A method for shaping a compressor bionic wavy trailing edge
By combining the biomimetic wavy trailing edge with the suction surface channel, the problem of insufficient synergy between the trailing edge and suction surface structures in compressor blade design is solved, thereby reducing flow losses and suppressing corner separation, and improving compressor performance.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2026-04-03
- Publication Date
- 2026-07-03
Smart Images
Figure CN122333635A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of compressor design, specifically relating to a method for creating a biomimetic wavy trailing edge for a compressor. Background Technology
[0002] In modern civil aviation aero engines, the compressor, as the core compression component, is highly susceptible to three-dimensional corner separation due to the interaction of the adverse pressure gradient and secondary flow. Corner separation significantly reduces efficiency and induces instability, posing a serious threat to the operation of aero engines. Therefore, suppressing corner separation is one of the key areas of flow control.
[0003] To suppress corner separation, researchers have developed various flow control techniques, mainly divided into two categories: active control and passive control. Active control methods include boundary layer suction, wall jetting, and plasma mechanisms, which typically require external energy input and are limited in engineering applications due to their system complexity. Passive control methods include non-axisymmetric endwalls, blade root rounding, and leading-edge shaping, which do not require external energy input and generally have the advantages of simple, reliable, and low-cost structures; however, their corner separation control effect is often inferior to that of active control methods.
[0004] In recent years, bionics has provided new insights into flow control. Researchers have drawn inspiration from biological structures such as bird wings and whale fins to develop a series of biomimetic blade design methods. For example, some studies have introduced wave-shaped structures at the leading edge of the blade to suppress channel vortex development through leading-edge vortices, thereby delaying stall. Other studies have incorporated biomimetic ribs or groove structures on the suction surface to enhance the kinetic energy of low-energy fluids and reduce corner losses. In the trailing edge region, biomimetic serrated structures have been shown to have significant noise reduction effects, but their application in suppressing corner separation remains relatively limited.
[0005] However, existing biomimetic leaf-shaped design methods have the following common shortcomings: The modification targets are singular: most methods only modify a local area of the leading edge, trailing edge, or suction surface independently, lacking a coordinated design of the trailing edge and suction surface structures. For example, the trailing edge serrated structure only changes the geometry of the trailing edge without linking it with the suction surface profile; the suction surface rib structure also does not consider the matching relationship with the trailing edge waveform.
[0006] Insufficient geometric transition and flow field synergy: Some modification methods (such as serrated trailing edge) have geometric discontinuities in the blade height direction, which can easily introduce secondary flow losses; while the local concavity of the suction surface is often set independently, and the geometric transition with the trailing edge region is not smooth, making it difficult to achieve superposition and synergy of flow control effects.
[0007] In summary, current technologies have not yet proposed a compressor blade design technique that can simultaneously consider both the trailing edge waveform and the suction surface channel, and achieve synergistic modification through a unified parameterization method. How to achieve joint control of the trailing edge and suction surface regions while maintaining geometric continuity and structural simplicity, thereby more effectively suppressing corner separation, remains a pressing technical challenge in this field. Summary of the Invention
[0008] The technical problem to be solved: To overcome the shortcomings of existing technologies, this invention provides a biomimetic wavy trailing edge design method for compressors. This method uses a biomimetic design based on the trailing edge of a bird's wing, which significantly suppresses angular separation in the compressor stator blades. The specific design structure is as follows: Figure 2 As shown, it specifically includes two structural features: ① The trailing edge forms a wavy shape through trigonometric functions. ② A smooth channel structure is formed on the suction surface of the blade. These two features together construct a bird-like trailing edge biomimetic structure. This invention achieves the coordinated design of the compressor blade trailing edge waveform and suction surface channel through parameterized geometric modeling. While ensuring geometric continuity, it jointly regulates the development of the wake and the accumulation of low-energy fluid in the corner region, thereby more effectively suppressing corner separation and reducing flow losses.
