Discrete adjoint tail nozzle thrust coefficient surface sensitivity calculation method and system

Abstract

The present application belongs to the field of aero-engine nozzle aerodynamic optimization, and discloses a discrete-adjoint nozzle thrust coefficient surface sensitivity calculation method and system. The surface sensitivity algorithm and system capture the response of the flow field to the nozzle thrust coefficient through the discrete-adjoint equation, take the spatial sensitivity as an intermediate bridge to separate the geometric direct effect and the flow field indirect effect, combine the radial basis function RBF-transfinite interpolation TFI to calculate the mapping derivative, and transfer the nozzle spatial structure grid deformation, so that the whole solving process is independent of the number of design variables, and high-precision and high-efficiency sensitivity calculation of the nozzle thrust coefficient to the surface parameters is realized. The surface sensitivity algorithm and system solve the problems of low optimization efficiency, poor precision and weak adaptability of the nozzle, realize accurate and efficient analysis of the influence of the nozzle thrust coefficient on the surface parameter sensitivity, provide key technical support for improving the nozzle thrust coefficient, and have engineering practical value.

Description

Technical Field

[0001] This invention belongs to the field of aerodynamic optimization technology for aero-engine exhaust nozzles, specifically relating to a method and system for calculating the surface sensitivity of discrete exhaust nozzle thrust coefficients. Background Technology

[0002] The exhaust nozzle is a core component of rocket and aircraft engines, and its thrust coefficient directly determines the engine's performance. The thrust coefficient of the exhaust nozzle is extremely sensitive to surface shape; therefore, accurate calculation of the thrust coefficient's sensitivity to surface parameters is necessary to guide optimization design. Currently, structured grid aerodynamic adjoint optimization methods mainly employ partially variational adjoint methods. After solving the adjoint equations, gradient calculations are still required for each perturbation design variable. As the number of perturbation design variables increases, the computational cost of gradient calculations increases significantly, limiting the application of structured grid aerodynamic adjoint optimization methods in large-scale, refined optimization design.

[0003] Currently, there is an urgent need to develop a method and system for calculating the surface sensitivity of the discrete accompanying tail nozzle thrust coefficient. Summary of the Invention

[0004] One technical problem to be solved by the present invention is to provide a method for calculating the surface sensitivity of the discrete accompanying nozzle thrust coefficient, and another technical problem to be solved by the present invention is to provide a system for calculating the surface sensitivity of the discrete accompanying nozzle thrust coefficient, so as to overcome the defects of the prior art.

[0005] The method for calculating the surface sensitivity of discrete accompanying tail nozzle thrust coefficient according to the present invention includes the following steps:

[0006] S01. Flow field solution;

[0007] Based on the spatial structure grid of the tail nozzle, the flow variables are solved by discretized Reynolds-averaged Navier-Stokes equations (RANS).

[0008] S02. Accompanying solution;

[0009] Based on the flow variables and the nozzle thrust coefficient, the discrete adjoint equation is solved to obtain the adjoint variables; the discrete adjoint equation reflects the sensitivity of the thrust coefficient to the flow variables.

[0010] S03. Calculate spatial sensitivity;

[0011] Based on flow variables, adjoint variables, and nozzle thrust coefficient, the spatial sensitivity of nozzle thrust coefficient to nozzle spatial structure grid is calculated; the spatial sensitivity is the sum of the explicit derivative of nozzle thrust coefficient to nozzle spatial structure grid and the indirect derivative of flow field transmitted by adjoint variables.

[0012] S04. Calculate the derivative of the mapping;

[0013] The radial basis function (RBF)-overlimit interpolation (TFI) is used to calculate the mapping derivative of the nozzle spatial structure mesh with respect to surface parameters; the mapping derivative reflects the effect of changes in surface parameters on the deformation of the nozzle spatial structure mesh.

[0014] S05. Surface sensitivity transfer;

[0015] Based on spatial sensitivity and mapping derivative, the surface sensitivity of the nozzle thrust coefficient to surface parameters is obtained through chain rule; the surface sensitivity of the nozzle thrust coefficient to surface parameters is the product of spatial sensitivity and mapping derivative.

