A bulge design method for presetting an arbitrary three-dimensional pressure distribution

Abstract

The application discloses a bulge design method of presetting arbitrary three-dimensional pressure distribution, comprising the following steps: inputting a preset three-dimensional pressure distribution and a leading edge line, generating a corresponding initial shock wave surface, discretizing the leading edge line into a plurality of discrete points and constructing a corresponding initial flow surface; solving the curvature radius and the flow surface pressure distribution of each initial flow surface point; based on the curvature radius and the pressure distribution, twisting the initial flow surface point to a virtual meridian plane, solving the flow parameters thereof; constructing a shock wave preset line of the initial shock wave surface and a corresponding local tangent surface; mapping the flow parameters to a three-dimensional Cartesian space, reconstructing an iterative flow surface, generating a three-dimensional flow field containing an iterative shock wave surface and an iterative bulge surface; judging the three-dimensional flow field coordinate error, if the three-dimensional flow field coordinate error is less than a preset threshold value, outputting the iterative bulge surface, otherwise, replacing the initial value with the current iterative flow surface and the shock wave surface and repeating the above steps until convergence. The application realizes the reverse design of the bulge with the arbitrary three-dimensional pressure distribution, and expands the flexibility of the bulge design.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, and in particular to a method for designing a bulge with a pre-defined arbitrary three-dimensional pressure distribution. Background Technology

[0002] In modern supersonic aircraft, the air intake system plays a crucial role in pre-compressing the incoming airflow to generate thrust and perform work, making it a vital component of the aircraft's propulsion system. To ensure the overall aerodynamic characteristics and the layout of avionics, the air intake system of modern supersonic aircraft is often located far from the nose. This allows low-energy flows generated at the front of the fuselage to potentially enter the air intake system. These low-energy flows reduce the compression efficiency of the air intake system and disrupt its operational stability, which is one of the problems that must be addressed in the air intake design of modern supersonic aircraft. Traditional air intake systems primarily address low-energy flows using methods such as boundary layer diverters and suction. While these methods effectively expel low-energy flows from the air intake, they require additional mechanical structures and actuators, affecting the aircraft's aerodynamic shape, increasing its weight and complexity, and reducing its overall performance. Since the beginning of the new century, a device called a bulge has been gradually applied to the inlet of the intake system. With its specific geometry and pressure distribution, this device can simultaneously achieve the purpose of efficiently compressing the incoming flow and removing low-energy flow from the intake system without adding additional mechanical structures, thus becoming 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 displace the precursor boundary layer. Both are closely related to the pressure distribution on the bulge surface. Directly designing the bulge in reverse 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 a paper entitled "Inverse design and Mach6 experimental investigation of a pressure controllable" in Volume 81, pp. 204-212 of the English journal Aerospace Science and Technology. The paper on "bump" proposed a pressure-controllable bump concept based on conventional conical flow theory and a new three-dimensional reverse design method, which can reverse design the bump configuration through a specified pressure distribution. In 2019, Zonghan Yu et al. published a paper entitled "A pressure-controllable bump based on the pressure-ridge concept" in Volume 87, Pages 133-140 of the same journal, which proposed an innovative pressure distribution design for the nose (bump) of hypersonic aircraft and discussed the challenges of high-speed air intake-airframe integration. In 2022, Cai Jia et al. published a paper entitled "Aerodynamic Design Method of Forebody / Compression Surface with Controllable Spanning Pressure Distribution and Its Flow Characteristics" in Volume 40, Issue 1, Pages 67-76 of the journal "Chinese Journal of Aerodynamics", which proposed an integrated aerodynamic design method for hypersonic forebody / compression surface based on controllable spanning pressure distribution. Two different close-fitting bumps and one conical guide bump were designed for the air intake lip model of a certain type of aircraft, and their flow capture characteristics and boundary layer displacement performance were analyzed.