[0009] The technical solution of this invention is: a method for creating a biomimetic wavy trailing edge of a compressor, comprising the following steps: Obtain the original compressor blade model and uniformly cut several element sections along the span; Based on the geometric characteristics of each element's cross section, construct the arc function within it; The axial chord length distribution of the basic element sections at different spanwise positions is adjusted by using waveform control functions to form a trailing edge geometry that varies in a wave-like manner along the spanwise direction; Calculate the thickness distribution on the suction side and pressure side of the prototype blade for each basic section, as well as the angle between the normal of each side profile and the axial direction. Under the same parameterization framework of the waveform control function, the coordinate transformation of the mid-arc function is performed, and the thickness distribution on the suction side, the thickness distribution on the pressure side, and the angle between the normal of each side surface and the axis are superimposed on the transformed mid-arc line while keeping them unchanged, so as to generate the biomimetic suction and pressure surface coordinates, thereby forming a flow guide channel on the suction side of the blade that is geometrically continuous with the wavy trailing edge. Based on the adjusted primitive cross-sectional geometry, a biomimetic wavy trailing edge blade is generated; the wavy geometry of the trailing edge and the flow guiding channel on the suction surface side are generated collaboratively through the same set of arc transformation methods, and the two are geometrically continuous and work together in the corner separation region for flow control. A further technical solution of the present invention is that the waveform control function is a trigonometric function, and its expression is:
[0010] In the formula, C a This represents the axial chord length of the prototype blade element cross section; A Indicates the amplitude of the control wavy trailing edge; T Indicates period; n Indicates phase; This indicates that the axial chord length of the primitive cross section has been modified using trigonometric functions; h Indicates the direction of expansion.
[0011] A further technical solution of the present invention is: the amplitude of the controlled wavy trailing edge A The value range is [0, 0.06]. C a The period T The value range of h is [0.01, 0.5]. blade h blade For the leaf height; n The value of is [0,1].
[0012] A further technical solution of the present invention is: the specific method for constructing the arc function is as follows: Construct an inscribed circle in each element section and obtain the coordinates of the center of the inscribed circle as discrete points of the mid-arc line; The discrete points are fitted using a cubic polynomial to generate the equation of the mid-arc line:
[0013] In the formula, y The coordinates represent the direction from the suction side to the pressure side. z The axis coordinates are represented by ; a, b, c, and d are the parameters controlling the cubic, quadratic, linear, and zeroth-order terms of the polynomial, respectively. The parameter values are obtained by fitting discrete points using the polyfit command in MATLAB. Adjusting parameters using the least squares method a , b, c, d The value of is used to fit the arc.
[0014] A further technical solution of the present invention is as follows: the specific process for calculating the thickness distribution on the suction side, the thickness distribution on the pressure side, and the angle between the normal to each side profile and the axial direction of the prototype blade of each basic section is as follows: Pressure surface thickness distribution thickness p The angle between the normal to the pressure surface and the axial direction. θ p The expression is as follows:
[0015] In the formula,y p , z p These represent the Y and Z coordinates of the pressure surface side of the airfoil in the basic section, respectively. y , z Let Y and Z represent the Y-axis coordinates and Z-axis coordinates of the intersection point of the pressure surface side normal and the mid-curve line, respectively; where... z p and z The values are all [z LE , z TE ], z LE and z TE These represent the Z coordinates of the leading edge and trailing edge of the blade, respectively. line p Represents the side spline of the pressure surface; Thickness distribution on the suction surface side, angle between the suction surface side normal and the axial direction:
[0016] In the formula, y s , z s These represent the Y and Z coordinates of the suction surface side of the blade section, respectively; y * , z * Let Y and Z represent the Y-axis coordinates and Z-axis coordinates of the intersection point of the suction side normal and the mid-arc line, respectively; where... z s and z * The values are all [z LE , z TE ], z LE and z TE These represent the Z coordinates of the leading edge and trailing edge of the blade, respectively. line s This represents the side spline of the suction surface.
[0017] A further technical solution of the present invention is: the coordinate transformation formula is:
[0018] The expression for the lateral coordinates of the pressure surface of the biomimetic blade shape:
[0019] The coordinate expression for the suction surface of the leaf after biomimetic design:
[0020] in, y camber and zcamber These represent the Y and Z coordinates of the mid-arc line after the biomimetic design; The Z-coordinate of the mid-arc line representing the starting position of the biomimetic design, i.e., the Z-coordinate of the starting position of the suction surface side channel structure; z ori The Z-coordinate of the mid-arc of the prototype; z LE This represents the Z-coordinate of the leading edge point of the blade; y ps and z ps These represent the Y and Z coordinates of the pressure surface side of the biomimetic design, respectively. y ss and z ss These represent the Y and Z coordinates of the biomimetic suction surface, respectively. L The depth control parameter for the flow guide channel, with values of [0, 1]; k This represents the scaling factor, which is changed by adjusting the parameter. L The value controls the depth of the suction surface side channel structure in the biomimetic design; L The larger the value, the deeper the groove on the suction surface.
