Wide-range time-varying wave-riding configuration design method based on curved shock wave theory

Abstract

The method for designing wide-range time-varying waverider configuration based on curved shock theory relates to the design of near-space hypersonic aircraft. According to the flight envelope, the range of flight Mach number is determined, and the design Mach number and flight altitude of each level waverider configuration of the wide-range time-varying waverider configuration are determined. According to the fixed three-dimensional leading edge profile and waverider area of the wide-range time-varying waverider configuration given by the flight task requirement, the shock profile equation of the basic flow field is adjusted, and each level waverider configuration with the same three-dimensional leading edge profile and waverider area is quickly solved and obtained according to the geometric relationship between the design curves by using the curved shock theory. According to the volume rate requirement, the upper surface of the waverider body is constructed as a plane or a convex surface. The wide-range time-varying waverider configuration is designed based on the curved shock theory by combining each level waverider configuration. The waverider configuration can be continuously changed according to the task requirement and flight environment, the aerodynamic performance under the flight envelope is effectively improved, and the wide-speed-range flight working condition and various flight tasks can be adapted.

Description

Technical Field

[0001] This invention relates to the field of near-space hypersonic vehicle design technology, and in particular to a wide-domain time-varying wave-riding shape design method based on bending shock wave theory. Background Technology

[0002] In recent years, scholars both at home and abroad have conducted extensive research on waverider configurations, proposing a series of waverider principles and methods, including wedge-guided waverider theory, cone-guided waverider theory, and kissing theory, achieving fruitful research results. Furthermore, waverider design has gradually entered the engineering development stage, with a series of waverider flight tests conducted both domestically and internationally, including those involving the X-51A, HTV-2, and ARRW.

[0003] Currently, most variant waverider schemes are based on a two-dimensional / conical fundamental flow field. Furthermore, designing waverider profiles for various discrete operating conditions requires pre-calculation of the fundamental flow field, making it difficult to achieve rapid analytical design of waverider profiles at various stages under wide-domain conditions. This significantly limits the design space and efficiency of wide-domain variant waverider profiles. Therefore, one of the current problems restricting the wide-domain performance of hypersonic waveriders is the lack of a wide-domain time-varying waverider profile design method based on bending shock wave theory. Summary of the Invention

[0004] The purpose of this invention is to address the aforementioned limitations of existing technologies by providing a wide-domain time-varying waverider shape design method based on curved shock wave theory. This method allows for continuous modification of the waverider shape according to the flight mission requirements across a wide speed range, effectively improving the aerodynamic performance below the flight envelope. While maintaining the three-dimensional leading-edge profile and waverider area of ​​the waverider shape, it enables rapid analytical design of waveriders at various stages. This provides a new approach to variant waverider design and improves the design efficiency of wide-domain variant waverider shapes.

[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solution.

[0006] The wide-domain time-varying wave-riding shape design method based on bending shock wave theory includes the following steps:

[0007] 1) Determine the flight Mach number range based on the flight envelope, and determine the design Mach number and flight altitude for each stage of the wide-range time-varying waverider shape;

[0008] 2) Based on the flight mission requirements, a fixed three-dimensional leading edge profile and waverider area for a wide-range time-varying waverider shape are given. The three-dimensional leading edge profile should meet the geometric requirements such as the aspect ratio of the waverider shape and take into account the matching with the waverider area.

[0009] 3) Adjust the shock wave profile equation of the basic flow field to match the design Mach number and flight altitude. Based on the geometric relationship between the design curves, use the bending shock wave theory to quickly solve for the lower surface of each level of waverider with the same three-dimensional leading edge profile and waverider area.

[0010] 4) Based on the volume ratio requirements, construct the upper surface of the waverider as a plane or convex surface to optimize the internal space and aerodynamic performance of the waverider; determine the tail edge shape of each stage of the waverider to ensure a smooth transition with the lower and upper surfaces of the waverider; the upper surface, lower surface, and tail edge of each stage of the waverider together constitute the shape of each stage of the waverider; combine the shapes of each stage of the waverider to realize the wide-domain time-varying waverider shape design based on the bending shock wave theory.

