Design method and family of thin airfoils with wide speed range and wide frequency band for wing-body fusion layout

Abstract

The present invention proposes a design method for a wide-speed-range, wide-frequency-band thin airfoil of a wing-body fusion layout and an airfoil family. The method is based on the analysis of the three-dimensional flow characteristics of the wing-body fusion layout, selects typical sub-, trans- and supersonic Mach number design points, balances the contradiction between induced drag and wave drag at different Mach numbers, and selects multi-band set frequency points as low-detectability design points for the wide-frequency-band low-detectability design of the wing-body fusion layout; uses an optimization design method combining low-dimensional large-scale and high-dimensional small-scale to search the design space, and realizes a multi-disciplinary efficient design of a wing-body fusion layout airfoil with aerodynamic and low-detectability; selects optimized sections by region for the wing, and uses a multi-frame orthogonal overlapping FFD method based on the optimized section for parameterization, introduces orthogonal control frames of different densities to realize refined hierarchical control of the optimized section airfoil, avoids the problem of inconsistent physical scale deformation at the leading and trailing edges of the wing, and takes into account the local refined design.

Description

Technical Field

[0001] The present invention relates to the technical field of airfoil design, and in particular to a design method and an airfoil family of a wide-speed-range, wide-frequency-band thin airfoil in a wing-body fusion layout. Background Art

[0002] Wide-speed range aircraft need to have better maneuverability, larger flight radius, and higher low-detection performance. At the same time, the detection equipment they face will cover a wide frequency range from P-band to Ka-band. In order to achieve the above-mentioned capability requirements of wide-speed range aircraft, the aerodynamic layout needs to further comprehensively consider professional design requirements such as low-detection, and on the other hand, it needs to improve the aerodynamic efficiency of the platform under multiple design points as much as possible.

[0003] In order to take into account the flight requirements in the sub-, trans- and supersonic ranges, wide-speed range aircraft have gradually shifted from the traditional fuselage, wing and tail configuration to a wing-body integrated tailless layout. The wing and fuselage are highly integrated, and generally use thin wings with a small aspect ratio and a large sweep angle to reduce resistance during supersonic flight. In order to take into account the design requirements of multiple aerodynamic design points and multiple low detectability design points, the design of a wide-speed range and wide-frequency band thin airfoil with a wing-body fusion layout will face the following severe challenges: 1) The three-dimensional flow effect of a wing with a small aspect ratio and a large sweep angle is obvious. The pressure distribution of a three-dimensional wing is distorted compared to a two-dimensional airfoil. The traditional design method mainly considers the wing plan shape, bending and twisting, and thickness distribution, while ignoring the refined design of the airfoil; 2) Aerodynamic design needs to take into account multiple speed domains, including sub-, trans- and supersonic speeds. The optimal aerodynamic shapes that adapt to different speed domains are contradictory, making it challenging to achieve a good wide-speed range aerodynamic design. Improving low-speed lift, reducing high-speed drag, and increasing the drag divergence Mach number are issues that need to be addressed urgently; 3) Low detectability design is gradually developing towards full-frequency and omnidirectional low detectability. It is necessary to explore the geometric characteristics of low detectability shapes in different frequency bands, and at the same time combine it with aerodynamic design to develop an efficient, high-precision, integrated and refined design method for aerodynamics and low detectability.

[0004] The design of thin airfoils in a wide speed range and wide frequency band of a wing-body fusion layout is a complex engineering problem. Its shape optimization design space is complex. It is necessary to select an appropriate design method according to the characteristics of the design problem, and at the same time, it is necessary to consider the multidisciplinary characteristics of aerodynamics and low detectability. For the aerodynamic design of a wing-body fusion layout with a wide speed range, the key is to compromise between transonic induced drag and supersonic wave drag. The difficulty lies in balancing the contradiction between induced drag and wave drag at different Mach numbers. If the aerodynamic design point is not representative, it may cause the designed airfoil to have good aerodynamic characteristics only in a single speed range, while the aerodynamic characteristics in other speed ranges remain unchanged or even decrease; for the low detectability design of a wing-body fusion layout with a wide frequency band, the key is to select the low detectability shape design space and coordinate the contradictions of the scattering reduction mechanism in different frequency bands. The difficulty lies in exploring the characteristics of the reduction of the scattering cross-sectional area in each frequency band and developing a low detectability optimization design method suitable for wide-band airfoils. At the same time, the multidisciplinary integrated design of aerodynamics and low-detectability requires sufficient deformation range to meet the requirements of proxy optimization, but the coupling of disciplinary characteristics leads to an increase in the nonlinearity of the target space and the number of local extreme values. The large-scale design space will further increase the complexity of the target space, requiring more samples to improve the fitting accuracy of the proxy model, which brings difficulties to the optimization of the proxy model; there are often multiple local extreme value solutions in the design space. If a small-scale design space is selected in the early stage of design, it may mislead the algorithm to fall into the local optimum too early, making it difficult to converge to the global optimal solution. In addition, in order to pursue supersonic cruise and maneuverability, the wing-body fusion layout adopts a thin wing design with a larger sweep angle and a smaller relative thickness. It has the characteristics of a sharp leading edge, a small relative thickness and relative curvature, and a maximum thickness point at the rear. As a result, when designing the profile shape parameterization, the deformation modeling technology FFD (Free Form Deformation) method is prone to inconsistent physical deformation scales, and the shape caused by the disturbance of the control points of the non-orthogonal control frame will cause the local surface transition to be not smooth. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention proposes a method for designing a thin airfoil in a wing-body fusion layout with a wide speed range and wide frequency band, and an airfoil family designed by using the method. This method is based on the analysis of the three-dimensional flow characteristics of the wing-body fusion layout. For the aerodynamic design of the wing-body fusion layout in a wide speed range, typical sub-, trans- and supersonic Mach number design points are selected to balance the contradiction between induced drag and wave drag at different Mach numbers. For the low-detectability design of the wing-body fusion layout in a wide frequency band, the scattering characteristics of the aircraft in the optical zone and the radar scattering cross-sectional area reduction mechanism are analyzed, and typical L-band, S-band, C-band and X-band set frequency points are selected as low-detectability design points; the optimization design method combining low-dimensional large scale and high-dimensional small scale is used to search the complex multi-peak design space to realize the aerodynamic and low-detectability multidisciplinary efficient design of the wing-body fusion layout airfoil, improve the aerodynamic and low-detectability comprehensive performance of the final shape, and improve the optimization efficiency; the wing is divided into regions to select the optimized section, and the multi-frame orthogonal overlapping FFD method is used for parameterization based on the optimized section. Orthogonal control frames with different densities are introduced to realize the refined layered control of the optimized section airfoil, avoid the physical scale deformation inconsistency problem at the leading and trailing edges of the wing, and take into account the local refined design.

