A low reynolds number based pressure gradient customized compressor blade design method and application

Abstract

The application provides a compressor blade design method based on pressure gradient customization under low Reynolds number and application. First, the blade near-wall flow field parameters are extracted, then the pressure gradient parameters at the separation point are quantified K s , the variation range of the separation / reattachment position and the boundary layer integral parameters with the Reynolds number is established K s , and the correlation model of the momentum thickness Reynolds number Re θs at the separation point, the separation scale and the boundary layer growth rate is established. On this basis, a high-precision blade modeling technology is developed, and the mapping relationship between the modeling parameters and the blade surface curvature is constructed. By adjusting the modeling parameters, the blade surface curvature near the separation point under low Reynolds number is corrected, and K s and the corresponding Re θs are accurately compensated to the level close to the high Reynolds number working condition. Finally, the effectiveness of the blade design method under low Reynolds number is verified through experimental measurement and numerical simulation. The application can significantly shorten the design cycle, has clear physical meaning and strong interpretability, and directly supports the accurate matching design of the low Reynolds number rotating-static part.

Description

Technical Field

[0001] This invention belongs to the field of aero-engine aerodynamic design technology, and relates to the aerodynamic design and boundary layer control of compressor blades in aero-engine compression systems at low Reynolds numbers. Specifically, it relates to a compressor blade design method and application based on pressure gradient customization at low Reynolds numbers. Background Technology

[0002] As the primary power source for high-altitude unmanned aerial vehicles (UAVs), the lightweight turbofan engine, when its service ceiling is increased to 20 km, experiences a drop in the compressor inlet Reynolds number (Re) to 10 due to the combination of the thin atmospheric environment and the small size effect. 4 ~10 5 At this low Reynolds number, the blade surface boundary layer thickens significantly, turbulent pulsation intensifies, flow channel blockage effect is enhanced, and mismatch between rotor and stationary components occurs, leading to a sharp decline in compressor efficiency and stability margin, severely restricting the high-altitude fuel economy and operational stability of turbofan engines. Compared to conventional Reynolds number conditions at ground level (~10... 6 At low Reynolds numbers, the flow field on the blade surface deviates significantly from the design state, rendering the blade design system based on ground operating conditions ineffective. There is an urgent need to develop high-efficiency, low-loss compressor blade design technology suitable for low Reynolds number conditions.

[0003] At low Reynolds numbers, the transition process on the blade and endwall surfaces is significant, becoming the core mechanism driving boundary layer thickening and increased lag angle. Therefore, precise control of the transition boundary layer is crucial for achieving efficient and low-loss design of low Reynolds number blades. However, due to the complexity and variability of transition modes at different Reynolds numbers, the sensitivity of blade surface separation scale and boundary layer growth rate to local key parameters is difficult to quantify, making the fine-grained control of the transition boundary layer on the blade surface and the matching design of upstream and downstream components extremely challenging.

[0004] Existing low Reynolds number blade design methods typically fail to adequately consider the critical impact of transition regulation on boundary layer development. Their design processes often rely on forward trial-and-error iterations or numerical optimization to obtain the final blade geometry. Empirical trial-and-error methods heavily depend on design experience, requiring repeated geometry-aerodynamic iterations for correction, resulting in a cumbersome process and long design cycles, making them ill-suited for complex and variable high-altitude conditions. Numerical optimization methods, on the other hand, are prone to the curse of dimensionality due to the high dimensionality of design variables and the need for large databases. Furthermore, these methods are limited by the accuracy of the optimization model, lack strict constraints from flow physics mechanisms, and are prone to generating physically infeasible solutions, leading to poor interpretability of the design.

[0005] In summary, existing compressor blade design methods suffer from drawbacks and shortcomings when dealing with low Reynolds number conditions, including long iteration cycles, unclear physical mechanisms, and poor interpretability. These limitations make it difficult to meet the performance requirements of high-altitude unmanned aerial vehicle (UAV) propulsion systems for compressor components. Therefore, how to effectively characterize and design constraints on the near-wall flow and boundary layer development of blades under low Reynolds number conditions, thereby supporting the matching design of stationary components and suppressing performance degradation, is a pressing technical problem to be solved in this field. Summary of the Invention

[0006] (a) Purpose of the invention To address the aforementioned shortcomings and deficiencies of existing technologies, and considering that although the spatial position of the blade suction surface separation point changes only slightly as the Reynolds number decreases, the momentum thickness Reynolds number at the separation point remains significant. θs () decreased significantly. Re θs The reduction leads to a sharp decrease in the amplification rate of perturbations within the separated shear layer, and a significant delay in the transition; simultaneously, Re θs The reduction in shear layer also decreases the frequency of vortex shedding within the shear layer, weakening momentum transport of the low-energy fluid near the wall at the end of the transition. This results in a significant downward shift of the turbulent reattachment location, rapid expansion of the separation zone, and a substantial thickening of the boundary layer. Therefore, Re θs It is a crucial parameter determining the low Reynolds number transition characteristics and boundary layer development, regulating Re θs This provides an effective way to achieve fine organization of boundary layer growth rates. Accordingly, this invention aims to provide a high-efficiency, low-loss design method and application for compressor blades at low Reynolds numbers, by constructing pressure gradient parameters at the blade separation point. K s With Re θs A correlation model between the separation scale and the transition boundary layer growth rate was developed, and a high-precision parametric blade modeling method was established, creating a blade design technology based on pressure gradient customization. This technology effectively solves the problems of long iteration cycles, unclear physical mechanisms, and poor interpretability in traditional design methods, significantly improving design efficiency and providing direct support for the accurate matching of upstream and downstream compressor components under low Reynolds number conditions.

