Bump design method for presetting any three-dimensional pressure distribution

Abstract

The invention discloses a bump design method for presetting any three-dimensional pressure distribution, which comprises the following steps: inputting preset three-dimensional pressure distribution and a leading edge line, generating a corresponding initial shock wave surface, dispersing the leading edge line into a plurality of discrete points, and constructing a corresponding initial flow surface; the curvature radius and flow surface pressure distribution of each initial flow surface inner point are solved; turning the initial flow surface point to a virtual meridian plane on the basis of the curvature radius and the pressure distribution, and solving the flow parameters of the initial flow surface point; constructing a shock wave preset line of the initial shock wave surface and a corresponding local osculating surface; the flow parameters are mapped to a three-dimensional Cartesian space, an iterative flow surface is obtained through reconstruction, and a three-dimensional flow field containing an iterative shock wave surface and an iterative bulge surface is generated; and judging the coordinate error of the three-dimensional flow field, if the coordinate error is smaller than a preset threshold value, outputting an iterative bump surface, otherwise, replacing the initial value with the current iterative flow surface and the shock wave surface, and repeating the above steps until convergence. According to the invention, the random three-dimensional pressure distribution realizes the reverse design of the bump, and the flexibility of the bump design is expanded.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and in particular to a bulge design method with preset arbitrary three-dimensional pressure distribution. Background Art

[0002] In modern supersonic aircraft, the air intake system pre-compresses the incoming airflow to facilitate subsequent thrust generation and work, and is a critical component of the aircraft's propulsion system. To ensure the overall aerodynamic characteristics of the aircraft and the layout of avionics equipment, the air intake system of modern supersonic aircraft is often located far from the nose. This allows low-energy airflow generated at the front of the aircraft to flow into the air intake system. This low-energy airflow reduces the compression efficiency of the air intake system and undermines its operational stability, presenting a challenge that must be addressed in the air intake of modern supersonic aircraft. Traditional air intake systems primarily address low-energy airflow through boundary layer diversion and extraction. While these methods can effectively expel low-energy airflow from the inlet, they require additional mechanical structures and actuators, which not only affects the aircraft's aerodynamic shape but also increases its weight and complexity, reducing its overall performance. Since the new century, a device called a bulge has gradually been used at the inlet of the intake system. Due to its specific geometric shape and pressure distribution, this device can simultaneously achieve the purpose of efficiently compressing the incoming flow and removing the low-energy flow from the intake system without adding additional mechanical structure. Therefore, it has become one of the research hotspots of supersonic intake systems in recent years.

[0003] The function of the bulge is to pre-compress the incoming flow and move the boundary layer of the forebody. Both are closely related to the pressure distribution on the surface of the bulge. Directly reverse designing the bulge based on the pressure distribution can obviously greatly improve the design flexibility of the bulge. Some scholars have explored this field. In 2018, Zonghan Yu et al. published an article entitled "Inverse design and Mach 6 experimental investigation of a pressure controllable In 2019, Zonghan Yu et al. published another paper entitled "A pressure-controllable bump based on the pressure-ridge concept" in the journal Volume 87, pages 133-140, proposing an innovative pressure distribution design for the head (bump) of a hypersonic aircraft and discussing the challenges of high-speed inlet-airframe integration. In 2022, Cai Jia et al. published a paper entitled "Aerodynamic design method and flow characteristics of forebody / compression surface with controllable spanwise pressure distribution" in the journal Journal of Aerodynamics, Volume 40, Issue 1, pages 67-76, proposing an aerodynamic design method for hypersonic forebody / compression surface integration based on controllable spanwise pressure distribution. They designed two different close bumps and a cone-guided bump for the inlet lip model of a certain aircraft, and analyzed their flow capture characteristics and boundary layer displacement performance.

[0004] The design of a bulge with a preset pressure distribution is essentially an inverse solution of the three-dimensional flow field using the wall pressure distribution as the design input. As shown in the above introduction, although research in this area has made great progress, these advances are all based on the classical tangential theory represented by the tangential cone, tangential axisymmetry, and tangential flow field method. This theory has two limitations when used for bulge design with a preset pressure distribution. First, the theory uses planes (tangential surfaces) to discretize the three-dimensional flow field and assumes that the flow on each tangential surface is axisymmetric. This requires that the shock wave intensity corresponding to the preset pressure distribution must be uniform everywhere, and the lateral pressure gradient behind the wave must be small. Otherwise, the actual flow surface constituting the three-dimensional flow field will become a curved surface, and the flow within the flow surface will deviate from the axisymmetric assumption, and the classical tangential theory will therefore become invalid. Secondly, the shape of each kissing surface in the classical kissing theory (here refers to the angle of each kissing surface in three-dimensional space) is determined by the shape of the shock wave. When the preset pressure distribution is relatively simple (for example, the lateral pressure gradient is small), a shock wave can be assumed and the shape of each kissing surface can be solved based on this shock wave to solve the entire three-dimensional flow field. This is also the common practice of the existing bulge design method with preset pressure distribution based on the kissing theory. However, when the preset pressure distribution is more complex (for example, when the lateral pressure gradient is large), the error of this approach will increase sharply, making it impossible to accurately solve the three-dimensional flow field corresponding to the design input, and the bulge will be difficult to be reverse designed. Due to the above two problems, in the existing bulge surface design method with preset pressure distribution, the pressure distribution as the design input can only make large changes along the flow direction. When the vertical flow direction (span direction) changes greatly, the accuracy of the method will drop significantly, and it is impossible to reverse design the bulge based on any three-dimensional preset pressure distribution. Summary of the Invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention proposes a bulge design method with a preset arbitrary three-dimensional pressure distribution to solve the above-mentioned technical problems.

[0006] This application proposes a bulge design method with a preset arbitrary three-dimensional pressure distribution, comprising the following steps:

[0007] S1: Input the preset three-dimensional pressure distribution and leading edge line, generate the initial shock wave surface corresponding to the three-dimensional pressure distribution, discretize the leading edge line into several discrete points, and construct several initial flow surfaces corresponding to each discrete point;

[0008] S2: Calculate the curvature radius corresponding to each point in each initial flow surface and the flow surface pressure distribution corresponding to each initial flow surface;

[0009] S3: Based on the curvature radius and pressure distribution of each initial flow surface, the points on the initial flow surface are twisted to the virtual meridian plane, and the flow parameters of the points on the initial flow surface on the virtual meridian plane are obtained using the improved two-dimensional characteristic line method;

[0010] S4: constructing a shock wave preset line of the initial shock wave surface, the shock wave preset line includes a plurality of longitudes and a plurality of latitudes, the longitudes and latitudes dividing the initial shock wave surface into a plurality of shock wave grids, and generating a plurality of local tangent surfaces of the initial flow surface corresponding to each shock wave grid;

[0011] S5: Based on the shock wave preset line and the local kissing surface, the flow parameters on each initial flow surface are mapped to the three-dimensional Cartesian space, each initial flow surface is reconstructed to obtain the corresponding iterative flow surface, and each iterative flow surface is integrated to obtain a three-dimensional flow field including the iterative shock wave surface and the iterative bulge surface;

[0012] S6: Calculate the error of the coordinates of each point in the three-dimensional flow field. If the coordinate error of each point is less than the preset value, output the iterative bulge surface. If the coordinate error of any point is greater than or equal to the preset value, replace the initial flow surface and initial shock wave surface with the iterative flow surface and iterative shock wave surface obtained by the current iterative calculation and perform the next round of iterative calculation, repeating steps S2-S6.

