Design method of von Karman waverider based on tangent axisymmetric von Karman waverider with horizontal projection line on leading edge

Abstract

The invention discloses a design method of a von Karman waverider based on a tangent axisymmetric von Karman waverider with a leading edge horizontal projection line, including: establishing an original reference flow field; solving the tangent plane, the tangent plane reference flow field, and the tangent plane reference flow field longitudinal shock wave corresponding to each shock wave bottom point; solving each tangent plane leading edge point from the leading edge horizontal projection line to form a three-dimensional leading edge line; obtaining the tangent plane streamline and the lower surface trailing edge point to form the lower surface of the waverider, forming the lower surface trailing edge line of the waverider; generating the tangent plane upper surface free streamline to form the upper surface of the waverider, forming the upper surface trailing edge line of the waverider; the upper surface trailing edge line of the waverider and the lower surface trailing edge line of the waverider form the bottom surface of the waverider, and the upper surface of the waverider, the lower surface of the waverider and the bottom surface of the waverider together form a tangent axisymmetric von Karman waverider based on the leading edge horizontal projection line. The invention is applied to the field of aerodynamic shape design of hypersonic aircraft, and improves the design freedom of the shape of the tangent axisymmetric von Karman waverider.

Description

Technical Field

[0001] The invention relates to the technical field of aerodynamic shape design of hypersonic aircraft, in particular to a design method of an axisymmetric von Karman waverider based on a leading edge horizontal projection line tangent to the axis. Background Art

[0002] Hypersonic aircraft refers to an aircraft with a flight Mach number greater than 5, powered by an air-breathing engine or a combination of engines or without power, and capable of long-distance flight in the atmosphere and across the atmosphere. Its application forms include hypersonic cruise missiles, hypersonic gliders, hypersonic manned / unmanned aircraft, space planes, hypersonic wide-speed range aircraft and other aircraft.

[0003] The waverider configuration utilizes the shock wave compression principle (waverider principle) to achieve the aerodynamic requirements of high lift-to-drag ratio under hypersonic flight conditions, making the waverider an ideal configuration for hypersonic aircraft.

[0004] The invention patent application with publication date of April 5, 2019 and publication number 109573092A discloses a method for designing a tangential axisymmetric von Karman waverider, such as Figure 1 As shown, the design method of the invention patent is to solve the three-dimensional leading edge line 2 of the waverider given the leading bottom projection line 1 of the accordion axisymmetric von Karman waverider, so as to solve the configuration of the accordion axisymmetric von Karman waverider, that is, the leading bottom projection line is used as the input parameter of the accordion axisymmetric von Karman waverider, and the three-dimensional leading edge line of the waverider is the output parameter, which determines that the leading edge line shape and sweep angle of the accordion axisymmetric von Karman waverider designed and generated by this method are output values. The above limitations make it impossible for this method to design the leading edge line shape and leading edge line sweep angle distribution law of the accordion axisymmetric von Karman waverider. For the convenience of the following description, the invention patent design method with a publication date of April 5, 2019 and a publication number of 109573092A is referred to as the original accordion axisymmetric von Karman waverider design method. Summary of the invention

[0005] As can be seen from the background technology, the original osculating axisymmetric von Karman waverider design method uses the leading edge bottom projection profile as an input parameter, so the leading edge line shape and the leading edge line sweep angle distribution law of the original osculating axisymmetric von Karman waverider cannot be designed. In view of the above-mentioned deficiencies in the prior art, the present invention provides a osculating axisymmetric von Karman waverider design method based on the leading edge horizontal projection profile line, which solves the problem that the original osculating axisymmetric von Karman waverider cannot design the leading edge line shape or the leading edge line sweep angle distribution law.

[0006] To achieve the above object, the present invention provides a method for designing an axisymmetric von Karman waverider based on a front horizontal projection line that tangents the axis, comprising the following steps:

[0007] S1, the supersonic axisymmetric flow field around the zero-angle-of-attack pointed von Karman curve body of revolution is taken as the original reference flow field;

[0008] S2, given the shock wave bottom profile and uniformly discretized it, to obtain n shock wave bottom points, solve the corresponding tangent plane, tangent plane reference flow field and tangent plane reference flow field longitudinal shock wave of each shock wave bottom point;

[0009] S3, given the leading edge horizontal projection line equation and the sweep angle distribution law, project the leading edge horizontal projection line along the y-axis direction to the longitudinal shock wave of each tangent plane reference flow field, solve each tangent plane leading edge point, and obtain the three-dimensional leading edge line based on the connecting line of all tangent plane leading edge points;

