Design method of fixed front edge molded line waverider based on axial symmetry flow field

Abstract

The invention relates to a fixed front edge molded line waverider design method based on an axisymmetric flow field, and the method comprises the steps: enabling a three-dimensional front edge molded line to rotate around a preset rotating shaft to form a revolution body, and enabling the revolution body to serve as a preset shock wave surface; projecting the three-dimensional front edge molded line along the extension direction of the rotating shaft to obtain a streamline tracking starting line, setting a shock wave outlet molded line as an arc, and projecting the streamline tracking starting line to a shock wave surface to obtain a streamline tracking starting point; taking the generatrix of the shock wave surface as an accurate shock wave molded line, and calculating an axisymmetric flow field at the downstream of the shock wave molded line by adopting an inverse characteristic line method; the method comprises the following steps: performing adaptive sub-partitioning on two-dimensional data in an axisymmetric flow field by taking a quadtree as a core data structure, performing hierarchical indexing through the quadtree to position a grid unit where a target point is located, and obtaining flow field information of the target point in combination with inverse distance interpolation; starting from the projection point of the streamline tracking starting line, continuous tracking is carried out in the axial symmetry flow field in the streamline direction, and all obtained tracking streamlines are fitted to obtain the fixed front edge molded line waverider.

Description

Technical Field

[0001] This disclosure relates to the field of aerodynamic layout design technology for hypersonic vehicles, specifically, to a design method for a waverider with a fixed leading edge profile based on an axisymmetric flow field. This disclosure not only addresses the design of waveriders with a fixed leading edge profile based on axisymmetric flow field control for wide-speed-range flight requirements, but can also be applied to the aerodynamic shape development of hypersonic cruise missiles, space vehicles, and transatmospheric vehicles, providing core technical support for improving the overall aerodynamic performance of aircraft. Background Technology

[0002] With the rapid development of defense science and technology and the aerospace industry, the development of wide-range hypersonic vehicles (flying at Mach numbers covering subsonic, transonic to hypersonic speeds) has become a focus of competition among countries. As the core aerodynamic layout of this type of vehicle, the design technology of wide-range waveriders has attracted much attention. Existing technologies have proposed various wide-range waverider design forms, such as series, parallel, variable Mach number, and deformable types. However, their core design focuses on improving the geometry of the waverider surface, which can only achieve good aerodynamic performance matching in the hypersonic / hypersonic stage. In the subsonic cruise or takeoff and landing stages, they generally suffer from low lift-to-drag ratio and poor maneuverability, making it difficult to meet the performance requirements of the entire flight envelope.

[0003] The concept of a fixed-planar-shape waverider offers a new approach to addressing the challenge of balancing performance across a wide speed range. This method, by optimizing the planar projection shape of the waverider, overcomes the limitations of traditional waverider designs that rely solely on flow field characteristics, achieving a preliminary balance between subsonic lift performance in the low-speed range and high lift-to-drag ratio in the hypersonic range. Among these methods, the close-cone method is currently the most widely used design approach for fixed-planar-shape waveriders. Based on this method, the precise geometric relationship between the design curve and the planar shape has been successfully derived, generating various waverider configurations such as single-sweep, double-sweep, "S"-shaped leading edge, and double-sweep with upper / lower anhedral fins, significantly improving the flexibility of shape control during the design process.

[0004] In the design system of waveriders with a fixed leading edge profile, besides the two key geometric boundaries of the shock exit profile (ICC) and the streamline tracking initiation line (FCT), the selection of the reference flow field is the core variable dimension that determines the design space and performance upper limit. Compared with traditional wedge-shaped and conical flow fields, axisymmetric flow fields have the advantages of continuous flow field structure and a wide range of parameter control. Using an axisymmetric flow field to replace the traditional flow field as the design reference is an effective technical approach to expand the design space of waveriders and improve the flexibility of aerodynamic performance control. In existing technologies, some scholars have attempted to generate waverider structures through axisymmetric flow fields, achieving preliminary effects such as increased volume, optimized lift-to-drag ratio, and improved lateral stability. However, many problems have been exposed in engineering applications: the design space is limited by the accuracy of flow field calculations, and the geometric accuracy control error of the leading edge profile often exceeds 5%; streamline tracing uses the traditional grid search method, and the time for a single point search can reach milliseconds, resulting in low overall efficiency; the volume ratio can only be adjusted within a range of 0.1 to 0.2, which is difficult to meet different load requirements. These defects severely limit the engineering application process of this type of waverider.