[0013] The bulge design method of this application has three main innovations:

[0014] (1) The method of using curved surfaces to discretize three-dimensional space is introduced into the design of bulges with preset pressure distribution. The flow field within each curved surface is calculated according to the preset pressure distribution, and then the flow fields within each curved surface are integrated to obtain the entire three-dimensional flow field.

[0015] (2) When calculating the flow field within each surface, this method assumes that the flow near each point on the surface can be approximated by different axis-symmetric flows with different symmetry axis positions. In this way, each point on the surface has its own axis of symmetry, so a more accurate approximation of the actual flow near each point can be obtained.

[0016] (3) The third major innovation of this method is to use the shock wave driven iteration method to solve the surface shape used in discretized three-dimensional space, so as to solve the problem that the classical tangent theory cannot determine the tangent surface shape when the pressure distribution is used as the design input.

[0017] Preferably, in S1, the process of constructing the initial flow surface includes:

[0018] S101: determining the direction of the tangential plane corresponding to the discrete point based on the shape of the leading edge line;

[0019] S102: Determine the pressure value of the discrete point by interpolation method according to the preset three-dimensional pressure distribution;

[0020] S103: Substitute the pressure value of the discrete point into the Rankine-Hugoniot shock wave transition relationship to obtain the corresponding shock wave angle and wall deflection angle. Determine the wall line and shock wave line of the tangent surface based on the shock wave angle and wall deflection angle. Integrate the wall line and shock wave line to obtain the initial flow surface.

[0021] The first step in this method is to construct an initial flow surface. Its purpose is to provide an initial value for the flow surface shape at each point on the leading edge line to ensure the smooth progress of subsequent iterative calculations. The leading edge line of the bulge is discretized into a series of points, and a tangent plane is constructed through each point. The angle of each tangent plane is determined by the shape of the leading edge according to classical tangent theory. In each tangent plane, the wall line and shock line are given, and the angle between them relative to the incoming flow direction is calculated based on the pressure value at the leading edge point using the Rankine-Hugoniot shock wave transition relationship.

[0022] Preferably, in S2, the process of solving the curvature radius includes:

[0023] S201: Divide each initial flow surface into a number of flow surface grids;

[0024] S202: Determine a first grid point on the initial flow surface to be solved, and extract a second grid point and a third grid point on two adjacent initial flow surfaces corresponding to the first grid point;

[0025] S203: Constructing a circular arc that passes through the first grid point, the second grid point, and the third grid point simultaneously, where the radius of the circular arc is the curvature radius corresponding to the first grid point.

[0026] The second step of this method is to calculate the curvature radius corresponding to each point in the flow field. In this method, each flow surface is divided into a number of flow surface grids, and what needs to be solved in this step is the curvature radius value corresponding to each grid point. When solving the curvature radius corresponding to a grid point, the grid points corresponding to the point on the two adjacent flow surfaces are extracted, and an arc is constructed through these three grid points. The radius of the arc is considered to be the curvature radius corresponding to the point to be solved. It should be noted that in the first iteration, the flow surface used to calculate the curvature radius of each point is obtained by the initial flow surface construction step. In the second and subsequent iterations, the flow surface used to calculate the curvature radius is obtained by the three-dimensional flow field reconstruction step in the previous iteration.

[0027] Preferably, in S2, the process of solving the flow surface pressure distribution includes:

[0028] S211: Projecting the geometric parameters of the wall line of the initial flow surface onto the plane where the preset three-dimensional pressure distribution is located to obtain a projection curve;

[0029] S212: Perform two-dimensional interpolation on each point on the projection curve to obtain the pressure value corresponding to each point on the projection curve;

[0030] S213: Assigning the pressure value of each point on the projection curve to the corresponding point on the wall line, and integrating the pressure values of each point on the wall line to obtain the flow surface pressure distribution corresponding to the initial flow surface.

[0031] The third step of this method is to obtain the flow surface pressure distribution, the purpose of which is to obtain the wall pressure corresponding to each surface used to discretize the three-dimensional space (the first round of iteration corresponds to the initial flow surface, and the subsequent iterations correspond to the iterative flow surface generated by the previous round of iteration).

[0032] Preferably, in S3, the flow around the point on the initial flow surface is approximated as an independent axisymmetric flow, and starting from the second round of iterative calculation, the curvature radius is two-dimensionally interpolated using the flow parameters obtained in the previous round of iterative calculation.

[0033] By twisting the points on the flow surface to the virtual meridian plane, the two-dimensional calculation method can solve the flow parameters on the flow surface in three-dimensional space. At the same time, the flow around each point on the flow surface is approximated as an independent axisymmetric flow, which means that each point on the flow surface has its own independent axis of symmetry, unlike the traditional two-dimensional characteristic line method where all points share a common axis of symmetry. At the same time, the flow parameters obtained from the previous round of iterative calculations are incorporated into the calculation process. With the help of these parameters, the curvature radius of each point is further interpolated in two dimensions during the unit process of solving each point on the flow surface, so that the flow parameters obtained from the previous round of iterations are corrected in this round of iterations. This step, combined with other steps, can solve the non-well-posed problem that exists in the ideal solution of supersonic three-dimensional flow fields.

[0034] Preferably, in S4, each longitude corresponds to an initial flow surface, and the longitude intersects the initial flow surface at a point on the leading edge line. The points corresponding to each longitude are connected to form a latitude line. The longitude is composed of several segments of longitude grid lines connected end to end. The longitude grid lines are the intersection lines of the initial shock wave surface and the local kissing surface.

[0035] In the S5 flow field reconstruction step, the meridians of the preset shock wave lines obtained in this step and the corresponding local kissing surfaces are used to reconstruct the two-dimensional flow field on the corresponding flow surface from the virtual meridian plane to the real three-dimensional space. The shape of the meridians depends on the iterative shock wave surface obtained in the previous round of iteration (the preset shock wave surface is used for the first round of iterative calculation). Each meridian is composed of several segments of meridian grid lines connected end to end, and the meridian grid lines are short straight lines.

[0036] Further preferably, S4 further includes:

[0037] S401: Determine the intersection of the initial flow surface and the leading edge line as a first intersection point, obtain the coordinates of the first intersection point and the coordinates of each vertex of the shock wave grid corresponding to the first intersection point;

[0038] S402: Calculate the normal vector of the mesh plane formed by the lines connecting each vertex using the cross product method;

[0039] S403: combining the normal vector and the free stream velocity vector to obtain a local tangent surface within the initial flow surface stress wave grid range, wherein the first intersection point is an intersection point between the local tangent surface and the grid plane;

[0040] S404: Determine another intersection point between the local tangent plane and the grid plane as a second intersection point, calculate the coordinates of the second intersection point, connect the first intersection point and the second intersection point, and solve for the meridian grid line in the grid plane;

[0041] S405: Using the second intersection point as the starting intersection point of the next shock wave grid, all corresponding meridian grid lines and local tangent surfaces in the initial flow surface are solved in sequence.

[0042] Each segment of the meridian grid line has a corresponding shock wave grid. For the meridian grid line that intersects with the leading edge line, its starting point is the intersection with the leading edge line. The grid plane is constructed based on the four vertices of the shock wave grid corresponding to the meridian grid line. Since the vertex coordinates of the starting point and the grid plane are known, the normal vector of the grid plane is obtained by performing a cross product calculation on the vectors of the sides where the starting point and the end point of the meridian grid line are located. Combining the normal vector with the free stream velocity vector, the local kissing surface corresponding to the grid plane can be calculated. Then, by finding another intersection point of the local kissing surface and the grid plane, the coordinates of the end point of the meridian grid line can be obtained. The starting point of the subsequent meridian grid line on the same meridian line is the end point of the previous meridian grid line. Similarly, the meridians and local kissing surfaces corresponding to all discrete points on the leading edge line can be solved, and the deflection direction of the local kissing surface is the deflection direction of the meridian line.

