A compressor non-axisymmetric endwall shaping method based on adjoint shape optimization

Abstract

The application provides a compressor non-axisymmetric end wall shaping method based on an adjoint shape optimization, and belongs to the technical field of aero-engine compressor design, in particular to: taking an axisymmetric end wall compressor as an optimization object, sequentially completing a cascade single-channel original geometric model establishment, structured grid division, obtaining the isentropic efficiency of the compressor designed by using the axisymmetric end wall through flow field simulation, establishing an optimization target and a constraint condition, solving the sensitivity of a design variable based on an adjoint shape optimization method, arranging control points on the outer surface of the end wall, combining the total displacement amount of the control points with the sensitivity calculation, realizing the end wall grid deformation through a radial basis function, iteratively optimizing the performance of the current end wall geometric configuration through simulation verification, and until the end wall meets the optimization target and the constraint condition. The application improves the optimization efficiency and shaping precision of the compressor end wall, improves the isentropic efficiency of the compressor, and guarantees the stability of the performance parameters of the optimized compressor.

Description

Technical Field

[0001] This application relates to the field of aero-engine compressor design, and in particular to a method for non-axisymmetric endwall shaping of compressors based on adjoint shape optimization. Background Technology

[0002] As a core component of aero engines, the compressor's efficiency directly affects the engine's thrust and fuel economy. Traditional compressors employ axisymmetric endwall designs, which are prone to secondary flow losses in the endwall region, leading to reduced efficiency. Existing non-axisymmetric endwall design methods largely rely on parametric modeling and experimental iterations, resulting in long optimization cycles and low sensitivity calculation accuracy, failing to meet the requirements for efficient and precise compressor design. Summary of the Invention

[0003] In view of this, this application provides a method for non-axisymmetric endwall modeling of compressors based on adjoint shape optimization, which solves the problems in the prior art and improves the efficiency and accuracy of non-axisymmetric endwall modeling of compressors.

[0004] This application provides a compressor non-axisymmetric endwall shaping method based on adjoint shape optimization, which adopts the following technical solution:

[0005] A compressor non-axisymmetric endwall modeling method based on adjoint shape optimization takes a compressor with an axisymmetric endwall design as the optimization object to obtain the optimized geometric configuration of the non-axisymmetric endwall. The compressor non-axisymmetric endwall modeling method includes:

[0006] Step 1: Extract a single blade passage of a compressor with an axisymmetric endwall design and establish the original geometric model of the single blade passage, which includes the compressor blades and the axisymmetric endwall.

[0007] Step 2: Divide the original geometric model into a structured mesh, and refine the mesh in the areas of the axisymmetric endwall surface and the blade surface;

[0008] Step 3: Import the structured mesh of the original geometric model into the flow field simulation software, set the boundary conditions and turbulence model, and solve the three-dimensional Reynolds-averaged Navier-Stokes equations to obtain the isentropic efficiency of the compressor with axisymmetric endwall design.

[0009] Step 4: Set a preset value for the improvement of isentropic efficiency with the optimization objective of maximizing the isentropic efficiency of the compressor under the optimized non-axisymmetric endwall geometry. Introduce the pressure ratio penalty function and the flow rate ratio penalty function to construct a constrained overall objective function.

[0010] Step 5: Based on the adjoint shape optimization method, solve the sensitivity of the overall objective function to the mesh node displacement of the current endwall as the design variable;

[0011] Step 6: Arrange control points on the outer surface of the current endwall according to preset rules, and densify the arrangement of control points in the areas corresponding to the leading edge and trailing edge of the blade on the outer surface of the current endwall.

[0012] Step 7: Calculate the total displacement of each control point based on the sensitivity. The total displacement is the sum of the cumulative displacement and the sensitivity-driven displacement. Control the total displacement of each control point within the range of 0.01 to 0.1 mm to avoid excessive mesh deformation.

