A method for designing an osculating class of waveriders with custom three-dimensional leading edges

Abstract

The application provides a method for designing osculating class waverider with customized three-dimensional leading edge, and relates to the field of aerodynamic configuration design, and comprises the following steps: S1, generating a three-dimensional leading edge line of a waverider meeting a requirement and a projection curve of the leading edge line on a trailing edge section; S2, constructing a non-circular arc segment shock wave outlet profile matched with the osculating class waverider; S3, solving an axisymmetric outer cone shock wave profile according to the non-circular arc segment shock wave outlet profile; S4, obtaining a triangular flow field and corresponding left-running characteristic line by using the characteristic line method according to the axisymmetric outer cone shock wave profile; S5, taking the left-running characteristic line as an initial value condition and giving a surface constraint condition to obtain an axisymmetric outer cone flow field matched with the triangular flow field; and S6, taking the axisymmetric outer cone flow field as a reference, and obtaining the osculating class waverider configuration meeting the three-dimensional leading edge constraint by using the proportional scaling and streamline tracking method. The application solves the problem that the three-dimensional leading edge of the osculating class waverider cannot be customized, and is suitable for waverider design with more complex geometric constraints.

Description

Technical Field

[0001] This invention relates to the field of aerodynamic shape design. More specifically, this invention relates to a method for designing closely spaced waveriders with customized three-dimensional leading edges. Background Technology

[0002] Traditional aircraft shape design typically involves first forming the aerodynamic shape based on geometric constraints, and then solving the flow field and obtaining aerodynamic performance based on the aerodynamic shape. However, the commonly used waverider design method is exactly the opposite. It usually involves first selecting a suitable flow field (two-dimensional / axisymmetric / three-dimensional flow field), and then deriving the streamline shape of the target aircraft based on the flow field information. Its flow field can be obtained by interpolation based on the selected reference flow field.

[0003] For high-speed aircraft that are feasible in engineering, in addition to high requirements for lift-to-drag ratio, volume ratio, structural feasibility, and aerodynamic performance, there are usually certain restrictions on geometry. That is, the conventional method of deriving the aerodynamic shape of the aircraft solely from the flow field is difficult to fully meet the geometric constraints. Therefore, existing technologies have proposed a method for obtaining a customizable three-dimensional leading-edge waverider that satisfies specific geometric constraints by targeting a pre-defined three-dimensional leading-edge profile. However, the following problems still exist:

[0004] Prior art 1: A design method for a conical waverider with a given three-dimensional leading edge line, as described in patent application number CN201711428331.5, determines the mapping relationship between the target geometry and the flow field by providing a given three-dimensional leading edge line and flow field parameters, but does not consider the influence of the shock profile. The final shock profile is a design quantity, not a control quantity. From the perspective of the construction method of the waverider flow field, the relationship between the three-dimensional leading edge line, the shock line, and the reference flow field in prior art 1 is achieved through the method of scissor-cutting cones. The reference flow field in different scissor-cutting planes has different shock angles, which is limiting. From the perspective of the construction method of the reference flow field, it is a series of flow fields with different shock angles determined by the three-dimensional leading edge line and given flow parameters. Prior art 1 includes multiple conical flow fields, but does not involve other flow fields outside of the conical flow fields (such as the convex shock wave reference flow field).

[0005] Prior art 2: A three-dimensional customizable leading edge streamline tracing waverider design method with patent application number CN202310898025.7. From the perspective of the shock line shape, the shock line of prior art 2 can only be a circular arc curve; from the perspective of the construction method of the reference flow field, since the shock line of prior art 2 can only be a circular arc curve, the corresponding radius of curvature is a constant value, and the reference flow field in different oscillating planes is the same flow field.

[0006] This shows that existing customizable waverider designs have not truly released the constraints of waverider geometry and flow field structure, resulting in deficiencies in their ability to meet waverider design space, specific shock line constraints, and design flexibility. Summary of the Invention

[0007] One object of the present invention is to solve at least the above-mentioned problems and / or defects, and to provide at least the advantages described below.

[0008] To achieve these objectives and other advantages of the present invention, a method for designing a closely spaced waverider with a customized three-dimensional leading edge is provided, comprising:

[0009] S1. Based on the geometric constraints of the waverider, generate the required three-dimensional leading edge line of the waverider and the projection curve of the leading edge line on the trailing edge section. C 1;

[0010] S2, with C 1. As a constraint, construct the non-circular arc segment shock wave exit profile and corresponding center of curvature that closely match the waverider-like body. O i ( m i , n i );

[0011] S3, based on the non-circular arc segment shock wave exit profile and center of curvature of S2. O i ( m i , n i Solve for the axisymmetric external cone shock profile;

[0012] S4. Using the axisymmetric external cone shock profile of S3 as the initial condition, the axisymmetric object surface, the triangular flow field region and the corresponding leftward characteristic line are obtained by using the characteristic line method.

[0013] S5. Using the leftward characteristic line of S4 as the initial condition, and given the constraint conditions of the axisymmetric object surface, obtain the axisymmetric external cone flow field that matches the triangular flow field region.

[0014] S6. Based on the axisymmetric outer cone flow field of S5, a closely spaced waverider configuration that satisfies the three-dimensional leading edge constraint is obtained by using scaling and streamline tracing methods.