[0043] Preferably, in S5, the reconstruction process of the initial flow surface includes:

[0044] S501: reconstructing a mapping shock line of the initial flow surface on the virtual meridian plane, and deflecting the mapping shock line according to the meridian corresponding to the initial flow surface and the direction determined by the local tangent plane to obtain a real shock line;

[0045] S502: Slicing the points of the initial flow surface mapped onto the virtual meridian plane in a direction away from the real shock wave line, wherein all points outside the real shock wave line are interior points of the initial flow surface;

[0046] S503: The initial flow surface is reconstructed layer by layer based on the interior points. Based on the reconstructed real shock wave lines and the flow parameters of the interior points on the virtual meridian plane, the positions of the interior points of each layer in the three-dimensional Cartesian space coordinate system are solved to generate the reconstructed iterative surface.

[0047] The reconstruction process is performed separately for each flow surface. For a specific flow surface, the reconstruction process includes two parts. First, the mapped shock wave line is reconstructed to obtain the real shock wave line, and then the interior points are reconstructed. The interior points are the internal grid points of the flow surface. The entire flow surface can be regarded as composed of several triangular grids. Except for the grid points on the real shock wave line, the remaining grid points in the flow surface are called interior points. The interior points on the flow surface are reconstructed layer by layer, starting from a layer of interior points close to the real shock wave line and advancing layer by layer in the direction away from the real shock wave line. Repeating layer by layer can complete the reconstruction of the interior points of the entire flow surface. Repeating the above reconstruction process for all flow surfaces can obtain the entire three-dimensional flow field including the iterative shock wave surface and the iterative bulge surface corresponding to the design input in this round of iteration.

[0048] Further preferably, the flow parameters include the axial position ξ, radial position ζ, static pressure p, density ρ, velocity V, and flow angle θ of a point on the initial flow surface on the virtual meridian plane, and S503 further includes:

[0049] S5031: Calculate the position of the interior point in the three-dimensional Cartesian coordinate system based on the axial position ξ, radial position ζ, flow angle θ of the interior point on the virtual meridian plane and the coordinates of the reconstructed real shock wave line;

[0050] S5032: Decompose the velocity V of the interior point on the virtual meridian plane into components Vx, Vy, and Vz in the X, Y, and Z directions;

[0051] S5033: Assign the static pressure p and density ρ of the interior point on the virtual meridian plane to the corresponding point in the three-dimensional Cartesian coordinate system.

[0052] Through three-dimensional coordinate mapping, velocity component decomposition and physical parameter assignment, the flow parameters on the virtual meridian plane are accurately transferred to the three-dimensional Cartesian space and coordinated reconstruction is achieved.

[0053] Preferably, in S6, the three-dimensional flow field obtained by the initial flow surface iterative calculation is not subjected to error judgment, and error judgment is performed starting from the three-dimensional flow field obtained by the second round of iterative calculation. The error judgment condition is max(E)<ε, where E is the relative error of the Cartesian coordinates of any point in the three-dimensional flow field, ε is the error preset value, and E is calculated as follows:

[0054]

[0055] Among them, X cur 、Y cur and Z cur is the Cartesian coordinate of the point obtained in this round of iteration, X last 、Y las t and Z last are the corresponding grid coordinates calculated in the previous iteration.

[0056] Error judgment is only carried out from the second round of iterative calculation to determine whether the result of the current iterative calculation meets the requirements. If so, the calculation is completed and the iterative bulge surface is output. Otherwise, the iterative flow surface passing through each discrete point obtained by the current iterative calculation will replace the initial flow surface at the beginning of the previous round of iterative calculation, and a new iterative cycle will begin. The above cycle judgment condition means that if the relative error of the Cartesian coordinates of any grid point in the flow field in two consecutive iterations exceeds or is equal to the preset value, the algorithm is considered to have not converged and iterative calculation needs to continue.

[0057] Compared with the prior art, the present invention has the following advantages:

[0058] This application proposes a bulge design method with a preset arbitrary three-dimensional pressure. The method proposed in this application can use arbitrary three-dimensional pressure distribution as design input to perform inverse solution of the three-dimensional flow field, which cannot be used in the classic kissing method, and realize the reverse design of the corresponding bulge, thereby greatly expanding the flexibility of bulge design. The method has three main innovations:

[0059] (1) The method of using curved surfaces to discretize three-dimensional space is introduced into the design of bulges with preset pressure distribution. The flow field within each curved surface is calculated according to the preset pressure distribution, and then the flow fields within each curved surface are integrated to obtain the entire three-dimensional flow field.

[0060] (2) When calculating the flow field within each surface, this method assumes that the flow near each point on the surface can be approximated by different axis-symmetric flows with different symmetry axis positions. In this way, each point on the surface has its own axis of symmetry, so a more accurate approximation of the actual flow near each point can be obtained.

[0061] (3) The third major innovation of this method is to use the shock wave driven iteration method to solve the surface shape used in discretized three-dimensional space, so as to solve the problem that the classical tangent theory cannot determine the tangent surface shape when the pressure distribution is used as the design input. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated into and constitute a part of this specification. The accompanying drawings illustrate the embodiments and, together with the description, serve to explain the principles of the invention. Other embodiments and many of the intended advantages of the embodiments will be readily apparent as they become better understood by reference to the following detailed description. Other features, objects, and advantages of the present application will become more apparent upon reading the detailed description of the non-limiting embodiments made with reference to the following drawings:

[0063] Figure 1 A diagram showing the steps of a bulge design method according to an embodiment of the present invention is shown;

[0064] Figure 2A functional schematic diagram of a bulge design method according to an embodiment of the present invention is shown;

[0065] Figure 3 A flow chart of the SDSI method according to a specific embodiment of the present invention is shown;

[0066] Figure 4 A schematic diagram of flow surface iteration according to a specific embodiment of the present invention is shown;

[0067] Figure 5 A schematic diagram of an initial flow surface structure according to a specific embodiment of the present invention is shown;

[0068] Figure 6 A schematic diagram of calculating the curvature radius according to a specific embodiment of the present invention is shown;

[0069] Figure 7 A schematic diagram of obtaining the flow surface pressure distribution according to a specific embodiment of the present invention is shown;

[0070] Figure 8 A schematic diagram of a three-dimensional flow field within a flow plane according to a specific embodiment of the present application is shown;

[0071] Figure 9 A schematic diagram of generating a shock wave preset line according to a specific embodiment of the present invention is shown;

[0072] Figure 10 A schematic diagram of flow field reconstruction according to a specific embodiment of the present invention is shown;

[0073] Figure 11a A schematic diagram of pressure distribution of a boost bulge according to a specific embodiment of the present invention is shown;

[0074] Figure 11b A schematic diagram of pressure distribution of a depressurized bulge according to a specific embodiment of the present invention is shown;

[0075] Figure 11c A schematic diagram of the pressure distribution of the lateral pressure bulge according to a specific embodiment of the present invention is shown;

[0076] Figure 12a A cloud diagram of a supercharged bulge simulation according to a specific embodiment of the present invention is shown;

[0077] Figure 12b A decompression bulge simulation cloud diagram according to a specific embodiment of the present invention is shown;

[0078] Figure 12c A lateral pressure bulge simulation cloud diagram according to a specific embodiment of the present invention is shown.

