Design method of variable Mach number "series" wide speed range waverider aircraft based on inverse design wall points

Abstract

The present invention relates to a design method for a variable Mach number "series" wide speed range waverider aircraft based on an inverse design wall point, comprising: S1. Given the design Mach number variation law and solving the free flow design Mach number; S2. Solving the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall point using a swirl characteristic line method; S3. Streamline tracking is performed in the variable Mach number "series" supersonic axisymmetric reference flow field to generate the aerodynamic shape of the variable Mach number "series" wide speed range waverider aircraft. The present invention can effectively improve the degree of freedom of the configuration design of the variable Mach number wide speed range waverider aircraft and enrich its design scheme.

Description

Technical Field

[0001] The present invention relates to the technical field of aerodynamic shape design of hypersonic aircraft, and in particular to a design method of a variable Mach number "serial" wide-speed range waverider aircraft based on inversely designed wall points. Background Art

[0002] With the highly integrated development of aerospace technology, the need to design aircraft with large airspace and wide speed range mission profile characteristics is becoming more and more urgent. Among them, the design of aerospace vehicles is the most typical. The concept of aerospace vehicles is that they take off from an airport like a conventional aircraft, fly at the edge of the atmosphere at hypersonic speed, and then return to the airport in the same way as a conventional aircraft lands. When an aerospace vehicle flies at hypersonic speed, its flight speed is close to the first cosmic speed. Driven by rocket engines, it can flexibly enter space and return to the atmosphere from space, and can be reused.

[0003] Aerospace vehicles need to have both high maneuverability and high acceleration, and require a high lift-to-drag ratio in the entire speed range. In the process of completing the round-trip flight between the earth and the sky, aerospace vehicles need to cross sub / trans / super / hypersonic speeds, experience dense and thin atmospheres, and face a complex and rapidly changing flight environment. The flow characteristics of the aircraft vary greatly, and the aerodynamic characteristics of the same shape in different speed ranges vary significantly. The same high lift-to-drag ratio and other performance requirements will lead to conflicting shape solutions.

[0004] On the other hand, 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 configuration an ideal configuration for hypersonic aircraft.

[0005] Therefore, based on the waverider configuration design, making full use of its aerodynamic advantages under hypersonic flight conditions, carrying out wide speed range / full speed range aircraft configuration design is an important development path to meet the development needs of aircraft. For the convenience of the following description, the wide speed range / full speed range aircraft design method designed using the waverider design theory is referred to as the wide speed range waverider aircraft design method.

[0006] At present, the design methods of wide-speed range waverider aircraft mainly include: combined splicing type, variable Mach number type, vortex lift waverider type, two-stage / multi-stage waverider type and deformation waverider type, etc. Among them, in the research on the configuration design method of variable Mach number wide-speed range waverider aircraft, a number of specific variable Mach number wide-speed range waverider aircraft design methods have been proposed by combining the variable Mach number design concept with the cone-guided waverider design theory, the kissing cone design theory and the kissing flow field design theory. For example, the Chinese patent with publication number CN106043737A discloses a "constant object surface-variable Mach number" wide-speed domain waverider design method, the Chinese patent with publication number CN106043738A discloses a "constant shock wave flow field-variable Mach number" wide-speed domain waverider design method, the Chinese patent with publication number CN107672821A discloses a variable Mach number "parallel" wide-speed domain waverider design method based on the tangent cone theory, and the Chinese patent with publication number CN109279044A discloses a variable Mach number tangent flow field aerodynamic shape design method for waverider bodies, etc. By understanding the above-mentioned wide-speed domain waverider design methods, it can be found that in these design methods, the variable Mach number design used is the "parallel" variable Mach number design thinking. It can be seen that the design scheme for wide-speed domain waverider design in the existing technical scheme is relatively single and lacks flexibility. Summary of the invention

[0007] The object of the present invention is to provide a design method for a variable Mach number "serial" wide speed range waverider aircraft based on inversely designed wall points.

[0008] To achieve the above-mentioned object of the invention, the present invention provides a design method of a variable Mach number "series" wide speed range waverider aircraft based on inverse design wall points, comprising:

[0009] S1. Given the variation law of the design Mach number, solve the free flow design Mach number;

[0010] S2. Solve the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall point using the rotating characteristic line method;

[0011] S3. Streamline tracking is performed in the variable Mach number "series" supersonic axisymmetric reference flow field to generate the aerodynamic shape of the variable Mach number "series" wide speed range waverider aircraft.

[0012] According to one aspect of the present invention, step S1 includes:

[0013] S11. Construct a formula for the Mach number variation law, and design the Mach number variation law based on the formula, which is expressed as:

[0014] Ma C (x) = Ma C(ini)+F C (x) (1)

[0015] Among them, Ma C (x) represents the variation law of the design Mach number at the wall, Ma C (ini) represents the design Mach number at the initial wall point, F C (x) represents the design Mach number variation function at the wall;

[0016] S12. Given the leading edge semi-cone angle, by solving the Taylor-Maccoll equation and using the dichotomy method, within a certain free flow Mach number range, search for the Mach number at the tip of the rotating body that satisfies the design Mach number Ma C The free stream Mach number at (ini).

[0017] According to one aspect of the present invention, step S2 includes:

[0018] Obtaining the Mach number variation law and the free flow design Mach number, and using the supersonic flow condition and zero angle of attack as input conditions, solving the variable Mach number "series" supersonic axisymmetric reference flow field using a rotating characteristic line method;

[0019] The position coordinates and flow parameters of the characteristic line grid nodes of the leading edge attached shock wave and the shock wave are obtained respectively;

[0020] The shape of the leading edge appendage shock wave is represented by the position coordinates of the characteristic line grid nodes on the leading edge appendage shock wave.

[0021] According to one aspect of the present invention, in step S2, in the step of solving the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall points, the inverse design solution of the geometric boundary adopts the Mach number inverse design direct wall point unit process or the Mach number inverse design inverse wall point unit process for solution.

[0022] According to one aspect of the present invention, in step S2, the step of using the Mach number inverse design direct wall point unit process to solve the variable Mach number "series" supersonic axisymmetric reference flow field includes:

[0023] Construct a direct wall point unit, and obtain known internal points, known wall points and wall points to be solved in the direct wall point unit;

[0024] Obtaining the position of the wall point to be solved based on the right characteristic line equation of the known interior point and the streamline equation of the known wall point;

[0025] Obtaining the static pressure of the wall point to be solved;

[0026] Obtaining the flow angle of the wall point to be solved according to the compatibility equation on the right characteristic line equation of the known interior point;

[0027] Obtaining the flow velocity and density of the wall point to be solved according to two compatibility equations on the streamlines of the known wall point and the wall point to be solved;

[0028] Euler correction is performed on the position, static pressure, flow angle, flow velocity and density of the wall point to be solved.

[0029] According to one aspect of the present invention, the step of obtaining the position of the wall point to be solved in the direct wall point unit based on the right characteristic line equation of the known interior point and the streamline equation of the known wall point includes:

[0030] Construct the streamline equation of the known wall point, expressed as:

[0031] y 12 -λ 12-13 x 12 =y 13 -λ 12-13 x 13 (2)

[0032] In the formula, x 12 ,y 12 represents the coordinates of the known wall point, x 13 , y13 represents the coordinates of the wall point to be solved, λ 12-13 is the slope of the streamline equation between the known wall point and the wall point to be solved;

[0033] Construct the right characteristic line equation of the known interior point, expressed as:

[0034] y 13 -λ 11-13 x 13 =y 11 -λ 11-13 x 11 (3)

[0035] In the formula, x 11 ,y 11 represents the coordinates of the known interior point, λ 11-13 is the slope of the right characteristic line equation between the known interior point and the wall point to be solved;

[0036] Solving equations (2) and (3) together, we can obtain the position coordinates (x 13 ,y 13 );

[0037] In the step of obtaining the static pressure of the wall point to be solved, the static pressure of the wall point to be solved (13) is expressed as:

[0038]

[0039] In the formula, p 13 represents the static pressure of the wall point to be solved, ρ 13 represents the density of the wall points to be solved, V 13 represents the velocity of the wall point to be solved, P total is the total pressure at each point on the streamline, which can be obtained by using the flow parameters of the known wall points in this unit process, and is expressed as:

[0040]

[0041] Among them, p 12 represents the static pressure at the known wall point, ρ 12 represents the density of the known wall points, V 12 represents the velocity of the known wall point;

[0042] In the step of obtaining the flow angle of the wall point to be solved according to the compatibility equation on the right characteristic line equation of the known interior point, the flow angle is expressed as:

[0043] Q _ p 13 -θ 13 =T _ (5)

[0044] Where:

[0045] T _ =-S _ (x 13 -x 11 )+Q _ p 11 -θ 11

[0046]

[0047]

[0048] θ 13 represents the flow angle of the wall point to be solved, α 11 represents the Mach angle at the known interior point, θ 11 represents the flow angle at the known internal point, δ represents 0 for plane flow and 1.0 for axisymmetric flow, M 11 represents the Mach number at the known interior point;

[0049] In the step of obtaining the flow velocity and density of the wall point to be solved according to the two compatibility equations on the streamline of the known wall point and the wall point to be solved, the flow velocity and density of the wall point to be solved are expressed as:

[0050] R 13 +p 13 =T 01 (6)

[0051] p 13 -A0ρ 13 =T 02 (7)

[0052] In the formula,

[0053] T 01 =R0V 12 +p 12

[0054] T 02 =p 12 -A0ρ 12

[0055] A0=ρ 12 V 12

[0056]

[0057] a 12 represents the speed of sound at the known wall point, V 12 represents the flow velocity at the known wall point, p 12 represents the static pressure at the known wall point, ρ 12 represents the density of the known wall points, p 13 represents the static pressure of the wall point to be solved, ρ 13 represents the density of the wall points to be solved, V 13 Represents the flow velocity of the wall point to be solved.

[0058] According to one aspect of the present invention, in step S2, the step of using the Mach number inverse design inverted wall point unit process to solve the variable Mach number "series" supersonic axisymmetric reference flow field includes:

[0059] Construct an inverted wall point unit, and obtain known interior points, known wall points, unknown interior points, and wall points to be solved in the inverted wall point unit; wherein the unknown interior point is the intersection of a backward extending right characteristic line passing through the wall point to be solved and a left characteristic line passing through the known interior point and the known wall point;

[0060] Based on the streamline equation of the known wall point, the left characteristic line equation between the known interior point and the known wall point, and the right characteristic line equation between the unknown interior point and the wall point to be solved, the position of the wall point to be solved is obtained;

[0061] Obtaining the static pressure of the wall point to be solved;

[0062] Determine the flow angle of the wall point to be solved by using a compatibility equation on a right-line characteristic line equation passing through the unknown interior point and the wall point to be solved;

[0063] Calculating the flow velocity and density of the wall point to be solved by using two compatible equations on the streamline passing through the known wall point;

[0064] Euler correction is performed on the position, static pressure, flow angle, flow velocity and density of the wall point to be solved.

[0065] According to one aspect of the present invention, the step of obtaining the position of the wall point to be solved based on the streamline equation of the known wall point, the known interior point and the left characteristic line equation of the known wall point, and the right characteristic line equation of the unknown interior point and the wall point to be solved comprises:

[0066] Construct the streamline equation of the known wall point, expressed as:

[0067] y 16 -λ 16-17 x 16 =y 17 -λ 16-17 x 17 (8)

[0068] In the formula, x 16 ,y 16 represents the coordinates of the known wall point, x 17 ,y 17 represents the coordinates of the wall point to be solved, λ 16-17 is the slope of the streamline equation between the known wall point and the wall point to be solved, the wall point to be solved is a predetermined solution point, and its coordinate x 17 is known, and the coordinate x of the wall point to be solved is obtained by using formula (8). 17 Find its coordinate y 17 ;

[0069] Construct the left characteristic line equation at the known interior point and the known wall point, expressed as:

[0070] y 14 -λ 14-16 x 14 =y 16 -λ 14-16 x16 (9)

[0071] In the formula, x 16 ,y 16 represents the coordinates of the known wall point, x 14 ,y 14 represents the coordinates of the known interior point (14), λ 14-16 is the slope of the left characteristic line equation at the known interior point and the known wall point;

[0072] Construct the right characteristic line equation of the unknown interior point and the wall point to be solved, expressed as:

[0073] y 15 -λ 15-17 x 15 =y 17 -λ 15-17 x 17 (10)

[0074] In the formula, λ 15-17 is the slope of the right characteristic line equation between the unknown interior point and the wall point to be solved;

[0075] Solving equations (9) and (10) together, we can obtain the coordinates of the unknown interior point (x 15 ,y 15 );

[0076] In the step of obtaining the static pressure of the wall point to be solved, the static pressure of the wall point to be solved is expressed as:

[0077]

[0078] In the formula, p 17 represents the static pressure of the wall point to be solved, ρ 17 represents the density of the wall points to be solved, V 17 represents the velocity of the wall point to be solved, P total is the total pressure at each point on the streamline, which can be obtained by using the flow parameters of the known wall points in this unit process, and is expressed as:

[0079]

[0080] Among them, p 16 represents the static pressure at the known wall point, ρ 16 represents the density of the known wall points, V 16 represents the velocity of the known wall point;

[0081] In the step of determining the flow angle of the wall point to be solved by using the compatibility equation on the right characteristic line equation passing through the unknown internal point and the wall point to be solved, the flow angle is expressed as:

[0082] Q _ p 17 -θ 17 =T _ (12)

[0083] Where:

[0084] T _ =-S _ (x 17 -x 15 )+Q _ p 15 -θ 15

[0085]

[0086]

[0087] θ 17 represents the flow angle of the wall point to be solved, α 15 represents the Mach angle at the unknown interior point, θ 15 represents the flow angle at the unknown internal point, δ represents 0 for plane flow and 1.0 for axisymmetric flow, M 15 represents the Mach number at the unknown interior point;

[0088] In the step of calculating the flow velocity and density of the wall point to be solved by using two compatibility equations on the streamline passing through the known wall point, the flow velocity and density of the wall point to be solved are expressed as:

[0089] R 17 +p 17 =T 01 (13)

[0090] p 17 -A0ρ 17 =T 02 (14)

[0091] In the formula,

[0092] T 01 =R0V 16 +p 16

[0093] T 02 =p 16 -A0ρ 16

[0094] A0=p 16 V 16

[0095]

[0096] a 16 represents the speed of sound at a known wall point, V 16 represents the flow velocity at the known wall point, p 12 represents the static pressure at the known wall point, ρ 16 represents the density of the known wall points, p 17 represents the static pressure of the wall point to be solved, ρ 17 represents the density of the wall points to be solved, V 17 Represents the flow velocity of the wall point to be solved.

[0097] According to one aspect of the present invention, in step S2, in the step of solving the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall point, the Mach number inverse design direct wall point unit process or the Mach number inverse design inverse wall point unit process is tested to verify the correctness of the solution process;

[0098] In step S2, in the step of solving by using the direct wall point unit process of Mach number inverse design or the inverse wall point unit process of Mach number inverse design, characteristic line meshing can be performed on the variable Mach number "series" supersonic axisymmetric reference flow field.

[0099] According to one aspect of the present invention, in S3, in the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall point solved in S2, according to the basic waverider design principle, one of the leading edge line, the upper surface bottom line and the lower surface bottom line is used as input, the remaining two characteristic lines are obtained and the upper surface, lower surface and bottom surface of the waverider aircraft are closed, so as to obtain the aerodynamic configuration of the variable Mach number "series" wide speed range waverider aircraft.

[0100] According to a solution of the present invention, the degree of freedom in the configuration design of a variable Mach number wide speed range waverider aircraft can be effectively improved, and its design solutions can be enriched.

[0101] According to one solution of the present invention, compared with the traditional waverider aircraft design method, the present invention has better wide speed range characteristics.

[0102] According to one scheme of the present invention, in solving the reference flow field of the Mach number inverse design wall points using the rotational characteristic line method, the process of determining the wall profile of a rotating body given the wall design Mach number distribution law can be realized by using the Mach number inverse design direct wall point unit process or the Mach number inverse design inverse wall point unit process; thereby, the configuration of a variable Mach number "series" wide speed range waverider aircraft can be generated in this reference flow field of the Mach number inverse design wall points.

