Wide-domain time-varying waverider shape design method based on bending shock wave theory

Abstract

The invention discloses a wide-domain time-varying waverider shape design method based on a bending shock wave theory, and relates to near space hypersonic flight vehicle design. And determining a flight Mach number range according to the flight envelope, and determining a design Mach number and a flight height of each level of waverider shape of the wide-domain time-varying waverider shape. A three-dimensional leading edge molded line and a waverider area of a fixed wide-domain time-varying waverider shape are given according to flight mission requirements. A shock wave molded line equation of the basic flow field is adjusted, and according to the geometrical relationship between the design curves, all levels of waverider shapes with the same three-dimensional front edge molded line and waverider area are obtained through rapid solving by means of the bending shock wave theory. According to the plot ratio requirement, the upper surface of the wave rider is constructed into a plane or a convex surface. And combining all levels of waverider shapes to realize wide-range time-varying waverider shape design based on the bending shock wave theory. The waverider appearance can be changed autonomously and continuously according to task requirements and the flight environment, the aerodynamic performance under the flight envelope is effectively improved, and the waverider can adapt to wide-speed-range flight working conditions and various flight tasks.

Description

Technical Field

[0001] The present invention relates to the technical field of near-space hypersonic aircraft design, and in particular to a wide-domain time-varying waverider shape design method based on bending shock wave theory. Background Art

[0002] In recent years, domestic and foreign scholars have conducted a lot of research on waverider configurations, and proposed a series of waverider principles and methods, including wedge-guide waverider theory, cone-guide waverider theory, and tangent theory, and achieved fruitful research results. In addition, waverider design has gradually entered the engineering development stage, and a series of waverider flight tests including X-51A, HTV-2, and ARRW have been carried out at home and abroad.

[0004] At present, most variant waverider schemes are based on two-dimensional / conical basic flow fields, and the basic flow fields need to be calculated in advance when designing the waverider profiles under various discrete working conditions, which makes it difficult to achieve rapid analytical design of various waveriders under wide-domain conditions, greatly limiting the design space and efficiency of wide-domain variant waverider profiles. It can be seen that one of the problems currently restricting the wide-domain performance of hypersonic waveriders is the lack of a wide-domain time-varying waverider profile design method based on the bending shock wave theory. Summary of the invention

[0005] The purpose of the present invention is to provide a wide-range time-varying waverider shape design method based on the bending shock wave theory in view of the above-mentioned status of the prior art, which can continuously change the waverider shape according to the flight mission requirements of a wide speed range, and effectively improve the aerodynamic performance under the flight envelope. While ensuring that the three-dimensional leading edge profile and waverider area of ​​the waverider shape remain unchanged, the rapid analytical design of waveriders at all levels is achieved. It provides a new idea for variant waverider design and improves the design efficiency of wide-range variant waverider shapes.

[0006] In order to achieve the above-mentioned object of the invention, the present invention adopts the following technical scheme.

[0007] The method for designing a wide-area time-varying waverider shape based on bending shock wave theory includes the following steps:

[0008] 1) Determine the flight Mach number range according to the flight envelope, and determine the design Mach number and flight altitude of each level of the wide-range time-varying waverider profile;

[0009] 2) According to the flight mission requirements, a fixed three-dimensional leading edge profile and waverider area of ​​a wide-range time-varying waverider profile are given. The three-dimensional leading edge profile should meet the geometric requirements such as the slenderness ratio of the waverider profile and consider the matching with the waverider area;

[0010] 3) The shock wave profile equation of the basic flow field is adjusted to match the design Mach number and flight altitude. According to the geometric relationship between the design curves, the curved shock wave theory is used to quickly solve the lower surface of each level of waverider with the same three-dimensional leading edge profile and waverider area;

[0011] 4) According to the volume ratio requirements, the upper surface of the waverider is constructed to be a plane or a convex surface to optimize the internal space and aerodynamic performance of the waverider; the shape of the trailing edge surface of each level of waverider is determined to ensure a smooth transition with the lower surface and the upper surface of the waverider; the upper surface of each level of waverider, the lower surface of each level of waverider and the trailing edge surface of each level of waverider together constitute the shape of each level of waverider; the shape of each level of waverider is combined to realize the design of wide-range time-varying waverider shape based on the bending shock wave theory.