[0005] Therefore, there is an urgent need to develop a design method for waveriders with a fixed leading edge profile that can overcome the limitations of existing technologies. This method should simultaneously take into account the flexibility of design parameters, the computational efficiency of streamline tracing, and the aerodynamic performance of the final product, so as to provide a high-performance and high-reliability aerodynamic layout solution for hypersonic vehicles with a wide speed range. Summary of the Invention

[0006] This disclosure proposes a design method for a waverider with a fixed leading edge based on an axisymmetric flow field, which can solve at least one of the technical problems listed in the background art. The technical solution adopted in this disclosure is as follows: This disclosure provides a design method for a waverider with a fixed leading edge based on an axisymmetric flow field, the method comprising: S100: Given a three-dimensional leading edge profile, the three-dimensional leading edge profile is rotated around a preset rotation axis to form a spiral body, and the spiral body is used as a preset shock wave surface; S200: Project the three-dimensional leading edge profile along the extension direction of the preset rotation axis to obtain the streamline tracing starting line (FCT). Set the shock wave exit profile (ICC) as an arc structure, and project the streamline tracing starting line (FCT) onto the preset shock wave surface to obtain the streamline tracing starting point. S300: Using the generatrix of the preset shock surface as the precise shock profile, the axisymmetric flow field downstream of the shock profile is calculated using the inverse characteristic line method (iMoC). S400: Using a quadtree as the core data structure, adaptive sub-partitioning is performed on the two-dimensional data in the axisymmetric flow field. The target point is located by hierarchical indexing through the quadtree, and the flow field information of the target point is obtained by combining inverse distance interpolation. S500: Starting from the projection point of the streamline tracing start line (FCT), continuous tracing is performed along the streamline direction in the axisymmetric flow field. All the tracing streamlines obtained are fitted into a closed spatial surface, and the closed spatial surface is used as the designed leading edge profile waverider.

[0007] Preferably, in S100, the three-dimensional leading edge profile is controlled by cubic quasi-uniform B-spline.

[0008] Preferably, in the case where the three-dimensional leading edge profile is controlled by cubic quasi-uniform B-spline, the coordinates of the control points satisfy x∈[0.00m, 6.00m], y∈[0.00m, 2.40m] and z∈[0.00m, 0.30m].

[0009] Preferably, in step S200, the distance between the three-dimensional leading edge profile and the preset rotation axis is adjusted. d (referred to as "rotation axis distance"), in order to ultimately change the volume ratio of the fixed leading edge profile waverider; The distance d ∈[-0.3m,0.3m].

[0010] Preferably, in S300, the inverse feature line method (iMoC) includes: Radiating streamlines and characteristic lines from a known point, their intersections yield an unknown solution point; Based on the known points and unknown solution points, a compatibility equation is established simultaneously; The coordinates and flow field parameters are solved using the compatibility equation. The parameters at each point on the shock wave profile are determined according to the oblique shock wave relation.

[0011] Preferably, in the inverse feature line method (iMoC), the calculation accuracy can be improved iteratively by using a prediction-correction method.

[0012] Preferably, the characteristic line method is used to fill in the blank area downstream of the shock wave dependent region.

[0013] Preferably, in S300, when the shock wave profile is a convex curve, the expansion flow is used as a substitute for the inverse characteristic line method in the section of the convex curve where it is not applicable.

[0014] Preferably, the axisymmetric flow field is an axisymmetric inviscid flow field.

[0015] Preferably, in step S400, the quadtree is stored using a rule-based storage method.

[0016] Preferably, in S400, the region of the axisymmetric flow field is recursively divided into four quadrants.

[0017] Preferably, in S400, the grid cell threshold of the sub-partition is preferably set to 300.

[0018] Preferably, the method further includes: S600: The Navier-Stokes equations are solved using the finite volume method to verify the aerodynamic performance of the fixed leading edge profile waverider; the Menter SST k-ω two-equation model is used as the turbulence model to simulate the turbulence effect of the axisymmetric flow field.

[0019] The beneficial effects of this disclosure are as follows: This disclosure proposes a design method for a waverider with a fixed leading edge profile based on an axisymmetric flow field. It achieves synergistic optimization of waverider performance and design efficiency through a closed-loop design process of "geometric boundary definition - benchmark flow field calculation - efficient streamline tracing - configuration generation and verification." This disclosure realizes the design of a waverider with a fixed leading edge profile by pre-setting an axisymmetric flow field, effectively expanding the design space. Simultaneously, the use of a quadtree improves streamline tracing efficiency by 39 times. The generated waverider achieves a maximum lift-to-drag ratio of 3.308 at Ma=8 and H=30km, with good agreement between the shock wave and the design curve, exhibiting excellent waveriding characteristics. By adjusting the rotation axis distance… d It can flexibly match volume ratio and lift-to-drag ratio, solving the problems of limited space and low control precision in existing designs, and is suitable for the aerodynamic layout design of hypersonic aircraft with a wide speed range.

