Blade aerodynamic-structure multi-disciplinary optimization design method and system based on turbulent flow discrete-adjoint method and equivalent stress model

Abstract

The application discloses a kind of blade aerodynamic-structure multidisciplinary optimization design method and system based on turbulent flow discrete companion method and equivalent stress model.The method comprises the following steps: constructing the equivalent stress model of blade, calculating the maximum equivalent stress of blade using the equivalent stress model;According to the maximum equivalent stress of blade, set the objective function of aerodynamic-structure multidisciplinary optimization design;Based on turbulent flow discrete companion method, the design variables of blade are optimized, so that the objective function reaches minimum value, and the optimized blade shape is obtained according to the design variables of blade.The application can significantly improve the aerodynamic performance of blade, reduce the maximum structural stress, has the characteristics such as high efficiency and high precision, and can be widely applied to the aerodynamic-structure multidisciplinary optimization design problem of blade.

Description

Technical Field

[0001] This invention belongs to the field of aerodynamic-structural multidisciplinary optimization design, and relates to a method and system for aerodynamic-structural multidisciplinary optimization design of blades, particularly a method and system for aerodynamic-structural multidisciplinary optimization design of blades based on the turbulence discrete adjoint method and the equivalent stress model. Background Technology

[0002] Rotor blades are crucial components in engines, responsible for functional switching, and their aerodynamic performance parameters directly impact fuel consumption and fuel economy. Furthermore, rotor blades bear significant loads during operation; insufficient blade strength can lead to cracks, breakage, and other malfunctions. Therefore, it is essential to conduct multidisciplinary aerodynamic-structural optimization design of rotor blades to improve structural strength, ensuring reliable operation while enhancing aerodynamic performance.

[0003] To simultaneously improve the aerodynamic performance and structural strength of blades, non-gradient methods, including surrogate models and evolutionary algorithms, are commonly used in industry and academia. These methods use blade bending, sweep, and airfoil as design parameters to couple the solution of flow control equations and structural equations. While these non-gradient methods are simple in principle and easy to implement algorithmically, their computational cost is related to the number of design variables. When the number of design variables is large, computational resource requirements are high, resulting in low optimization efficiency. In contrast, in blade aerodynamic-structural optimization design based on gradient methods, the sensitivity calculation time of the direct difference method is linearly related to the dimensionality of the design parameters. When there are many design parameters, the optimization efficiency is low. Furthermore, the sensitivity of the direct difference method is highly sensitive to the magnitude of perturbations in the design parameters. The adjoint method, on the other hand, has a sensitivity calculation time almost independent of the number of design parameters, showing significant application potential in refined optimization design. However, the adjoint method is complex, requiring the simultaneous derivation of adjoint equations for both the flow field and the structural field, involving the transfer of adjoint variables at the fluid-structure interface. Developing adjoint solvers is challenging. Therefore, in the field of blade internal flow optimization design, the adjoint method is mainly used for single-discipline optimization design problems involving aerodynamics and structure.

[0004] Therefore, how to design a multidisciplinary optimization design method for blade aerodynamics and structure to achieve blade aerodynamic and structural optimization design controlled by multiple design variables, and to accurately and quickly improve the aerodynamic and structural performance of blades, is an urgent problem to be solved. Summary of the Invention

[0005] This invention addresses the limitations of existing multidisciplinary aerodynamic-structural optimization design methods for blades by proposing a method and system based on the turbulence discrete adjoint method and equivalent stress model. This invention addresses the multidisciplinary aerodynamic-structural optimization design problem of blades, enabling efficient aerodynamic-structural optimization design controlled by multiple design variables, and accurately and rapidly improving the aerodynamic and structural performance of blades.

[0006] The technical solution adopted in this invention is as follows:

[0007] A multidisciplinary aerodynamic-structural optimization design method for blades based on the turbulence discrete adjoint method and equivalent stress model includes the following steps:

[0008] Construct an equivalent stress model for the blade and use the equivalent stress model to calculate the maximum equivalent stress of the blade;

[0009] The objective function for aerodynamic-structural multidisciplinary optimization design is set based on the maximum equivalent stress of the blade.