[0012] In step 2), the three-dimensional leading edge profile (LEPC) of the wide-area time-varying waverider profile is given by the combination of its exit capture profile (FCT) in the yoz plane and the horizontal projection profile (PPC) in the xoy plane, as shown below:

[0013] (1)

[0014] (2)

[0015] Where w is the half-length of the waverider.

[0016] In step 3), the shock wave profile equation of the basic flow field is adjusted to match the design Mach number and flight altitude. According to the geometric relationship between the design curves, the bending shock wave theory is used to quickly solve the lower surface of each level of waverider body with the same three-dimensional leading edge profile and waverider area. The specific process is:

[0017] 3.1) Determine the design Mach number M of the current first-stage waverider shape from step 1) i , Flight altitude H i and inflow conditions;

[0018] 3.2) Given the shock wave profile equation of the basic flow field, the shock wave exit profile (SWPC) is solved according to the three-dimensional leading edge profile (LEPC) of the fixed wide-domain time-varying waverider shape given in step 2) and the geometric relationship between the design curves;

[0019] 3.3) According to 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 tangent surface is quickly obtained by using the flow field analysis method based on the curved shock wave theory, and the parametric expression of the lower surface of the waverider considering the incoming flow conditions and the shock wave shape is realized through coordinate transformation;

[0020] 3.4) Adjust the shock wave line equation of the basic flow field, repeat steps 3.2)-3.3), and obtain M with the waveriding area given in step 2)i Stage waverider shape;

[0021] 3.5) Adjust the design Mach number M i , repeat steps 3.1)-3.4) to obtain various levels of waverider shapes with the three-dimensional leading edge profile and waverider area given in step 2).

[0022] Furthermore, the specific process of step 3.2) is as follows:

[0023] 3.2.1) Given an axisymmetric basic flow field, the equation of the curved shock wave profile is as follows:

[0024] (3)

[0025] The shock wave in the tangent plane is obtained by scaling the curved shock wave in the axisymmetric basic flow field, and its equation satisfies:

[0026] (4)

[0027] Where k is the kiss-plane scaling factor.

[0028] 3.2.2) Establish the geometric relationship between the three-dimensional leading edge profile of the waverider (LEPC), the exit capture profile of the waverider (FCT), the horizontal projection profile of the waverider (PPC) and the shock exit profile (SWPC):

[0029] For any leading edge point B0 on ​​LEPC, its tangent plane intersects with SWPC at point D and with FCT at point B. The tangent line of LEPC at point B0 intersects with the tangent line of FCT at point B and the tangent line of SWPC at point D at point E. Here, the tangent segments BE and DE are both located within the exit cross section. The sweep angle λ of LEPC at point B0 is determined by the following formula:

[0030] (5)

[0031] The following angle relationships exist within triangle BDE:

[0032] (6)

[0033] The angle β between the tangent line BE and the horizontal direction can be derived from formula (1):

[0034] (7)

[0035] The angle γ between the tangent segments BE and DE is calculated by the following formula:

[0036] (8)

[0037] 3.2.3) Solve the analytical expression of shock wave exit profile (SWPC):

[0038] The position information of the shock point D in 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, and is calculated as follows:

[0039] (9)

[0040] Substituting equations (1), (2), (5) to (8) into equation (9), we get the analytical expression of SWPC as follows:

[0041] (10)

[0042] Among them, f(y), p(y) and c(y) are design inputs, (y D , z D ) is the design output. The above process is repeated along the LEPC (which means that the variable (varies within [-w, w]), the shock wave exit profile SWPC can be obtained.

