A method for adjoint optimization design of aircraft based on low dissipation scheme

Abstract

The present invention is specifically a method for aircraft adjoint optimization design based on a low-dissipation format, comprising the following steps: Step 1: Given an initial shape of an aircraft to be optimized, a CFD grid of the initial shape is generated; and the aircraft is parameterized based on the initial shape to obtain design variables; Step 2: Optimization objectives and constraints are set, and a mathematical model of the optimization problem is established; Step 3: A high-precision convergent flow field solution calculated using the low-dissipation AUSMPWP format is obtained to obtain the aerodynamic objective function value of the optimization mathematical model; and discrete adjoint equations and sensitivity equations are constructed and solved based on the low-dissipation AUSMPWP format to obtain the gradient of the objective function in the optimization mathematical model with respect to the design variables; Step 4: Based on the aerodynamic objective function value and gradient information obtained in Step 3, a sequential quadratic programming optimization algorithm is used to optimize and solve the optimization problem of Step 2, thereby realizing low-dissipation adjoint optimization design of the aircraft.

Description

Technical Field

[0001] The present invention belongs to the fields of computational fluid dynamics and aircraft optimization design, and in particular relates to an aircraft adjoint optimization design method based on a low dissipation format. Background Art

[0002] Numerical optimization design methods based on CAE software are widely used in aircraft design due to their efficiency and reliability. Optimization algorithms can be categorized as gradient-free or gradient-based, depending on whether they require information about the gradient of the objective function. Gradient-free algorithms require only the value of the objective function during the optimization process, without requiring information such as the gradient or derivative. Gradient-free algorithms treat the objective function solution process as a black box, oblivious to the specific solution details. Therefore, gradient-free design systems are simple to build and require no additional solvers, reducing development complexity. However, these systems require exponentially more calls to the objective function as the number of design variables increases, making them difficult to apply to high-dimensional design problems such as refined aircraft design. Gradient-based algorithms, on the other hand, require a linear increase in the number of objective function calls with the number of design variables. They require only one solution of the governing equation, one solution of the adjoint equation, and multiple perturbation calculations to quickly obtain the gradient of the objective function with respect to the design variables. Therefore, gradient-based optimization algorithms are a more suitable choice for aerodynamic shape optimization problems with a large number of design variables.

[0003] For gradient algorithms, it is necessary to obtain the derivative of the objective function with respect to each design variable. There are three common methods for calculating derivatives: finite difference method, complex variable difference method and adjoint equation method. The computational complexity of the finite difference method and the complex variable difference method is proportional to the number of design variables, and in the refined aerodynamic shape optimization design, hundreds or thousands of large-scale design variables need to be applied. If the finite difference method and the complex variable difference method are used, calculating the gradient once requires repeatedly calling CFD to solve the objective function, resulting in a huge computational cost. The adjoint equation method, by solving the adjoint equation of the original model, only needs one solution to obtain the partial derivatives of the objective function with respect to all design variables, thus achieving a basic decoupling between the computational complexity and the number of design variables, and has high accuracy, which has significant advantages in large-scale design variable problems.

[0004] In the optimization design of aircraft aerodynamic shapes, the adjoint equation can be divided into discrete adjoint equations (Discrete Adjoint) and continuous adjoint equations (Continuous Adjoint) according to the different methods of constructing and solving the adjoint equations. The continuous adjoint equation combines the integral form of the objective function and the flow field control equations with respect to the flow field solution vector and the design variables through the Lagrange multiplier method, and combines the variational terms with respect to the flow field solution vector to form a continuous adjoint equation and its boundary conditions. The gradient calculation is constructed through the variational terms with respect to the design variables. The discrete adjoint method directly derives the discrete form of the adjoint equation from the already discretized objective function and flow field control equations. If the form of the adjoint equation completely corresponds to the discrete form of the original flow field control equation, the exact derivative corresponding to the discrete form of the objective function and control equation can be solved.

[0005] At present, when solving aerodynamic problems with discrete adjoint methods, the adjoint variables are more sensitive than flow field variables because the adjoint equations require the first-order derivative information of the flow field. The variational derivation of residual terms includes the variational derivation of inviscid residuals and viscous residuals. In existing discrete adjoint methods, inviscid residuals are mostly discretized using central difference formats and relatively simple upwind formats (such as Roe format and Vanleer format). When using such formats, fewer template units are involved in variational derivation, and the design system development is less difficult. However, in the discrete adjoint design system, the accuracy and robustness of the adjoint equations are mainly affected by the form of inviscid residual processing. In the above existing discrete adjoint optimization design systems, the main problems are as follows: 1. The central difference grid is used. When using the first formula, it performs poorly in transonic / hypersonic flows and relies on artificial dissipation, resulting in problems such as difficult convergence and low accuracy. At the same time, the central difference format is difficult to further process and reduce to a first-order accuracy form to improve the robustness of the adjoint equation; second, the upwind format such as the Vanleer format has large numerical dissipation, which can easily erase some flow field details, resulting in inaccurate boundary layer analysis and large resistance prediction deviation; third, the upwind format such as the Roe format is difficult to converge under high Mach number conditions, and usually entropy correction is required to improve convergence, but it will affect the calculation accuracy.

[0006] Therefore, constructing a high-precision, low-dissipation format discrete adjoint optimization design method that is suitable for complex three-dimensional working conditions of aircraft and can achieve high-fidelity flow field and adjoint field solutions has important academic value and practical engineering significance. Summary of the Invention

[0007] In order to solve the problems existing in the prior art, the present invention proposes an aircraft adjoint optimization design method based on a low-dissipation format. The method selects the AUSMPWP format, an improved format of the AUSM (Advection Upstream Splitting Method) format, as the inviscid flux discretization method, and performs discrete adjoint design by constructing an adjoint equation and a sensitivity equation based on the AUSMPWP format. The AUSMPWP format is based on the AUSM series framework and can adapt to the full speed range through Mach number splitting and pressure weighting function correction without adding artificial dissipation. Therefore, it can reduce numerical dissipation and improve the boundary layer resolution capability, thereby achieving high accuracy.

[0008] The present invention is achieved through the following technical solutions:

[0009] A method for adjoint optimization design of an aircraft based on a low dissipation format comprises the following steps:

[0010] Step 1: Given the initial shape of the aircraft to be optimized, generate a CFD computational mesh of the initial shape; and parameterize the aircraft based on the initial shape to obtain design variables;

[0011] Step 2: Set the optimization goal and constraints, and establish a mathematical model for the optimization problem;

[0012] Step 3: Use the low-dissipation AUSMPWP format to perform CFD calculations to obtain the converged flow field solution vector and objective function value; construct and solve the discrete adjoint equation and sensitivity equation based on the low-dissipation AUSMPWP format to obtain the gradient of the objective function with respect to the design variables in the mathematical model of the optimization problem;

[0013] Step 4: Based on the objective function value obtained in step 3 and the gradient of the design variables, the sequential quadratic programming optimization algorithm is used to optimize and solve the optimization problem in step 2 to achieve the adjoint optimization design of low dissipation of the aircraft.

[0014] Furthermore, in step 1, the specific process of parameterizing the aircraft based on the initial shape is as follows:

[0015] For the given initial shape of the aircraft that needs to be optimized, the free deformation method is used to parameterize the geometric shape: an FFD control frame is established around the area to be deformed of the initial shape of the aircraft, and the Z coordinate of the node controlled by the FFD control frame is set to The amount of change As the design variable, the subscript Indicates the control nodes, , The number of nodes of the FFD box is controlled. By changing the design variables, deformation perturbations are applied to the surface mesh to achieve deformation of the initial shape and obtain the surface mesh of the new shape. Then, the inverse distance weighted interpolation mesh deformation method is used to interpolate and deform the spatial mesh based on the surface mesh of the new shape to obtain the CFD calculation mesh of the new shape.

[0016] Furthermore, in step 2, the process of establishing the mathematical model of the optimization problem is as follows: selecting aerodynamic performance parameters to construct the objective function; selecting the Z-axis coordinate change of the control node of the FFD control frame; As the design variable; the aerodynamic performance parameters of the optimized aircraft do not deteriorate compared with the aerodynamic performance parameters of the initial shape of the aircraft as the aerodynamic constraint.