[0007] (II) Technical Solution To achieve the objective of this invention and solve its technical problems, the present invention adopts the following technical solution: The first objective of this invention is to provide a compressor blade design method based on pressure gradient customization. This method achieves precise matching of the rotor-stationary components at low Reynolds numbers by finely controlling the boundary layer growth rate, thereby improving the compressor's high-altitude efficiency and stability margin. The core technical solution of this method includes the following steps: extraction of blade surface boundary layer parameters, construction of a pressure gradient-boundary layer characteristic correlation model, high-precision parameterized blade geometry modeling, directional compensation and control of pressure gradient parameters, and numerical / experimental verification of aerodynamic performance. The key technical aspect lies in establishing the pressure gradient parameters at the separation point. K s With momentum, thickness, Reynolds number θs A quantitative correlation model between separation scale and boundary layer growth rate. The specific implementation process is as follows: SS1. Prototype Blade Surface Boundary Layer Parameter Extraction: Obtain surface load distribution and near-wall boundary layer velocity profile data of the prototype blade at different low Reynolds numbers, locate the laminar separation point and turbulent reattachment point on the blade surface, solve for the boundary layer integral parameters, and simultaneously calculate the pressure gradient parameters at the separation point. K s With momentum, thickness, Reynolds number θs The boundary layer integral parameters include at least the displacement thickness. and momentum thickness i ; SS2. Construction of the Pressure Gradient-Boundary Layer Property Correlation Model: Quantization K s Separation Scale L bs And the variation of boundary layer integral parameters with Reynolds number, establish K s With Re θs , L bs The correlation model between the growth rate of the boundary layer and the growth rate of the boundary layer, in which L bs Defined as the distance between the laminar separation point and the turbulent reattachment point; SS3. High-precision parametric modeling of blade geometry: The blade is parametrically modeled using Class Shape Transformation (CST) with class functions. C ( Define the basic shape of the blade using shape functions. S ( The basic shape is modified, by C ( )and S ( Multiplying these components and adding a function characterizing the trailing edge features to fit the blade profile, will... C ( )and S ( The control parameters are used as shaping variables to establish a mapping relationship between each shaping variable and the blade surface curvature distribution; SS4. Targeted Compensation and Control of Pressure Gradient Parameters: The region near the laminar separation point on the suction surface at low Reynolds numbers is designated as the geometric correction region to ensure optimal performance at the target Reynolds number. K s and corresponding Re θs The control objective is to compensate to a level close to the baseline Reynolds number. Under the condition of blade geometry constraints, the local directional correction of the geometry correction region is achieved by optimizing and adjusting various shaping variables to obtain the compensated modified blade geometry. SS5. Numerical / Experimental Verification of Aerodynamic Performance: Numerical calculations and / or experimental measurements were performed on the reconstructed modified blades under different Reynolds number conditions to verify the improvement effect of directional compensation for pressure gradient parameters.

[0008] The second objective of this invention is to provide a compressor blade designed using the pressure gradient-based compressor blade design method described above.

[0009] (III) Technical Effects Compared with existing technologies, this invention provides a compressor blade design method and application based on pressure gradient customization at low Reynolds numbers, which has the following advantages: (1) The physical mechanism is clear, highly interpretable, and yields significant performance gains. At low Reynolds numbers, the boundary layer on the compressor blade surface thickens significantly, causing the flow field to deviate severely from the design state, resulting in mismatch between the rotor and stationary components. Momentum thickness Reynolds number Re θs The reduction in Reynolds number is the decisive physical factor for the rapid thickening of the boundary layer at low Reynolds numbers. θs This allows for precise control of boundary layer development characteristics. Based on this physical understanding, this invention constructs pressure gradient parameters at the blade separation point. K s With Re θs A quantitative correlation model between the separation scale and the growth rate of the transition boundary layer. Combined with high-precision parametric blade modeling technology, this will... K s With Re θs This method achieves precise compensation to near-high Reynolds number operating conditions, thereby enabling quantitative control over the separation scale and boundary layer growth rate. Compared to traditional methods such as empirical iteration or numerical optimization, this method focuses on the essential physical mechanism of boundary layer thickening at low Reynolds numbers. The design process has a clear theoretical basis and can reduce the critical Reynolds number of the blade by more than 50%, significantly enhancing the blade's adaptability to low Reynolds number operating conditions.