[0004] The design of a bulge with a pre-defined pressure distribution is essentially a reverse solution of a three-dimensional flow field with the wall pressure distribution as the design input. As mentioned above, although significant progress has been made in this area, this progress is based on classical tangential theory, represented by tangential cone, tangential axisymmetric, and tangential flow field methods. This theory has two limitations when used for bulge design with a pre-defined pressure distribution. First, it uses a plane (tangential surface) to discretize the three-dimensional flow field and assumes that the flow at each tangential surface is axisymmetric. This requires that the shock wave intensity corresponding to the pre-defined pressure distribution be uniform everywhere, and that the transverse pressure gradient behind the wave 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, thus rendering the classical tangential theory invalid. Secondly, in classical scissor-cutting theory, the shape of each scissor-cutting surface (referring to the angle of each scissor-cutting surface in three-dimensional space) is determined by the shock wave shape. When the preset pressure distribution is relatively simple (e.g., a small lateral pressure gradient), a shock wave can be assumed, and the shape of each scissor-cutting surface can be solved based on this shock wave to solve the entire three-dimensional flow field. This is also the common practice in existing scissor-cutting theory-based preset pressure distribution bulge design methods. However, when the preset pressure distribution is more complex (e.g., a large lateral pressure gradient), 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 thus making it difficult to reverse-engineer the bulge. Due to the above two problems, in existing preset pressure distribution bulge surface design methods, the pressure distribution used as the design input can only be changed significantly along the flow direction. When the change is large in the direction perpendicular to the flow direction (spanwise), the accuracy of the method will decrease significantly, making it impossible to reverse-engineer the bulge based on any three-dimensional preset pressure distribution. Summary of the Invention

[0005] To address the shortcomings of the existing technology, this invention proposes a bulge design method with a preset arbitrary three-dimensional pressure distribution to solve the aforementioned technical problems.

[0006] This application proposes a method for designing a bulge with a pre-defined 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 surface corresponding to the three-dimensional pressure distribution, and discretize the leading edge line into several discrete points, constructing several initial flow surfaces corresponding to each discrete point;

[0008] S2: Solve for the radius of curvature at each point within each initial flow surface and the flow surface pressure distribution corresponding to each initial flow surface;

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

[0010] S4: Construct the initial shock wave surface's shock wave preset line, which includes several meridians and several parallels. The meridians and parallels divide the initial shock wave surface into several shock wave grids, generating several local cut surfaces of the initial flow surface corresponding to each shock wave grid.

[0011] S5: Based on the shock wave preset line and local tangent surface, the flow parameters on each initial flow surface are mapped to 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 containing iterative shock wave surface and 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 surface with the iterative flow surface and iterative shock surface obtained by the current iteration calculation and perform the next round of iteration calculation. Repeat steps S2-S6.

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

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

[0015] (2) When calculating the flow field in each surface, this method assumes that the flow near each point on the surface can be approximated by different axisymmetric flows with different axisymmetric positions. In this way, each point on the surface has its own axisymmetric, thus obtaining a more accurate approximation of the real flow near each point.

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

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

[0018] S101: Determine the direction of the kissing plane corresponding to the discrete point based on the shape of the leading edge;

[0019] S102: Determine the pressure values ​​at discrete points using interpolation based on a preset three-dimensional pressure distribution;

[0020] S103: Substitute the pressure values ​​at discrete points into the Rankine-Hugoniot shock transition relation to obtain the corresponding shock angle and wall deflection angle. Determine the wall line and shock line of the tangent surface based on the shock angle and wall deflection angle, and integrate the wall line and shock line to obtain the initial flow surface.

[0021] The first step of this method is the construction of the initial flow surface. Its purpose is to provide an initial value for the flow surface shape at each point along the leading edge, ensuring the smooth progress of subsequent iterative calculations. The leading edge 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 based on classical tangent theory. Within each tangent plane, a wall line and a shock line are given, and the angle between them relative to the incoming flow direction is calculated using the Rankine-Hugoniot shock transition relation based on the pressure value at the leading edge point.

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

[0023] S201: Divide each initial flow surface into several flow surface grids;

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

[0025] S203: Construct an arc that passes through the first grid point, the second grid point, and the third grid point simultaneously. The radius of the arc is the radius of curvature corresponding to the first grid point.