[0010] S4, tracing streamlines from the leading edge points of each tangent plane to the bottom plane to obtain the tangent plane streamlines and the trailing edge points of the lower surface, obtaining the lower surface of the waverider body based on the lofting of all the tangent plane streamlines, and obtaining the trailing edge line of the lower surface of the waverider body based on the connecting line of the trailing edge points of the lower surface of all the tangent planes;

[0011] S5, on each tangent plane, projecting the leading edge point of the tangent plane along the x-axis direction to the bottom cross section of the waverider body, generating the trailing edge point of the upper surface of the tangent plane, and then generating the free streamline of the upper surface of the tangent plane, lofting the upper surface of the waverider body based on all the free streamlines of the upper surface of the tangent plane, and forming the trailing edge line of the upper surface of the waverider body based on the connecting line of the trailing edge points of the upper surface of the tangent plane;

[0012] S6, obtaining the bottom surface of the waverider based on the trailing edge line of the upper surface of the waverider and the trailing edge line of the lower surface of the waverider, and obtaining the axially symmetric von Karman waverider based on the leading edge horizontal projection line based on the upper surface of the waverider, the lower surface of the waverider and the bottom surface of the waverider.

[0013] In one embodiment, in S1, the supersonic axisymmetric flow field of a body of revolution around a zero angle of attack pointed von Karman curve is calculated using a rotating characteristic line method.

[0014] In one embodiment, S2 specifically includes:

[0015] S2.1, determine the cross section of the bottom of the waverider, give the shock wave bottom profile at the cross section of the bottom of the waverider, and evenly discretize it to obtain n shock wave bottom points; wherein the cross section of the bottom of the waverider is a plane with the same x-axis coordinate value as the bottom of the waverider;

[0016] S2.2, calculate the radius of curvature Ri and the center of the curvature circle of the bottom point of the i-th shock wave, and then obtain the curvature circle, and use the curvature circle as the bottom shock wave of the tangent plane reference flow field of the i-th shock wave bottom point. The center of the curvature circle is also the axis of the tangent plane reference flow field of the i-th shock wave bottom point. Connect the i-th shock wave bottom point and the center of the curvature circle to obtain a straight line segment, and use the plane passing through the straight line segment and perpendicular to the bottom cross section of the waverider body as the tangent plane corresponding to the i-th shock wave bottom point, referred to as the i-th tangent plane;

[0017] S2.3, the ratio of the radius Ri of the curvature circle at the bottom point of the i-th shock wave to the radius R of the bottom shock wave of the original reference flow field in S1, Ri / R, is used as the scaling ratio of the i-th tangent plane reference flow field to the original reference flow field;

[0018] S2.4, in the i-th tangent plane, the original reference flow field in S1 is scaled by Ri / R times, and the scaled reference flow field is translated so that the bottom cross section of the translated reference flow field is flush with the bottom cross section of the waverider body, and the axis of the translated reference flow field coincides with the axis of the tangent reference flow field at the bottom point of the i-th shock wave; the scaled and translated reference flow field is used as the i-th tangent plane reference flow field, and the i-th tangent plane reference flow field longitudinal shock wave is obtained;

[0019] S2.5, using the methods of steps S2.2 to S2.4, obtain the tangent plane, tangent plane reference flow field, and tangent plane reference flow field longitudinal shock wave corresponding to n shock wave bottom points.

[0020] In one embodiment, S3 specifically includes:

[0021] S3.1, define the horizontal section as a plane with a given y-axis coordinate value, and in the horizontal section, give the equation of the horizontal projection line of the leading edge and the distribution law of the sweep angle;

[0022] S3.2, at the i-th tangent plane, project the leading edge horizontal projection profile line along the y-axis direction to the longitudinal shock wave of the i-th tangent plane reference flow field, and solve to obtain the i-th discrete point of the leading edge horizontal projection profile line and the discrete point of the three-dimensional leading edge line at the i-th tangent plane. Since the leading edge horizontal projection profile line is a two-dimensional leading edge line, the i-th discrete point of the leading edge horizontal projection profile line is referred to as the i-th two-dimensional leading edge point, and the discrete point of the three-dimensional leading edge line at the i-th tangent plane is referred to as the i-th tangent plane leading edge point;

[0023] S3.3, based on step S3.2, n front edge points of the tangent plane are generated, and the lines connecting the n front edge points of the tangent plane form a three-dimensional front edge line.