[0011] In step 2), the three-dimensional leading edge profile (LEPC) of the wide-domain time-varying waverider profile is given by combining its exit capture profile (FCT) in the yoz plane and its horizontal projection profile (PPC) in the xoy plane, as shown below:

[0012] (1)

[0013] (2)

[0014] Where w is the half-span of the waverider.

[0015] In step 3), the shock wave profile equation of the basic flow field is adjusted to match the design Mach number and flight altitude. Based on the geometric relationship between the design curves, the lower surfaces of each stage of the waverider with the same three-dimensional leading edge profile and waverider area are quickly obtained using bending shock wave theory. The specific process is as follows:

[0016] 3.1) Determine the design Mach number M of the current first-order waverider shape from step 1). i Flight altitude H i and incoming flow conditions;

[0017] 3.2) Given the shock wave profile equation of the basic flow field, solve the shock wave exit profile (SWPC) based on the three-dimensional leading edge profile (LEPC) of the fixed wide-area time-varying wave-riding shape given in step 2) and the geometric relationship between the design curves.

[0018] 3.3) Based on the shock angle and shock curvature of the three-dimensional curved shock wave at the three-dimensional leading edge profile of the waverider, the Taylor series expression of the streamlines in each cross section is quickly obtained by the flow field analysis method based on the curved shock wave theory, and the parameterized expression of the lower surface of the waverider considering the incoming flow conditions and shock wave shape is realized by coordinate transformation.

[0019] 3.4) Adjust the shock wave profile equation of the basic flow field, repeat steps 3.2)-3.3), and obtain M with the wave-riding area given in step 2).i The shape of a multiplicative wave;

[0020] 3.5) Adjusting the design Mach number M i Repeat steps 3.1)-3.4) to obtain waverider profiles of each level with the three-dimensional leading edge profile and waverider area given in step 2).

[0021] Furthermore, the specific process of step 3.2) is as follows:

[0022] 3.2.1) The equation for the curved shock wave profile in a given axisymmetric basic flow field is as follows:

[0023] (3)

[0024] The shock wave within the tangential plane is obtained by scaling the bending shock wave in the axisymmetric basic flow field, and its equation satisfies:

[0025] (4)

[0026] Where k is the scaling factor of the kiss section.

[0027] 3.2.2) Establish the geometric relationships between the waverider three-dimensional leading edge profile (LEPC), the waverider exit capture profile (FCT), the waverider horizontal projection profile (PPC), and the shock wave exit profile (SWPC):

[0028] For any leading edge point B0 on ​​the LEPC, its kissing plane intersects the SWPC at point D and the FCT at point B. The tangent of the LEPC at point B0 intersects the tangent of the FCT at point B and the tangent of the SWPC at point D at point E. Here, tangent segments BE and DE are both located within the exit section. The sweep angle λ of the LEPC at point B0 is determined by the following formula:

[0029] (5)

[0030] The following angular relationships exist within triangle BDE:

[0031] (6)

[0032] The angle β between the tangent BE and the horizontal direction can be obtained by differentiating equation (1):

[0033] (7)

[0034] The angle γ between tangent segments BE and DE is calculated by the following formula:

[0035] (8)

[0036] 3.2.3) Solve for the analytical expression of the shock wave exit profile (SWPC):

[0037] The position of shock point D within the kissing plane where the leading edge point B0 is located is determined by the angle α of the kissing plane and the distance between point B and point D, calculated as follows:

[0038] (9)

[0039] Substituting equations (1), (2), and (5) to (8) into equation (9), we obtain the analytical expression for SWPC as follows:

[0040] (10)

[0041] Where f(y), p(y), and c(y) are the design inputs, (y D , z D This is the design output. Repeat the above process along LEPC (meaning variables...). By varying within [-w, w], the shock wave exit profile SWPC can be obtained.