[0013] Step 8: Using the radial basis function method, an interpolation field is established based on the total displacement of each control point, and the displacement of each grid node of the current end wall is calculated. The grid of the current end wall is then deformed to form the grid and geometric configuration of the non-axisymmetric end wall.

[0014] Step 9: Replace the endwall mesh in the original geometric model with the current endwall mesh to form a new structured mesh and import it into the flow field simulation software. Use the boundary conditions and turbulence model in Step 3 to perform flow field simulation, obtain the isentropic efficiency, pressure ratio and flow rate of the compressor under the current endwall geometry configuration, and verify the performance of the current endwall geometry configuration.

[0015] Step 10: Determine whether the compressor's isentropic efficiency improvement value under the current endwall geometry has reached the preset value of the isentropic efficiency improvement value; if yes, output the geometry of the non-axisymmetric endwall formed in step 8; if no, repeat steps 5 to 9 for iteration until the compressor's isentropic efficiency under the latest endwall geometry meets the optimization target, and output the latest geometry of the non-axisymmetric endwall. In each iteration, the current endwall in steps 5 to 8 is the non-axisymmetric endwall formed in step 8 of the previous optimization process.

[0016] Optionally, in step 2, the grid side lengths of the axisymmetric endwall surface and the blade surface are less than or equal to... ,in, This is the chord length of the leaf blade;

[0017] The grid gradient inside the cascade channel is controlled within 1.2, the grid orthogonality of the structured grid is greater than or equal to 0.85, and the maximum grid stretch ratio of the structured grid is less than or equal to 20.

[0018] Optionally, in step 4, the preset value for the isentropic efficiency improvement is 0.3%.

[0019] Optionally, in step 4, the overall objective function is:

[0020] ;

[0021] in, Describe the overall objective function. This represents the isentropic efficiency of the compressor under the current endwall geometry. This represents the pressure ratio penalty function. This represents the flow-to-penalty function. The penalty factor is the pressure ratio. This is the traffic ratio penalty factor.

[0022] Optionally, in step 5, the formula for calculating the sensitivity of the overall objective function to the mesh node displacements of the current endwall as design variables is:

[0023] ;

[0024] in, Let be the overall objective function. For the current end wall Displacement of each grid node For sensitivity, For Lagrange operators, This represents the transpose of a vector. The flow control equations are as follows: For the flow field variables of the blade cascade channel under the current endwall geometry.

[0025] Optionally, in step 6, the vertical distance between the control point on the outer surface of the current endwall corresponding to the leading and trailing edges of the blade and the outer surface of the current endwall is... The spacing between adjacent control points on the outer surface of the front endwall, corresponding to the leading and trailing edges of the blade, is... ,in, The blade pitch;

[0026] Except for the regions on the outer surface of the current endwall corresponding to the leading and trailing edges of the blade, the vertical distance between the control points and the outer surface of the current endwall is 1. The spacing between adjacent control points in the region other than the area on the outer surface of the current endwall corresponding to the leading and trailing edges of the blade is 0. ,in, This is the chord length of the blade.

[0027] Optionally, in step 7, the formula for calculating the total displacement is:

[0028] ;

[0029] in, For the first Total displacement of each control point For the current number The cumulative displacement of each control point Let be the overall objective function. For the current end wall Displacement of each grid point For sensitivity, For displacement coefficients, .

[0030] Optionally, in step 8, the formula for calculating the displacement of each grid node is:

[0031] ;

[0032] in, For the current end wall Displacement of each grid node For the current end wall The coordinates of each grid node. For the first The coordinates of the control points The total number of control points. For radial basis functions, For the first The weighting coefficients of each control point The following formula can be used to solve for:

[0033] ;

[0034] in, For the first The coordinates of the control points For the first The total displacement of each control point.

