An aerodynamic shape optimization design method, system, device and storage medium

Abstract

The application provides a kind of aerodynamic shape optimization design method, system, equipment and storage medium, belong to aerodynamic shape optimization design field, including: generating aerodynamic shape design variable and determining optimization target;Through radial basis function dynamic mesh updating model grid;Solve steady flow field and jacobian matrix;Adopting pre-solution analysis combines golden section method to calculate maximum pre-solution gain;Through the gradient method of reconstructed pre-solution gain companion to calculate design variable gradient;Adopting nonlinear conjugate gradient method iterative optimization.The application does not need to repeat singular value decomposition, only through algebraic calculation to complete gradient solving, while ensuring the optimization accuracy of flow stability, greatly reduces the computing overhead, significantly improves the optimization efficiency of multivariate complex aerodynamic shape, adapts to engineering large-scale design requirements.

Description

Technical Field

[0001] This invention belongs to the field of aerodynamic shape optimization design, and specifically relates to an aerodynamic shape optimization design method, system, device and storage medium. Background Technology

[0002] Aerodynamic shape refers to the surface contour and overall shape of an object specifically designed to conform to airflow, reduce air resistance, and utilize air lift. It is the core of aerodynamic design in fields such as aviation. As the requirements for the aerodynamic performance of industrial equipment gradually increase, the flow stability problem of aerodynamic shapes is becoming increasingly prominent. Flow stability describes the evolution tendency of a basic flow after being disturbed: if the disturbance decays and the flow returns to its original state, the system is stable; if the disturbance is amplified and triggers a flow transition to another state, the system becomes unstable. This significantly impacts human production and daily life, potentially causing a series of aerodynamic problems such as load pulsation, vibration, and noise, severely restricting the performance, safety, and efficiency of numerous industrial equipment in fields such as aerospace, wind engineering, and construction. Therefore, the key technological requirements for aerodynamic shape control and design addressing flow stability permeate all aspects of national strategic importance, including the independent development of domestically produced large aircraft, the implementation of wind power efficiency enhancement, and the improvement of public safety (building wind resistance).

[0003] Existing aerodynamic shape optimization design techniques primarily focus on aerodynamic performance under conventional operating conditions, neglecting the necessary flow instability issues under extreme conditions. This has led to long-term limitations in practical applications. To incorporate flow instability into the shape optimization design framework, it is essential to deeply analyze the flow instability mechanism and construct efficient stability evaluation indices. Among these, gradient optimization design, which uses pre-solved gain to characterize flow stability, has a relatively complete theoretical foundation, strong universality and computational reliability for different flow instability mechanisms, and demonstrates potential for engineering applications.

[0004] However, most existing gradient optimization methods based on pre-defined gain employ the finite difference method to calculate the gradient of the gain with respect to design variables. The computational cost of this method increases linearly with the number of design variables, making it unsuitable for complex flow problems. Furthermore, calculating the gradient of the pre-defined gain with respect to design variables using the finite difference method requires applying a perturbation to each design variable and repeating the CFD solution and pre-defined gain calculation for each perturbation. The computational cost of this approach is linearly related to the number of design variables, while practical engineering optimization problems often involve a large number of design parameters, leading to unacceptable computational overhead and ultimately a significant reduction in optimization efficiency. Summary of the Invention

[0005] To address the problems of high computational cost and difficulty in adapting to complex multivariate engineering using existing pre-gain optimization methods, this invention provides an aerodynamic shape optimization design method. This invention redesigns the adjoint gradient calculation method based on pre-gain, retaining the advantages of traditional adjoint methods in single CFD calculations and single-step linear equation solving, while eliminating the need for repeated singular value decomposition calculations of the pre-gain; instead, it only requires algebraic calculations, thus significantly improving optimization efficiency.

[0006] To achieve the above objectives, the present invention provides the following technical solution: An aerodynamic shape optimization design method includes the following steps: The geometric parameters of the target aerodynamic shape are fitted and solved as CST parameters using the CST shape parameterization method, and the CST parameters are used as design variables for aerodynamic shape optimization. The subcritical flow state of the aerodynamic shape near the instability threshold is determined by numerical simulation, and the flow characteristic frequency corresponding to the subcritical flow state is extracted. The optimization objective of the aerodynamic shape is to minimize the maximum pre-solution gain under the subcritical flow state, and the flow characteristic frequency is used to limit the search range of the maximum pre-solution gain. The aerodynamic shape model is generated based on the design variables of the aerodynamic shape optimization, and the initial mesh is updated by the aerodynamic shape model. The flow numerical simulation is performed based on the Navier-Stokes equations and the updated mesh to calculate the steady flow solution. The Jacobian matrix is ​​obtained by flux difference approximation based on the steady flow solution. The initial mesh is a flow field calculation mesh pre-generated based on the target aerodynamic shape. The maximum pre-solution gain is calculated iteratively based on the Jacobian matrix and subcritical flow state. If the maximum pre-solution gain does not converge, the CST parameters are updated. When the iterative difference of the maximum pre-solution gain is less than the preset convergence threshold, the optimization terminates and the optimal CST parameters and the corresponding aerodynamic optimized shape are output.

[0007] Preferably, the geometric parameters include contour coordinate parameters, area, thickness, and curvature; The method of fitting and solving the geometric parameters of the target aerodynamic shape into CST parameters by CST parameterization is as follows: the contour coordinate parameters, area, thickness and curvature are input into the CST fitting equation constructed by the class function and Bernstein polynomial shape function, and the CST parameters are obtained by the least squares method. The CST parameters are used as the design variables for aerodynamic shape optimization.