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

[0027] Preferably, in S2, the solution process for the surface pressure distribution includes:

[0028] S211: Project the geometric parameters of the wall line of the initial flow surface onto the plane containing the preset three-dimensional pressure distribution to obtain the 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: Assign the pressure values ​​of each point on the projection curve to the corresponding points on the wall line, and integrate 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, which aims to obtain the wall pressure corresponding to each surface used in discrete three-dimensional space (the first iteration corresponds to the initial flow surface, and subsequent iterations correspond to the iterative flow surface generated in the previous iteration).

[0032] Preferably, in S3, the flow around the point on the initial flow surface is approximately an independent axisymmetric flow. Starting from the second iteration calculation, the radius of curvature is interpolated in two dimensions using the flow parameters obtained from the previous iteration calculation.

[0033] By twisting the points on the flow surface onto a virtual meridional plane, the two-dimensional computational method can solve for 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, meaning 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. In addition, the flow parameters obtained from the previous iteration are incorporated into the calculation process. Using these parameters, the curvature radius of each point is further interpolated in two dimensions during the process of solving the element in the flow surface, so that the flow parameters obtained from the previous iteration are corrected in the current iteration. This step, combined with other steps, can solve the unsteady problem in the ideal solution of supersonic three-dimensional flow fields.

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

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

[0036] Furthermore, S4 also includes:

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

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

[0039] S403: Combining the normal vector and the free flow velocity vector, the local shear surface of the initial flow surface within the stress wave grid range is obtained. The first intersection point is an intersection point between the local shear surface and the grid plane.

[0040] S404: Determine another intersection point between the local cutting plane and the grid plane as the 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 lines in the grid plane;

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

[0042] Each meridian grid line has a corresponding shock grid. For a meridian grid line that intersects the leading edge, its starting point is the intersection point with the leading edge. Based on the four vertices of the shock grid corresponding to this meridian grid line, a grid plane is constructed. Since the coordinates of the starting point and the vertices of the grid plane are known, the normal vector of the grid plane is obtained by cross-product of the vectors of the edges containing the starting and ending points of the meridian grid line. Combining the normal vector with the free flow velocity vector, the local tangent plane corresponding to this grid plane can be calculated. Then, by finding another intersection point between the local tangent plane and the grid plane, the coordinates of the ending point of the meridian grid line can be obtained. The starting point of the subsequent meridian grid line on the same meridian is the ending point of the previous meridian grid line, and so on. The meridians and local tangent planes corresponding to all discrete points on the leading edge can be solved. The deflection direction of the local tangent plane is the deflection direction of the meridian.

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

[0044] S501: Reconstruct the shock line of the initial flow surface onto the virtual meridional plane and deflect the mapped shock line according to the direction determined by the meridian corresponding to the initial flow surface and the local tangent plane to obtain the real shock line.

[0045] S502: The points mapped from the initial flow surface onto the virtual meridional surface are layered along the direction away from the real shock line, wherein the points located outside the real shock line are all interior points of the initial flow surface.

[0046] S503: Reconstruct the initial flow surface layer by layer of interior points. Based on the reconstructed real shock line and the flow parameters of the interior points on the virtual meridional surface, solve the position of the interior points of each layer in the three-dimensional Cartesian coordinate system and 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, reconstructing the mapped shock line to obtain the real shock line, and then reconstructing the interior points. 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 line, the remaining grid points inside the flow surface are called interior points. The interior points on the flow surface are reconstructed layer by layer, starting from the layer of interior points close to the real shock line and moving layer by layer away from the real shock line. Repeating this 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 corresponding to the design input in this iteration, including the iterative shock surface and the iterative bulge surface.

[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 meridional plane. S503 also includes:

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

[0050] S5032: Decompose the velocity V of the interior point on the virtual meridional 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 meridional plane to the corresponding point in the three-dimensional Cartesian coordinate system.