[0010] The blade design variables are optimized based on the turbulent discrete adjoint method to minimize the objective function, and the optimized blade shape is obtained based on the blade design variables.

[0011] Furthermore, the specific steps for constructing the equivalent stress model of the blade are as follows:

[0012] Calculate the aerodynamic bending moment and centrifugal bending moment of the blade;

[0013] Calculate the combined bending moment of the blade section and the bending stress at the point located on the section based on the aerodynamic bending moment and the centrifugal bending moment;

[0014] Calculate the centrifugal tensile stress on the blade cross section, and calculate the total equivalent stress at any point on the cross section based on the centrifugal tensile stress and the bending stress to obtain the equivalent stress model.

[0015] Furthermore, the calculation of the maximum equivalent stress of the blade using the equivalent stress model specifically involves: calculating the total equivalent stress at each point at the root of the blade using the equivalent stress model, and selecting the largest total equivalent stress as the maximum equivalent stress.

[0016] Furthermore, the objective function of the aerodynamic-structural multidisciplinary optimization design is:

[0017]

[0018] Where Λ0, Λ1, Λ2, Λ3 are weighting coefficients, and S gen0 , π0, σ0 represent the outlet entropy, mass flow rate, total pressure ratio, and maximum equivalent stress of the original blade, respectively. gen , π and σ represent the outlet entropy, mass flow rate, total pressure ratio, and maximum equivalent stress of the optimized blade, respectively.

[0019] Furthermore, the optimization of blade design variables based on the turbulence discrete adjoint method to minimize the objective function specifically includes:

[0020] Obtain the discrete adjoint equation corresponding to the objective function, solve the discrete adjoint equation to obtain the adjoint field corresponding to the objective function; calculate the gradient of the objective function with respect to the design variables based on the perturbation design variables of the adjoint field corresponding to the objective function, and gradually adjust the blade design variables along the negative direction of the objective function gradient using the steepest descent method based on the gradient information, so that the objective function reaches the minimum value.

[0021] Furthermore, the process of solving the discrete adjoint equation to obtain the adjoint field corresponding to the objective function specifically includes: using the simplified five-step Runge-Kutta method to solve the discrete adjoint equation in time and combining multigrid technology and local time step size technology to accelerate convergence and obtain the adjoint field of the objective function.

[0022] Furthermore, by adjusting the weighting coefficients in the objective function, single-disciplinary optimization design of blade aerodynamics or structure can be achieved.

[0023] A multidisciplinary aerodynamic-structural optimization design system for blades based on the turbulence discrete adjoint method and equivalent stress model, used to implement the above method, includes:

[0024] Equivalent stress calculation module: used to build the equivalent stress model of the blade and calculate the maximum equivalent stress of the blade using the equivalent stress model;

[0025] Objective function construction module: used to set the objective function for aerodynamic-structural multidisciplinary optimization design based on the maximum equivalent stress of the blade;

[0026] Blade Shape Optimization Module: This module is used to optimize blade design variables based on the turbulence discrete adjoint method, so as to minimize the objective function and obtain the optimized blade shape based on the blade design variables.

[0027] A computer device, the computer device comprising:

[0028] One or more processors;

[0029] Memory, used to store one or more programs;

[0030] When the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned multidisciplinary optimization design method for blade aerodynamics and structure based on the turbulence discrete adjoint method and equivalent stress model.

[0031] A computer-readable storage medium storing computer instructions that, when executed by one or more processors, cause the one or more processors to perform the steps in the method described above.

[0032] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0033] 1. This invention proposes for the first time to use equivalent stress as the objective function for aerodynamic-structural multidisciplinary optimization design based on the adjoint method. The maximum equivalent stress is calculated through the equivalent model, which reduces the high computational cost of obtaining the sensitivity of the objective function by calculating the static equilibrium equation of the structure under repeated disturbance design variables. It solves the problem that the adjoint method is difficult to use for aerodynamic-structural multidisciplinary optimization design of blades, avoids the coupled solution of aerodynamic-structural adjoint equations, and reduces the development difficulty of the adjoint solution program.