[0043] Furthermore, the specific process of step 3.3) is as follows:

[0044] 3.3.1) Given the incoming flow conditions, according to the shock angle and shock curvature of the three-dimensional bending shock wave at the three-dimensional leading edge of the waverider, the oblique shock wave relationship, the first-order bending shock wave equations and the second-order bending shock wave equations are solved to obtain the aerodynamic parameters, the first-order derivatives and the second-order derivatives of the aerodynamic parameters immediately after the leading edge of the waverider is adjacent to the bending shock wave:

[0045] The first-order bending shock wave equations are as follows:

[0046] (11)

[0047] Where, 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, and other variables are defined as follows:

[0048] (12)

[0049] Where p is pressure, δ is stream angle, ρ is density, V is stream velocity, ω is vorticity, is the shock wave angle, s is the streamline direction, is the shock wave direction, and Y is the ordinate in the tangent plane coordinate system.

[0050] The second-order bending shock wave equations are as follows:

[0051] (13)

[0052] The coefficients in the formula are also expressions of the incoming flow conditions and shock wave angles, and the other variables are defined as follows:

[0053] (14)

[0054] 3.3.2) When the derivatives of the aerodynamic parameters along the streamlines at the leading edge shock wave point are known, the streamlines behind the curved shock wave in the tangent plane can be quickly solved using the following Taylor series:

[0055] (15)

[0056] Where X is the horizontal coordinate in the tangent plane coordinate system, the subscript 0 represents the parameters at the leading edge of the waverider (i.e., the starting point of the streamline), and each coefficient is constructed by the aerodynamic parameters and their derivatives of various orders:

[0057] (16)

[0058] 3.3.3) According to the angle of the kissing plane , the streamlines in each two-dimensional tangent plane are restored to the real three-dimensional Cartesian coordinate system, and the parametric expression of the lower surface of the waverider considering the incoming flow conditions and the shock wave shape is obtained:

[0059] (17)

[0060] Among them, the variable From 0 to The above process is repeated along the LEPC (which means that the variable y D The streamlines in each tangent plane are combined to form a complete lower surface of the waverider.

[0061] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0062] The wide-range time-varying waverider shape based on the bending shock wave theory generated by the present invention can continuously change the waverider shape according to the flight mission requirements in a wide speed range under the premise that the three-dimensional leading edge profile and the waverider area remain unchanged, thereby effectively improving the aerodynamic performance under the full flight envelope. The parametric expression of the waverider shape not only considers the direct influence of the incoming flow conditions and the shock wave shape, but also facilitates designers to flexibly adjust the input according to the constraints. In addition, the use of the bending shock wave theory realizes the rapid analytical design of waveriders at all levels, greatly improving the design efficiency while ensuring the design accuracy. Broaden the design space of variant waverider aircraft and improve the design efficiency of wide-range variant waverider shapes. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1This is a flow chart of the design method of wide-area time-varying waverider shape based on bending shock wave theory.

[0064] Figure 2 The schematic diagram of the design principle of the wide-area time-varying waverider shape based on the bending shock wave theory. (a) is the overall three-dimensional view, (b) is the half-section perspective view, and (c) is the exit cross-sectional view.

[0065] Figure 3 Schematic diagram of the design curve of the wide-area time-varying waverider shape in different planes based on the bending shock wave theory, where (a) is the exit cross section and (b) is the horizontal projection.

[0066] Figure 4 Schematic diagram of the waverider surface shape of the wide-area time-varying waverider shape under different incoming flows based on the bending shock wave theory.

[0067] Figure 5 This is an overall schematic diagram of the wide-area time-varying waverider shape under different incoming flows based on the bending shock wave theory.