[0006] The technical solution of the present invention is:

[0007] The method for designing a wide-speed, wide-frequency-band thin airfoil in a wing-body fusion layout comprises the following steps:

[0008] Step 1: Select the initial airfoil, construct the original configuration of the wing-body fusion layout, generate the aerodynamic calculation grid, and determine the optimized design state;

[0009] Step 2: For the original configuration, determine several optimized sections, arrange multiple orthogonal overlapping FFD control frames according to the optimized sections, and arrange design variables for the single-sided wing of the wing-body fusion layout;

[0010] Step 3: Establish a mathematical model for low-dimensional large-scale optimization problems: Determine the optimization goal to reduce the drag coefficient at subsonic, transonic and supersonic speeds, and reduce the scattering cross-sectional area of ​​the optimized configuration in the L band, S band, C band and X band; Select the change in the Z coordinate of the node of the FFD control box As the design variable; the lift coefficient under the design state is selected to be equal to the set value as the aerodynamic constraint, and the maximum thickness of the optimized airfoil at the optimized section is not less than the maximum thickness of the initial airfoil;

[0011] Step 4: For the low-dimensional large-scale optimization problem established in step 3, a multi-objective optimization method based on a proxy model is used to optimize the parameters and obtain the Pareto frontier of low-dimensional large-scale proxy optimization;

[0012] Step 5: Extract the optimized configuration with the best supersonic performance from the Pareto front obtained in step 4 as the new initial configuration, determine several optimized sections again, arrange multiple orthogonal overlapping FFD control frames according to the optimized sections, and refine the design variables of the single-sided wing layout of the wing-body fusion layout; establish a mathematical model for the local section parameter optimization problem, and use the optimization algorithm based on the adjoint gradient for optimization design to obtain the final configuration of the wing-body fusion layout and a wide-speed domain and wide-frequency band airfoil family composed of airfoils at each optimized section.

[0013] Furthermore, in step 2, optimized sections are selected at three positions: wing root, wing center, and wing tip of a single wing in a wing-body fusion layout, wherein the optimized section at the wing center is located at 50% of the wing span.

[0014] Furthermore, in step 2, the specific process of arranging multiple orthogonal overlapping FFD control frames according to the optimized profile and designing the variables of the single-sided wing arrangement of the wing-body fusion layout is as follows:

[0015] Arrange the FFD control frame along the wing span according to the selected optimized section, arrange the orthogonal FFD control frame along the wing chord according to three different densities: sparse, sub-dense, and fine, and then merge the orthogonal FFD frames of the three densities to form a multi-frame orthogonal overlapping FFD control frame;

[0016] The Z coordinates of the nodes of the multi-frame orthogonal overlapping FFD control frame at the optimized section The amount of change As a design variable, , where the subscript i represents the i-th control node, and n is the sum of the number of nodes of the FFD control boxes of all optimized sections.

[0017] Furthermore, in step 2, in the sparse control frame, each optimized section has 2 design variables, and a total of 6 design variables are used to parameterize the single wing; in the sub-dense control frame, each optimized section has 4 design variables, and a total of 12 design variables are used to parameterize the single wing; in the dense control frame, each optimized section has 10 design variables, and a total of 30 design variables are used to parameterize the single wing; then the total number of design variables after merging into a multi-frame orthogonal overlapping FFD control frame is 48.

[0018] Furthermore, in step 3, the mathematical model of the low-dimensional large-scale optimization problem is

[0019]

[0020] in:

[0021]

[0022] Indicates the drag coefficient of the original configuration in subsonic cruise state, represents the drag coefficient of the original configuration in transonic cruise state, represents the drag coefficient of the original configuration in supersonic cruise state, Indicates the drag coefficient of the optimized configuration in subsonic cruise state, represents the drag coefficient of the optimized configuration in transonic cruise state, It represents the drag coefficient of the optimized configuration in supersonic cruise state; represents the scattering cross-sectional area of ​​the original configuration at the set frequency point in the L band, represents the scattering cross-sectional area of ​​the original configuration at the set frequency point in the S band, It represents the scattering cross-sectional area of ​​the original configuration at the set frequency point in the C band. represents the scattering cross-sectional area of ​​the original configuration at the set frequency point in the X-band, It represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the L band. It represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the S band. It represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the C band. It represents the scattering cross-section of the optimized configuration at the set frequency point in the X-band; represents the maximum thickness of the airfoil at the kth optimized section in the original configuration, represents the maximum thickness of the airfoil at the kth optimized section in the optimized configuration; They represent the optimization objective functions, respectively, which correspond to reducing the drag coefficient at sub-, trans- and supersonic speeds.

[0023] Furthermore, the specific process of step 4 is as follows: in the set design space, the Latin hypercube sampling method is used to sample the airfoil design variables at the optimized section to obtain samples; the RBF-TFI method is used to deform and generate the aerodynamic and RCS calculation grids of the samples; the aerodynamic and RCS calculation grids of the samples are used to perform CFD calculations and RCS calculations on the samples under the optimized design state determined in step 1 to obtain the aerodynamic and RCS data of the samples; based on the aerodynamic and RCS data of the samples, a Kriging proxy model is established; based on the Kriging proxy model, a multi-objective optimization algorithm is used to optimize and solve the optimization mathematical model established in step 3 until convergence, and the Pareto frontier of low-dimensional large-scale proxy parameter optimization is obtained.