[0034] 2. To address the problem of high computational costs in refined aerodynamic-structural optimization design with a large number of design variables, the multidisciplinary aerodynamic-structural optimization design method for blades based on the turbulence discrete adjoint method and stress equivalent model provided in this invention can efficiently improve aerodynamic and structural performance. Attached Figure Description

[0035] Figure 1 This is a flowchart of the method in an embodiment of the present invention.

[0036] Figure 2 This is a comparison diagram of the blade shape of NASA Rotor67 with the original blade obtained by changing the blade sweep in an embodiment of the present invention.

[0037] Figure 3 The following is a schematic diagram of the bending moment calculation of the blade in the embodiment of the present invention: aerodynamic bending moment (a), centrifugal bending moment (b).

[0038] Figure 4 This is a schematic diagram of the principal inertial axis of the blade cross section in an embodiment of the present invention.

[0039] Figure 5 This is a flowchart illustrating the calculation of the adjoint gradient of the adjoint equation in an embodiment of the present invention.

[0040] Figure 6 This is a curve showing the change of parameters during the optimization design process in an embodiment of the present invention.

[0041] Figure 7 This is a comparison diagram of the blade shape before and after optimization in an embodiment of the present invention.

[0042] Figure 8 The curves showing the variation of the outlet performance parameters along the blade height before and after optimization in this embodiment of the invention are shown. Detailed Implementation

[0043] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings and specific examples.

[0044] like Figure 1 As shown, a multidisciplinary optimization design method for blade aerodynamics and structure based on the turbulence discrete adjoint method and equivalent stress model includes the following steps:

[0045] Construct an equivalent stress model for the blade and use this model to calculate the maximum equivalent stress on the blade. The specific steps are as follows:

[0046] To calculate the aerodynamic bending moment of the blade, the pressure on any infinitesimal surface element of the rotor blade can be expressed as pdA, where pdA is the pressure along the outward normal direction of the infinitesimal surface element. Distance from the infinitesimal surface to the leaf root The aerodynamic bending moment of the rotor blades

[0047] To calculate the centrifugal bending moment of the blade, for any unit volume dV inside the blade, its mass dm = ρdV, and its distance to the axis of rotation is... The straight-line distance r from the body center of the infinitesimal element to the centroid of the leaf root root Assuming the blade rotation speed is Ω, then in the rotating reference frame, this element is subjected to centrifugal force. Centrifugal bending moment M on the leaf root grav =∫(r root ×G).

[0048] Calculate the combined bending moment and bending stress. The combined bending moment is equal to the algebraic sum of the aerodynamic bending moment and the centrifugal bending moment acting on the cross section, M. x =M aero,x +M grav,x M y =M aero,y +M grav,y M z =M aero,z +M grav,z Calculate the principal axes of inertia ξ and η of the cross section, and the principal moment of inertia J. ξ and J η and the combined bending moment (M) x M y M z ) Decompose along the principal axis of inertia of the cross section onto the cross section (M) ξ M η Thus, for any point A on the cross section, the local coordinate η relative to the principal axis of inertia is... A and ξ A Bending stress at point A

[0049] Calculate the centrifugal tensile stress and total equivalent stress. For any section i of the blade, calculate the centrifugal tensile stress σ of the section. i The centrifugal force G generated by the nth infinitesimal element above the cross section is equal to that force. n,i The component G perpendicular to the cross section n,i With the area A of the cross section i The ratio, The total equivalent stress σ at any point A on section i A =σbend,A +σ i .

[0050] The maximum stress on a blade is generally located at the blade root section. Therefore, the total equivalent stress at each point at the blade root is calculated using an equivalent stress model, and the largest total equivalent stress is selected as the maximum equivalent stress.

[0051] The objective function I for aerodynamic-structural multidisciplinary optimization design is set based on the maximum equivalent stress of the blade:

[0052]

[0053] Where Λ0, Λ1, Λ2, Λ3 are weighting coefficients, and S gen0 , π0, σ0 represent the outlet entropy, mass flow rate, total pressure ratio, and maximum equivalent stress of the original blade, respectively. gen , π and σ represent the outlet entropy, mass flow rate, total pressure ratio, and maximum equivalent stress of the optimized blade, respectively.