[0103] According to one solution of the present invention, the present invention is to carry out the research on the configuration design method of variable Mach number wide speed range waverider aircraft in a new way, which is different from other existing technical solutions. This is a further enrichment and development of the aerodynamic configuration research of variable Mach number wide speed range waverider aircraft, which is conducive to the further development of the configuration research of wide speed range waverider aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] Figure 1 is a flowchart schematically showing a method for designing a variable Mach number "tandem" wide speed range waverider aircraft according to an embodiment of the present invention;

[0105] Figure 2 Schematically represents a flow model of a variable Mach number "series" supersonic axisymmetric reference flow field based on an inversely designed wall point according to an embodiment of the present invention;

[0106] Figure 3 is a characteristic line grid schematically representing a direct wall point unit process of Mach number inverse design according to one embodiment of the present invention;

[0107] Figure 4 is a characteristic line grid schematically representing a process of inverting a wall point unit in a Mach number inverse design according to an embodiment of the present invention;

[0108] Figure 5 is a characteristic line grid schematically representing a test Mach number inverse design direct wall point unit process according to one embodiment of the present invention;

[0109] Figure 6 is a characteristic line grid schematically representing a test Mach number inverse design inversion wall point unit process according to one embodiment of the present invention;

[0110] Figure 7 Schematically shows the first division of the supersonic axisymmetric reference flow field region around the pointed body of revolution according to one embodiment of the present invention;

[0111] Figure 8 Schematically shows the second division of the supersonic axisymmetric reference flow field region around the pointed body of revolution according to one embodiment of the present invention;

[0112] Fig. 9 is a schematic diagram schematically showing a configuration of a wide speed range waverider aircraft generating a Mach number inverse design wall point in a reference flow field of a Mach number inverse design wall point according to an embodiment of the present invention;

[0113] Fig.10 is a schematic diagram schematically showing the design of the leading edge line, streamline and trailing edge line of a waverider aircraft according to one embodiment of the present invention;

[0114] Fig.11 Schematically represents a characteristic line grid of a reference flow field generated by using a Mach number inverse design direct wall point unit process and a Mach number inverse design inverse wall point unit process respectively according to an embodiment of the present invention;

[0115] Fig.12 is a schematic diagram schematically showing the definition of bottom profile parameters of a wide-speed waverider aircraft according to a Mach number inverse design wall point according to an embodiment of the present invention;

[0116] Fig.13 is a diagram schematically showing a comparison of Mach number inverse design wall point wide speed range waverider aircraft configurations generated by using a Mach number inverse design direct wall point unit process and a Mach number inverse design inverse wall point unit process respectively according to an embodiment of the present invention;

[0117] Description of reference numerals:

[0118] 1 represents the supersonic incoming flow; 2 represents the starting point of the rotating body generatrix designed by the given design Mach number; 3 represents the semi-apex angle of the rotating body tip cone; 4 represents the initial wall point taken on the rotating body generatrix; 5 represents the intersection of the left characteristic line emitted by 4 and the leading edge shock wave; 6 represents the intersection of the rotating body generatrix and the bottom plane of the reference flow field; 7 represents the intersection of the attached shock wave and the bottom plane of the reference flow field; 8 represents the straight shock wave of the attached shock wave at the tip of the rotating body; 9 represents the curved shock wave part of the attached shock wave; 10 represents the length of the designed reference flow field; 11 represents the known internal point in the process of Mach number inverse design of direct wall point unit; 12 represents the known wall point in the process of Mach number inverse design of direct wall point unit; 13 represents the Mach number inverse design of 14 represents the wall points to be solved in the process of calculating the direct wall point unit; 15 represents the unknown internal points in the process of Mach number inverse design inverse wall point unit; 16 represents the known wall points in the process of Mach number inverse design inverse wall point unit; 17 represents the wall points to be solved in the process of Mach number inverse design inverse wall point unit; 18 represents the known internal points in the process of testing the direct wall point unit of Mach number inverse design; 19 represents the known wall points in the process of testing the direct wall point unit of Mach number inverse design; 20 represents the wall points to be solved in the process of testing the direct wall point unit of Mach number inverse design; 21 represents the known internal points in the process of testing the inverse wall point unit of Mach number inverse design; 2 2 represents an unknown internal point in the process of testing the inverse wall point unit of Mach number inverse design; 23 represents a known wall point in the process of testing the inverse wall point unit of Mach number inverse design; 24 represents the wall point to be solved in the process of testing the inverse wall point unit of Mach number inverse design; 25 represents the intersection of the right characteristic line extending from 5 and the generatrix of the rotating body; 26 represents the intersection of the left characteristic line passing through 7 and the generatrix of the rotating body; 27 represents the leading edge appendage shock wave in the reference flow field of the wall point of Mach number inverse design; 28 represents the axisymmetric rotating body for generating the reference flow field of the wall point of Mach number inverse design; 29 represents the leading edge line of the wide speed domain waverider aircraft of the wall point of Mach number inverse design; 30 represents the trailing edge line of the upper surface of the wide speed domain waverider aircraft of the wall point of Mach number inverse design; 3 1 represents the trailing edge line of the waverider surface of the Mach number inverse design wall point wide speed domain waverider aircraft; 32 represents the supersonic free flow in the Mach number inverse design wall point reference flow field; 33 represents the point on the trailing edge line of the upper surface of the waverider aircraft; 34 represents the straight line passing through point 33 and parallel to the axial coordinate axis of the cylindrical coordinate system; 35 represents the point on the leading edge line of the waverider aircraft; 36 represents the streamline passing through point 35 on the leading edge line; 37 represents the point on the trailing edge line of the waverider surface of the waverider aircraft; 38 represents the characteristic line grid of the Mach number inverse design wall point reference flow field generated by the Mach number inverse design direct wall point unit process; 39 represents the characteristic line grid of the Mach number inverse design wall point reference flow field generated by the Mach number inverse design inverse wall point unit process;40 represents the x^' coordinate of the intersection of the bottom profile of the upper surface of the waverider and the x^' coordinate axis; 41 represents the shock wave radius of the bottom cross section of the rotating body; 42 represents the shock wave profile of the attached shock wave at the bottom of the rotating body in the reference flow field of the Mach number inverse design wall point; 43 represents the half width of the wide speed domain waverider configuration of the Mach number inverse design wall point; 44 represents the wide speed domain waverider configuration of the Mach number inverse design wall point generated by the Mach number inverse design direct wall point unit process; 45 represents the wide speed domain waverider configuration of the Mach number inverse design wall point generated by the Mach number inverse design inverse wall point unit process. ; DETAILED DESCRIPTION

[0119] The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. The embodiments cannot be described one by one here, but the embodiments of the present invention are not therefore limited to the following embodiments.

[0120] like Figure 1 As shown, according to one embodiment of the present invention, a design method of a variable Mach number "series" wide speed range waverider aircraft based on an inversely designed wall point of the present invention comprises:

[0121] S1. Given the variation law of the design Mach number, solve the free flow design Mach number;

[0122] S2. Solve the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall point using the rotating characteristic line method;

[0123] S3. Streamline tracking is performed in the variable Mach number "series" supersonic axisymmetric reference flow field to generate the aerodynamic shape of the variable Mach number "series" wide speed range waverider aircraft.

[0124] In the following description, the variable Mach number "series" wide speed range waverider based on the inverse design wall points can be simply referred to as the wide speed range waverider based on the Mach number inverse design wall points, and the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall points can be simply referred to as the reference flow field of the Mach number inverse design wall points.

[0125] According to an embodiment of the present invention, in step S1, in the step of given design Mach number variation law and solving the free flow design Mach number, the design of the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall point is an aerodynamic inverse design method using the swirl characteristic line method. The core of its design is to determine the wall profile of the rotating body by inverse design using the given rotation body wall design Mach number distribution law. Figure 3As shown in FIG. 1 , the design parameters of the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall point include: supersonic incoming flow condition 1, reference flow field length 10, leading edge semi-cone angle 3, and the variation law of the design Mach number of the rotating body wall. Among them, the variation law of the design Mach number of the rotating body wall is determined by formula (1).