[0035] In summary, this application includes the following beneficial technical effects:

[0036] This application precisely locates efficiency-sensitive regions through adjoint shape optimization and introduces penalty functions for pressure ratio and flow ratio to ensure the stability of performance parameters after endwall optimization. The sensitivity of all design variables can be obtained by solving the adjoint equation once, which greatly improves the optimization efficiency. It solves the problems of low efficiency in design sensitivity calculation, inability to quickly locate endwall regions that significantly affect compressor isentropic efficiency, insufficient endwall shaping accuracy, and unstable optimization results in existing non-axisymmetric endwall optimization methods. It adopts a combination of radial basis function mesh deformation and specific control point distribution to ensure reliable mesh quality after deformation. The non-axisymmetric endwall after shaping can reduce secondary flow losses by more than 30%, thereby improving compressor isentropic efficiency by at least 0.3%. Attached Figure Description

[0037] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart of a compressor non-axisymmetric endwall modeling method based on adjoint shape optimization. Detailed Implementation

[0039] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0040] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0041] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0042] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0043] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0044] This application provides a method for non-axisymmetric endwall design of compressors based on adjoint shape optimization.

[0045] This application focuses on optimizing a compressor with an axisymmetric endwall design, resulting in an optimized geometry for a non-axisymmetric endwall. Specifically:

[0046] like Figure 1 As shown, a method for designing the non-axisymmetric endwall of a compressor based on adjoint shape optimization includes:

[0047] Step 1: Establish the original geometric model of a single blade cascade channel: Extract a single blade cascade channel of a compressor with an axisymmetric endwall design, and establish the original geometric model of the single blade cascade channel including the compressor blades and axisymmetric endwall. In this embodiment, a 3D modeling software is used to establish the original geometric model of the single blade cascade channel. The 3D modeling software can be UG or CATIA. The original geometric model specifically includes: endwall surface, blade surface, casing surface corresponding to the blade cascade channel, periodic surface of the blade cascade channel, inlet surface of the blade cascade channel, and outlet surface of the blade cascade channel. UG stands for Unigraphics, an integrated design and modeling software; CATIA stands for Computer Aided Three-dimensional Interactive Application, a 3D design software.

[0048] Step 2, dividing the structured mesh: Divide the original geometric model into a structured mesh, and refine the mesh in the areas of the axisymmetric endwall surface and blade surface.

[0049] Step 3: Obtain the isentropic efficiency of the compressor with axisymmetric endwall design: Import the structured mesh of the original geometric model into the flow field simulation software, set the boundary conditions and turbulence model, and solve the three-dimensional Reynolds-averaged Navier-Stokes equations to obtain the isentropic efficiency of the compressor with axisymmetric endwall design.

[0050] Step 4, establish optimization objectives and constraints: set a preset value for the improvement of isentropic efficiency with the optimization objective of maximizing the isentropic efficiency of the compressor under the optimized non-axisymmetric endwall geometry, and introduce pressure ratio penalty function and flow ratio penalty function to construct a constrained overall objective function.

[0051] Step 5, Solve for design variable sensitivity: Based on the adjoint shape optimization method, solve for the sensitivity of the total objective function to the mesh node displacement of the current endwall as the design variable.

[0052] Step 6, establish grid control points: arrange control points on the outer surface of the current endwall according to preset rules, and densify the arrangement of control points in the areas corresponding to the leading edge and trailing edge of the blade on the outer surface of the current endwall.

[0053] Step 7: Calculate the total displacement of each control point based on sensitivity: The total displacement is the sum of the cumulative displacement and the sensitivity-driven displacement, and the total displacement of each control point is controlled within the range of 0.01 to 0.1 mm to avoid excessive mesh deformation.

[0054] Step 8, End Wall Mesh Deformation: Using the radial basis function method, an interpolation field is established based on the total displacement of each control point, and the displacement of each mesh node of the current end wall is calculated. The mesh of the current end wall is then deformed to form the mesh and geometric configuration of the non-axisymmetric end wall.