[0024] Furthermore, the specific process of step 5 is as follows:

[0025] Step 5.1: extracting the optimized configuration with the best supersonic performance from the Pareto front obtained in step 4 as a new initial configuration, and generating an aerodynamic calculation grid of the initial configuration using ANSYS ICEM;

[0026] Step 5.2: Based on the initial configuration obtained in step 5.1, three optimized sections of the wing root, wing mid-wing, and wing tip are determined, and parameterization is performed using multi-frame orthogonal overlapping FFD to determine the design variables for local section parameter optimization, where the number of design variables is greater than the number of design variables in step 2;

[0027] Step 5.3: Establish a mathematical model for the local profile parameter optimization problem. The specific mathematical expression is as follows:

[0028]

[0029] Where f represents the optimization objective function; represents the drag coefficient in subsonic cruise state with optimized configuration, represents the drag coefficient in the transonic cruise state with optimized configuration, represents the drag coefficient in supersonic cruise state with optimized configuration; represents the scattering cross-sectional area of ​​the initial configuration at the set frequency point in the L band, represents the scattering cross-sectional area of ​​the initial configuration at the set frequency point in the S band, represents the scattering cross-sectional area of ​​the initial configuration at the set frequency point in the C band, It represents the scattering cross-section of the initial configuration at the set frequency point in the X-band; represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the L band, represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the S band, It represents the scattering cross-section area of ​​the optimized configuration at the set frequency point in the C band. It represents the scattering cross-section area of ​​the optimized configuration at the set frequency point in the X-band; represents the maximum thickness of the airfoil at the kth optimized section in the initial configuration, represents the maximum thickness of the airfoil at the kth optimized section in the adjoint optimized configuration; represents weight;

[0030] Step 5.4: For the adjoint optimized configuration, the flow field is calculated based on the RANS equations, and the multilayer fast multipole method is used to solve the Maxwell equations for electromagnetic field calculation, and the result is , , , , , , , and perform weighted coupling to obtain the value of the objective function f;

[0031] Step 5.5: Construct and solve the flow field discrete adjoint equation according to the flow field solution vector to obtain the aerodynamic target , , Gradient of the design variable; construct and solve the electromagnetic discrete adjoint equation to obtain the gradient of the low detectability target with respect to the design variable; superimpose the gradient of the aerodynamic target with respect to the design variable and the gradient of the low detectability target with respect to the design variable to obtain the gradient of the objective function f with respect to the design variable;

[0032] Step 5.6: Feed the objective function value obtained in step 5.4 and the gradient of the objective function with respect to the design variables obtained in step 5.5 back to the SQP optimization algorithm to determine whether the optimization convergence criteria are met. If the optimization convergence criteria are not met, calculate the search direction and step size through the SQP optimization algorithm, obtain new design variables, update the accompanying optimization configuration, and go to step 5.4 for the next round of optimization iteration. Repeat this cycle until the optimization iteration converges, and finally obtain the optimized wing-body fusion layout shape.

[0033] Furthermore, in step 5.2, in the sparse control frame, each optimized section has 8 design variables, and a total of 24 design variables are used to parameterize the single wing; in the sub-dense control frame, each optimized section has 16 design variables, and a total of 48 design variables are used to parameterize the single wing; in the dense control frame, each optimized section has 30 design variables, and a total of 90 design variables are used to parameterize the single wing; then the total number of design variables after merging into a multi-frame orthogonal overlapping FFD control frame is 162.

[0034] Furthermore, the design state is subsonic flight Ma=0.80, transonic flight Ma=0.90, and supersonic flight Ma=1.50; the airfoil family includes airfoils at three optimized sections: wing root, wing mid-wing, and wing tip, which are described using the CST method:

[0035]

[0036] Where y represents the ordinate corresponding to the upper or lower surface of the airfoil, x represents the abscissa corresponding to the upper or lower surface of the airfoil, and A i represents the fitting coefficient, n represents the order of the CST parameterization method, n=7, y tail represents the y coordinate of the step at the trailing edge of the airfoil;

[0037] The parameters of the upper surface of the wing root airfoil obtained by fitting are:

[0038]

[0039] The parameters of the lower surface of the wing root airfoil obtained by fitting are:

[0040]

[0041] The parameters of the upper surface of the mid-wing airfoil obtained by fitting are:

[0042]

[0043] The parameters of the lower surface of the mid-wing airfoil obtained by fitting are:

[0044]

[0045] The parameters of the upper surface of the wingtip airfoil obtained by fitting are:

[0046]

[0047] The parameters of the lower surface of the wingtip airfoil obtained by fitting are:

[0048] .

[0049] Furthermore, the parameters of the upper surface of the wing root airfoil obtained by fitting are:

[0050]

[0051] The parameters of the lower surface of the wing root airfoil obtained by fitting are:

[0052]

[0053] The parameters of the upper surface of the mid-wing airfoil obtained by fitting are:

[0054]

[0055] The parameters of the lower surface of the mid-wing airfoil obtained by fitting are:

[0056]

[0057] The parameters of the upper surface of the wingtip airfoil obtained by fitting are:

[0058]

[0059] The parameters of the lower surface of the wingtip airfoil obtained by fitting are:

[0060] .