[0126] Ma C (x) = Ma C (ini)+F C (x) (1)

[0127] In the formula, the variation law of the design Mach number at the wall is C (x) The design Mach number Ma of the initial wall point 4 C (ini) and the design Mach number variation function F at the wall C In this embodiment, the design Mach number variation law at the wall surface F c (x) A variety of function forms can be selected, such as constant Mach number gradient, cubic curve Mach number distribution, inverse tangent Mach number distribution, etc.

[0128] In this embodiment, due to the pointed head of the generatrix of the rotating body, the head of the reference flow field is a pointed cone flow field, that is, Figure 2 The area enclosed by the starting point 2-initial wall point 4-the intersection 5 of the left characteristic line emitted by the initial wall point 4 and the leading edge shock wave (see the area enclosed by the lines 2, 4, and 5 in the figure). Therefore, in the design parameters, the Mach number Ma at the pointed cone wall (see the lines 2 and 4 in the figure) formed by the starting point 2-initial wall point 4 is C (ini), the Mach number Ma after the straight shock wave (see the line 2 and 5 in the figure) formed by the starting point 2-the intersection 5 of the left characteristic line emitted by the initial wall point 4 and the leading edge shock wave S and the freestream Mach number Ma ∞ There is a definite relationship between them. Therefore, when solving the free flow design Mach number, the following method can be used:

[0129] Under the given leading edge semi-cone angle 3, by solving the Taylor-Maccoll equation and using the dichotomy method, within a certain free flow Mach number range, the Mach number at the tip of the cone is searched to meet the design Mach number Ma. C The free stream Mach number at (ini).

[0130] like Figure 1 As shown, according to an embodiment of the present invention, the rotating body determined by the design parameters in step S1 can generate a leading edge appendage shock wave and a supersonic axisymmetric reference flow field behind the shock wave under the action of zero angle of attack and supersonic incoming flow condition 1. In this embodiment, Figure 1The reason why the generatrix of the middle body of revolution is set as a dotted line is to indicate that the generatrix of the middle body of revolution is unknown before the solution of the benchmark flow field, and it is determined in the process of solving the benchmark flow field.

[0131] In this embodiment, under the given incoming flow conditions (incoming flow Mach number, static pressure and static temperature), the rotating characteristic line method is used to inversely design and solve the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall point. The rotating characteristic line method can be found in "Gas Dynamics, MJ Zuo Ke Luo, JD Hoffman, National Defense Industry Press, 1984, p138-195", which will not be introduced in detail here. In addition, for the convenience of the following description, the document "Gas Dynamics, MJ Zuo Ke Luo, JD Hoffman, National Defense Industry Press, 1984" is referred to as document [1] in the present invention.

[0132] According to one embodiment of the present invention, in step S2, in the step of solving the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall point using the rotational characteristic line method, when the design Mach number distribution law of the wall based on the previous step is given, how to inversely design the shape of the wall of the rotating body from the distribution law is the key to the design reference flow field. In this embodiment, the shape of the wall of the rotating body is inversely designed by giving the design Mach number distribution law of the wall of the axisymmetric rotating body. Furthermore, a unit process of solving the wall coordinates from the wall design Mach number distribution is used to achieve inverse design.

[0133] In this regard, the present invention proposes two unit processes for solving wall coordinates through the wall design Mach number distribution law, which are Mach number inverse design direct wall point unit process and Mach number inverse design inverse wall point unit process. The essence of these two solution processes is to use the direct wall method (i.e., Mach number inverse design direct wall point unit process) or the inverse wall method (i.e., Mach number inverse design inverse wall point unit process) to carry out the process of inverse designing the wall of a rotating body with a known wall design Mach number distribution law.

[0134] The following introduces the two unit processes for solving the wall coordinates through the wall design Mach number distribution law:

[0135] According to one embodiment of the present invention, the step of solving the variable Mach number "series" supersonic axisymmetric reference flow field by using the Mach number inverse design direct wall point unit process includes:

[0136] like Figure 3 As shown, a direct wall point unit is constructed, and known internal points 11, known wall points 12 and wall points to be solved 13 in the direct wall point unit are obtained;

[0137] like Figure 3As shown, the position of the wall point 13 to be solved can be obtained by the streamline equation of the known wall point 12 and the right characteristic line equation of the wall point 11 to be solved. Since the design Mach number of the wall point 13 to be solved is known, the total pressure at each point on the streamline is equal (that is, the total pressure at the known wall point 12 and the wall point 13 to be solved is equal), and the static pressure at the wall point 13 to be solved can be obtained by the total static pressure relationship;

[0138] According to the compatibility equation on the right characteristic line equation at the known internal point 11, the flow angle at the wall point 13 to be solved can be obtained;

[0139] According to the two compatibility equations on the streamlines of the known wall point 12 and the wall point 13 to be solved, the flow velocity and density at the wall point 13 to be solved can be calculated;

[0140] The above steps complete the Euler estimation calculation; then, the average value of each flow parameter is used to perform the Euler correction calculation to obtain the precise position of the wall point 13 to be solved and the corresponding flow parameters (including static pressure, flow angle, flow velocity and density), and the Mach number inverse design direct wall point unit process can be completed.

[0141] Based on the above description, the specific calculation equation solved by the direct wall point unit process using the Mach number inverse design is further explained as follows:

[0142] Construct the streamline equation at 12 known wall points, expressed as:

[0143] y 12 -λ 12-13 x 12 =y 13 -λ 12-13 x 13 (2)

[0144] In the formula, x 12 ,y 12 represents the coordinates of the known wall point 12, x 13 ,y 13 represents the coordinates of the wall point 13 to be solved, λ 12-13 is the slope of the streamline equation at the known wall point 12 and the wall point 13 to be solved;

[0145] Construct the right characteristic line equation of the known interior point 11, expressed as:

[0146] y 13 -λ 11-13 x 13 =y 11 -λ 11-13 x 11 (3)

[0147] In the formula, x11 ,y 11 represents the coordinates of the known interior point 11, λ 11-13 is the slope of the right characteristic line equation at the known interior point 11 and the wall point 13 to be solved;

[0148] The combined equations (2) and (3) can be used to obtain the coordinates (x 13 ,y 13 ).

[0149] Then, the total static pressure relationship can be used to find the static pressure at point 13 on the wall:

[0150]

[0151] In the formula, p 13 represents the static pressure at the wall point 13 to be solved, ρ 13 represents the density of the wall point 13 to be solved, V 13 represents the velocity of the wall point 13 to be solved, P total is the total pressure at each point on the streamline, which can be obtained by using the flow parameters of the known wall point 12 in this unit process, and is expressed as:

[0152]

[0153] Among them, p 12 represents the static pressure at the known wall point 12, ρ 12 represents the density of the known wall point 12, V 12 represents the velocity of the known wall point 12;

[0154] By using the compatibility equation at the known internal point 11, the flow angle θ at point 13 can be calculated 13 :

[0155] Q _ p 13 -θ 13 =T _ (5)

[0156] Where:

[0157] T _ =-S - (x 13 -x 11 )+Q _ p 11 -θ 11

[0158]

[0159]

[0160] θ13 represents the flow angle of the wall point 13 to be solved, α 11 represents the Mach angle at the known interior point 11, θ 11 represents the flow angle at the known interior point 11, δ represents 0 for plane flow and 1.0 for axisymmetric flow, M 11 represents the Mach number at the known interior point 11;

[0161] Finally, the velocity and density at the wall point 13 to be solved can be calculated using the two compatibility equations of the streamline at the known wall point 12:

[0162] R 13 +p 13 =T 01 (6)

[0163] p 13 -A0ρ 13 =T 02 (7)

[0164] In the formula,

[0165] T 01 =R0V 12 +p 12

[0166] T 02 =p 12 -A0ρ 12

[0167] A0=ρ 12 V 12

[0168]

[0169] a 12 represents the speed of sound at the known wall point 12, V 12 represents the flow velocity at the known wall point 12, p 12 represents the static pressure at the known wall point 12, ρ 12 represents the density of the known wall point 12, p 13 represents the static pressure at the wall point 13 to be solved, ρ 13 represents the density of the wall point 13 to be solved, V 13 Represents the flow velocity at the wall point 13 to be solved.