[0079] The meaning of the numbers in the figure:

[0080] Shock surface 1, discrete point 2, initial flow surface 3, meridian 4, wall line 5, shock line 6, projection plane 7, projection curve 8, meridian grid line 9, local tangent surface 10, normal vector 11, free stream velocity vector 12, local tangent surface group 13, mapped shock line 14, two-dimensional flow field 15, real shock line 16, first layer interior point 17, second layer interior point 18, third layer interior point 19, fourth layer interior point 20, fifth layer interior point 21, sixth layer interior point 22. DETAILED DESCRIPTION

[0081] The present application will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the relevant invention and are not intended to limit the invention. It should also be noted that, for ease of description, only portions relevant to the relevant invention are shown in the accompanying drawings.

[0082] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0083] This application proposes a bulge design method with preset arbitrary three-dimensional pressure distribution. Figure 1 FIG. 4 shows a step diagram of a bulge design method according to an embodiment of the present invention. Figure 1 As shown, the bulge design method includes the following steps:

[0084] S1: Input the preset three-dimensional pressure distribution and leading edge line, generate the initial shock wave surface 1 corresponding to the three-dimensional pressure distribution, discretize the leading edge line into a number of discrete points 2, and construct a number of initial flow surfaces 3 corresponding to each discrete point 2;

[0085] S2: Calculate the curvature radius corresponding to each point in each initial flow surface 3 and the flow surface pressure distribution corresponding to each initial flow surface 3;

[0086] S3: Based on the curvature radius and pressure distribution of each initial flow surface 3, the points on the initial flow surface 3 are twisted to the virtual meridian plane, and the flow parameters of the points on the initial flow surface 3 on the virtual meridian plane are obtained using the improved two-dimensional characteristic line method;

[0087] S4: constructing a shock wave preset line of the initial shock wave surface 1, the shock wave preset line including a plurality of longitude lines 4 and a plurality of latitude lines, the longitude lines 4 and the latitude lines dividing the initial shock wave surface 1 into a plurality of shock wave grids, and generating a plurality of local tangent surfaces of the initial flow surface 3 corresponding to each shock wave grid;

[0088] S5: Based on the shock wave preset line and the local kissing surface, the flow parameters on each initial flow surface 3 are mapped to the three-dimensional Cartesian space, each initial flow surface 3 is reconstructed to obtain the corresponding iterative flow surface, and each iterative flow surface is integrated to obtain a three-dimensional flow field including the iterative shock wave surface 1 and the iterative bulge surface;

[0089] S6: Calculate the error of the coordinates of each point in the three-dimensional flow field. If the coordinate error of each point is less than the preset value, output the iterative bulge surface. If the coordinate error of any point is greater than or equal to the preset value, replace the initial flow surface 3 and the initial shock wave surface 1 with the iterative flow surface and the iterative shock wave surface 1 obtained by the current iterative calculation and perform the next round of iterative calculation, repeating steps S2-S6.

[0090] The core of this invention is a bulge design method using Shockwave Driven Surface Iteration (SDSI). This method is essentially a three-dimensional flow field inverse solution method using the flow field leading edge line and wall pressure distribution as design inputs. It can realize the inverse design of bulges using the bulge leading edge line and any three-dimensional pressure distribution as design inputs. Compared with traditional methods based on the kissing theory, the SDSI method has three major innovations:

[0091] First, the method of discretizing curved surfaces into three-dimensional space is introduced into the design of bulge surfaces with a preset three-dimensional pressure distribution. The flow field within each flow surface is calculated based on the preset pressure distribution, and then the flow fields within each flow surface are integrated to obtain the entire three-dimensional flow field.

[0092] Second, unlike the classical tangent theory, which assumes that the flow field within each tangent plane is a standard axisymmetric flow field, the SDSI method, when calculating the flow field within each flow surface, assumes that the flow near each point within the flow surface can be approximated by different axisymmetric flows with different symmetry axes. This way, each point within the flow surface has its own axis of symmetry, rather than sharing a single axis of symmetry as in the classical tangent theory. This allows for a more accurate approximation of the actual flow near each point. The combination of the first two core concepts can solve three-dimensional flow fields with nonuniform shock waves and large transverse pressure gradients behind the waves.

[0093] Third, the third major innovation of the SDSI method is the use of shock-driven iteration to solve the surface shape used in discretized three-dimensional space, addressing the problem that the classical kissing theory cannot determine the kissing surface shape when the pressure distribution is used as the design input. The SDSI method uses a preset three-dimensional pressure distribution to perform multiple rounds of iterative solutions to the entire three-dimensional flow field. In each round of iteration, the shock surface 1 obtained in the previous round of iteration is used to calculate the surface shape corresponding to the current round of iteration. In this way, the shape of the shock surface 1 and the shape of each initial flow surface 3 (starting from the second round of iteration, the initial flow surface 3 is replaced by the iterative flow surface calculated in the previous round of iteration) will change in each round of iteration. After several rounds of iteration, the flow surface shape with sufficient accuracy can be obtained, thus realizing the inverse solution of the three-dimensional flow field based on the preset three-dimensional pressure distribution and the reverse design of the bulge.

[0094] Figure 2FIG. 4 shows a functional schematic diagram of a bulge design method according to an embodiment of the present invention. Figures 1-2 As shown, this application mainly uses the preset three-dimensional pressure distribution and the bulge leading edge line as design inputs to generate a three-dimensional shock wave surface 1 corresponding to the preset three-dimensional pressure distribution, and then solves the bulge surface corresponding to the design input through the SDSI method.

[0095] Figure 3 FIG. 4 shows a schematic diagram of flow surface iteration according to a specific embodiment of the present invention, as shown in FIG. Figures 1 to 3 As shown, Figure 3 The figures show the shapes of the shock surface 1 and the bulge surface corresponding to the initial flow surface 3, as well as the iterative flow surface obtained after the first and second rounds of iteration, and the shapes of the shock surface 1 and the bulge surface after iteration. The curves indicated by the arrows in the figure are the intersection lines of the shock surface 1 and the bulge surface with the bottom plane in the above-mentioned state. It can be seen that the entire three-dimensional flow field is solved by multiple iterations. The shape of the shock surface 1 will change in each round of iteration, and the shape of the surface used to discretize the three-dimensional space (i.e., the iterative flow surface) will also change. After multiple rounds of iteration, the flow surface shape tends to converge. At this time, the flow fields in each flow surface are integrated to obtain the three-dimensional flow field and bulge surface corresponding to the design input.

[0096] Figure 4 FIG. 4 shows a flow chart of the SDSI method according to a specific embodiment of the present invention. Figures 1 to 4 As shown, this method generates the corresponding initial shock wave surface 1 by inputting a preset arbitrary three-dimensional pressure distribution. In the first round of iteration, the initial value of the flow surface is first estimated, that is, the construction of the initial flow surface 3. The shape of the initial flow surface 3 is the initial surface shape for discretizing the three-dimensional space. Based on the constructed initial flow surface 3, the curvature radius of the initial flow surface 3 is calculated and the flow surface pressure distribution is obtained. The curvature radius of each point in the initial flow surface 3 and the wall pressure value corresponding to each initial flow surface 3 are obtained. Further, based on the initial shock wave surface 1, a shock wave preset line is constructed. Combined with the curvature radius and the wall pressure value, the flow field in the initial flow surface 3 is calculated to obtain the corresponding initial flow surface 3. The two-dimensional flow field 15 located in the virtual meridian plane (including the flow parameters of each point on the initial flow surface 3) is calculated, and the above calculation process is performed on each initial flow surface 3. The three-dimensional flow field is reconstructed in combination with the shock wave preset line and the two-dimensional flow field 15, and a new surface shape for discretizing the three-dimensional space can be obtained (that is, several iterative flow surfaces located in the reconstructed three-dimensional flow field). The error judgment is performed on the iterative flow surface. If the judgment requirements are met, the bulge surface corresponding to the design input is output. If the judgment requirements are not met, the iterative flow surface obtained in this round of iteration replaces the initial flow surface 3 at the beginning of the calculation for a second round of iteration. The same is true for each subsequent iterative calculation process. Figure 5 FIG. 4 shows a schematic diagram of the initial flow surface structure according to a specific embodiment of the present invention. Figures 1 to 5 As shown, in S1, the construction process of the initial flow surface 3 includes:

[0097] S101: determining the direction of the tangential plane corresponding to the discrete point 2 based on the shape of the leading edge line;

[0098] S102: Determine the pressure value of discrete point 2 by interpolation according to the preset three-dimensional pressure distribution;

[0099] S103: Substitute the pressure value of discrete point 2 into the Rankine-Hugoniot shock wave transition relationship to obtain the corresponding shock wave angle and wall deflection angle. Determine the wall line 5 and shock wave line 6 of the tangent surface based on the shock wave angle and wall deflection angle. Integrate the wall line 5 and shock wave line 6 to obtain the initial flow surface 3.