[0055] Step 9, verify the performance of the new endwall: Replace the endwall mesh in the original geometric model with the mesh of the current endwall to form a new structured mesh and import it into the flow field simulation software. Use the boundary conditions and turbulence model in Step 3 to perform flow field simulation, obtain the isentropic efficiency, pressure ratio and flow rate of the compressor under the current endwall geometry, and verify the performance of the current endwall geometry.

[0056] Step 10: Determine whether the new endwall meets the optimization objectives and constraints: Determine whether the compressor's isentropic efficiency improvement value under the current endwall geometry reaches the preset value of the isentropic efficiency improvement value.

[0057] Step 11, output the geometry of the non-axisymmetric endwall: If yes, output the geometry of the non-axisymmetric endwall formed in step 8; if no, repeat steps 5 to 9 for iteration until the isentropic efficiency of the compressor under the latest endwall geometry meets the optimization objective, and output the latest geometry of the non-axisymmetric endwall. In each iteration, the current endwall in steps 5 to 8 is the non-axisymmetric endwall formed in step 8 of the previous optimization process; the cumulative displacement of the control point in step 7 in each iteration is the total displacement of the control point calculated in step 7 of the previous optimization process.

[0058] In step 2, ICEM CFD is used to generate a structured mesh for the original geometric model, with the mesh edge length of the axisymmetric endwall surface and blade surface being less than or equal to... ,in, The blade chord length is specified; the mesh gradient inside the blade cascade channel is controlled within 1.2, the mesh orthogonality of the structured mesh is greater than or equal to 0.85, and the maximum mesh stretch ratio of the structured mesh is less than or equal to 20. In this embodiment, the blade chord length is specified. The blade spacing is 50mm, the blade pitch is 40mm, the internal mesh count of the blade channel is 1.4 million, the mesh orthogonality is 0.85, the maximum mesh stretch ratio is 18, the axisymmetric endwalls are cylindrical with a radius of 120mm, and the inlet and outlet lengths of the blade channel are both 100mm. ICEM CFD, short for Integrated Computer Engineering and Manufacturing Code for Computational Fluid Dynamics, is a mesh generation and preprocessing software.

[0059] For step 3, in this embodiment of the application, the inlet total temperature is set in the simulation software STAR-CCM+. Total pressure Export back pressure SST is used Using the three-dimensional Reynolds-averaged Navier-Stokes equations of the turbulence model, the isentropic efficiency of the compressor with an axisymmetric endwall design is obtained as 88.5%, the initial pressure ratio is 2.1, and the flow rate is 20.19 kg / s. STAR-CCM+ is a continuum mechanics simulation software based on star cluster calculations.

[0060] In step 4, the preset value for the isentropic efficiency improvement is 0.3%. The overall objective function is:

[0061] ;

[0062] in, Represent the overall objective function; This represents the isentropic efficiency of the compressor under the current endwall geometry. This represents the pressure ratio penalty function. , To simulate the pressure ratio, To design the target pressure ratio, For the allowable pressure ratio deviation, ; This represents the flow-to-penalty function. , To simulate traffic, To design traffic, For the allowable flow deviation, ; The penalty factor is the pressure ratio. As a flow rate penalty factor, in the embodiments of this application, .

[0063] In step 5, the formula for determining the sensitivity of the overall objective function to the mesh node displacements of the current endwall as design variables is as follows:

[0064] ;

[0065] in, Let be the overall objective function. For the current end wall Displacement of each grid node For sensitivity, For Lagrange operators, This represents the transpose of a vector. The flow control equations are as follows: The flow field variables for the blade cascade channel under the current endwall geometry include air mass density, airflow velocity, and static pressure. Specifically, for the overall objective function, the first solution to the sensitivity of the overall objective function to the grid node displacements of the current endwall as design variables is performed. To achieve the isentropic efficiency of a compressor with an axisymmetric endwall design, in subsequent iterations... This refers to the isentropic efficiency of the compressor under the non-axisymmetric endwall geometry formed in step 8 of the previous optimization process.