[0054] Then, the blade design variables are optimized based on the turbulence discrete adjoint method to minimize the objective function, and the optimized blade shape is obtained based on the blade design variables. Specifically, this includes:

[0055] Obtain the objective function I of the aerodynamic-structural multidisciplinary optimization design. The discrete adjoint equation of the objective function is as follows:

[0056]

[0057] Where R is the flow control equation, and w = (w1, w2, w3, w4, w5, w6) T Ψ represents the conserved flow variables in the mass equation, the three-directional momentum equation, the energy equation, and the turbulence model equation; Ψ = (ψ1, ψ2, ψ3, ψ4, ψ5, ψ6) T , which is the accompanying variable corresponding to the flow variable.

[0058] Then, the simplified five-step Runge-Kutta method is used to solve the discrete adjoint equations in time, and the convergence is accelerated by combining multigrid technology and local time step size technology to obtain the adjoint field corresponding to the objective function.

[0059] Furthermore, by adjusting the weighting coefficients in the objective function, single-disciplinary optimization design of blade aerodynamics or structure can be achieved.

[0060] In one specific embodiment of the present invention, the aerodynamic-structural optimization design of the transonic rotor blades of NASA Rotor 67 is taken as the research object. The objective functions include maximum equivalent stress, outlet entropy, flow rate constraint, and total pressure ratio constraint. The blade design speed is 16043 RPM, the tip clearance is 1 mm, the number of blades is 22, the inlet total temperature is 288 K, the inlet total pressure is 1 ATM, and the design pressure ratio is 1.63. The blades are made of titanium metal with a material density of 4500 kg / m^3, a Young's modulus of 1.16e11 PA, and a Poisson's ratio of 0.32. The optimized design condition is selected as the near-peak efficiency condition, with an outlet back pressure of 1.04 ATM.

[0061] The first stage involves constructing an equivalent stress model for the blade, using the equivalent stress model to calculate the maximum equivalent stress of the blade, and validating the effectiveness of the model using commercial software.

[0062] The maximum stress on a blade is generally located at the blade root section. Therefore, the total equivalent stress at each point at the blade root is calculated using an equivalent stress model, and the largest total equivalent stress is selected as the maximum equivalent stress.

[0063] To verify the effectiveness of the equivalent stress model, several three-dimensional blades with varying bends and sweeps are first generated based on the original Rotor 67 blade. The maximum equivalent stress of these blades is then calculated using the equivalent stress model and compared with the original Rotor 67. Commercial software is used to verify whether the equivalent model accurately reflects the trend of maximum stress variation. These three-dimensional blades with varying sweeps are obtained by superimposing Gaussian radial basis functions on the leading edge of the blades. The method for changing the blade shape here is consistent with the method for changing the blade shape in the optimization design below. The expression for the Gaussian radial basis function is as follows: Where, α N These are design variables used to perturb the blade sweep, where N is the design variable number and r is the variable name. N Let be the distance from the center of the Nth design variable disturbance to the rotation axis, and r be the distance from any point on the leading edge of the blade to the blade rotation axis. |rr N | is the distance from any point on the leading edge to the center of the disturbance, α N To control the decay rate of the radial basis function and ensure the blade root remains stationary, the final disturbance at the leading edge needs to be multiplied by a linear decay coefficient from the blade tip to the blade root. h(r) = rr hub Taking four design parameters as an example, by changing the blade sweep according to Table 1, the leading edge disturbance center is located at 25%, 50%, 75%, and 100% of the blade height, respectively. hub Let α be the axial chord length at the leaf root. Taking blade1 as an example, α1, α2, α3, and α4 are all equal to 0.1c. hub This indicates that the disturbance magnitude corresponding to the four design parameters is 0.1c.hub The blades are swept back overall. A comparison of the shapes of the six blades after the sweepback modification with the original blade shapes is shown in Table 1. Figure 2 As shown.