[0021] A further technical solution of the present invention is: the amplitude in the waveform control function A ,cycle T Phase n and the depth control parameters of the flow guide channel. k The starting position Z-coordinate of the suction surface side channel structure The following optimization algorithm was used for selection: Step 1: Use the Latin hypercube sampling method to sample the amplitude values. A ,cycle T Phase n and the depth control parameters of the flow guide channel. k The starting position Z-coordinate of the suction surface side channel structure Uniform sampling is performed within the parameter design space to generate several sets of geometric parameter samples; for each set of geometric parameter samples, a corresponding biomimetic wavy trailing edge blade geometric model is generated according to the aforementioned compressor biomimetic wavy trailing edge modeling method, and the blade geometric model is numerically simulated using computational fluid dynamics to obtain the total pressure loss coefficient of the blade cascade corresponding to each sample. Step 2: Using the geometric parameter samples as input and the corresponding total pressure loss coefficient as output, construct and train a radial basis function surrogate model. The radial basis function surrogate model is used to approximately characterize the mapping relationship between the geometric parameters and the total pressure loss coefficient. Step 3: Based on the trained radial basis function surrogate model, a genetic algorithm is used to search for the optimal combination of geometric parameters that minimizes the total pressure loss coefficient within the parameter design space, as the predicted optimal shape; Step 4: The predicted optimal shape is verified using computational fluid dynamics. If the verification result meets the preset convergence criterion, the geometric parameter combination is determined as the final selected shape parameter. If it does not meet the criterion, the verification result is added to the training sample set, the radial basis function surrogate model is retrained, and steps 2 to 4 are repeated until the convergence criterion is met.
[0022] A further technical solution of the present invention is: the biomimetic wavy trailing edge shape starts at a preset spanwise position upstream of the trailing edge of the blade, and the arc line changes and thickness is mapped from the starting position to the trailing edge line. A further technical solution of the present invention includes the step of writing the modified primitive section geometry into a geometry file and importing it into a mesh generation tool for structured mesh generation.
[0023] A compressor blade is manufactured using the aforementioned biomimetic wavy trailing edge shaping method. The trailing edge of the blade exhibits a spanwise wavy change, and a flow guide channel is formed on the suction side near the trailing edge, which is geometrically continuous with the wavy trailing edge. The wavy trailing edge and the flow guide channel are generated collaboratively through the same parameterized framework.
[0024] Beneficial effects The beneficial effects of this invention are as follows: Through the synergistic design of the wavy trailing edge and the suction surface channel, this invention can effectively control the development of the wake and the accumulation of low-energy fluid in the corner region. Verification by examples shows that in a high-load axial compressor, the biomimetic wavy trailing edge blade designed using the method of this invention reduces the total pressure loss by 5.3% and increases the static pressure rise coefficient by 2.79% at the design angle of attack; under near-stall conditions (10° angle of attack), the total pressure loss is reduced by 10.79% and the static pressure rise coefficient is increased by 3.78%. Flow field analysis shows that the volume of low-energy fluid in the suction surface trailing edge region is significantly reduced, and corner separation is effectively suppressed. Specific effects are as follows: 1. This invention overcomes the limitations of traditional methods that only modify a single region. It simultaneously generates a wavy trailing edge and a suction-surface flow-guiding channel using the same set of mid-arc transformation methods. These two elements are geometrically continuous and coupled in flow control: the wavy trailing edge alters the wake development and shedding vortex structure, while the suction-surface channel regulates the transport path of low-energy fluid in the corner region, resulting in synergistic effects. Comparative experiments show that the performance improvement of this invention is significantly greater than the simple superposition of a single wavy trailing edge and a single suction-surface channel.
[0025] 2. This invention uses trigonometric functions to control the trailing edge chord length variation, allowing for flexible adjustment of the wavy morphology through three parameters: amplitude, period, and phase. Simultaneously, it utilizes a thickness mapping method to maintain the thickness distribution of the prototype blade, changing only the mid-curve morphology. The invention employs a small number of control parameters with clear physical meanings, facilitating rapid shape adjustment based on flow field characteristics, and can be combined with optimization algorithms to achieve global optimization.