[0042] Furthermore, the specific process of step 3.3) is as follows:

[0043] 3.3.1) Given the incoming flow conditions, based on the shock angle and shock curvature of the three-dimensional curved shock wave at the three-dimensional leading edge profile of the waverider, solve the oblique shock wave equations, the first-order curved shock wave equations, and the second-order curved shock wave equations to obtain the aerodynamic parameters, first-order derivatives, and second-order derivatives of the aerodynamic parameters immediately adjacent to the curved shock wave at the leading edge of the waverider:

[0044] The first-order bending shock wave equations are as follows:

[0045] (11)

[0046] In the formula, coefficients A, B, E, C, and G can be calculated from the incoming flow conditions and shock wave angle. Subscripts 1 and 2 represent the upstream and downstream flow parameters of the shock wave, respectively. Other variables are defined as follows:

[0047] (12)

[0048] Where p is pressure, δ is the flow angle, ρ is density, V is flow velocity, and ω is vorticity. Where s is the shock wave angle and s is the streamline direction. The direction of the shock wave is Y, and Y is the ordinate in the tangent plane coordinate system.

[0049] The second-order bending shock wave equations are as follows:

[0050] (13)

[0051] The coefficients in the formula are also expressions for the incoming flow conditions and shock angle, and the other variables are defined as follows:

[0052] (14)

[0053] 3.3.2) Given the derivatives of the aerodynamic parameters along the streamline at the leading edge shock point, the streamline behind the curved shock wave in the tangential plane can be quickly solved using the following Taylor series:

[0054] (15)

[0055] In the formula, X is the abscissa in the cross-sectional coordinate system, the subscript 0 indicates the parameter at the leading edge of the waverider (i.e., the starting point of the streamline), and the coefficients are constructed from the aerodynamic parameters and their derivatives:

[0056] (16)

[0057] 3.3.3) Based on the angle of the anastomosis surface By restoring the streamlines within each two-dimensional cross-section to the true three-dimensional Cartesian coordinate system, a parametric expression for the lower surface of the waverider considering the incoming flow conditions and shock wave shape is obtained:

[0058] (17)

[0059] Among them, variables From 0 to Repeat the above process along LEPC (meaning variable y) D (Variation within [-w, w]), and combine the streamlines within each cut surface to form the complete lower surface of the waverider.

[0060] Compared with the prior art, the beneficial effects achieved by the technical solution of this invention are:

[0061] The wide-domain time-varying waverider shape generated using this invention, based on curved shock wave theory, can continuously change its shape according to the flight mission requirements across a wide velocity range, while maintaining the three-dimensional leading-edge profile and waverider area, effectively improving aerodynamic performance across the entire flight envelope. The parametric expression of the waverider shape not only considers the direct influence of incoming flow conditions and shock wave shape but also allows designers to flexibly adjust the input according to constraints. Furthermore, the use of curved shock wave theory enables rapid analytical design of waveriders at various stages, significantly improving design efficiency while ensuring design accuracy. This expands the design space for variant waverider aircraft and enhances the design efficiency of wide-domain variant waverider shapes. Attached Figure Description

[0062] Figure 1This is a flowchart of a wide-domain time-varying wave-riding shape design method based on bending shock wave theory.

[0063] Figure 2 This is a schematic diagram illustrating the design principle of a wide-domain time-varying wave-riding profile based on the bending shock wave theory. (a) is the overall three-dimensional view, (b) is a half-section perspective view, and (c) is the exit section view.

[0064] Figure 3 The diagram shows the design curves of the wide-domain time-varying wave-riding shape based on the bending shock wave theory in different planes. Among them, (a) is the exit section and (b) is the horizontal projection.