[0061] Beneficial effects:

[0062] The present invention proposes a wide-speed-domain, wide-frequency-band thin airfoil design method and an airfoil family for a wing-body fusion layout. The optimized section is selected by partitioning the wing to preliminarily reduce the dimension of the optimization problem. A multi-frame orthogonal overlapping FFD (FreeForm Deformation) method is used for parameterization based on the optimized section. Control frames of different densities are introduced to realize hierarchical control of the wing surface geometry, which can avoid non-physical deformation of the leading and trailing edges of the wing and take into account local refined design. A low-dimensional large-scale and high-dimensional small-scale combined optimization method is used to optimize the wide-speed-domain, wide-frequency-domain thin airfoil for a wing-body fusion layout. After a good initial optimization solution is obtained at a low-dimensional large-scale, a high-dimensional small-scale optimization design method based on discrete adjoint is combined with it, and the optimization design is performed again on a series of good initial solutions to improve the aerodynamic and low-detectability performance of the final shape and improve the optimization efficiency.

[0063] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0065] Figure 1 This is a flow chart of the design method of a wide-speed, wide-frequency-band thin airfoil with wing-body fusion layout according to the present invention;

[0066] Figure 2 It is an optimized cross-section solution of a wing-body fusion layout with a wide speed range and wide frequency band thin airfoil according to an embodiment of the present invention;

[0067] Figure 3 A schematic diagram of a multi-frame orthogonal overlapping FFD control frame used in an embodiment of the present invention;

[0068] Figure 4 The wing root airfoil optimized by the embodiment of the present invention is compared with the initial airfoil;

[0069] Figure 5 Comparison between the mid-wing airfoil optimized by the embodiment of the present invention and the initial airfoil;

[0070] Figure 6 Comparison between the wing tip airfoil optimized by the embodiment of the present invention and the initial airfoil;

[0071] Figure 7 Comparison of CFD results of surface pressure distribution between the optimized configuration of the wing-body fusion layout and the initial configuration at Ma=0.80 for configuring the optimized airfoil family;

[0072] Figure 8Comparison of CFD results of surface pressure distribution between the optimized configuration of the wing-body fusion layout and the initial configuration at Ma=0.90 for configuring the optimized airfoil family;

[0073] Fig. 9 Comparison of CFD results of surface pressure distribution between the optimized configuration of the wing-body fusion layout and the initial configuration at Ma=1.50 for configuring the optimized airfoil family;

[0074] Fig.10 Comparison of the drag coefficient results of the optimized configuration of the wing-body fusion layout of the optimized airfoil family and the initial configuration at subsonic speed;

[0075] Fig.11 Comparison of drag coefficient results at transonic speed between the optimized configuration of the wing-body fusion layout and the initial configuration of the optimized airfoil family;

[0076] Fig.12 Comparison of drag coefficient results at supersonic speed between the optimized configuration of the wing-body fusion layout and the initial configuration for configuring the optimized airfoil family;

[0077] Fig.13 Comparison of RCS results at typical L-band frequencies between the optimized configuration of the wing-body fusion layout and the initial configuration for configuring the optimized airfoil family;

[0078] Fig.14 Comparison of RCS results at typical S-band frequencies between the optimized configuration of the wing-body fusion layout and the initial configuration for configuring the optimized airfoil family;

[0079] Fig.15 Comparison of RCS results at typical C-band frequencies between the optimized configuration of the wing-body fusion layout and the initial configuration for configuring the optimized airfoil family;

[0080] Fig.16 The RCS results of the optimized configuration of the wing-body fusion layout of the optimized airfoil family are compared with the initial configuration at typical frequencies in the X-band. DETAILED DESCRIPTION

[0081] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0082] This embodiment adopts the proposed wing-body fusion layout wide speed range wide frequency band thin airfoil design method to optimize the design of the wing-body fusion layout small aspect ratio large swept wing considering the comprehensive requirements of aerodynamics, low detectability, wide speed range, and wide frequency band, such as Figure 1 As shown, the optimization design method used in this embodiment includes the following steps:

[0083] Step 1: Select NACA64A204 airfoil as the initial airfoil, build a 3D model of a wing-body fusion layout with a small aspect ratio and a large swept wing according to the NGAD three-view drawing as the original configuration, generate an aerodynamic calculation grid, and determine the optimal design state: subsonic flight Ma=0.80, transonic flight Ma=0.90, and supersonic flight Ma=1.50.

[0084] Step 2: For the original configuration, determine several optimized sections, arrange multiple orthogonal overlapping FFD control frames according to the optimized sections, and arrange design variables for the single-sided wing of the wing-body fusion layout.

[0085] Based on the linear variation of the spanwise cross-sectional area of ​​the three-dimensional model of the wing-body fusion layout with a small aspect ratio and a large sweepback wing built in step 1, the geometric transition of the wing surface is controlled by the three sections of the wing root, wing mid-wing and wing tip, and the three optimized sections of the wing root, wing mid-wing and wing tip are determined, such as Figure 2 As shown, the optimized section in the wing is located at the 50% position in the wing span direction. According to the optimized section, multiple orthogonal overlapping FFD (Free Form Deformation) control frames are arranged, and the wing-body fusion layout with a small aspect ratio and a large swept wing is parameterized to determine the design variables and design space.

[0086] In this embodiment, the establishment process of the multi-frame orthogonal overlapping FFD parameterization method is as follows: the FFD control frame is arranged along the wing span according to the selected optimized profile, and the orthogonal FFD control frame is arranged along the wing chord according to three different densities: sparse, sub-dense, and fine. Then, the orthogonal FFD frames of the three densities are merged to form a multi-frame orthogonal overlapping FFD control frame, as shown in the schematic diagram. Figure 3 As shown in the figure, Sparse, Middle, and Dense represent the sparse, sub-dense, and dense control boxes of the design variables respectively.