[0015] Preferably, in S1, with C 1. Midpoint of the line connecting the two endpoints O The origin of the coordinate system is defined by the length direction from the top to the bottom of the waverider. X The positive direction of the axis is perpendicular to... X The direction of the axis upward isY The positive direction of the axis is perpendicular to... XOY The outward direction of the plane is Z Establish a three-dimensional rectangular coordinate system along the positive direction of the axis. OXYZ;

[0016] In S2, the method for obtaining the shock wave exit profile of the non-circular arc segment is as follows:

[0017] S21, with C 1 represents the free-flow surface constraint line. C 1 in Z Projection on axis AB The direction to the right of the line is taken as Z The positive direction of the axis will be projected. AB The direction of the perpendicular bisector upwards is taken as Y The positive direction of the axis will be projected. AB The midpoint is taken as the origin of the coordinate system. O Establish a rectangular coordinate system ZOY ;

[0018] S22, in a rectangular coordinate system ZOY Within the third and fourth quadrants, by projection AB Construct a non-circular segment shock wave exit profile for the chord length, and the left endpoint of the non-circular segment shock wave exit profile... A exist Z On the negative half of the axis, the right end point B exist Z On the positive half-axis of the shaft, and the non-circular arc segment shock wave exit profile passes through Y The axis is divided into the right half of the non-circular arc segment shock wave exit profile and the left half of the non-circular arc segment shock wave exit profile.

[0019] S23. Control equations based on the shock wave exit profile of a non-circular arc segment. y = f ( z (Any point on the non-circular arc shock wave exit profile line) P i ( z i , y i The corresponding center of curvature O i ( m i , n i and radius of curvature R i It is characterized by the following formula:

[0020]

[0021] In the above formula, mi , n i They are O i x and y coordinates z i , y i They are P i x and y coordinates f′ (z i ) It is the governing equation y = f ( z )right z The first derivative in z= z i The value of time, f′′(z i ) It is the governing equation y = f ( z )right z The second derivative in z= z i The value of time, R i For any point P i ( z i , y i The corresponding radius of curvature, i =1, 2, 3... N ;

[0022] S24, Traversal P i ( z i , y i ), and center all curvature O i ( m i , n i Connect the points to obtain the curvature center distribution curve corresponding to the shock wave exit profile of the non-circular arc segment.

[0023] Preferably, in S3, the procedure for solving the axisymmetric external cone shock profile is as follows:

[0024] S31. Connect any point on the shock wave exit profile of the right half of the non-circular arc segment. P i and its center of curvature O iObtain the fluid close contact line O i P i Flow close-up line O i P i The equation of the straight line is:

[0025]

[0026] In the above formula, z i , y i They are P i x and y coordinates m i , n i They are O i The x and y coordinates;

[0027] S32, will C 1 and O i P i Solving the equations of the straight line simultaneously, for y, z Solve to obtain the intersection point. F i (0, y Fi , z Fi ), the intersection point F i and O i The distance is used as the shock radius before scaling. r i ,but r i It is characterized by the following formula:

[0028]

[0029] In the above formula, y Fi , z Fi Intersection points F i of Y axis coordinates and Z Axis coordinates;

[0030] S33, Intersection point F i (0, y Fi ,z Fi coordinates y Fi , z Fi Substituting the surface equation of the three-dimensional leading edge of the waverider f(x,y, z)= In 0, the intersection point is obtained. F i Corresponding to the three-dimensional leading edge of the waverider X Axis coordinates x Fi to determine the point D i ( x Fi , r i );

[0031] S34. Repeat S31-S33 to obtain a series of D i ( x Fi , r i A defined set of points D ;

[0032] S35. For any point P i ,Will r i exist P i The corresponding fluid close surface line O i P i Dimensionless processing is performed within the flow field to obtain the dimensionless shock wave radius. r i ′ and intersection F i of X Axis coordinates x Fi ′ to determine the point D i ′ ( x Fi ′ , r i ′ ), r i ′ and x Fi ′ Characterized by the following formula:

[0033]

[0034] In the above formula, R i It is any point on the non-circular arc shock wave exit profile line. P i The radius of curvature;

[0035] S36, Traverse all points P i Repeat S35 to obtain a series of... D i ′ ( x Fi ′ , r i ′ A defined set of points D ′ ,based on D ′ A corresponding axisymmetric external cone shock profile I is obtained, which corresponds to the shock exit profile of the right half non-circular arc segment.

[0036] Wherein, the left endpoint of the axisymmetric external cone shock wave profile I D 1 ′ Corresponding shock radius r 1 ′ minimum, right endpoint D N ′ Corresponding shock radius r N ′ maximum;

[0037] S37. Traverse all points on the shock wave exit profile of the left semicircular arc segment. P i Using the same method as S31-S36, an axisymmetric external cone shock profile II corresponding to the shock exit profile of the left half non-circular arc segment is obtained;

[0038] By combining axisymmetric external conical shock profile I and axisymmetric external conical shock profile II, the axisymmetric external conical shock profile corresponding to the non-circular arc segment shock exit profile is obtained.