[0020] In this disclosure, a given three-dimensional leading edge profile is rotated to form a preset shock surface, and the leading edge profile is projected along the rotation axis to obtain the streamline tracing starting line (FCT). After the shock shape is given, the axisymmetric flow field is calculated using the inverse characteristic line method, and the flow field is supplemented by combining the characteristic line method. The flow field data is divided into sub-partitions using a quadtree as the data structure to improve the efficiency of point finding and streamline tracing, and accelerate streamline tracing. Finally, streamlines are traced from the FCT projection point to generate a waverider with a fixed leading edge profile.

[0021] Compared with the prior art, this disclosure has the following advantages: (1) High design flexibility: It innovatively adopts axisymmetric flow field to replace traditional wedge flow and conical flow as the design benchmark, combined with the rotation axis distance d Continuous adjustment can generate diverse waverider shapes with different volume ratios to meet target aerodynamic performance requirements; (2) High efficiency of streamline tracing: The flow field data is adaptively partitioned and managed through a quadtree data structure, and an efficient spatial indexing mechanism is constructed. The efficiency improvement is more obvious as the number of grid cells increases, which significantly shortens the design cycle. (3) Excellent aerodynamic performance: The waverider generated by this method exhibits excellent aerodynamic performance under hypersonic design conditions; the position of the shock wave on the lower surface matches the design ICC curve well, and the waverider characteristics are significant, which provides a guarantee for the aircraft to achieve long range and high maneuverability; (4) Highly adjustable: The rotation axis distance has been established. d A quantitative correlation model with waverider volume ratio and lift-to-drag ratio is used to precisely adjust the distance between the rotation axes. d It can achieve flexible matching of volume ratio and lift-to-drag ratio to meet the performance requirements under different mission profiles; (5) Wide engineering applicability: This design method can generate the shape of a waverider with a given three-dimensional leading edge profile. The performance optimization of the waverider in a wide speed range can be achieved by customizing the leading edge profile. It is suitable for the aerodynamic layout design of hypersonic aircraft in a wide speed range and has good prospects for engineering transformation. Attached Figure Description

[0022] The accompanying drawings, which form part of this application, are used to provide a further understanding of this disclosure. The illustrative embodiments of this disclosure and their descriptions are used to explain this disclosure and do not constitute an undue limitation of this disclosure.

[0023] Figure 1 This is a schematic flowchart of a waverider design method based on an axisymmetric flow field with a fixed leading edge, as described in this disclosure.

[0024] Figure 2 This is a schematic diagram of the design of a waverider with a fixed leading edge profile based on an axisymmetric flow field as described in this disclosure. The diagram clearly shows the spatial relationship of the core design elements such as the leading edge profile, shock surface, and axis of rotation.

[0025] Figure 3 This is a schematic diagram of the axisymmetric flow field calculated using the inverse characteristic line method as described in this disclosure.

[0026] Figure 4 This is a schematic diagram of a grid cell with interwoven reverse left-hand feature lines and streamlines as described in this disclosure.

[0027] Figure 5 This is a schematic diagram of the waverider with a fixed leading edge profile as described in this disclosure. It presents the overall configuration of the waverider designed in this disclosure in three dimensions and clearly shows the leading edge feature with an upward reflection.

[0028] Figure 6 These are comparative cross-sections of the trailing edge of the waverider at different rotation axis distances as described in this disclosure, comparing the rotation axis distances. d The thickness differences of the trailing edge section of the waverider under three working conditions (-0.3m, 0m, and 0.3m) visually reflect the distance between the rotation axes. d The effect of controlling the plot ratio.

[0029] Figure 7 The curves showing the lift and drag characteristics of a waverider with a fixed leading edge profile based on an axisymmetric flow field, as described in this disclosure, vary with the angle of attack. They present the variation patterns of the lift coefficient, drag coefficient, and lift-to-drag ratio of three waveriders at different angles of attack, including the influence of bottom drag.

[0030] Figure 8 The curve showing the change of the aerodynamic focus position of the waverider with the angle of attack based on the axisymmetric flow field is described in this disclosure. It shows the change of the axial position of the focus at different angles of attack. Combined with the position of the center of gravity, the longitudinal static stability of the waverider can be preliminarily judged.

[0031] Figure 9 The pressure distribution diagram of the trailing edge section of the waverider with a fixed leading edge profile based on axisymmetric flow field as described in this disclosure clearly shows the shock wave attachment state on the lower surface of the waverider and the pressure variation law along the flow direction, verifying the excellent waveriding characteristics. Detailed Implementation

[0032] The present disclosure will now be described in detail with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in the present application can be combined with each other.