[0052] By using three-dimensional coordinate mapping, velocity component decomposition, and physical parameter assignment, the flow parameters on the virtual meridional plane are accurately transferred and collaboratively reconstructed into three-dimensional Cartesian space.

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

[0054]

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

[0056] Error judgment is performed only from the second iteration. To determine whether the result of the current iteration meets the requirements, if it does, the calculation is completed and the obtained iterative bulge surface is output. Otherwise, the iterative flow surface obtained by the current iteration through each discrete point will replace the initial flow surface at the beginning of the previous iteration and a new iteration 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 not to have converged and iterative calculation needs to continue.

[0057] Compared with the prior art, the beneficial effects of this application are as follows:

[0058] This application proposes a method for designing bulges with preset arbitrary three-dimensional pressure. This method can use arbitrary three-dimensional pressure distributions, which are not applicable to the classical kissing method, as design input to perform inverse solving of the three-dimensional flow field, thereby realizing the inverse design of the corresponding bulge. This greatly expands the flexibility of bulge design. The method includes three main innovations:

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

[0060] (2) When calculating the flow field in each surface, this method assumes that the flow near each point on the surface can be approximated by different axisymmetric flows with different axisymmetric positions. In this way, each point on the surface has its own axisymmetric, thus obtaining a more accurate approximation of the real flow near each point.

[0061] (3) The third major innovation of this method is to use the shock wave driven iteration method to solve the surface shape for discrete three-dimensional space, so as to solve the problem that the classical kissing theory cannot determine the kissing surface shape when the pressure distribution is used as the design input. Attached Figure Description

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

[0063] Figure 1 The diagram illustrates the steps of a bulge design method according to an embodiment of the present invention.

[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 flowchart 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 the initial flow surface structure according to a specific embodiment of the present invention is shown;

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

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

[0070] Figure 8 A three-dimensional flow diagram of the in-flow field according to a specific embodiment of this application is shown;

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

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

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

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

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

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

[0079] The meaning of each number in the diagram:

[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 10, Normal vector 11, Free flow velocity vector 12, Local tangent 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 Implementation

[0081] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0082] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0083] This application proposes a method for designing bulges with a pre-defined arbitrary three-dimensional pressure distribution. Figure 1 The diagram illustrates the steps of a bulge design method according to an embodiment of the present invention, as follows: 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 surface 1 corresponding to the three-dimensional pressure distribution, and discretize the leading edge line into several discrete points 2, construct several initial flow surfaces 3 corresponding to each discrete point 2;

[0085] S2: Solve for the radius of curvature of each point within each initial flow surface 3 and the flow surface pressure distribution corresponding to each initial flow surface 3;

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

[0087] S4: Construct the initial shock wave preset line of the initial shock wave surface 1. The shock wave preset line includes several meridians 4 and several parallels. The meridians 4 and parallels divide the initial shock wave surface 1 into several shock wave grids, and generate several local cut surfaces of the initial flow surface 3 corresponding to each shock wave grid.

[0088] S5: Based on the shock wave preset line and local tangent surface, the flow parameters on each initial flow surface 3 are mapped to the three-dimensional Cartesian space, and each initial flow surface 3 is reconstructed to obtain the corresponding iterative flow surface. The iterative flow surfaces are integrated to obtain a three-dimensional flow field containing 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 surface 1 with the iterative flow surface and the iterative shock surface 1 obtained by the current iteration calculation and perform the next round of iteration calculation. Repeat steps S2-S6.

