Topological optimization design method for air-cooled turbine blade

Abstract

The invention discloses a topological optimization rapid design method for an air-cooled turbine blade, and belongs to the technical field of aero-engine and gas turbine design. According to the method, a topological optimization mathematical model considering the coupling effect of an aerodynamic load, a temperature load and a centrifugal load is established, and automatic optimization of blade inner cavity material distribution is realized through sensitivity analysis and pseudo-density updating by taking blade skin flexibility minimization as a target. On the basis, a turbine blade engineering design process based on topological optimization is provided, and a similar double-layer-wall multi-layer composite low-inertia blade structure configuration is formed. According to the method, the problems of multidisciplinary serial connection, experience dependence, stress concentration and low cooling efficiency in traditional blade design are solved, and collaborative improvement of the blade structure efficiency and the cooling performance is achieved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of air-cooled turbine blade design, and particularly relates to a topological optimization design method of an air-cooled turbine blade. BACKGROUND

[0002] In an aero-engine, a turbine blade is a core component for completing heat-work conversion to form final thrust, and works in an extreme environment of high temperature, high pressure and high rotating speed, and bears thermal load, aerodynamic load, centrifugal force and the coupling effect of multiple physical fields. With the continuous increase of turbine inlet temperature, the traditional blade structure and design method have been difficult to meet the needs of high-performance engines.

[0003] At present, the turbine inlet temperature of an aero-engine is continuously increased, while the performance improvement of high-temperature materials tends to slow down. The turbine blade designed based on the traditional structure and design method is increasingly difficult to meet the use requirements of future high-performance aero-engines, and a blade design method with new structural characteristics and considering the multi-disciplinary design contradiction needs to be proposed. The traditional turbine cooling blade is designed in the idea of "material removal", and the cooling flow path is arranged in the blade first, so the blade has a regular internal cavity and a large number of combined structures of film holes, impact holes and turbulence columns. The obvious defect of this structure is that the discrete film holes cannot guarantee the complete and effective coverage of the film cooling gas, and the stress distribution in the blade is uneven due to the large geometric shape and stress area of the internal ribs, solid walls and other load-bearing structures. At the same time, various holes / columns bring serious stress concentration and produce a complex stress state. Therefore, a large margin needs to be reserved during blade design to ensure the safe and reliable work of the stress concentration area under extreme conditions. In addition, the traditional design process has problems such as multi-disciplinary series, dependence on experience and low iteration efficiency, and it is difficult to realize automatic optimization under the coupling of multiple physical fields. SUMMARY

[0004] Based on the problems existing in the above background technology, the application aims to provide a topological optimization design method of an air-cooled turbine blade, which solves the problem that the traditional blade structure and design method have been difficult to meet the needs of high-performance engines.

[0005] The application provides a topological optimization design method of an air-cooled turbine blade, characterized by comprising the following steps: Step 1: establishing a blade geometric model, and defining a design domain and a non-design domain according to the blade geometric model, wherein the design domain is a solid internal profile area of the blade airfoil, and the non-design domain is a skin area of the airfoil outer profile surface; Step 2: taking the minimum compliance of the blade non-design domain, i.e. the skin position, as an optimization target and taking the total volume fraction of the material as a constraint condition, establishing a topological optimization mathematical model of the air-cooled turbine blade, and comprehensively considering the coupling effect of aerodynamic load, temperature load and centrifugal load. Step 3, a topology optimization sensitivity model is constructed according to the gas turbine blade topology optimization mathematical model; Step 4, a blade finite element model is obtained by performing finite element processing on the blade geometric model, the blade finite element model includes meshing, displacement constraint, aerodynamic load, temperature load and centrifugal load; Step 5, the sensitivity model takes the blade as a whole as a topology optimization solving object, defines the pseudo-density of the element in the design domain as a design variable, defines the minimum compliance of the skin as an optimization target, and iteratively calculates the blade finite element model until the compliance of the skin meets the convergence condition, to obtain the pseudo-density of the element in the design domain after optimization; Step 6, threshold processing is performed on the pseudo-density of the element in the design domain, and the design domain is reconstructed to generate a final blade internal cavity structure design scheme.