[0017] Furthermore, step 3 specifically includes the following sub-steps:

[0018] Step 3.1: Based on the CFD computational grid, use the low-dissipation AUSMPWP format to perform CFD calculations and obtain the converged flow field solution vector and objective function value;

[0019] Step 3.2: Based on the obtained converged flow field solution vector, the discrete adjoint equation and sensitivity equation are constructed and solved based on the low-dissipation AUSMPWP format to obtain the gradient of the objective function with respect to the design variables; specifically:

[0020] The mathematical model of the optimization problem is expressed as follows:

[0021]

[0022] in The objective function constructed for the aerodynamic performance parameters is: is the flow field conservation variable, that is, the flow field solution vector obtained in step 3.1, is the design variable, For the residual of the flow field solution, introduce the adjoint variable , transform the mathematical model of the optimization problem into an unconstrained optimization problem and construct the Lagrangian function as follows:

[0023]

[0024] in Represents the accompanying variable The transpose of

[0025] The discrete adjoint equation constructed based on the low-dissipation AUSMPWP format is as follows:

[0026]

[0027] The sensitivity equation constructed based on the low-dissipation AUSMPWP format is as follows, where is the spatial grid, For the surface mesh:

[0028]

[0029] In the above adjoint equation and sensitivity equation, the residual The inviscid residuals in are discretized using the AUSMPWP format;

[0030] The adjoint variable is obtained by solving the discrete adjoint equation Finally, the flow field solution vector and the adjoint variables are substituted into the sensitivity equation to obtain the gradient of the aerodynamic performance parameters with respect to the design variables.

[0031] After obtaining the gradient of the aerodynamic performance parameters with respect to the design variables, the gradient of the objective function with respect to the design variables is calculated according to the following formula:

[0032]

[0033] in is the number of aerodynamic performance parameters, For the aerodynamic performance parameters, For the The weight coefficient of each aerodynamic performance parameter.

[0034] Furthermore, the process of constructing the discrete adjoint equation based on the low-dissipation AUSMPWP format is as follows:

[0035] The discrete adjoint equation is of the form:

[0036]

[0037]

[0038] Where, is the residual The inviscid residual in , is the residual The viscous residual in ; the low dissipation AUSMPWP format is used to construct the inviscid residual Conserved variables of the convection field The partial derivative of The process is as follows:

[0039] Calculate the inviscid residual In the computational grid The conserved variables of the flow field are varied in three directions to obtain the partial derivatives of the inviscid residual with respect to the conserved variables of the flow field in three directions;

[0040] The derivation process of the partial derivative of the inviscid residual on the conservation variable of the flow field in a certain direction is as follows:

[0041] Establishing inviscid residual variation expression:

[0042]

[0043] Where, Indicates the The inviscid residual on the grid cells, Indicates the The right interface flux of each grid cell is Indicates the The left interface flux of each grid cell is represents the variation of the corresponding sign, Indicates the Inviscid residual variation on grid cells, Indicates the The right interface flux variation of each grid cell is: Indicates the The left interface flux variation of each grid cell is expressed as follows:

[0044]

[0045]

[0046] in:

[0047]

[0048]

[0049]

[0050]

[0051] Where, Indicates the The original variables on the left side of the right interface of the grid unit, Indicates the The original variables on the right side of the right interface of the grid unit, Indicates the The original variables on the left side of the left interface of the grid unit, Indicates the The original variables on the right side of the left interface of each grid unit; Indicates the The conserved variable of the flow field in the second grid cell to the left of the grid cell is, Indicates the The conserved variable of the flow field of the first grid cell to the left of the grid cell is, Indicates the The flow field conservation variables of the grid cells are: Indicates the The conservation variable of the flow field of the first grid cell to the right of the grid cell is, Indicates the The conserved variables of the flow field in the second grid cell to the right of the grid cell; represents the partial differential of the corresponding sign;

[0052] The above The right interface flux variation of each grid cell , No. The left interface flux variation of each grid cell Substitute into the inviscid residual variation In, we get:

[0053]

[0054] Multiply the above formula by the adjoint variable of the corresponding grid cell And summing them, we get:

[0055]

[0056] in, For the The adjoint variable of the second grid cell to the left of the grid cell The transpose of For the The adjoint variable of the first grid cell to the left of the grid cell The transpose of For the Adjoint variables of grid cells The transpose of For the The adjoint variable of the first grid cell to the right of the grid cell The transpose of For the The adjoint variable of the second grid cell to the right of the grid cell The transpose of

[0057] The inviscid residual is varied Substitute into the above formula, and combine After sorting out the items, we get:

[0058]

[0059] Further expanding the partial derivatives of the conserved variables of the flow field at each interface flux, we obtain:

[0060] No. The surface flux at the right interface of the grid cell is The partial derivative of the flow field conservation variable of a grid cell is:

[0061]

[0062] No. The surface flux at the left interface of the grid cell is The partial derivative of the flow field conservation variable of a grid cell is:

[0063]

[0064] No. The surface flux at the left interface of the grid cell is The partial derivative of the flow field conservation variable of a grid cell is:

[0065]

[0066] No. The surface flux at the right interface of the grid cell is The partial derivative of the flow field conservation variable of a grid cell is:

[0067]

[0068] in, Indicates the The positive flux on the right interface of each grid cell is Indicates the The negative flux on the right interface of each grid cell, Indicates the The positive flux on the left interface of each grid cell is Indicates the The negative flux on the left interface of each grid cell is Indicates the The positive flux on the left interface of each grid cell is Indicates the The negative flux on the left interface of each grid cell is Indicates the The positive flux on the right interface of each grid cell is Indicates the Negative flux at the right interface of the grid cell;

[0069] In the expansion formula of partial derivatives of the interface flux on the conservation variable of the flow field, the AUSMPWP format is introduced to convert the derivative form of each interface flux to the original interface variable , , , , , , , , , , , to expand;

[0070] Among them for The expansion process is:

[0071] First, construct the following expression to calculate the derivative of the interface sound velocity with respect to the original interface variable:

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079] in, , , In order, they are The grid and The grid interface is at , , Surface normal vectors in three directions, 、 They are the x component, y component and z component of the surface normal vector respectively; For the The grid and The total velocity on the left side of the grid interface is For the The grid and The combined velocity on the right side of the grid interface; For the The grid and The total enthalpy on the left side of the grid interface; For the The grid and The pressure on the left side of the grid interface; is the adiabatic constant; For the The grid and The density on the left side of the grid interface; For the The grid and The arithmetic mean of the total enthalpy on both sides of the grid interface; The first definition based on the calorimetric perfect gas The grid and The interface sound velocity of the grid; The first field defined in the AUSMPWP format to improve shock wave capture capability The grid and The interface sound velocity of the grid; the final For the The grid and The partial derivative of the newly defined interface sound velocity at the grid interface with respect to the original variable of the flow field on the left side of the interface;

[0080] Then construct the following expressions to calculate the partial derivatives of the Mach number splitting function and the pressure splitting function with respect to the original variables of the interface:

[0081]

[0082]

[0083]

[0084]

[0085] Where, For the The grid and Mach number splitting function at the grid interface; For the The grid and Pressure splitting function at the interface of the grids; For the The grid and The Mach number on the left side of the grid interface, For the The grid and The Mach number on the right side of the grid interface;

[0086] Then construct the following expression to calculate the partial derivative of the pressure flux term with respect to the original interface variable:

[0087]

[0088]

[0089]

[0090]

[0091] in, For the The grid and The pressure flux at the grid interface is , In order, they are The grid and The pressure splitting function on the left and right sides of the interface at the grid interface; , are the pressures on the left and right sides of the interface respectively;

[0092] Then construct the following expression to calculate the partial derivative of the pressure-based weight coefficient with respect to the original variable:

[0093]

[0094]

[0095]

[0096]