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

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

[0092] Second, unlike the classical herringbone theory which assumes that the flow field within each herringbone plane is a standard axisymmetric flow field, the SDSI method, when calculating the flow field within each flow plane, assumes that the flow near each point within the flow plane can be approximated by different axisymmetric flows with different symmetry axes at different positions. Thus, each point within the flow plane has its own axis of symmetry, unlike the classical herringbone theory where each point within a herringbone plane shares a single axis of symmetry. This allows for a more accurate approximation of the actual flow near each point. Combining these two core concepts enables the solution of three-dimensional flow fields with non-uniform 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 wave-driven iteration to solve for the surface shape in discrete three-dimensional space, thus addressing the problem that classical kissing theory cannot determine the kissing surface shape when pressure distribution is used as the design input. The SDSI method uses a preset three-dimensional pressure distribution to perform multiple iterations on the entire three-dimensional flow field. In each iteration, the shock wave surface 1 obtained from the previous iteration is used to calculate the surface shape corresponding to the current iteration. In this way, the shape of the shock wave surface 1 and the shapes of each initial flow surface 3 (from the second iteration onwards, the initial flow surface 3 is replaced by the iterative flow surface calculated from the previous iteration) will change in each iteration. After several iterations, a flow surface shape with sufficient accuracy can be obtained, thus realizing the reverse solution of the three-dimensional flow field based on the preset three-dimensional pressure distribution and the reverse design of the bulge.

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

[0095] Figure 3 A schematic diagram of flow surface iteration according to a specific embodiment of the present invention is shown, such as Figures 1-3 As shown, Figure 3 The figure shows 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, the iterative shock surface 1 and the bulge surface after the first and second iterations. 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 states. It can be seen that the entire three-dimensional flow field is solved iteratively multiple times. The shape of the shock surface 1 changes in each iteration, and the shape of the surface used to discretize the three-dimensional space (i.e., the iterative flow surface) also changes. After multiple iterations, the flow surface shape tends to converge. At this time, the flow field in each flow surface is integrated to obtain the three-dimensional flow field and bulge surface corresponding to the design input.

[0096] Figure 4 A flowchart of the SDSI method according to a specific embodiment of the present invention is shown, as follows: Figures 1-4 As shown, this method generates an initial shock surface 1 by inputting a preset arbitrary three-dimensional pressure distribution. In the first iteration, the initial value of the flow surface is estimated, i.e., the construction of the initial flow surface 3. The shape of the initial flow surface 3 is the initial curved surface shape used for discretizing three-dimensional space. Based on the constructed initial flow surface 3, the radius of curvature and flow surface pressure distribution are calculated for the initial flow surface 3, obtaining the radius of curvature of each point within the initial flow surface 3 and the wall pressure value corresponding to each initial flow surface 3. Furthermore, based on the initial shock surface 1, a preset shock line is constructed. Combining the radius of curvature and wall pressure value, the flow field within the initial flow surface 3 is calculated, obtaining the corresponding flow field of each initial flow surface 3. The two-dimensional flow field 15 located within the virtual meridional plane (containing the flow parameters of each point on the initial flow surface 3) is calculated as described above for each initial flow surface 3. Combining the shock wave preset line and the two-dimensional flow field 15, a three-dimensional flow field is reconstructed, which yields a new surface shape for discrete three-dimensional space (i.e., several iterative flow surfaces located within the reconstructed three-dimensional flow field). Error judgment is performed on the iterative flow surfaces. 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 iteration replaces the initial flow surface 3 at the beginning of the calculation for the second iteration. The subsequent iteration calculation process is carried out in the same manner. Figure 5 A schematic diagram of the initial flow surface structure according to a specific embodiment of the present invention is shown, such as... Figures 1-5 As shown, in S1, the construction process of the initial flow surface 3 includes:

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

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

[0099] S103: Substitute the pressure value at discrete point 2 into the Rankine-Hugoniot shock wave transition relation 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 initial values, namely the construction of the initial flow surface 3. Its purpose is to provide an initial value for the flow surface shape at each point on the leading edge to ensure the smooth progress of subsequent iterative calculations. Specifically, the leading edge is discretized into a series of discrete points 2, and a tangent surface is constructed through each discrete point 2. The angle of each tangent surface is determined by the shape of the leading edge according to the classical tangent theory. In each tangent 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 using the Rankine-Hugoniot shock transition relation based on the pressure value at the discrete point 2.

[0101] Furthermore, in Figure 5 Taking discrete point 2 on the leading edge as an example, the direction of the tangent surface (i.e., the initial flow surface 3) is first determined based on the shape of the leading edge. Then, the pressure at discrete point 2 is determined by interpolation in the preset three-dimensional pressure distribution. This pressure is substituted into the Rankine-Hugoniot shock wave transition relation 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 for each discrete point 2 is constructed in the above manner.