[0010] (2) The design process is efficient and the time cost is significantly optimized. Based on the pressure gradient-boundary layer characteristic correlation model, the pressure gradient parameters at any Reynolds number can be obtained. K s By combining high-precision parametric modeling methods, the curvature distribution of the target area of ​​the blade can be quantitatively reconstructed, directly obtaining the final optimized blade shape. This greatly simplifies the design path, completely avoids the repeated trial and error process in traditional design, and has significant time benefits and application value in engineering practice. Attached Figure Description

[0011] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart illustrating the compressor blade design method of the present invention. Figure 2 For different Reynolds numbers K s With Re θs Correspondence diagram; Figure 3 For different Reynolds numbers K s A schematic diagram showing the correspondence between the separation scale and the scale. Figure 4 For different Reynolds numbers K s A schematic diagram showing the correspondence between the maximum thickness of the separation bubble and the thickness of the separation bubble; Figure 5 The diagram shows the comparison of fitting errors before and after correction using the CST parameterization method. (a) is before correction, and (b) is after correction. Figure 6 The total pressure loss coefficient before and after correction oh Comparison diagram; Figure 7 To correct the lag angle Δ at the exit before and after β Comparison diagram. Detailed Implementation

[0013] This invention aims to provide a high-efficiency, low-loss design method and application for compressor blades at low Reynolds numbers. To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be described in more detail below with reference to the accompanying drawings. The described embodiments are some, but not all, embodiments of this invention, and are exemplary and intended to explain the invention, not to limit it. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0014] Example 1: Design Method The compressor blade design method based on pressure gradient customization provided in this invention achieves precise matching of the rotor-stationary components at low Reynolds numbers by finely controlling the boundary layer growth rate, thereby improving the compressor's high-altitude efficiency and stability margin. The core technical solution of this method includes the following steps: extraction of blade surface boundary layer parameters, construction of a pressure gradient-boundary layer characteristic correlation model, high-precision parametric modeling of blade geometry, directional compensation and control of pressure gradient parameters, and numerical / experimental verification of aerodynamic performance. The key technical aspect lies in establishing the pressure gradient parameters at the separation point. K s With momentum, thickness, Reynolds number θs A quantitative correlation model between separation scale and boundary layer growth rate. For example... Figure 1 As shown, the specific implementation process of this compressor blade design method is as follows: SS1. Extraction of boundary layer parameters from the prototype blade surface: High-precision measurements and numerical simulations of the three-dimensional flow field inside the compressor at different Reynolds numbers were conducted to extract key flow field parameters in the near-wall region of the blades. Utilizing a variable Reynolds number cascade wind tunnel experimental platform, a steady-state flow field measurement device was employed, consisting of a wall hydrostatic porosimeter array deployed on the blade surface and steady-state flow field measurement devices such as hot-wire anemometers, laser Doppler velocimetry, or particle image velocimetry. Combined with high-fidelity numerical calculations using Large Eddy Simulation (LES), the load distribution on the blade surface and the near-wall boundary layer velocity profile at different Reynolds numbers were obtained. Different Reynolds number conditions were achieved by adjusting the incoming flow density, viscosity, and characteristic velocity, while maintaining consistency in the cascade inlet Mach number, incident angle, and geometric installation angle under each condition to ensure comparability of load comparisons. During high-fidelity numerical calculations, the first layer height of the mesh in the near-wall region of the blade surface satisfied y... + The requirement is <1. At least 20 mesh layers are arranged in the boundary layer to accurately capture the velocity gradient. At the same time, the normal and chord meshes are refined in the areas where the separation bubble may occur to suppress the interference of numerical dissipation on the transition position. Steady-state or unsteady-state calculations are performed under different low Reynolds number conditions. The static pressure distribution on the blade surface is extracted through post-processing to characterize the load distribution, and the boundary layer velocity profile is extracted along the blade surface normal.

[0015] In this embodiment of the invention, the laminar separation, transition initiation point, and reattachment position on the blade surface are accurately located based on the "platform-like" load distribution or the zero-point criterion of wall shear force. Preferably, the starting and ending points of the plateau-like load distribution are used as the initial determination positions of the laminar separation point and the turbulent reattachment point. Furthermore, the wall shear stress is calculated based on the near-wall velocity profile, and the positions of the laminar separation point and the turbulent reattachment point are verified at the positions where the wall shear stress is zero, thereby improving the stability and repeatability of the location of the laminar separation point and the turbulent reattachment point. Simultaneously, the transition initiation point is defined as the chordal position where the growth of disturbance energy within the separated shear layer changes from a gradual increase to a significant increase, and consistency is checked through the near-wall velocity profile shape factor and the abrupt change in the shear layer velocity gradient.