[0100] The first step of the SDSI method is the estimation of the initial value, that is, the construction of the initial flow surface 3. Its purpose is to provide an initial value for the flow surface shape of each point on the leading edge line to ensure the smooth progress of subsequent iterative calculations. Specifically, the leading edge line is discretized into a series of discrete points 2, and a kissing surface is constructed through each discrete point 2. The angle of each kissing surface is determined by the shape of the leading edge line according to the classical kissing theory. In each kissing surface, a wall line 5 and a shock line 6 are given. The angle between the wall line 5 and the shock line 6 relative to the incoming flow direction is calculated according to the pressure value at the discrete point 2 using the Rankine-Hugoniot shock wave transition relationship.

[0101] Further, in Figure 5 In the figure, taking discrete point 2 on the leading edge line as an example, the direction of the kissing surface (i.e., the initial flow surface 3) is first determined based on the shape of the leading edge line. Then, the pressure at the discrete point 2 is determined by interpolation in the preset three-dimensional pressure distribution. The pressure is substituted into the Rankine-Hugoniot shock wave transition relationship to calculate the shock wave angle and the wall deflection angle. Then, the wall line 5 and the shock wave line 6 can be determined based on the two angles. The initial flow surface 3 corresponding to each discrete point 2 is constructed using the above method.

[0102] Specifically, for the first round of iterative calculation, the surface shape used is the constructed initial flow surface 3. Starting from the second round of iterative calculation, the surface shapes used are all iterative flow surfaces generated in the previous round of iteration.

[0103] Figure 6 FIG. 4 shows a schematic diagram of calculating the curvature radius according to a specific embodiment of the present invention, as shown in FIG. Figures 1 to 6 As shown, in S2, the process of solving the curvature radius includes:

[0104] S201: Divide each initial flow surface 3 into a plurality of flow surface grids;

[0105] S202: determining a first grid point on the initial flow surface 3 to be solved, and extracting a second grid point and a third grid point corresponding to the first grid point on two adjacent initial flow surfaces 3;

[0106] S203: Constructing a circular arc that passes through the first grid point, the second grid point, and the third grid point simultaneously, where the radius of the circular arc is the curvature radius corresponding to the first grid point.

[0107] The second step of the SDSI method is to calculate the curvature radius corresponding to each point on the flow surface. Specifically, taking the first round of iterative calculation as an example, each initial flow surface 3 is divided into several flow surface grids, and the curvature radius value corresponding to the grid point on the flow surface grid is required. When solving the curvature radius corresponding to a grid point, it is necessary to extract the grid points corresponding to the point on the two adjacent initial flow surfaces 3. An arc is constructed through these three grid points, and the radius of the arc is considered to be the curvature radius corresponding to the grid point to be solved.

[0108] Specifically, Figure 6 Take the calculation of the curvature radius of A1 and B1 as an example. As shown in the figure, the initial flow surface 3 is the surface used to discretize the three-dimensional space. When solving the curvature radius of point A1, the grid points A2 and A3 corresponding to A1 on the two adjacent initial flow surfaces 3 are extracted. Here, A1 is the first grid point, A2 and A3 are the second and third grid points respectively. The arc is constructed through A1, A2 and A3, and the radius of the arc is calculated to be R A1 , then R A1 The curvature radius corresponding to point A1 is obtained, and similarly the curvature radius R corresponding to point B1 is obtained. B1 It should be noted that in the first round of iteration, the flow surface used to calculate the curvature radius of each point is obtained by the initial value estimation step (i.e., initial flow surface 3). In the second and subsequent iterations, the flow surface used to calculate the curvature radius is obtained by the three-dimensional flow field reconstruction step in the previous round of iteration (i.e., iterative flow surface).

[0109] Figure 7 FIG. 4 shows a schematic diagram of obtaining the flow surface pressure distribution according to a specific embodiment of the present invention. Figures 1 to 7 As shown in Figure 2, the solution process of the flow surface pressure distribution in S2 includes:

[0110] S211: Projecting the geometric parameters of the wall line 5 of the initial flow surface 3 onto the plane where the preset three-dimensional pressure distribution is located (i.e., the projection plane 7) to obtain a projection curve 8;

[0111] S212: Perform two-dimensional interpolation on each point on the projection curve 8 to obtain the pressure value corresponding to each point on the projection curve 8;

[0112] S213 : Assigning the pressure value of each point on the projection curve 8 to the corresponding point on the wall line 5 , and integrating the pressure values of each point on the wall line 5 to obtain the flow surface pressure distribution corresponding to the initial flow surface 3 .

[0113] The third step of the SDSI method is to obtain the pressure distribution on the flow surface. Its purpose is to obtain the wall pressure corresponding to each surface used for discretizing the three-dimensional space (the first round of iteration corresponds to the initial flow surface 3, and the subsequent iterations correspond to the iterative flow surface generated by the previous round of iteration). Taking the first round of iteration as an example, Figure 7 The initial flow surface 3 in is calculated, the projection plane 7 is the plane where the preset three-dimensional pressure distribution is located, and the wall line 5 is located on the initial flow surface 3. The wall line 5 on the initial flow surface 3 is projected onto the projection plane 7 to obtain the projection curve 8. Then, based on the preset three-dimensional pressure distribution, two-dimensional interpolation is performed on each point on the projection curve 8 to obtain the pressure values corresponding to these points. These values are assigned to the corresponding points on the wall line 5. The pressure distribution corresponding to the initial flow surface 3 is obtained by integrating the pressure values of each point on the wall line 5. The above process is repeated for each initial flow surface 3 to obtain the flow surface pressure distribution corresponding to each initial flow surface 3.

[0114] Figure 8 A schematic diagram of a three-dimensional flow field in a flow plane according to a specific embodiment of the present application is shown. Figures 1 to 8 As shown in FIG. 3 , the flow around the point on the initial flow surface 3 in S3 is approximately an independent axisymmetric flow. Starting from the second round of iterative calculation, the curvature radius is two-dimensionally interpolated using the flow parameters obtained in the previous round of iterative calculation.

[0115] The fourth step in the SDSI method is the calculation of the flow field within the surface. Its purpose is to calculate the flow parameters for each discretized three-dimensional surface, providing the basis for the reconstruction of the three-dimensional flow field in subsequent steps. This calculation utilizes a development of the two-dimensional method of characteristic lines (2D-MOC), which differs from the classic 2D-MOC in three ways. First, each point on the surface is twisted onto a virtual meridian plane, allowing the two-dimensional calculation method to solve for the flow parameters on the surface in three-dimensional space. Second, the flow around each point on the surface is approximated as an independent axisymmetric flow. This means that each point on the surface has its own axis of symmetry, rather than sharing a common axis of symmetry as in 2D-MOC. Third, the flow parameters obtained from the previous iteration are incorporated into the calculation process. These parameters are used to perform a two-dimensional interpolation of the curvature radius at each point in the unit process for solving each point. This results in a correction of the flow parameters obtained from the previous iteration in the current calculation. This calculation method, combined with other steps, can address the ill-posedness problem that often occurs in the inverse solution of supersonic three-dimensional flow fields. After this step, the six flow variables, including the axial position (ξ), radial position (ζ), static pressure (p), density (ρ), velocity (V), and flow angle (θ) of each point on the flow surface on the virtual meridian plane, will be solved. They will be integrated into a three-dimensional flow field in the Cartesian coordinate system in the fifth step of flow field reconstruction.