[0033] The following detailed descriptions are exemplary and intended to provide further detailed explanation of this disclosure. Unless otherwise specified, all technical terms used in this disclosure have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. The terminology used in this disclosure is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this disclosure.

[0034] like Figure 1 As shown, this disclosure provides a design method for a waverider with a fixed leading edge based on an axisymmetric flow field, the method including steps S100 to S600.

[0035] Step S100: Given a three-dimensional leading edge profile, rotate the three-dimensional leading edge profile around a preset rotation axis to form a spiral body, and use the spiral body as a preset shock wave surface.

[0036] Furthermore, in S100, the three-dimensional leading edge profile is controlled by cubic quasi-uniform B-spline.

[0037] Furthermore, in the three-dimensional leading edge profile controlled by cubic quasi-uniform B-spline, the coordinates of the control points satisfy x∈[0.00m, 6.00m], y∈[0.00m, 2.40m] and z∈[0.00m, 0.30m].

[0038] Understandably, given a three-dimensional leading-edge profile as the design reference boundary, the three-dimensional leading-edge profile is precisely controlled using a cubic quasi-uniform B-spline. This B-spline curve has the advantages of high interpolation accuracy and good shape controllability. However, it should be noted that the coordinates of the B-spline control points must meet the dual requirements of engineering design and aerodynamic performance: therefore, the tip of the waverider with the fixed leading-edge profile is taken as the origin. x The axial (flow direction) coordinate range is limited to 0.00m to 6.00m to cover the fuselage length range of typical aircraft; y The span (axis) coordinate range is limited to 0.00m~2.40m to match the preset half span design index; z The axial (normal) coordinate range is limited to -0.45m to 0.00m, and the aerodynamic layout feature with upward reflection is achieved through negative offset. The three-dimensional leading edge profile is rotated around a preset rotation axis to form a spiral body, which is the preset shock surface.

[0039] Step S200: Project the three-dimensional leading edge profile along the extension direction of the preset rotation axis to obtain the streamline tracing starting line (FCT). Set the shock wave exit profile (ICC) as an arc structure, and project the streamline tracing starting line (FCT) onto the preset shock wave surface to obtain the streamline tracing starting point.

[0040] Furthermore, in step S200, the distance between the three-dimensional leading edge profile and the preset rotation axis is adjusted. d (referred to as "rotation axis distance"), in order to ultimately change the volume ratio of the fixed leading edge profile waverider.

[0041] Furthermore, the distance d ∈[-0.3m,0.3m].

[0042] It is understandable that the three-dimensional leading edge profile is projected along the extension direction of the rotation axis to obtain the streamline tracing starting line (FCT); the shock exit profile (ICC) is set as an arc, and the FCT is projected onto a preset shock surface; the resulting projection point can be used as the streamline tracing starting point; a distance is introduced. d As a key control parameter, it is used to precisely adjust the distance between the three-dimensional leading edge profile and the preset rotation axis. d This alters the radial distance between the streamlines and the axis of rotation in the flow field, enabling continuous control of the waverider volume fraction and providing flexible configuration solutions for different load requirements.

[0043] Step S300: Using the generatrix of the preset shock surface as the precise shock profile, calculate the axisymmetric flow field downstream of the shock profile using the inverse characteristic line method (iMoC). The axisymmetric flow field is as follows: Figure 3 As shown.

[0044] Furthermore, in S300, the inverse feature line method (iMoC) includes: Radiating streamlines and characteristic lines from a known point, their intersections yield an unknown solution point; Based on the known points and unknown solution points, a compatibility equation is established simultaneously; The coordinates and flow field parameters are solved using the compatibility equation. The parameters at each point on the shock wave profile are determined according to the oblique shock wave relation.

[0045] Furthermore, in the inverse feature line method (iMoC), the calculation accuracy can be improved iteratively through a predictor-corrector method.

[0046] Furthermore, in S300, when the shock wave profile is a convex curve, the expansion flow is used as a substitute for the inverse characteristic line method in the section of the convex curve where it is not applicable.

[0047] Furthermore, the axisymmetric flow field is preferably an axisymmetric inviscid flow field.

[0048] It is understandable that by using the generatrix of the pre-defined shock surface as the precise shock profile, the inverse characteristic line method (iMoC) is used to numerically calculate the axisymmetric inviscid flow field downstream of the shock profile. Compared with the traditional Euler equation solution, this method has the advantages of high computational efficiency and high shock capture accuracy, and can effectively obtain the distribution characteristics of core parameters such as velocity, pressure, and density in the flow field. For ease of understanding, the calculation process of the inverse characteristic line method can be referred to steps (1) to (4).