[0065] Figure 4 This is a schematic diagram of the waverider surface shape under different incoming flows, based on the theory of curved shock waves, representing a wide-domain time-varying waverider shape.

[0066] Figure 5 This is a schematic diagram of the overall shape of the wide-domain time-varying wave-riding structure based on the bending shock wave theory under different incoming flows.

[0067] The markings in the figure are as follows: 1 represents the three-dimensional leading edge profile of the waverider (i.e., LEPC line), 2 represents the exit capture profile of the waverider (i.e., FCT line), 3 represents the horizontal projection profile of the waverider (i.e., PPC line), 4 represents the shock exit profile (i.e., SWPC line), 5 represents the kissing plane, 6 represents the curved shock wave within the kissing plane, 7 represents the streamline within the kissing plane, 8 represents the three-dimensional curved shock wave surface, 9 represents the trailing edge line of the lower surface of the waverider (i.e., LSPC line), 10 represents the symmetry plane of the waverider, 11 represents the lower surface of the waverider, 12 represents the upper surface of the waverider, and 13 represents the trailing edge surface of the waverider. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of this invention clearer, the following embodiments will be used in conjunction with the accompanying drawings to further illustrate the invention. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. Rather, the invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of the invention as defined by the claims. Furthermore, to provide the public with a better understanding of the invention, some specific details are described in detail below. Those skilled in the art will fully understand the invention even without these detailed descriptions.

[0069] like Figures 1-5 As shown, the wide-domain time-varying wave-riding shape design method based on curved shock wave theory includes the following steps:

[0070] (1) Determine the flight Mach number range [M1, M2] based on the flight envelope, and determine the design Mach number M for each stage of the wide-range time-varying waverider profile. i and flight altitude Hi ;

[0071] (2) According to the flight mission requirements, a fixed three-dimensional leading edge profile 1 (i.e. LEPC line) and wave-riding area S of the wide-area time-varying wave-riding shape are given. The three-dimensional leading edge profile 1 should meet the geometric requirements such as the slenderness ratio of the wave-riding shape.

[0072] (3) See Figures 2-4 Adjust the shock wave profile equation of the basic flow field, and use the bending shock wave theory to quickly solve for the lower surface 11 of each level of waverider with the same three-dimensional leading edge profile 1 and waverider area S based on the geometric relationship between the design curves.

[0073] (4) See Figure 5 According to the volume ratio requirement, the upper surface 12 of the waverider is constructed to be either planar or convex, which together with the lower surface 11 of each level of waverider generated in step (3) and the trailing edge surface 13 of each level of waverider constitutes the waverider shape of each level. By combining the waverider shapes of each level, the wide-domain time-varying waverider shape design based on the bending shock wave theory is realized.

[0074] See Figure 2 In step (2), the three-dimensional leading edge profile 1 of the wide-domain time-varying waverider shape is given by the combination of its waverider exit capture profile 2 (i.e., FCT line) in the yoz plane and the waverider horizontal projection profile 3 (i.e., PPC line) in the xoy plane, as shown below:

[0075] (1)

[0076] (2)

[0077] Where w is the half-span of the waverider.

[0078] The three-dimensional leading edge profile 1 of the wide-domain time-varying waverider shape, combined with the trailing edge line 9 (i.e., the LSPC line) on the lower surface of the waverider, defines the complete waverider shape.

[0079] In step (3), the shock wave profile equation of the basic flow field is adjusted, and the lower surface 11 of each stage of the waverider with the same three-dimensional leading edge profile 1 and waverider area S is obtained quickly by using the bending shock wave theory based on the geometric relationship between the design curves. The specific process is as follows:

[0080] (3.1) Determine the design Mach number M of the current first-order waverider shape from step (1). i Flight altitude H i and incoming flow conditions;

[0081] (3.2) Given the shock wave profile equation of the basic flow field, the shock wave exit profile 4 (i.e. SWPC line) is solved by combining the geometric relationship between the design curves according to the three-dimensional leading edge profile 1 of the fixed wide-area time-varying wave-riding profile given in step (2).