[0006] Further, in step 2, the gas turbine blade topology optimization mathematical model is: wherein, is the compliance of the blade non-design domain, i.e. the skin position, is the stiffness matrix of the skin position, F is the total load vector, U is the node displacement vector, V i is the volume of the i-th element in the design domain, x i represents the pseudo-density of the i-th finite element element, F m is the aerodynamic load vector, F th is the temperature load vector, F ω is the centrifugal force load vector, is a constant value close to zero to avoid the singularity of the stiffness matrix.

[0007] Further, in step 3, the topology optimization sensitivity model is: wherein, is the compliance of the blade non-design domain, i.e. the skin position, K is the stiffness matrix, U is the node displacement vector, is a selection control operator, x i represents the pseudo-density of the finite element element, λ is the adjoint vector, is the element shape function matrix, is the element integral microelement position vector, is the rotational acceleration vector, is the initial density of the design domain, is the coefficient vector of the element, ΔT is the temperature difference, φ is a column vector, B i is the shape function derivative matrix of the element, D i0 is the initial elastic matrix of the element; The RAMP model used interpolates the material parameters to obtain: where p, q are interpolation factors, i.e. the penalty function of material in topology optimization; x i represents the pseudo-density of the finite element unit, D i is the elastic matrix, is the initial elastic matrix, is the coefficient vector, is the initial coefficient vector, , E(x i ) is the elastic modulus of the unit, a(x i ) is the linear expansion coefficient of the unit.

[0008] Further, in step 3, the specific process of constructing a topology optimization sensitivity model according to the air-cooled turbine blade topology optimization mathematical model is as follows: The minimum compliance of the blade non-design domain, i.e. the skin position, is taken as the optimization objective function, and the sensitivity of the compliance to the design variable is expressed as: (1) where, is the compliance of the blade non-design domain, i.e. the skin position, is the stiffness matrix of the skin position, is the stiffness matrix of the i-th finite element unit, U is the node displacement vector, and x i represents the pseudo-density in the i-th finite element unit, is a selection control operator indicating whether the unit is at the skin position or not; The adjoint vector method is used for calculation and solution, and the adjoint vector λ is introduced, so that , and the sensitivity formula is: (2) where, is the compliance of the blade non-design domain, i.e. the skin position, is the stiffness matrix of the i-th finite element unit, U is the node displacement vector, and F is the load of the unit, is a selection control operator, x i represents the pseudo-density in the i-th finite element unit, and λ is the adjoint vector introduced for solution; The load F in formula (2) is decomposed and dispersed according to the aerodynamic load, temperature load and centrifugal force load borne by the blade, and the sensitivity formula is: (3) where, is the compliance of the blade non-design domain, i.e. the skin position, K is the stiffness matrix, and U is the node displacement vector, To select the control operator, x i F represents the pseudo density of the i-th finite element. m F is the aerodynamic load vector. th F is the temperature load vector. ω Let λ be the centrifugal force load vector, and λ be the adjoint vector. The first-order partial derivative of the aerodynamic load vector with respect to the element pseudo-density is: (4) in, x is the aerodynamic load vector at the element node. i This represents the pseudo-density of a finite element; Centrifugal load vector The derivative of the pseudo-density is solved as follows: (5) in: Centrifugal load vector at the element node, x i This represents the pseudo-density of a finite element. For a unit shape function matrix, Let the integral element be the position vector of the unit. Let be the rotational acceleration vector. The blade rotates at a constant angular velocity ω around the Z-axis. , The initial density; Temperature load vector The derivative of the pseudo-density is solved as follows: (6) in, x is the temperature load vector at the element node. i Let ΔT represent the pseudo-density of the finite element, ΔT be the temperature difference, and φ be the column vector. For three-dimensional problems, we have... B i Let D be the derivative matrix of the shape functions of the i-th element. i0 Let be the initial elasticity matrix of the i-th element. Let be the coefficient vector of the i-th unit. E(x) i Let a(x) be the elastic modulus of the element. i () represents the element linear expansion coefficient; Substituting formulas (4), (5), and (6) into formula (3) yields the topology optimization sensitivity model.

