Double-waverider front body / air inlet channel integrated reverse design method
By controlling the shock wave shape of the outer waveband and the pressure distribution on the inner waveband using the three-dimensional bending shock wave theory and the characteristic line method, the problem of uncontrollable external flow shock wave and internal flow pressure distribution in the integrated design of dual waveband forebody/inlet in the existing technology is solved, and efficient improvement of aircraft lift-to-drag ratio and compression efficiency is achieved.
Patent Information
- Application Number
- CN202510966248.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-14
- Publication Date
- 2025-11-14
AI Technical Summary
The lack of existing technology has led to the lack of a design method that can simultaneously control the external shock wave and internal pressure distribution of a dual-wave forebody/inlet integrated aircraft, resulting in insufficient inlet compression efficiency and uncontrollable lift-to-drag ratio of the aircraft.
The three-dimensional curved shock wave theory and the characteristic line method are used to control the shock wave shape of the outer waveband and the wall pressure distribution of the inner waveband. The three-dimensional curved characteristic line method is used to design a three-dimensional curved characteristic line reference surface and a compression scheme on the exit section of the three-dimensional inner inlet. This achieves the design of the compression efficiency of the dual waveband forebody/inlet. By constructing the geometry using symmetrical planes and reference surfaces, a dual waveband forebody/inlet integrated aircraft with controllable outer shock wave and inner pressure distribution is obtained.
It enables simultaneous control of external shock wave and internal pressure distribution in a dual-wave forebody/inlet integrated aircraft, improving the compression efficiency of the inlet and the lift-to-drag ratio of the aircraft, expanding the design space, and providing a theoretical basis and technical support for integrated aircraft design.
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Figure CN120951455A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of near-space hypersonic vehicles, and in particular to a reverse design method for an integrated dual-waverider forebody / inlet. Background Technology
[0002] With the continuous development and progress of science and technology, people's pursuit of flight speed, altitude, and distance is constantly increasing. Hypersonic flight refers to flight at speeds exceeding Mach 5 within the atmosphere. Hypersonic vehicles possess immense military, economic, and civilian value due to their advantages such as large airspace, ultra-high speed, long distance, and high precision. As a multidisciplinary research field integrating aerospace, materials science, gas dynamics, control technology, and computer technology, hypersonic flight represents a strategic high ground in aerospace technology, a key force for future space control and ensuring space superiority, and a carrier for large-scale space exploration. It is a vehicle technology with broad development and application prospects. The integrated design of the propulsion system and airframe is crucial for achieving air-breathing hypersonic flight. A good integrated airframe / propulsion system design can meet the comprehensive aerodynamic / propulsion performance requirements of designers for air-breathing hypersonic vehicles.
[0003] The airframe of an air-breathing hypersonic vehicle comprises a forebody, fuselage, wings, and aftbody. The propulsion system of an air-breathing hypersonic vehicle primarily relies on a scramjet / subsonic ramjet engine, including components such as the inlet, isolation section, combustion chamber, and nozzle. The placement and number of scramjet / subsonic ramjet engines on the airframe should be designed according to the flight mission requirements, and their forms vary. The inlet needs to provide compressed airflow that meets the parameter requirements for the ramjet engine's combustion chamber; the upstream capture airflow required may be interfered with by various components of the airframe. The combustion chamber and nozzle, being primarily internal components, have upstream flow mainly constrained by the performance parameters of the inlet or combustion chamber outlet, and are largely unaffected by the flow interference from other airframe components. Therefore, the core of the integrated design of the airframe / propulsion system of an air-breathing hypersonic vehicle is the integrated design of the airframe and inlet; the key constraint on improving overall performance lies in the lack of an efficient integrated airframe / inlet design methodology.