[0170] After the above-mentioned Euler estimation calculation, the Euler correction algorithm is then performed to obtain the precise coordinates and flow parameters of the wall point 13 to be solved;

[0171] At this point, according to the above analysis process, the corresponding program can be written to realize the Mach number inverse design direct wall point unit process.

[0172] According to another embodiment of the present invention, the step of solving the variable Mach number "series" supersonic axisymmetric reference flow field by using the Mach number inverse design inverted wall point unit process includes:

[0173] Construct an inverted wall point unit, and obtain a known interior point 14, a known wall point 16, an unknown interior point 15, and a wall point to be solved 17 in the inverted wall point unit; wherein the unknown interior point 15 is the intersection of a right-running characteristic line extending through the wall point to be solved 17 and a left-running characteristic line passing through the known interior point 14 and the known wall point 16;

[0174] In this embodiment, in the process of inverse wall point unit of Mach number inverse design, the wall point 17 to be solved is a predetermined solution point, whose x coordinate and design Mach number are known, while the y coordinate, density, velocity and flow angle need to be determined using the characteristic line method.

[0175] like Figure 4 As shown, since the unknown interior point 15 is the right-extending characteristic line C through the wall point 17 to be solved _ With left characteristic line (see Figure 4 The intersection of the line connecting the known interior point 14 and the known wall point 16 is unknown, so the position of the unknown interior point 15 and its flow parameters are unknown. Once the position and flow parameters of the unknown interior point 15 are determined, the right characteristic line (see Figure 4 The compatibility equation on the line connecting the unknown internal point 15 and the wall point 17 to be solved can determine the flow angle at the wall point 17 to be solved;

[0176] The y coordinate of the wall point 17 to be solved can be obtained by using the streamline equations of the known wall point 16 and the wall point 17 to be solved (i.e., streamline 16-17). The velocity and density of the wall point 17 to be solved can be obtained by using the compatibility equations on the known wall point 16 and the wall point 17 to be solved (i.e., streamline 16-17).

[0177] Therefore, in order to solve the position parameters of the wall point 17 to be solved, it is necessary to first determine the position of the unknown internal point 15 and various flow parameters. The position of the unknown internal point 15 can be calculated by extending the right characteristic line 15-17 (see Figure 4 The line connecting the unknown interior point 15 and the wall point 17 to be solved) and the left characteristic line 14-16 (see Figure 4 The flow parameters of the unknown interior point 15 are determined by linear interpolation between the known interior point 14 and the known wall point 16.

[0178] Since characteristic lines 15-17 (see Figure 4The slope of the line connecting the unknown interior point 15 and the wall point 17 to be solved depends on the unknown flow parameters at the unknown interior point 15 and the wall point 17 to be solved. Therefore, each time the improved Euler prediction-correction method is calculated, the prediction-correction method needs to be used to determine the position of the unknown interior point 15.

[0179] In this embodiment, when the parameters of the wall point 17 to be solved are determined by the basic estimation method, the position of the unknown internal point 15 is determined by the following auxiliary estimation-correction method.

[0180] First, the flow parameters of the unknown interior point 15 are taken to be equal to the flow parameters of the known wall point 16, so the characteristic lines 15-17 (see Figure 4 The slope λ of the line connecting the unknown interior point 15 and the wall point 17 to be solved 15-17 It is determined;

[0181] Next, apply the slope λ 15-17 The value of can be used to calculate the backward right characteristic line 15-17 (see Figure 4 The position of the unknown interior point 15 on the line connecting the unknown interior point 15 and the wall point 17 to be solved).

[0182] Again, linear interpolation is performed between the known interior point 14 and the known wall point 1 to determine the flow parameters of the unknown interior point 15 .

[0183] Finally, the flow parameters of the unknown interior point 15 obtained above are used to perform the correction method calculation, and then determine the position of the unknown interior point 15. This step of correction method calculation is repeated until the position of the unknown interior point 15 converges to the desired allowable error range.

[0184] In this embodiment, after the position of the unknown interior point 15 is determined, the calculation steps of the basic prediction method for determining the flow parameters of the wall point 17 to be solved are completed. Then, the unknown interior point 15 is redefined using the auxiliary prediction-correction method described above (where the slope of the characteristic line 15-17 is determined by the average value of the flow parameters between the unknown interior point 15 and the wall point 17 to be solved), thus completing the calculation steps of the basic correction method. If necessary, the calculation steps of this basic correction method can be repeated multiple times.

[0185] Based on the above description, the specific calculation equation solved by the inverse wall point unit process using the Mach number inverse design is further explained as follows:

[0186] Construct the streamline equation for the known wall point 16, expressed as:

[0187] y 16 -λ 16-17 x16 =y 17 -λ 16-17 x 17 (8)

[0188] In the formula, x 16 ,y 16 Represents the coordinates of the known wall point 16, x 17 ,y 17 represents the coordinates of the wall point 17 to be solved, λ 16-17 is the slope of the streamline equation at the known wall point 16 and the wall point 17 to be solved. Using equation (8), the y coordinate of the wall point 17 to be solved can be obtained by the preset x coordinate.

[0189] The left characteristic line equation of the known interior point 14 and the known wall point 16 is constructed and expressed as:

[0190] y 14 -λ 14-16 x 14 =y 16 -λ 14-16 x 16 (9)

[0191] In the formula, x 16 ,y 16 Represents the coordinates of the known wall point 16, x 14 ,y 14 represents the coordinates of the known interior point 14, λ 14-16 is the slope of the left characteristic line equation at the known interior point 14 and the known wall point 16;

[0192] Construct the right characteristic line equation of the unknown interior point 15 and the wall point 17 to be solved, which can be expressed as:

[0193] y 15 -λ 15-17 x 15 =y 17 -λ 15-17 x 17 (10)

[0194] In the formula, λ 15-17 is the slope of the right characteristic line equation between the unknown interior point 15 and the wall point 17 to be solved;

[0195] The combined equations (9) and (10) can be used to obtain the coordinates (x 15 ,y 15 ); On this basis, the flow parameters of the unknown interior point 15 can be determined by linear interpolation between the known interior point 14 and the known wall point 16.

[0196] Then, the total static pressure relationship can be used to find the static pressure at point 17 on the wall:

[0197]

[0198] In the formula, p 17 represents the static pressure at the wall point 17 to be solved, ρ 17 represents the density of the wall point 17 to be solved, V 17 represents the velocity of the wall point 17 to be solved, P total is the total pressure at each point on the streamline, which can be obtained by using the flow parameters of the known wall point 16 in this unit process, and is expressed as:

[0199]

[0200] Among them, p 16 represents the static pressure at the known wall point 16, ρ 16 represents the density of the known wall point 16, V 16 represents the velocity of the known wall point 16;

[0201] By using the compatibility equation at the unknown internal point 15, the flow angle θ at the wall point 17 to be solved can be obtained 17 :

[0202] Q _ p 17 -θ 17 =T _ (12)

[0203] Where:

[0204] T _ =-S _ (x 17 -x 15 )+Q _ p 15 -θ 15

[0205]

[0206]

[0207] θ 17 represents the flow angle of the wall point 17 to be solved, α 15 represents the Mach angle at the unknown interior point 15, θ 15 represents the flow angle at the unknown internal point 15, δ represents 0 for plane flow and 1.0 for axisymmetric flow, M 15 represents the Mach number at the unknown interior point 15;

[0208] Finally, the velocity and density at the wall point 17 to be solved can be calculated using the two compatibility equations of the streamline at the known wall point 16:

[0209] R 17 +p 17 =T 01 (13)

[0210] p 17 -A0ρ 17 =T 02 (14)

[0211] In the formula,

[0212] T 01 =R0V 16 +p 16

[0213] T 02 =p 16 -A o ρ 16

[0214] A0=ρ 16 V 16

[0215]

[0216] a 16 represents the speed of sound at the known wall point 16, V 16 represents the flow velocity at the known wall point 16, p 12 represents the static pressure at the known wall point 16, ρ 16 represents the density of the known wall point 16, p 17 represents the static pressure at the wall point 17 to be solved, ρ 17 represents the density of the wall point 17 to be solved, V 17 Represents the flow velocity at the wall point 17 to be solved.

[0217] After the above-mentioned Euler estimation calculation, the Euler correction algorithm is performed to obtain the precise coordinates and flow parameters of the 17 wall points to be solved.