[0068] The marks in the figure are: 1 represents the three-dimensional leading edge profile of the waverider (i.e., LEPC line), 2 represents the waverider exit capture profile (i.e., FCT line), 3 represents the waverider horizontal projection profile (i.e., PPC line), 4 represents the shock wave exit profile (i.e., SWPC line), 5 represents the kissing surface, 6 represents the curved shock wave in the kissing surface, 7 represents the streamline in the kissing surface, 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 waverider symmetry plane, 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 DESCRIPTION

[0069] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following embodiments will further illustrate the present invention in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. On the contrary, the present invention encompasses any substitutions, modifications, equivalent methods and schemes made on the essence and scope of the present invention as defined by the claims. Further, in order to enable the public to have a better understanding of the present invention, some specific details are described in detail in the following detailed description of the present invention. For those skilled in the art, the present invention can be fully understood without the description of these details.

[0070] like Figures 1 to 5 As shown, the wide-area time-varying waverider shape design method based on bending shock wave theory includes the following steps:

[0071] (1) Determine the flight Mach number range [M1, M2] based on the flight envelope, and determine the design Mach number M of each level of the wide-band time-varying waverider profile i and flight altitude Hi ;

[0072] (2) A fixed three-dimensional leading edge profile 1 (i.e., LEPC line) and a waverider area S of a wide-band time-varying waverider profile are given according to the flight mission requirements. The three-dimensional leading edge profile 1 should meet the geometric requirements such as the slenderness ratio of the waverider profile;

[0073] (3) See Figure 2 to Figure 4 , adjusting the shock wave profile equation of the basic flow field, and using the curved shock wave theory to quickly solve the lower surface 11 of each level of waverider body with the same three-dimensional leading edge profile 1 and waverider area S according to the geometric relationship between the design curves;

[0074] (4) See Figure 5 According to the volume ratio requirement, the upper surface 12 of the waverider is constructed to be a plane or a convex surface, which together with the lower surface 11 of each level of the waverider generated by step (3) and the trailing edge surface 13 of each level of the waverider constitutes the waverider shape of each level. The waverider shapes of each level are combined to realize the design of wide-range time-varying waverider shape based on the bending shock wave theory.

[0075] See also Figure 2 In (a), in step (2), the three-dimensional leading edge profile 1 of the wide-band 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:

[0076] (1)

[0077] (2)

[0078] Where w is the half-length of the waverider.

[0079] The three-dimensional leading edge profile 1 of the wide-band time-varying waverider shape combined with the trailing edge line 9 (ie, LSPC line) on the lower surface of the waverider body defines the complete waverider shape.

[0080] In step (3), the shock wave profile equation of the basic flow field is adjusted, and according to the geometric relationship between the design curves, the bending shock wave theory is used to quickly solve and obtain the lower surface 11 of each level of waverider body with the same three-dimensional leading edge profile 1 and waverider area S. The specific process is as follows:

[0081] (3.1) Determine the design Mach number M of the current first-stage waverider shape from step (1): i , Flight altitude H i and inflow conditions;

[0082] (3.2) Given the shock wave profile equation of the basic flow field, according to the three-dimensional leading edge profile 1 of the fixed wide-domain time-varying waverider shape given in step (2), combined with the geometric relationship between the design curves, the shock wave exit profile 4 (i.e., SWPC line) is solved;

[0083] (3.3) According to the shock wave angle and the shock wave curvature of the three-dimensional curved shock wave surface 8 at the three-dimensional leading edge profile 1 of the waverider, the Taylor series expression of the streamlines in each tangent surface is quickly obtained by using the flow field analysis method based on the curved shock wave theory, and the parameterized expression of the lower surface 11 of the waverider considering the incoming flow conditions and the shock wave shape is realized by coordinate transformation;

[0084] (3.4) Adjust the shock wave line equation of the basic flow field, repeat steps (3.2)-(3.3), and obtain M with the waveriding area S given in step (2) i The lower surface of the waverider body is 11;

[0085] (3.5) Adjust the design Mach number M i Repeat steps (3.1)-(3.4) to obtain the lower surface 11 of each level of waverider body having the three-dimensional leading edge profile 1 and the waverider area S given in step (2), see Figure 4 .