[0008] Preferably, the CST parameters are updated using the pre-determined gain adjoint gradient method and the nonlinear conjugate gradient method, specifically including the following steps: Based on the determined flow characteristic frequency, Jacobian matrix and grid weighting matrix, a weighted pre-operator is constructed. The weighted pre-operator is then subjected to minimum singular value decomposition to obtain the response modes. The first adjoint variable is calculated based on the response mode and the current maximum pre-solution gain; based on the constraints of the optimization functional, a system of linear equations is established and solved, and the second adjoint variable is calculated from the first adjoint variable, the Jacobian matrix and its conjugate transpose. The partial derivatives of the Jacobian matrix correlation terms and residuals with respect to the CST parameters are calculated using the finite difference approximation. Then, by combining the first and second adjoint variables with the maximum pre-solution gain, the gradient of the maximum pre-solution gain with respect to the CST parameters is calculated according to the derivation relationship of the pre-solution gain adjoint gradient method. Using the current gradient, the gradient of the previous iteration, and the descent direction, the optimal descent direction for this iteration is calculated using the nonlinear conjugate gradient method. Along the descent direction, a one-dimensional search is performed using the golden section method to find the optimal step size that minimizes the maximum pre-solution gain. The CST parameters are updated numerically using the current CST parameters, optimal step size, and optimized descent direction to obtain new CST parameters. The maximum pre-solution gain is then checked to determine if it has converged. If it has not converged, the iteration continues; if it has converged, the optimization is complete.

[0009] Preferably, the aerodynamic shape model is generated from the design variables based on aerodynamic shape optimization, and the initial mesh is updated driven by the aerodynamic shape model, specifically including: Based on the design variables of aerodynamic shape optimization, the coordinates of each point on the aerodynamic shape surface are calculated by CST parametric equations to determine the thickness distribution, curvature distribution and boundary morphology, and to generate an aerodynamic shape model. Based on the initial mesh pre-generated from the aerodynamic shape before optimization, a radial basis function interpolation model is constructed with the boundary nodes and internal nodes of the initial mesh as the reference. The aerodynamic shape model provides new boundary constraints. By utilizing the global interpolation characteristics of the radial basis function interpolation model, the initial mesh is driven to undergo global smooth deformation, and the computational mesh adapted to the new aerodynamic shape is obtained.

[0010] Preferably, the step of performing flow numerical simulation based on the Navier-Stokes equations and the updated grid to calculate the steady-state flow solution; and obtaining the Jacobian matrix through flux difference approximation based on the steady-state flow solution, specifically includes: Using the updated computational grid as the solution domain, the Navier-Stokes Navier-Stokes equations are adopted as the flow control equations. The control equations are semi-discretized to obtain nonlinear residual operators. The finite volume method is used to iteratively update the flow variables on the updated grid; the iteration continues until the residuals of all grid cells are less than a set threshold, satisfying the steady convergence condition, and the steady flow solution under the current aerodynamic shape is obtained; the flow variables are the fluid physical quantities on each grid cell in the flow field, including density, velocity and pressure. Based on the steady-state solution of the flow, the Jacobian matrix is ​​formed by applying a disturbance to the flow variables and calculating the residual difference, and then using flux difference approximation to calculate the partial derivatives of the nonlinear residual operator with respect to the flow variables. After traversing all grid cells and flow variables, the Jacobian matrix is ​​formed.

[0011] Preferably, the step of iteratively calculating the maximum pre-solution gain based on the Jacobian matrix and subcritical flow state specifically includes: Based on the subcritical flow state of aerodynamic shape optimization design, the flow characteristic frequency corresponding to the state is extracted, and the frequency search interval with the maximum pre-solution gain is set with this as the center. Based on the updated computational grid, all grid cells are traversed, and a diagonal grid weighting matrix is ​​constructed using the area of ​​the grid cells. This grid weighting matrix is ​​used to quantify the weight of different grid regions in the stability assessment. The initial golden section search is performed by determining two search frequency points within the set frequency search interval using the golden section method. For the current golden section frequency point, a weighted pre-solution operator is constructed and calculated by combining the Jacobian matrix and the grid weighted matrix. Singular value decomposition (SVD) is performed on the weighted pre-determining operator to obtain the pre-determining gain at the current frequency. The pre-determining gains corresponding to the two golden section points are compared. The interval with larger gain is retained, and the interval with smaller gain is discarded, thus gradually narrowing the frequency search range. Repeat the frequency point update, pre-solution operator calculation, and singular value decomposition process until the frequency search interval is less than the set threshold, and output the maximum pre-solution gain of the midpoint within the interval.

[0012] Preferably, the step of determining the subcritical flow state of the aerodynamic shape near the instability threshold through numerical simulation and extracting the flow characteristic frequency corresponding to the subcritical flow state specifically involves: determining the subcritical flow state of the aerodynamic shape near the instability threshold through numerical simulation, analyzing the disturbance response characteristics of the flow field under the subcritical flow state, and extracting the corresponding flow characteristic frequency from the flow field disturbance response characteristics of the subcritical flow state.

[0013] This invention also proposes an aerodynamic shape optimization design system, comprising: The variable generation module is used to fit and solve the geometric parameters of the target aerodynamic shape into CST parameters through the CST shape parameterization method, and use the CST parameters as design variables for aerodynamic shape optimization; it determines the subcritical flow state of the aerodynamic shape near the instability criticality through numerical simulation, and extracts the flow characteristic frequency corresponding to the subcritical flow state; it takes minimizing the maximum pre-solution gain under the subcritical flow state as the aerodynamic shape optimization objective, and the flow characteristic frequency is used to limit the search interval of the maximum pre-solution gain. The matrix generation module is used to generate an aerodynamic shape model based on the design variables of aerodynamic shape optimization, and the aerodynamic shape model drives the update of the initial mesh; based on the Navier-Stokes equations and the updated mesh, flow numerical simulation is performed to calculate the steady flow solution; based on the steady flow solution, the Jacobian matrix is ​​obtained through flux difference approximation; the initial mesh is a flow field calculation mesh pre-generated based on the target aerodynamic shape. The optimization module is used to iteratively calculate the maximum pre-solution gain based on the Jacobian matrix and subcritical flow state. If the maximum pre-solution gain does not converge, the CST parameters are updated. When the iterative difference of the maximum pre-solution gain is less than the preset convergence threshold, the optimization terminates and outputs the optimal CST parameters and the corresponding aerodynamic optimized shape.