[0218] At this point, according to the above analysis process, the corresponding program can be written to realize the Mach number inverse design and inversion wall point unit process.

[0219] According to an embodiment of the present invention, in step S2, in order to verify the correctness of the Mach number inverse design direct wall point unit process and the Mach number inverse design inverse wall point unit process proposed by the present invention, the present invention adopts the following methods for testing. They are introduced below respectively:

[0220] 1) Test Mach number inverse design direct wall point unit process

[0221] In order to test the correctness of the direct wall point unit process of Mach number inverse design, the present invention provides a direct wall point unit process of testing the Mach number inverse design.

[0222] Figure 5 The unit process of determining the position and flow parameters of a wall point 20 to be solved by using a known interior point 18 and a known wall point 19 as initial value points is shown. Different from the direct wall point unit process given in the literature [1], this unit process does not give the wall boundary conditions at the wall point 20 to be solved, but instead gives the wall design Mach number at the wall point 20 to be solved.

[0223] It should be noted that compared with the direct wall point unit process of Mach number inverse design, the calculation logic and steps of this unit process are the same. The only difference is the use of the calculation equation. That is, the calculation equation at the known point is given by Figure 3 The left-moving characteristic line equation (left-moving compatibility equation) at the known interior point 11-known wall point 12 becomes Figure 5 The right-hand characteristic line equation (right-hand compatibility equation) at the known interior point 18 and the known wall point 19 is: Figure 3 The right-hand characteristic line equation (right-hand compatibility equation) at the known interior point 11 and the wall point 13 to be solved becomes Figure 5 The midpoint is known, the internal point 18 is the left characteristic line equation (left compatibility equation) to be solved at the wall point 20. This needs to be paid attention to in the process of programming.

[0224] Since Example 17.2 in the literature [1] is used to explain the calculation steps and results of the direct wall point unit process, the point data in Example 17.2 can be used to numerically verify this unit process. The specific verification method is as follows:

[0225] First, use the flow parameter results of the unknown wall point obtained in Example 17.2 to calculate the Mach number at the unknown wall point and use it as the input parameter for the wall point 20 to be solved in this unit process;

[0226]

[0227] Secondly, assign the initial value point data given in Example 17.2 to points 18 and 19 in this unit process. Table 1 gives the initial value data of each point in the numerical example of the direct wall point unit process for the test Mach number inverse design in the numerical verification.

[0228]

[0229] Table 1

[0230] Table 2 gives the comparison of the calculation results of the numerical example of the direct wall point unit process of the test Mach number inverse design in the numerical verification.

[0231]

[0232] Table 2

[0233] The program written by the test Mach number inverse design direct wall point unit process is used to calculate the numerical example given in Table 1. The numerical calculation conditions are exactly the same as those in Example 17.2. The program calculation results are shown in Table 2. It can be seen from the table that the calculation results of the written program are consistent with the data results in Example 17.2, thus proving the correctness of the Mach number inverse design direct wall point unit process.

[0234] 2) Test Mach number inverse design inverse wall point unit process

[0235] In order to test the correctness of the inverse wall point unit process of Mach number inverse design, the present invention provides a process for testing the inverse wall point unit of Mach number inverse design.

[0236] Figure 6 The unit process of determining the position and flow parameters of a wall point 24 to be solved by using a known interior point 21 and a known wall point 23 as initial value points is shown. Different from the inverted wall point unit process given in the literature [1], this unit process does not give the position of the wall point 24 to be solved. y The coordinates and flow angle are replaced by the wall design Mach number at the wall point 24 to be solved.

[0237] Compared with the Mach number inverse design inverse wall point unit process, the calculation logic and steps of this unit process are the same. The only difference is the use of the calculation equation. That is, the calculation equation at the known point is given by Figure 4 The left-moving characteristic line equation (left-moving compatibility equation) at the known interior point 14 of the midpoint and the known wall point 16 becomes Figure 6 The right characteristic line equation (right compatibility equation) at the known interior point 21 and the known wall point 23 at the midpoint is given by: Figure 4 The right-hand characteristic line equation (right-hand compatibility equation) at the unknown interior point 15 to the wall point 17 to be solved becomes Figure 6 The unknown internal point 22 is the left characteristic line equation (left compatibility equation) to be solved at the wall point 24. This needs to be paid attention to in the process of programming.

[0238] Since Example 17.3 in the literature [1] is used to explain the calculation steps and results of the inverted wall point unit process, the point data in Example 17.3 can be used to numerically verify this unit process. The specific verification method is as follows:

[0239] First, use the flow parameter results of the unknown wall point obtained in Example 17.3 to calculate the Mach number at the unknown wall point and use it as the input parameter for the wall point 24 to be solved in this unit process;

[0240]

[0241] Secondly, the x-coordinate data of the unknown wall point is assigned to the x-coordinate of the wall point 24 to be solved in this unit process; the given initial value point data is assigned to the known internal point 21 and the known wall point 23 in this unit process. Table 3 gives the initial value data of each point in the numerical example of the unit process of inverse design of the inverted wall point in the test Mach number in the numerical verification.

[0242]

[0243] Table 3

[0244] Table 4 gives the comparison of the calculation results of the numerical example of the inverse wall point unit process for the test Mach number inverse design in the numerical verification.

[0245]

[0246] Table 4

[0247] The program written by the inverse wall point unit process of the test Mach number inverse design is used to calculate the numerical examples given in Table 3. The numerical calculation conditions are exactly the same as those of Example 17.3. The program calculation results are shown in Table 4. It can be seen from the table that the calculation results of the written program are consistent with the data results in Example 17.3, thus proving the correctness of the inverse wall point unit process of the Mach number inverse design.

[0248] According to one embodiment of the present invention, in step S2, when using the Mach number inverse design direct wall point unit process or the Mach number inverse design inverted wall point unit process to solve the Mach number inverse design wall point reference flow field, different divisions of the reference flow field can facilitate the implementation of these two unit processes and the solution of the entire reference flow field.

[0249] In this embodiment, when the direct wall method is used, the reference flow field is Figure 7 It is appropriate to divide it in the following way: that is, it is divided into a flow field part 4-5-25 extended by the initial value line 4-5 and a flow field part 5-7-6-25 surrounded by the curved shock wave 9 and the curved wall surface 25-6 of the rotating body. Figure 7 The characteristic line grid diagram shown is applicable to the solution process using the direct wall method (i.e., the Mach number inverse design direct wall point unit process), which is essentially the use of the right-running characteristic line to advance the solution of the flow field.

[0250] According to another embodiment of the present invention, when the inverted wall method is used, the reference flow field is Figure 8 It is appropriate to divide it in the following way: that is, it is divided into the leading edge shock wave dependent area flow field part 2-5-7-26-4 surrounded by the attached shock wave 2-5-7 and the rotating body wall 2-4-26 and the isentropic main compression area flow field part 26-7-6 surrounded by the left characteristic line 26-7 and the rotating body wall 26-6. Figure 8 The characteristic line grid diagram shown is applicable to the solution process using the inverted wall method (i.e., the Mach number inverse design inverted wall point unit process), which is essentially the use of left-running characteristic lines to advance the solution of the flow field.

[0251] Figure 7 and Figure 8 The division of the two benchmark flow field structures shown is only to facilitate the implementation of the characteristic line solving program using different unit processes, and there is no other difference except the first time.

[0252] According to an embodiment of the present invention, in step S3, streamline tracing is performed in the reference flow field of the Mach number inverse design wall point to generate the wide-speed domain waverider aircraft aerodynamic configuration of the Mach number inverse design wall point. Fig. 9 As shown, in the reference flow field of the Mach number inverse design wall point solved by S2, according to the basic waverider design principle, one of the leading edge line, the upper surface bottom line and the lower surface bottom line is used as input, the remaining two characteristic lines are obtained and the upper surface, lower surface and bottom surface of the waverider aircraft are closed, so as to obtain the aerodynamic configuration of the wide speed range waverider aircraft at the Mach number inverse design wall point.

[0253] In the embodiment of the present invention, the upper surface bottom line is selected as the input of the configuration, and the leading edge line and the lower surface bottom line are obtained in sequence. It should be noted that the design method in the present invention is not limited to this; that is, the design of the aerodynamic configuration of the wide-speed domain waverider aircraft with Mach number inverse design wall points can also be carried out by using the leading edge line and the lower surface bottom line as input.