[0097] Where, The AUSMPWP format is defined in The grid and The first weight function based on pressure at the grid interface, The AUSMPWP format is defined in The grid and The first weight function based on pressure at the grid interface; For the The grid and The function used to determine the pressure contribution on the left and right sides of the interface at the intersection of the grids;

[0098] Finally, the partial derivative of the interface velocity with respect to the original interface variable is constructed, and different treatments are performed according to the different directions of the interface velocity as follows:

[0099] Determine the velocity direction at the interface by the interface Mach number:

[0100]

[0101] in, is the interface Mach number, For the The grid and The Mach number on the left side of the grid interface is For the The grid and The Mach number on the right side of the grid interface;

[0102] for :

[0103]

[0104]

[0105] for :

[0106]

[0107]

[0108] Where, is the first value determined after considering the influence of the pressure weight function. The grid and The Mach number on the left side of the grid interface; is the first value determined after considering the influence of the pressure weight function. The grid and The Mach number on the right side of the grid interface; For the The grid and The Mach number splitting function on the right side of the grid interface; For the The grid and The Mach number splitting function on the left side of the grid interface;

[0109] For the The grid and The flux on the left side of the grid interface , the complete AUSMPWP format can be written as:

[0110]

[0111] Where, Indicates the The grid and The surface area of ​​the grid interface, is the transformation matrix from the curvilinear coordinate system to the Cartesian coordinate system under the structured grid;

[0112] Write the partial derivatives of the flux term with respect to the original variables of the flow field in the above complete AUSMPWP format into a matrix form, and then substitute the derivatives of the interface sound velocity with respect to the original variables of the interface, the partial derivatives of the Mach number splitting function and the pressure splitting function with respect to the original variables of the interface, the partial derivatives of the pressure flux term with respect to the original variables of the interface, the partial derivatives of the pressure-based weight coefficient with respect to the original variables, and the partial derivatives of the interface velocity with respect to the original variables of the interface into the derivative formula of the flux term with respect to the original variables of the flow field in the complete AUSMPWP format to obtain the derivative form of the flux term with respect to the original variables of the interface. :

[0113]

[0114]

[0115]

[0116]

[0117] In the above formula, 、 and are intermediate variables introduced for convenience of description, 、 In order, they are The grid and The density on both sides of the grid interface; 、 In turn, they are in the physical coordinate system, along Direction The grid and The velocities on both sides of the grid interface; 、 They are respectively in the physical coordinate system, along the y direction The grid and The velocities on both sides of the grid interface; 、 They are respectively in the physical coordinate system, along the z direction The grid and The velocities on both sides of the grid interface; 、 In order, they are The grid and The total enthalpy on both sides of the grid interface.

[0118] Furthermore, the process of constructing the sensitivity equation based on the low-dissipation AUSMPWP format is as follows:

[0119] The sensitivity equation is of the form:

[0120]

[0121]

[0122] In the above formula is the total derivative of the objective function with respect to the design variables, is the partial derivative of the objective function with respect to the spatial grid, is the partial derivative of the space grid with respect to the surface grid, is the partial derivative of the surface mesh with respect to the design variables, is the partial derivative of the flow field residual with respect to the spatial grid, which is the inviscid residual of the flow field and viscous residuals Partial derivatives with respect to the spatial grid are formed;

[0123] Constructing inviscid residuals using the low-dissipation AUSMPWP scheme Space Grid The partial derivative of The specific process is as follows:

[0124] Calculate the inviscid residual In the computational grid The spatial grid is varied in three directions to obtain the partial derivatives of the inviscid residual with respect to the spatial grid in three directions;

[0125] The derivation process of the partial derivative of the inviscid residual with respect to the spatial grid in a certain direction is as follows:

[0126] Establishing the inviscid residual variation in space expression:

[0127]

[0128] Where, Indicates the The inviscid residual in the grid cell space is Indicates the The right interface flux on the grid cell space is Indicates the The left interface flux on the grid cell space is represents the variation of the corresponding sign, Indicates the The inviscid residual variation in the grid cell space, Indicates the The right interface flux variation on the grid cell space is: Indicates the The left interface flux variation on the grid cell space;

[0129] Considering the grid interface flux variation on the spatial grid, we get

[0130]

[0131]

[0132] in, In turn, they are expressed in The grid points on the right interface of the grid unit, Indicates in The surface normal vector on the right interface of the grid unit; In turn, they represent The grid points on the left interface of the grid unit, Indicates in The surface normal vector on the left interface of the grid cell;

[0133] The above 、 Substitute into the inviscid residual variation on space In the expression, we get:

[0134]

[0135] in The expansion process is:

[0136] In structured grids, , 、 They are the x component, y component and z component of the surface normal vector respectively;

[0137] First, construct the following expression to calculate the derivative of the interface sound velocity in space with respect to the surface normal:

[0138]

[0139]

[0140]

[0141]

[0142]

[0143] In the above formula, is the Hamiltonian operator, For the The grid and The surface normal vector in space at the interface of the grids; For the The grid and The total velocity on the left and right sides of the grid interface; For the The grid and The total enthalpy of the space on both sides of the grid interface; The first definition based on the calorimetric perfect gas The grid and The interface sound speed on the grid space; The first field defined in the AUSMPWP format to improve shock wave capture capability The grid and The interface sound speed on the grid space; the final For the The grid and The partial derivative of the interface sound velocity with respect to the surface normal vector in the newly defined space at the interface of the grids;

[0144] Then construct the following expressions to calculate the surface normal partial derivatives of the Mach number splitting function and the pressure splitting function:

[0145]

[0146]

[0147] in

[0148]

[0149] Where, For the The grid and Mach number splitting function in space at the interface of the grids; For the The grid and The pressure splitting function in the space at the interface of the grids; For the The grid and The Mach number in the space to the left of the grid interface;

[0150] Then construct the following expression to calculate the surface normal partial derivative of the interface pressure flux term:

[0151]

[0152] In the process of constructing the sensitivity equation, the calculation of the pressure weight coefficient does not require surface normal information, and the partial derivative of the pressure weight coefficient with respect to the surface normal is taken as 0;

[0153] Finally, construct the partial derivative of the interface velocity with respect to the interface normal:

[0154] Determine the velocity direction at the interface by the interface Mach number:

[0155]

[0156] in, is the interface Mach number in space, For the The grid and The left Mach number in space at the grid interface is, For the The grid and The Mach number on the right side of the space at the grid interface;

[0157] for :

[0158]

[0159]

[0160] for :

[0161]

[0162]

[0163] Where, is the first value determined after considering the influence of the pressure weight function. The grid and The Mach number in the space to the left of the grid interface; is the first value determined after considering the influence of the pressure weight function. The grid and The Mach number in the space to the right of the grid interface; For the The grid and The Mach number splitting function in the space to the right of the grid interface; For the The grid and The Mach number splitting function in the space to the left of the grid interface;

[0164] Write the partial derivative of the flux term with respect to the normal vector into a matrix form, and then substitute the derivative of the interface sound velocity with respect to the normal direction, the partial derivative of the Mach number splitting function and the pressure splitting function with respect to the normal direction, the partial derivative of the interface pressure flux term with respect to the normal direction, the partial derivative of the pressure-based weight coefficient with respect to the normal direction, and the partial derivative of the interface velocity with respect to the normal direction into the partial derivative of the flux term with respect to the normal direction, and obtain the partial derivative of the inviscid residual with respect to the normal direction based on the AUSMPWP format as follows:

[0165]

[0166] In the above formula 、 In order, they are The grid and The density of the space on the left and right sides of the grid interface; 、 In turn, they are in the physical coordinate system, along Direction The grid and The velocity in the space on the left and right sides of the grid interface; 、 They are respectively in the physical coordinate system, along the y direction The grid and The velocity in the space on the left and right sides of the grid interface; 、 They are respectively in the physical coordinate system, along the z direction The grid and The velocity in the space on the left and right sides of the grid interface; 、 In order, they are The grid and The total enthalpy in the space on both sides of the grid interface.