[0009] Furthermore, in step 4, the mesh is a quadrilateral hexahedral mesh; the number of mesh layers in the skin area is not less than 3; and the number of mesh layers in the area where the blade trailing edge becomes smaller is not less than 5.

[0010] Furthermore, in step 5, the sensitivity model modifies the blade finite element model based on the pseudo-density, performs FEA calculation, sensitivity analysis, sensitivity filtering and boundary smoothing based on parameters, and updates the pseudo-density iteratively to calculate skin compliance using the OC or ESO / BESO method.

[0011] Furthermore, in step 6, the threshold processing includes: setting a density threshold, treating units with a pseudo density greater than the density threshold as solid materials and units with a density less than the density threshold as pores, creating a clear boundary between solids and pores, and gradually adjusting the density threshold until a result that meets the requirements of function, weight, and structural feasibility is selected; The geometric reconstruction of the design domain includes: smoothing the obvious boundaries between solids and holes to generate a smooth structure, preserving the cooling design structure, and generating the final blade internal cavity structure design scheme.

[0012] Furthermore, the cooling design structure includes film cooling, impingement cooling, and turbulence ribs.

[0013] Compared with traditional blade structures and design methods, the advantages of this invention are: 1. The air-cooled turbine blade topology optimization design method of this invention transforms the traditional serial, manual design mode into a parallel, automated optimization process. Designers no longer need to rely entirely on experience for initial configuration design; the computer automatically finds the optimal material distribution through topology optimization, reducing the number of repeated manual iterations, shortening the design cycle, and supporting rapid selection of multiple options.

[0014] 2. The air-cooled turbine blade topology optimization design method of the present invention, by simultaneously considering aerodynamics, heat transfer and structural mechanics in the optimization model, can automatically balance and coordinate the design requirements between different disciplines (such as weight reduction and strength, cooling and stress), find the global optimal or suboptimal solution from the system level, realize the systematic solution of complex engineering problems, not only improve the blade performance, but also ensure R&D efficiency and quality control through rapid iterative optimization. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described 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. The above and other objects, features, and advantages of the present invention will become clearer through the accompanying drawings. The same reference numerals indicate the same parts in all the drawings. The drawings are not intentionally drawn to scale to actual dimensions; the focus is on illustrating the main points of the invention.

[0016] Figure 1 This is a flowchart of a topology optimization design method for air-cooled turbine blades.

[0017] Figure 2 This is a three-dimensional structural diagram of a common air-cooled turbine blade.

[0018] Figure 3 This is a schematic diagram of the design domain and non-design domain for the topology optimization of this invention.

[0019] Figure 4 This is a schematic diagram of the finite element model of the blade.

[0020] Figure 5 This is a schematic diagram of the geometric reconstruction of the blade topology optimization results of the present invention.

[0021] Figure 6 This invention presents a low-inertia turbine blade structure configuration based on topology optimization.

[0022] Figure 7 The image shows the von Mises stress distribution of the original turbine blade in the embodiment.

[0023] Figure 8 The image shows the von Mises stress distribution diagram at the blade root section of the original turbine blade in the embodiment.

[0024] Figure 9 The image shows the von Mises stress distribution of the optimized turbine blade in this embodiment.

[0025] Figure 10 The image shows the von Mises stress distribution diagram of the root section of the optimized turbine blade in the embodiment. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0027] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0028] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0029] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0030] like Figure 1 As shown, the present invention provides a method for topology optimization design of air-cooled turbine blades, characterized in that it includes: Step 1: Establish the blade geometric model and define the design domain and non-design domain based on the model. The design domain is the solid inner region of the blade body, and the non-design domain is the skin region of the outer surface of the blade body. For example... Figure 2 As shown, common air-cooled turbine blades consist of four main parts: blade body, rim plate, extension root, and tenon. The blade body has an internal structure containing cooling components. The rim plate, extension root, and tenon are flow channel structures and impeller connection structures, and are not considered as optimization domains. However, as positioning and force transmission structures and some load application points, they are retained as non-design domains during optimization.