[0024] In one embodiment, in S3.1, the front edge horizontal projection line is a two-dimensional front edge line, and its line equation is a cubic polynomial, which is:

[0025] x=a h z 3 +b h z 2 +c h z+d h ,z∈[0,L2] (1)

[0026] Among them, x is the vertical coordinate value of the rectangular coordinate system, z is the horizontal coordinate value of the rectangular coordinate system, and a h 、b h 、c h d h is the coefficient of the equation, which is calculated by the following equations (2)-(5):

[0027]

[0028]

[0029] c h =tan(ψ Ph1 ) (4)

[0030] d h =x Ph1 (5)

[0031] Among them, (z Ph1 , x Ph1 ) is the coordinate value of the end point of the longitudinal symmetry plane of the horizontal projection line of the leading edge, (z Ph2 , x Ph2 ) is the coordinate value of the left end point of the wing tip, L2 is the half span, ψ Ph1 is the sweep angle of the symmetry plane, ψ Ph2 is the wingtip sweep angle.

[0032] In one embodiment, S4 is specifically:

[0033] S4.1, in the i-th tangent plane, starting from the i-th tangent plane leading edge point, trace the downstream streamline to the bottom cross section of the waverider body to obtain the i-th tangent plane streamline. The end point of the streamline is the i-th tangent plane discrete point on the trailing edge line of the lower surface of the waverider body, referred to as the i-th tangent plane lower surface trailing edge point;

[0034] S4.2, based on step S4.1, generate n tangent plane streamlines and n tangent plane lower surface trailing edge points, the n tangent plane streamlines are lofted to generate a waverider surface as the lower surface of the waverider body, and the n tangent plane lower surface trailing edge points are connected to form a trailing edge line of the lower surface of the waverider body.

[0035] In one of the embodiments, in S5, in the i-th tangent plane, a line connecting the leading edge point of the i-th tangent plane and the trailing edge point of the upper surface of the i-th tangent plane is used as a free streamline on the upper surface of the i-th tangent plane.

[0036] The present invention provides a design method for an axisymmetric von Karman waverider based on a tangent axisymmetric leading edge horizontal projection profile. The method takes the leading edge horizontal projection profile as an input condition, and can design the leading edge line shape and the leading edge line sweep angle distribution. This solves the problem that the original axisymmetric von Karman waverider cannot design the leading edge line shape and the leading edge line sweep angle distribution law, and improves the design freedom of the appearance of the tangent axisymmetric von Karman waverider. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0038] Figure 1 It is a schematic diagram of the geometrical line of the tangent axisymmetric von Karman waverider;

[0039] Figure 2 Flow chart of the design method of the axisymmetric von Karman waverider based on the front edge horizontal projection line tangent to the embodiment;

[0040] Figure 3 Schematic diagram of the characteristic profile of the bottom plane of the shock wave in this embodiment;

[0041] Figure 4 This is a schematic diagram of the reference flow field of the tangent plane in this embodiment;

[0042] Figure 5 Schematic diagram of the horizontal projection line of the leading edge in this embodiment;

[0043] Figure 6 This is a schematic diagram of solving the three-dimensional leading edge line from the leading edge horizontal projection line in this embodiment;

[0044] Figure 7 A schematic diagram of constructing streamlines and free streamlines on the tangent plane in this embodiment;

[0045] Figure 8 Schematic diagram of the shock bottom profile, leading edge horizontal projection profile and three-dimensional leading edge line (including discrete points) output by the implementation case program in this embodiment;

[0046] Fig. 9 Schematic diagram of n tangent plane streamlines of an implementation case in this embodiment;

[0047] Fig.10 It is a schematic diagram of the lower surface of the waverider of the implementation case in this embodiment;

[0048] Fig.11 Schematic diagram of the upper surface and bottom surface of the waverider of the implementation case in this embodiment;

[0049] Fig.12 The configuration diagram of the von Karman waverider based on the front edge horizontal projection line tangent to the axisymmetric von Karman waverider constructed for the implementation case in this embodiment, wherein: (a) is a front view, and (b) is a top view;

[0050] Fig.13 This is the Mach number flow field diagram of the bottom cross section of the waverider body of the implementation case obtained by numerical calculation in the design flight state (incoming flow Mach number 6.0, angle of attack 0°, altitude 26km) in this embodiment.