[0016] Furthermore, the discretization method for the Reynolds-averaged Navier-Stokes equations (RANS) of S01 is the finite volume method (FVM); the spatial structure grid of the tail nozzle of S01 includes the nozzle portion and the far-field portion.

[0017] Furthermore, the discrete adjoint equation of S02 is as follows:

[0018] ;

[0019] in: The tail nozzle thrust coefficient is the ratio of actual thrust to ideal thrust. For flow-conserving variables, , For incoming static pressure, For the incoming flow density, It consists of three velocity components in three directions. The total energy of the fluid; This is the Jacobian matrix of the flow field residuals with respect to the flow variables; Let be the partial derivative of the thrust coefficient with respect to the flow variable. It is a companion variable.

[0020] Furthermore, the spatial sensitivity of S03 is calculated as follows:

[0021] ;

[0022] in, The spatial sensitivity of the nozzle thrust coefficient to the nozzle spatial structure grid. This is the explicit derivative of the nozzle thrust coefficient with respect to the nozzle spatial structure grid. The flow field indirect derivative is passed on by the accompanying variables; These are the node coordinates of the tail nozzle spatial structure mesh.

[0023] Furthermore, the surface parameters of S04 are the coordinates of the mesh nodes on the surface of the tailpipe wall; the radial basis function RBF is a Gaussian function.

[0024] Furthermore, the formula for calculating the surface sensitivity of S05 is as follows:

[0025] ;

[0026] in, The surface sensitivity of the tail nozzle thrust coefficient to surface parameters; The derivative matrix of the spatial structure mesh of the tail nozzle with respect to the surface parameters; These are the surface parameters of the tail nozzle.

[0027] Furthermore, the tail nozzle thrust coefficient is defined as the ratio of actual thrust to ideal thrust, and the calculation formula is as follows:

[0028] ;

[0029] in, For real thrust, For ideal thrust; For quality flow, The airflow velocity; Due to environmental pressures, Indicates gas, For specific heat ratio, It is the ratio of the total pressure at the nozzle inlet to the ambient pressure; This is the ratio of the total temperature at the nozzle inlet to the ambient temperature; in ideal thrust, only the mass flow rate... The remaining quantities are given by the boundary conditions and need to be calculated.

[0030] The discrete-time nozzle thrust coefficient surface sensitivity calculation system of the present invention includes:

[0031] a. Flow field solution module: Based on the spatial structure grid of the tail nozzle, the discretized Reynolds-averaged Navier-Stokes equations (RANS) are solved to obtain the flow variables;

[0032] b. Adjoint solution module: Based on the flow variables and the tail nozzle thrust coefficient, the discrete adjoint equation is solved to obtain the adjoint variables;

[0033] c. Spatial Sensitivity Calculation Module: Based on flow variables, associated variables, and nozzle thrust coefficient, calculate the spatial sensitivity of the nozzle thrust coefficient to the nozzle spatial structure grid.

[0034] d. Mapping derivative calculation module: The radial basis function (RBF)-overlimit interpolation (TFI) is used to calculate the mapping derivative of the nozzle spatial structure mesh with respect to the surface parameters;

[0035] e. Surface sensitivity transfer module: Based on spatial sensitivity and mapping derivative, the surface sensitivity of the nozzle thrust coefficient to surface parameters is obtained through chain rule transfer.

[0036] f. Optimization module: Adjusting nozzle surface parameters based on surface sensitivity This increases the thrust coefficient of the tail nozzle.

[0037] The discrete adjoint surface sensitivity calculation method and system for nozzle thrust coefficient of the present invention captures the response of the flow field to the nozzle thrust coefficient through discrete adjoint equations. It separates the direct geometric effect and the indirect flow field effect by using spatial sensitivity as an intermediate bridge. It combines radial basis function (RBF)-overlimit interpolation (TFI) to calculate the mapping derivative and transfer the deformation of the nozzle spatial structure grid. This makes the entire solution process independent of the number of design variables, and realizes high-precision and high-efficiency sensitivity calculation of nozzle thrust coefficient to surface parameters.