[0031] The division of the design domain and non-design domain in this invention is as follows: Figure 3 and Figure 4 As shown, the blade body is considered the design domain, and its shape is the flow channel surface, which controls the gas flow direction. Therefore, during topology optimization, the outer surface of the blade body should be set as a skin. The thickness of the skin should refer to the blade's manufacturing process; for example, if cast, a skin thickness of not less than 0.5 mm is recommended. To ensure that the structure, shape, and density of the skin area of ​​the blade body remain unchanged during optimization, it is also designated as a non-design domain. The topology optimization region is solidified by removing the cooling structure of the inner part of the blade body, making it a solid inner shape, and this is designated as the design domain. The final design and non-design domains of the blade body are shown below. Figure 4 .

[0032] Step 2: With the goal of minimizing the compliance of the non-design domain of the blade, i.e., the skin position, and with the total material integral as the constraint, establish a mathematical model for the topology optimization of the air-cooled turbine blade. The mathematical model for the topology optimization of the air-cooled turbine blade comprehensively considers the coupling effects of aerodynamic loads, temperature loads, and centrifugal loads.

[0033] Specifically, in step 2, the mathematical model for the topology optimization of the air-cooled turbine blade is as follows: in, For the compliance of the blade in the non-designed area, i.e., the skin area, Let F be the stiffness matrix at the skin location, F be the overall load vector, U be the nodal displacement vector, and V be the stiffness matrix at the skin location. i To determine the volume of the i-th element in the design domain, x i F represents the pseudo density of the i-th finite element. m F is the aerodynamic load vector. th F is the temperature load vector. ω The centrifugal force load vector, It is a constant value close to zero to avoid the singularity of the stiffness matrix.

[0034] The mathematical model for topology optimization of air-cooled turbine blades is established based on the fundamental principles of topology optimization design and the working physics of aero-engine turbine blades. The topology optimization employs the variable density method, which discretizes the continuous design domain into a finite element mesh and introduces pseudo-density variables. Indicates the material existence of each unit, when A value of 1 indicates a solid material; when... A value of 0 indicates no material. Material properties are interpolated based on pseudo-density. To prevent singularity in the stiffness matrix, ... Greater than a constant that approaches 0. .

[0035] objective function For the compliance of the blade in the non-designed area, i.e., the skin area, based on the principle of virtual work, compliance... U, according to the finite element theory F=KU, the blade compliance can be calculated. .

[0036] Limitations Based on the force principles of aero-engine turbine blades, the function of turbine blades is to convert the thermal energy of incoming airflow into mechanical energy and transmit rotational torque to the rotor and shaft. According to the principles of thermoelasticity, the main loads they experience are aerodynamic loads from the airflow on the blade surface, thermal stress loads from temperature, and centrifugal loads from rotation.

[0037] Limitations The volume fraction constraint is a constraint on the amount of material used, imposed based on the functional requirements and manufacturing process needs of the blade.

[0038] Step 3: Construct a topology optimization sensitivity model based on the mathematical model of air-cooled turbine blade topology optimization; specifically, the topology optimization sensitivity model is as follows: in, Let K represent the compliance of the blade outside the design domain, i.e., the skin region; K be the stiffness matrix; and U be the nodal displacement vector. To select the control operator, x i The pseudo-density of the finite element is represented by λ, where λ is the adjoint vector. For a unit shape function matrix, Let the integral element be the position vector of the unit. Let be the rotational acceleration vector. For the initial density of the design domain, Let B be the coefficient vector of the unit, ∆T be the temperature difference, φ be the column vector, and B be the coefficient vector of the unit. i Let D be the derivative matrix of the shape functions of the element. i0 The initial elasticity matrix of the element; The RAMP model was used to interpolate the material parameters, resulting in: In the formula, p and q are interpolation factors, i.e., the penalty functions of materials in topology optimization; x i D represents the pseudo-density of a finite element. i For the elasticity matrix, The initial elasticity matrix, For the coefficient vector, For the initial coefficient vector, E(x) i Let a(x) be the elastic modulus of the element. i ) represents the elemental linear expansion coefficient.