[0167] Furthermore, the optimization solution process in step 4 is specifically to feed back the optimization objective function value and its corresponding gradient to the optimization algorithm to determine whether the optimization convergence criteria are met. If the optimization convergence criteria are not met, the optimization algorithm will calculate the search direction and step size, obtain new design variables, and obtain a new shape through FFD parameterization, and return to step 3 for the next round of optimization iteration. This cycle will continue until the optimization iteration converges, and finally the optimized aircraft shape and aerodynamic data will be obtained.

[0168] Beneficial effects:

[0169] The present invention proposes an aircraft adjoint optimization design method based on a low-dissipation format. The method selects the AUSMPWP format, an improved format of the AUSM (Advection Upstream Splitting Method) format, as the inviscid flux discretization method. Discrete adjoint design is performed by constructing an adjoint equation and a sensitivity equation based on the AUSMPWP format. The AUSMPWP format is based on the AUSM series framework and can adapt to the full speed range through Mach number splitting and pressure weighting function correction. It does not require the addition of artificial dissipation, thereby reducing numerical dissipation, improving the boundary layer resolution capability, and achieving higher precision in the optimization design. BRIEF DESCRIPTION OF THE DRAWINGS

[0170] Figure 1 is a flow chart of an embodiment of the present invention;

[0171] Figure 2 The ONERA M6 surface mesh according to an embodiment of the present invention;

[0172] Figure 3 The initial configuration of ONERA M6 and the FFD control frame in an embodiment of the present invention;

[0173] Figure 4 This is a comparison of the ONERA M6 wing before and after optimization according to an embodiment of the present invention;

[0174] Figure 5 Iteration history of optimization targets in different formats according to the embodiments of the present invention. DETAILED DESCRIPTION

[0175] In order to make the technical problems, technical solutions and beneficial effects solved by the present invention more clearly understood and to enable those skilled in the art to better understand the solutions of the present invention, the present invention is further described and fully explained below in conjunction with the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention.

[0176] This embodiment takes the M6 ​​wing as an example, and adopts the aircraft accompanying optimization design method based on the low dissipation format proposed in the present invention to carry out drag reduction optimization design for the M6 ​​wing. The design working conditions are: free flow Mach number 0.8395, Reynolds number .like Figure 1 As shown, the embodiment of the present invention is implemented through the following technical solutions:

[0177] A method for adjoint optimization design of an aircraft based on a low dissipation format comprises the following steps:

[0178] Step 1: Given the initial shape of the aircraft to be optimized, generate the CFD mesh of the initial shape, such as Figure 2 As shown; and based on the initial shape, the aircraft is parameterized to obtain design variables;

[0179] For a given initial shape of an aircraft that needs to be optimized, the free form deformation (FFD) method is used to parameterize the geometric shape.

[0180] Specifically: Create an FFD control frame around the area to be deformed, such as Figure 3 As shown, the Z coordinates of the nodes of the FFD control frame The amount of change As the design variable, where the subscript i represents the i-th control node and n is the number of all FFD box control nodes; by changing the design variable, a deformation perturbation is applied to the surface mesh, thereby deforming the initial shape and obtaining a surface mesh of a new shape. Then, the inverse distance weighting interpolation (IDW) mesh deformation method is used to interpolate and deform the spatial mesh based on the surface mesh of the new shape to obtain the CFD calculation mesh of the new shape;

[0181] In this embodiment, the FFD control frame is as follows Figure 3As shown, three control sections are arranged along the span direction of the wing, namely the wing root, wing mid-section and wing tip, and eight control frames are arranged along the chord direction of the wing. The control frames at the leading edge and trailing edge of the wing are fixed, and the nodes of the six control frames between the leading edge and trailing edge of the wing are movable. The changes in the Z-axis coordinates of these movable nodes are design variables. There are six design variables above and below each span-wise control section of the wing. In this embodiment, there are a total of 36 design variables.

[0182] Step 2: Set the optimization goal and constraints, and establish a mathematical model for the optimization problem;

[0183] Specifically, the mathematical model of the optimization problem is established by selecting the aerodynamic performance parameter I to construct the optimization objective function F, and selecting the Z-axis coordinate change of the node of the FFD control frame. As the design variable, the aerodynamic performance parameters are selected as the aerodynamic constraints. The specific mathematical expression of the mathematical model of the optimization problem is as follows:

[0184]

[0185]

[0186] Where: F is the objective function of the optimization design, the aerodynamic performance parameters I include the lift coefficient, drag coefficient, and pitch moment coefficient, m is the number of aerodynamic performance parameters, and the subscript ori represents the initial value of the corresponding variable. is the weight coefficient;

[0187] In this embodiment, the design conditions are: free flow Mach number 0.8395, Reynolds number ; The optimization design target is the resistance coefficient Minimum, the optimization design variable is the Z-axis coordinate change of the 36 frame nodes obtained in step 1 , the geometric constraint is that the maximum thickness does not decrease, and the aerodynamic constraint is that the lift coefficient is fixed to The specific mathematical expression of the mathematical model of the optimization problem in this embodiment is as follows:

[0188]

[0189]

[0190] Where, 、 are the lift coefficient and the drag coefficient, respectively. is the maximum thickness of the airfoil constraint frame section after optimization, is the initial maximum thickness of the airfoil constraint frame section;

[0191] Step 3: Use the low-dissipation AUSMPWP format to perform calculations and obtain the converged flow field solution vector and aerodynamic objective function value. Based on the low-dissipation AUSMPWP format, the discrete adjoint equation and sensitivity equation are constructed and solved to obtain the gradient of the objective function with respect to the design variables in the mathematical model of the optimization problem. This specifically includes the following sub-steps:

[0192] Step 3.1: Based on the mesh obtained in step 1, a high-precision CFD solution is performed using the low-dissipation AUSMPWP format to obtain the converged flow field solution vector and aerodynamic objective function value;

[0193] Step 3.2: Based on the converged flow field solution vector, the discrete adjoint equation and sensitivity equation are constructed and solved based on the low-dissipation AUSMPWP format to obtain the gradient of the objective function with respect to the design variables; specifically:

[0194] The aerodynamic optimization problem is expressed as follows:

[0195]

[0196] in The objective function constructed for the aerodynamic performance parameters is: is the flow field conservation variable, that is, the flow field solution vector obtained in step 3.1, is the design variable, For the residual of the flow field solution, introduce the adjoint variable , transform the above formula into an unconstrained optimization problem and construct the Lagrangian function as follows:

[0197]

[0198] The discrete adjoint equation constructed based on the low-dissipation AUSMPWP format is as follows:

[0199]

[0200] The sensitivity equation constructed based on the low-dissipation AUSMPWP format is as follows, where is the spatial grid, For the surface mesh:

[0201]

[0202] In the above adjoint equation and sensitivity equation, the residual The inviscid residuals in are discretized using the AUSMPWP format;

[0203] The adjoint variable is obtained by solving the discrete adjoint equation Finally, the flow field solution vector and the adjoint variables are substituted into the sensitivity equation to obtain the gradient of the aerodynamic performance parameters with respect to the design variables.

[0204] After obtaining the gradient of each aerodynamic performance parameter with respect to the design variable, the gradient of the objective function with respect to the design variable is calculated according to the following formula:

[0205]

[0206] In this embodiment, the process of constructing the discrete adjoint equation based on the low-dissipation AUSMPWP format is:

[0207] The discrete adjoint equation is of the form:

[0208]

[0209]

[0210] Where, is the residual The inviscid residual in , is the residual The key to constructing the adjoint equation in the AUSMPWP format is how to construct the partial derivatives of the inviscid residual with respect to the conserved variables of the flow field. The specific process is as follows:

[0211] Calculate the inviscid residual In the computational grid The conservative variables of the flow field are varied in three directions, and the partial derivatives of the conservative variables of the flow field in three directions are obtained. As an example of the direction inviscid residual, the subscript for Direction grid cell number, the rest and The derivation of the inviscid residual in the direction is of the same form;

[0212]

[0213] Where, Indicates the The inviscid residual on the grid cells, Indicates the The right interface flux of each grid cell is Indicates the The left interface flux of each grid cell is represents the variation of the corresponding symbol, for example Indicates the Inviscid residual variation on grid cells, Indicates the The right interface flux variation of each grid cell is: Indicates the The left interface flux variation of each grid cell is expressed as follows:

[0214]

[0215]

[0216] in:

[0217]

[0218]

[0219]

[0220]

[0221] Where, Indicates the The original variables on the left side of the right interface of the grid unit, Indicates the The original variables on the right side of the right interface of the grid unit, Indicates the The original variables on the left side of the left interface of the grid unit, Indicates the The original variables on the right side of the left interface of each grid cell are obtained by second-order MUSCL interpolation; Indicates the The conserved variable of the flow field at the second grid cell to the left of the grid cell is, Indicates the The conserved variable of the flow field of the first grid cell to the left of the grid cell is, Indicates the The flow field conservation variables of the grid cells are: Indicates the The conservation variable of the flow field of the first grid cell to the right of the grid cell is, Indicates the The conserved variables of the flow field in the second grid cell to the right of the grid cell; represents the partial differential of the corresponding sign;

[0222] The above The right interface flux variation of each grid cell , No. The left interface flux variation of each grid cell Substitute into Directional Inviscid Residual Variation In, we get:

[0223]

[0224] Consider the The 5 template elements that contribute to the inviscid residual of the grid element are multiplied by the adjoint variable of the corresponding grid element. And summing them, we get:

[0225]

[0226] in, For the The adjoint variable of the second grid cell to the left of the grid cell The transpose of For the The adjoint variable of the first grid cell to the left of the grid cell The transpose of For the Adjoint variables of grid cells The transpose of For the The adjoint variable of the first grid cell to the right of the grid cell The transpose of For the The adjoint variable of the second grid cell to the right of the grid cell The transpose of

[0227] The inviscid residual is varied Substitute into the above formula, and combine After sorting out the items, we get:

[0228]

[0229] In order to facilitate the derivation, the partial derivatives of the conserved variables of the flow field at each interface flux are further expanded, where:

[0230] No. The surface flux at the right interface of the grid cell is The partial derivative of the flow field conservation variable of a grid cell is:

[0231]

[0232] No. The surface flux at the left interface of the grid cell is The partial derivative of the flow field conservation variable of a grid cell is:

[0233]

[0234] No. The surface flux at the left interface of the grid cell is The partial derivative of the flow field conservation variable of a grid cell is:

[0235]

[0236] No. The surface flux at the right interface of the grid cell is The partial derivative of the flow field conservation variable of a grid cell is:

[0237]

[0238] in, Indicates the The positive flux on the right interface of each grid cell is Indicates the The negative flux on the right interface of each grid cell, Indicates the The positive flux on the left interface of each grid cell is Indicates the The negative flux on the left interface of each grid cell is Indicates the The positive flux on the left interface of each grid cell is Indicates the The negative flux on the left interface of each grid cell is Indicates the The positive flux on the right interface of each grid cell is Indicates the Negative flux at the right interface of the grid cell;

[0239] Next, in the above-mentioned expansion formula of the partial derivative of the interface flux on the conservation variable of the flow field, the derivative form of the interface flux term on the original interface variable is expanded and the AUSMPWP format is introduced:

[0240] Common need , , , , , , , , , , , to expand;

[0241] Below Let’s take this as an example to explain:

[0242] First, construct the following expression to calculate the derivative of the interface sound velocity with respect to the original interface variable:

[0243]

[0244]

[0245]

[0246]

[0247]

[0248]

[0249]

[0250] in, , , In order, they are The grid and The grid interface is at , , Surface normal vectors in three directions, 、 They are the x component, y component and z component of the surface normal vector respectively; For the The grid and The total velocity on the left side of the grid interface is, For the The grid and The combined velocity on the right side of the grid interface; For the The grid and The total enthalpy on the left side of the grid interface; For the The grid and The pressure on the left side of the grid interface; is the adiabatic constant; For the The grid and The density on the left side of the grid interface; For the The grid and The arithmetic mean of the total enthalpy on both sides of the grid interface; The first definition based on the calorimetric perfect gas The grid and The interface sound velocity of the grid; The first field defined in the AUSMPWP format to improve shock wave capture capability The grid and The interface sound velocity of the grid; the final For the The grid and The partial derivative of the newly defined interface sound velocity at the grid interface with respect to the original variable of the flow field on the left side of the interface;

[0251] Then construct the following expressions to calculate the partial derivatives of the Mach number splitting function and the pressure splitting function with respect to the original interface variables:

[0252]

[0253]

[0254]

[0255]

[0256] Where, For the The grid and Mach number splitting function at the grid interface; For the The grid and Pressure splitting function at the grid interface; For the The grid and The Mach number on the left side of the grid interface, For the The grid and The Mach number on the right side of the grid interface;

[0257] Then construct the following expression to calculate the partial derivative of the pressure flux term with respect to the original interface variable:

[0258]

[0259]

[0260]

[0261]

[0262] in, For the The grid and The pressure flux at the grid interface is , In order, they are The grid and The pressure splitting function on the left and right sides of the interface at the grid interface; , are the pressures on the left and right sides of the interface respectively;

[0263] Then construct the following expression to calculate the partial derivative of the pressure-based weight coefficient with respect to the original variable:

[0264]

[0265]

[0266]

[0267]

[0268] Where, The AUSMPWP format is defined in The grid and The first weight function based on pressure at the grid interface, The AUSMPWP format is defined in The grid and The first weight function based on pressure at the grid interface; For the The grid and The function used to determine the pressure contribution on the left and right sides of the interface at the intersection of the grids;

[0269] Finally, the partial derivative of the interface velocity with respect to the original interface variable is constructed, and different treatments are performed according to the different directions of the interface velocity as follows:

[0270] Determine the velocity direction at the interface by the interface Mach number:

[0271]

[0272] in, is the interface Mach number, For the The grid and The Mach number on the left side of the grid interface is For the interface Mach number on the right;

[0273] for :

[0274]

[0275]

[0276] for :

[0277]

[0278]

[0279] Where, is the first value determined after considering the influence of the pressure weight function. The grid and The Mach number on the left side of the grid interface; is the first value determined after considering the influence of the pressure weight function. The grid and The Mach number on the right side of the grid interface; For the The grid and The Mach number splitting function on the right side of the grid interface; For the The grid and The Mach number splitting function on the left side of the grid interface;

[0280] For the The grid and The flux on the left side of the grid interface , the complete AUSMPWP format can be written as:

[0281]

[0282] Where, Indicates the The grid and The surface area of ​​the grid interface, is the transformation matrix from the curvilinear coordinate system to the Cartesian coordinate system under the structured grid;

[0283] Write the partial derivatives of the flux term with respect to the original variables of the flow field in the above complete AUSMPWP format into a matrix form, and then substitute the derivatives of the interface sound velocity with respect to the original variables of the interface, the partial derivatives of the Mach number splitting function and the pressure splitting function with respect to the original variables of the interface, the partial derivatives of the pressure flux term with respect to the original variables of the interface, the partial derivatives of the pressure-based weight coefficient with respect to the original variables, and the partial derivatives of the interface velocity with respect to the original variables of the interface into the derivative formula of the flux term with respect to the original variables of the flow field in the complete AUSMPWP format to obtain the derivative form of the flux term with respect to the original variables of the interface. :

[0284]

[0285]

[0286]

[0287]

[0288] In the above formula, 、 and are intermediate variables introduced for convenience of description, 、 In order, they are The grid and The density on both sides of the grid interface; 、 In turn, they are in the physical coordinate system, along Direction The grid and The velocities on both sides of the grid interface; 、 They are respectively in the physical coordinate system, along the y direction The grid and The velocities on both sides of the grid interface; 、 They are respectively in the physical coordinate system, along the z direction The grid and The velocities on both sides of the grid interface; 、 In order, they are The grid and The total enthalpy on both sides of the grid interface.

[0289] for and The inviscid residual in the direction is expressed with the subscript for Directional grid cell number, using subscripts for Directional grid cell number, then the subscript Replace with or , that is, we get and Derivation of the inviscid residual in the direction.