[0116] exist Figure 8In the figure, it is assumed that points A, B, and C are the three points to be solved on the flow surface, and the actual flow around the three points is a general three-dimensional flow, as shown in the black box on the left side of the figure. When solving, it is assumed that the flow around the three points is an axisymmetric flow as shown in the black box on the right side of the figure. It is not difficult to see that the flow around each point has its own axis of symmetry, so that an accurate approximation of the original three-dimensional flow around the three points can be achieved.

[0117] Figure 9 FIG. 4 shows a schematic diagram of generating a shock wave preset line according to a specific embodiment of the present invention. Figures 1 to 9 As shown, in S4, each longitude line 4 corresponds to an initial flow surface 3, and the longitude line 4 intersects the initial flow surface 3 at a point on the leading edge line. The points corresponding to each longitude line 4 are connected to form a latitude line. The longitude line 4 is composed of several segments of longitude grid lines 9 connected end to end. The longitude grid lines 9 are the intersection lines of the initial shock wave surface 1 and the local kissing surface 10.

[0118] Furthermore, S4 also includes:

[0119] S401: Determine the intersection of the initial flow surface 3 and the leading edge line as a first intersection point, obtain the coordinates of the first intersection point and the coordinates of each vertex of the shock wave grid corresponding to the first intersection point;

[0120] S402: Calculate the normal vector 11 of the mesh plane formed by the lines connecting each vertex using the cross product method;

[0121] S403: combining the normal vector 11 and the free stream velocity vector 12, solving for the local tangent plane 10 within the shock wave grid corresponding to the initial flow surface 3, wherein the first intersection point is an intersection point of the local tangent plane 10 and the grid plane;

[0122] S404: Determine another intersection point between the local tangent plane 10 and the grid plane as a second intersection point, calculate the coordinates of the second intersection point, connect the first intersection point and the second intersection point, and solve for the meridian grid line 9 of the meridian line 4 in the grid plane;

[0123] S405: Using the second intersection point as the starting intersection point of the next shock wave grid, all corresponding meridian grid lines 9 and local tangent surfaces 10 in the initial flow surface 3 are solved in sequence.

[0124] In the S5 flow field reconstruction step, the meridian 4 and the corresponding local kissing surface 10 obtained in this step are used to reconstruct the two-dimensional flow field 15 on the corresponding flow surface from the virtual meridian plane to the real three-dimensional space. The shape of the meridian 4 depends on the shock wave surface 1 obtained in the previous round of iteration (the calculation for the first round of iteration is based on the initial value estimation step, that is, the initial shock wave surface 1 is used). Each meridian 4 is composed of several short straight lines connected end to end. Each short straight line is called a meridian grid line 9. These meridian grid lines 9 are the intersection lines of the shock wave surface 1 and the corresponding local kissing surface 10.

[0125] by Figure 9 Taking the local kissing surface group 13 composed of the meridian 4 in the figure and the corresponding series of deflected local kissing surfaces 10 as an example, in the figure, the dark surface and the grid on it are the shock wave surface 1 and shock wave grid obtained in the previous round of iteration or initial value estimation step, the discrete point 2 in the figure is the intersection of a surface (initial flow surface 3 / iterative flow surface) used to discretize the three-dimensional space and the leading edge line, the meridian 4 is generated along the flow direction starting from the discrete point 2, and the generation process of the meridian grid line 9 is shown in the enlarged view on the right side of the figure. In the figure, A, B, C, and D are shock wave grid points of the shock wave surface 1, and the meridian grid line 9 is a grid line on the meridian 4 to be determined, and its endpoints are E and F, respectively. E and F correspond to the first intersection point and the second intersection point in steps S403-S405, where point E is the intersection point of the upstream meridian grid line 9 and the straight line AB, and its position is known. Therefore, the generation of the downstream meridian grid line 9 is equivalent to finding the position of point F. Since the coordinates of A, B, C, and D are known, they can be obtained by taking and The cross product of ABCD calculates the normal vector 11 of plane ABCD, which is recorded as Then, combining the normal vector 11 and the free stream velocity vector 12, we can obtain the local tangent plane 10 of the grid ABCD. By finding the intersection of the local tangent plane 10 and the line CD, we can find the position of point F, thus completing the generation of the meridian grid line 9. Repeating the above process will obtain the meridian line 4 passing through the discrete point 2 and the local tangent plane group 13 consisting of a series of deflected local tangent planes 10. Repeating the above process for each discrete point 2 on the leading edge line will obtain all meridian lines 4 and the corresponding local tangent planes 10.

[0126] Figure 10 FIG. 4 shows a schematic diagram of flow field reconstruction according to a specific embodiment of the present invention. Figures 1 to 10 As shown, in S5, the reconstruction process of the initial flow surface 3 includes:

[0127] S501: reconstructing the mapping shock line 14 of the shock line 6 of the initial flow surface 3 on the virtual meridian plane, and deflecting the mapping shock line 14 in the direction determined by the meridian 4 corresponding to the initial flow surface 3 and the local tangent plane 10 to obtain the real shock line 16;

[0128] S502: The points mapped onto the virtual meridian plane of the initial flow surface 3 are layered along a direction away from the real shock line 16, wherein all points outside the real shock line 16 are inner points of the initial flow surface 3;

[0129] S503: Reconstruct the interior points of the initial flow surface 3 layer by layer. Based on the reconstructed real shock wave line 16 and the flow parameters of the interior points on the virtual meridian plane, the position of the interior points of each layer in the three-dimensional Cartesian space coordinate system is solved to generate the reconstructed iterative surface.

[0130] Furthermore, the flow parameters include the axial position ξ, radial position ζ, static pressure p, density ρ, velocity V, and flow angle θ of a point on the initial flow surface 3 on the virtual meridian plane. S503 also includes:

[0131] S5031: Calculate the position of the interior point in the three-dimensional Cartesian coordinate system based on the axial position ξ, radial position ζ, flow angle θ of the interior point on the virtual meridian plane and the coordinates of the reconstructed real shock line 16;

[0132] S5032: Decompose the velocity V of the interior point on the virtual meridian plane into components Vx, Vy, and Vz in the X, Y, and Z directions;

[0133] S5033: Assign the static pressure p and density ρ of the interior point on the virtual meridian plane to the corresponding point in the three-dimensional Cartesian coordinate system.

[0134] In the three-dimensional flow field reconstruction step, the flow parameters on the virtual meridian plane corresponding to each flow surface obtained from the flow field calculation step will be mapped to the real three-dimensional Cartesian space, so as to obtain the three-dimensional flow field corresponding to the design input in this round of iteration. This mapping is performed on each flow surface separately. For a specific flow surface, the reconstruction process includes two parts: first, reconstructing the mapping shock line 14 on the virtual meridian plane, and then reconstructing the internal points. The so-called internal points are internal grid points. The entire flow surface is composed of several triangular grids. Except for the grid points on the mapping shock line 14, the remaining grid points are called internal points. The following takes a certain flow surface as an example and combines Figure 10 Describe the specific process of reconstruction.