[0026] 3. For example Figure 8 and Figure 9 As shown, the suction surface channel significantly reduces the size of the suction surface separation region, while the spiral point (F1 and F2) structures within the separation region are significantly suppressed, which helps reduce airflow dissipation losses at the suction surface. The wavy trailing edge effectively suppresses the formation of trailing edge vortices (TV), reduces the intensity of flow around the trailing edge, reduces the formation of reverse flow at the root, and effectively improves the flow field performance in the trailing edge region. The combined effect of these two elements significantly improves the mixing of the airflow between the trailing edge and beyond, resulting in a significant reduction in the total pressure loss coefficient. Attached Figure Description
[0027] Figure 1 This is a technical roadmap of a method for creating a biomimetic wavy trailing edge of a compressor, as described in an embodiment of the present invention. Figure 2 This is a schematic diagram of the biomimetic wavy tail edge design in an embodiment of the present invention; Figure 3 This is a schematic diagram showing the cross-sectional division of the original model elements; Figure 4 This is a schematic diagram of the inscribed circle of the element cross section in an embodiment of the present invention; Figure 5 This is a schematic diagram of the coordinate transformation of the biomimetic model in an embodiment of the present invention; Figure 6 A schematic diagram of a biomimetic structural grid; Figure 7 A comparison diagram of low-energy fluid distribution between the prototype and the biomimetic design; Figure 8 A comparison diagram of the static pressure rise coefficient contour map and the limiting streamline; Figure 9 This is a comparison diagram of axial vorticity contour plot and three-dimensional streamline. Detailed Implementation
[0028] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.
[0029] Bionics is a discipline that studies the structure and properties of biological systems, aiming to imitate and apply them in the field of engineering. Over millions of years of evolution, organisms in nature have developed numerous forms and structures with excellent aerodynamic properties. By translating these biological principles into engineering solutions, bionics provides entirely new design ideas for the field of modern fluid dynamics control. Currently, some bionic structures have been applied to corner separation control and have achieved strong flow control effects. (Jiezhong DONG, Wuli CHU, Haoguang ZHANG, et al. Investigation of non-uniform leading-edge tubercles in compressor cascade: Based on multi-objective optimization and data mining) Using the convex nodule at the leading edge of a whale fin as a reference, a non-uniform leading-edge convex nodule was designed for the compressor cascade, and numerical simulation and optimization design were carried out. The results show that the whale fin bionic structure increased the stall angle of attack from 7.9° to 11.6°, improving the margin by 46.8%, and significantly reducing the total secondary flow energy in the cascade channel. Flow field analysis shows that the main reason for the reduction in secondary kinetic energy is the formation of leading-edge vortex pairs with opposite directions to the channel vortex, which inhibits the development of channel vortices and delays the occurrence of corner stall. (Chongjia Guo, Xudong Yang, Ji-ang Han et al. Effect of a Bionic Blade Rib on the Loss Characteristics of a Highly Loaded Compressor Cascade. Aerospace Science and Technology) Referring to the flow separation control and stall mechanism of the peregrine falcon, various biomimetic rib structures were incorporated into the suction surface of the compressor blade cascade to control corner separation. Numerical simulation studies show that within the angle of attack range of -9° to 6°, the biomimetic rib structures can reduce corner losses to varying degrees. The T-shaped biomimetic rib structure exhibits the best overall loss reduction effect. The vortex structure inside the biomimetic rib enhances the kinetic energy of the low-energy fluid in the corner boundary layer. The size and intensity of the channel vortex decrease, resulting in a 9.87% reduction in losses.(Wenfeng Xu, Zeming Wang, Chengxi Tang et al. Effect of endwall bionicchamber with different depths and placements on compressor performance. Aerospace Science and Technology) Inspired by the structure of dragonfly wings, a bionic endwall cavity structure was constructed. Numerical studies revealed that the vortex structure generated by the bionic endwall cavity structure enhances turbulent kinetic energy. When the cavity depth is 0.2% of the blade height, the flow loss of the blade cascade is reduced by 11.2%, and the degree of improvement in flow loss first increases and then decreases with increasing cavity depth.
[0030] Biomimetic designs for trailing edges are primarily used for noise control. (Wenjun Yang, Yinhao Wang, Dongdong Sui et al. Research on aerodynamic performance and noise reduction of non-uniform serrated trailing edges for an axial compressor. Physics of Fluids) Based on bird tail feathers, a serrated trailing edge structure was designed in the compressor stage stator blade. Numerical studies showed that the serrated trailing edge structure exhibited excellent noise reduction, lowering noise by 7.81 dB. Currently, biomimetic trailing edge designs for reducing corner separation are relatively rare. This paper proposes a biomimetic wavy trailing edge design method for compressor blades based on the structure of bird tail feathers. This method can significantly improve the total pressure loss under design conditions and near-stall conditions. The design structure is simple, reliable, and has a high degree of freedom.