[0004] Existing integrated designs of dual-wave forebody / inlet achieve effective coupling of external compression flow and internal contraction flow through the continuous transition of the curvature of the internal and external flow shock waves on the design cross section, realizing integrated design of the two at the aerodynamic level. However, in the above designs, the incident shock wave of the dual-wave forebody and inlet is a straight shock wave, resulting in insufficient inlet compression efficiency and an inability to effectively organize the flow field behind the shock wave. To address these issues, Li Yiqing et al., based on this design concept, further conducted research on the integrated design of dual-wave forebody / inlet and initially proposed a dual-wave forebody / inlet design method with controllable pressure distribution to improve the compression efficiency of the inlet. Although this method can reproduce the pre-designed wall pressure to a certain extent, the three-dimensional shape of the shock wave, especially the shock wave shape within the design cross section, is uncontrollable. It is necessary to continuously iterate the inlet capture shape to meet the inlet flow requirements, and there is a certain degree of overflow at the inlet lip. The lift-to-drag ratio of the integrated aircraft is uncontrollable, limiting the design freedom of this configuration. Therefore, one of the problems currently limiting the performance of hypersonic vehicles is the lack of an integrated reverse design method for dual-wave forebody / inlet that allows for simultaneous control of both external shock wave and internal pressure distribution. Summary of the Invention
[0005] In view of this, this application provides a reverse design method for an integrated dual-wavefront forebody / inlet, which solves the problems in the prior art and realizes simultaneous control of the external shock wave and internal pressure distribution of the integrated dual-wavefront forebody / inlet aircraft.
[0006] This application provides a reverse design method for an integrated dual-wavelength forebody / inlet duct, employing the following technical solution: A reverse design method for an integrated dual-wavelength forebody / inlet includes the following steps: According to the design requirements, the projection of the leading edge capture profile of the dual waverider onto the design section is specified. The projection of the leading edge capture profile onto the design section is divided into an outer waverider band and an inner waverider band. The outer waverider band and the inner waverider band are connected by a two-dimensional plane waverider band with curvature of ∞. Control the shock wave shape in the outer waveband and control the wall pressure distribution in the inner waveband; Based on the given wall pressure distribution, the internal wave compression profile is solved using the three-dimensional bending characteristic line method. Based on the given incident shock wave curve, the external wave compression profile is solved using the three-dimensional bending shock wave theory and the three-dimensional bending characteristic line method. Design the three-dimensional internal inlet duct outlet section and the projection of the three-dimensional internal inlet duct lip onto the design section, and obtain the three-dimensional configuration of the three-dimensional internal inlet duct lip based on the shock wave relationship. Based on the compression profile, the geometry of the integrated internal and external waverider aircraft is constructed to obtain a dual waverider forebody / inlet integrated aircraft in which the distribution of external shock waves and internal pressure can be controlled simultaneously during the design.
[0007] Optionally, the specific steps for controlling the shock wave in the outer band and the wall pressure distribution in the inner band include: Discretize the outer and inner multiplication bands and solve for the radius of curvature and center of curvature of the outer and inner multiplication bands at each discrete point; The reference axis is obtained by connecting each discrete point of the outer multiplication band and the inner multiplication band with the corresponding curvature center, and the reference surface is obtained by stretching each reference axis along the direction perpendicular to the paper plane. By changing the reference plane of each inner waveband, the pressure distribution on the wall can be controlled; by changing the reference plane of each outer waveband, the shock wave of the outer waveband can be controlled.
[0008] Optionally, for each inner band reference surface, a cubic curve design is used to change the pressure distribution curve in each inner band reference surface to achieve control over the wall pressure distribution.