[0064] Table 1. Design parameters of NASA Rotor 67: Blade sweep design parameters

[0065] <![CDATA[α1]]> <![CDATA[α2]]> <![CDATA[α3]]> <![CDATA[α4]]> blade1 <![CDATA[0.1c hub ]]> <![CDATA[0.1c hub ]]> <![CDATA[0.1c hub ]]> <![CDATA[0.1c hub ]]> blade2 <![CDATA[0.1c hub ]]> <![CDATA[-0.1c hub ]]> <![CDATA[0.1c hub ]]> <![CDATA[-0.1c hub ]]> blade3 <![CDATA[-0.1c hub ]]> <![CDATA[0.1c hub ]]> <![CDATA[-0.1c hub ]]> <![CDATA[0.1c hub ]]> blade4 <![CDATA[-0.1c hub ]]> <![CDATA[-0.1c hub ]]> <![CDATA[-0.1c hub ]]> <![CDATA[-0.1c hub ]]> blade5 <![CDATA[-0.1c hub ]]> <![CDATA[0.1c hub ]]> <![CDATA[0.1c hub ]]> <![CDATA[-0.1c hub ]]> blade6 <![CDATA[0.1c hub ]]> <![CDATA[-0.1c hub ]]> <![CDATA[-0.1c hub ]]> <![CDATA[0.1c hub ]]>

[0066] Calculate the aerodynamic bending moment of the blade ( Figure 3 For any infinitesimal element on the surface of a rotor blade, the pressure it experiences can be expressed as pdA, where the normal direction to the infinitesimal element is... Distance from the infinitesimal surface to the leaf root Thus, the aerodynamic bending moment of the rotor blades The aerodynamic bending moments of the original blade and the six four-design-parameter blade sweep-off shapes described in the above steps are shown in the first column of Table 2. The table compares the bending moments calculated by the program with those calculated by Ansys to verify the accuracy of the program's calculations. Using the bending moments calculated by the commercial software Ansys Workbench as a reference value, the error between the program's calculated bending moments and the reference values ​​is small, indicating that the program's calculation results have high accuracy. After changing the design parameters and obtaining a new blade shape, the new bending moment values ​​calculated by the program still match the reference values ​​well, further verifying the stability and reliability of the program under different design conditions. Furthermore, as the design parameters change, the new bending moment data clearly reflects the trend of bending moment changes. This indicates that the program can not only accurately calculate the numerical value of the bending moment but also effectively capture the pattern of bending moment changes with the design, thus providing strong support for further design optimization.

[0067] Table 2 Bending Moments for Different Blade Designs

[0068]

[0069]

[0070] Calculate the centrifugal bending moment of the blade ( Figure 3 For a volume element dV inside the blade, its mass dm = ρdV, and its distance to the axis of rotation is r, the straight-line distance r from the body center of the infinitesimal element to the centroid of the blade root is... root Assuming the blade rotation speed is Ω, then in the rotating reference frame, this element experiences a centrifugal force G = dmΩ. 2 r, the centrifugal bending moment M experienced by the leaf root grav =∫(r root ×G). The centrifugal force bending moment of the original blade and the six four-design parameters of the blade sweeping shape in the above steps are shown in the second column of Table 2.

[0071] Calculate the combined bending moment and bending stress. The combined bending moment is equal to the algebraic sum of the aerodynamic bending moment and the centrifugal bending moment acting on the cross section, M. x =M aero,x +M grav,x M y =M aero,y +M grav,y M z =M aero,z +M grav,z The combined bending moment of the original blade and the six design parameters of the blade sweeping shape in the above steps is shown in the third column of Table 2. Calculation section ( Figure 4 Principal axes of inertia ξ and η, principal moments of inertia J ξ and J η and the combined bending moment (M) x M y M z ) Decompose along the principal axis of inertia of the cross section onto the cross section (M) ξ M η Thus, for any point A on the cross section, the local coordinate η relative to the principal axis of inertia is... A and ξ A Bending stress at point A