[0016] The displacement thickness is determined by integral calculation based on the boundary layer velocity profile. Boundary layer integral parameters such as momentum thickness (θ), with the outer edge velocity of the boundary layer as the most important parameter. U e Reaching mainstream speed U ∞ The normal distance from the wall at a predetermined percentage (e.g., 99%) is used as the boundary layer thickness. d Boundary layer displacement thickness and momentum thickness i based on U e Solving the normalized velocity profile surface integral, respectively satisfying and ,in U For the flow velocity component, U ∞ As the mainstream speed, r ∞ As the mainstream density, n The coordinates are the wall normal coordinates; and based on Calculate the pressure gradient parameters at the separation point K s ,based on i and U e Calculate the momentum-thickness Reynolds number Re θs = U e i / n ,in n This refers to kinematic viscosity.

[0017] SS2. Construction of the pressure gradient-boundary layer property correlation model: Quantify the pressure gradient parameters at the blade separation point K s Separation Scale L bsBased on the separation / reattachment location and the variation of boundary layer integral parameters with Reynolds number, a system is established. K s With respect to the momentum-thickness Reynolds number at the separation point θs Separation Scale L bs A correlation model between the growth rate of the boundary layer and the growth rate of the boundary layer.

[0018] In this embodiment of the invention, K s With satisfying mathematical relations This constitutes the first correlation sub-model, where is the Polhausen parameter, which can be determined using the least squares method. Based on numerical calculation results for four different Reynolds number Re conditions, and combined with literature data, the following parameters are determined: l θ The value is -0.093 ( Figure 2 When Re increases from 4.5 × 10⁻⁶ 5 Reduced to 1.5×10 5 At that time, it was observed K s The absolute value increased by 3 times, indicating a significant enhancement of the adverse pressure gradient at the separation point, corresponding to Re θs Reduced by 46%. Due to Re θs This directly determines the growth rate of disturbances within the separated shear layer. At low Reynolds numbers, the instability location of the separated shear layer will shift significantly downstream, greatly delaying the transition triggering and turbulent reattachment process, resulting in a sharp increase in the size of the separated bubble and a synchronous acceleration of boundary layer growth.

[0019] The distance from the laminar separation point to the turbulent reattachment point is defined as the separation scale. L bs It satisfies the following empirical relation , S sep This represents the distance from the leading edge of the blade to the laminar separation point. Parameters are determined using the least squares method. C , D Then, the steps are derived. L bs and K s The second correlation sub-model ( Figure 3 ), a , b These are the coefficients determined by the least squares fitting method.

[0020] by L bs / S sep As an intermediate variable, the maximum relative thickness of the separation bubble is further established. and Ks The third correlation sub-model , ,in The boundary layer displacement thickness at the laminar separation point can be approximated by the maximum relative thickness of the separation bubble. A 1. B 1 and C 1 represents the coefficients determined by the least squares fitting method, and and Both are based on the outer edge velocity of the boundary layer. U e The result is obtained by calculating the criterion integral. The above results show that when Re increases from 4.5 × 10⁻⁶... 5 Reduced to 1.5×10 5 hour, K s When the absolute value increases to three times its original value, Re θs A 46% reduction corresponds to a 133% increase in separation scale and a 147% increase in relative boundary layer thickness.

[0021] Based on the above analysis, the results can be obtained at different Reynolds numbers. K s With Re θs Separation Scale L bs The model is constructed to correlate the growth rate of the boundary layer. The model has two-way prediction and control capabilities: (1) For any target Reynolds number, it can accurately determine the working condition. K s Re θs (1) Separation scale and boundary layer growth rate; (2) By directional adjustment of the blade suction surface K s This enables quantitative control of the separation scale and boundary layer growth rate, meeting the precise matching requirements of the rotor-stator components under this operating condition.

[0022] SS3. High-precision parametric modeling of blade geometry: High-precision parametric modeling of blades is the key to achieving... K s The key to precise control lies in this invention, which improves the Class Shape Transformation (CST) method for high-precision parametric blade shaping. This improvement is based on a class function. C ( ) and shape function S ( The algorithm formula satisfies the following conditions: multiplying the components by a function representing the trailing edge characteristics to fit the blade profile. , The dimensionless x-axis represents the blade. The dimensionless ordinate of the blade; The dimensionless thickness of the trailing edge of the blade. C ( () is a category function used to define the basic shape of the blade; S ( The shape function () is used to modify the basic shape. The category function is generally defined as... , N 1 , N 2 These are control parameters. N 1 and N 2 Different values ​​correspond to different basic shapes. Shape function Generally adopted n Linear weighted summation of Bernstein polynomials of order 1 n The Bernstein polynomial of order 1 is in the form of , n Let be the order of the polynomial. x The value range is [0,1], and the coefficient is... Defined as From the above, we can derive the shape function in CST parameterization. The expression is , A i The control coefficients are used. The final blade suction or pressure profiles are fitted using the following functions: For a given blade, the suction surface and pressure surface are respectively adopted... n When performing CST parameterization on a Bernstein polynomial of order 1, if we take N 1 = 0.5 N 2=1, then we have 2( n +1) undetermined coefficients A i If the coordinates of the discrete points on the blade are known, the coefficients can be determined using the least squares method. A i Then the CST parameterization process can be completed, and the fitting error can be obtained. It is worth noting that the leading edge shape of compressor blades is generally quite complex, with significant curvature variations. In this case, the control parameters... N 1, N Using values ​​of 0.5 and 1 respectively may result in larger leading edge fitting errors. Therefore, this invention improves the original CST method, that is, by... N 1, N 2 is also used as a fitting variable to improve fitting accuracy through adaptive leading edge shape, such as... Figure 5As shown in the figure, the improved average fitting error decreased by 23.8%, and the maximum fitting error was less than 7 × 10⁻⁶. -4 This meets the accuracy requirements of wind tunnel testing for model test pieces.