[0049] Step (1) is based on the theory of characteristics, such as Figure 4 As shown, assuming that the flow field parameters are known at points 1 and 2 on the shock wave profile, streamline C0 (representing the fluid trajectory) is emitted from known point 1, and a reverse left-hand characteristic line C+ is emitted from known point 2 (the flow field parameters satisfy a specific conservation relationship along the characteristic line direction). The intersection point 4 of the two lines is the unknown solution point to be solved. The plane coordinates of the intersection point 4 are determined by solving the characteristic line equation and the streamline equation simultaneously. Then, the flow field parameters of the intersection point 4 are obtained by solving the compatibility equation.

[0050] Step (2) Take the intersection point 4 obtained by the solution as a new known point, and emit a reverse right characteristic line C- from it. This characteristic line intersects with the line connecting known point 1 and known point 2 to obtain intersection point 3. Intersection point 3 is another unknown point. The flow field parameters of intersection point 3 can be determined by the flow field continuity equation.

[0051] Step (3) involves eliminating numerical discretization errors by using an iterative calculation method based on prediction and correction. Initial parameter values ​​are obtained during the prediction phase, and the calculation results are corrected through error feedback during the correction phase. The iterative convergence criterion is set to a parameter deviation of less than 10 between two consecutive calculations. -5 This ensures that the calculation accuracy of the flow field parameters meets the engineering design requirements.

[0052] Step (4) The initial flow field parameters at each point on the shock wave profile can be accurately determined according to the oblique shock wave relation. This oblique shock wave relation is derived based on the conservation law of gas dynamics and can accurately reflect the parameter change law before and after the shock wave. The calculation process can be carried out by gradually advancing from left to right to solve the unknown solution points. The intersection of the streamline at the starting point of the streamline and the left-moving characteristic line is used as the boundary point of the object surface of the wave rider to ensure the matching of the flow field and the object surface.

[0053] Furthermore, the method of characteristics is used to fill in the blank region downstream of the shock wave dependent region. This is because the surface boundary of the blank region of the flow field downstream of the shock wave dependent region is set as a straight line, which simplifies the calculation complexity and ensures the continuity and smoothness of the flow field, providing complete flow field data support for subsequent streamline tracing.

[0054] Step S400: Adaptively sub-partition the two-dimensional data in the axisymmetric flow field using a quadtree as the core data structure, locate the grid cell where the target point is located through hierarchical indexing using the quadtree, and obtain the flow field information of the target point by combining inverse distance interpolation.

[0055] Understandably, in order to solve the problem of low efficiency in traditional streamline tracing grid search, we can use the Cartesian grid generation idea and a quadtree as the core data structure to perform adaptive sub-partitioning on the two-dimensional axisymmetric flow field data. This data structure has the characteristics of high spatial indexing efficiency and fast retrieval speed, which can significantly improve the efficiency of target point positioning.

[0056] Furthermore, in S400, the quadtree is stored using a rule-based storage method.

[0057] Furthermore, in S400, the region of the axisymmetric flow field is recursively divided into four quadrants.

[0058] Furthermore, in S400, the grid cell threshold of the sub-partition is preferably set to 300.

[0059] It is understood that the quadtree can adopt a regularized storage method, taking the entire region of the axisymmetric flow field as the root node, and recursively dividing it into child nodes according to the four quadrants. The grid cell threshold for each sub-partition is set to 300. When the number of grid cells stored in a certain region exceeds the threshold, the region can be automatically divided into four sub-regions of equal area. The data storage and region division process is repeated until the number of grid cells in all sub-regions does not exceed the threshold, thus achieving balanced partitioning of the data in the axisymmetric flow field.

[0060] In the quadtree, an optimization strategy of "non-leaf nodes only store indexes and data is stored in leaf nodes" can be adopted. After the non-leaf nodes complete the sub-region partitioning, they immediately release the stored original data point information and only retain the index address of the child nodes, which can effectively save memory space. For flow fields containing tens of thousands of grid cells, the memory saving ratio can reach more than 40%.

[0061] Regarding streamline tracing, the step of locating the grid cell containing the target point through hierarchical indexing of the quadtree and obtaining the flow field information of the target point by inverse distance interpolation can include: firstly, quickly determining the leaf node containing the target point through hierarchical indexing from the root node to the leaf node of the quadtree; then, accurately searching within the local grid of the leaf node to determine the grid cell containing the target point; and finally, calculating the flow field information of the target point using inverse distance interpolation, with the interpolation error controlled within 0.5% to ensure streamline tracing accuracy.