[0066] In this embodiment of the application, the absolute value of the sensitivity is found to be the largest in the endwall region near the leading edge of the blade by solving the sensitivity.

[0067] In step 6, the vertical distance between the control point on the outer surface of the current endwall and the region corresponding to the leading and trailing edges of the blade is... The spacing between adjacent control points on the outer surface of the front endwall, corresponding to the leading and trailing edges of the blade, is... ,in, The blade pitch; the vertical distance between the control point and the outer surface of the current endwall, excluding the regions on the outer surface of the current endwall corresponding to the leading and trailing edges of the blade, is 0. The spacing between adjacent control points in the region other than the area on the outer surface of the current endwall corresponding to the leading and trailing edges of the blade is 0. ,in, This refers to the blade chord length. In this embodiment, approximately 500 control points are arranged.

[0068] In step 7, the formula for calculating the total displacement is:

[0069] ;

[0070] in, For the first Total displacement of each control point For the current number The cumulative displacement of each control point Let be the overall objective function. For the current end wall Displacement of each grid point For sensitivity, For displacement coefficients, .

[0071] In step 8, the formula for calculating the displacement of each grid node is:

[0072] ;

[0073] in, For the current end wall The displacement of each grid node; For the current end wall The coordinates of each grid node; For the first The coordinates of the control points; This represents the total number of control points. The radial basis functions are used; in this embodiment, quadratic basis functions are employed. , For shape parameters, Take 1 to 2 times the average distance of the control points; For the first The weighting coefficients for each control point; in this embodiment of the application, The value is 1mm.

[0074] The following formula can be used to solve for:

[0075] ;

[0076] in, For the first The coordinates of the control points For the first The total displacement of each control point.

[0077] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for non-axisymmetric endwall design of a compressor based on adjoint shape optimization, characterized in that, Taking a compressor with an axisymmetric endwall design as the optimization target, the optimized geometric configuration of the non-axisymmetric endwall is obtained. The non-axisymmetric endwall design method for compressors includes: Step 1: Extract a single blade passage of a compressor with an axisymmetric endwall design and establish the original geometric model of the single blade passage, which includes the compressor blades and the axisymmetric endwall. Step 2: Divide the original geometric model into a structured mesh, and refine the mesh in the areas of the axisymmetric endwall surface and the blade surface; Step 3: Import the structured mesh of the original geometric model into the flow field simulation software, set the boundary conditions and turbulence model, and solve the three-dimensional Reynolds-averaged Navier-Stokes equations to obtain the isentropic efficiency of the compressor with axisymmetric endwall design. Step 4: Set a preset value for the improvement of isentropic efficiency with the optimization objective of maximizing the isentropic efficiency of the compressor under the optimized non-axisymmetric endwall geometry. Introduce the pressure ratio penalty function and the flow rate ratio penalty function to construct a constrained overall objective function. Step 5: Based on the adjoint shape optimization method, solve the sensitivity of the overall objective function to the mesh node displacement of the current endwall as the design variable; Step 6: Arrange control points on the outer surface of the current endwall according to preset rules, and densify the arrangement of control points in the areas corresponding to the leading edge and trailing edge of the blade on the outer surface of the current endwall. Step 7: Calculate the total displacement of each control point based on the sensitivity. The total displacement is the sum of the cumulative displacement and the sensitivity-driven displacement. Control the total displacement of each control point within the range of 0.01 to 0.1 mm. Step 8: Using the radial basis function method, an interpolation field is established based on the total displacement of each control point, and the displacement of each grid node of the current end wall is calculated. The grid of the current end wall is then deformed to form the grid and geometric configuration of the non-axisymmetric end wall. Step 9: Replace the endwall mesh in the original geometric model with the current endwall mesh to form a new structured mesh and import it into the flow field simulation software. Use the boundary conditions and turbulence model in Step 3 to perform flow field simulation, obtain the isentropic efficiency, pressure ratio and flow rate of the compressor under the current endwall geometry configuration, and verify the performance of the current endwall geometry configuration. Step 10: Determine whether the compressor's isentropic efficiency improvement value under the current endwall geometry has reached the preset value of the isentropic efficiency improvement value; if yes, output the geometry of the non-axisymmetric endwall formed in step 8; if no, repeat steps 5 to 9 for iteration until the compressor's isentropic efficiency under the latest endwall geometry meets the optimization target, and output the latest geometry of the non-axisymmetric endwall. In each iteration, the current endwall in steps 5 to 8 is the non-axisymmetric endwall formed in step 8 of the previous optimization process.