[0051] Figure Number:

[0052] x represents the coordinate value in the longitudinal direction of the rectangular coordinate system, y represents the coordinate value in the normal direction of the rectangular coordinate system, z represents the coordinate value in the transverse direction of the rectangular coordinate system, and O represents the origin of the rectangular coordinate system;

[0053] xi represents the axial coordinate axis of the i-th tangent plane reference flow field in the cylindrical coordinate system, which is parallel to the x-axis; ri represents the radial coordinate axis of the i-th tangent plane reference flow field in the cylindrical coordinate system;

[0054] 1 represents the bottom projection line of the leading edge line;

[0055] 2 represents the three-dimensional leading edge line;

[0056] 3 represents the shock bottom line;

[0057] 4 represents the left end point of the shock wave bottom line;

[0058] 5 represents the right end point of the shock bottom line;

[0059] 6 represents the i-th discrete point on the shock bottom line, referred to as the i-th shock bottom point;

[0060] 7 represents the center of curvature of the bottom point of the i-th shock wave, which is also the axis of the tangent plane reference flow field at the bottom point of the i-th shock wave;

[0061] 8 represents the curvature circle of the bottom point of the i-th shock wave, which is also the bottom shock wave of the tangent plane reference flow field at the bottom point of the i-th shock wave;

[0062] 9 represents the tangent plane corresponding to the bottom point of the i-th shock wave, referred to as the i-th tangent plane;

[0063] 10 represents the cross section of the bottom of the waverider, which is a plane with the same x-coordinate value as the bottom of the waverider;

[0064] 11 represents the longitudinal shock wave of the i-th tangent plane reference flow field;

[0065] 12 represents the longitudinal wall of the i-th tangent plane reference flow field reference body;

[0066] 13 represents the horizontal projection line of the leading edge, which is a two-dimensional leading edge line;

[0067] 14 represents the end point of the longitudinal symmetry surface of the horizontal projection line of the leading edge;

[0068] 15 represents the left end point of the wing tip of the horizontal projection line of the leading edge;

[0069] 16 represents the right end point of the wing tip of the horizontal projection line of the leading edge;

[0070] 17 represents a three-dimensional leading edge line;

[0071] 18 represents the i-th discrete point of the front edge horizontal projection line. Since the front edge horizontal projection line is a two-dimensional front edge line, the discrete point is referred to as the i-th two-dimensional front edge point.

[0072] 19 represents the discrete point of the three-dimensional front edge line on the i-th tangent plane, referred to as the i-th tangent plane front edge point;

[0073] 20 represents the i-th tangent plane streamline;

[0074] 21 represents the end point of the i-th tangent plane streamline, which is also the i-th tangent plane discrete point on the trailing edge line of the lower surface of the waverider, referred to as the i-th tangent plane lower surface trailing edge point;

[0075] 22 represents the free streamline on the surface of the i-th tangent plane;

[0076] 23 represents the i-th tangent plane discrete point on the trailing edge line of the upper surface of the waverider, which is also the end point of the free streamline on the upper surface of the i-th tangent plane, referred to as the i-th tangent plane upper surface trailing edge point;

[0077] 24 represents the shock bottom profile and its discrete points output by the implementation case program;

[0078] 25 represents the front edge horizontal projection line and its discrete points output by the implementation case program;

[0079] 26 represents the three-dimensional front edge line and its discrete points output by the implementation case program;

[0080] 27 represents n tangent plane streamlines of the implementation case;

[0081] 28 indicates that n tangent plane streamlines are laid out to generate a waverider surface as the lower surface of the waverider body;

[0082] 29 indicates that the line connecting the trailing edge points of the lower surface of the n tangent planes constitutes the trailing edge line of the lower surface of the waverider;

[0083] 30 represents the upper surface of the waverider formed by lofting n free streamlines on the upper surface of the tangent plane;

[0084] 31 represents the trailing edge line of the upper surface of the waverider formed by connecting the trailing edge points of the n tangent planes;

[0085] 32 denotes the bottom surface of the waverider body formed by the trailing edge line of the upper surface and the trailing edge line of the lower surface of the waverider body;

[0086] 33 represents a front view of the shock wave theory design line of the bottom of the waverider body of the implementation case in the design flight state;

[0087] 34 represents a top view of the shock wave theory design line of the bottom of the waverider body in the design flight state of the implementation case.

[0088] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0089] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0090] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0091] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0092] like Figure 2 The figure shows a design method of an axisymmetric von Karman waverider based on a leading edge horizontal projection profile that is cut into pieces according to the embodiment, which mainly includes the following steps S1 to S6.