[0062] Step S500: Starting from the projection point of the streamline tracing start line (FCT), continuously trace along the streamline direction in the axisymmetric flow field, fit all the traced streamlines into a closed spatial surface, and use the closed spatial surface as the designed leading edge profile waverider.

[0063] Understandably, in the axisymmetric flow field calculated in S300, the projection point of the FCT on the preset shock surface is used as the starting point for streamline tracing. Continuous tracing is performed along the streamline direction (i.e., the natural direction of the streamlines) in the axisymmetric flow field. The tracing step size is dynamically adjusted according to the flow field gradient, reducing the step size to 0.01m in areas with drastic changes in flow field parameters and expanding it to 0.05m in areas with gentler changes, thus balancing efficiency and accuracy. After completing streamline tracing at all starting points, all the obtained tracing streamlines are surface-fitted to form a closed spatial surface, which is the final waverider structure with a fixed leading edge profile, such as... Figure 5 As shown.

[0064] Step S600: Solve the Navier-Stokes equations using the finite volume method to verify the aerodynamic performance of the fixed leading edge profile waverider; use the Menter SST k-ω two-equation model as the turbulence model to simulate the turbulence effect of the axisymmetric flow field.

[0065] Understandably, in order to fully verify the aerodynamic performance of the waverider with a fixed leading edge profile, the three-dimensional compressible Navier-Stokes equations are solved using the finite volume method. These equations can accurately describe the viscous and compressibility effects of the hypersonic flow field, and provide a systematic numerical simulation of the aerodynamic performance of the waverider, including its lift-drag characteristics and stability.

[0066] Furthermore, in numerical calculations, inviscid flux can be discretized using the Roe scheme, which has the advantages of strong shock wave capture capability and low numerical dissipation; spatial accuracy can be achieved through second-order reconstruction using the weighted Green-Gauss formula, and the gradient limiter can be an improved Barth limiter, which can effectively suppress numerical oscillations; viscous flux can be calculated using a second-order central scheme to ensure the accurate transmission of viscous effects.

[0067] Furthermore, the turbulence model can adopt the Menter SST k-ω two-equation model, which combines the advantages of the k-ω model near the wall and the k-ε model in the far field, and can accurately simulate the turbulence effect of the hypersonic flow field; in the time direction, a second-order accurate dual-time-step method can be used, which is solved by the LU-SGS (Lower-Upper Symmetric Gauss-Seidel) implicit propagation scheme.

[0068] Furthermore, the computational grid is generated using a partitioned structured grid technique. The grids at the shock discontinuity locations are oriented along the shock direction to avoid numerical errors caused by the grids being orthogonal to the shock. The viscous layer normal grid is strictly perpendicular to the waverider wall, and the height of the first layer grid satisfies the requirement of y+≈1 to ensure accurate simulation of near-wall flow. The leading edge and shock intersection regions with large flow direction parameter gradients are subjected to grid refinement. Furthermore, under typical leading-edge profile waverider design conditions (Mach number Ma=8, flight altitude H=30km, angle of attack α covering the commonly used range of -4° to 12°), the lift-drag characteristics (lift coefficient, drag coefficient, lift-drag ratio), longitudinal stability (pitch moment coefficient, pressure center position) and waverider characteristics (shock wave attachment state, pressure distribution) of the waverider can be verified.

[0069] For ease of understanding, the following working principles can be referenced when implementing this disclosure: (1) Setting design parameters ① Parameter determination of the three-dimensional leading edge profile: a cubic quasi-uniform B-spline can be used for precise control to ensure the smoothness of the curve. The overall length of the generated leading edge profile is 6.00m, the half-span is 2.40m, and the z-axis coordinate is negatively distributed, forming an obvious upward inversion feature, which can improve the roll stability of the generated waverider shape.

[0070] ② The distance between the three-dimensional leading edge profile and the preset rotation axis d : For systematic research distance d The impact on waverider performance can be defined at three typical levels, with the baseline shape named MOVE_0. The control shape is obtained by moving a preset rotation axis up or down. d =-0.3m (named MOVE_-0.3) and d =0.3m (named MOVE_0.3), and the movement of the rotation axis does not affect the leading edge profile, and the three shapes have a consistent leading edge profile.

[0071] ③ Design conditions: Select the typical cruise conditions of the hypersonic vehicle, i.e., Mach number Ma=8, flight altitude H=30km, and evaluate the angle of attack in the flight state. α It covers a range of -4° to 12°, including typical operating conditions such as cruise (α=0°~4°), maneuver (α=8°~12°), and descent (α=-4°).