[0039] Preferably, in S6, the method for obtaining a closely spaced waverider configuration that satisfies the three-dimensional leading edge constraint is as follows:

[0040] S61. Using the axisymmetric external cone flow field as known conditions, obtain the compression surface of the waverider by scaling and streamline tracing methods.

[0041] S62. Obtain the shock surface of the waverider based on the axisymmetric external cone shock profile;

[0042] S63, will C 1 along X Axial stretching yields the free-flow surface of the waverider;

[0043] S64. Using the free-flowing surface of the waverider as a constraint, assemble the shock surface, compression surface and free-flowing surface of the waverider to obtain a closely related waverider configuration that satisfies the three-dimensional leading edge constraint.

[0044] Preferably, in S61, the compression surface is obtained in the following way:

[0045] S6101, any point on the axisymmetric external cone shock wave profile. D i ′ ( x Fi ′ , r i ′ ),Will r i ′ and x Fi ′ Scale the wave to obtain the scaled shock radius. r ki and x Fki to determine the point D ki ( x Fki , r ki ), r ki and x Fki Characterized by the following formula:

[0046]

[0047] In the above formula, R i It is any point D i ′ ( x Fi ′ , r i ′ The corresponding non-circular arc segment shock wave exit profile point P i The radius of curvature;

[0048] S6102, Traverse all pointsD i ′ Repeat S6101 to obtain a series of... D ki ( x Fki , r ki A defined set of points D ki ,according to D ki A scaled-down axisymmetric external cone shock profile and the corresponding axisymmetric external cone flow field are obtained.

[0049] S6103, at the right end of the axisymmetric external cone shock profile based on the proportional scaling r kN Top cut r ki Get points F ki The position, with point F ki Starting from the point parallel to X The straight line of the axis intersects the axisymmetric external cone shock profile at... D ki ;

[0050] S6104, from point D ki Tracing downstream to the shock wave radius based on the scaled axisymmetric outer cone flow field r kN Up, and with r kN Intersect at point Q ki Thus, a streamline D is obtained. ki Q ki ;

[0051] S6105, Repeat S6103-S6104 to traverse D ki ( x Fki , r ki The corresponding radius of curvature r ki A series of streamlines D are obtained. ki Q ki The defined compression surface of the waverider.

[0052] Preferably, in S62, the shock wave surface is obtained in the following way:

[0053] S6201. Take any point on the axisymmetric external cone shock profile after scaling. D ki ( xFki , r ki ),according to D ki A position is obtained x Fki , radius is r ki Non-circular arc shock wave exit profile;

[0054] S6202, Repeat S6201 to iterate. D ki This yields a shock surface of the waverider composed of a series of non-circular arc segment shock wave exit profiles.

[0055] The present invention has at least the following beneficial effects:

[0056] Firstly, this invention achieves dual design of the flow field structure and shock wave structure of the waverider by providing a three-dimensional leading edge line and a circular shock wave line. Simultaneously, by combining closely related methods and through reverse design, constraints on the reference flow field are obtained, extending the selection of the reference flow field from a conical flow field to a more general axisymmetric flow field. This expands the design space, design flexibility, and ability to meet specific constraints of the waverider. Specifically:

[0057] 1. In terms of specific implementation, this invention determines the mapping relationship between target geometry and flow field by giving a three-dimensional leading edge line and shock wave profile. The shock wave profile is a control quantity rather than a design quantity.

[0058] 2. From the perspective of the construction method of the waverider flow field, the relationship between the three-dimensional leading edge line, shock line and reference flow field of the present invention is established by the close contact method. The reference flow fields in different close contact planes can come from the same reference flow field or from different reference flow fields, which has better adaptability.

[0059] 3. From the perspective of constructing the reference flow field, this invention obtains the geometric shape of the leading edge shock wave in the reference flow field by determining the position information through multiple three-dimensional leading edge lines and shock wave lines, forming a reference flow field shock wave curve that meets the requirements of waverider construction, and its derivative is the shock wave angle. Thus, the reference flow field is calculated in reverse. The reference flow field obtained by this method can be the same reference flow field or different reference flow fields. It can be a conical flow field, a concave shock wave reference flow field, or a convex shock wave reference flow field, making it more adaptable.

[0060] Secondly, this invention expands the shape of the shock line and increases the design flexibility of the waverider body customized for the leading edge. That is, this invention expands the shock line into a general curve that is second-differentiable and continuous. The shock line can be any concave curve that satisfies the continuity of the second derivative.

[0061] Meanwhile, this patent realizes the mapping relationship between the three-dimensional leading edge line, shock line and reference flow field through dimensionless processing, scaling and arrangement. The invention combines the oscillation method under different curvature radii to convert the constraints of different oscillation surface reference flow fields into the constraints of the same dimensionless reference flow field by scaling, which further releases the constraints of the waverider geometry and flow field structure, expands the customizable waverider design space of the three-dimensional leading edge line and the ability to meet specific shock line constraints.