[0014] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement any of the steps in the aerodynamic shape optimization design method.

[0015] The present invention also provides a computer-readable storage medium storing a computer program that, when loaded by a processor, can execute any of the steps in the aerodynamic shape optimization design method.

[0016] The aerodynamic shape optimization design method provided by this invention has the following beneficial effects: This invention generates a model using CST parameters and drives mesh updates. It solves the steady flow field based on the Navier-Stokes equations and obtains the Jacobian matrix through flux difference approximation. The core matrix can be obtained in a single flow field calculation, avoiding repetitive CFD solutions caused by variable-wise perturbations. Simultaneously, it iteratively calculates the maximum pre-solution gain based on the Jacobian matrix and flow state. If convergence fails, the CST parameters are updated; if convergence occurs, the optimal shape is output. The entire process eliminates the need for repeated singular value decomposition, completing gradient-related calculations and parameter updates solely through algebraic iterations. By reconstructing the pre-solution gain and accompanying gradient calculation framework, this invention fundamentally solves the problem of the linear increase in computational cost in the finite difference method as the number of design variables increases. It replaces repetitive CFD and singular value decomposition with algebraic calculations throughout, significantly reducing computational overhead while maintaining the accuracy of flow stability optimization. This significantly improves the optimization efficiency of complex multi-variable aerodynamic shapes, making it suitable for large-scale engineering design needs. Attached Figure Description

[0017] To more clearly illustrate the embodiments and design schemes of the present invention, the accompanying drawings required for this embodiment will be briefly described below. 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.

[0018] Figure 1 This is a flowchart of the aerodynamic shape optimization design method of Embodiment 1 of the present invention. Detailed Implementation

[0019] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0020] Aerodynamic shapes, such as the streamlined design of an airplane's wings, fuselage, and nose, generate lift to fly. The bullet-shaped nose of high-speed trains uses an extreme aerodynamic shape to reduce wind noise and drag at high speeds. The blades and fairings of wind turbines adopt aerodynamic shapes to efficiently capture wind energy and improve power generation efficiency, while also reducing air resistance, wind noise, and airflow disturbance. The streamlined taper and chamfered corners of the facades of super high-rise buildings use aerodynamic shapes to disperse airflow and reduce wind load and building sway.

[0021] Example 1 Based on this, the present invention proposes an aerodynamic shape optimization design method, which specifically includes the following steps: Step 1: The geometric parameters of the target aerodynamic shape are fitted and solved into CST parameters using the CST shape parameterization method. These CST parameters are used as design variables for aerodynamic shape optimization. Numerical simulation is used to determine the subcritical flow state near the instability threshold of the aerodynamic shape, and the flow characteristic frequencies corresponding to the subcritical flow state are extracted. Minimizing the maximum pre-solution gain under the subcritical flow state is the aerodynamic shape optimization objective, and the flow characteristic frequencies are used to limit the search range for the maximum pre-solution gain. In this embodiment, near-instability threshold refers to a subcritical state where the flow has not yet become unstable but is extremely close to the instability threshold; it is the critical edge between stable and unstable flow. The subcritical state near instability threshold is slightly below the critical condition, has not triggered instability, but is extremely close to the critical point; at this point, the flow is most sensitive to disturbances, the pre-solution gain reaches its maximum, and it is the weakest point in flow stability and the most critical state requiring optimization.

[0022] Specifically, the geometric parameters include profile coordinate parameters, area, thickness, and curvature. The geometric parameters of the target aerodynamic shape are fitted and solved as CST parameters using the CST parameterization method. Specifically, the profile coordinate parameters, area, thickness, and curvature are input into the CST fitting equation constructed by the class function and Bernstein polynomial shape function, and the CST parameters are obtained by solving the least squares method. The CST parameters are used as design variables for aerodynamic shape optimization.

[0023] CST parameters are mathematical parameterizations of aerodynamic shapes. The shape contour coordinates can be directly obtained by solving the parameters through preset CST fitting equations, and then the corresponding aerodynamic shape model can be automatically generated based on the CST parameters.

[0024] Step 2: Generate an aerodynamic shape model based on the design variables of aerodynamic shape optimization, and update the initial mesh driven by the aerodynamic shape model; perform flow numerical simulation based on the Navier-Stokes equations and the updated mesh to calculate the steady flow solution; obtain the Jacobian matrix by flux difference approximation based on the steady flow solution; the initial mesh is the flow field calculation mesh pre-generated based on the target aerodynamic shape.

[0025] Step 3: Iteratively calculate the maximum pre-solution gain based on the Jacobian matrix and subcritical flow state. If the maximum pre-solution gain does not converge, update the CST parameters. When the iterative difference of the maximum pre-solution gain is less than the preset convergence threshold, the optimization terminates and the optimal CST parameters and the corresponding aerodynamic optimized shape are output.

[0026] It should be noted that the maximum pre-solution gain is a core indicator for quantifying the stability of subcritical flow. It is specifically used to measure the amplification ability of an uninstable flow to disturbances, and its calculation is only meaningful in engineering applications under subcritical conditions. The subcritical flow state is not a single numerical value, but a set of flow condition parameters close to the instability threshold.

[0027] As a preferred embodiment, updating the CST parameters using the pre-determined gain adjoint gradient method and the nonlinear conjugate gradient method specifically includes the following steps: A weighted pre-operator is constructed based on the determined flow characteristic frequency, Jacobian matrix, and grid weighting matrix. The response modes are obtained by performing minimum singular value decomposition on the weighted pre-operator.

[0028] The first adjoint variable is calculated based on the response mode and the current maximum pre-solution gain; based on the constraints of the optimization functional, a system of linear equations is established and solved, and the second adjoint variable is calculated from the first adjoint variable, the Jacobian matrix and its conjugate transpose.