[0072] ④ External geometric parameters: The reference area of ​​each waverider is taken as the projected area of ​​the waverider in the plane, and the preferred value is 7.48m²; the reference length is taken as the total flow length of 6.0m; the center of gravity is located at 2 / 3 of the total length (i.e., 66.7% of the total length) based on engineering experience. x =4.0m), providing a benchmark for stability analysis.

[0073] (2) Flow field calculation and waverider generation ① First, streamline tracing starts (FCT) and shock wave profile is used, and shock wave exit profile (ICC) is set as an arc structure.

[0074] ② The axisymmetric flow field downstream of the shock profile was calculated using the inverse characteristic line method (iMoC). The slope angle at the starting point of the shock profile was set to 8° (greater than the Mach angle of 7.18° when Ma=8, to ensure shock wave attachment). Three iterations were performed using the prediction-correction method to ensure that the convergence error of the flow field parameters was less than 10. -5 .

[0075] ③ Due to the influence of the shock wave angle, the flow field range obtained under some solution conditions is relatively small. To expand the flow field area, the method of characteristics is used to calculate the flow field beyond the shock-dependent area. For simplicity, the boundary of the complementary area is set as a straight line. The surface boundary of the complementary area is set along... x A straight line tangent to the object surface in the positive direction of the axis ensures a smooth transition of the flow field.

[0076] ③ The flow field data is partitioned using a quadtree. In practice, the axisymmetric flow field contains 7744 computing nodes and 7569 grid cells. After being partitioned by a quadtree, it forms 106 sub-regions. The number of grid cells in each sub-region is controlled to be less than 300. The high gradient region near the shock wave has more sub-regions to ensure retrieval accuracy.

[0077] ④ Discretize the FCT curve, setting the number of discrete points to 120. Simultaneously trace streamlines starting from the 120 projection points of the FCT to generate corresponding streamlines at different distances. d The shapes of the three waveriders, verified by geometric measurements, show that the thickness of the trailing edge sections of the three waveriders, from thickest to thinnest, are MOVE_-0.3 (0.52m), MOVE_0 (0.45m), and MOVE_0.3 (0.38m), consistent with the variation of the volume ratio. Figure 6 As shown.

[0078] (3) Aerodynamic performance test results ① Lift-drag characteristics: The aerodynamic performance of the three waverider shapes exhibits a consistent pattern, with the maximum lift-drag ratio achieved at α=0° (cruise angle of attack). This characteristic is beneficial for improving the cruise efficiency of the aircraft. Volumetric efficiency and maximum lift-drag ratio show a significant negative correlation, as detailed in Table 1, reflecting the range... d Effectiveness of the control; after deducting bottom drag, due to the elimination of the adverse effects of the low-pressure area at the tail, the maximum lift-to-drag ratio of the three waverider shapes is increased by approximately 0.3 to 0.5. The lift-to-drag characteristics maintain a consistent trend with the angle of attack, and the lift-to-drag ratio remains stable at a high level within the range of α = 0° to 4°, making it suitable for cruise operation. Figure 7 As shown.

[0079] Table 1. Volume Ratio and Maximum Lift-to-Drag Ratio

[0080] ②Longitudinal stability: such as Figure 8As shown, with the center of gravity (66.7% of the total length) as the reference, longitudinal static stability is achieved when the aerodynamic focus is located behind the center of gravity. Test results show that MOVE_-0.3 exhibits stable longitudinal static stability within the angle of attack range of α=0°~12°, with the focus located behind 66.7% of the total length. MOVE_0 is stable below α=10°, but above α=10°, the focus shifts forward to before the center of gravity, resulting in moderate static stability. MOVE_0.3 has its focus located before the center of gravity from α=0° to 12°, and this stability increases with distance. d As the volume increases, the longitudinal stability of the waverider gradually decreases.

[0081] ③ Wave properties: such as Figure 9 As shown, when the design angle of attack α=0°, the flow field visualization results show that the shock waves of the three waverider shapes are all closely attached to the leading edge of the lower surface, with no obvious shock wave detachment phenomenon; the high-pressure airflow is confined between the shock wave and the lower surface of the waverider; the shock wave position matches the design ICC curve well, showing excellent waveriding effect, which verifies the effectiveness of this disclosure.

[0082] In summary, the waverider design method based on axisymmetric flow field with a fixed leading edge profile provided in this disclosure can achieve synergistic optimization of waverider performance and design efficiency through a closed-loop design process of "geometric boundary definition - benchmark flow field calculation - efficient streamline tracing - configuration generation and verification". This disclosure achieves the design of a waverider with a fixed leading edge profile by pre-setting an axisymmetric flow field, effectively expanding the design space. Simultaneously, the use of a quadtree improves streamline tracing efficiency by 39 times. The generated waverider achieves a maximum lift-to-drag ratio of 3.308 at Ma=8 and H=30km, with the shock wave matching the design curve well and exhibiting excellent waveriding characteristics. By adjusting the rotation axis distance... d It can flexibly match volume ratio and lift-to-drag ratio, solving the problems of limited space and low control precision in existing designs, and is suitable for the aerodynamic layout design of hypersonic aircraft with a wide speed range.