[0062] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0063] Figure 1 This is the three-dimensional leading edge profile of the waverider of the present invention;

[0064] Figure 2 The three-dimensional leading edge line of the waverider in this invention is YOZ Projection curves on a plane C 1;

[0065] Figure 3 The three-dimensional leading edge line of the waverider in this invention is XOY Projection curves on a plane C 2;

[0066] Figure 4 This is a schematic diagram of the exit profile and curvature center distribution curve of the non-circular arc segment shock wave corresponding to S2 of the present invention and closely matched with the waverider;

[0067] Figure 5 This is a schematic diagram of the method for obtaining the axisymmetric external cone shock profile corresponding to S3 of the present invention;

[0068] Figure 6 This is a schematic diagram of the axisymmetric external cone shock profile corresponding to S3 of the present invention;

[0069] Figure 7 This is a schematic diagram of the triangular flow field region based on the axisymmetric external cone shock profile corresponding to S4 of the present invention;

[0070] Figure 8 This is a schematic diagram of the axisymmetric external cone flow field based on the axisymmetric external cone shock profile corresponding to S5 of the present invention;

[0071] Figure 9 This is a schematic diagram of the scaling and streamline tracing corresponding to S62 of the present invention;

[0072] Figure 10 This is a schematic diagram of the assembly process of the shock surface, compression surface and free flow surface of the wave rider corresponding to S64 of the present invention.

[0073] Figure 11 It is the closely related waverider configuration that satisfies the three-dimensional leading edge constraint corresponding to S6 of the present invention. Detailed Implementation

[0074] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0075] This invention provides a customizable intensive waverider design method for a three-dimensional leading edge. It provides a three-dimensional leading edge line conforming to waverider geometric constraints, constructs a non-circular segment shock profile matching the three-dimensional leading edge, inversely calculates a reference flow field set matching the three-dimensional leading edge and the non-circular segment shock, and uses an optimization design method to select a reference flow field from the reference flow field set that meets the design conditions. Within the reference flow field, intensive techniques are used to obtain an intensive waverider configuration that simultaneously satisfies performance indicators and three-dimensional leading edge constraints. The specific technical solution is as follows:

[0076] S1. Based on the geometric constraints of the waverider, generate the required three-dimensional leading edge line of the waverider and the projection curve of the leading edge line on the trailing edge section, such as... Figures 1-3 As shown, the specific operation steps are as follows:

[0077] S11, taking the horizontal rightward direction as X The positive direction of the axis, perpendicular to X Axial upward Y The positive direction of the axis, perpendicular to the right-hand rule. XOY Plane outwards Z The positive direction of the axis, with the three-dimensional leading edge in YO Projection curve of the Z-plane C 1. Midpoint of the line connecting the two endpoints O Establish a three-dimensional rectangular coordinate system with the origin as the coordinate origin. OXYZ ;

[0078] S12. Based on the customized requirements for the three-dimensional leading edge of the waverider, provide the surface equation of the three-dimensional leading edge line of the waverider. f(x, y,z)= 0, where x , y , z The equations of the surfaces are respectively f(x,y,z)= The unknown is 0;

[0079] S13, align the three-dimensional leading edge line to... YOZ Plane projection yields the projection curve. C 1: f( 0 ,y,z)= 0, Projection Curve C 1 in Z Projection on axis AB The length is the width of the waverider b,in f( 0 ,y,z)= 0 is the projection curve C The equation of 1, YOZ The plane is a three-dimensional rectangular coordinate system OXYZ middle Y shaft and Z The plane formed by the axes y , z The equations of the curves are respectively f( 0 ,y,z)= 0 y coordinates and z coordinate;

[0080] S14, align the three-dimensional leading edge line to... XOY Plane projection yields the projection curve. C 2: f(x,y, 0 )= 0, Projection Curve C 2 in X Projection on axis CD The length is the length of the waverider. a ,in f(x,y, 0 )= 0 is the projection curve C Equation 2, XOY The plane is a three-dimensional rectangular coordinate system OXYZ middle X shaft and Y The plane formed by the axes x , y The equations of the curves are respectively f(x,y, 0 )= 0 x coordinates and y coordinate.

[0081] S2. Using the projection curve of S1 as a constraint, construct the non-circular arc segment shock wave exit profile and the curvature center distribution curve of the flow close contact surface that match the closely matched waverider, such as... Figure 4 As shown, the specific operation steps are as follows:

[0082] S21, using the projection curve described in S13 C 1 represents the free-flow surface constraint line, and the free-flow surface constraint line is located at... Z Projection on axis AB The direction to the right of the line is the horizontal axis. Z The positive direction of the axis, along the straight line AB The vertical bisector points upwards along the y-axis. Y The positive direction of the axis, with AB The midpoint is the origin of the coordinate system. O Establish a rectangular coordinate system ZOY ;

[0083] in,C 1 represents the free-flow surface constraint line. AB For the free flow surface constraint line in Z Projection on the axis;

[0084] S22. Constructing a non-circular arc segment shock wave exit profile that closely matches a waverider, including:

[0085] S2201, along the straight line of S21 AB Construct a non-circular shock wave exit profile for the chord length. The non-circular shock wave exit profile is located in the third and fourth quadrants of the rectangular coordinate system. The left endpoint of the non-circular shock wave exit profile... A exist Z On the negative half of the axis, the right end point B exist Z On the positive half-axis of the shaft;

[0086] S2202. Give the governing equations for the shock wave exit profile in the non-circular arc segment. y = f ( z The commonly used non-circular arc segment shock wave exit profiles are the shock wave profiles controlled by elliptical arc segments and the exit profiles that are twice differentiable.