[0072] Calculate the centrifugal tensile stress and total equivalent stress. For any section i of the blade, calculate the centrifugal tensile stress σ of the section. i The centrifugal force G generated by the nth infinitesimal element above the cross section is equal to that force. n,i The component G perpendicular to the cross section n,i With the area A of the cross section i The ratio, The total equivalent stress σ at any point A on section i A =σ bend,A +σ i The maximum equivalent stress of the original blade and the six four-design parameters of the blade in the above steps is shown in Table 3. The table compares the maximum equivalent stress calculated by the program with the Von-Mises stress calculated by Ansys to verify the effectiveness of the bending moment calculated by the program and its ability to accurately capture the influence of blade sweep variation on the maximum stress. Because commercial software uses the maximum value of Von-Mises stress as the maximum stress, which does not correspond to the definition of stress calculated by the program, Table 3 mainly verifies whether the program can accurately capture the change in the maximum stress of the blade. Taking blade2 and blade6 as examples, the maximum stress calculated by Ansys increased by 14.41% and 17.62% respectively compared to the original Rotor 67 blade, and the corresponding equivalent stress increased by 0.58% and 0.61% respectively, indicating that the equivalent model can accurately reflect the trend of blade stress variation.

[0073] Table 3 Maximum stress of NASA Rotor 67 and 6 types of sweeping blades

[0074]

[0075] In the second stage, aerodynamic and structural performance parameters are used together as objective functions to derive the discrete adjoint equations for turbulence:

[0076] Based on the above method for calculating the total equivalent stress of the blades, an objective function for aerodynamic-structural multidisciplinary optimization design is defined. Where Λ0, Λ1, Λ2, and Λ3 are weighting coefficients, selected according to specific design requirements, and S gen0 , π0 and σ0 represent the outlet entropy, mass flow rate, total pressure ratio, maximum equivalent stress, and S of the original blade, respectively. gen , π and σ represent the outlet entropy, mass flow rate, total pressure ratio, and maximum equivalent stress of the optimized blade, respectively. The design requirement of this embodiment is to reduce the maximum equivalent stress of the blade without reducing the isentropic efficiency. To achieve this design requirement, Λ0 = 0.1, Λ1 = 10, Λ2 = 10, and Λ3 = 10 are set.

[0077] The discrete adjoint equations of an aerodynamic-structural multidisciplinary problem are calculated with the objective function as the underlying principle. According to the adjoint method, the objective function primarily influences the adjoint equations. The right-hand side constant term, R is the flow control equation, Ψ is the turbulence-related variable, Ψ T = (ψ1,ψ2,ψ3,ψ4,ψ5,ψ6), calculated using the inverse mode of the automatic differentiation tool TAPENADE. Comment out input variables, output variables, and constants in the code so that Tapenade can identify the variables that need to be differentiated. The discrete adjoint equation is solved using a simplified five-step Runge-Kutta time-progression method, and multigrid techniques and local time step sizes are used to accelerate convergence. The specific steps are as follows:

[0078] First, the main subroutines of the flow field solver are differentiated using the inverse mode of the automatic differentiation tool, and then manually assembled according to the expression of the adjoint equation. It is worth noting that the subroutines of the fluid solver require further optimization to ensure a clear structure and modular design in the source code. Input variables, output variables, and constants must be commented in the code so that TapenaDE can identify the variables that need to be differentiated.

[0079] In flow field calculations, the convection terms of the flow control equations are spatially discretized using the classical JST scheme. Therefore, when calculating the differential residuals, the influence of the artificial viscosity term needs to be considered.

[0080] The flow field residual R can be further written as a combination of the convection term R1, the artificial viscosity term R2, the diffusion term R3, and the source term R4:

[0081] R1(α,w)+R2(α,w)+R3(α,w,μ l ,μ t )+R4(α,w)=0,

[0082] Where μ l and μ t These are the laminar viscosity coefficient and the turbulent viscosity coefficient, respectively. R4 contains the rotating source term and the turbulent equation source term.

[0083] residuals of the adjoint equation The first term on the right-hand side can be derived from the derivative of the convection term with respect to the conserved variable. The derivative of the artificial viscosity term with respect to the conserved variables The derivative of the diffusion term with respect to the conserved variable The derivative of the source term with respect to the conserved variable The cumulative composition. Furthermore, after the flow field fully converges, the derivative of the objective function with respect to the conserved variables... Since it is a constant, it only needs to be calculated once before solving the adjoint equation.