[0254] Example 1

[0255] The design process of this step of the specific embodiment is as follows:

[0256] like Fig.10As shown, the shape of the attached shock wave 2-7 in the wall point reference flow field is inversely designed according to the coordinate value of the discrete point 33 on the bottom profile 30 of the upper surface according to the Mach number obtained in the aforementioned step S2, and a straight line 34 passing through the point 33 and parallel to the axial coordinate axis of the cylindrical coordinate system intersects with the attached shock wave 2-7, and the intersection point 35 is a point on the leading edge line, referred to as the leading edge point 35; starting from the leading edge point 35, according to the Mach number obtained in the aforementioned step S2, the flow parameters on each characteristic line grid node behind the attached shock wave in the wall point reference flow field are inversely designed, and the streamline tracing method is used to solve the corresponding points 33 and 34. 35 of the streamline 36 (the streamline tracing method is a well-known technology in the art, for details, please refer to "Theory of Hypersonic Waverider Design", Liu Jun, Ding Feng, et al., Science Press, 2020, p73-74", which will not be repeated here); solve the streamline 36 until the bottom cross section, and its intersection 37 with the bottom cross section is the point on the bottom profile of the lower surface; use the same method to solve all leading edge points and all streamlines passing through the leading edge points, and obtain all bottom profile points of the lower surface, all leading edge points constitute the leading edge line of the waverider aircraft, and all bottom profile points of the lower surface constitute the bottom profile of the lower surface.

[0257] In this embodiment, the streamlines at all discrete points are lofted into the lower surface, and the straight lines at all discrete points parallel to the axial coordinate axis of the cylindrical coordinate system constitute the upper surface. Then, the upper surface, the lower surface and the bottom surface are closed to obtain the aerodynamic configuration of the wide-speed range waverider aircraft at the Mach number inverse design wall point.

[0258] At this point, the design of the variable Mach number "serial" wide-speed range waverider aircraft based on the inverse-design wall points has been completed.

[0259] Embodiment 2:

[0260] This embodiment uses the atmospheric conditions at 25 km as the design flight conditions, that is, the supersonic flow condition 1; the reference flow field length 10 is 1 m; the leading edge semi-cone angle 3 is 10.0 degrees; the Mach number variation law of the rotating body wall design is C (ini) is 7.0, and the design Mach number variation function F at the wall C (x) is the constant Mach number gradient form, and the design Mach number variation law at the final wall surface Ma C (x) is:

[0261]

[0262] Where, L represents the reference flow field length 10, L ini express Figure 1 The x-coordinate value at the midpoint 4 can generally be taken as 0.01L.

[0263] In this embodiment, when solving the reference flow field of the Mach number inverse design wall point using the rotational characteristic line method, the Mach number inverse design direct wall point unit process and the Mach number inverse design inverse wall point unit process are used respectively. The characteristic line grid of the generated reference flow field is as follows: Fig.11 As shown. Fig.11 It can be seen that the reference flow field characteristic line grid 38 generated by the direct wall point unit process using the Mach number inverse design is slightly different from the reference flow field characteristic line grid 39 generated by the inverse wall point unit process using the Mach number inverse design, which also verifies the correctness of the present invention from a certain aspect.

[0264] like Fig.12 As shown, when generating the wide-speed domain waverider configuration of the Mach number inverse design wall point, the quadratic curve shown in equation (16) is used as the upper surface bottom profile 30 of the waverider. The designed waverider half-width 43 is set to 0.8r s ; Among them, r s is the shock wave radius of the bottom cross section of the rotating body, that is, the length of 41.

[0265] x′=r0+a0y′ 2 (16)

[0266] In the formula, r0 represents the x' coordinate of the intersection of the quadratic curve and the x' coordinate axis, that is, the length of 40, which is taken as 0.3r s ; a0 is the coefficient of the bottom profile 30 of the upper surface, and its value can be solved by geometric conditions as follows:

[0267] Fig.13 The Mach number inverse design wall point wide speed domain waverider configurations generated by using the Mach number inverse design direct wall point unit process and the Mach number inverse design inverse wall point unit process are given respectively; it can be seen that the configurations generated using the two unit processes are slightly different, which shows that the corresponding unit process can be selected according to actual needs during the configuration generation process.

[0268] The above contents are merely examples of specific solutions of the present invention. For devices and structures not described in detail therein, it should be understood that they can be implemented by adopting general devices and general methods available in the art.

[0269] The above is only one solution of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A design method for a variable Mach number "series" wide speed range waverider aircraft based on inverse design wall points, comprising: S1. Given the variation law of the design Mach number, solve the free flow design Mach number; Among them, include: S11. Construct a formula for the Mach number variation law, and design the Mach number variation law based on the formula, which is expressed as: Ma C (x)=Ma C (in)+F C (x) (1) Among them, Ma C (x) represents the variation law of the design Mach number at the wall, Ma C (ini) represents the design Mach number at the initial wall point, F C (x) represents the design Mach number variation function at the wall; S12. Given the leading edge semi-cone angle, by solving the Taylor-Maccoll equation and using the dichotomy method, within a certain free flow Mach number range, search for the Mach number at the tip of the rotating body to be the design Mach number Ma. C The free stream Mach number at (ini); S2. Solving the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall point by using the rotating characteristic line method; wherein, in the step of solving the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall point, the inverse design solution of the geometric boundary adopts the Mach number inverse design direct wall point unit process or the Mach number inverse design inverse wall point unit process to solve, then step S2 includes: Obtaining the Mach number variation law and the free flow design Mach number, and using the supersonic flow condition and zero angle of attack as input conditions, solving the variable Mach number "series" supersonic axisymmetric reference flow field using a rotating characteristic line method; The position coordinates and flow parameters of the characteristic line grid nodes of the leading edge attached shock wave and the shock wave are obtained respectively; The shape of the leading edge appendage shock wave is represented by the position coordinates of the characteristic line grid nodes on the leading edge appendage shock wave; S3. Streamline tracking is performed in the variable Mach number "series" supersonic axisymmetric reference flow field to generate the aerodynamic shape of the variable Mach number "series" wide speed range waverider aircraft.

2. The design method of variable Mach number "series" wide speed range waverider aircraft according to claim 1 is characterized in that: In step S2, the step of using the Mach number inverse design direct wall point unit process to solve the variable Mach number "series" supersonic axisymmetric reference flow field includes: Constructing a direct wall point unit, and obtaining known internal points (11), known wall points (12), and wall points to be solved (13) in the direct wall point unit; Obtaining the position of the wall point (13) to be solved based on the right characteristic line equation of the known interior point (11) and the streamline equation of the known wall point (12); Obtaining the static pressure of the wall point (13) to be solved; Calculating the flow angle of the wall point (13) to be solved according to the compatibility equation on the right characteristic line equation of the known interior point (11); Obtaining the flow velocity and density of the wall point (13) to be solved according to two compatible equations on the streamlines of the known wall point (12) and the wall point (13) to be solved; Euler correction is performed on the position, static pressure, flow angle, flow velocity and density of the wall point (13) to be solved.