[0086] Furthermore, the specific process of step (3.2) is as follows:

[0087] (3.2.1) Given an axisymmetric basic flow field, the curved shock wave profile equation is as follows:

[0088] (3)

[0089] The in-plane curved shock wave 6 in the in-plane curved surface 5 is obtained by scaling the curved shock wave in the axisymmetric basic flow field, and its equation satisfies:

[0090] (4)

[0091] Where k is the kiss-plane scaling factor.

[0092] (3.2.2) Establish the geometric relationship between the waverider three-dimensional leading edge profile 1, the waverider exit capture profile 2, the waverider horizontal projection profile 3 and the shock wave exit profile 4:

[0093] 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 of the waverider, its tangent plane 5 intersects with the shock wave exit profile 4 at point D, and intersects with the waverider exit capture profile 2 at point B. The tangent line of the three-dimensional leading edge profile 1 of the waverider at point B0 intersects with the tangent line of the waverider exit capture profile 2 at point B and the tangent line of the shock wave exit profile 4 at point D at point E. Here, the tangent segments BE and DE are both located within the exit cross section. The sweep angle λ of the three-dimensional leading edge profile 1 of the waverider at point B0 is determined by the following formula:

[0094] (5)

[0095] like Figure 2 As shown in (c) in the figure, the following angle relationship exists in triangle BDE:

[0096] (6)

[0097] The angle β between the tangent line BE and the horizontal direction can be derived from formula (1):

[0098] (7)

[0099] The angle γ between the tangent segments BE and DE is calculated by the following formula:

[0100] (8)

[0101] (3.2.3) Solve the analytical expression of shock wave exit profile 4:

[0102] The position information of the shock point D in the kissing surface 5 where the leading edge point B0 is located is determined by the angle α of the kissing surface 5 and the distance between point B and point D, and is calculated as follows:

[0103] (9)

[0104] Substituting equations (1), (2), (5) to (8) into equation (9), the analytical expression of the shock wave exit profile 4 is obtained as follows:

[0105] (10)

[0106] Among them, f(y), p(y) and c(y) are design inputs, (y D , z D ) is the design output. The above process is repeated along the waverider three-dimensional leading edge profile 1 (which means that the variable (varies within [-w, w]), the shock wave exit profile 4 can be obtained.

[0107] Furthermore, the specific process of step (3.3) is as follows:

[0108] (3.3.1) Given the incoming flow conditions, according to 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 oblique shock wave relationship, the first-order curved shock wave equations and the second-order curved shock wave equations are solved to obtain the aerodynamic parameters, the first-order derivatives and the second-order derivatives of the aerodynamic parameters after the leading edge 1 of the waverider is adjacent to the three-dimensional curved shock surface 8:

[0109] The first-order bending shock wave equations are as follows:

[0110] (11)

[0111] Where, 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, and other variables are defined as follows:

[0112] (12)

[0113] Where p is pressure, δ is stream angle, ρ is density, V is stream velocity, ω is vorticity, is the shock wave angle, s is the streamline direction, is the shock wave direction, and Y is the ordinate in the tangent plane coordinate system.

[0114] The second-order bending shock wave equations are as follows:

[0115] (13)

[0116] The coefficients in the formula are also expressions of the incoming flow conditions and shock wave angles, and the other variables are defined as follows:

[0117] (14)

[0118] (3.3.2) When the derivatives of the aerodynamic parameters along the streamlines at the leading edge shock wave point are known, the streamlines 7 in the kissing plane after the curved shock wave 6 in the kissing plane 5 can be quickly solved using the following Taylor series:

[0119] (15)

[0120] Where X is the abscissa in the tangent plane coordinate system, the subscript 0 represents the parameters at the leading edge of the waverider (i.e., the starting point of streamline 7 in the tangent plane), and each coefficient is constructed by the aerodynamic parameters and their derivatives of various orders:

[0121] (16)

[0122] (3.3.3) According to the angle of the incision , the streamlines in each two-dimensional tangent plane are restored to the real three-dimensional Cartesian coordinate system, and the parameterized expression of the lower surface 11 of the waverider body considering the incoming flow conditions and the shock wave shape is obtained:

[0123] (17)

[0124] Among them, the variable From 0 to Repeat the above process along the waverider three-dimensional front edge profile 1 (which means that the variable y D The streamlines in each tangent plane are combined to form a complete lower surface of the waverider 11.