[0023] As a preferred option, by adjusting the blade profile x ( The leaf surface curvature distribution is obtained by performing second-order differentiation. k ( By applying small perturbations to each modeling variable and calculating... k ( The change in the shape variables is used to determine the direction and sensitive range of the influence of each shape variable on the curvature distribution. A sensitivity matrix is ​​established and a mapping relationship between each shape variable and the blade surface curvature distribution is formed, which is used for subsequent local directional geometric correction and pressure gradient parameter compensation control.

[0024] SS4. Targeted compensation and control of pressure gradient parameters: The region near the laminar separation point on the suction surface at low Reynolds numbers is designated as the geometric correction region to ensure that the target Reynolds number is achieved. K s and corresponding Re θs The control objective is to compensate to a level close to the baseline Reynolds number. Under the condition of blade geometry constraints, the local directional correction of the geometry correction region is achieved by optimizing and adjusting various shaping variables, so as to obtain the compensated modified blade geometry.

[0025] After fitting the parametric model, blade geometry reconstruction based on pressure gradient control is implemented. Given that the laminar separation point on the suction surface is located at approximately 33% of the axial chord length at low Reynolds numbers, the shape function control coefficient is adjusted. A i Directional correction is applied to the local curvature distribution near the separation region, K s and corresponding Re θs The airfoil design was optimized by precisely compensating to a level close to the high Reynolds number reference condition.

[0026] Preferably, the reference Reynolds number condition is selected as the ground normal operating condition or the Reynolds number condition corresponding to the prototype blade design point; the range of the geometric correction region is determined by the arc length interval extending upstream and downstream of the blade surface from the location of the laminar flow separation point on the blade suction surface, covering the local high curvature gradient region near the laminar flow separation point; outside the geometric correction region, the prototype blade profile remains unchanged, and a continuity constraint is applied at the boundary of the region so that there are no geometric inflection points or curvature abrupt changes at the boundary of the correction region.

[0027] Under the condition of satisfying the geometric constraints of the blade, based on the mapping relationship between each shaping variable and the blade surface curvature distribution, optimization adjustments are made. C ( ) and / or S ( The control parameters of the instrument enable local directional correction of the geometric correction region, so that the corrected result under the target Reynolds number condition is obtained. K s and corresponding Re θs The blade converges to a preset threshold range at the reference Reynolds number level. The blade geometric constraints include at least the lower limit of the leading edge radius, the lower limit of the minimum thickness, the upper limit of the trailing edge thickness, and the first-order continuity constraint of the profile. During the local orientation correction process, amplitude boundaries are applied to each shape variable to ensure that the modified blade meets the strength requirements of processing, manufacturing, and assembly, while avoiding non-physical pressure peaks and premature separation of the boundary layer caused by sudden changes in local curvature.

[0028] The following control strategy is used to perform targeted correction on the local curvature distribution within the geometric correction region: firstly, only the category function is adjusted. C ( ) control parameters N 1. N 2. By changing the overall curvature level of the neighborhood of the separation point on the suction surface and obtaining the first stage compensation, the shape function is adjusted after satisfying the preset feasible region. S ( The control parameters are used to finely shape the pressure gradient distribution before and after the separation point; and during the iteration process, the load distribution and near-wall velocity profile under the target Reynolds number condition are recalculated after each update of the shaping variables to update the parameters. K s and corresponding Re θs And based on the correlation model, the separation scale was verified. L bs The trend of the boundary layer growth rate characteristic quantity shows that when the change in the modeling variable is lower than the preset convergence threshold for two or more consecutive iterations, and K s With Re θs The iteration terminates when the deviation meets the preset threshold range, thereby reducing the risk of nonlinear divergence caused by the coupling of design variables and improving the convergence of compensation iteration through hierarchical control.

[0029] More preferably, multiple spanwise profiles are selected along the blade height direction to establish CST parametric models, and geometric correction regions near the separation point are determined and processed on each spanwise profile. K s and corresponding Re θs Directional compensation is applied, while spanwise smooth continuity constraints are imposed on the shape variables of adjacent spanwise sections to ensure the continuity of the curvature distribution of the modified blades along the spanwise direction and reduce additional losses in three-dimensional flow.