[0009] Optionally, for each outer band reference surface, a cubic curve is used to specify the incident shock wave and change the shock wave curve in the reference surface to achieve control of the outer band shock wave. Optional, the governing equations for three-dimensional bending shock waves are as follows: ; ; ; ; ; ; ; ; ; ; In the above formula, p For pressure, r For density, T For temperature, m and l For two orthogonal directions along the shock wave surface, n The normal to the shock surface, i For reference parameters, V m and V l The velocity along the shock wave surface, Vn The velocity perpendicular to the shock wave surface, c For specific heat ratio, R The gas constant is... K nm For the shock surface along the curve m Normal curvature of direction, K nl For the shock surface along the curve l Normal curvature of direction, K gl Curves on the shock surface l geodesic curvature, K gm Curves on the shock surface m geodesic curvature, t gm Curve on the shock surface m geodesic torsion, p 1 represents the pressure before the shock wave. p 2 represents the pressure after the shock wave. r 1 represents the density before the shock wave. r 2 represents the density after the shock wave. m and l For two orthogonal directions along the shock wave surface, n The normal to the shock surface, j For reference parameters, V 1m For shock front m velocity in direction, V 2m For shock wave m velocity in direction, V 1n For shock front n velocity in direction, V 2n For the shock wave trailing edge n velocity in direction, c Specific heat ratio.
[0010] Optionally, the governing equations for the three-dimensional bending characteristic line method are as follows: ; ; ; ; ; ; ; ; ; ; In the above formula, s and l These represent the directions of the feature lines in the reference plane. f The direction is perpendicular to the reference plane. P and D For the pressure gradient within the reference plane, W The pressure gradient perpendicular to the reference plane, V For the velocity vector in the reference plane, w The velocity vector perpendicular to the reference plane, p For pressure, r For density, d For airflow deflection angle, m Let y be the Mach angle, a be the speed of sound, and y be the local radius of curvature.
[0011] Optionally, the specific process for obtaining the three-dimensional configuration of the three-dimensional inlet lip is as follows: The three-dimensional internal inlet duct's inner waveband extends downstream along the compression profile and intersects with the surface obtained by the projection of the three-dimensional internal inlet duct lip onto the design cross section along the flow direction, thus obtaining the three-dimensional configuration of the three-dimensional internal inlet duct lip.
[0012] In summary, this application includes the following beneficial technical effects: The design method presented in this application enables simultaneous control of the external shock wave and internal pressure distribution of an integrated dual-waverider forebody / inlet aircraft. The adjustment of the external and internal flow fields is independent of each other. This method, while ensuring the compression efficiency of the internal inlet, can further improve the lift-to-drag ratio of the aircraft. The dual-waverider forebody / inlet integrated reverse design method, which allows for simultaneous control of the external shock wave and internal pressure distribution, further expands the reverse design space for waverider forebody and inlet systems, providing a theoretical basis and technical support for integrated aircraft design. Attached Figure Description
[0013] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0014] Figure 1 This is a schematic diagram of the integrated configuration design of an embodiment of this application. Figure 2 This is a schematic diagram of the aerodynamic model design for the given external shock wave and internal wall pressure in the embodiments of this application.
[0015] Figure 3This is a schematic diagram of the integrated configuration of the dual-wavefront forebody / inlet in an embodiment of this application.
[0016] Figure labeling: 1. Inner waveband; 2. Outer waveband; 3. Center of curvature; 4. Reference plane; 5. Plane of symmetry; 6. Discrete point; 7. Two-dimensional plane waveband; 8. Incident shock wave; 9. Wall pressure distribution; 10. Projection of the inner flow leading edge capture profile (FCT) onto the top view; 11. Projection of the outer flow leading edge capture profile (FCT) onto the top view; 12. Upper surface; 13. Outer waveband compression profile; 14. Inner waveband compression profile; 15. Three-dimensional inner-turn inlet; 16. Inner flow leading edge capture profile; 17. Outer flow leading edge capture profile; 18. Inner and outer flow transition section; 19. Three-dimensional configuration of the lip of the three-dimensional inner-turn inlet; 20. Exit section of the three-dimensional inner-turn inlet. Detailed Implementation
[0017] The embodiments of this application will now be described in detail with reference to the accompanying drawings.
[0018] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0019] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.
[0020] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.
[0021] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.
[0022] This application provides a reverse design method for an integrated dual-wavefront forebody / inlet.