[0087] Specifically, the Z coordinates of the nodes of the multi-frame orthogonal overlapping FFD control frames at the optimized section are The amount of change As a design variable, , a mapping between the surface grid and the design variables is established, where the subscript i represents the i-th control node, and n is the sum of the number of nodes of the FFD control boxes of all optimized sections; the coordinate axis is defined as: the X-axis is in the aircraft symmetry plane, pointing to the incoming flow direction along the wing chord line, the Y-axis is perpendicular to the symmetry plane and points to the right wing, and the Z-axis is in the symmetry plane, perpendicular to the X-axis and points upward, satisfying the right-hand system; in this embodiment, in the Sparse control box, each optimized section has 2 design variables, and a total of 6 design variables are used to parameterize the single-sided wing; in the Middle control box, each optimized section has 4 design variables, and a total of 12 design variables are used to parameterize the single-sided wing; in the Dense control box, each optimized section has 10 design variables, and a total of 30 design variables are used to parameterize the single-sided wing; then the total number of design variables after merging into multiple orthogonal overlapping FFD control boxes is 48, and these 48 design variables are used as low-dimensional large-scale proxy optimization parameters for the optimized section airfoil.

[0088] According to the design variables, in the set design space, the surface mesh is deformed by changing the design variables and then applying deformation disturbance to the surface mesh, so as to achieve deformation and obtain a surface mesh with a new shape. Then, the radial basis function (RBF) and infinite interpolation (TFI) mesh deformation methods are used to interpolate and deform the space mesh based on the surface mesh of the new shape to obtain a CFD calculation mesh with a new shape.

[0089] Step 3: Establish a mathematical model for low-dimensional large-scale optimization problems, determine the optimization goal to reduce the drag coefficient at subsonic, transonic and supersonic speeds, and reduce the scattering cross-sectional area (RCS) of the optimized configuration in the L-band, S-band, C-band and X-band; select the change in the Z-coordinate of the node of the FFD control box As the design variable; the lift coefficient under the design state is selected to be equal to the set value as the aerodynamic constraint, and the maximum thickness of the optimized airfoil at the optimized section is not less than the maximum thickness of the initial airfoil. The specific mathematical expression is:

[0090]

[0091] in:

[0092]

[0093] Indicates the drag coefficient of the original configuration in subsonic cruise state, represents the drag coefficient of the original configuration in transonic cruise state, represents the drag coefficient of the original configuration in supersonic cruise state, Indicates the drag coefficient of the optimized configuration in subsonic cruise state, represents the drag coefficient of the optimized configuration in transonic cruise state, It represents the drag coefficient of the optimized configuration in supersonic cruise state; represents the scattering cross-sectional area of ​​the original configuration at the set frequency point in the L band, represents the scattering cross-sectional area of ​​the original configuration at the set frequency point in the S band, It represents the scattering cross-sectional area of ​​the original configuration at the set frequency point in the C band. represents the scattering cross-sectional area of ​​the original configuration at the set frequency point in the X-band, It represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the L band. It represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the S band. It represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the C band. It represents the scattering cross-section of the optimized configuration at the set frequency point in the X-band; represents the maximum thickness of the airfoil at the kth optimized section in the original configuration, represents the maximum thickness of the airfoil at the kth optimized section in the optimized configuration; They represent the optimization objective functions, respectively, which correspond to reducing the drag coefficient at sub-, trans- and supersonic speeds.

[0094] Step 4: For the low-dimensional large-scale optimization problem established in step 3, a multi-objective optimization method based on a proxy model is used to optimize the parameters and obtain the Pareto frontier of low-dimensional large-scale proxy optimization.

[0095] The specific process is as follows: in the set design space, the Latin hypercube sampling method is used to sample the airfoil design variables at the optimized section to obtain samples; the RBF-TFI method is used to deform and generate the aerodynamic and RCS calculation grids of the samples; the aerodynamic and RCS calculation grids of the samples are used to perform CFD calculations and RCS calculations on the samples under the optimized design state determined in step 1 to obtain the aerodynamic and RCS data of the samples; based on the aerodynamic and RCS data of the samples, a Kriging proxy model is established; based on the Kriging proxy model, a multi-objective optimization algorithm is used to optimize and solve the optimization mathematical model established in step 3 until convergence, and the Pareto frontier of low-dimensional large-scale proxy parameter optimization is obtained.

[0096] Step 5: Extract the optimized configuration with the best supersonic performance from the Pareto front obtained in step 4 as the new initial configuration, determine several optimized sections again, arrange multiple orthogonal overlapping FFD control frames according to the optimized sections, and refine the design variables of the single-sided wing layout of the wing-body fusion layout; establish a mathematical model for the local section parameter optimization problem, and use the optimization algorithm based on the adjoint gradient for optimization design. The optimization design here belongs to the high-dimensional small-scale parameter refinement design, so as to obtain the final configuration of the wing-body fusion layout and the wide-speed domain and wide-frequency band airfoil family composed of the airfoils at each optimized section.

[0097] The specific process is as follows:

[0098] Step 5.1: extracting the optimized configuration with the best supersonic performance from the Pareto front obtained in step 4 as a new initial configuration, and generating an aerodynamic calculation grid of the initial configuration using ANSYS ICEM;

[0099] Step 5.2: Based on the initial configuration obtained in step 5.1, the geometric transition of the wing surface is still controlled by the three sections of the wing root, wing center, and wing tip, and the three optimized sections of the wing root, wing center, and wing tip are determined. The multi-frame orthogonal overlapping FFD is used for parameterization to determine the design variables for local section parameter optimization. The specific process is similar to step 2. The FFD control frame is arranged along the span direction of the wing according to the selected optimized section, and the orthogonal FFD control frame is arranged along the chord direction of the wing according to three different densities: sparse, sub-dense, and fine. Then, the orthogonal FFD frames of the three densities are merged to form a multi-frame orthogonal overlapping FFD control frame. The Z coordinates of the nodes of the multi-frame orthogonal overlapping FFD control frame at the optimized section are still used. The amount of change As design variables, in this step, the dimension of design variables is higher than that in step 2. In the Sparse control frame, each optimized section has 8 design variables, and a total of 24 design variables are used to parameterize the single wing; in the Middle control frame, each optimized section has 16 design variables, and a total of 48 design variables are used to parameterize the single wing; in the Dense control frame, each optimized section has 30 design variables, and a total of 90 design variables are used to parameterize the single wing; the total number of design variables after merging into multiple orthogonal overlapping FFD control frames is 162.