[0029] The partial derivatives of the Jacobian matrix correlation terms and residuals with respect to the CST parameters are calculated using the finite difference approximation. Then, by combining the first and second adjoint variables with the maximum pre-solution gain, and following the derivation of the pre-solution gain adjoint gradient method, the gradient of the maximum pre-solution gain with respect to the CST parameters is calculated.

[0030] Using the current gradient, the gradient of the previous iteration, and the descent direction, the optimized descent direction for this iteration is calculated using the nonlinear conjugate gradient method. Along the descent direction, a one-dimensional search is performed using the golden section method to find the optimal step size that minimizes the maximum pre-solution gain.

[0031] The CST parameters are updated numerically using the current CST parameters, optimal step size, and optimized descent direction to obtain new CST parameters. The maximum pre-solution gain is then checked to determine if it has converged. If it has not converged, the iteration continues; if it has converged, the optimization is complete.

[0032] As a preferred embodiment, an aerodynamic shape model is generated based on the design variables for aerodynamic shape optimization, and the initial mesh is updated driven by the aerodynamic shape model, specifically including: Based on the design variables of aerodynamic shape optimization, the coordinates of each point on the aerodynamic shape surface are calculated through CST parametric equations to determine the thickness distribution, curvature distribution and boundary morphology, and generate an aerodynamic shape model.

[0033] Based on the initial mesh pre-generated based on the aerodynamic shape before optimization, a radial basis function interpolation model is constructed using the boundary nodes and internal nodes of the initial mesh as references.

[0034] The aerodynamic shape model provides new boundary constraints. By utilizing the global interpolation characteristics of the radial basis function interpolation model, the initial mesh is driven to undergo global smooth deformation, and the computational mesh adapted to the new aerodynamic shape is obtained.

[0035] As a preferred embodiment, flow numerical simulation is performed based on the Navier-Stokes equations and the updated grid to calculate the steady-state flow solution; using the steady-state flow solution as a reference, the Jacobian matrix is ​​obtained through flux difference approximation, specifically including: Using the updated computational grid as the solution domain, the Navier-Stokes (NS) equations are adopted as the flow control equations. The control equations are semi-discretized to obtain nonlinear residual operators.

[0036] The finite volume method is used to iteratively update the flow variables on the updated grid. The iteration continues until the residuals of all grid cells are less than a set threshold, satisfying the steady convergence condition, and the steady solution of the flow under the current aerodynamic shape is obtained. The flow variables are the fluid physical quantities on each grid cell in the flow field, including density, velocity and pressure.

[0037] Based on the steady-state solution of the flow, the Jacobian matrix is ​​formed by applying a disturbance to the flow variables and calculating the residual difference, and then using flux difference approximation to calculate the partial derivatives of the nonlinear residual operator with respect to the flow variables. After traversing all grid cells and flow variables, the Jacobian matrix is ​​formed.

[0038] As a preferred embodiment, the maximum pre-solution gain is calculated iteratively based on the Jacobian matrix and the subcritical flow state, specifically including: Based on the subcritical flow state of aerodynamic shape optimization design, the flow characteristic frequency corresponding to this state is extracted, and the frequency search interval with the maximum pre-solution gain is set around this state.

[0039] Based on the updated computational grid, all grid cells are traversed, and a diagonal grid weighting matrix is ​​constructed using the area of ​​each grid cell. This grid weighting matrix is ​​used to quantify the weight of different grid regions in the stability assessment.

[0040] The initial golden section search is performed by determining two search frequency points within the set frequency search interval using the golden section method. For the current golden section frequency point, a weighted pre-solution operator is constructed and calculated by combining the Jacobian matrix and the grid weighted matrix.

[0041] Singular value decomposition (SVD) is performed on the weighted pre-determiner to obtain the pre-determiner gain at the current frequency. The pre-determiner gains corresponding to the two golden section points are compared, and the interval with larger gain is retained while the interval with smaller gain is discarded, thus gradually narrowing the frequency search range.

[0042] Repeat the frequency point update, pre-solution operator calculation, and singular value decomposition process until the frequency search interval is less than the set threshold, and output the maximum pre-solution gain of the midpoint within the interval.

[0043] As a preferred embodiment, the subcritical flow state of the aerodynamic shape near the instability threshold is determined by numerical simulation, and the flow characteristic frequency corresponding to the subcritical flow state is extracted. Specifically, the subcritical flow state of the aerodynamic shape near the instability threshold is determined by numerical simulation, and the disturbance response characteristics of the flow field under the subcritical flow state are analyzed, and the corresponding flow characteristic frequency is extracted from the flow field disturbance response characteristics of the subcritical flow state.

[0044] Example 2 This embodiment uses the airfoil structure of an aircraft wing as an example to further illustrate the aerodynamic shape optimization design method proposed in this invention.

[0045] This invention provides an aerodynamic shape optimization design method. In this embodiment, the aerodynamic shape is specifically an airfoil, such as... Figure 1 As shown, it includes the following steps: Step 1. Based on the geometric parameters of the reference airfoil, generate airfoil design variables and determine the flow state and airfoil shape optimization objectives for airfoil optimization design.

[0046] Step 1-1. Select the reference airfoil for the aircraft and obtain the geometric parameters of the surface of the reference airfoil; wherein, the geometric parameters include profile coordinate parameters, area, thickness and camber.

[0047] Steps 1-2. Determine the CST parameters (classification function-shape function transformation) as airfoil design variables based on the geometric parameters of the reference airfoil. First, determine the class function parameters, then construct the shape function using Bernstein polynomials as the core. The shape function is a linear combination of several order basis functions, and its combination coefficients are the core CST parameters to be solved. Next, integrate the class function and the shape function into a CST fitting equation. Use the least squares method to minimize the error between the airfoil coordinates calculated by the fitting equation and the actual coordinates of the reference airfoil, thus obtaining the complete CST parameters of the airfoil shape.