[0102] Specifically, for the first round of iteration calculation, the surface shape used is the constructed initial flow surface 3. From the second round of iteration calculation onwards, the surface shape used is the iterative flow surface generated in the previous round of iteration.

[0103] Figure 6 A schematic diagram illustrating the calculation of the radius of curvature according to a specific embodiment of the present invention is shown, such as... Figures 1-6 As shown, the process of solving for the radius of curvature in S2 includes:

[0104] S201: Divide each initial flow surface 3 into several flow surface grids;

[0105] S202: Determine the first grid point on the initial flow surface 3 to be solved, and extract the second and third grid points on two adjacent initial flow surfaces 3 that correspond to the first grid point;

[0106] S203: Construct an arc that passes through the first grid point, the second grid point, and the third grid point simultaneously. The radius of the arc is the radius of curvature corresponding to the first grid point.

[0107] The second step of the SDSI method is to calculate the radius of curvature corresponding to each point on the flow surface. Specifically, taking the first iteration as an example, each initial flow surface 3 is divided into several flow surface grids. The radius of curvature corresponding to the grid points on the flow surface grids is required. When solving for the radius of curvature corresponding to a grid point, it is necessary to extract the grid points corresponding to that point on 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 radius of curvature corresponding to the grid point to be solved.

[0108] Specifically, with Figure 6 Taking the calculation of the radius of curvature of A1 and B1 as an example, as shown in the figure, the initial flow surface 3 is the surface used for discretizing three-dimensional space. When solving for the radius of curvature 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, and A2 and A3 are the second and third grid points, respectively. An arc is constructed through A1, A2, and A3, and the radius of the arc is calculated to be R. A1 Then R A1 For point A1, we can obtain the radius of curvature; similarly, we can obtain the radius of curvature R for point B1. B1 It should be noted that in the first iteration, the flow surface used to calculate the radius of curvature at each point is obtained from the initial value estimation step (i.e., initial flow surface 3). In the second and subsequent iterations, the flow surface used to calculate the radius of curvature is obtained from the three-dimensional flow field reconstruction step in the previous iteration (i.e., iterative flow surface).

[0109] Figure 7 A schematic diagram illustrating the acquisition of flow surface pressure distribution according to a specific embodiment of the present invention is shown, such as... Figures 1-7 As shown, the solution process for the surface pressure distribution in S2 includes:

[0110] S211: Project 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 the 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: Assign the pressure values ​​of each point on the projection curve 8 to the corresponding points on the wall line 5, and integrate 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 surface pressure distribution. Its purpose is to obtain the wall pressure corresponding to each surface used in discrete three-dimensional space (the first iteration corresponds to the initial flow surface 3, and subsequent iterations correspond to the iterative flow surfaces generated in the previous iteration). Taking the first iteration as an example, for... Figure 7 The initial flow surface 3 is calculated, and the projection plane 7 is the plane where the preset three-dimensional pressure distribution is located. 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 value corresponding to these points. These values ​​are assigned to the corresponding points on the wall line 5. By integrating the pressure values ​​of each point on the wall line 5, the pressure distribution corresponding to the initial flow surface 3 is obtained. 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 within a flow surface according to a specific embodiment of this application is shown, such as... Figures 1-8 As shown in S3, the flow around the point on the initial flow surface 3 is approximately an independent axisymmetric flow. Starting from the second iteration, the radius of curvature is interpolated in two dimensions using the flow parameters obtained from the previous iteration.