[0100] Step 5.3: Establish a mathematical model for the local profile parameter optimization problem. The specific mathematical expression is as follows:

[0101]

[0102] Where f represents the optimization objective function; represents the drag coefficient in subsonic cruise state with optimized configuration, represents the drag coefficient in the transonic cruise state with optimized configuration, represents the drag coefficient in supersonic cruise state with optimized configuration; represents the scattering cross-sectional area of ​​the initial configuration at the set frequency point in the L band, represents the scattering cross-sectional area of ​​the initial configuration at the set frequency point in the S band, represents the scattering cross-sectional area of ​​the initial configuration at the set frequency point in the C band, It represents the scattering cross-section of the initial configuration at the set frequency point in the X-band; represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the L band, represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the S band, It represents the scattering cross-section area of ​​the optimized configuration at the set frequency point in the C band. It represents the scattering cross-section area of ​​the optimized configuration at the set frequency point in the X-band; represents the maximum thickness of the airfoil at the kth optimized section in the initial configuration, represents the maximum thickness of the airfoil at the kth optimized section in the adjoint optimized configuration; Represents weight.

[0103] Step 5.4: For the adjoint optimized configuration, high-precision flow field calculation is performed based on the RANS equation, and the multi-layer fast multipole method is used to solve the Maxwell equations for high-precision electromagnetic field calculation to obtain , , , , , , , and perform weighted coupling to obtain the value of the objective function f;

[0104] Step 5.5: Construct and solve the flow field discrete adjoint equation according to the flow field solution vector to obtain the aerodynamic target , , Gradient of the design variable; construct and solve the electromagnetic discrete adjoint equation to obtain the gradient of the low detectability target with respect to the design variable; superimpose the gradient of the aerodynamic target with respect to the design variable and the gradient of the low detectability target with respect to the design variable to obtain the gradient of the objective function f with respect to the design variable;

[0105] Step 5.6: Feed the objective function value obtained in step 5.4 and the gradient of the objective function with respect to the design variables obtained in step 5.5 back to the SQP optimization algorithm to determine whether the optimization convergence criteria are met. If the optimization convergence criteria are not met, calculate the search direction and step size through the SQP optimization algorithm, obtain new design variables, update the accompanying optimization configuration, and go to step 5.4 for the next round of optimization iteration. Repeat this cycle until the optimization iteration converges, and finally obtain the optimized wing-body fusion layout shape.

[0106] The airfoils at three optimized sections are intercepted from the final wing-body fusion layout shape, and the intercepted airfoil coordinates are fitted. The CST method is used to describe the airfoil. The unified expressions of the three airfoils at the wing root, wing mid-wing, and wing tip are:

[0107]

[0108] Where y represents the ordinate corresponding to the upper or lower surface of the airfoil, x represents the abscissa corresponding to the upper or lower surface of the airfoil, and A i represents the fitting coefficient, n represents the order of the CST parameterization method, in this embodiment n=7, y tail represents the y coordinate of the step at the trailing edge of the airfoil;

[0109] The parameters of the upper surface of the wing root airfoil obtained by fitting are:

[0110]

[0111] The parameters of the lower surface of the wing root airfoil obtained by fitting are:

[0112]

[0113] The optimized wing root airfoil is as follows: Figure 4 As shown, its characteristics are: the curvature of the wing root airfoil is reduced, the leading edge becomes sharper, it is more symmetrical, and it has obvious supersonic airfoil characteristics, which helps to reduce the supersonic wave drag of the wing.

[0114] The parameters of the upper surface of the mid-wing airfoil obtained by fitting are:

[0115]

[0116] The parameters of the lower surface of the mid-wing airfoil obtained by fitting are:

[0117]

[0118] The optimized mid-wing airfoil is as follows: Figure 5 As shown, its characteristics are: the curvature of the airfoil in the middle of the wing is reduced, the curvature of the leading edge is increased and becomes sharper, which reduces the nose-down moment of the wing while maintaining the lift characteristics at subsonic and transonic speeds.

[0119] The parameters of the upper surface of the wingtip airfoil obtained by fitting are:

[0120]

[0121] The parameters of the lower surface of the wingtip airfoil obtained by fitting are:

[0122]

[0123] The optimized wingtip airfoil is as follows: Figure 6 As shown in the figure, its characteristics are: the camber of the wingtip airfoil near the leading and trailing edges increases, and the leading edge radius decreases, which helps to reduce the wave drag of the head during supersonic flight and improve the lift-to-drag ratio of supersonic cruise. The lower surface of the leading edge is concave, and there is a certain front load compared to the original airfoil at transonic speed, which can increase some lift and help to weaken the separation vortex at the leading edge of the wing and reduce the subsonic induced drag of the wing. The increase in camber also helps to have better lift characteristics at low and transonic speeds.

[0124] Figure 7 The CFD results of surface pressure distribution of the whole machine configuration of the wing-body fusion layout of the assembled optimized airfoil family and the initial configuration at Ma=0.80 are compared. Figure 8 The CFD results of surface pressure distribution of the wing-body fusion layout configuration of the assembled optimized airfoil family and the initial configuration at Ma=0.90 are compared. Fig. 9 The CFD results of surface pressure distribution of the wing-body fusion layout configuration of the assembled optimized airfoil family and the initial configuration at Ma=1.50 are compared. It can be seen that under subsonic and transonic conditions, there is no obvious shock wave on the model surface, so the drag coefficient is slightly reduced. Under supersonic conditions, obvious shock waves appear on the outer wing section, the low-pressure area of ​​the model expands, the pressure recovery is gentle, and the shock wave is greatly weakened, so the drag coefficient is significantly reduced.