[0038] The discrete-time nozzle thrust coefficient surface sensitivity calculation method and system of the present invention solves the problems of low efficiency, poor accuracy and weak adaptability of nozzle optimization, realizes accurate and efficient analysis of the influence of nozzle thrust coefficient on surface parameter sensitivity, provides key technical support for improving nozzle thrust coefficient, and has practical engineering value. Attached Figure Description

[0039] Figure 1 This is a flowchart of the method for calculating the surface sensitivity of the discrete accompanying tail nozzle thrust coefficient according to the present invention.

[0040] Figure 2 The tail nozzle reference shape is shown in the embodiment.

[0041] Figure 3 The tail nozzle thrust coefficient convergence process in the embodiment;

[0042] Figure 4 The diagram shows a symmetrical comparison of the tail nozzle before and after optimization, as shown in the example. Detailed Implementation

[0043] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0044] like Figure 1 As shown, the method for calculating the surface sensitivity of the discrete accompanying tail nozzle thrust coefficient of the present invention includes the following steps:

[0045] S01. Flow field solution;

[0046] Based on the spatial structure grid of the tail nozzle, the flow variables are solved by discretized Reynolds-averaged Navier-Stokes equations (RANS).

[0047] S02. Accompanying solution;

[0048] Based on the flow variables and the nozzle thrust coefficient, the discrete adjoint equation is solved to obtain the adjoint variables; the discrete adjoint equation reflects the sensitivity of the thrust coefficient to the flow variables.

[0049] S03. Calculate spatial sensitivity;

[0050] Based on flow variables, adjoint variables, and nozzle thrust coefficient, the spatial sensitivity of nozzle thrust coefficient to nozzle spatial structure grid is calculated; the spatial sensitivity is the sum of the explicit derivative of nozzle thrust coefficient to nozzle spatial structure grid and the indirect derivative of flow field transmitted by adjoint variables.

[0051] S04. Calculate the derivative of the mapping;

[0052] The radial basis function (RBF)-overlimit interpolation (TFI) is used to calculate the mapping derivative of the nozzle spatial structure mesh with respect to surface parameters; the mapping derivative reflects the effect of changes in surface parameters on the deformation of the nozzle spatial structure mesh.

[0053] S05. Surface sensitivity transfer;

[0054] Based on spatial sensitivity and mapping derivative, the surface sensitivity of the nozzle thrust coefficient to surface parameters is obtained through chain rule; the surface sensitivity of the nozzle thrust coefficient to surface parameters is the product of spatial sensitivity and mapping derivative.

[0055] Furthermore, the discretization method for the Reynolds-averaged Navier-Stokes equations (RANS) of S01 is the finite volume method (FVM); the spatial structure grid of the tail nozzle of S01 includes the nozzle portion and the far-field portion.

[0056] Furthermore, the discrete adjoint equation of S02 is as follows:

[0057] ;

[0058] in: The tail nozzle thrust coefficient is the ratio of actual thrust to ideal thrust. For flow-conserving variables, , For incoming static pressure, For the incoming flow density, It consists of three velocity components in three directions. The total energy of the fluid; This is the Jacobian matrix of the flow field residuals with respect to the flow variables; Let be the partial derivative of the thrust coefficient with respect to the flow variable. It is a companion variable.

[0059] Furthermore, the spatial sensitivity of S03 is calculated as follows:

[0060] ;

[0061] in, The spatial sensitivity of the nozzle thrust coefficient to the nozzle spatial structure grid. This is the explicit derivative of the nozzle thrust coefficient with respect to the nozzle spatial structure grid. The flow field indirect derivative is passed on by the accompanying variables; These are the node coordinates of the tail nozzle spatial structure mesh.

[0062] Furthermore, the surface parameters of S04 are the coordinates of the mesh nodes on the surface of the tailpipe wall; the radial basis function RBF is a Gaussian function.

[0063] Furthermore, the formula for calculating the surface sensitivity of S05 is as follows:

[0064] ;

[0065] in, The surface sensitivity of the tail nozzle thrust coefficient to surface parameters; The derivative matrix of the spatial structure mesh of the tail nozzle with respect to the surface parameters; These are the surface parameters of the tail nozzle.