[0290] In this embodiment, the process of constructing the sensitivity equation based on the low-dissipation AUSMPWP format is specifically as follows:

[0291] The sensitivity equation is of the form:

[0292]

[0293]

[0294] In the above formula is the total derivative of the objective function with respect to the design variables, is the partial derivative of the objective function with respect to the spatial grid, is the partial derivative of the space grid with respect to the surface grid, is the partial derivative of the surface mesh with respect to the design variables, is the partial derivative of the flow field residual with respect to the spatial grid, which is the inviscid residual of the flow field and viscous residuals Partial derivatives with respect to the spatial grid are formed;

[0295] As with the discrete adjoint equation, the inviscid residual is discretized using the AUSMPWP format. The key to constructing the sensitivity equation considering the AUSMPWP format is how to construct , that is, the inviscid residual For the partial derivatives of the spatial grid, the specific process is as follows:

[0296] Calculate the inviscid residual In the computational grid The spatial grid is varied in three directions to obtain the partial derivatives of the inviscid residual with respect to the spatial grid in three directions. As an example of the direction inviscid residual, the subscript for Direction grid cell number, the rest and The derivation of the inviscid residual in the direction is of the same form;

[0297] Since the AUSMPWP format does not include mesh motion related terms, The directional inviscid residual variation is:

[0298]

[0299] Where, Indicates the The inviscid residual on the grid cells, Indicates the The right interface flux of each grid cell is Indicates the The left interface flux of each grid cell is represents the variation of the corresponding symbol, for example Indicates the Inviscid residual variation on grid cells, Indicates the The right interface flux variation of each grid cell is: Indicates the The left interface flux variation of each grid cell;

[0300] Consider the variation of the grid interface flux on the spatial grid:

[0301]

[0302]

[0303] in, In turn, they are expressed in The grid points on the right interface of the grid unit, Indicates in The surface normal vector on the right interface of the grid unit; In turn, they represent The grid points on the left interface of the grid unit, Indicates in The surface normal vector on the left interface of the grid cell;

[0304] The above 、 Substitute into In the residual variation in the direction space, we get:

[0305]

[0306] The key to the above formula is how to obtain the partial derivative of the flux term with respect to the surface normal in the AUSMPWP format. Directional Let's take this as an example:

[0307] In structured grids, , 、 They are the x-component, y-component and z-component of the surface normal vector respectively;

[0308] First, construct the following expression to calculate the derivative of the sound velocity at the interface with respect to the surface normal:

[0309]

[0310]

[0311]

[0312]

[0313]

[0314] In the above formula, is the Hamiltonian operator, For the The grid and The surface normal vector in space at the interface of the grids; For the The grid and The total velocity on the left and right sides of the grid interface; For the The grid and The total enthalpy of the space on both sides of the grid interface; The first definition based on the calorimetric perfect gas The grid and The interface sound speed on the grid space; The first field defined in the AUSMPWP format to improve shock wave capture capability The grid and The interface sound speed on the grid space; the final For the The grid and The partial derivative of the interface sound velocity with respect to the surface normal vector in the newly defined space at the interface of the grids;

[0315] Then construct the following expressions to calculate the surface normal partial derivatives of the Mach number splitting function and the pressure splitting function:

[0316]

[0317]

[0318] in

[0319]

[0320] Where, For the The grid and Mach number splitting function in space at the interface of the grids; For the The grid and The pressure splitting function in the space at the interface of the grids; For the The grid and The Mach number in the space to the left of the grid interface.

[0321] Then construct the following expression to calculate the surface normal partial derivative of the interface pressure flux term:

[0322]

[0323] In the process of constructing the sensitivity equation, the calculation of the pressure weight coefficient does not require surface normal information, and the partial derivative of the pressure weight coefficient with respect to the surface normal is taken as 0;

[0324] Finally, the partial derivative of the interface velocity with respect to the interface normal is constructed, and different treatments are performed according to the different directions of the interface velocity as follows:

[0325] Determine the velocity direction at the interface by the interface Mach number:

[0326]

[0327] in, is the interface Mach number in space, For the The grid and The left Mach number in space at the grid interface is, For the The grid and The Mach number on the right side of the space at the grid interface;

[0328] for :

[0329]

[0330]

[0331] for :

[0332]

[0333]

[0334] Where, is the first value determined after considering the influence of the pressure weight function. The grid and The Mach number in the space to the left of the grid interface; is the first value determined after considering the influence of the pressure weight function. The grid and The Mach number in the space to the right of the grid interface; For the The grid and The Mach number splitting function in the space to the right of the grid interface; For the The grid and The Mach number splitting function in the space to the left of the grid interface;

[0335] Write the partial derivative of the flux term with respect to the normal vector into a matrix form, and then substitute the derivative of the interface sound velocity with respect to the normal direction, the partial derivative of the Mach number splitting function and the pressure splitting function with respect to the normal direction, the partial derivative of the interface pressure flux term with respect to the normal direction, the partial derivative of the pressure-based weight coefficient with respect to the normal direction, and the partial derivative of the interface velocity with respect to the normal direction into the partial derivative of the flux term with respect to the normal direction, and obtain the partial derivative of the inviscid residual with respect to the normal direction based on the AUSMPWP format as follows:

[0336]

[0337] In the above formula 、 In order, they are The grid and The density of the space on the left and right sides of the grid interface; 、 In turn, they are in the physical coordinate system, along Direction The grid and The velocity in the space on the left and right sides of the grid interface; 、 They are respectively in the physical coordinate system, along the y direction The grid and The velocity in the space on the left and right sides of the grid interface; 、 They are respectively in the physical coordinate system, along the z direction The grid and The velocity in the space on the left and right sides of the grid interface; 、 In order, they are The grid and The total enthalpy in the space on both sides of the grid interface.

[0338] Step 4: Use the sequential quadratic programming optimization algorithm to optimize and solve the optimization problem in step 2 to achieve the low dissipation adjoint optimization design of the aircraft;

[0339] Specifically: the optimization objective function and its corresponding gradient are fed back to the optimization algorithm to determine whether the optimization convergence criterion is met. If the optimization convergence criterion is not met, the optimization algorithm will calculate the search direction and step size, obtain new design variables, and obtain a new shape through FFD parameterization. Return to step 3 for the next round of optimization iteration, and repeat this cycle until the optimization iteration converges, and finally obtain the optimized aircraft shape and aerodynamic data.

[0340] In this embodiment, the optimized wing shape is as follows: Figure 4 As shown, in order to prove the design accuracy of the method of the present invention, the discrete adjoint optimization based on the traditional upwind VanLeer format is used as a control, and the resistance convergence process is shown in Figure 5 As shown in the figure, it can be seen that after 15 generations of optimization iterations, the drag coefficient of the method of the present invention has basically converged, but there is still a downward trend, which proves that the optimization design efficiency of the method of the present invention is high; the drag coefficient in the initial state of the adjoint optimization design method based on the low dissipation format of the present invention is , when the optimization of the method of the present invention is completed , the resistance is reduced by 28.1 counts; in contrast, the initial resistance coefficient of the adjoint optimization design method based on the VanLeer format is , when the optimization is finished , drag was reduced by 25.5 counts, demonstrating the high precision of the optimization design method of the present invention. Therefore, the optimization design using a low-dissipation format can effectively improve optimization efficiency and drag reduction space. The optimization results of this example show that the optimization design system proposed in this invention has great engineering application potential in typical wing optimization design.