[0082] (3.3) Based on the shock angle and shock curvature of the three-dimensional curved shock surface 8 at the three-dimensional leading edge profile 1 of the waverider, the Taylor series expression of the streamlines in each cut surface is quickly obtained by the flow field analysis method based on the curved shock theory, and the parameterized expression of the lower surface 11 of the waverider considering the incoming flow conditions and shock shape is realized by coordinate transformation.

[0083] (3.4) Adjust the shock wave profile equation of the basic flow field, repeat steps (3.2)-(3.3), and obtain M with the wave-riding area S given in step (2). i Lower surface 11 of the wave-riding body;

[0084] (3.5) Adjusting the design Mach number M i Repeat steps (3.1)-(3.4) to obtain the lower surfaces 11 of each stage of the waverider with the three-dimensional leading edge profile 1 and waverider area S given in step (2), see [link to relevant documentation]. Figure 4 .

[0085] Furthermore, the specific process of step (3.2) is as follows:

[0086] (3.2.1) The equation for the curved shock wave profile in the given axisymmetric basic flow field is as follows:

[0087] (3)

[0088] The curved shock wave 6 within the cut surface 5 is obtained by scaling the curved shock wave in the axisymmetric basic flow field, and its equation satisfies:

[0089] (4)

[0090] Where k is the scaling factor of the kiss section.

[0091] (3.2.2) Establish the geometric relationship between the three-dimensional leading edge profile 1 of the waverider, the exit capture profile 2 of the waverider, the horizontal projection profile 3 of the waverider, and the shock exit profile 4:

[0092] like Figure 2As shown in (b), the three-dimensional leading edge profile 1 of the waverider is symmetrical about the waverider symmetry plane 10. For any leading edge point B0 on ​​the three-dimensional leading edge profile 1, its tangent plane 5 intersects the shock exit profile 4 at point D and the waverider exit capture profile 2 at point B. The tangent of the three-dimensional leading edge profile 1 at point B0 intersects the tangent of the waverider exit capture profile 2 at point B and the tangent of the shock exit profile 4 at point D at point E. Here, tangent segments BE and DE are both located within the exit section. The sweep angle λ of the three-dimensional leading edge profile 1 at point B0 is determined by the following formula:

[0093] (5)

[0094] like Figure 2 As shown in (c), the following angular relationships exist within triangle BDE:

[0095] (6)

[0096] The angle β between the tangent BE and the horizontal direction can be obtained by differentiating equation (1):

[0097] (7)

[0098] The angle γ between tangent segments BE and DE is calculated by the following formula:

[0099] (8)

[0100] (3.2.3) Solve for the analytical expression of the shock wave exit profile 4:

[0101] The position of shock point D within the kissing plane 5, where the leading edge point B0 is located, is determined by the angle α of the kissing plane 5 and the distance between point B and point D, as calculated below:

[0102] (9)

[0103] Substituting equations (1), (2), and (5) to (8) into equation (9), we obtain the analytical expression for the shock wave exit profile 4 as follows:

[0104] (10)

[0105] Where f(y), p(y), and c(y) are the design inputs, (y D , z D This is the design output. Repeat the above process along the three-dimensional leading edge profile 1 of the waverider (meaning variables...). By varying within [-w, w], the shock wave exit profile 4 can be obtained.