[0030] SS5. Aerodynamic performance numerical / experimental verification: Numerical calculations and / or experimental measurements were performed on the reconstructed modified blades under different Reynolds number conditions to verify the improvement effect of directional compensation for pressure gradient parameters. The prototype and modified blades were compared and evaluated and their performance verified under multiple different Reynolds number conditions, with verification indicators including at least the total pressure loss coefficient. oh With the export lagging angle Δ β And combined with the critical Reynolds number Re cr The effect of directional compensation of pressure gradient parameters on improving the sensitivity to performance degradation at low Reynolds numbers was determined, among which Re cr Defined as oh or Δ β The Reynolds number at which the slope increases abruptly as the Reynolds number decreases.

[0031] It should be noted that in this embodiment, the pressure gradient parameter at the separation point is... K s As a controllable intermediate variable connecting geometry and flow: on the one hand, it is obtained through high-precision measurement and high-fidelity calculation in step SS1. K s and corresponding Re θs With observable measurements such as the separation bubble scale, the reliability of the correlation model input is ensured; on the other hand, step SS2 establishes... K s With Re θs , L bs The correlation model between the boundary layer growth rate and the boundary layer growth rate, step SS3 introduces an improved CST and... N 1. N 2. Control parameters are incorporated into the fitting variables to improve the parameterization accuracy in regions with complex leading-edge curvature, ensuring that local geometric corrections accurately fall within the neighborhood of the separation point. Step SS4 employs a hierarchical control strategy to reduce the risk of nonlinear divergence caused by variable coupling, and constructs closed-loop iteration termination conditions through feasible region and convergence criteria. Finally, within the range of multiple Reynolds numbers... oh With Δ β Consistency verification is performed to ensure that the compensation effect is verifiable across operating conditions.

[0032] It should also be noted that the core innovation of this invention lies in establishing a multi-level quantitative correlation model between the pressure gradient parameter Ks and key boundary layer characteristics. This model not only reveals the physical mechanism of laminar separation bubble formation and evolution under low Reynolds number conditions, but more importantly, it provides an operable approach to achieve directional control of the pressure gradient through local geometric correction. Compared with traditional blade optimization methods that rely on experience or large-scale parameter scanning, this invention, through a physical model-driven directional compensation strategy, can achieve the target performance with fewer design iterations, significantly improving design efficiency. Furthermore, the improved CST parameterization method, by incorporating categorical function control parameters into the optimization variables, maintains the compactness of the parameterization representation while enhancing its adaptability to complex leading-edge geometry, laying a foundation for accuracy in subsequent gradient-based optimization iterations. The established mapping relationship between each shape variable and the blade surface curvature distribution clarifies the influence domain and intensity of each shape variable on the curvature distribution, making the geometric correction process more targeted and controllable, avoiding design divergence caused by blind adjustments. In practical applications, this method can be extended to the rotor-stator matching design of multi-stage compressors. By implementing pressure gradient compensation on each stage of the blades, the interstage flow parameters can be optimized in a coordinated manner across the entire operating range, thereby improving the high-altitude performance and stability margin of the compressor system.

[0033] Example 2: Verification Example Based on Example 1 above, Example 2 further provides a set of comparative examples for verifying the effectiveness of directional compensation control of pressure gradient parameters. The prototype blade from Example 1 is selected as the baseline (B), and the modified blade obtained in step SS4 is used as the redesign (R). Within the same blade cascade test section or the same numerical computation domain, under the condition of maintaining consistent inlet Mach number, incident angle, turbulence intensity level, and geometric installation angle, different Reynolds number conditions are constructed, covering 4.5 × 10⁻⁶. 5 3.5×10 5 2.5×10 5 1.5×10 5 Representative operating conditions were used to characterize the typical low Reynolds number effect during the transition from the normal ground state to the low-density high-altitude state.

[0034] Under various Reynolds number conditions, the total pressure at the inlet and outlet of the blade cascade, as well as the outlet velocity vector, were obtained for both B and R blades, and the total pressure loss coefficient was calculated. oh With the export lagging angle Δ β As a performance evaluation metric, among oh Δ represents the total pressure loss of the airflow after passing through the cascade. β This characterizes the degree of deviation of the outlet flow direction from the design flow direction; simultaneously, it extracts the critical Reynolds number Re using the piecewise linear fitting inflection point criterion described in Example 1.cr Re cr Defined as oh or Δ β The Reynolds number exhibits a sharp increase in slope as the Reynolds number decreases.