[0087] S23. Obtain the center of curvature at any point on the non-circular arc shock wave exit line;

[0088] Based on the governing equations of the shock wave exit profile in the non-circular arc segment, the results are obtained at any point on the shock wave exit profile in the non-circular arc segment. P i ( z i , y i The corresponding center of curvature O i ( m i , n i and radius of curvature R i :

[0089]

[0090] in, z i , y i These are the arbitrary points mentioned above. P i x and y coordinates m i , n i These are the centers of curvature. O ix and y coordinates f′(z i ) The governing equations described in S2202 y = f ( z )right z The first derivative in z= z i The value of time, f′′ (z i ) Governing equations y = f ( z )right z The second derivative in z= z i The value of time, R i For any point on the non-circular arc shock wave exit profile line P i ( z i , y i The corresponding radius of curvature, i =1, 2, 3, ... N , N are positive integers and N ≥1;

[0091] S24. Traverse any point on the shock wave exit profile of the non-circular arc segment. P i ( z i , y i ), get points P i ( z i , y i The center of curvature of ) O i ( m i , n i ), all centers of curvature O i ( m i , n i The line connecting these points represents the curvature center distribution curve of the shock wave exit profile in the non-circular arc segment. i =1, 2, 3, ... N , N are positive integers and N ≥1;

[0092] S25, Position the non-circular arc segment shock wave exit profile as described in S21. Y The right side of the axis is the shock wave exit profile of the right half of the non-circular arc segment, and the left side is the shock wave exit profile of the left half of the non-circular arc segment.

[0093] S3. Solve for the axisymmetric external cone shock profile based on the non-circular arc segment shock profile of S2, such as... Figures 5-6 As shown, the specific operation steps are as follows:

[0094] S31, Connect any point on the right half of the non-circular arc segment shock wave exit profile line described in S25. P i and its center of curvature O i Obtain the fluid close contact line O i P i Flow close-up line O i P i The equation of the straight line is:

[0095]

[0096] in, z i , y i These are the arbitrary points mentioned above. P i x and y coordinates m i , n i These are the centers of curvature. O i x and y coordinates i =1, 2, 3, ... N , N are positive integers and N ≥1;

[0097] S32, Obtain the fluid close contact surface line O i P i Intersection with the free-flow surface constraint line described in S21 F i Shock radius before scaling r i ;

[0098] Projection curve C 1. The equation of the free-flow surface constraint line f(0,y,z)=0 Closely related to flow surface line Oi P i Solving the equations of the straight line simultaneously, for y, z Solve the problem to obtain the intersection point. F i (0, y Fi , z Fi ), intersection F i With the curvature center described in S23 O i The distance is the shock wave radius before scaling. r i :

[0099]

[0100] in, y Fi , z Fi Intersection points F i of Y axis coordinates and Z Axis coordinates n i , m i These are the centers of curvature. O i of Y axis coordinates and Z Axis coordinates r i The shock wave radius before scaling. i =1, 2, 3, ... N , N are positive integers and N ≥1;

[0101] S33, Intersection point F i (0, y Fi , z Fi coordinates y Fi , z Fi Substituting the surface equation of the three-dimensional leading edge of the waverider f(x,y, z)= 0, to get the corresponding x Fi coordinates, where x Fi It is the intersection point F i On the three-dimensional leading edge of the waverider described in S1, corresponding toX Axis coordinates i =1, 2, 3, ... N , N are positive integers and N ≥1;

[0102] S34, obtain a result from ( x Fi , r i ) Determined point D i ,in x Fi It is the intersection point F i On the three-dimensional leading edge of the waverider described in S1, corresponding to X Axis coordinates r i It is the intersection point F i (0, y Fi , z Fi ) and center of curvature O i ( m i , n i The distance is the shock wave radius before scaling. D i It is by ( x Fi , r i ) definite point, i =1, 2, 3, ... N , N are positive integers and N ≥1;

[0103] S35. Traverse any point on the shock wave exit profile of the right half of the non-circular arc segment. P i Repeat S31-S34 to obtain a series of ( x Fi , r i ) Determined point D i ,in, D i It is by ( x Fi , r i ) definite point, x Fi It is the intersection point F iOn the three-dimensional leading edge of the waverider described in S1, corresponding to X Axis coordinates r i It is the intersection point F i (0, y Fi , z Fi ) and center of curvature O i ( m i , n i The distance is the shock wave radius before scaling. i =1, 2, 3, ... N , N are positive integers and N ≥1;

[0104] S36. For any point P i ,Will r i exist P i The corresponding fluid close surface line O i P i Dimensionless processing is performed within the flow field to obtain the dimensionless shock wave radius. r i ′ and intersection F i of X Axis coordinates x Fi ′ to determine the point D i ′ ( x Fi ′ , r i ′ ), r i ′ and x Fi ′ Characterized by the following formula:

[0105]

[0106] In the above formula, R i It is any point on the non-circular arc shock wave exit profile line. P i The radius of curvature;

[0107] S37, Traverse all points P i Repeat S36 to obtain a series of... D i ′ ( x Fi ′ , r i ′ A defined set of points D ′ ,based on D ′ A corresponding axisymmetric external cone shock profile I is obtained, which corresponds to the shock exit profile of the right half non-circular arc segment.