[0084] After calculating the equivalent stress using the equivalent stress model, the objective function I of the aerodynamic-structural multidisciplinary optimization design is only related to the flow variable w and the node coordinates x of the flow field calculation grid. Therefore, it avoids repeatedly disturbing the design variables to calculate the static equilibrium equation of the structure and obtain the stress gradient with respect to the design variables, thus improving the efficiency of aerodynamic calculation.

[0085] After obtaining the residuals of the adjoint equations, the boundary conditions of the flow control equations are then applied. The residuals on the boundary of the adjoint equation are accumulated into the inner field, w bc Represents the flow variables at the boundary:

[0086]

[0087] After obtaining the complete residual calculation procedure for the adjoint equation, the adjoint equation is solved by adding a pseudo-time term. Referring to the flow control equation, the discrete adjoint equation is solved using a simplified five-step Runge-Kutta time-progression method. Multigrid techniques and local time step sizes are used to accelerate convergence. The simplified five-step Runge-Kutta method can be expressed as:

[0088]

[0089] β1, β2, β3, β4, and β5 are the coefficients of the five-step Runge-Kutta, with values ​​of [missing values]. Δt is the local time step, and V is the volume of each cell in the grid. Ψn Ψ represents the value of the accompanying variable at the nth pseudo-time step. 0 R represents the initial adjoint variables read in the simplified five-step Runge-Kutta sequence during a single time advance. 0 ad Indicates the use of Ψ 0 The calculated adjoint equation residual, Ψ 1 ,...Ψ 5 R represents the intermediate variables generated by the simplified five-step Runge-Kutta time progression. 4 ad Indicated by Ψ 4 The calculated adjoint equation residuals, and finally the adjoint variable value Ψ at the (n+1)th pseudo-time step. n+1 Equal to Ψ 5 In order to quickly reduce the residuals, a multigrid method was adopted, which introduces a series of progressively coarsening grids. First, high-frequency errors are eliminated on the densest grid, and then the solution is transferred to the coarser grid through interpolation to eliminate low-frequency errors. Finally, the solution is transferred back to the denser grid through interpolation.

[0090] After obtaining the convergent adjoint field, calculate the gradient of the objective function with respect to the design variables. The new blade shape is obtained using the steepest descent method, and the flowchart is as follows: Figure 5 As shown, the convergence of the optimization is determined based on the optimization design index.

[0091] During the optimization process, the curves showing the changes in the aerodynamic and structural parameters of interest are as follows: Figure 6 As shown, for the optimized blade, the change in maximum stress was verified using Ansys (Table 4).

[0092] Table 4 Comparison of maximum Von-Miels stress of blades before and after optimization design calculated by Ansys

[0093] original leaf Optimize blades Von Miels maximum stress (Pa) 5.4670e8 4.5956e8(-15.94％)

[0094] Using an equivalent stress model to assess stress changes reduces the time cost of calculating stress gradients with respect to design variables using structural static equilibrium equations. Table 5 compares the time costs required for aerodynamic-structural multidisciplinary optimization using the equivalent stress model and the direct difference method within a design step, where N... α T represents the number of design variables. f and T s This refers to the computation time for the flow field and structural field. As the number of design variables increases, the time required for the direct difference method increases linearly, while the time cost of the equivalent stress model remains unchanged.

[0095] Table 5 Comparison of Time Costs

[0096] Equivalent stress model Direct difference method Time cost <![CDATA[3*T flow ]]> <![CDATA[(N α +1)*T f +(N α +1)*T s ]]>

[0097] Based on the results of the above aerodynamic-structural optimization design Figure 7 and Figure 8 The curves showing the changes in blade shape and exit aerodynamic parameters along the blade height before and after optimization are presented. The comparison shows that while the adiabatic efficiency increases slightly, the maximum stress of the blade decreases significantly, indicating that this invention is applicable to multidisciplinary aerodynamic-structural optimization design and has high computational efficiency. Therefore, the multidisciplinary aerodynamic-structural optimization design method for blades based on the turbulent discrete adjoint method and equivalent stress model proposed in this invention has the characteristics of high efficiency and high accuracy.