[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this disclosure and not to limit them. Although this disclosure has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of this disclosure. Any modifications or equivalent substitutions that do not depart from the spirit and scope of this disclosure should be covered within the protection scope of the claims of this disclosure.

Claims

1. A design method for a waverider with a fixed leading edge based on an axisymmetric flow field, characterized in that, The method includes: S100: Given a three-dimensional leading edge profile, the three-dimensional leading edge profile is rotated around a preset rotation axis to form a spiral body, and the spiral body is used as a preset shock wave surface; S200: Project the three-dimensional leading edge profile along the extension direction of the preset rotation axis to obtain the streamline tracing starting line (FCT). Set the shock wave exit profile (ICC) as an arc structure, and project the streamline tracing starting line (FCT) onto the preset shock wave surface to obtain the streamline tracing starting point. S300: Using the generatrix of the preset shock surface as the precise shock profile, the axisymmetric flow field downstream of the shock profile is calculated using the inverse characteristic line method (iMoC). S400: Using a quadtree as the core data structure, adaptive sub-partitioning is performed on the two-dimensional data in the axisymmetric flow field. The target point is located by hierarchical indexing through the quadtree, and the flow field information of the target point is obtained by combining inverse distance interpolation. S500: Starting from the projection point of the streamline tracing start line (FCT), continuous tracing is performed along the streamline direction in the axisymmetric flow field. All the tracing streamlines obtained are fitted into a closed spatial surface, and the closed spatial surface is used as the designed leading edge profile waverider.

2. The design method for a waverider with a fixed leading edge based on an axisymmetric flow field as described in claim 1, characterized in that, In S100, the three-dimensional leading edge profile is controlled by cubic quasi-uniform B-spline.

3. The design method for a waverider with a fixed leading edge based on an axisymmetric flow field as described in claim 2, characterized in that, In the three-dimensional leading edge profile controlled by cubic quasi-uniform B-spline, the coordinates of the control points satisfy x∈[0.00m, 6.00m], y∈[0.00m, 2.40m] and z∈[0.00m, 0.30m].

4. The design method for a waverider with a fixed leading edge based on an axisymmetric flow field as described in claim 1, characterized in that, In step S200, the distance between the three-dimensional leading edge profile and the preset rotation axis is adjusted. d This is to ultimately change the volume fraction of the fixed leading-edge profile waverider. The distance d ∈[-0.3m,0.3m].

5. The design method for a waverider with a fixed leading edge based on an axisymmetric flow field as described in claim 1, characterized in that, In S300, the inverse feature line method (iMoC) includes: Radiating streamlines and characteristic lines from a known point, their intersections yield an unknown solution point; Based on the known points and unknown solution points, a compatibility equation is established simultaneously; The coordinates and flow field parameters are solved using the compatibility equation. The parameters at each point on the shock wave profile are determined according to the oblique shock wave relation.

6. The design method for a waverider with a fixed leading edge based on an axisymmetric flow field as described in claim 5, characterized in that, In the inverse feature line method (iMoC), the calculation accuracy can be improved iteratively through the prediction-correction method; For the blank area downstream of the shock wave dependent region, the method of characteristics is used for supplementary calculation.

7. The design method for a waverider with a fixed leading edge based on an axisymmetric flow field as described in claim 1, characterized in that, In S300, when the shock wave profile is a convex curve, the section of the convex curve for which the inverse characteristic line method is not applicable is calculated using an expansion flow substitution.

8. The design method for a waverider with a fixed leading edge based on an axisymmetric flow field as described in claim 1, characterized in that, The axisymmetric flow field is preferably an axisymmetric inviscid flow field.

9. The design method for a waverider with a fixed leading edge based on an axisymmetric flow field as described in claim 1, characterized in that, In S400, the quadtree is stored using a rule-based method; The region of the axisymmetric flow field is recursively divided into four quadrants; The grid cell threshold for the sub-partition is preferably set to 300.

10. The design method for a waverider with a fixed leading edge based on an axisymmetric flow field as described in claim 1, characterized in that, The method further includes: S600: The Navier-Stokes equations are solved using the finite volume method to verify the aerodynamic performance of the fixed leading edge profile waverider; the Menter SST k-ω two-equation model is used as the turbulence model to simulate the turbulence effect of the axisymmetric flow field.

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