[0108] Wherein, the left endpoint of the axisymmetric external cone shock wave profile I D 1 ′ Corresponding shock radius r 1 ′ minimum, right endpoint D N ′ Corresponding shock radius r N ′ maximum;

[0109] Similarly, repeat S3 to obtain a smooth axisymmetric external cone shock profile II corresponding to the shock exit profile of the left half non-circular arc segment.

[0110] By combining axisymmetric external conical shock profile I and axisymmetric external conical shock profile II, the axisymmetric external conical shock profile corresponding to the non-circular arc segment shock exit profile is obtained;

[0111] S4. Using the axisymmetric external cone shock profile of S3 as initial conditions, the axisymmetric object surface, the triangular flow field region, and the corresponding leftward characteristic lines are obtained using the characteristic line method, such as... Figure 7 As shown, the specific operation steps are as follows:

[0112] S41. Using the axisymmetric external cone shock profile as the initial condition, the characteristic line method is used to obtain the axisymmetric object plane located on the left side above the axisymmetric external cone shock profile and the left-moving characteristic line located on the right side above the axisymmetric external cone shock profile.

[0113] S42. The axisymmetric object plane, the left-moving characteristic line and the axisymmetric outer cone shock wave profile intersect in pairs to form a triangular flow field region.

[0114] S5. Using the leftward characteristic line of S4 as the initial condition, and given the surface constraints, obtain the axisymmetric external cone flow field that matches the triangular flow field, such as... Figure 8As shown, the specific operation steps are as follows:

[0115] S5101, Given the surface angle of the object... x The pattern of change, namely θ=f(x) Then the surface of the object ,in θ For object angle, x It is the independent variable. f(x) The angle of the object follows x The changing pattern, r(x) It is the surface expression of the object;

[0116] S5102, Given the surface pressure as x The pattern of change, namely p=f(x) ,in p For surface pressure, x It is the independent variable. f (x) The surface pressure follows x The changing pattern;

[0117] S5103, Given the Mach number of the surface, x The pattern of change, namely Ma=f(x) ,in Ma The Mach number of the object surface. x It is the independent variable. f(x) The Mach number of the surface is related to the object. x The changing pattern;

[0118] S52. Based on the surface constraint conditions, the characteristic line method is used to obtain a triangular flow field from top to bottom, including an axisymmetric surface and an axisymmetric external cone shock profile.

[0119] S53. Assemble the triangular flow field using the leftward characteristic line described in S41 as a constraint to obtain an axisymmetric external cone flow field that matches the triangular flow field.

[0120] S6. Based on the axisymmetric outer cone flow field of S5, a closely spaced waverider configuration satisfying three-dimensional leading-edge constraints is obtained using scaling and streamline tracing methods, such as... Figures 9-11 As shown, the specific operation steps are as follows:

[0121] S61. Using the axisymmetric external cone flow field described in S53 as known conditions, obtain the compression surface of the waverider using scaling and streamline tracing methods, including:

[0122] S6101, any point on the axisymmetric external cone shock wave profile. D i ′ ( x Fi ′ , r i′ ),Will r i ′ and x Fi ′ Scale the wave to obtain the scaled shock radius. r ki and x Fki to determine the point D ki ( x Fki , r ki ), r ki and x Fki Characterized by the following formula:

[0123]

[0124] In the above formula, R i It is any point D i ′ ( x Fi ′ , r i ′ The corresponding non-circular arc segment shock wave exit profile point P i The radius of curvature;

[0125] S6102, Traverse all points D i ′ Repeat S6101 to obtain a series of... D ki ( x Fki , r ki A defined set of points D ki ,according to D ki A scaled-down axisymmetric external cone shock profile and the corresponding axisymmetric external cone flow field are obtained.

[0126] S6103, at the right end of the axisymmetric external cone shock profile based on the proportional scaling r kN Top cut r ki Get points F ki The position, with point Fki Starting from the point parallel to X The straight line of the axis intersects the axisymmetric external cone shock profile at... D ki ;

[0127] S6104, from point D ki Tracing downstream to the shock wave radius based on the scaled axisymmetric outer cone flow field r kN Up, and with r kN Intersect at point Q ki Thus, a streamline D is obtained. ki Q ki ;

[0128] S6105, Repeat S6103-S6104 to traverse D ki ( x Fki , r ki The corresponding radius of curvature r ki A series of streamlines D are obtained. ki Q ki The defined compression surface of the waverider; wherein, i =1, 2, 3, ... N , N are positive integers and N ≥1;

[0129] S62. Obtain the shock surface of the waverider body based on the axisymmetric external cone shock profile.

[0130] S6201. Take any point on the axisymmetric external cone shock profile after scaling. D ki ( x Fki , r ki ),according to D ki A position is obtained x Fki , radius is r ki Non-circular arc shock wave exit profile;

[0131] S6202, Repeat S6201 to iterate. D ki This yields a shock surface of a waverider composed of a series of non-circular arc segment shock wave exit profiles;

[0132] S63, along the free-flowing surface constraint line described in S21 XAxial stretching yields the free-flow surface of the waverider;

[0133] S64. Using the free-flowing surface of the waverider as a constraint, assemble the shock surface, compression surface, and free-flowing surface of the waverider to obtain a closely related waverider configuration that satisfies the three-dimensional leading edge constraint.