[0039] The specific derivation process of the topology optimization sensitivity model is as follows: The objective function is to minimize the compliance of the blade outside the design domain, i.e., the skin region. The sensitivity of compliance to design variables is expressed as: (1) in, For the compliance of the blade in the non-designed area, i.e., the skin area, Here is the stiffness matrix for the skin location. Let U be the stiffness matrix of the i-th finite element, U be the nodal displacement vector, and x be the stiffness matrix of the i-th finite element. i This represents the pseudo density of the i-th finite element. The selection control operator for whether the unit is in the skinned position; The adjoint vector method is used for calculation and solution, introducing the adjoint vector λ, so that... The sensitivity formula is: (2) in, For the compliance of the blade in the non-designed area, i.e., the skin area, Let be the stiffness matrix of the i-th finite element, U be the nodal displacement vector, and F be the element load. To select the control operator, x i Let λ represent the pseudo density of the i-th finite element, and λ be the adjoint vector introduced by the solution. The load F in formula (2) is decomposed and discretized according to the aerodynamic load, temperature load, and centrifugal force load on the blade. The sensitivity formula is: (3) in, Let K represent the compliance of the blade outside the design domain, i.e., the skin region; K be the stiffness matrix; and U be the nodal displacement vector. To select the control operator, x i F represents the pseudo density of the i-th finite element. m F is the aerodynamic load vector. th F is the temperature load vector. ω Let λ be the centrifugal force load vector, and λ be the adjoint vector. The first-order partial derivative of the aerodynamic load vector with respect to the element pseudo-density is: (4) in, x is the aerodynamic load vector at the element node. i This represents the pseudo-density of a finite element; Centrifugal load vector The derivative of the pseudo-density is solved as follows: (5) in: Centrifugal load vector at the element node, x i This represents the pseudo-density of a finite element. For a unit shape function matrix, Let the integral element be the position vector of the unit. Let be the rotational acceleration vector. The blade rotates at a constant angular velocity ω around the Z-axis. , The initial density; Temperature load vector The derivative of the pseudo-density is solved as follows: (6) in, x is the temperature load vector at the element node. i Let ΔT represent the pseudo-density of the finite element, ΔT be the temperature difference, and φ be the column vector. For three-dimensional problems, we have... B i Let D be the derivative matrix of the shape functions of the i-th element. i0 Let be the initial elasticity matrix of the i-th element. Let be the coefficient vector of the i-th unit. E(x) i Let a(x) be the elastic modulus of the element. i () represents the element linear expansion coefficient; Substituting formulas (4), (5), and (6) into formula (3) yields the topology optimization sensitivity model.

[0040] Step 4: Perform finite element analysis on the blade geometry model to obtain the blade finite element model. This model includes mesh generation, displacement constraints, aerodynamic loads, temperature loads, and centrifugal loads. For example... Figure 4 As shown, the mesh is a quadrilateral hexahedral mesh; the number of mesh layers in the skin area is not less than 3; the number of mesh layers in the area where the blade trailing edge becomes smaller is not less than 5.

[0041] Step 5: The sensitivity model treats the entire blade as the topology optimization solution object, defines the pseudo-density of the elements within the design domain as the design variable, and defines the minimum compliance of the skin as the optimization objective. Iterative calculations are performed on the finite element model of the blade until the skin compliance meets the convergence condition, obtaining the optimized pseudo-density of the elements within the design domain; specifically, as follows... Figure 1 As shown, the sensitivity model modifies the blade finite element model based on the pseudo-density, performs FEA calculations, sensitivity analysis, sensitivity filtering and boundary smoothing based on parameters, and updates the pseudo-density using the OC or ESO / BESO method to iteratively calculate skin compliance.