[0048] The class function is used to determine the leading edge radius, trailing edge angle, and overall thickness distribution trend of the airfoil; the shape function is composed of a linear combination of Bernstein polynomial basis functions, and its combination coefficients are used as optimization design variables.

[0049] Steps 1-3. Determine the subcritical flow state (the pre-critical state of flow instability before instability) of the reference airfoil near the instability threshold through numerical simulation. This subcritical flow state serves as the flow state for airfoil optimization design, with the optimization objective being the maximum gain under this state. The airfoil optimization design flow state includes flow state parameters and flow characteristic frequencies. The flow state parameters mainly include angle of attack, Mach number, and Reynolds number. Simulate flows at different angles of attack at certain Mach and Reynolds numbers to confirm the instability critical angle of attack. Select the near-instability subcritical state as the optimization design state. Perform a Fourier transform on the simulated flow field lift fluctuation signal, or analyze the flow field's response characteristics to disturbances, to extract the flow characteristic frequencies under this subcritical flow state. The flow characteristic frequencies are used to limit the search interval for the maximum pre-solution gain.

[0050] Step 2. Based on the airfoil design variables, generate the airfoil shape model using the radial basis function dynamic mesh method, and update the initial mesh.

[0051] The CST fitting equations are used to analytically process the current airfoil design variables (CST parameters) to accurately calculate the discrete coordinates of the upper and lower surfaces of the airfoil. Then, the Radial Basis Function (RBF) dynamic mesh method is used to construct an RBF interpolation model based on the boundary and internal nodes of the initial mesh. The coordinates of the new airfoil surface nodes are then substituted into the model as constraints, and the new coordinates of all internal nodes are calculated using the global interpolation properties of the RBF function, thus updating the entire computational model. The initial mesh is a pre-generated flow field calculation mesh based on the reference airfoil.

[0052] This process ensures that the computational mesh remains high-quality, without negative volume or distortion, even when the airfoil undergoes continuous and smooth deformation, thus ensuring the stability and reliability of the subsequent numerical solution of the Navier-Stokes equations.

[0053] Step 3. Based on the flow control equations, namely the Navier-Stokes (NS) equations, and based on the updated grid, perform flow numerical simulation, calculate the steady-state solution of the flow, perform flux difference approximation, and calculate the Jacobian matrix.

[0054] The flow solution is based on the Navier-Stokes equations, and its corresponding semi-discretization formula is written as: (1); In the formula: q is the flow variable (a vector composed of density, velocity, pressure, etc.). t Let R be the time, R be the nonlinear residual operator after spatial discretization, p0 be the current airfoil design variable, and X be the spatial coordinates.

[0055] For the current design variables The computational model below uses the finite volume method to continuously update the flow variable q for each grid until the nonlinear operators (residuals) R of all control volumes are less than a threshold. The flow variable at this point is the steady-state solution of the flow. .

[0056] Jacobian matrix is The flux difference approximation is used for calculation: ; In the formula, This represents the magnitude of each small perturbation applied.

[0057] In each grid, the unit vector The value is set to 1 at this grid cell and 0 at other grid cells. After applying a perturbation and a unit vector to the flow variable q, the residuals after the perturbation are calculated, and the difference between the residuals after the perturbation and the residuals of the steady solution is calculated to obtain the residual difference value. The residual difference value is divided by the applied perturbation to obtain the corresponding partial derivative. This calculation is performed iteratively for all grid cells and flow variables to finally form the complete Jacobian matrix A. The Jacobian matrix A is the core linear operator describing the evolution of flow perturbation and is the basis for subsequent pre-solution analysis and adjoint gradient solution.

[0058] Step 4. Based on the Jacobian matrix and airfoil optimization design, the flow state is designed. The maximum pre-solution gain is calculated using the pre-solution analysis method. The value of the maximum pre-solution gain is used to determine whether the optimization has converged. If it has converged, the optimization ends; otherwise, continue to Step 5.

[0059] Specifically, if the optimization converges, it means that the current airfoil shape has minimized the maximum pre-solution gain and achieved optimal flow stability. Obtaining a converged airfoil shape by minimizing the maximum pre-solution gain means that airfoil optimization with the goal of improving flow stability has been achieved.

[0060] The preliminary analysis is as follows: As described in step 3, solve for the flow steady-state solution under the current computational model. Defined as: (2) Reynolds decomposition of the flow variables , Let be the disturbance quantity. Substituting into equation (1), we obtain the dynamic equation using Taylor expansion:

[0061] (3) In the formula, It is an external excitation. The Jacobian matrix A is solved in step 3. Harmonic assumptions are made for the external excitation and its response. , ( (representing the conjugate complex number), substituting it into equation (3) yields the transfer function between system forcing and response:

[0062] (4) In the formula, These are the Fourier transform components of the flow variables. For the Fourier transform components of the external excitation, i Let ω be the imaginary unit, ω be the perturbation frequency, and I be the identity matrix. That is, the matrix form of the pre-solution operator.

[0063] Define the norm of the state variable as ,in , is a positive definite weighted matrix; This represents the conjugate transpose of a matrix.

[0064] The system's amplification of the input forced input, i.e., the pre-decomposition gain. Therefore, it can be defined as: (5) The forced and response modes and their corresponding gains are solved using weighted singular value decomposition (SVD) with pre-solved operators: (6) In the formula, For the corresponding left singular vector, This corresponds to the right singular vector.

[0065] Singular values ​​on the diagonal The gain is the gain of each order. The frequency gain curve obtained from this can characterize the amplification characteristics of the system for external inputs of different frequencies. The maximum pre-determined gain characterizes the system stability to a certain extent.

[0066] The larger the pre-solution gain, the more easily the flow is disturbed and becomes unstable; the optimization objective is to minimize the maximum pre-solution gain in order to improve flow stability.

[0067] Therefore, the detailed process for calculating the pre-solution gain in step 4 is as follows: Step 4-1. Flow characteristic frequencies in the flow state based on airfoil optimization design Set the frequency range for searching maximum gain. ;in, , These represent the minimum and maximum frequencies, respectively. According to relevant theory, the maximum pre-determined gain is achieved at the flow characteristic frequency, therefore it is necessary to ensure... .