[0106] Furthermore, the specific process of step (3.3) is as follows:

[0107] (3.3.1) Given the incoming flow conditions, based on the shock angle and shock curvature of the three-dimensional curved shock surface 8 at the three-dimensional leading edge profile 1 of the waverider, solve the oblique shock wave relation, the first-order curved shock wave equation set, and the second-order curved shock wave equation set to obtain the aerodynamic parameters, first-order derivatives, and second-order derivatives of the aerodynamic parameters immediately adjacent to the three-dimensional curved shock surface 8 at the leading edge 1 of the waverider:

[0108] The first-order bending shock wave equations are as follows:

[0109] (11)

[0110] In the formula, coefficients A, B, E, C, and G can be calculated from the incoming flow conditions and shock wave angle. Subscripts 1 and 2 represent the upstream and downstream flow parameters of the shock wave, respectively. Other variables are defined as follows:

[0111] (12)

[0112] Where p is pressure, δ is the flow angle, ρ is density, V is flow velocity, and ω is vorticity. Where s is the shock wave angle and s is the streamline direction. The direction of the shock wave is Y, and Y is the ordinate in the tangent plane coordinate system.

[0113] The second-order bending shock wave equations are as follows:

[0114] (13)

[0115] The coefficients in the formula are also expressions for the incoming flow conditions and shock angle, and the other variables are defined as follows:

[0116] (14)

[0117] (3.3.2) Given the derivatives of the aerodynamic parameters along the streamlines at the leading edge shock point, the streamlines 7 within the bend shock 6 behind the bend shock 5 can be quickly solved using the following Taylor series:

[0118] (15)

[0119] In the formula, X is the abscissa in the tangential plane coordinate system, and the subscript 0 indicates the parameter at the leading edge of the waverider (i.e., the starting point of streamline 7 in the tangential plane). The coefficients are constructed from the aerodynamic parameters and their derivatives.

[0120] (16)

[0121] (3.3.3) Based on the angle of the slit plane By restoring the streamlines within each two-dimensional cross-section to the true three-dimensional Cartesian coordinate system, a parametric expression for the lower surface 11 of the waverider considering the incoming flow conditions and shock wave shape is obtained:

[0122] (17)

[0123] Among them, variables From 0 to Repeat the above process along the three-dimensional leading edge profile 1 of the waverider (meaning the variable y...). D (Variation within [-w, w]), and combine the streamlines within each cut surface to form the complete lower surface 11 of the waverider.

[0124] See Figure 5 The wide-domain time-varying waverider shape designed based on bending shock wave theory in this invention is composed of a lower surface 11, an upper surface 12, and a trailing edge 13 of the waverider. The lower surface 11 of the waverider is designed according to bending shock wave theory; all levels of the upper surface of the waverider are the same horizontal plane. This design simplifies the structure of the waverider and facilitates subsequent design of convex upper surfaces to meet requirements such as loading and centroidal coefficient.

[0125] Based on the theory of flexural shock waves, the wide-range time-varying waverider shape has the same three-dimensional leading edge profile and waverider area at each stage. Therefore, the lower surface 11 of the waverider shape can be made of a deformable, high-temperature resistant flexible skin. Optionally, the flexible skin includes an aerogel insulation layer, an elastic matrix layer, and a highly anisotropic support layer arranged sequentially from the outside to the inside. The aerogel insulation layer provides excellent thermal insulation performance, protecting the internal structure from high temperatures. The elastic matrix layer provides the necessary elasticity and flexibility, allowing the skin to deform continuously at different flight Mach numbers. The highly anisotropic support layer provides the necessary strength and stability, ensuring that the skin is not damaged during deformation. Based on the precise calculation of the deformation, load-bearing capacity, and high-temperature resistance requirements of each stage of the waverider shape within a wide Mach number range for the flight mission, the materials used for each layer of the skin are selected to ensure continuous and stable deformation of the wide-range time-varying waverider shape within the flight envelope.