[0066] Furthermore, the tail nozzle thrust coefficient is defined as the ratio of actual thrust to ideal thrust, and the calculation formula is as follows:

[0067] ;

[0068] in, For real thrust, For ideal thrust; For quality flow, The airflow velocity; Due to environmental pressures, Indicates gas, For specific heat ratio, It is the ratio of the total pressure at the nozzle inlet to the ambient pressure; This is the ratio of the total temperature at the nozzle inlet to the ambient temperature; in ideal thrust, only the mass flow rate... The remaining quantities are given by the boundary conditions and need to be calculated.

[0069] The discrete-time nozzle thrust coefficient surface sensitivity calculation system of the present invention includes:

[0070] a. Flow field solution module: Based on the spatial structure grid of the tail nozzle, the discretized Reynolds-averaged Navier-Stokes equations (RANS) are solved to obtain the flow variables;

[0071] b. Adjoint solution module: Based on the flow variables and the tail nozzle thrust coefficient, the discrete adjoint equation is solved to obtain the adjoint variables;

[0072] c. Spatial Sensitivity Calculation Module: Based on flow variables, associated variables, and nozzle thrust coefficient, calculate the spatial sensitivity of the nozzle thrust coefficient to the nozzle spatial structure grid.

[0073] d. Mapping derivative calculation module: The radial basis function (RBF)-overlimit interpolation (TFI) is used to calculate the mapping derivative of the nozzle spatial structure mesh with respect to the surface parameters;

[0074] e. Surface sensitivity transfer module: Based on spatial sensitivity and mapping derivative, the surface sensitivity of the nozzle thrust coefficient to surface parameters is obtained through chain rule transfer.

[0075] f. Optimization module: Adjusting nozzle surface parameters based on surface sensitivity This increases the thrust coefficient of the tail nozzle.

[0076] Example: In this example, the nozzle design pressure ratio NPR is given as 11.64, and the throat height H is given as follows: * =0.24m, tail nozzle reference shape see Figure 2 A total of 286 design variables were arranged. Figure 2 In the diagram, R is the nozzle inlet radius, and W... * H represents the width of the larynx. * ΔZ1 is the height of the throat passage, and ΔZ1 is the Z-axis offset between the midpoint of the inlet and the midpoint of the throat passage. L 1 The length of the contraction segment. L 2 The length of the expansion segment. L 3 This represents the total length of the nozzle. Based on flight conditions, the aircraft's climb point at Mach number Ma=0.3 and NPR=5.0, and its cruise point at Mach number Ma=1.8 and NPR=11.64 were selected for optimization. The optimization iteration process is detailed in [link to optimization process]. Figure 3 A comparison of the symmetrical surfaces before and after nozzle optimization is shown in the image. Figure 4 , Figure 4 In the figure, the x-coordinate X represents the x-coordinate of the nozzle symmetry plane, and the y-coordinate Z represents the x-coordinate of the nozzle symmetry plane. Under the Mach number Ma=0.3 condition, the optimized thrust coefficient increases from 0.945 to 0.973, and under the Mach number Ma=1.8 condition, the thrust coefficient increases from 0.9953 to 0.9963. Furthermore, the discrete adjoint nozzle thrust coefficient surface sensitivity calculation method and system of this invention require only 9 seconds to solve the gradient, compared to 860 seconds using the partial variational adjoint method, representing a two-order-of-magnitude improvement in computational efficiency.