[0068] Step 4-2. Construct a one-dimensional optimization problem and search for the maximum pre-solution gain within the frequency range. The airfoil optimization objective is to minimize the maximum pre-solution gain. Therefore, we can first solve a one-dimensional optimization problem within the frequency range to calculate the maximum value of the pre-solution gain:

[0069] ; Step 4-3. Based on the frequency range, determine the golden section points for efficient iterative search; for example, determine two golden section points. , When calculating the golden ratio, the two endpoints with the larger frequency range are used as the basis, and the difference between the two endpoints is calculated. The minimum frequency and the difference are then used to calculate the two golden ratio points, and the corresponding formula is:

[0070] ; .

[0071] Step 4-4. Based on the updated mesh, calculate the mesh weighting matrix; traverse each mesh cell of the flow field and calculate its area (for two-dimensional airfoil flow fields) or volume (for three-dimensional flow fields). For example, for a structured mesh on an airfoil surface, the polygon area can be calculated using the coordinates of the cell vertices; for an unstructured mesh, the volume can be calculated using the vertex coordinates of a tetrahedron / hexahedron. Use the area (or volume) of each mesh cell as the main diagonal of the matrix, and set the remaining off-diagonal elements to 0 to obtain the mesh weighting matrix. Q This is used to quantify the weight of different grid regions in flow stability assessment. The grid weighting matrix can reflect the weight of different grid cells in flow field analysis (for example, cells with larger areas have a more significant impact on the global flow field).

[0072] Steps 4-5. For any golden section point, for example... Based on the Jacobian matrix and the grid weighting matrix, the corresponding weighted pre-solution operator is calculated and singular value decomposition is performed to obtain the corresponding initial pre-solution gain. ; in, , The matrix form of the pre-solution operator, This is the initially selected forced frequency in the golden section method.

[0073] Steps 4-6. Update the frequency range using the golden ratio method. If the initial pre-determined gain of the first golden section point is greater than that of the second golden section point, discard the second golden section point and use the frequency corresponding to the first golden section point as the minimum range of the new frequency range. Conversely, if the initial pre-determined gain of the first golden section point is less than that of the second golden section point, discard the first golden section point and use the frequency corresponding to the second golden section point as the maximum range of the new frequency range. Finally, the updated frequency range is generated.

[0074] Step 4-7. Repeat steps 4-3 to 4-6 until the frequency range is less than the set threshold, then output the maximum pre-determination gain. The convergence of the optimization is determined by whether the difference between the current target value and the previous value is less than a threshold.

[0075] Step 5. Based on the pre-solution gain adjoint gradient method, generate the gradient descent direction of the optimization objective with respect to the design variables. The gradient descent direction is the design variable update direction that rapidly reduces the maximum pre-solution gain, used to guide the airfoil shape optimization towards a more flow-stable direction.

[0076] With maximum pre-solution gain As the optimization objective, combined with constraint functions Perform flow stability optimization design: (7) In the formula, For the design variables of the k-th iteration, These are the initial design variables.

[0077] The gradient of the constraint function with respect to the design variables is calculated using the finite difference method. The inverse matrix of the weighted pre-solution operator is: (8) In the formula, This is the forced frequency corresponding to the maximum gain calculated using the golden section method.

[0078] Find the minimum singular value of this matrix: (9) In the formula, For the corresponding left singular vector, For the corresponding singular values.

[0079] Based on the singular value relationship between inverse matrices: . It is actually a response mode.

[0080] set up Then there is The optimization objective is equivalent to: (10) The corresponding optimized functional is: (11) In the formula, The first adjoint vector, This is the second adjoint vector.

[0081] To simplify the calculation, let the gradient of the functional with respect to all parameters except the design variables be zero. The gradient is: (12) (13) Gradient of the response mode is obtained as follows: (14) Right now And matrix J is a conjugate symmetric matrix. ,Right now Since the accompanying mode and the direct mode are equal, the present invention can be set as follows: This is called the first adjoint variable. Taking the gradient of the gain and substituting this relationship, we get:

[0082] (15) Right now , .

[0083] Then, let the gradient of the functional with respect to the time-invariant solution also be 0: (16) Jacobian matrix The finite difference method is used to approximate the steady-state solution of the flow. The second derivative matrix Further derivation:

[0084] (17) In the formula, Indicates the variable Tiny perturbations.

[0085] A system of linear equations was obtained. Solve It is the second accompanying variable.

[0086] At this point, the functional has been applied to all variables except the design variables. The gradients of all other parameters are 0, and the final partial derivatives with respect to the design variables are: (18) set up These are the partial derivatives of the Jacobian matrix vector product and the residual with respect to the design variables, respectively. Both are approximated using finite difference. The gradient and partial derivative of the final gain with respect to the design variables are equal. The gradient of the pre-solution gain with respect to the design variables is given by formula (19): (19) matrix Solving for: (20) This invention makes , ,but: (twenty one) It is independent of the constant solution, and placing it inside or outside the derivative does not affect the derivative value. Furthermore, according to the chain rule: (twenty two) Finally, we only need to use a first-order approximation to calculate the derivative (in the code implementation, the real and imaginary parts of the vector need to be separated and combined): (twenty three) Step 6. Based on the gradient descent direction of the design variables, calculate the current optimization descent direction and optimize the airfoil design variables using the nonlinear conjugate gradient method, then return to Step 2.

[0087] Using the gradient obtained in step 5 as input, the optimal update step size and iteration direction are determined by the nonlinear conjugate gradient method, and the CST design variables (classification function parameters, Bernstein polynomial combination coefficients) of the airfoil are smoothly updated.

[0088] The updated design variables are returned to step 2, the airfoil shape and computational mesh are regenerated, and a new round of iterative optimization is started until the maximum pre-solution gain meets the convergence condition, and finally the airfoil shape with optimal flow stability is obtained.