[0023] A reverse design method for an integrated dual-wavelength forebody / inlet includes the following steps: like Figure 1 As shown, in step 1, the projection of the leading-edge capture profile (FCT) of the dual-wavelength capture body onto the design section is specified according to the design requirements. The projection of the leading-edge capture profile onto the design section is divided into an outer wavelength capture band 2 and an inner wavelength capture band 1. The outer wavelength capture band 2 and the inner wavelength capture band 1 are connected by a two-dimensional plane wavelength capture band 7 with a curvature of ∞. FCT stands for WieFlow Capture Tube.
[0024] like Figure 1 and Figure 2 As shown, step 2 involves controlling the shock wave shape in the outer band 2 and controlling the wall pressure distribution 9 in the inner band 1; specifically: Discretize the outer multiplication band 2 and the inner multiplication band 1, and solve for the radius of curvature and center of curvature 3 of each discrete point 6 of the outer multiplication band 2 and the inner multiplication band 1; connect each discrete point 6 of the outer multiplication band 2 and the inner multiplication band 1 with the corresponding center of curvature 3 to obtain a reference axis, and stretch each reference axis along a direction perpendicular to the paper to obtain a reference surface 4; change the reference surface 4 of each inner multiplication band 1 to control the wall pressure distribution 9, and change the reference surface 4 of each outer multiplication band 2 to control the shock wave of the outer multiplication band 2.
[0025] Specifically, for each inner waveband 1, a cubic curve design is used to change the pressure distribution curve in the reference surface 4 of each inner waveband 1 to control the wall pressure distribution 9. For each outer waveband 2, a cubic curve is used to specify the incident shock wave 8, and the shock wave curve in the reference surface 4 of the outer waveband 2 is changed to control the shock wave of the outer waveband 2. In step 2, adjusting the wall pressure distribution 9 in the internal flow field can further improve the compression performance of the air intake. Adjusting the external flow shock wave in the external flow field can further improve the lift-drag performance of the aircraft.
[0026] Then, the projections 10 and 11 of the internal flow leading edge capturing profile (FCT) on the top view are designed. Based on the given pressure distribution and shock wave curve, different compression profiles for the internal wave-multiplying band 1 and the external wave-multiplying band 2 are solved using the three-dimensional curved shock wave equation and the three-dimensional curved streamline characteristic line method, respectively. Based on the compression profiles in different reference planes and the angle between the reference plane and the symmetry plane 5, the integrated compression profile of the double wave-multiplying band is obtained through coordinate transformation in the corresponding external compression flow field or internal contraction flow field. See steps 3 and 4 for details.
[0027] Step 3: Based on the given wall pressure distribution 9, solve the inner wave compression profile 14 using the three-dimensional bending characteristic line method.
[0028] Step 4: Based on the given incident shock wave curve 8, solve the external wave compression profile 13 using the three-dimensional bending shock wave theory and the three-dimensional bending characteristic line method.
[0029] The governing equations for three-dimensional bending shock waves are as follows: ; ; ; ; ; ; ; ; ; ; In the above formula, p For pressure, r For density, T For temperature, m and l For two orthogonal directions along the shock wave surface, n The normal to the shock surface, i For reference parameters, V m and V l The velocity along the shock wave surface, V n The velocity perpendicular to the shock wave surface, c For specific heat ratio, R The gas constant is... K nm For the shock surface along the curve m Normal curvature of direction, K nlFor the shock surface along the curve l Normal curvature of direction, K gl Curves on the shock surface l geodesic curvature, K gm Curves on the shock surface m geodesic curvature, t gm Curve on the shock surface m The geodesic torsion. p 1 represents the pressure before the shock wave. p 2 represents the pressure after the shock wave. r 1 represents the density before the shock wave. r 2 represents the density after the shock wave. m and l For two orthogonal directions along the shock wave surface, n The normal to the shock surface, j For reference parameters, V 1m For shock front m velocity in direction, V 2m For shock wave m velocity in direction, V 1n For shock front n velocity in direction, V 2n For the shock wave trailing edge n velocity in direction, c Specific heat ratio.