[0135] The two-dimensional flow field 15 in the figure is composed of the flow parameters mapped on the virtual meridian plane. The mapped shock line 14 is the mapping of the shock line 6 of the flow surface to be reconstructed on the virtual meridian plane. The meridian 4 corresponds to the flow surface to be reconstructed. The real shock line 16 is the reconstructed curve of the mapped shock line 14 in the Cartesian coordinate system. The reconstruction process of the mapped shock line 14 is to deflect the mapped shock line 14 of the shock line 6 on the virtual meridian plane according to the direction determined by the meridian 4 and its corresponding series of local tangent surfaces 10 that deflect with the flow, and finally obtain the real shock line 16 located in the Cartesian coordinate system.

[0136] After the reconstruction of the real shock line 16 is completed, the reconstruction of the inner points can be started. The reconstruction of the inner points is carried out layer by layer, starting from the inner points closest to the real shock line 16 and moving away from the real shock line 16 layer by layer. Figure 10Where 17-22 represent the inner points of the first to sixth layers respectively. During reconstruction, the position of the inner point 17 of the first layer in the three-dimensional Cartesian coordinate system is solved according to the coordinates of the reconstructed real shock line 16 and the axial position (ξ), radial position (ζ) and flow angle (θ) of the inner point 17 of the first layer in the virtual meridian plane. Then, the velocity components V of the inner point 17 of the first layer in each direction in the Cartesian coordinate system are calculated. X 、V Y and V Z Finally, the static pressure (p) and density (ρ) properties of each interior point in the virtual meridian plane are assigned to the corresponding interior point in Cartesian space, completing the reconstruction of the first layer of interior points 17. Repeating this process layer by layer completes the interior point reconstruction of the entire flow surface. Repeating this process for each flow surface completes the reconstruction of each flow surface, obtaining the entire three-dimensional flow field corresponding to the design input in this iteration, including the shock surface 1 and the bulge surface.

[0137] The final step in the SDSI method is error determination. This step determines whether the results of the current iteration meet the requirements. If so, the calculation is completed and the resulting bulge surface is output. Otherwise, the flow surface passing through each leading edge point obtained in the current iteration replaces the flow surface calculated in the previous iteration, and a new iteration begins.

[0138] Preferably, in S6, the three-dimensional flow field obtained by the iterative calculation of the initial flow surface 3 is not subjected to error judgment, and error judgment is performed starting from the three-dimensional flow field obtained by the second round of iterative calculation. Figure 3 It can be seen that the error judgment condition is max(E)<ε, where E is the relative error of the Cartesian coordinates of any point in the three-dimensional flow field, ε is the error preset value, and E is calculated as follows:

[0139]

[0140] Among them, X cur 、Y cur and Z cur is the Cartesian coordinate of the point obtained in this round of iteration, X last 、Y last and Z last are the corresponding grid coordinates calculated in the previous iteration.

[0141] Specifically, the preset value of ε is 2%-2.5%, which can achieve the reverse design accuracy required for the project.

[0142] Error judgment is only performed from the second round of iterative calculation to determine whether the result of the current iterative calculation meets the requirements. If so, the calculation is completed and the iterative bulge surface is output. Otherwise, the iterative flow surface passing through each discrete point 2 obtained by the current iterative calculation will replace the initial flow surface 3 at the beginning of the previous round of iterative calculation, and a new iterative cycle will begin. The above cycle judgment condition means that if the relative error of the Cartesian coordinates of any grid point in the flow field in two consecutive iterations exceeds or equals the preset value, the algorithm is considered to have not converged and iterative calculation needs to continue.

[0143] Method validity verification:

[0144] In order to verify the effectiveness of the SDSI method proposed in this patent, the following Figures 11a-11c The three typical pressure distributions shown are used as design inputs for reverse design of the bulge, and the resulting bulge is numerically simulated and the results are analyzed. Figure 11a It shows a schematic diagram of the pressure distribution of the boost bulge according to a specific embodiment of the present invention, Figure 11b A schematic diagram of pressure distribution of a depressurized bulge according to a specific embodiment of the present invention is shown. Figure 11c A schematic diagram of the pressure distribution of the transverse pressure bulge according to a specific embodiment of the present invention is shown. During the verification process, the bulge is reversely designed using the three typical pressure distributions shown in the figure as design inputs, and the resulting bulge is numerically simulated and the results are analyzed.

[0145] These three typical pressure distributions are named pressure-increasing distribution, pressure-decreasing distribution, and transverse pressure distribution. The pressure-increasing distribution is characterized by a gradual increase in pressure along the flow direction with a small transverse pressure gradient; the pressure-decreasing distribution is characterized by a decrease in pressure along the flow direction with a similarly small transverse pressure gradient; and the transverse pressure distribution is characterized by a small pressure change along the flow direction but a gradual decrease in pressure laterally from the symmetry plane.

[0146] Because the SDSI method does not account for viscous effects, a density-based Euler equation solver was used in the numerical simulations. The fluid was considered a perfect gas with a specific heat ratio of 1.4. The governing equations were discretized using the finite control volume method. To ensure stability, an implicit method was used in the solution. To ensure accuracy, the inviscid flux vector was calculated using the Roe-FDS method. The spatial discretization was performed using the second-order upwind method, and the gradient was calculated using the least-squares element basis method. A structured grid was used in the simulations. To improve the resolution at the leading edge and shock wave, a pressure gradient-based grid adaptation method was adopted. After two adaptations, the number of grid elements in each case was approximately 20 to 30 million. The incoming flow Mach number was 6, the pressure was 4512 Pa, and the static temperature was set to 217 K. These flow parameters are approximately the same as the atmospheric conditions at an altitude of 21 km.

[0147] Figure 12a It shows a simulation cloud diagram of a supercharged bulge according to a specific embodiment of the present invention. Figure 12b It shows a depressurization bulge simulation cloud diagram according to a specific embodiment of the present invention, Figure 12c A simulation cloud map of a transverse pressure bulge according to a specific embodiment of the present invention is shown. The three cloud maps are comparisons of the pressure distribution obtained by simulation and the preset pressure distribution. The cloud map in the figure is the pressure distribution obtained by simulation, and the thick solid line is the preset value. It can be seen from the figure that the pressure distribution obtained by simulation is basically consistent with the preset value, with only a slight gap at the rear of the transverse pressure bulge. Statistics show that the maximum error between the surface pressure of the bulge obtained by simulation and the preset pressure is about 4.9%, which can meet the needs of engineering practice. The above simulation results prove that the three-dimensional flow field inverse solution method based on shock wave driven surface iteration proposed in this application can realize the reverse design of bulges with preset arbitrary three-dimensional pressure distribution. This method will provide a solid foundation for related engineering exploration.

[0148] The present application proposes a bulge design method with a preset arbitrary three-dimensional pressure. By artificially discretizing the flow surface into a three-dimensional space, the flow field in each flow surface is solved instead of the direct solution of the three-dimensional flow field. When solving each flow surface, it is assumed that the flow around each point on the flow surface is an axisymmetric flow with different symmetry axis positions, and the axis of symmetry of the axisymmetric flow at each point is different, to ensure a more accurate approximation to the original three-dimensional flow. At the same time, the shock wave driven iteration method is used to solve the flow surface shape in the discrete three-dimensional space to solve the problem that the flow field solution method based on the classical kissing theory cannot determine the shape of the kissing surface when the pressure distribution is used as the design input. The shape of the shock wave surface 1 and the iterative flow surface in each round of iteration will change. When the three-dimensional flow field is solved by multiple iterations, the shape of the flow surface tends to converge. At this time, the flow fields in each flow surface are integrated to obtain the three-dimensional flow field and bulge surface corresponding to the design input.