[0089] In the above scheme, the present invention accurately transforms the reference airfoil geometry into design variables through CST parameterization, uses radial basis functions (RBF) to ensure the mesh quality after airfoil deformation to support accurate Navier-Stokes (NS) equation solution, obtains the Jacobian matrix through flux difference approximation, combines pre-solution analysis and the golden section method to quantify the global flow stability index (maximum pre-solution gain), uses the pre-solution gain adjoint gradient method to solve the gradient descent direction of design variables, and finally uses the nonlinear conjugate gradient method to efficiently iteratively optimize design variables.

[0090] Based on the same inventive concept, this invention also proposes an aerodynamic shape optimization design system, comprising: The variable generation module is used to fit and solve the geometric parameters of the target aerodynamic shape into CST parameters using the CST shape parameterization method, and use the CST parameters as design variables for aerodynamic shape optimization. The subcritical flow state of the aerodynamic shape near the instability criticality is determined through numerical simulation, and the flow characteristic frequency corresponding to the subcritical flow state is extracted. The aerodynamic shape optimization objective is to minimize the maximum pre-solution gain under the subcritical flow state, and the flow characteristic frequency is used to limit the search range of the maximum pre-solution gain.

[0091] The matrix generation module is used to generate an aerodynamic shape model based on the design variables of aerodynamic shape optimization, and the aerodynamic shape model drives the update of the initial mesh; based on the Navier-Stokes equations and the updated mesh, flow numerical simulation is performed to calculate the steady flow solution; based on the steady flow solution, the Jacobian matrix is ​​obtained through flux difference approximation; the initial mesh is a flow field calculation mesh pre-generated based on the target aerodynamic shape.

[0092] The optimization module is used to iteratively calculate the maximum pre-solution gain based on the Jacobian matrix and subcritical flow state. If the maximum pre-solution gain does not converge, the CST parameters are updated. When the iterative difference of the maximum pre-solution gain is less than the preset convergence threshold, the optimization terminates and outputs the optimal CST parameters and the corresponding aerodynamic optimized shape.

[0093] Each module in the aforementioned aerodynamic shape optimization design system can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in the processor of a computer device in hardware form or independent of it, or stored in the memory of a computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0094] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor executes the computer program to implement the steps in the embodiments of the aerodynamic shape optimization design method. Specific implementation methods can be found in the method embodiments, and will not be repeated here.

[0095] Furthermore, the present invention also provides a non-transitory computer-readable storage medium containing instructions, on which a computer program is stored. When executed by a processor, the computer program can implement the steps in the embodiments of the aerodynamic shape optimization design method. Specific implementation methods can be found in the method embodiments, and will not be repeated here.

[0096] Those skilled in the art will understand that embodiments of the present invention can provide 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.

[0097] If the integrated unit module is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of the present invention can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying computer program code to a storage device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks.

[0098] It should be noted that the specific embodiments described above enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although the present invention has been described in detail in this specification and embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention; and all technical solutions and improvements that do not depart from the spirit and scope of the present invention are covered within the protection scope of the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims. Any simple variations or equivalent substitutions of technical solutions that can be readily obtained by those skilled in the art within the scope of the technology disclosed in the present invention are within the protection scope of the present invention.

Claims

1. A method for optimizing aerodynamic shape, characterized in that, Includes the following steps: The geometric parameters of the target aerodynamic shape are fitted and solved as CST parameters using the CST shape parameterization method, and the CST parameters are used as design variables for aerodynamic shape optimization. The subcritical flow state of the aerodynamic shape near the instability threshold is determined by numerical simulation, and the flow characteristic frequency corresponding to the subcritical flow state is extracted. The optimization objective of the aerodynamic shape is to minimize the maximum pre-solution gain under the subcritical flow state, and the flow characteristic frequency is used to limit the search range of the maximum pre-solution gain. The aerodynamic shape model is generated based on the design variables of aerodynamic shape optimization, and the initial mesh is updated by the aerodynamic shape model. Numerical flow simulations were performed based on the Navier-Stokes equations and the updated grid to calculate steady flow solutions. Based on the steady flow solution, the Jacobian matrix is ​​obtained through flux difference approximation; the initial grid is a pre-generated flow field calculation grid based on the target aerodynamic shape. The maximum pre-solution gain is calculated iteratively based on the Jacobian matrix and subcritical flow state. If the maximum pre-solution gain does not converge, the CST parameters are updated. When the iterative difference of the maximum pre-solution gain is less than the preset convergence threshold, the optimization terminates and the optimal CST parameters and the corresponding aerodynamic optimized shape are output.

2. The aerodynamic shape optimization design method according to claim 1, characterized in that, The geometric parameters include contour coordinate parameters, area, thickness, and curvature; The method of fitting and solving the geometric parameters of the target aerodynamic shape into CST parameters by CST parameterization is as follows: the contour coordinate parameters, area, thickness and curvature are input into the CST fitting equation constructed by the class function and Bernstein polynomial shape function, and the CST parameters are obtained by the least squares method. The CST parameters are used as the design variables for aerodynamic shape optimization.

3. The aerodynamic shape optimization design method according to claim 2, characterized in that, The CST parameters are updated using the pre-determined gain adjoint gradient method and the nonlinear conjugate gradient method, specifically including the following steps: Based on the determined flow characteristic frequency, Jacobian matrix and grid weighting matrix, a weighted pre-operator is constructed. The weighted pre-operator is then subjected to minimum singular value decomposition to obtain the response modes. The first adjoint variable is calculated based on the response mode and the current maximum pre-solution gain; based on the constraints of the optimization functional, a system of linear equations is established and solved, and the second adjoint variable is calculated from the first adjoint variable, the Jacobian matrix and its conjugate transpose. The partial derivatives of the Jacobian matrix correlation terms and residuals with respect to the CST parameters are calculated using the finite difference approximation. Then, by combining the first and second adjoint variables with the maximum pre-solution gain, the gradient of the maximum pre-solution gain with respect to the CST parameters is calculated according to the derivation relationship of the pre-solution gain adjoint gradient method. Using the current gradient, the gradient of the previous iteration, and the descent direction, the optimal descent direction for this iteration is calculated using the nonlinear conjugate gradient method. Along the descent direction, a one-dimensional search is performed using the golden section method to find the optimal step size that minimizes the maximum pre-solution gain. The CST parameters are updated numerically using the current CST parameters, optimal step size, and optimized descent direction to obtain new CST parameters. The maximum pre-solution gain is then checked to determine if it has converged. If it has not converged, the iteration continues; if it has converged, the optimization is complete.