[0031] Based on the problems existing in the prior art, this invention proposes a method for designing a biomimetic wavy trailing edge of a compressor, comprising the following steps: Obtain the original compressor blade model and uniformly cut several element sections along the span; Based on the geometric characteristics of each element's cross section, construct the arc function within it; The axial chord length distribution of the basic element sections at different spanwise positions is adjusted by using waveform control functions to form a trailing edge geometry that varies in a wave-like manner along the spanwise direction; Calculate the thickness distribution on the suction side and pressure side of the prototype blade for each basic section, as well as the angle between the normal of each side profile and the axial direction. Under the same parameterization framework of the waveform control function, the coordinate transformation of the mid-arc function is performed, and the thickness distribution on the suction side, the thickness distribution on the pressure side, and the angle between the normal of each side surface and the axis are superimposed on the transformed mid-arc line while keeping them unchanged, so as to generate the biomimetic suction and pressure surface coordinates, thereby forming a flow guide channel on the suction side of the blade that is geometrically continuous with the wavy trailing edge. Based on the adjusted primitive cross-sectional geometry, a biomimetic wavy trailing edge blade is generated; the wavy geometry of the trailing edge and the flow guiding channel on the suction surface side are generated collaboratively through the same set of arc transformation methods, and the two are geometrically continuous and work together in the corner separation region for flow control.
[0032] The present invention also proposes a compressor blade, which is made by the aforementioned biomimetic wavy trailing edge shaping method of the compressor. The trailing edge of the blade has a spanwise wavy shape, and a flow guide channel that is geometrically continuous with the wavy trailing edge is formed in the region near the trailing edge on the suction side. The wavy trailing edge and the flow guide channel are generated collaboratively through the same parameterized framework.
[0033] The above technical solution will be further analyzed below with reference to the accompanying drawings and examples: In one embodiment, taking a high-load axial compressor as an example, the flow control effect of the design method in diagonal separation is verified by numerical simulation. Table 1 shows some design parameters of the axial compressor.
[0034] Table 1
[0035] Reference Figure 1 The diagram shows a technical roadmap for a biomimetic wavy trailing edge design method for compressor blades. The following explanation uses this axial compressor as an example to illustrate the specific design steps: Step 1: Divide the original blade model into primitive levels and obtain the coordinates of the mid-arc line; Obtain the original axial compressor blade model; Reference Figure 3 As shown, 101 basic sections were cut along the spanwise direction of the blade profile; Reference Figure 4 As shown, an inscribed circle is constructed in each element section, and the coordinates of the center of the inscribed circle are obtained as discrete points of the mid-arc line.
[0036] Step 2: Fit the coordinates of the discrete points of the mid-arc line obtained from each element section in Step 1 using the least squares method with a cubic function. The fitting equation is: (1) in, y The positive direction of the axis is the direction from the suction side to the pressure side. z This indicates the axial direction of the compressor blades.
[0037] Step 3: After obtaining the mid-arc equations for different element sections, the tail edge chord length is controlled by trigonometric functions. The governing equation for the axial chord length is: (2) In this example, It is 0.126m. A and T The value is obtained through algorithm optimization. A The value is 0.00693m. T The value is 0.0216m, and the value of n is 0.753. h represents the blade spanwise position, with a value of [0, 0.16m].
[0038] The trigonometric function is used to adjust the axial chord length distribution of the basic section at different spanwise positions, forming a trailing edge geometry that varies in a wavy manner along the spanwise direction; Step 4: Calculate the thickness distribution on the suction side and pressure side of the prototype blade for each basic section, as well as the angle between the normal of each side profile and the axial direction. For the coordinate points of the suction and pressure sides of the blade at different cross-sections, the least squares method is used to fit cubic spline curves to obtain the profile equations of the suction and pressure surfaces of the blade surface, denoted as . line p and line s The formula for a cubic spline curve is: (3) Where n represents the number of discrete points on both sides of the prototype blade element cross section, and in this example, n is 81. a i , b i , c i , d i These represent the zeroth, first, second, and third degree parameters of the spline curve formula, respectively; z i The z-coordinate represents the discrete point; line This represents the Z-coordinate of the fitted line.