[0126] See Figure 5Taking Mach numbers of 20-5 as an example, the wide-range time-varying waverider shape based on bending shock wave theory has a nine-level waverider lower surface. During flight, as the Mach number decreases, the flexible skin of the waverider surface continuously deforms to adapt to different flight conditions. The upper surfaces of each waverider level are all horizontal planes; subsequent design of convex upper surfaces can meet requirements such as loading and pressure coefficient. The wide-range time-varying waverider shape begins gliding from Mach 20, at which point the waverider surface is the lower surface of the first-level waverider (M20). When gliding to Mach 15, the flexible skin of the waverider surface has continuously deformed into the lower surface of the first-level waverider (M15). This process continues until gliding to Mach 5, where the flexible skin of the waverider surface has continuously deformed into the lower surface of the first-level waverider (M5). The waverider shape continuously changes according to mission requirements, allowing for precise adjustments and effectively improving the aerodynamic performance along the entire flight envelope. This not only improves flight efficiency but also enhances the stability and safety of the aircraft.

[0127] The above embodiments are merely preferred embodiments of the present invention and should not be considered as limiting the scope of the present invention. All equivalent variations and improvements made within the scope of the present invention should still fall within the patent coverage of the present invention.

Claims

1. A wide-domain time-varying wave-riding shape design method based on bending shock wave theory, characterized in that... Includes the following steps: 1) Determine the flight Mach number range based on the flight envelope, and determine the design Mach number and flight altitude for each stage of the wide-range time-varying waverider shape; 2) Based on the flight mission requirements, a fixed three-dimensional leading edge profile and waverider area for a wide-range time-varying waverider shape are given. The three-dimensional leading edge profile should meet the aspect ratio of the waverider shape and take into account the matching with the waverider area. 3) Adjust the shock wave profile equations of the basic flow field to match the design Mach number and flight altitude. Based on the geometric relationship between the design curves, use the bending shock wave theory to quickly solve for the lower surfaces of each stage of the waverider with the same three-dimensional leading edge profile and waverider area. The specific process is as follows: 3.1) Determine the design Mach number M of the current first-order waverider shape from step 1). i Flight altitude H i and incoming flow conditions; 3.2) Given the shock wave profile equation of the basic flow field, solve the shock wave exit profile based on the three-dimensional leading edge profile of the fixed wide-domain time-varying wave-riding shape given in step 2) and the geometric relationship between the design curves. 3.3) Based on the shock wave angle and shock wave curvature of the three-dimensional curved shock wave at the three-dimensional leading edge profile of the waverider, the Taylor series expression of the streamlines in each cross section is quickly obtained by the flow field analysis method based on the curved shock wave theory, and the parameterized expression of the lower surface of the waverider considering the incoming flow conditions and shock wave shape is realized by coordinate transformation. 3.4) Adjust the shock wave profile equation of the basic flow field, repeat steps 3.2)-3.3), and obtain M with the wave-riding area given in step 2). i The shape of a multiplicative wave; 3.5) Adjusting the design Mach number M i Repeat steps 3.1)-3.4) to obtain waverider profiles of each level with the three-dimensional leading edge profile and waverider area given in step 2). 4) Based on the volume ratio requirements, construct the upper surface of the waverider as a plane or convex surface to optimize the internal space and aerodynamic performance of the waverider; determine the tail edge shape of each stage of the waverider to ensure a smooth transition with the lower and upper surfaces of the waverider; the upper surface, lower surface, and tail edge of each stage of the waverider together constitute the shape of each stage of the waverider; combine the shapes of each stage of the waverider to realize the wide-domain time-varying waverider shape design based on the bending shock wave theory.

2. The wide-domain time-varying wave-riding shape design method based on bending shock wave theory as described in claim 1, characterized in that... In step 2), the three-dimensional leading edge profile of the wide-domain time-varying waverider shape is given by the combination of its exit capture profile in the yoz plane and its horizontal projection profile in the xoy plane, as shown below: (1) (2) Where w is the half-span of the waverider.