[0093] S1, taking the supersonic axisymmetric flow field around the zero-angle-of-attack pointed von Karman curve body of revolution as the original reference flow field, specifically:

[0094] The supersonic axisymmetric flow field of the von Karman curve body of revolution around the zero angle of attack tip is calculated using the rotating characteristic line method and used as the original reference flow field. The rotating characteristic line method comes from the invention patented design method of tangent axisymmetric von Karman waverider with the publication date of June 30, 2020 and the publication number of CN109573092B. The bottom shock wave radius of the original reference flow field is defined as R.

[0095] S2, given the shock wave bottom profile, and evenly discretize it to obtain n shock wave bottom points, solve the tangent plane, tangent plane reference flow field, and tangent plane reference flow field longitudinal shock wave corresponding to each shock wave bottom point.

[0096] refer to Figure 3 , Figure 4 , the specific implementation process of step S2 is:

[0097] S2.1, given the x-coordinate value x of the bottom of the waverider b , x=x b The plane 10 is the bottom cross section of the waverider; Figure 3 As shown, a shock wave bottom profile 3 is given in the bottom cross section of the waverider body, and its left and right endpoints are points 4 and 5 respectively. The shock wave bottom profile 3 is uniformly discretized to obtain n shock wave bottom points;

[0098] S2.2, the i-th discrete point on the shock wave bottom profile is point 6, which is referred to as the i-th shock wave bottom point 6. The curvature radius Ri and the curvature center point 7 of the i-th shock wave bottom point 6 are calculated, and then the curvature circle 8 is obtained. The curvature circle 8 is used as the bottom shock wave of the tangent plane reference flow field of the i-th shock wave bottom point. The curvature center point 7 is also the axis of the tangent plane reference flow field of the i-th shock wave bottom point. The i-th shock wave bottom point 6 and the curvature center point 7 are connected to obtain a straight line segment 6-7. The plane passing through the straight line segment 6-7 and perpendicular to the bottom cross section of the waverider body is used as the tangent plane 9 corresponding to the i-th shock wave bottom point 6, which is referred to as the i-th tangent plane 9;

[0099] S2.3, taking the ratio Ri / R of the radius of the curvature circle Ri of the bottom point 6 of the i-th shock wave to the radius R of the bottom shock wave of the original reference flow field defined in S1 as the scaling ratio of the i-th tangent plane reference flow field to the original reference flow field, and defining Ri / R equal to η;

[0100] S2.4, in the i-th tangent plane 9, the original reference flow field obtained by solving step S1 is scaled proportionally by η times; then the scaled reference flow field is translated so that the bottom cross section of the translated reference flow field is flush with the bottom cross section of the waverider body, that is, flush with plane 10, and the axis of the translated reference flow field coincides with the axis of the tangent reference flow field at the bottom point of the i-th shock wave, that is, coincides with the center of curvature 7; the scaled and translated reference flow field is used as the i-th tangent plane reference flow field, and then the i-th tangent plane reference flow field longitudinal shock wave 11 is obtained; 12 is the longitudinal wall of the i-th tangent plane reference flow field reference body corresponding to 11;

[0101] S2.5, using the methods of steps S2.2 to S2.4, obtain the tangent plane, tangent plane reference flow field, and tangent plane reference flow field longitudinal shock wave corresponding to the n shock wave bottom points.

[0102] S3, given the leading edge horizontal projection line equation and the sweep angle distribution law, project the leading edge horizontal projection line along the y-axis direction to the longitudinal shock wave of each tangent plane reference flow field, solve each tangent plane leading edge point, and connect all the tangent plane leading edge points to form a three-dimensional leading edge line.

[0103] refer to Figure 5 , the specific implementation process of step S3 is:

[0104] S3.1, given the y-axis coordinate value y of the horizontal projection line of the leading edge h , y=y h The plane is the horizontal section of the designed leading edge horizontal projection line. In this horizontal section, the leading edge horizontal projection line equation and the sweep angle distribution law are given;

[0105] like Figure 5 As shown, the front edge horizontal projection line 13 in this embodiment is a two-dimensional front edge line 15-14-16, the left and right end points are point 15 and point 16 respectively, and the end point of the longitudinal symmetry plane is point 14. The equation of the front edge horizontal projection line 13 is a cubic polynomial, which is:

[0106] x=a h z 3 +b h z 2 +c h z+d h ,z∈[0,L2] (1)

[0107] Among them, a h , bh, c h d h As the coefficient of the equation, the coordinate value of the end point of the longitudinal symmetry plane of the horizontal projection line of the leading edge can be input based on equation (1) (z Ph1 , xPh1 ), the coordinate value of the left end point of the wingtip (z Ph2 , x Ph2 ), half span L2, symmetry plane sweep angle ψ Ph1 and the wingtip sweep angle ψ Ph2 , and the coefficient a of the equation is derived h , b h 、c h ,d h , the calculation formula is shown in (2)-(5):