[0077] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. For those skilled in the art, all features disclosed in the present invention, or all steps in all methods or processes disclosed, except for mutually exclusive features and / or steps, can be combined in any way without departing from the principles of the present invention. The present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A surface sensitivity algorithm for tail nozzle thrust coefficient based on discrete adjoints, characterized in that, Includes the following steps: S01. Flow field solution; Based on the spatial structure grid of the tail nozzle, the flow variables are solved by discretized Reynolds-averaged Navier-Stokes equations (RANS). The discretization method for the Reynolds-averaged Navier-Stokes equations (RANS) is the finite volume method (FVM); the tail nozzle spatial structure grid of S01 includes the nozzle part and the far field part. S02. Accompanying solution; Based on the flow variables and the nozzle thrust coefficient, the discrete adjoint equation is solved to obtain the adjoint variables; the discrete adjoint equation reflects the sensitivity of the thrust coefficient to the flow variables. The discrete adjoint equation is as follows: ； in: The tail nozzle thrust coefficient is the ratio of actual thrust to ideal thrust. For flow-conserving variables, , For incoming static pressure, For the incoming flow density, It consists of three velocity components in three directions. The total energy of the fluid; This is the Jacobian matrix of the flow field residuals with respect to the flow variables; This is the partial derivative of the thrust coefficient with respect to the flow variable. As a companion variable; S03. Calculate spatial sensitivity; Based on flow variables, adjoint variables, and nozzle thrust coefficient, the spatial sensitivity of nozzle thrust coefficient to nozzle spatial structure grid is calculated; the spatial sensitivity is the sum of the explicit derivative of nozzle thrust coefficient to nozzle spatial structure grid and the indirect derivative of flow field transmitted by adjoint variables. The spatial sensitivity is calculated as follows: ； in, The spatial sensitivity of the nozzle thrust coefficient to the nozzle spatial structure grid. This is the explicit derivative of the nozzle thrust coefficient with respect to the nozzle spatial structure grid. The flow field indirect derivative is the one passed over by the accompanying variables; The coordinates of the nodes in the spatial structure mesh of the tail nozzle; S04. Calculate the derivative of the mapping; The radial basis function (RBF)-overlimit interpolation (TFI) is used to calculate the mapping derivative of the nozzle spatial structure mesh with respect to surface parameters; the mapping derivative reflects the effect of changes in surface parameters on the deformation of the nozzle spatial structure mesh. S05. Surface sensitivity transfer; Based on spatial sensitivity and mapping derivative, the surface sensitivity of the nozzle thrust coefficient to surface parameters is obtained through chain rule; the surface sensitivity of the nozzle thrust coefficient to surface parameters is the product of spatial sensitivity and mapping derivative.

2. The surface sensitivity algorithm for tail nozzle thrust coefficient based on discrete adjoint as described in claim 1, characterized in that, The surface parameters of S04 are the coordinates of the mesh nodes on the surface of the tailpipe wall; the radial basis function RBF is a Gaussian function.

3. The surface sensitivity algorithm for tail nozzle thrust coefficient based on discrete adjoint as described in claim 2, characterized in that, The formula for calculating the surface sensitivity of S05 is as follows: ； in, The surface sensitivity of the tail nozzle thrust coefficient to surface parameters; The derivative matrix of the spatial structure mesh of the tail nozzle with respect to the surface parameters; These are the surface parameters of the tail nozzle.

4. The surface sensitivity algorithm for tail nozzle thrust coefficient based on discrete adjoint as described in claim 3, characterized in that, The tail nozzle thrust coefficient is defined as the ratio of actual thrust to ideal thrust, and the calculation formula is as follows: ； in, For real thrust, For ideal thrust; For quality flow, The airflow velocity; Due to environmental pressures, Indicates gas, For specific heat ratio, It is the ratio of the total pressure at the nozzle inlet to the ambient pressure; This is the ratio of the total temperature at the nozzle inlet to the ambient temperature; in ideal thrust, only the mass flow rate... The remaining quantities are given by the boundary conditions and need to be calculated.

5. A computational system for a surface sensitivity algorithm for nozzle thrust coefficient based on discrete adjoints, used to implement the surface sensitivity algorithm for nozzle thrust coefficient based on discrete adjoints as described in claim 4, characterized in that, include: a. Flow field solution module: Based on the spatial structure grid of the tail nozzle, the discretized Reynolds-averaged Navier-Stokes equations (RANS) are solved to obtain the flow variables; b. Adjoint solution module: Based on the flow variables and the tail nozzle thrust coefficient, the discrete adjoint equation is solved to obtain the adjoint variables; c. Spatial Sensitivity Calculation Module: Based on flow variables, associated variables, and nozzle thrust coefficient, calculate the spatial sensitivity of the nozzle thrust coefficient to the nozzle spatial structure grid. d. Mapping derivative calculation module: The radial basis function (RBF)-overlimit interpolation (TFI) is used to calculate the mapping derivative of the nozzle spatial structure mesh with respect to the surface parameters; e. Surface sensitivity transfer module: Based on spatial sensitivity and mapping derivative, the surface sensitivity of the nozzle thrust coefficient to surface parameters is obtained through chain rule transfer. f. Optimization module: Adjusting nozzle surface parameters based on surface sensitivity This increases the thrust coefficient of the tail nozzle.

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