[0035] Figure 6~Figure 7 The total pressure loss coefficient (ω) and exit lag angle (Δ) of the baseline (B) and redesigned (R) blades were compared. β Characteristics of Reynolds number evolution: The prototype blade is very sensitive to the low Reynolds number effect. When the Reynolds number is below the critical value (3.5 × 10⁻⁶), the blade becomes extremely sensitive to the low Reynolds number effect. 5 When the regression angle is low, the loss and lag angle begin to rise sharply, and the performance deteriorates rapidly; conversely, the modified blades exhibit excellent robustness under operating conditions, with the lowest Reynolds number (1.5 × 10⁻⁶). 5 Loss and lag angle under ) and high Reynolds number (4.5×10) 5 The operating conditions remained basically the same, but the critical Reynolds number decreased by more than 50%. These results indicate that by adjusting the pressure gradient parameter at the separation point... K s and its corresponding Re θs Directional compensation control that converges to the benchmark Reynolds number operating level can effectively suppress the loss growth and outlet flow angle deviation caused by the expansion of the separated bubble scale and the rapid thickening of the boundary layer at low Reynolds numbers, significantly improve the matching characteristics of the rotor-stationary components at low Reynolds numbers, and thus enhance the high-altitude efficiency and stability margin of the compressor.

[0036] The objectives of this invention have been fully and effectively achieved through the above embodiments. Those skilled in the art will understand that this invention includes, but is not limited to, the contents described in the accompanying drawings and the specific embodiments described above. Although the invention has been described with reference to what is currently considered the most practical and preferred embodiments, it should be understood that the invention is not limited to the disclosed embodiments, and any modifications that do not depart from the functional and structural principles of the invention will be included within the scope of the claims.

Claims

1. A compressor blade design method based on pressure gradient customization, characterized in that, include: SS1. Obtain surface load distribution and near-wall boundary layer velocity profile data of prototype blades at different low Reynolds numbers, locate the laminar separation point and turbulent reattachment point on the blade surface, solve for the boundary layer integral parameters, and simultaneously calculate the pressure gradient parameters at the separation point. K s With momentum, thickness, Reynolds number θs The boundary layer integral parameters include at least the displacement thickness. and momentum thickness θ ; SS2. Quantification K s Separation Scale L bs And the variation of boundary layer integral parameters with Reynolds number, establish K s With Re θs , L bs The correlation model between the growth rate of the boundary layer and the growth rate of the boundary layer, in which L bs Defined as the distance between the laminar separation point and the turbulent reattachment point; SS3. Parametric modeling of the blades is performed using the CST method, employing a category function. C ( Define the basic shape of the blade using shape functions. S ( The basic shape is modified, by C ( )and S ( Multiplying these components and adding a function characterizing the trailing edge features to fit the blade profile, will... C ( )and S ( The control parameters are used as shaping variables to establish a mapping relationship between each shaping variable and the blade surface curvature distribution; SS4. Determine the region near the laminar separation point on the suction surface at low Reynolds numbers as the geometric correction region to ensure that the target Reynolds number is achieved. K s and the corresponding Re θs The control objective is to compensate to a level close to the baseline Reynolds number. Under the condition of blade geometry constraints, the local directional correction of the geometry correction region is achieved by optimizing and adjusting various shaping variables to obtain the compensated modified blade geometry. SS5. Perform numerical calculations and / or experimental measurements on the compensated and reconstructed modified blades under different Reynolds number conditions to verify the improvement effect of directional compensation of pressure gradient parameters.

2. The method according to claim 1, characterized in that, In step SS1, the surface load distribution and near-wall boundary layer velocity profile of the prototype blade are obtained based on experimental measurements and / or numerical simulations: The experimental measurements relied on the variable Reynolds number blade cascade wind tunnel experimental platform. The static pressure distribution on the blade surface was obtained by an array of static pressure measuring holes arranged on the blade surface, and the load distribution on the blade surface was obtained by converting the pressure coefficient. At the same time, near-wall velocity data was obtained in the normal direction of the blade surface by hot wire velocimetry, laser Doppler velocimetry or particle image velocimetry, and a boundary layer velocity profile was formed. The numerical simulation employs a high-fidelity numerical calculation method based on large eddy simulation. The height of the first layer of the mesh in the near-wall region of the blade surface satisfies y + The requirement is <1. At least 20 mesh layers are arranged in the boundary layer to accurately capture the velocity gradient. Steady-state or unsteady-state calculations are performed under different low Reynolds number conditions. The static pressure distribution on the blade surface is extracted through post-processing to characterize the load distribution, and the boundary layer velocity profile is extracted along the blade surface normal.

3. The method according to claim 1 or 2, characterized in that, In step SS1, the load distribution is obtained by the distribution of the static pressure coefficient on the blade surface along the chord or along the arc length of the blade surface. The starting and ending positions of the load distribution showing plateau characteristics are used as the initial judgment positions of the laminar separation point and the turbulent reattachment point. The wall shear stress is further calculated based on the near-wall velocity profile, and the positions of the laminar separation point and the turbulent reattachment point are verified at the position where the wall shear stress is zero.