[0125] See also Figure 5 The wide-range time-varying waverider shape designed based on the bending shock wave theory of the present invention is composed of the waverider lower surface 11, the waverider upper surface 12 and the waverider trailing edge surface 13. The waverider lower surface 11 is designed according to the bending shock wave theory; the waverider upper surfaces of each level are the same horizontal plane. This design simplifies the structure of the waverider and facilitates the subsequent design of the convex upper surface to meet the requirements of loading and pressure center coefficient.

[0126] The wide-range time-varying waverider shape based on the bending shock wave theory has the same three-dimensional leading edge profile and waverider area at each level, so a deformable high-temperature resistant flexible skin can be selected for the lower surface 11 of the waverider shape. Optionally, the flexible skin includes an aerogel insulation layer, an elastic matrix layer and a high anisotropic support layer arranged in sequence from the outside to the inside. The aerogel insulation layer provides excellent thermal insulation performance and protects the internal structure from high temperature. The elastic matrix layer provides the necessary elasticity and flexibility so that the skin can be continuously deformed at different flight Mach numbers. High anisotropic support layer: provides the necessary strength and stability to ensure that the skin will not be damaged during the deformation process. According to the flight mission, the deformation, load-bearing and high-temperature resistance performance requirements of each level of waverider shape within a wide Mach number range are accurately calculated, and the materials used for each layer of the skin are selected to ensure that the deformation of the wide-range time-varying waverider shape is continuous and stable under the flight envelope.

[0127] See also Figure 5Taking the flight Mach number of 20 to 5 as an example, the wide-range time-varying waverider shape based on the bending shock wave theory has nine levels of waverider lower surfaces. During the flight, as the Mach number decreases, the flexible skin of the waverider surface will continuously deform to adapt to different flight conditions. The upper surfaces of each level of waveriders are the same horizontal plane, and the convex upper surface can be supplemented to meet the requirements of loading and pressure center coefficient. The wide-range time-varying waverider shape starts to glide from M20, at which time the waverider surface is the lower surface of the M20 first-level waverider; when gliding to M15, the flexible skin of the waverider surface has been continuously deformed to the lower surface of the M15 first-level waverider. By analogy, when gliding to M5, the flexible skin of the waverider surface has been continuously deformed to the lower surface of the M5 first-level waverider. The waverider shape changes continuously according to the mission requirements, and can be accurately adjusted according to the mission requirements, effectively improving the aerodynamic performance under the entire flight envelope. It not only improves the flight efficiency, but also enhances the stability and safety of the aircraft.

[0128] The above embodiments are only preferred embodiments of the present invention and cannot be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the present invention.

Claims

1. A wide-range time-varying waverider shape design method based on bending shock wave theory, characterized by The following steps are involved: 1) Determine the flight Mach number range according to the flight envelope, and determine the design Mach number and flight altitude of each level of the wide-range time-varying waverider profile; 2) According to the flight mission requirements, a fixed three-dimensional leading edge profile and waverider area of ​​a wide-range time-varying waverider profile are given, wherein the three-dimensional leading edge profile should satisfy the slenderness ratio of the waverider profile and consider matching with the waverider area; 3) The shock wave profile equation of the basic flow field is adjusted to match the design Mach number and flight altitude. According to the geometric relationship between the design curves, the curved shock wave theory is used to quickly solve the lower surface of each level of waverider with the same three-dimensional leading edge profile and waverider area; 4) According to the volume ratio requirements, the upper surface of the waverider is constructed to be a plane or a convex surface to optimize the internal space and aerodynamic performance of the waverider; the shape of the trailing edge surface of each level of waverider is determined to ensure a smooth transition with the lower surface and the upper surface of the waverider; the upper surface of each level of waverider, the lower surface of each level of waverider and the trailing edge surface of each level of waverider together constitute the shape of each level of waverider; the shape of each level of waverider is combined to realize the design of wide-range time-varying waverider shape based on the bending shock wave theory.