[0098] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0099] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0100] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0101] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0102] The above specific embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A multidisciplinary optimization design method for blade aerodynamics and structure based on the turbulence discrete adjoint method and equivalent stress model, characterized in that, Includes the following steps: Construct an equivalent stress model for the blade and use the equivalent stress model to calculate the maximum equivalent stress of the blade; The objective function for aerodynamic-structural multidisciplinary optimization design is set based on the maximum equivalent stress of the blade. The blade design variables are optimized based on the turbulent discrete adjoint method to minimize the objective function, and the optimized blade shape is obtained based on the blade design variables. The specific steps for constructing the equivalent stress model of the blade are as follows: Calculate the aerodynamic bending moment and centrifugal bending moment of the blade; Calculate the combined bending moment of the blade section and the bending stress at the point located on the section based on the aerodynamic bending moment and the centrifugal bending moment; Calculate the centrifugal tensile stress on the blade cross section, and calculate the total equivalent stress at any point on the cross section based on the centrifugal tensile stress and the bending stress to obtain the equivalent stress model; The objective function for the aerodynamic-structural multidisciplinary optimization design is: ， Where I is the objective function, These are the weighting coefficients. These are the outlet entropy, mass flow rate, total pressure ratio, and maximum equivalent stress of the original blade, respectively. These are the optimized blade outlet entropy, mass flow rate, total pressure ratio, and maximum equivalent stress, respectively. The optimization of blade design variables based on the turbulence discrete adjoint method to minimize the objective function specifically includes: Obtain the discrete adjoint equation of the objective function, solve the discrete adjoint equation to obtain the adjoint field corresponding to the objective function; calculate the gradient of the objective function with respect to the blade design variables based on the adjoint field corresponding to the objective function, and use the steepest descent method to gradually adjust the blade design variables along the negative direction of the objective function gradient to make the objective function reach a minimum value.

2. The blade aerodynamic-structural multidisciplinary optimization design method based on the turbulence discrete adjoint method and equivalent stress model according to claim 1, characterized in that, The calculation of the maximum equivalent stress of the blade using the equivalent stress model specifically involves: calculating the total equivalent stress of all nodes at the root of the blade using the equivalent stress model, and selecting the largest total equivalent stress as the maximum equivalent stress.

3. The blade aerodynamic-structural multidisciplinary optimization design method based on the turbulence discrete adjoint method and equivalent stress model according to claim 1, characterized in that, The method of solving the discrete adjoint equation to obtain the adjoint field corresponding to the objective function specifically includes: using the simplified five-step Runge-Kutta method to solve the discrete adjoint equation in time and combining multigrid technology and local time step size technology to accelerate convergence and obtain the adjoint field of the objective function.

4. The blade aerodynamic-structural multidisciplinary optimization design method based on the turbulence discrete adjoint method and equivalent stress model according to claim 1, characterized in that, By adjusting the weighting coefficients in the objective function, single-disciplinary optimization design of blade aerodynamics or structure can be achieved.

5. A multidisciplinary optimization design system for blade aerodynamics and structure based on the turbulence discrete adjoint method and equivalent stress model, characterized in that, For implementing the method as described in any one of claims 1 to 4, comprising: Equivalent stress calculation module: used to build the equivalent stress model of the blade and calculate the maximum equivalent stress of the blade using the equivalent stress model; Objective function construction module: used to set the objective function for aerodynamic-structural multidisciplinary optimization design based on the maximum equivalent stress of the blade; Blade Shape Optimization Module: This module is used to optimize blade design variables based on the turbulence discrete adjoint method, so that the objective function reaches a minimum value, and obtains the optimized blade shape based on the blade design variables.

6. A computer device, characterized in that, The computer device includes: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the blade aerodynamic-structural multidisciplinary optimization design method based on the turbulence discrete adjoint method and equivalent stress model as described in any of claims 1 to 4.

7. A computer-readable storage medium storing computer instructions, characterized in that, When the computer instructions are executed by one or more processors, the one or more processors are caused to perform the steps of the method according to any one of claims 1 to 4.

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