2. The compressor non-axisymmetric endwall shaping method based on adjoint shape optimization according to claim 1, characterized in that, In step 2, the grid side lengths of the axisymmetric endwall surface and the blade surface are less than or equal to... ,in, This is the chord length of the leaf blade; The grid gradient inside the cascade channel is controlled within 1.2, the grid orthogonality of the structured grid is greater than or equal to 0.85, and the maximum grid stretch ratio of the structured grid is less than or equal to 20.

3. The compressor non-axisymmetric endwall shaping method based on adjoint shape optimization according to claim 1, characterized in that, In step 4, the preset value for the isentropic efficiency improvement is 0.3%.

4. The compressor non-axisymmetric endwall shaping method based on adjoint shape optimization according to claim 1, characterized in that, In step 4, the overall objective function is: ； in, Describe the overall objective function. This represents the isentropic efficiency of the compressor under the current endwall geometry. This represents the pressure ratio penalty function. This represents the flow-to-penalty function. The penalty factor is the pressure ratio. This is the traffic ratio penalty factor.

5. The compressor non-axisymmetric endwall shaping method based on adjoint shape optimization according to claim 1, characterized in that, In step 5, the formula for determining the sensitivity of the overall objective function to the mesh node displacements of the current endwall as design variables is as follows: ； in, Let be the overall objective function. For the current end wall Displacement of each grid node For sensitivity, For Lagrange operators, This represents the transpose of a vector. The flow control equations are as follows: For the flow field variables of the blade cascade channel under the current endwall geometry.

6. The compressor non-axisymmetric endwall shaping method based on adjoint shape optimization according to claim 1, characterized in that, In step 6, the vertical distance between the control point on the outer surface of the current endwall and the region corresponding to the leading and trailing edges of the blade is... The spacing between adjacent control points on the outer surface of the front endwall, corresponding to the leading and trailing edges of the blade, is... ,in, The blade pitch; Except for the regions on the outer surface of the current endwall corresponding to the leading and trailing edges of the blade, the vertical distance between the control points and the outer surface of the current endwall is 1. The spacing between adjacent control points in the region other than the area on the outer surface of the current endwall corresponding to the leading and trailing edges of the blade is 0. ,in, This is the chord length of the blade.

7. The compressor non-axisymmetric endwall shaping method based on adjoint shape optimization according to claim 5, characterized in that, In step 7, the formula for calculating the total displacement is: ； in, For the first Total displacement of each control point For the current number The cumulative displacement of each control point Let be the overall objective function. For the current end wall Displacement of each grid point For sensitivity, For displacement coefficients, .

8. The compressor non-axisymmetric endwall shaping method based on adjoint shape optimization according to claim 7, characterized in that, In step 8, the formula for calculating the displacement of each grid node is: ； in, For the current end wall Displacement of each grid node For the current end wall The coordinates of each grid node. For the first The coordinates of the control points The total number of control points. For radial basis functions, For the first The weighting coefficients of each control point The following formula can be used to solve for: ； in, For the first The coordinates of the control points For the first The total displacement of each control point.

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