[0030] The governing equations of the three-dimensional bending characteristic line method are as follows: ; ; ; ; ; ; ; ; ; ; In the above formula, s and l These represent the directions of the feature lines in the reference plane. f The direction is perpendicular to the reference plane. P and D For the pressure gradient within the reference plane,W The pressure gradient perpendicular to the reference plane, V For the velocity vector in the reference plane, w The velocity vector perpendicular to the reference plane, p For pressure, r For density, d For airflow deflection angle, m Let y be the Mach angle, a be the speed of sound, and y be the local radius of curvature.
[0031] Step 5, as follows Figure 3 As shown, the three-dimensional internal inlet duct outlet section 20 and the projection of the lip of the three-dimensional internal inlet duct 15 onto the designed section are designed, and the three-dimensional configuration 19 of the lip of the three-dimensional internal inlet duct 15 is obtained according to the shock wave relationship. The outlet section 20 of the three-dimensional internal inlet duct can be designed according to requirements. The wave-riding band 1 inside the three-dimensional internal inlet duct 15 extends downstream along the compression profile, intersecting with the surface obtained by the projection of the lip of the three-dimensional internal inlet duct 15 onto the designed section along the flow direction to obtain the three-dimensional configuration 19 of the lip of the three-dimensional internal inlet duct.
[0032] Step 6: Based on the compression profile, perform geometric construction on the integrated internal and external waverider aircraft to obtain a dual waverider forebody / inlet integrated aircraft in which the distribution of external shock waves and internal pressure can be controlled simultaneously during the design.
[0033] The method described in this application yields an integrated dual-wavefront forebody / inlet configuration where the distribution of both the external shock wave and the internal pressure is simultaneously controllable. The integrated configuration includes a symmetry plane 5, an upper surface 12, an external wavefront compression profile 13, an internal wavefront compression profile 14, a three-dimensional internal rotating inlet 15, an internal flow leading edge capture profile 16, an external flow leading edge capture profile 17, an internal and external flow transition section 18, a three-dimensional configuration of the lip of the three-dimensional internal rotating inlet 19, and a three-dimensional internal rotating inlet outlet section 20.
[0034] This design method enables simultaneous control of the external shock wave and internal pressure distribution of an integrated dual-waverider forebody / inlet aircraft. In the internal flow field, adjusting the pressure distribution on each reference surface provides a higher-compression-quality airflow to the subsequent inlet. In the external flow field, adjusting the shock wave shape on each reference surface further enhances the lift-to-drag ratio of the integrated aircraft. The adjustments to the internal and external flow fields are independent of each other, allowing this method to further improve the lift-to-drag ratio while ensuring the compression efficiency of the internal inlet. This dual-waverider forebody / inlet integrated reverse design method, which allows for simultaneous control of both external shock wave and internal pressure distribution, further expands the reverse design space for waverider forebody and inlet systems, providing a theoretical basis and technical support for integrated aircraft design.
[0035] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A reverse design method for an integrated dual-wavelength forebody / inlet, characterized in that, Includes the following steps: According to the design requirements, the projection of the leading edge capture profile of the dual waverider onto the design section is specified. The projection of the leading edge capture profile onto the design section is divided into an outer waverider band and an inner waverider band. The outer waverider band and the inner waverider band are connected by a two-dimensional plane waverider band with curvature of ∞. Control the shock wave shape in the outer waveband and control the wall pressure distribution in the inner waveband; Based on the given wall pressure distribution, the internal wave compression profile is solved using the three-dimensional bending characteristic line method. Based on the given incident shock wave curve, the external wave compression profile is solved using the three-dimensional bending shock wave theory and the three-dimensional bending characteristic line method. Design the three-dimensional internal inlet duct outlet section and the projection of the three-dimensional internal inlet duct lip onto the design section, and obtain the three-dimensional configuration of the three-dimensional internal inlet duct lip based on the shock wave relationship. Based on the compression profile, the geometry of the integrated internal and external waverider aircraft is constructed to obtain a dual waverider forebody / inlet integrated aircraft in which the distribution of external shock waves and internal pressure can be controlled simultaneously during the design.