[0039] The thickness distribution on the pressure side is obtained by solving a series of equations. thickness p and suction side thickness distribution thickness s and the angle between the suction side normal and the axis. θ s The angle between the pressure side normal and the axial direction θ p The specific calculation process is as follows: pressure side spline linep The equation of the normal is (4) Among them, z p This represents the Z-coordinate of the pressure side of the blade section of the basic element.
[0040] The thickness distribution and normal angle distribution on the pressure side are as follows: (5) Among them, y p and z p y and z represent the Y and Z coordinates of the pressure side of the airfoil in the basic section, respectively; y and z represent the Y-axis and Z-axis coordinates of the intersection of the pressure side normal and the mid-curve, respectively. Where z p The values of z are both [z LE , z TE By combining equations (1), (4), and (5), the distribution law of the thickness and normal angle of the pressure-side blade can be obtained.
[0041] The normal equation of the suction side spline lines is: (6) The thickness distribution and normal angle distribution on the suction side can be represented by equation (7). (7) Among them, y s , z s The Y and Z coordinates represent the suction side of the blade section; y and z represent the Y-axis and Z-axis coordinates of the intersection of the suction side normal and the mid-curve, respectively. Where z... s The values of z are both [z LE , z TE ].
[0042] By combining equations (1), (6), and (7), the thickness and normal angle distribution of the suction side blade can be obtained.
[0043] Step 5: Obtain the coordinates of the mid-arc line after shaping through coordinate transformation. The transformation equation is: (8) The coordinates of the pressure side of the airfoil can be represented as: (9) The coordinates of the suction side of the blade can be represented as: (10) Among them, z ST The z-coordinate of the mid-arc line representing the starting position of the wavy trailing edge shape, in this example z STThe value is 0.0074m, and parameter L controls the depth of the groove on the suction side. In this example, the value is 0.948. Figure 5 A schematic diagram showing the coordinate changes on the suction and pressure sides is presented.
[0044] The amplitude in the waveform control function described in this embodiment A ,cycle T Phase n and the depth control parameters of the flow guide channel. k The starting position Z-coordinate of the suction surface side channel structure The following optimization algorithm was used for selection: Step (1): The Latin hypercube sampling method is used to sample the amplitude values. A ,cycle T Phase n and the depth control parameters of the flow guide channel. k The starting position Z-coordinate of the suction surface side channel structure Within the parameter design space, 100 uniform samplings are performed to generate several sets of geometric parameter samples. For each set of geometric parameter samples, a corresponding biomimetic wavy trailing edge blade geometric model is generated according to the aforementioned compressor biomimetic wavy trailing edge modeling method. The blade geometric model is numerically simulated using computational fluid dynamics to obtain the total pressure loss coefficient of the blade cascade corresponding to each sample. Step (2): Using the geometric parameter samples as input and the corresponding total pressure loss coefficient as output, construct and train a radial basis function surrogate model. The radial basis function surrogate model is used to approximately characterize the mapping relationship between the geometric parameters and the total pressure loss coefficient. Step (3): Based on the trained radial basis function surrogate model, a genetic algorithm is used to search for the optimal combination of geometric parameters that minimizes the total pressure loss coefficient in the parameter design space, as the predicted optimal shape; Step (4): The predicted optimal shape is verified by computational fluid dynamics. If the verification result meets the preset convergence criterion, the geometric parameter combination is determined as the final selected shape parameter. If it does not meet the criterion, the verification result is added to the training sample set, the radial basis function surrogate model is retrained, and steps 2 to 4 are repeated until the convergence criterion is met.
[0045] Step 6: Write the shape coordinates into the geometry file, and then import the geometry file into NUMECA / autogrid5 for structured mesh drawing. Figure 6 A schematic diagram of the grid structure is shown.
[0046] To illustrate the corner separation control effect of the biomimetic wavy trailing edge design of the compressor blades, Table 2 compares the total pressure loss and static pressure rise coefficient of the prototype and the biomimetic design at the design angle of attack and a 10° angle of attack. At the design angle of attack, the biomimetic design reduces the total pressure loss by 5.3% and increases the static pressure rise coefficient by 2.79%. At a 10° angle of attack, the total pressure loss is reduced by 10.79%, and the static pressure rise coefficient is increased by 3.78%.
[0047] Figure 7 The distribution of low-energy fluids in the prototype and biomimetic design at a 10° angle of attack was compared. The biomimetic design significantly reduced the volume of low-energy fluids in the trailing edge region of the suction surface.