[0134] Compared with the prior art, the construction of the reference flow field of the present invention is more complex to meet the constraints of different shock wave profiles. That is, in each osculating plane, the radius of curvature of the reference flow field of the present invention changes with the curvature of the shock wave profile. Therefore, the reference flow field in each osculating plane is no longer a reference flow field with a fixed radius of curvature, but is obtained by dimensionlessly processing the same dimensionless reference flow field with the relationship between the radius of curvature and the size of the radius of curvature.

[0135] Therefore, the main effects of this embodiment include: ① solving the problem to a certain extent that the approximate outline of the waverider cannot be predetermined; ② the introduction of close-fitting technology makes the design of waveriders more flexible than the three-dimensional leading edge customizable streamline tracing type; ③ providing a high-quality and efficient method and technical guarantee for waverider configuration design that meets actual engineering needs; ④ compared with traditional design technology, the waverider designed using the technology of this invention can achieve the high performance of traditional waveriders while also meeting the geometric constraints of actual engineering on the waverider to a certain extent; ⑤ enriching the design technology of practical waveriders, providing a very effective technical approach for designing waveriders with more complex geometric constraints that meet engineering practical needs, and having strong economic benefits.

[0136] The above solution is merely an illustration of a preferred example and is not limited thereto. When implementing this invention, appropriate substitutions and / or modifications can be made according to the user's needs.

[0137] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. It can be applied to various fields suitable for the present invention. Other modifications can be readily made by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and examples shown and described herein.

Claims

1. A method of designing a custom three-dimensional leading edge osculating class waverider design, characterized by, Comprise: S1, generating a three-dimensional leading edge line of the waverider body and a projection curve of the leading edge line on the trailing edge section satisfying the requirements according to the constraint on the waverider body geometry C 1; S2, with C 1 as constraints, construct the non-circular arc shock wave exit profile matched with the close class waverider and the corresponding curvature center O i ( m i , n i ); S3. The non-circular-arc shock exit profile and the center of curvature according to S2 O i ( m i , n i ), solving the axisymmetric outer-cone shock profile; S4, taking the axisymmetric outer cone shock wave profile line of S3 as the initial condition, the characteristic line method is used to obtain the axisymmetric body surface, triangular flow field area and corresponding left-running characteristic line; S5, taking the left-running characteristic line of S4 as the initial condition, the constraint condition of axisymmetric body surface is given, and the axisymmetric outer cone flow field matched with the triangular flow field area is obtained; S6, taking the axisymmetric outer cone flow field of S5 as the reference, the osculating class waverider configuration satisfying the three-dimensional leading edge constraint is obtained by using the proportional scaling and streamline tracking method.

2. The method of designing close class three-dimensional forebody tailored ogive rider design of claim 1, wherein, In S1, with C 1 midpoint of the two end points O as the coordinate origin, with the length direction from the top to the bottom of the wave multiplier as X the positive direction of the axis, perpendicular to X the direction upward along the axis as Y the positive direction of the axis, perpendicular to XOY the outward direction of the plane as Z the positive direction of the axis, establish a three-dimensional rectangular coordinate system OXYZ; In S2, the non-circular arc shock wave outlet profile line is obtained in the following way: S21, with C 1 represents the free-flow surface constraint line. C 1 in Z Projection on axis AB The direction to the right of the line is taken as Z The positive direction of the axis will be projected. AB The direction of the perpendicular bisector upwards is taken as Y The positive direction of the axis will be projected. AB The midpoint is taken as the origin of the coordinate system. O Establish a rectangular coordinate system ZOY ; S22, in a rectangular coordinate system ZOY Within the third and fourth quadrants, by projection AB Construct a non-circular segment shock wave exit profile for the chord length, and the left endpoint of the non-circular segment shock wave exit profile... A exist Z On the negative half of the axis, the right end point B exist Z On the positive half-axis of the shaft, and the non-circular arc segment shock wave exit profile passes through Y The axis is divided into the right half of the non-circular arc segment shock wave exit profile and the left half of the non-circular arc segment shock wave exit profile. S23, Control equation based on non-circular arc segment shock wave outlet profile y = f ( z ),non-circular arc segment shock wave outlet profile P i ( z i , y i )corresponding curvature center O i ( m i , n i )and curvature radius R i characterized by the following formula: In the above formula, m i , n i are the abscissa and ordinate of O i , z i , y i are the abscissa and ordinate of P i , f′(z i ) is the value of the first derivative of the control equation y = f ( z ) with respect to z at z= z i , f′′(z i ) is the value of the second derivative of the control equation y = f ( z ) with respect to z at z= z i , R i is the radius of curvature corresponding to the point P i ( z i , y i ), i =1, 2, 3, …; N ; S24, traversing P i ( z i , y i ) and connecting all the curvature centers O i ( m i , n i ) to obtain a curvature center distribution curve corresponding to the non-circular arc shock wave outlet profile.