3. The design method of variable Mach number "tandem" wide speed range waverider aircraft according to claim 2 is characterized in that: The step of obtaining the position of the wall point to be solved (13) in the direct wall point unit based on the right characteristic line equation of the known interior point (11) and the streamline equation of the known wall point (12) comprises: The streamline equation of the known wall point (12) is constructed as follows: y 12 -l 12-13 x 12 =y 13 -l 12-13 x 13 (2) In the formula, x 12 ,y 12 represents the coordinates of the known wall point (12), x 13 ,y 13 represents the coordinates of the wall point (13) to be solved, λ 12-13 is the slope of the streamline equation between the known wall point (12) and the wall point to be solved (13); The right characteristic line equation of the known interior point (11) is constructed as follows: y 13 -l 11-13 x 13 =y 11 -l 11-13 x 11 (3) In the formula, x 11 ,y 11 represents the coordinates of the known interior point (11), λ 11-13 is the slope of the right characteristic line equation between the known interior point (11) and the wall point (13) to be solved; The simultaneous solution of equations (2) and (3) yields the position coordinates (x 13 ,y 13 ); In the step of obtaining the static pressure of the wall point (13) to be solved, the static pressure of the wall point (13) to be solved is expressed as: In the formula, p 13 represents the static pressure of the wall point (13) to be solved, ρ 13 represents the density of the wall point (13) to be solved, V 13 represents the velocity of the wall point (13) to be solved, P total is the total pressure at each point on the streamline, which can be obtained by using the flow parameters of the known wall point (12) in this unit process, and is expressed as: Among them, p 12 represents the static pressure at the known wall point (12), ρ 12 represents the density of the known wall point (12), V 12 represents the velocity of the known wall point (12); In the step of obtaining the flow angle of the wall point (13) to be solved according to the compatibility equation on the right characteristic line equation of the known interior point (11), the flow angle is expressed as: Q - p 13 -θ 13 =T - (5) Where: T - =-S - (x 13 -x 11 )+Q - p 11 -θ 11 θ 13 represents the flow angle of the wall point (13) to be solved, α 11 represents the Mach angle at the known interior point (11), θ 11 represents the flow angle at the known interior point (11), δ represents 0 for plane flow and 1.0 for axisymmetric flow, M 11 represents the Mach number at the known interior point (11); In the step of obtaining the flow velocity and density of the wall point (13) to be solved according to the two compatibility equations on the streamline of the known wall point (12) and the wall point (13) to be solved, the flow velocity and density of the wall point (13) to be solved are expressed as: R0V 13 +p 13 =T 01 (6) p 13 -A0ρ 13 =T 02 (7) In the formula, T 01 =R0V 12 +p 12 T 02 =p 12 -A0ρ 12 A0=ρ 12 V 12 a 12 represents the speed of sound at the known wall point (12), V 12 represents the flow velocity at the known wall point (12), p 12 represents the static pressure at the known wall point (12), ρ 12 represents the density of the known wall point (12), p 13 represents the static pressure of the wall point (13) to be solved, ρ 13 represents the density of the wall point (13) to be solved, V 13 represents the flow velocity of the wall point (13) to be solved.

4. The design method of variable Mach number "series" wide speed range waverider aircraft according to claim 1 is characterized in that: In step S2, the step of using the Mach number inverse design inverse wall point unit process to solve the variable Mach number "series" supersonic axisymmetric reference flow field includes: Constructing an inverted wall point unit, and obtaining a known interior point (14), a known wall point (16), an unknown interior point (15), and a wall point to be solved (17) in the inverted wall point unit; wherein the unknown interior point (15) is the intersection of a right-running characteristic line extending through the wall point to be solved (17) and a left-running characteristic line passing through the known interior point (14) and the known wall point (16); Based on the streamline equation of the known wall point (16), the left characteristic line equation of the known interior point (14) and the known wall point (16), and the right characteristic line equation of the unknown interior point (15) and the wall point (17) to be solved, the position of the wall point (17) to be solved is obtained; Obtaining the static pressure of the wall point (17) to be solved; Determining the flow angle of the wall point (17) to be solved by using a compatibility equation on a right characteristic line equation passing through the unknown internal point (15) and the wall point (17) to be solved; Calculating the flow velocity and density of the wall point (17) to be solved by using two compatible equations on the streamline passing through the known wall point (16); Euler correction is performed on the position, static pressure, flow angle, flow velocity and density of the wall point (17) to be solved.

5. The design method of variable Mach number "tandem" wide speed range waverider aircraft according to claim 4 is characterized in that: The step of obtaining the position of the wall point (17) to be solved based on the streamline equation of the known wall point (16), the left characteristic line equation of the known interior point (14) and the known wall point (16), and the right characteristic line equation of the unknown interior point (15) and the wall point (17) to be solved comprises: The streamline equation of the known wall point (16) is constructed as: y 16 -l 16-17 x 16 =y 17 -l 16-17 x 17 (8) In the formula, x 16 ,y 16 represents the coordinates of the known wall point (16), x 17 ,y 17 represents the coordinates of the wall point (17) to be solved, λ 16-17 is the slope of the streamline equation between the known wall point (16) and the wall point (17) to be solved, the wall point (17) to be solved is a predetermined solution point, and its coordinate x 17 is known, and the coordinate x of the wall point (17) to be solved is obtained by using equation (8). 17 Find its coordinate y 17 ; The left characteristic line equation of the known interior point (14) and the known wall point (16) is constructed as follows: y 14 -l 14-16 x 14 =y 16 -l 14-16 x 16 (9) In the formula, x 16 ,y 16 represents the coordinates of the known wall point (16), x 14 ,y 14 represents the coordinates of the known interior point (14), λ 14-16 is the slope of the left characteristic line equation at the known interior point (14) and the known wall point (16); The right characteristic line equation of the unknown interior point (15) and the wall point to be solved (17) is constructed and expressed as: y 15 -l 15-17 x 15 =y 17 -l 15-17 x 17 (10) In the formula, λ 15-17 is the slope of the right characteristic line equation between the unknown interior point (15) and the wall point (17) to be solved; The coordinates (x) of the unknown interior point (15) are obtained by solving equations (9) and (10) simultaneously. 15 ,y 15 ); In the step of obtaining the static pressure of the wall point (17) to be solved, the static pressure of the wall point (17) to be solved is expressed as: In the formula, p 17 represents the static pressure of the wall point (17) to be solved, ρ 17 represents the density of the wall point (17) to be solved, V 17 represents the velocity of the wall point (17) to be solved, P total is the total pressure at each point on the streamline, which can be obtained by using the flow parameters of the known wall point (16) in this unit process, and is expressed as: Among them, p 16 represents the static pressure at the known wall point (16), ρ 16 represents the density of the known wall point (16), V 16 represents the velocity of the known wall point (16); In the step of determining the flow angle of the wall point (17) to be solved by using the compatibility equation on the right characteristic line equation passing through the unknown internal point (15) and the wall point (17) to be solved, the flow angle is expressed as: Q-p 17 -θ 17 =T - (12) Where: T - =-S - (x 17 -x 15 )+Q - p 15 -θ 15 θ 17 represents the flow angle of the wall point (17) to be solved, α 15 represents the Mach angle at the unknown interior point (15), θ 15 represents the flow angle at the unknown interior point (15), δ represents 0 for plane flow and 1.0 for axisymmetric flow, M 15 represents the Mach number at the unknown interior point (15); In the step of calculating the flow velocity and density of the wall point (17) to be solved by using two compatible equations on the streamline passing through the known wall point (16), the flow velocity and density of the wall point (17) to be solved are expressed as: R0V 17 +p 17 =T 01 (13) p 17 -A0ρ 17 =T 02 (14) In the formula, T 01 =R0V 16 +p 16 T 02 =p 16 -A0ρ 16 A0=ρ 16 V 16 a 16 represents the speed of sound at the known wall point (16), V 16 represents the flow velocity at the known wall point (16), p 12 represents the static pressure at the known wall point (16), ρ 16 represents the density of the known wall point (16), p 17 represents the static pressure of the wall point (17) to be solved, ρ 17 represents the density of the wall point (17) to be solved, V 17 represents the flow velocity of the wall point (17) to be solved.

6. The design method of a variable Mach number "tandem" wide speed range waverider aircraft according to any one of claims 1 to 5, characterized in that: In step S2, in the step of solving the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall point, the Mach number inverse design direct wall point unit process or the Mach number inverse design inverse wall point unit process is tested to verify the correctness of the solution process; In step S2, in the step of solving by using the direct wall point unit process of Mach number inverse design or the inverse wall point unit process of Mach number inverse design, characteristic line meshing can be performed on the variable Mach number "series" supersonic axisymmetric reference flow field.

7. The design method of a variable Mach number "tandem" wide speed range waverider aircraft according to any one of claims 1 to 5, characterized in that: In S3, in the variable Mach number "series" supersonic axisymmetric reference flow field based on the inverse design wall point solved in S2, according to the basic waverider design principle, one of the leading edge line, the upper surface bottom line and the lower surface bottom line is used as input, the remaining two characteristic lines are obtained and the upper surface, lower surface and bottom surface of the waverider aircraft are closed, so as to obtain the aerodynamic configuration of the variable Mach number "series" wide speed range waverider aircraft.

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