[0048] To illustrate the performance of the biomimetic design, Table 3 compares the loss coefficients of the prototype with those of a single wavy trailing edge design, and a single suction surface channel design with those of the biomimetic design. The single wavy trailing edge slightly increases losses at both angles of attack; the single suction surface channel design reduces losses at 0° and 10° angles of attack by 6.00% and 10.14%, respectively. The biomimetic design combining a single wavy trailing edge and a single suction surface channel further reduces losses in both operating conditions, with a 6.19% reduction in design loss and a 10.22% reduction in loss at a 10° angle of attack. The design of this invention differs from existing wavy trailing edges in the following ways: Existing serrated trailing edges are used in noise control, while the biomimetic trailing edge design in this invention is primarily used to reduce flow losses, resulting in a significant difference in application scope. Furthermore, the trailing edge design in this invention uses trigonometric functions to construct the wavy structure, resulting in a smooth transition, which is more beneficial in reducing airflow dissipation losses in aerodynamic control.
[0049] Table 2
[0050] Table 3
[0051] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.
Claims
1. A method for designing a biomimetic wavy trailing edge of a compressor, characterized in that, Includes the following steps: Obtain the original compressor blade model and uniformly cut several element sections along the span; Based on the geometric characteristics of each element's cross section, construct the arc function within it; The axial chord length distribution of the basic element sections at different spanwise positions is adjusted by using waveform control functions to form a trailing edge geometry that varies in a wave-like manner along the spanwise direction; Calculate the thickness distribution on the suction side and pressure side of the prototype blade for each basic section, as well as the angle between the normal of each side profile and the axial direction. Under the same parameterization framework of the waveform control function, the coordinate transformation of the mid-arc function is performed, and the thickness distribution on the suction side, the thickness distribution on the pressure side, and the angle between the normal of each side surface and the axis are superimposed on the transformed mid-arc line while keeping them unchanged, so as to generate the biomimetic suction and pressure surface coordinates, thereby forming a flow guide channel on the suction side of the blade that is geometrically continuous with the wavy trailing edge. Based on the adjusted primitive cross-sectional geometry, a biomimetic wavy trailing edge blade is generated; the wavy geometry of the trailing edge and the flow guiding channel on the suction surface side are generated collaboratively through the same set of arc transformation methods, and the two are geometrically continuous and work together in the corner separation region for flow control.
2. The method for creating a biomimetic wavy trailing edge of a compressor according to claim 1, characterized in that: The waveform control function is a trigonometric function, and its expression is: In the formula, C a This represents the axial chord length of the prototype blade element cross section; A Indicates the amplitude of the control wavy trailing edge; T Indicates period; n Indicates phase; This indicates that the axial chord length of the primitive cross section has been modified using trigonometric functions; h Indicates the direction of expansion.
3. The method for creating a biomimetic wavy trailing edge of a compressor according to claim 2, characterized in that: The amplitude of the control wavy trailing edge A The value range is [0, 0.06]. C a The period T The value range of h is [0.01, 0.5]. blade h blade For the leaf height; n The value of is [0, 1].
4. The method for creating a biomimetic wavy trailing edge of a compressor according to claim 2, characterized in that: The specific method for constructing the arc function is as follows: Construct an inscribed circle in each element section and obtain the coordinates of the center of the inscribed circle as discrete points of the mid-arc line; The discrete points are fitted using a cubic polynomial to generate the equation of the mid-arc line: In the formula, y The coordinates represent the direction from the suction side to the pressure side. z Indicates the axial coordinate; a , b , c , d These are the parameters that control the cubic, quadratic, linear, and zeroth-degree terms of the polynomial, respectively. The parameter values are obtained by fitting discrete points using the polyfit command in MATLAB. Adjusting parameters using the least squares method a , b, c, d The value of is used to fit the arc.