[0042] Step 6, as follows Figure 5 As shown, the pseudo-density of the units within the design domain is thresholded and the geometry of the design domain is reconstructed to generate the final blade internal cavity structure design scheme. In step 6, the thresholding process includes: setting a density threshold, treating units with a pseudo-density greater than the density threshold as solid materials and units with a pseudo-density less than the density threshold as pores, creating a clear boundary between solids and pores, and gradually adjusting the density threshold until a result that meets the requirements of function, weight, and structural feasibility is selected; The geometric reconstruction of the design domain includes: smoothing the obvious boundaries between solids and holes to generate a smooth structure, preserving the cooling design structure, and generating the final blade internal cavity structure design scheme. The cooling design structure includes film cooling, impingement cooling, and turbulence ribs.

[0043] Taking a certain type of single-crystal high-temperature alloy turbine blade as an example, the topology optimization design method for air-cooled turbine blades of the present invention is implemented. The structure of the single-crystal high-temperature alloy turbine blade is as follows: Figure 2As shown, the blade weighs 157g and is mainly composed of the blade body, edge plate, extension root, and tenon. Internally, it employs a classic longitudinal multi-rib structure, forming a serpentine airflow path. Further topology optimization will be conducted on the material distribution within the blade body cavity. The blade operates at a rotational speed N = 18000 r / min. Aerodynamic loads, temperature loads, and centrifugal loads at actual operating conditions were applied to the model, with fixed constraints applied at the tenon. Strength analysis was performed on the original model, and the results are as follows: Figures 7-8 As shown, the leading and trailing edges of the leaf root experience greater stress, with a maximum stress of 856 MPa.

[0044] A topology optimization design method was used for the single-crystal superalloy turbine blade, employing an air-cooled turbine blade topology optimization approach. This method ensured the aerodynamic shape of the blade remained unchanged while optimizing the material distribution within the turbine blade cavity. Hexahedral elements and shell elements were used to simulate the solid portion and skin of the blade, respectively. The skin element was used to bear aerodynamic loads and extract skin compliance as the optimization objective. Based on practical design requirements, features such as spoilers and tail slots needed to be retained; a portion of the leading edge was removed to leave space for the film cooling vents; and a base thickness of 0.5 mm was maintained on the blade. The finite element model is shown below. Figure 4 As shown, the unit size is 0.1mm. The blue area is the design domain, the gray area is the non-design domain, and the pink area is the skin, which is also a non-design domain.

[0045] The optimization objective was to minimize skin compliance, with a constraint volume ratio of less than 0.3, while considering three actual operating conditions: centrifugal load, aerodynamic load, and thermal load. The optimization results are as follows: Figure 6 As shown in the figure, the blade forms a quasi-double-walled multi-layered composite structure during topology optimization. The blade's back exhibits a double-thin-walled structure, enhancing circumferential stiffness and suppressing circumferential deformation under centrifugal force and aerodynamic loads. The transverse, longitudinal, and diagonal ribs form continuous force transmission paths along the blade direction, constructing a multi-directional stiffening system and forming an orthogonal anisotropic support network. This network distributes centrifugal loads throughout the entire cross-sectional load-bearing element, reducing the local stress concentration factor. Due to centrifugal force, the material distribution gradually decreases from the blade root to the blade tip, which helps reduce root stress.

[0046] Based on the topology optimization results and considering the blade manufacturability, the blade model is reconstructed. The reconstruction result is as follows: Figure 5 As shown, the reconstructed model has a mass of 158g. Strength calculations were performed on the reconstructed model, and the results are as follows. Figure 9 , Figure 10 As shown, the overall stress level of the blade is significantly lower than that of the original model, with a maximum stress of 786 MPa, a decrease of 11%.