4. The aerodynamic shape optimization design method according to claim 2, characterized in that, The aerodynamic shape model is generated from the design variables based on aerodynamic shape optimization, and the initial mesh is updated driven by the aerodynamic shape model. Specifically, this includes: Based on the design variables of aerodynamic shape optimization, the coordinates of each point on the aerodynamic shape surface are calculated by CST parametric equations to determine the thickness distribution, curvature distribution and boundary morphology, and to generate an aerodynamic shape model. Based on the initial mesh pre-generated from the aerodynamic shape before optimization, a radial basis function interpolation model is constructed with the boundary nodes and internal nodes of the initial mesh as the reference. The aerodynamic shape model provides new boundary constraints. By utilizing the global interpolation characteristics of the radial basis function interpolation model, the initial mesh is driven to undergo global smooth deformation, and the computational mesh adapted to the new aerodynamic shape is obtained.

5. The aerodynamic shape optimization design method according to claim 4, characterized in that, The flow numerical simulation is performed based on the Navier-Stokes equations and the updated grid to calculate the steady-state solution of the flow. Based on the steady-state solution of the flow, the Jacobian matrix is ​​obtained through flux difference approximation, specifically including: Using the updated computational grid as the solution domain, the Navier-Stokes Navier-Stokes equations are adopted as the flow control equations. The control equations are semi-discretized to obtain nonlinear residual operators. The finite volume method is used to iteratively update the flow variables on the updated grid; the iteration continues until the residuals of all grid cells are less than a set threshold, satisfying the steady convergence condition, and the steady flow solution under the current aerodynamic shape is obtained; the flow variables are the fluid physical quantities on each grid cell in the flow field, including density, velocity and pressure. Based on the steady-state solution of the flow, the Jacobian matrix is ​​formed by applying a disturbance to the flow variables and calculating the residual difference, and then using flux difference approximation to calculate the partial derivatives of the nonlinear residual operator with respect to the flow variables. After traversing all grid cells and flow variables, the Jacobian matrix is ​​formed.

6. The aerodynamic shape optimization design method according to claim 5, characterized in that, The calculation of the maximum pre-solution gain based on the Jacobian matrix and subcritical flow state iteratively includes: Based on the subcritical flow state of aerodynamic shape optimization design, the flow characteristic frequency corresponding to the state is extracted, and the frequency search interval with the maximum pre-solution gain is set with this as the center. Based on the updated computational grid, all grid cells are traversed, and a diagonal grid weighting matrix is ​​constructed using the area of ​​the grid cells. This grid weighting matrix is ​​used to quantify the weight of different grid regions in the stability assessment. The initial golden section search is performed by determining two search frequency points within the set frequency search interval using the golden section method. For the current golden section frequency point, a weighted pre-solution operator is constructed and calculated by combining the Jacobian matrix and the grid weighted matrix. Singular value decomposition (SVD) is performed on the weighted pre-determining operator to obtain the pre-determining gain at the current frequency. The magnitudes of the pre-determining gains corresponding to the two golden section points are compared. The interval with larger gain is retained, and the interval with smaller gain is discarded, thus gradually narrowing the frequency search range. Repeat the frequency point update, pre-solution operator calculation, and singular value decomposition process until the frequency search interval is less than the set threshold, and output the maximum pre-solution gain of the midpoint within the interval.

7. The aerodynamic shape optimization design method according to claim 1, characterized in that, The process of determining the subcritical flow state of the aerodynamic shape near the instability threshold through numerical simulation and extracting the flow characteristic frequency corresponding to the subcritical flow state specifically involves: determining the subcritical flow state of the aerodynamic shape near the instability threshold through numerical simulation, analyzing the disturbance response characteristics of the flow field under the subcritical flow state, and extracting the corresponding flow characteristic frequency from the flow field disturbance response characteristics of the subcritical flow state.

8. An aerodynamic shape optimization design system, characterized in that, include: The variable generation module is used to fit and solve the geometric parameters of the target aerodynamic shape into CST parameters through the CST shape parameterization method, and use the CST parameters as design variables for aerodynamic shape optimization; it determines the subcritical flow state of the aerodynamic shape near the instability criticality through numerical simulation, and extracts the flow characteristic frequency corresponding to the subcritical flow state; it takes minimizing the maximum pre-solution gain under the subcritical flow state as the aerodynamic shape optimization objective, and the flow characteristic frequency is used to limit the search interval of the maximum pre-solution gain. The matrix generation module is used to generate an aerodynamic shape model based on the design variables of aerodynamic shape optimization, and the initial mesh is updated driven by the aerodynamic shape model. Numerical flow simulations were performed based on the Navier-Stokes equations and the updated grid to calculate steady flow solutions. Based on the steady flow solution, the Jacobian matrix is ​​obtained through flux difference approximation; the initial grid is a pre-generated flow field calculation grid based on the target aerodynamic shape. The optimization module is used to iteratively calculate the maximum pre-solution gain based on the Jacobian matrix and subcritical flow state. If the maximum pre-solution gain does not converge, the CST parameters are updated. When the iterative difference of the maximum pre-solution gain is less than the preset convergence threshold, the optimization terminates and outputs the optimal CST parameters and the corresponding aerodynamic optimized shape.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is loaded by the processor, it is able to perform the steps of the method according to any one of claims 1 to 7.

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