2. The dual-wavelength forebody / inlet integrated reverse design method according to claim 1, characterized in that, The specific steps for controlling shock waves in the outer band and controlling the wall pressure distribution in the inner band include: Discretize the outer and inner multiplication bands and solve for the radius of curvature and center of curvature of the outer and inner multiplication bands at each discrete point; The reference axis is obtained by connecting each discrete point of the outer multiplication band and the inner multiplication band with the corresponding curvature center, and the reference surface is obtained by stretching each reference axis along the direction perpendicular to the paper plane. By changing the reference plane of each inner waveband, the pressure distribution on the wall can be controlled; by changing the reference plane of each outer waveband, the shock wave of the outer waveband can be controlled.
3. The dual-wavelength forebody / inlet integrated reverse design method according to claim 2, characterized in that, For each inner band reference surface, a cubic curve design is used to change the pressure distribution curve in each inner band reference surface to achieve control over the wall pressure distribution.
4. The dual-wavelength forebody / inlet integrated reverse design method according to claim 3, characterized in that, For each outer band reference plane, a cubic curve is used to specify the incident shock wave and change the shock wave curve in the reference plane to achieve control of the outer band shock wave.
5. The dual-wavelength forebody / inlet integrated reverse design method according to claim 4, characterized in that, The governing equations for three-dimensional bending shock waves are as follows: ; ; ; ; ; ; ; ; ; ; In the above formula, p For pressure, ρ For density, T For temperature, m and l For two orthogonal directions along the shock wave surface, n The normal to the shock surface, i For reference parameters, V m and V l The velocity along the shock wave surface, V n The velocity perpendicular to the shock wave surface, γ For specific heat ratio, R The gas constant is... K nm For the shock surface along the curve m Normal curvature of direction, K nl For the shock surface along the curve l Normal curvature of direction, K gl Curves on the shock surface l geodesic curvature, K gm Curves on the shock surface m geodesic curvature, τ gm Curve on the shock surface m geodesic torsion, p 1 represents the pressure before the shock wave. p 2 represents the pressure after the shock wave. ρ 1 represents the density before the shock wave. ρ 2 represents the density after the shock wave. m and l For two orthogonal directions along the shock wave surface, n The normal to the shock surface, j For reference parameters, V 1m For shock front m velocity in direction, V 2m For shock wave m velocity in direction, V 1n For shock front n velocity in direction, V 2n For the shock wave trailing edge n velocity in direction, γ Specific heat ratio.
6. The dual-wavelength forebody / inlet integrated reverse design method according to claim 5, characterized in that, The governing equations of the three-dimensional bending characteristic line method are as follows: ; ; ; ; ; ; ; ; ; ; In the above formula, s and l These represent the directions of the feature lines in the reference plane. φ The direction is perpendicular to the reference plane. P and D For the pressure gradient within the reference plane, W The pressure gradient perpendicular to the reference plane, V For the velocity vector in the reference plane, w The velocity vector perpendicular to the reference plane, p For pressure, ρ For density, δ For airflow deflection angle, μ Let y be the Mach angle, a be the speed of sound, and y be the local radius of curvature.
7. The dual-wavelength forebody / inlet integrated reverse design method according to claim 1, characterized in that, The specific process for obtaining the three-dimensional configuration of the three-dimensional internal intake lip is as follows: The three-dimensional internal inlet duct's inner waveband extends downstream along the compression profile and intersects with the surface obtained by the projection of the three-dimensional internal inlet duct lip onto the design cross section along the flow direction, thus obtaining the three-dimensional configuration of the three-dimensional internal inlet duct lip.