[0115] The fourth step of the SDSI method is the in-surface flow field calculation. Its purpose is to calculate the flow parameters for each discrete 3D surface, providing a foundation for the reconstruction of the 3D flow field in subsequent steps. The calculation employs a development of the 2D characteristic line method (2D-MOC), which differs from the classic 2D-MOC in three ways. First, each point on the flow surface is twisted onto a virtual meridional plane, allowing the 2D calculation method to solve for the flow parameters on the surface in 3D space. Second, the flow around each point on the flow surface is approximated as an independent axisymmetric flow, meaning that each point on the flow surface has its own axis of symmetry, instead of 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, using these parameters to perform 2D interpolation of the radius of curvature at each point during the element solving process. Thus, the flow parameters obtained from the previous iteration are corrected in this round of calculation. Combining the above calculation method with other steps can solve the unsteady problem in the inverse solution of supersonic 3D flow fields. After this step, the six flow variables at each point on the flow surface on the virtual meridional plane, namely axial position (ξ), radial position (ζ), static pressure (p), density (ρ), velocity (V), and flow angle (θ), will be solved. These variables will be integrated into a three-dimensional flow field in Cartesian coordinates in the fifth flow field reconstruction step.

[0116] exist Figure 8In this problem, we assume that points A, B, and C in the figure are three points to be solved on the flow surface. 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 the problem, we assume 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 easy to see that the flow around each point has its own axis of symmetry. In this way, we can achieve an accurate approximation of the original three-dimensional flow around the three points.

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

[0118] Furthermore, S4 also includes:

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

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

[0121] S403: Combining the normal vector 11 and the free flow velocity vector 12, the local tangent 10 within the shock grid range corresponding to the initial flow surface 3 is obtained. The first intersection point is an intersection point between the local tangent 10 and the grid plane.

[0122] S404: Determine another intersection point between the local cutting surface 10 and the grid plane as the 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 4 in the grid plane;

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

[0124] In the S5 flow field reconstruction step, the meridian 4 and the corresponding local tangent plane 10 obtained in this step are used to reconstruct the two-dimensional flow field 15 on the corresponding flow surface from the virtual meridional plane to the real three-dimensional space. The shape of the meridian 4 depends on the shock surface 1 obtained in the previous iteration (for the first iteration calculation, it is based on the initial value estimation step, that is, the initial shock 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 surface 1 and the corresponding local tangent plane 10.

[0125] by Figure 9 Taking the meridian 4 and the corresponding series of deflected local cut surfaces 10 as an example, the dark curved surface and the grid on it are the shock surface 1 and shock grid obtained in the previous iteration or initial value estimation step. The discrete point 2 in the figure is the intersection of a surface (initial flow surface 3 / iterated flow surface) used for discrete three-dimensional space and the leading edge line. The meridian 4 is generated from the discrete point 2 along the flow direction. 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 the shock grid points of the shock surface 1. The meridian grid line 9 is a grid line on the meridian 4 to be determined. 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. Point E is the intersection point of the upstream meridian grid line 9 and the straight line AB. 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, it can be obtained by taking and The cross product is used to calculate the normal vector 11 of plane ABCD, denoted as . Then, by combining the normal vector 11 and the free-flow velocity vector 12, the local tangent plane 10 of the grid ABCD can be obtained. By finding the intersection point of the local tangent plane 10 and the line CD, the position of point F can be determined, thus completing the generation of the meridian grid line 9. Repeating the above process will yield the meridian 4 passing through discrete point 2 and a series of deflected local tangent planes 10 forming a local tangent plane group 13. Repeating the above process for each discrete point 2 on the leading edge will yield all meridians 4 and their corresponding local tangent planes 10.

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

[0127] S501: Reconstruct the shock line 6 of the initial flow surface 3 onto the mapped shock line 14 on the virtual meridian plane, and deflect the mapped shock line 14 according to the direction determined by the meridian 4 and the local tangent plane 10 corresponding to the initial flow surface 3 to obtain the real shock line 16.

[0128] S502: The points of the initial flow surface 3 mapped onto the virtual meridional surface are layered along the direction away from the real shock line 16, wherein the points located outside the real shock line 16 are all interior points of the initial flow surface 3.

[0129] S503: Perform layer-by-layer interior point reconstruction on the initial flow surface 3. Based on the reconstructed real shock line 16 and the flow parameters of the interior points on the virtual meridional surface, solve the position of the interior points in the three-dimensional Cartesian coordinate system of each layer, and 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 the point on the initial flow surface 3 on the virtual meridional plane. S503 also includes:

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

[0132] S5032: Decompose the velocity V of the interior point on the virtual meridional 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 meridional plane to the corresponding point in the three-dimensional Cartesian coordinate system.