4. The method according to claim 3, characterized in that, In step SS1, the boundary layer outer edge velocity is used. U e Reaching mainstream speed U ∞ The boundary layer thickness is defined as the normal distance from the wall at a predetermined ratio. δ Boundary layer displacement thickness and momentum thickness θ based on U e Solving the normalized velocity profile surface integral, respectively satisfying ,in U For the flow velocity component, U ∞ As the mainstream speed, ρ ∞ As the mainstream density, n The coordinates are the wall normal coordinates; and based on the laminar separation point... Calculate pressure gradient parameters K s ,based on θ and U e Calculate the momentum-thickness Reynolds number Re θs = U e θ / ν ,in ν This refers to kinematic viscosity.

5. The method according to claim 4, characterized in that, In step SS2, the association model includes at least: for characterization K s With Re θs The first associated sub-model of the correspondence relationship ,in λ θ The parameter is a dimensionless Polhausen parameter, and λ θ The values ​​are based on sample sets at different Reynolds numbers. Re θs , K s Determined by least squares fitting; used to characterize K s and L bs The second association sub-model of correspondence ,in S sep This is the distance from the leading edge of the blade to the laminar separation point. a , b These are the coefficients determined by the least squares fitting method; used to characterize... K s The third correlation sub-model corresponding to the boundary layer growth rate ,in The maximum displacement thickness of the separation bubble. The boundary layer displacement thickness at the laminar separation point. A 1. B 1 and C 1 represents the coefficients determined by the least squares fitting method, and and Both are based on the outer edge velocity of the boundary layer. U e The result is obtained by calculating the criterion integral.

6. The method according to claim 1, characterized in that, In step SS3, the CST method is used to parametrically express the blade suction and pressure surface profiles respectively, and its algorithm formula satisfies , , , These are the chord coordinates. x Normal coordinates y Trailing edge thickness Δ y T dimensionless number, C String length; category function Used to define the basic outline boundaries of the leading and trailing edges of the blade. N 1. N 2 is its control parameter; shape function S ( Used to correct the basic shape of the blade and employ n The form of a linear weighted sum of Bernstein polynomials of order 1 satisfies , A i For the corresponding i The control parameters of the order.

7. The method according to claim 6, characterized in that, In step SS3, by adjusting the blade profile... The leaf surface curvature distribution is obtained by performing second derivative. By applying small perturbations to each modeling variable and calculating... The changes in the shape variables are used to determine the direction and sensitive range of the influence of each shape variable on the curvature distribution. A sensitivity matrix is ​​established, and a mapping relationship between each shape variable and the leaf surface curvature distribution is formed.

8. The method according to claim 7, characterized in that, In step SS4, the reference Reynolds number condition is selected as the ground normal operating condition or the Reynolds number condition corresponding to the prototype blade design point; the range of the geometric correction region is determined by the arc length interval extending upstream and downstream of the blade surface from the location of the laminar flow separation point on the blade suction surface, covering the local high curvature gradient region near the laminar flow separation point; outside the geometric correction region, the prototype blade profile remains unchanged, and a continuity constraint is applied at the boundary of this region.

9. The method according to claim 8, characterized in that, In step SS4, under the condition of satisfying the blade geometric constraints, based on the mapping relationship between each shaping variable and the blade surface curvature distribution, optimization is performed to adjust... and / or The control parameters enable local directional correction of the geometric correction region, so that the corrected result under the target Reynolds number condition is obtained. K s and corresponding Re θs The blade converges to a preset threshold range at the benchmark Reynolds number level, wherein the blade geometric constraints include at least the lower limit of the leading edge radius, the lower limit of the minimum thickness, the upper limit of the trailing edge thickness, and the first-order continuity constraint of the profile.

10. The method according to claim 9, characterized in that, In step SS4, the local curvature distribution within the geometric correction region is directionally corrected using the following control strategy: First, only adjust the category function. control parameters N 1. N 2. By changing the overall curvature level of the neighborhood of the separation point on the suction surface and obtaining the first stage compensation, the shape function is adjusted after satisfying the preset feasible region. The control parameters are used to finely shape the pressure gradient distribution before and after the separation point; and during the iteration process, the load distribution and near-wall velocity profile under the target Reynolds number condition are recalculated after each update of the shaping variables to update the parameters. K s and corresponding Re θs And based on the correlation model, the separation scale was verified. L bs The trend of the boundary layer growth rate characteristic quantity shows that when the change in the modeling variable is lower than the preset convergence threshold for two or more consecutive iterations, and K s With Re θs The iteration terminates when the deviation meets the preset threshold range.

11. The method according to claim 1, characterized in that, In step SS5, the prototype blade and the modified blade are compared and evaluated and their performance verified under multiple different Reynolds number conditions. The verification index includes at least the total pressure loss coefficient. ω With the export lagging angle Δ β And combined with the critical Reynolds number Re cr The effect of directional compensation of pressure gradient parameters on improving the sensitivity to performance degradation at low Reynolds numbers was determined, among which Re cr Defined as ω or Δ β The Reynolds number at which the slope increases abruptly as the Reynolds number decreases.

12. A compressor blade, characterized in that, Its design adopts the compressor blade design method based on pressure gradient customization as described in any one of claims 1 to 11.

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