[0149] The above description is merely a preferred embodiment of the present application and an illustration of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to the technical solutions formed by the specific combination of the above-mentioned technical features, but also encompasses other technical solutions formed by any combination of the above-mentioned technical features or their equivalents without departing from the above-mentioned inventive concept. For example, a technical solution formed by replacing the above-mentioned features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A method for designing a bulge with a preset arbitrary three-dimensional pressure distribution, characterized in that: The following steps are involved: S1: Input a preset three-dimensional pressure distribution and a leading edge line, generate an initial shock wave surface corresponding to the three-dimensional pressure distribution, discretize the leading edge line into a plurality of discrete points, and construct a plurality of initial flow surfaces corresponding to each of the discrete points; S2: solving the curvature radius corresponding to each point in each of the initial flow surfaces and the flow surface pressure distribution corresponding to each of the initial flow surfaces; S3: Based on the curvature radius of each of the initial flow surfaces and the pressure distribution of the flow surfaces, twisting the points on the initial flow surfaces to a virtual meridian plane, and obtaining flow parameters of the points on the initial flow surfaces on the virtual meridian plane using an improved two-dimensional characteristic line method; S4: constructing a preset shock wave line of the initial shock wave surface, wherein the preset shock wave line includes a plurality of longitudes and a plurality of latitudes, wherein the longitudes and the latitudes divide the initial shock wave surface into a plurality of shock wave grids, and generating a plurality of local tangent surfaces of the initial flow surface corresponding to each of the shock wave grids; S5: Based on the shock wave preset line and the local kissing surface, mapping the flow parameters on each of the initial flow surfaces into a three-dimensional Cartesian space, reconstructing each of the initial flow surfaces to obtain a corresponding iterative flow surface, and integrating each of the iterative flow surfaces to obtain a three-dimensional flow field including an iterative shock wave surface and an iterative bulge surface; S6: Perform error calculation on the coordinates of each point in the three-dimensional flow field. If the coordinate error of each point is less than a preset value, output the iterative bulge surface. If the coordinate error of any point is greater than or equal to the preset value, replace the initial flow surface and the initial shock wave surface with the iterative flow surface and the iterative shock wave surface obtained by the current iterative calculation and perform the next round of iterative calculation, repeating steps S2-S6.

2. The bulge design method according to claim 1, characterized in that: In S1, the construction process of the initial flow surface includes: S101: determining the direction of the tangential plane corresponding to the discrete point based on the shape of the leading edge line; S102: Determine the pressure value of the discrete point by interpolation according to the preset three-dimensional pressure distribution; S103: Substituting the pressure value of the discrete point into the Rankine-Hugoniot shock wave transition relationship to obtain the corresponding shock wave angle and wall deflection angle, determining the wall line and shock wave line of the tangent surface according to the shock wave angle and the wall deflection angle, and integrating the wall line and the shock wave line to obtain the initial flow surface.

3. The bulge design method according to claim 1, characterized in that: In S2, the process of calculating the curvature radius includes: S201: Divide each of the initial flow surfaces into a plurality of flow surface grids; S202: Determine a first grid point on the initial flow surface to be solved, and extract a second grid point and a third grid point on two adjacent initial flow surfaces corresponding to the first grid point; S203: Constructing a circular arc that passes through the first grid point, the second grid point, and the third grid point simultaneously, where the radius of the circular arc is the curvature radius corresponding to the first grid point.

4. The bulge design method according to claim 1, characterized in that: In S2, the process of solving the flow surface pressure distribution includes: S211: Projecting the wall line geometric parameters of the initial flow surface onto the plane where the preset three-dimensional pressure distribution is located to obtain a projection curve; S212: Perform two-dimensional interpolation on each point on the projection curve to obtain a pressure value corresponding to each point on the projection curve; S213: Assigning the pressure value of each point on the projection curve to the corresponding point on the wall line, and integrating the pressure values of each point on the wall line to obtain the flow surface pressure distribution corresponding to the initial flow surface.

5. The bulge design method according to claim 1, characterized in that: In S3, the flow around the point on the initial flow surface is approximated as an independent axisymmetric flow, and starting from the second round of iterative calculation, the curvature radius is two-dimensionally interpolated using the flow parameters obtained in the previous round of iterative calculation.

6. The bulge design method according to claim 1, characterized in that: In S4, each of the meridians corresponds to an initial flow surface, and the meridians intersect with the initial flow surface at a point on the leading edge line. The points corresponding to each meridian are connected to form the latitude lines. The meridians are composed of several segments of meridian grid lines connected end to end, and the meridian grid lines are the intersection lines of the initial shock wave surface and the local kissing surface.

7. The bulge design method according to claim 6, characterized in that: Said S4 further comprises: S401: Determine an intersection of the initial flow surface and the leading edge line as a first intersection, and obtain coordinates of the first intersection and coordinates of vertices of the shock wave grid corresponding to the first intersection; S402: Calculating the normal vector of the mesh plane formed by the lines connecting the vertices using a cross product method; S403: combining the normal vector and the free stream velocity vector, solving the local tangent surface within the shock wave grid corresponding to the initial flow surface, wherein the first intersection point is an intersection point of the local tangent surface and the grid plane; S404: Determine another intersection point between the local tangential surface and the grid plane as a second intersection point, calculate the coordinates of the second intersection point, connect the first intersection point and the second intersection point, and solve for the meridian grid line of the meridian in the grid plane; S405: Using the second intersection point as the starting intersection point of the next shock wave grid, sequentially solving all the corresponding meridian grid lines and the local tangent surfaces in the initial flow surface.

8. The bulge design method according to claim 1, characterized in that: In S5, the reconstruction process of the initial flow surface includes: S501: reconstructing a mapping shock line of the shock line of the initial flow surface on the virtual meridian plane, and deflecting the mapping shock line according to a meridian corresponding to the initial flow surface and a direction determined by the local tangent plane to obtain a real shock line; S502: Slicing the points of the initial flow surface mapped onto the virtual meridian plane in a direction away from the real shock wave line, wherein all points outside the real shock wave line are interior points of the initial flow surface; S503: Reconstruct the inner points of the initial flow surface layer by layer, and based on the reconstructed real shock wave lines and the flow parameters of the inner points on the virtual meridian plane, solve the positions of the inner points of each layer in the three-dimensional Cartesian space coordinate system to generate a reconstructed iterative surface.

9. The bulge design method according to claim 8, characterized in that: The flow parameters include the axial position ξ, radial position ζ, static pressure p, density ρ, velocity V and flow angle θ of the point on the initial flow surface on the virtual meridian plane, and S503 further includes: S5031: Calculating the position of the interior point in a three-dimensional Cartesian coordinate system according to the axial position ξ, radial position ζ, flow angle θ of the interior point on the virtual meridian plane and the coordinates of the reconstructed real shock wave line; S5032: Decompose the velocity V of the interior point on the virtual meridian plane into components V in the X, Y, and Z directions x 、V y 、V z ; S5033: Assign the static pressure p and density ρ of the interior point on the virtual meridian plane to the corresponding point in the three-dimensional Cartesian coordinate system.

10. The bulge design method according to claim 1, characterized in that: In S6, the three-dimensional flow field obtained by the initial flow surface iterative calculation is not subjected to error judgment. Error judgment is performed starting from the three-dimensional flow field obtained by the second round of iterative calculation. The error judgment condition is max(E)<ε, where E is the relative error of the Cartesian coordinates of any point in the three-dimensional flow field, ε is the error preset value, and E is calculated as follows: Among them, X cur 、Y cur and Z cur is the Cartesian coordinate of the point obtained in this round of iteration, X last 、Y last and Z last are the corresponding grid coordinates calculated in the previous iteration.

Images