[0341] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A method for aircraft adjoint optimization design based on a low dissipation format, characterized by: The following steps are involved: Step 1: Given the initial shape of the aircraft to be optimized, generate the CFD calculation mesh of the initial shape; The aircraft is parameterized based on the initial shape to obtain design variables; Step 2: Set the optimization goal and constraints, and establish a mathematical model for the optimization problem; Step 3: Use the low-dissipation AUSMPWP format to perform CFD calculations to obtain the converged flow field solution vector and objective function value; Based on the low-dissipation AUSMPWP format, the discrete adjoint equation and sensitivity equation are constructed and solved to obtain the gradient of the objective function with respect to the design variables in the mathematical model of the optimization problem. It includes the following sub-steps: Step 3.1: Based on the CFD computational grid, use the low-dissipation AUSMPWP format to perform CFD calculations and obtain the converged flow field solution vector and objective function value; Step 3.2: Based on the obtained converged flow field solution vector, the discrete adjoint equation and sensitivity equation are constructed and solved based on the low-dissipation AUSMPWP format to obtain the gradient of the objective function with respect to the design variables; specifically: The mathematical model of the optimization problem is expressed as follows: in The objective function constructed for the aerodynamic performance parameters is: is the flow field conservation variable, that is, the flow field solution vector obtained in step 3.1, is the design variable, For the residual of the flow field solution, introduce the adjoint variable , transform the mathematical model of the optimization problem into an unconstrained optimization problem and construct the Lagrangian function as follows: in Represents the accompanying variable The transpose of The discrete adjoint equation constructed based on the low-dissipation AUSMPWP format is as follows: The sensitivity equation constructed based on the low-dissipation AUSMPWP format is as follows, where is the spatial grid, For the surface mesh: In the adjoint and sensitivity equations, the residual The inviscid residuals in are discretized using the AUSMPWP format; The adjoint variable is obtained by solving the discrete adjoint equation Finally, the flow field solution vector and the adjoint variables are substituted into the sensitivity equation to obtain the gradient of the aerodynamic performance parameters with respect to the design variables. After obtaining the gradient of the aerodynamic performance parameters with respect to the design variables, the gradient of the objective function with respect to the design variables is calculated according to the following formula: in is the number of aerodynamic performance parameters, For the aerodynamic performance parameters, For the The weight coefficient of each aerodynamic performance parameter; Step 4: Based on the objective function value obtained in step 3 and the gradient of the design variables, the sequential quadratic programming optimization algorithm is used to optimize and solve the optimization problem in step 2 to achieve the adjoint optimization design of low dissipation of the aircraft.

2. The method for aircraft companion optimization design based on a low dissipation format according to claim 1, characterized in that: The specific process of parameterizing the aircraft based on the initial shape in step 1 is as follows: For the given initial shape of the aircraft that needs to be optimized, the free deformation method is used to parameterize the geometric shape: an FFD control frame is established around the area to be deformed of the initial shape of the aircraft, and the Z coordinate of the node controlled by the FFD control frame is set to The amount of change As the design variable, where the subscript Indicates the control nodes, , The number of nodes of the FFD box is controlled. By changing the design variables, deformation perturbations are applied to the surface mesh to achieve deformation of the initial shape and obtain the surface mesh of the new shape. Then, the inverse distance weighted interpolation mesh deformation method is used to interpolate and deform the spatial mesh based on the surface mesh of the new shape to obtain the CFD calculation mesh of the new shape.

3. The method for aircraft companion optimization design based on a low dissipation format according to claim 1, characterized in that: The process of establishing the mathematical model of the optimization problem in step 2 is as follows: select aerodynamic performance parameters to construct the objective function; select the Z-axis coordinate change of the control node of the FFD control frame As the design variable; the aerodynamic performance parameters of the optimized aircraft do not deteriorate compared with the aerodynamic performance parameters of the initial shape of the aircraft as the aerodynamic constraint.

4. The method for aircraft companion optimization design based on a low dissipation format according to claim 1, characterized in that: The process of constructing the discrete adjoint equation based on the low-dissipation AUSMPWP format is as follows: The discrete adjoint equation is of the form: Where, is the residual The inviscid residual in , is the residual The viscous residual in ; the low dissipation AUSMPWP format is used to construct the inviscid residual Conserved variables of the convection field The partial derivative of The process is as follows: Calculate the inviscid residual In the computational grid The conserved variables of the flow field are varied in three directions to obtain the partial derivatives of the inviscid residual with respect to the conserved variables of the flow field in three directions; The derivation process of the partial derivative of the inviscid residual on the conservation variable of the flow field in a certain direction is as follows: Establishing inviscid residual variation expression: Where, Indicates the The inviscid residual on the grid cells, Indicates the The right interface flux of each grid cell is Indicates the The left interface flux of each grid cell is represents the variation of the corresponding sign, Indicates the Inviscid residual variation on grid cells, Indicates the The right interface flux variation of each grid cell is: Indicates the The left interface flux variation of each grid cell is expressed as follows: in: Where, Indicates the The original variables on the left side of the right interface of the grid unit, Indicates the The original variables on the right side of the right interface of the grid unit, Indicates the The original variables on the left side of the left interface of the grid unit, Indicates the The original variables on the right side of the left interface of each grid unit; Indicates the The conserved variable of the flow field at the second grid cell to the left of the grid cell is, Indicates the The conserved variable of the flow field of the first grid cell to the left of the grid cell is, Indicates the The flow field conservation variables of the grid cells are: Indicates the The conservation variable of the flow field of the first grid cell to the right of the grid cell is, Indicates the The conserved variables of the flow field in the second grid cell to the right of the grid cell; represents the partial differential of the corresponding sign; The first The right interface flux variation of each grid cell , No. The left interface flux variation of each grid cell Substitute into the inviscid residual variation In, we get: Multiply the above formula by the adjoint variable of the corresponding grid cell And summing them, we get: in, For the The adjoint variable of the second grid cell to the left of the grid cell The transpose of For the The adjoint variable of the first grid cell to the left of the grid cell The transpose of For the Adjoint variables of grid cells The transpose of For the The adjoint variable of the first grid cell to the right of the grid cell The transpose of For the The adjoint variable of the second grid cell to the right of the grid cell The transpose of The inviscid residual is varied Substitute into the above formula, and combine After sorting out the items, we get: Further expanding the partial derivatives of the conserved variables of the flow field at each interface flux, we obtain: No. The surface flux at the right interface of the grid cell is The partial derivative of the flow field conservation variable of a grid cell is: No. The surface flux at the left interface of the grid cell is The partial derivative of the flow field conservation variable of a grid cell is: No. The surface flux at the left interface of the grid cell is The partial derivative of the flow field conservation variable of a grid cell is: No. The surface flux at the right interface of the grid cell is The partial derivative of the flow field conservation variable of a grid cell is: in, Indicates the The positive flux on the right interface of each grid cell is Indicates the The negative flux on the right interface of the grid cell is Indicates the The positive flux on the left interface of each grid cell is Indicates the The negative flux on the left interface of each grid cell, Indicates the The positive flux on the left interface of each grid cell is Indicates the The negative flux on the left interface of each grid cell, Indicates the The positive flux on the right interface of each grid cell is Indicates the Negative flux at the right interface of the grid cell; In the expansion formula of partial derivatives of the interface flux on the conservation variable of the flow field, the AUSMPWP format is introduced to convert the derivative form of each interface flux to the original interface variable , , , , , , , , , , , to expand; Among them for The expansion process is: First, construct the following expression to calculate the derivative of the interface sound velocity with respect to the original interface variable: in, , , In order, they are The grid and The grid interface is at , , Surface normal vectors in three directions, 、 They are the x component, y component and z component of the surface normal vector respectively; For the The grid and The total velocity on the left side of the grid interface is For the The grid and The combined velocity on the right side of the grid interface; For the The grid and The total enthalpy on the left side of the grid interface; For the The grid and The pressure on the left side of the grid interface; is the adiabatic constant; For the The grid and The density on the left side of the grid interface; For the The grid and The arithmetic mean of the total enthalpy on both sides of the grid interface; The first definition based on the calorimetric perfect gas The grid and The interface sound velocity of the grid; The first field defined in the AUSMPWP format to improve shock wave capture capability The grid and The interface sound velocity of the grid; the final For the The grid and The partial derivative of the newly defined interface sound velocity at the grid interface with respect to the original variable of the flow field on the left side of the interface; Then construct the following expressions to calculate the partial derivatives of the Mach number splitting function and the pressure splitting function with respect to the original interface variables: Where, For the The grid and Mach number splitting function at the grid interface; For the The grid and Pressure splitting function at the interface of the grids; For the The grid and The Mach number on the left side of the grid interface, For the The grid and The Mach number on the right side of the grid interface; Then construct the following expression to calculate the partial derivative of the pressure flux term with respect to the original interface variable: in, For the The grid and The pressure flux at the grid interface is , In order, they are The grid and The pressure splitting function on the left and right sides of the interface at the grid interface; , are the pressures on the left and right sides of the interface respectively; Then construct the following expression to calculate the partial derivative of the pressure-based weight coefficient with respect to the original variable: Where, The AUSMPWP format is defined in The grid and The first weight function based on pressure at the grid interface, The AUSMPWP format is defined in The grid and The first weight function based on pressure at the grid interface; For the The grid and The function used to determine the pressure contribution on the left and right sides of the interface at the intersection of the grids; Finally, the partial derivative of the interface velocity with respect to the original interface variable is constructed, and different treatments are performed according to the different directions of the interface velocity as follows: Determine the velocity direction at the interface by the interface Mach number: in, is the interface Mach number, For the The grid and The Mach number on the left side of the grid interface is For the The grid and The Mach number on the right side of the grid interface; for : for : Where, is the first value determined after considering the influence of the pressure weight function. The grid and The Mach number on the left side of the grid interface; is the first value determined after considering the influence of the pressure weight function. The grid and The Mach number on the right side of the grid interface; For the The grid and The Mach number splitting function on the right side of the grid interface; For the The grid and The Mach number splitting function on the left side of the grid interface; For the The grid and The flux on the left side of the grid interface , the complete AUSMPWP format can be written as: Where, Indicates the The grid and The surface area of ​​the grid interface, is the transformation matrix from the curvilinear coordinate system to the Cartesian coordinate system under the structured grid; The partial derivatives of the flux term with respect to the original variables of the flow field under the complete AUSMPWP format are written in matrix form, and then the derived derivatives of the interface sound velocity with respect to the original variables of the interface, the partial derivatives of the Mach number splitting function and the pressure splitting function with respect to the original variables of the interface, the partial derivatives of the pressure flux term with respect to the original variables of the interface, the partial derivatives of the pressure-based weight coefficient with respect to the original variables, and the partial derivatives of the interface velocity with respect to the original variables of the interface are substituted into the derivative formula of the flux term with respect to the original variables of the flow field under the complete AUSMPWP format to obtain the derivative form of the flux term with respect to the original variables of the interface. : In the above formula, 、 and are intermediate variables introduced for convenience of description, 、 In order, they are The grid and The density on both sides of the grid interface; 、 In turn, they are in the physical coordinate system, along Direction The grid and The velocities on both sides of the grid interface; 、 They are respectively in the physical coordinate system, along the y direction The grid and The velocities on both sides of the grid interface; 、 They are respectively in the physical coordinate system, along the z direction The grid and The velocities on both sides of the grid interface; 、 In order, they are The grid and The total enthalpy on both sides of the grid interface.