5. The method for creating a biomimetic wavy trailing edge of a compressor according to claim 4, characterized in that: The specific process for calculating the thickness distribution on the suction side, the thickness distribution on the pressure side, and the angle between the normal to each side profile and the axial direction of the prototype blade for each element section is as follows: Pressure surface thickness distribution thickness p The angle between the normal to the pressure surface and the axial direction. θ p The expression is as follows: In the formula, y p , z p These represent the Y and Z coordinates of the pressure surface side of the airfoil in the basic section, respectively. y , z Let Y and Z represent the Y-axis coordinates and Z-axis coordinates of the intersection point of the pressure surface side normal and the mid-curve line, respectively; where... z p and z The values are all [z LE , z TE ], z LE and z TE These represent the Z coordinates of the leading edge and trailing edge of the blade, respectively. line p Represents the side spline of the pressure surface; Thickness distribution on the suction surface side, angle between the suction surface side normal and the axial direction: In the formula, y s , z s These represent the Y and Z coordinates of the suction surface side of the blade section, respectively; y * , z * Let Y and Z represent the Y-axis coordinates and Z-axis coordinates of the intersection point of the suction side normal and the mid-arc line, respectively; where... z s and z * The values are all [z LE , z TE ], z LE and z TE These represent the Z coordinates of the leading edge and trailing edge of the blade, respectively. line s This represents the side spline of the suction surface.
6. The method for creating a biomimetic wavy trailing edge of a compressor according to claim 5, characterized in that: The coordinate transformation formula is as follows: The expression for the lateral coordinates of the pressure surface of the biomimetic blade shape: The coordinate expression for the suction surface of the leaf after biomimetic design: in, y camber and z camber These represent the Y and Z coordinates of the mid-arc line after the biomimetic design; The Z-coordinate of the mid-arc line representing the starting position of the biomimetic design, i.e., the Z-coordinate of the starting position of the suction surface side channel structure; z ori The Z-coordinate of the mid-arc of the prototype; z LE This represents the Z-coordinate of the leading edge point of the blade; y ps and z ps These represent the Y and Z coordinates of the pressure surface side of the biomimetic design, respectively. y ss and z ss These represent the Y and Z coordinates of the biomimetic suction surface, respectively. L The depth control parameter for the flow guide channel, with values of [0, 1]; k This represents the scaling factor, which is changed by adjusting the parameter. L The value controls the depth of the suction surface side channel structure in the biomimetic design; L The larger the value, the deeper the groove on the suction surface.
7. The method for creating a biomimetic wavy trailing edge of a compressor according to claim 6, characterized in that: The amplitude in the waveform control function A ,cycle T Phase n and the depth control parameters of the flow guide channel. k The starting position Z-coordinate of the suction surface side channel structure The following optimization algorithm was used for selection: Step 1: Use the Latin hypercube sampling method to sample the amplitude values. A ,cycle T Phase n and the depth control parameters of the flow guide channel. k The starting position Z-coordinate of the suction surface side channel structure Uniform sampling is performed within the parameter design space to generate several sets of geometric parameter samples; for each set of geometric parameter samples, a corresponding biomimetic wavy trailing edge blade geometric model is generated according to the method described in claim 1, and the blade geometric model is numerically simulated using computational fluid dynamics to obtain the total pressure loss coefficient of the blade cascade corresponding to each sample. Step 2: Using the geometric parameter samples as input and the corresponding total pressure loss coefficient as output, construct and train a radial basis function surrogate model. The radial basis function surrogate model is used to approximately characterize the mapping relationship between the geometric parameters and the total pressure loss coefficient. Step 3: Based on the trained radial basis function surrogate model, a genetic algorithm is used to search for the optimal combination of geometric parameters that minimizes the total pressure loss coefficient within the parameter design space, as the predicted optimal shape; Step 4: The predicted optimal shape is verified using computational fluid dynamics. If the verification result meets the preset convergence criterion, the geometric parameter combination is determined as the final selected shape parameter. If it does not meet the criterion, the verification result is added to the training sample set, the radial basis function surrogate model is retrained, and steps 2 to 4 are repeated until the convergence criterion is met.
8. The method for creating a biomimetic wavy trailing edge of a compressor according to claim 1, characterized in that: The biomimetic wavy trailing edge shape starts at a preset spanwise position upstream of the trailing edge of the blade, and the arc line changes and thickness is mapped from the starting position to the trailing edge line.
9. The method for creating a biomimetic wavy trailing edge of a compressor according to claim 1, characterized in that: It also includes the steps of writing the modified primitive section geometry into a geometry file and importing it into a mesh generation tool for structured mesh generation.
10. A compressor blade, characterized in that, The blade is manufactured using the biomimetic wavy trailing edge shaping method of any one of claims 1-9. The trailing edge of the blade has a spanwise wavy shape, and a flow guide channel that is geometrically continuous with the wavy trailing edge is formed in the region near the trailing edge on the suction side. The wavy trailing edge and the flow guide channel are generated collaboratively through the same parameterized framework.