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

3. The method for designing a wide-range time-varying waverider shape based on bending shock wave theory as claimed in claim 1, characterized in that In step 3), the shock wave profile equation of the basic flow field is adjusted to match the design Mach number and flight altitude. According to the geometric relationship between the design curves, the bending shock wave theory is used to quickly solve the lower surface of each level of waverider body with the same three-dimensional leading edge profile and waverider area. The specific process is: 3.1) Determine the design Mach number M of the current first-stage waverider shape from step 1) i , Flight altitude H i and inflow conditions; 3.2) Given the shock wave profile equation of the basic flow field, the shock wave exit profile is solved according to the three-dimensional leading edge profile of the fixed wide-domain time-varying waverider shape given in step 2) and the geometric relationship between the design curves; 3.3) According to 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 tangent surface is quickly obtained by using the flow field analysis method based on the curved shock wave theory, and the parametric expression of the lower surface of the waverider considering the incoming flow conditions and the shock wave shape is realized through coordinate transformation; 3.4) Adjust the shock wave line equation of the basic flow field, repeat steps 3.2)-3.3), and obtain M with the waveriding area given in step 2) i Stage waverider shape; 3.5) Adjust the design Mach number M i , repeat steps 3.1)-3.4) to obtain various levels of waverider shapes with the three-dimensional leading edge profile and waverider area given in step 2).

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

5. The method for designing a wide-range time-varying waverider shape based on bending shock wave theory as claimed in claim 3, characterized in that The specific process of step 3.3) is: 3.3.1) Given the incoming flow conditions, according to the shock angle and shock curvature of the three-dimensional bending shock wave at the three-dimensional leading edge of the waverider, the oblique shock wave relationship, the first-order bending shock wave equations and the second-order bending shock wave equations are solved to obtain the aerodynamic parameters, the first-order derivatives and the second-order derivatives of the aerodynamic parameters immediately after the leading edge of the waverider is adjacent to the bending shock wave: The first-order bending shock wave equations are as follows: (11) Where, 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, and other variables are defined as follows: (12) in, p is pressure, δ is stream angle, ρ is density, V is stream velocity, ω is vorticity, is the shock wave angle, s is the streamline direction, is the shock wave direction, Y is the ordinate in the tangent plane coordinate system; The second-order bending shock wave equations are as follows: (13) The coefficients in the formula are also expressions of the incoming flow conditions and shock wave angles, and the other variables are defined as follows: (14) 3.3.2) When the derivatives of the aerodynamic parameters along the streamlines at the leading edge shock wave point are known, the streamlines behind the curved shock wave in the tangent plane can be quickly solved using the following Taylor series: (15) Where X is the horizontal coordinate in the tangent plane coordinate system, the subscript 0 represents the parameters at the leading edge of the waverider, which is the starting point of the streamline. The coefficients are constructed by the aerodynamic parameters and their derivatives: (16) 3.3.3) According to the angle of the kissing plane , the streamlines in each two-dimensional tangent plane are restored to the real three-dimensional Cartesian coordinate system, and the parameterized expression of the lower surface of the waverider considering the incoming flow conditions and the shock wave shape is obtained: (17) in, variable From 0 to ; Repeat the above process along the three-dimensional leading edge of the waverider, and the variable y D It varies within [-w, w] and combines the streamlines within each tangent plane to form a complete lower surface of the waverider.

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