimization, high-fidelity CFD analysis is used to optimize the blade flow field in detail and correct the structure. Through multiple iterations of flow field analysis and geometric correction, the blade achieves optimal performance in key performance indicators such as aerodynamic efficiency, stability and stall margin.

2. The design method for supersonic compressor blades based on vortex wave interference according to claim 1, characterized in that, In S1.2, the shaping parameters include the blade height. H String length c Blade tip gap g Initial shape leaf height position h 0, number of control sections m Control points for each section n suction and pressure surface arc length chord coordinates Cross-sectional position The local torsional angle function of the cross section is θ ( h The curvature of the cross-sectional curve is k ( s ); The first and second derivatives of the local torsion angle function of the cross section represent spanwise load and gradient, respectively, and the first derivative of the curvature of the cross section curve represents the geometric undulation frequency.

3. The design method for supersonic compressor blades based on vortex wave interference according to claim 2, characterized in that, In S1.3.1, the number of reference sections is based on geometric scale. Satisfy the following formula: ； In the formula, The spanwise average section spacing H For leaf height, h 0 represents the initial leaf height position; In S1.3.2, the number of cross sections encrypted based on flow characteristics. Satisfy the following formula: ； in, ； In the formula, For encryption height coefficient, For encryption height, To increase the spacing; In S1.3.3, the lower limit of the cross section driven by torsional variation constraint. The following formula: ； in, ； In the formula, This is for interpolation error. The second derivative of the local torsional angle function of the cross section; In S1.3.4, the number of control sections m Satisfy the following formula: 。 4. The design method for supersonic compressor blades based on vortex interference according to claim 2, characterized in that, In S1.4.1, the blade is divided into three segments along the chord length, including: the leading edge segment. Middle section and tail edge segment The middle section includes the shock wave section. ,in The location of the shock wave center Encrypt the half-width ratio of the shock wave region; Different control point densifications were performed on the four segments to obtain the control point counts for the leading edge segment, trailing edge segment, mid-chord segment, and shock wave segment; Based on the number of control points in the leading edge segment, trailing edge segment, mid-chord segment, and shock wave segment, the number of cross-sectional control points encrypted based on geometric features is obtained.

5. The design method for supersonic compressor blades based on vortex wave interference according to claim 4, characterized in that, The number of leading edge control points Satisfy the following formula: ； In the formula, The length of the leading edge segment. The spacing between control points on the leading edge segment; The number of control points on the trailing edge segment Satisfy the following formula: ； In the formula, The length of the trailing edge segment. The distance between control points on the trailing edge segment; The number of control points in the middle section Satisfy the following formula: ； In the formula, The spacing between control points in the middle section; The number of shock band control points Satisfy the following formula: ； In the formula, The spacing between control points in the shock wave band; The number of cross-sectional control points encrypted based on geometric features satisfies the following formula: 。 6. The design method for supersonic transonic compressor blades based on vortex wave interference according to claim 5, characterized in that, In S1.4.2, the curvature derivative constraint method is used to limit the geometric reconstruction error, and the following requirements are set for each interpolation interval: ； in, The spacing between control points in each segment, including , , and ; It is the first derivative function of the curvature of the cross-section curve; To account for the allowable curvature discretization error, the minimum number of control points for each segment can be calculated in reverse to correct the number of section control points in S1.4.

1.

7. The design method for supersonic compressor blades based on vortex wave interference according to claim 1, characterized in that, In S1.5, the radial basis function interpolation satisfies the following formula: ； In the formula, It is the blade surface function to be interpolated. It is a radial basis function. It is the distance between the interpolation point and the control point. It is the weight of each control point. It is a polynomial term.

8. The design method for supersonic transonic compressor blades based on vortex wave interference according to claim 1, characterized in that, S2 specifically includes the following steps: S2.1 Sample generation and size determination; Before establishing the proxy model, a certain number of design samples are generated to create a sample database. Latin hypercube sampling is used to ensure sample diversity and coverage. Since there is a coverage relationship between the number of samples and the dimension of variables, a lower limit for the sample size is set. ,in , Take 8~15; when d When the relationship is large or the geometric-aerodynamic relationship is strongly nonlinear, start with a smaller one. N The initial agent is trained and then dynamically expanded based on the error until the accuracy target is reached. To improve the effectiveness of the samples, geometric and physical feasibility filters are applied first to remove obviously infeasible points and prevent the training set from being diluted by invalid samples. All design variables are uniformly linearly normalized to [0,1]. Output indicators can be logarithmically transformed as needed to improve numerical condition numbers. S2.2, Agent model construction and accuracy verification; S2.2.1 After generating the sample database, a surrogate model is trained based on the sample data; a radial basis function neural network is used as the surrogate model. The input of the surrogate model is the geometric parameters of the compressor blades, and the output is the relevant aerodynamic performance indicators of the flow field, including the compressor's total pressure ratio, efficiency, and stall margin. S2.2.2 By mapping the input and output of the design samples, the relationship between the input and output is established using the RBFNN training algorithm; RBFNN accurately fits the complex relationship between aerodynamic performance and design variables through multi-layer nonlinear transformation; the trained neural network is validated, and the model is tested using partial sample data during the validation process; the accuracy is evaluated by calculating the prediction error of the model. If the accuracy is high, the model can be used in the global optimization process; S2.3, Global Optimization; Based on S2.2, global optimization is performed using genetic algorithms, NSGA-II, particle swarm optimization, or differential evolution. By continuously evaluating the aerodynamic performance under different design parameters and gradually adjusting the design parameters based on these results, the optimal solution is finally found. During the optimization process, representative designs are selected from the Pareto front or the best set of individuals every few generations, CFD is recalculated, and new data is added to the training set and the RBFNN is updated incrementally.

9. The design method for supersonic compressor blades based on vortex wave interference according to claim 1, characterized in that, S3 specifically includes the following steps: S3.1 Perform coupling control of shock wave and leakage vortex; In the blade tip region, the local expansion and compression effects are changed by fine-tuning the shape of the blade leading edge and mid-chord section to control the stability of the shock wave position. If the CFD prediction shows that the shock wave deviates significantly from the expected position, the surface curvature of the blade is further slightly changed to adjust the streamline shape. In the case of excessive leakage vortex intensity, the vortex entrainment is weakened by increasing the local curvature, thereby reducing the flow loss caused by the shock wave and leakage vortex. S3.2 Optimize the separation zone and stall margin; In the downstream section of the blade, the expansion of the separation zone is suppressed; boundary layer separation is delayed by adjusting the local trailing edge thickness or camber distribution to reduce the separation area; static pressure distribution and loss distribution are monitored by CFD, and if the flow stall occurs prematurely, the torsion angle distribution is optimized again to rematch the incoming flow angle of attack with the local aerodynamic load, improve the stall margin, and enhance the working stability of the compressor. S3.3 Numerical verification; After the local adjustments in S3.1 and S3.2 are completed, CFD verification is performed on each candidate geometry scheme. If the relative deviation between the simulation results and the surrogate model prediction is too large, the sample is used as a new benchmark to retrain the surrogate model, forming a closed-loop correction process. Some of the final designs are further verified in wind tunnel experiments to confirm the reliability of the numerical prediction.

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