[0125] The above-mentioned airfoil family is assembled into the whole configuration of the wing-body fusion layout, and CFD calculation and electromagnetic field calculation are performed on the design state selected in step 1 to verify the excellent aerodynamic and low detectability performance of the wing and airfoil family designed in this embodiment in a wide speed range and wide frequency band. The aerodynamic coefficients obtained by CFD are as follows: Figures 10 to 12 As shown. It can be seen that compared with the initial shape (indicated by Ori in the figure), the subsonic and transonic drag characteristics of the designed shape (indicated by Opt in the figure) are slightly improved, and the drag coefficient is reduced by 1.3 counts and 4.4 counts respectively. The supersonic drag characteristics are greatly improved, and the drag coefficient is reduced by 8.5 counts. The calculated RCS results are as follows Figure 13~Figure 16 As shown, it can be seen that compared with the initial shape, the low detectable characteristics of the designed shape are greatly improved, and the average forward RCS values ​​are reduced by 42%, 35%, 83% and 92% respectively, and the RCS is significantly reduced.

[0126] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary 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 designing a thin airfoil with a wing-body fusion layout with a wide speed range and wide frequency band, characterized by: The following steps are involved: Step 1: Select the initial airfoil, construct the original configuration of the wing-body fusion layout, generate the aerodynamic calculation grid, and determine the optimized design state; Step 2: For the original configuration, determine several optimized sections, arrange multiple orthogonal overlapping FFD control frames according to the optimized sections, and arrange design variables for the single-sided wing of the wing-body fusion layout; Step 3: Establish a mathematical model for low-dimensional large-scale optimization problems: Determine the optimization goal to reduce the drag coefficient at subsonic, transonic and supersonic speeds, and reduce the scattering cross-sectional area of ​​the optimized configuration in the L band, S band, C band and X band; Select the change in the Z coordinate of the node of the FFD control box As the design variable; the lift coefficient under the design state is selected to be equal to the set value as the aerodynamic constraint, and the maximum thickness of the optimized airfoil at the optimized section is not less than the maximum thickness of the initial airfoil; Step 4: For the low-dimensional large-scale optimization problem established in step 3, a multi-objective optimization method based on a proxy model is used to optimize the parameters and obtain the Pareto frontier of low-dimensional large-scale proxy optimization; Step 5: Extract the optimized configuration with the best supersonic performance from the Pareto front obtained in step 4 as the new initial configuration, determine several optimized sections again, arrange multiple orthogonal overlapping FFD control frames according to the optimized sections, and refine the design variables of the single-sided wing layout of the wing-body fusion layout; establish a mathematical model for the local section parameter optimization problem, and use the optimization algorithm based on the adjoint gradient for optimization design to obtain the final configuration of the wing-body fusion layout and a wide-speed domain and wide-frequency band airfoil family composed of airfoils at each optimized section.

2. According to claim 1, a method for designing a wide-speed, wide-frequency-range thin airfoil with a wing-body fusion layout, characterized in that: In step 2, optimized sections are selected at the root, middle and tip of the wing on one side of the wing in the wing-body fusion layout, among which the optimized middle section is located at the 50% position in the wing span.

3. According to claim 2, a method for designing a wide-speed, wide-frequency-range thin airfoil with a wing-body fusion layout is characterized by: In step 2, the multi-frame orthogonal overlapping FFD control frames are arranged according to the optimized section. The specific process of the design variables of the wing-body fusion layout single-sided wing arrangement is as follows: Arrange the FFD control frame along the wing span according to the selected optimized section, arrange the orthogonal FFD control frame along the wing chord according to three different densities: sparse, sub-dense, and fine, and then merge the orthogonal FFD frames of the three densities to form a multi-frame orthogonal overlapping FFD control frame; The Z coordinates of the nodes of the multi-frame orthogonal overlapping FFD control frame at the optimized section The amount of change As a design variable, , where the subscript i represents the i-th control node, and n is the sum of the number of nodes of the FFD control boxes of all optimized sections.

4. According to claim 3, a method for designing a wide-speed, wide-frequency-range thin airfoil with a wing-body fusion layout is characterized by: In step 2, in the sparse control frame, each optimized section has 2 design variables, and a total of 6 design variables are used to parameterize the single wing; in the sub-dense control frame, each optimized section has 4 design variables, and a total of 12 design variables are used to parameterize the single wing; in the dense control frame, each optimized section has 10 design variables, and a total of 30 design variables are used to parameterize the single wing; the total number of design variables after merging into a multi-frame orthogonal overlapping FFD control frame is 48.

5. According to claim 3, a method for designing a wide-speed, wide-frequency-range thin airfoil with a wing-body fusion layout is characterized by: In step 3, the mathematical model of the low-dimensional large-scale optimization problem is: in: Indicates the drag coefficient of the original configuration in subsonic cruise state, represents the drag coefficient of the original configuration in transonic cruise state, represents the drag coefficient of the original configuration in supersonic cruise state, Indicates the drag coefficient of the optimized configuration in subsonic cruise state, represents the drag coefficient of the optimized configuration in transonic cruise state, It represents the drag coefficient of the optimized configuration in supersonic cruise state; represents the scattering cross-sectional area of ​​the original configuration at the set frequency point in the L band, represents the scattering cross-sectional area of ​​the original configuration at the set frequency point in the S band, It represents the scattering cross-sectional area of ​​the original configuration at the set frequency point in the C band. represents the scattering cross-sectional area of ​​the original configuration at the set frequency point in the X-band, It represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the L band. It represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the S band. It represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the C band. It represents the scattering cross-section of the optimized configuration at the set frequency point in the X-band; represents the maximum thickness of the airfoil at the kth optimized section in the original configuration, represents the maximum thickness of the airfoil at the kth optimized section in the optimized configuration; They represent the optimization objective functions, respectively, which correspond to reducing the drag coefficient at sub-, trans- and supersonic speeds.