3. The wide-domain time-varying wave-riding shape design method based on bending shock wave theory as described in claim 1, characterized in that the specific process of step 3.2) is as follows: 3.2.1) The equation for the curved shock wave profile in a given axisymmetric basic flow field is as follows: (3) The shock wave within the tangential plane is obtained by scaling the bending shock wave in the axisymmetric basic flow field, and its equation satisfies: (4) in, k is the scaling factor for the kiss section; 3.2.2) Establish the geometric relationship between the three-dimensional leading edge profile of the waverider, the exit capture profile of the waverider, the horizontal projection profile of the waverider, and the shock wave exit profile: For any leading edge point B0 on ​​the three-dimensional leading edge profile of the waverider, its tangent plane intersects the shock exit profile at point D and the waverider exit capture profile at point B; the tangent of the three-dimensional leading edge profile of the waverider at point B, the tangent of the waverider exit capture profile at point B, and the tangent of the shock exit profile at point D intersect at point E; here, tangent segments BE and DE are both located within the exit section; the sweep angle λ of the three-dimensional leading edge profile of the waverider at point B0 is determined by the following formula: (5) The following angular relationships exist within triangle BDE: (6) The angle β between the tangent BE and the horizontal direction can be obtained by differentiating equation (1): (7) The angle γ between tangent segments BE and DE is calculated by the following formula: (8) 3.2.3) Solve for the analytical expression of the shock wave exit profile: The position of shock point D within the kissing plane where the leading edge point B0 is located is determined by the angle α of the kissing plane and the distance between point B and point D, calculated as follows: (9) Substituting equations (1), (2), and (5) to (8) into equation (9), we obtain the analytical expression for the shock wave exit profile as follows: (10) Where f(y), p(y), and c(y) are the design inputs, (y D , z D This is the design output; repeat the above process along the three-dimensional leading edge profile of the waverider, with variables... Variations within [-w, w] yield the shock wave exit profile.

4. The wide-domain time-varying wave-riding shape design method based on bending shock wave theory as described in claim 1, characterized in that... The specific process of step 3.3) is as follows: 3.3.1) Given the incoming flow conditions, based on the shock angle and shock curvature of the three-dimensional curved shock wave at the three-dimensional leading edge profile of the waverider, solve the oblique shock wave equations, the first-order curved shock wave equations, and the second-order curved shock wave equations to obtain the aerodynamic parameters, first-order derivatives, and second-order derivatives of the aerodynamic parameters immediately adjacent to the curved shock wave at the leading edge of the waverider: The first-order bending shock wave equations are as follows: (11) In the formula, coefficients A, B, E, C, and G can be calculated from the incoming flow conditions and shock wave angle. Subscripts 1 and 2 represent the upstream and downstream flow parameters of the shock wave, respectively. Other variables are defined as follows: (12) in, p is pressure, δ is flow angle, ρ is density, V is flow velocity, and ω is vorticity. Where s is the shock wave angle and s is the streamline direction. Y represents the direction of the shock wave, and Y is the ordinate in the coordinate system of the kiss-shaped plane. The second-order bending shock wave equations are as follows: (13) The coefficients in the formula are also expressions for the incoming flow conditions and shock angle, and the other variables are defined as follows: (14) 3.3.2) Given the derivatives of the aerodynamic parameters along the streamline at the leading edge shock point, the streamline behind the curved shock wave in the tangential plane can be quickly solved using the following Taylor series: (15) In the formula, X is the abscissa in the tangential plane coordinate system, and the subscript 0 indicates the parameter at the leading edge of the waverider, which is the starting point of the streamline. The coefficients are constructed from the aerodynamic parameters and their derivatives. (16) 3.3.3) Based on the angle of the anastomosis surface By restoring the streamlines within each two-dimensional cross-section to the true three-dimensional Cartesian coordinate system, a parametric expression for the lower surface of the waverider considering the incoming flow conditions and shock wave shape is obtained: (17) in, variable From 0 to Repeat the above process along the three-dimensional leading edge profile of the waverider, with variable y D It varies within [-w, w] and combines the streamlines within each cut surface to form the complete lower surface of the waverider.

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