[0108]

[0109]

[0110] c h =tan(ψ Ph1 ) (4)

[0111] d h =x Ph1 (5)

[0112] S3.2, reference Figure 6 , at the i-th tangent plane 9, the leading edge horizontal projection profile 13 is projected along the y direction to the i-th tangent plane reference flow field longitudinal shock wave 11, and the i-th discrete point 18 of the leading edge horizontal projection profile and the discrete point 19 of the three-dimensional leading edge line at the i-th tangent plane are obtained by solving. Since the leading edge horizontal projection profile 13 is a two-dimensional leading edge line, the i-th discrete point of the leading edge horizontal projection profile is referred to as the i-th two-dimensional leading edge point 18, and the discrete point of the three-dimensional leading edge line at the i-th tangent plane is referred to as the i-th tangent plane leading edge point 19;

[0113] S3.3, using the method of step S3.2, generate n front edge points of the tangent plane, and the lines connecting the n front edge points of the tangent plane form a three-dimensional front edge line 17.

[0114] like Figure 8 As shown, 24, 25 and 26 respectively represent the shock wave bottom profile and its discrete points, the leading edge line horizontal projection profile and its discrete points, and the three-dimensional leading edge line and its discrete points output by the implementation case program.

[0115] S4, trace the streamlines from the n leading edge points of the tangent plane to the bottom plane, and obtain n tangent plane streamlines and n lower surface trailing edge points. The n tangent plane streamlines are laid out to form the lower surface of the waverider body, and the lines connecting the n trailing edge points of the lower surface of the tangent plane form the trailing edge line of the lower surface of the waverider body.

[0116] like Figure 7As shown, in the i-th tangent plane, starting from the i-th tangent plane leading edge point 19, the downstream streamline is traced to the bottom cross section of the waverider body, and the i-th tangent plane streamline 20 is obtained. The end point 21 of the streamline 20 is the i-th tangent plane discrete point on the trailing edge line of the lower surface of the waverider body, referred to as the i-th tangent plane lower surface trailing edge point 21;

[0117] Using the same method as above, Fig. 9 As shown, n tangent plane streamlines 27 and n tangent plane lower surface trailing edge points are generated; Fig.10 As shown, n tangent plane streamlines 27 are lofted to generate a waverider surface 28 as the lower surface 28 of the waverider body, and the line connecting the trailing edge points of the lower surface of the n tangent planes forms a trailing edge line 29 of the lower surface of the waverider body.

[0118] S5, in n tangent planes, project the n leading edge points of the tangent planes along the x-axis direction to the bottom cross section of the waverider body, generate n trailing edge points of the upper surface of the tangent planes, and then generate n free streamlines on the upper surface of the tangent planes. The n free streamlines on the upper surface of the tangent planes are laid out to form the upper surface of the waverider body, and the lines connecting the trailing edge points on the upper surface of the tangent planes form the trailing edge line of the upper surface of the waverider body.

[0119] The specific solution method for the surface free streamline on the i-th tangent plane is:

[0120] like Figure 7 As shown, in the i-th tangent plane, the line 19 - 23 connecting the leading edge point 19 of the i-th tangent plane and the trailing edge point 23 of the upper surface of the i-th tangent plane is used as the free streamline 22 of the upper surface of the i-th tangent plane.

[0121] like Fig.11 As shown, n free streamlines on the upper surface of the tangent plane are laid out to form the upper surface 30 of the waverider body, and the line connecting the trailing edge points on the upper surface of the n tangent planes forms the trailing edge line 29 of the upper surface of the waverider body.

[0122] S6, such as Fig.11 As shown, the waverider upper surface trailing edge line 31 and the lower surface trailing edge line 29 constitute the waverider bottom surface 32, and the waverider upper surface 30, the waverider lower surface 28 and the waverider bottom surface 32 together constitute an axisymmetric von Karman waverider based on the leading edge horizontal projection line. Fig.12 A front view 33 and a top view 34 of an axisymmetric von Karman waverider configuration based on the front edge horizontal projection profile are shown.

[0123] The design method in this embodiment is further explained below in conjunction with specific implementation cases.

[0124] In this implementation case, the flow Mach number of 6.0, the angle of attack of 0° and the altitude of 26 km are used as the design flight conditions. The method provided by the present invention is used to generate the implementation case shape of the axisymmetric von Karman waverider configuration based on the leading edge horizontal projection line, and the numerical simulation of the implementation case shape is carried out.