[0047] In summary, the air-cooled turbine blade topology optimization design method of this invention, by simultaneously considering aerodynamics, heat transfer, and structural mechanics in the optimization model, can automatically balance and coordinate design requirements between different disciplines (such as weight reduction and strength, cooling and stress), find the globally optimal or suboptimal solution at the system level, and realize the systematic solution of complex engineering problems. Designers do not need to rely entirely on experience for initial configuration design, which not only improves blade performance, but also ensures R&D efficiency and quality control through rapid iterative optimization.

[0048] The above are merely preferred embodiments of the present invention and are not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for topology optimization design of air-cooled turbine blades, characterized in that, include: Step 1: Establish the blade geometric model and define the design domain and non-design domain based on the blade geometric model. The design domain is the solid inner region of the blade body, and the non-design domain is the skin region of the outer surface of the blade body. Step 2: With the goal of minimizing the compliance of the non-design domain of the blade, i.e., the skin position, and with the total material integral as the constraint, establish a mathematical model for the topology optimization of the air-cooled turbine blade. The mathematical model for the topology optimization of the air-cooled turbine blade comprehensively considers the coupling effects of aerodynamic loads, temperature loads, and centrifugal loads. Step 3: Construct a topology optimization sensitivity model based on the mathematical model of air-cooled turbine blade topology optimization; Step 4: Perform finite element processing on the blade geometry model to obtain the blade finite element model, which includes mesh generation, displacement constraints, aerodynamic loads, temperature loads, and centrifugal loads. Step 5: The sensitivity model treats the entire blade as the topology optimization solution object, defines the pseudo density of the elements in the design domain as the design variable, and defines the minimum compliance of the skin as the optimization objective. Iterative calculations are performed on the finite element model of the blade until the skin compliance meets the convergence condition, and the optimized pseudo density of the elements in the design domain is obtained. Step 6: Threshold the pseudo-density of the elements in the design domain and reconstruct the geometry of the design domain to generate the final blade internal cavity structure design scheme.

2. The air-cooled turbine blade topology optimization design method according to claim 1, characterized in that, In step 2, the mathematical model for topology optimization of the air-cooled turbine blade is as follows: in, For the compliance of the blade in the non-designed area, i.e., the skin area, Let F be the stiffness matrix at the skin location, F be the overall load vector, U be the nodal displacement vector, and V be the stiffness matrix at the skin location. i To design the volume of the i-th element in the domain, x i F represents the pseudo density of the i-th finite element. m F is the aerodynamic load vector. th F is the temperature load vector. ω The centrifugal force load vector, It is a constant value close to zero to avoid the singularity of the stiffness matrix.

3. The air-cooled turbine blade topology optimization design method according to claim 1, characterized in that, In step 3, the topology optimization sensitivity model is: in, Let K represent the compliance of the blade outside the design domain, i.e., the skin region; K be the stiffness matrix; and U be the nodal displacement vector. To select the control operator, x i The pseudo-density of the finite element is represented by λ, where λ is the adjoint vector. For a unit shape function matrix, Let the integral element be the position vector of the unit. Let be the rotational acceleration vector. For the initial density of the design domain, Let B be the coefficient vector of the unit, ∆T be the temperature difference, φ be the column vector, and B be the coefficient vector of the unit. i Let D be the derivative matrix of the shape functions of the element. i0 The initial elasticity matrix of the element; The RAMP model was used to interpolate the material parameters, resulting in: In the formula, p and q are interpolation factors, i.e., the penalty functions of materials in topology optimization; x i D represents the pseudo-density of a finite element. i For the elasticity matrix, The initial elasticity matrix, For the coefficient vector, For the initial coefficient vector, E(x) i Let a(x) be the elastic modulus of the element. i ) represents the elemental linear expansion coefficient.