6. According to claim 1, a method for designing a wide-speed, wide-frequency-range thin airfoil with a wing-body fusion layout, characterized in that: The specific process of step 4 is as follows: in the set design space, the Latin hypercube sampling method is used to sample the airfoil design variables at the optimized section to obtain samples; the RBF-TFI method is used to deform and generate the aerodynamic and RCS calculation grids of the samples; the aerodynamic and RCS calculation grids of the samples are used to perform CFD calculations and RCS calculations on the samples under the optimized design state determined in step 1 to obtain the aerodynamic and RCS data of the samples; based on the aerodynamic and RCS data of the samples, a Kriging proxy model is established; based on the Kriging proxy model, a multi-objective optimization algorithm is used to optimize and solve the optimization mathematical model established in step 3 until convergence, and the Pareto frontier of low-dimensional large-scale proxy parameter optimization is obtained.

7. According to claim 5, a method for designing a wide-speed, wide-frequency-range thin airfoil with a wing-body fusion layout is characterized by: The specific process of step 5 is: Step 5.1: extracting the optimized configuration with the best supersonic performance from the Pareto front obtained in step 4 as a new initial configuration, and generating an aerodynamic calculation grid of the initial configuration using ANSYS ICEM; Step 5.2: Based on the initial configuration obtained in step 5.1, three optimized sections of the wing root, wing mid-wing, and wing tip are determined, and parameterization is performed using multi-frame orthogonal overlapping FFD to determine the design variables for local section parameter optimization, where the number of design variables is greater than the number of design variables in step 2; Step 5.3: Establish a mathematical model for the local profile parameter optimization problem. The specific mathematical expression is as follows: Where f represents the optimization objective function; represents the drag coefficient in subsonic cruise state with optimized configuration, represents the drag coefficient in the transonic cruise state with optimized configuration, represents the drag coefficient in supersonic cruise state with optimized configuration; represents the scattering cross-sectional area of ​​the initial configuration at the set frequency point in the L band, represents the scattering cross-sectional area of ​​the initial configuration at the set frequency point in the S band, represents the scattering cross-sectional area of ​​the initial configuration at the set frequency point in the C band, It represents the scattering cross-section of the initial configuration at the set frequency point in the X-band; represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the L band, represents the scattering cross-sectional area of ​​the optimized configuration at the set frequency point in the S band, It represents the scattering cross-section area of ​​the optimized configuration at the set frequency point in the C band. It represents the scattering cross-section area of ​​the optimized configuration at the set frequency point in the X-band; represents the maximum thickness of the airfoil at the kth optimized section in the initial configuration, represents the maximum thickness of the airfoil at the kth optimized section in the adjoint optimized configuration; represents weight; Step 5.4: For the adjoint optimized configuration, the flow field is calculated based on the RANS equations, and the multilayer fast multipole method is used to solve the Maxwell equations for electromagnetic field calculation, and the result is , , , , , , , and perform weighted coupling to obtain the value of the objective function f; Step 5.5: Construct and solve the flow field discrete adjoint equation according to the flow field solution vector to obtain the aerodynamic target , , Gradient of the design variable; construct and solve the electromagnetic discrete adjoint equation to obtain the gradient of the low detectability target with respect to the design variable; superimpose the gradient of the aerodynamic target with respect to the design variable and the gradient of the low detectability target with respect to the design variable to obtain the gradient of the objective function f with respect to the design variable; Step 5.6: Feed the objective function value obtained in step 5.4 and the gradient of the objective function with respect to the design variables obtained in step 5.5 back to the SQP optimization algorithm to determine whether the optimization convergence criteria are met. If the optimization convergence criteria are not met, calculate the search direction and step size through the SQP optimization algorithm, obtain new design variables, update the accompanying optimization configuration, and go to step 5.4 for the next round of optimization iteration. Repeat this cycle until the optimization iteration converges, and finally obtain the optimized wing-body fusion layout shape.

8. According to claim 7, a method for designing a wide-speed, wide-frequency-range thin airfoil with a wing-body fusion layout is characterized by: In step 5.2, in the sparse control frame, each optimized section has 8 design variables, and a total of 24 design variables are used to parameterize the single-sided wing; in the sub-dense control frame, each optimized section has 16 design variables, and a total of 48 design variables are used to parameterize the single-sided wing; In the fine control frame, each optimized section has 30 design variables, and a total of 90 design variables are used to parameterize the single wing; after merging into multiple orthogonal overlapping FFD control frames, the total number of design variables is 162.

9. A family of airfoils is obtained by using any of the methods of claims 1 to 8, characterized in that: The design state is subsonic flight Ma=0.80, transonic flight Ma=0.90, and supersonic flight Ma=1.50; the airfoil family includes airfoils at three optimized sections: wing root, wing mid-wing, and wing tip, which are described using the CST method: Where y represents the ordinate corresponding to the upper or lower surface of the airfoil, x represents the abscissa corresponding to the upper or lower surface of the airfoil, and A i represents the fitting coefficient, n represents the order of the CST parameterization method, n=7, y tail represents the y coordinate of the step at the trailing edge of the airfoil; The parameters of the upper surface of the wing root airfoil obtained by fitting are: The parameters of the lower surface of the wing root airfoil obtained by fitting are: The parameters of the upper surface of the mid-wing airfoil obtained by fitting are: The parameters of the lower surface of the mid-wing airfoil obtained by fitting are: The parameters of the upper surface of the wingtip airfoil obtained by fitting are: The parameters of the lower surface of the wingtip airfoil obtained by fitting are: 。 10. The airfoil family according to claim 9, characterized in that: The parameters of the upper surface of the wing root airfoil obtained by fitting are: The parameters of the lower surface of the wing root airfoil obtained by fitting are: The parameters of the upper surface of the mid-wing airfoil obtained by fitting are: The parameters of the lower surface of the mid-wing airfoil obtained by fitting are: The parameters of the upper surface of the wingtip airfoil obtained by fitting are: The parameters of the lower surface of the wingtip airfoil obtained by fitting are: 。

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