3. The method of designing close class three-dimensional forebody-fitted waveriders of claim 2, wherein, In S3, the flow of solving the axisymmetric outer cone shock wave profile line is as follows: S31, connecting any point on the right half non-circular arc shock wave outlet profile P i and its curvature center O i obtaining the flow osculating surface line O i P i , the flow osculating surface line O i P i The linear equation of the straight line is: In the above formulae, z i , y i are the abscissa and ordinate, respectively, P i of the point m i , n i are the abscissa and ordinate, respectively, O i of the point S32, the straight line equation of C 1 and O i P i are solved to obtain the intersection point y、z F i (0, y Fi , z Fi ), the distance between the intersection point F i and O i is taken as the shock radius before scaling r i , then r i is characterized by the following formula:​ In the above formula, y Fi , z Fi Intersection points F i of Y axis coordinates and Z Axis coordinates; S33, the intersection point F i (0, y Fi , z Fi ) coordinates y Fi , z Fi substituted into the curved surface equation of the three-dimensional leading edge line of the waverider f(x,y,z)= 0, the intersection point F i on the three-dimensional leading edge line of the waverider X axis coordinates x Fi , and further determine the point D i ( x Fi , r i ) S34, repeating S31-S33, to obtain a set of points determined by a series of D i ( x Fi , r i ) determined by a series of D ; S35. For any point P i ,Will r i exist P i The corresponding fluid close surface line O i P i Dimensionless processing is performed within the flow field to obtain the dimensionless shock wave radius. r i ′ and intersection F i of X Axis coordinates x Fi ′ to determine the point D i ′ ( x Fi ′ , r i ′ ), r i ′ and x Fi ′ Characterized by the following formula: In the above formula, R i is the radius of curvature of any point on the non-circular-arc shock exit profile P i ​ S36, traverse all points P i , repeat S35, get a series of point sets determined by D i ′ ( x Fi ′ , r i ′ ) determined by the point set D ′ , based on D ′ , a right half non-circular arc shock wave outlet profile corresponding to the axisymmetric outer cone shock wave profile I; wherein the left end point of the axisymmetric outer-cone shockwave profile I D 1 ′ corresponding shockwave radius r 1 ′ minimum, right end point D N ′ corresponding shockwave radius r N ′ maximum; S37, traverse all points on the left half circular arc shock exit profile P i Using the same method as S31-S36, a second axisymmetric outer-cone shock profile II corresponding to the left half non-circular arc shock exit profile is obtained. The axisymmetric outer cone shock wave profile line I and the axisymmetric outer cone shock wave profile line II are combined to obtain the axisymmetric outer cone shock wave profile line corresponding to the non-circular arc shock wave outlet profile line.

4. The method of designing close class three-dimensional forebody tailored ogive rider design of claim 3, wherein, In S6, the osculating class waverider configuration satisfying the three-dimensional leading edge constraint is obtained in the following way: S61, taking the axisymmetric outer cone flow field as the known condition, the compression surface of the waverider is obtained by using the proportional scaling and streamline tracking method; S62, based on the axisymmetric outer cone shock wave profile line, the shock wave surface of the waverider is obtained; S63, to C 1 along X axis to obtain the free stream surface of the waverider. S64, taking the free stream surface of the waverider as the constraint, the shock wave surface, compression surface and free stream surface of the waverider are assembled to obtain the osculating class waverider configuration satisfying the three-dimensional leading edge constraint.

5. The method in accordance with claim 4 for custom three-dimensional leading edge close class waverider design, wherein, In S61, the compression surface is obtained in the following way: S6101、scaling the shock radius of the axisymmetric outer-cone shock wave profile D i ′ x Fi ′ r i ′ r i ′ x Fi ′ r ki x Fki D ki x Fki r ki r ki x Fki are characterized by the following equations:​​​​​​​​​​​ In the above formula, R i is an arbitrary point D i ′ ( x Fi ′ , r i ′ ) the corresponding non-circular arc shock wave exit profile point P i radius of curvature; S6102, Traverse all points D i ′ Repeat S6101 to obtain a series of... D ki ( x Fki , r ki A defined set of points D ki ,according to D ki A scaled-down axisymmetric external cone shock profile and the corresponding axisymmetric external cone flow field are obtained. S6103, at the right end of the axisymmetric external cone shock profile based on the proportional scaling r kN Top cut r ki Get points F ki The position, with point F ki Starting from the point parallel to X The straight line of the axis intersects the axisymmetric external cone shock profile at... D ki ; S6104、From point D ki downstream to the shock radius r kN up, and intersects r kN at point Q ki , thereby obtaining a stream line D ki Q ki ; S6105, repeat S6103-S6104 to traverse D ki ( x Fki , r ki ) corresponding radius of curvature r ki , get a series of by the flow line D ki Q ki determined by the compression surface of the wave rider.

6. The method in accordance with claim 4 for custom three-dimensional leading edge close class waverider design, wherein, In S62, the shock wave surface is obtained in the following way: S6201、In the scaled axisymmetric outer cone shock wave profile, take any point D ki ( x Fki , r ki ), according to D ki get a non-circular arc segment shock wave outlet profile with a position of x Fki and a radius of r ki ; S6202, repeat S6201 to traverse D ki The shock wave surface of the waverider is composed of a series of non-circular arc shock wave exit profile sets.

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