5. The method for aircraft adjoint optimization design based on a low dissipation format according to claim 1, characterized in that: The specific process of constructing the sensitivity equation based on the low-dissipation AUSMPWP format is as follows: The sensitivity equation is of the form: In the above formula is the total derivative of the objective function with respect to the design variables, is the partial derivative of the objective function with respect to the spatial grid, is the partial derivative of the space grid with respect to the surface grid, is the partial derivative of the surface mesh with respect to the design variables, is the partial derivative of the flow field residual with respect to the spatial grid, which is the inviscid residual of the flow field and viscous residuals Partial derivatives with respect to the spatial grid are formed; Constructing inviscid residuals using the low-dissipation AUSMPWP scheme Space Grid The partial derivative of The specific process is as follows: Calculate the inviscid residual In the computational grid The spatial grid is varied in three directions to obtain the partial derivatives of the inviscid residual with respect to the spatial grid in three directions; The derivation process of the partial derivative of the inviscid residual with respect to the spatial grid in a certain direction is as follows: Establishing the inviscid residual variation in space expression: Where, Indicates the The inviscid residual in the grid cell space is Indicates the The right interface flux on the grid cell space is Indicates the The left interface flux on the grid cell space is represents the variation of the corresponding sign, Indicates the The inviscid residual variation in the grid cell space, Indicates the The right interface flux variation on the grid cell space is: Indicates the The left interface flux variation on the grid cell space; Considering the grid interface flux variation on the spatial grid, we get in, In turn, they are expressed in The grid points on the right interface of the grid unit, Indicates in The surface normal vector on the right interface of the grid unit; In turn, they represent The grid points on the left interface of the grid unit, Indicates in The surface normal vector on the left interface of the grid cell; Will 、 Substitute into the inviscid residual variation on space In the expression, we get: in The expansion process is: In structured grids, , 、 They are the x component, y component and z component of the surface normal vector respectively; First, construct the following expression to calculate the derivative of the interface sound velocity in space with respect to the surface normal: In the above formula, is the Hamiltonian operator, For the The grid and The surface normal vector in space at the interface of the grids; For the The grid and The total velocity on the left and right sides of the grid interface; For the The grid and The total enthalpy of the space on both sides of the grid interface; The first definition based on the calorimetric perfect gas The grid and The interface sound speed on the grid space; The first field defined in the AUSMPWP format to improve shock wave capture capability The grid and The interface sound speed on the grid space; the final For the The grid and The partial derivative of the interface sound velocity with respect to the surface normal vector in the newly defined space at the interface of the grids; Then construct the following expressions to calculate the surface normal partial derivatives of the Mach number splitting function and the pressure splitting function: in Where, For the The grid and Mach number splitting function in space at the interface of the grids; For the The grid and The pressure splitting function in the space at the interface of the grids; For the The grid and The Mach number in the space to the left of the grid interface; Then construct the following expression to calculate the surface normal partial derivative of the interface pressure flux term: In the process of constructing the sensitivity equation, the calculation of the pressure weight coefficient does not require surface normal information, and the partial derivative of the pressure weight coefficient with respect to the surface normal is taken as 0; Finally, construct the partial derivative of the interface velocity with respect to the interface normal: Determine the velocity direction at the interface by the interface Mach number: in, is the interface Mach number in space, For the The grid and The left Mach number in space at the grid interface is, For the The grid and The Mach number on the right side of the space at the grid interface; for : for : Where, is the first value determined after considering the influence of the pressure weight function. The grid and The Mach number in the space to the left of the grid interface; is the first value determined after considering the influence of the pressure weight function. The grid and The Mach number in the space to the right of the grid interface; For the The grid and The Mach number splitting function in the space to the right of the grid interface; For the The grid and The Mach number splitting function in the space to the left of the grid interface; Write the partial derivative of the flux term with respect to the normal vector into a matrix form, and then substitute the derivative of the interface sound velocity with respect to the normal direction, the partial derivative of the Mach number splitting function and the pressure splitting function with respect to the normal direction, the partial derivative of the interface pressure flux term with respect to the normal direction, the partial derivative of the pressure-based weight coefficient with respect to the normal direction, and the partial derivative of the interface velocity with respect to the normal direction into the partial derivative of the flux term with respect to the normal direction, and obtain the partial derivative of the inviscid residual with respect to the normal direction based on the AUSMPWP format as follows: In the above formula 、 In order, they are The grid and The density of the space on the left and right sides of the grid interface; 、 In turn, they are in the physical coordinate system, along Direction The grid and The velocity in the space on the left and right sides of the grid interface; 、 They are respectively in the physical coordinate system, along the y direction The grid and The velocity in the space on the left and right sides of the grid interface; 、 They are respectively in the physical coordinate system, along the z direction The grid and The velocity in the space on the left and right sides of the grid interface; 、 In order, they are The grid and The total enthalpy in the space on both sides of the grid interface.

6. The method for aircraft adjoint optimization design based on a low dissipation format according to claim 1, characterized in that: The optimization solution process in step 4 is specifically to feed back the optimization objective function value and its corresponding gradient to the optimization algorithm to determine whether the optimization convergence criteria are met. If the optimization convergence criteria are not met, the optimization algorithm will calculate the search direction and step size, obtain new design variables, and obtain a new shape through FFD parameterization, and return to step 3 for the next round of optimization iteration. This cycle continues until the optimization iteration converges, and finally the optimized aircraft shape and aerodynamic data are obtained.

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