[0125] Table 1 Leading edge line shape parameters and leading edge line sweep angle distribution of the implementation case

[0126]

[0127] Table 1 shows the leading edge line shape parameters and the leading edge line sweep angle distribution law. It can be seen that the patent of the present invention solves the problem that the original tangential axisymmetric von Karman waverider cannot design the leading edge line shape and the leading edge line sweep angle distribution law, and improves the design freedom of the tangential axisymmetric von Karman waverider shape.

[0128] Fig.13 The Mach number flow field diagram of the bottom cross section of the waverider body in the implementation case is shown. Fig.13 The middle dashed line 33 represents the theoretical design line of the shock wave at the bottom of the waverider in the design flight state of the implementation case. Fig.13 It can be seen that although the calculation condition is a viscous flow field, the overflow from the high-pressure area on the lower surface to the low-pressure area on the upper surface on both sides of the configuration is small, which verifies that the waverider configuration generated by the present invention has good waveriding characteristics; at the same time, the shape and position of the numerically calculated shock wave at the bottom of the waverider are in good agreement with the theoretical design values, which verifies the correctness of the patented waverider design method of the present invention and the effectiveness of the design procedure.

[0129] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification and drawings under the inventive concept of the present invention, or directly / indirectly applied in other related technical fields are included in the patent protection scope of the present invention.

Claims

1. A design method for an axisymmetric von Karman waverider based on a front-edge horizontal projection line, characterized in that: The steps include: S1, the supersonic axisymmetric flow field around the zero-angle-of-attack pointed von Karman curve body of revolution is taken as the original reference flow field; S2, given the shock wave bottom profile and uniformly discretized it, to obtain n shock wave bottom points, solve the corresponding tangent plane, tangent plane reference flow field and tangent plane reference flow field longitudinal shock wave of each shock wave bottom point; S3, given the leading edge horizontal projection line equation and the sweep angle distribution law, project the leading edge horizontal projection line along the y-axis direction to the longitudinal shock wave of each tangent plane reference flow field, solve each tangent plane leading edge point, and obtain the three-dimensional leading edge line based on the connecting line of all tangent plane leading edge points; S4, tracing streamlines from the leading edge points of each tangent plane to the bottom plane to obtain the tangent plane streamlines and the trailing edge points of the lower surface, obtaining the lower surface of the waverider body based on the lofting of all the tangent plane streamlines, and obtaining the trailing edge line of the lower surface of the waverider body based on the connecting line of the trailing edge points of the lower surface of all the tangent planes; S5, on each tangent plane, projecting the leading edge point of the tangent plane along the x-axis direction to the bottom cross section of the waverider body, generating the trailing edge point of the upper surface of the tangent plane, and then generating the free streamline of the upper surface of the tangent plane, lofting the upper surface of the waverider body based on all the free streamlines of the upper surface of the tangent plane, and forming the trailing edge line of the upper surface of the waverider body based on the connecting line of the trailing edge points of the upper surface of the tangent plane; S6, obtaining the bottom surface of the waverider based on the trailing edge line of the upper surface of the waverider and the trailing edge line of the lower surface of the waverider, and obtaining the axially symmetric von Karman waverider based on the leading edge horizontal projection line based on the upper surface of the waverider, the lower surface of the waverider and the bottom surface of the waverider.

2. The design method of an axisymmetric von Karman waverider based on a front edge horizontal projection line tangent to the front edge according to claim 1, characterized in that: In S1, the supersonic axisymmetric flow field around a zero angle of attack pointed von Karman curve body of revolution is calculated using the method of rotating characteristic lines.