4. The air-cooled turbine blade topology optimization design method according to claim 3, characterized in that, In step 3, the specific process of constructing the topology optimization sensitivity model based on the mathematical model of air-cooled turbine blade topology optimization is as follows: The objective function is to minimize the compliance of the blade outside the design domain, i.e., the skin region. The sensitivity of compliance to design variables is expressed as: （1） in, For the compliance of the blade in the non-designed area, i.e., the skin area, Here is the stiffness matrix for the skin location. Let U be the stiffness matrix of the i-th finite element, U be the nodal displacement vector, and x be the stiffness matrix of the i-th finite element. i This represents the pseudo density of the i-th finite element. The selection control operator for whether the unit is in the skinned position; The adjoint vector method is used for calculation and solution, introducing the adjoint vector λ, so that... The sensitivity formula is: （2） in, For the compliance of the blade in the non-designed area, i.e., the skin area, Let be the stiffness matrix of the i-th finite element, U be the nodal displacement vector, and F be the element load. To select the control operator, x i Let λ represent the pseudo density of the i-th finite element, and λ be the adjoint vector introduced by the solution. The load F in formula (2) is decomposed and discretized according to the aerodynamic load, temperature load, and centrifugal force load on the blade. The sensitivity formula is: （3） in, Let K represent the compliance of the blade outside the design domain, i.e., the skin region; K be the stiffness matrix; and U be the nodal displacement vector. To select the control operator, x i F represents the pseudo density of the i-th finite element. m F is the aerodynamic load vector. th F is the temperature load vector. ω Let λ be the centrifugal force load vector, and λ be the adjoint vector. The first-order partial derivative of the aerodynamic load vector with respect to the element pseudo-density is: （4） in, x is the aerodynamic load vector at the element node. i This represents the pseudo-density of a finite element; Centrifugal load vector The derivative of the pseudo-density is solved as follows: （5） in: Centrifugal load vector at the element node, x i This represents the pseudo-density of a finite element. For a unit shape function matrix, Let the integral element be the position vector of the unit. Let be the rotational acceleration vector. The blade rotates at a constant angular velocity ω around the Z-axis. , The initial density; Temperature load vector The derivative of the pseudo-density is solved as follows: （6） in, x is the temperature load vector at the element node. i Let ΔT represent the pseudo-density of the finite element, ΔT be the temperature difference, and φ be the column vector. For three-dimensional problems, we have... B i Let D be the derivative matrix of the shape functions of the i-th element. i0 Let be the initial elasticity matrix of the i-th element. Let be the coefficient vector of the i-th unit. E(x) i Let a(x) be the elastic modulus of the element. i () represents the element linear expansion coefficient; Substituting formulas (4), (5), and (6) into formula (3) yields the topology optimization sensitivity model.

5. The air-cooled turbine blade topology optimization design method according to claim 1, characterized in that, In step 4, the mesh is a quadrilateral hexahedral mesh; the number of mesh layers in the skin area is not less than 3; and the number of mesh layers in the area where the blade trailing edge becomes smaller is not less than 5.

6. The air-cooled turbine blade topology optimization design method according to claim 1, characterized in that, In step 5, the sensitivity model modifies the blade finite element model based on the pseudo-density, performs FEA calculations, sensitivity analysis, sensitivity filtering and boundary smoothing based on parameters, and updates the pseudo-density iteratively to calculate skin compliance using the OC or ESO / BESO method.

7. The air-cooled turbine blade topology optimization design method according to claim 6, characterized in that, In step 6, the threshold processing includes: setting a density threshold, treating units with a pseudo density greater than the density threshold as solid materials and units with a density less than the density threshold as pores, creating a clear boundary between solids and pores, and gradually adjusting the density threshold until a result that meets the requirements of function, weight, and structural feasibility is selected; The geometric reconstruction of the design domain includes: smoothing the obvious boundaries between solids and holes to generate a smooth structure, preserving the cooling design structure, and generating the final blade internal cavity structure design scheme.

8. The air-cooled turbine blade topology optimization design method according to claim 7, characterized in that, The cooling design structure includes film cooling, impact cooling, and turbulence ribs.

Images