3. The design method of an axisymmetric von Karman waverider based on a front edge horizontal projection line tangent to the front edge according to claim 1, characterized in that: S2 specifically includes: S2.1, determine the cross section of the bottom of the waverider, give the shock wave bottom profile at the cross section of the bottom of the waverider, and evenly discretize it to obtain n shock wave bottom points; wherein the cross section of the bottom of the waverider is a plane with the same x-axis coordinate value as the bottom of the waverider; S2.2, calculate the radius of curvature Ri and the center of the curvature circle of the bottom point of the i-th shock wave, and then obtain the curvature circle, and use the curvature circle as the bottom shock wave of the tangent plane reference flow field of the i-th shock wave bottom point. The center of the curvature circle is also the axis of the tangent plane reference flow field of the i-th shock wave bottom point. Connect the i-th shock wave bottom point and the center of the curvature circle to obtain a straight line segment, and use the plane passing through the straight line segment and perpendicular to the bottom cross section of the waverider body as the tangent plane corresponding to the i-th shock wave bottom point, referred to as the i-th tangent plane; S2.3, the ratio of the radius Ri of the curvature circle at the bottom point of the i-th shock wave to the radius R of the bottom shock wave of the original reference flow field in S1, Ri / R, is used as the scaling ratio of the i-th tangent plane reference flow field to the original reference flow field; S2.4, in the i-th tangent plane, the original reference flow field in S1 is scaled by Ri / R times, and the scaled reference flow field is translated so that the bottom cross section of the translated reference flow field is flush with the bottom cross section of the waverider body, and the axis of the translated reference flow field coincides with the axis of the tangent reference flow field at the bottom point of the i-th shock wave; the scaled and translated reference flow field is used as the i-th tangent plane reference flow field, and the i-th tangent plane reference flow field longitudinal shock wave is obtained; S2.5, using the methods of steps S2.2 to S2.4, obtain the tangent plane, tangent plane reference flow field, and tangent plane reference flow field longitudinal shock wave corresponding to n shock wave bottom points.

4. The design method of an axisymmetric von Karman waverider based on a front-edge horizontal projection line tangent to the front-edge horizontal projection line according to claim 1, 2 or 3, characterized in that: S3 specifically includes: S3.1, define the horizontal section as a plane with a given y-axis coordinate value, and in the horizontal section, give the equation of the horizontal projection line of the leading edge and the distribution law of the sweep angle; S3.2, at the i-th tangent plane, project the leading edge horizontal projection profile line along the y-axis direction to the longitudinal shock wave of the i-th tangent plane reference flow field, and solve to obtain the i-th discrete point of the leading edge horizontal projection profile line and the discrete point of the three-dimensional leading edge line at the i-th tangent plane. Since the leading edge horizontal projection profile line is a two-dimensional leading edge line, the i-th discrete point of the leading edge horizontal projection profile line is referred to as the i-th two-dimensional leading edge point, and the discrete point of the three-dimensional leading edge line at the i-th tangent plane is referred to as the i-th tangent plane leading edge point; S3.3, based on step S3.2, n front edge points of the tangent plane are generated, and the lines connecting the n front edge points of the tangent plane form a three-dimensional front edge line.

5. The design method of an axisymmetric von Karman waverider based on a front edge horizontal projection line tangent to the front edge according to claim 4, characterized in that: In S3.1, the front edge horizontal projection line is a two-dimensional front edge line, and its line equation is a cubic polynomial, which is: x=a h z 3 +b h z 2 +c h z+d h ,z∈[0,L2] (1) Among them, x is the vertical coordinate value of the rectangular coordinate system, z is the horizontal coordinate value of the rectangular coordinate system, and a h 、b h 、c h d h is the coefficient of the equation, which is calculated by the following equations (2)-(5): c h =tan(ψ Ph1 ) (4) d h =x Ph1 (5) Among them, (z Ph1 , x Ph1 ) is the coordinate value of the end point of the longitudinal symmetry plane of the horizontal projection line of the leading edge, (z Ph2 , x Ph2 ) is the coordinate value of the left end point of the wing tip, L2 is the half span, ψ Ph1 is the sweep angle of the symmetry plane, ψ Ph2 is the wingtip sweep angle.

6. The design method of an axisymmetric von Karman waverider based on a front-edge horizontal projection line tangent to the front-edge horizontal projection line according to claim 1, 2 or 3, characterized in that: S4 is specifically: S4.1, in the i-th tangent plane, starting from the i-th tangent plane leading edge point, trace the downstream streamline to the bottom cross section of the waverider body to obtain the i-th tangent plane streamline. The end point of the streamline is the i-th tangent plane discrete point on the trailing edge line of the lower surface of the waverider body, referred to as the i-th tangent plane lower surface trailing edge point; S4.2, based on step S4.1, generate n tangent plane streamlines and n tangent plane lower surface trailing edge points, the n tangent plane streamlines are lofted to generate a waverider surface as the lower surface of the waverider body, and the n tangent plane lower surface trailing edge points are connected to form a trailing edge line of the lower surface of the waverider body.

7. The design method of an axisymmetric von Karman waverider based on a front-edge horizontal projection line tangent to the front-edge horizontal projection line according to claim 1, 2 or 3, characterized in that: In S5, in the i-th tangent plane, the line connecting the leading edge point of the i-th tangent plane and the trailing edge point of the upper surface of the i-th tangent plane is taken as the free streamline of the upper surface of the i-th tangent plane.

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