[0134] In the 3D flow field reconstruction step, the flow parameters corresponding to each flow surface on the virtual meridional plane, obtained from the in-flow field calculation step, are mapped to the real 3D Cartesian space, thus obtaining the 3D flow field corresponding to the design input in this iteration. This mapping is performed separately for each flow surface. For a specific flow surface, the reconstruction process includes two parts: first, reconstructing the mapped shock line 14 on the virtual meridional plane, and then reconstructing the inliers. Inliers are internal grid points. The entire flow surface is composed of several triangular grids; except for the grid points on the mapped shock line 14, the remaining grid points are called inliers. The following section uses a flow surface as an example... Figure 10 Explain the specific process of reconstruction.

[0135] The two-dimensional flow field 15 in the figure consists of flow parameters mapped onto the virtual meridional plane. The mapped shock line 14 is the mapping of the shock line 6 of the flow surface to be reconstructed onto the virtual meridional plane. Meridian 4 corresponds to the flow surface to be reconstructed. The real shock line 16 is the reconstruction 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 meridional plane according to the direction determined by 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 reconstructing the true shock line 16, the reconstruction of the interior points can begin. The reconstruction of the interior points is carried out layer by layer, starting from the layer of interior points closest to the true shock line 16 and progressing layer by layer towards the direction away from the true shock line 16. Figure 10Points 17-22 represent the inner points of the first to sixth layers, respectively. During reconstruction, the position of the inner point 17 in the three-dimensional Cartesian coordinate system is solved based on 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 in the virtual meridional plane. Then, the velocity components V of the inner point 17 in each direction in the Cartesian coordinate system are calculated. X V Y and V Z Finally, the static pressure (p) and density (ρ) characteristics of each interior point in the virtual meridional plane are assigned to the corresponding interior points in Cartesian space, thus completing the reconstruction of the first layer of interior points 17. Repeating the above process layer by layer completes the reconstruction of the interior points of the entire flow surface. Repeating the above 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 wave surface 1 and the bulge surface.

[0137] The final step of the SDSI method is error checking. This step aims to determine if the calculation results in the current iteration meet the requirements. If they do, the calculation is complete and the resulting bulge surface is output. Otherwise, the flow surface obtained in the current iteration, passing through each leading edge point, will replace the flow surface calculated in the previous iteration, and a new iteration cycle will begin.

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

[0139]

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

[0141] Specifically, a preset value of ε of 2%-2.5% is sufficient to achieve the reverse design accuracy required for engineering.

[0142] Error judgment is performed only from the second iteration calculation. In order to determine whether the result of the current iteration calculation meets the requirements, if it does, the calculation is completed and the obtained iterative bulge surface is output. Otherwise, the iterative flow surface obtained by the current iteration calculation through each discrete point 2 will replace the initial flow surface 3 at the beginning of the previous iteration calculation, and a new iteration 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] To verify the effectiveness of the SDSI method proposed in this patent, the following method was used: Figures 11a-11c The three typical pressure distributions shown were used as design inputs to reverse engineer the bulge. The resulting bulge was numerically simulated and the results were analyzed. Figure 11a A schematic diagram of the pressure distribution of the booster bulge according to a specific embodiment of the present invention is shown. Figure 11b A schematic diagram of the pressure distribution of the pressure-reducing bulge according to a specific embodiment of the present invention is shown. Figure 11c A schematic diagram of the pressure distribution of a transverse pressure bulge according to a specific embodiment of the present invention is shown. The verification process uses the three typical pressure distributions shown in the figure as design inputs to reverse design the bulge, performs numerical simulation on the obtained bulge, and analyzes the results.

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

[0146] Since the SDSI method does not consider viscosity effects, a density-based Euler equation solver was used in the numerical simulation. 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, spatial discretization employed a second-order upwind method, and gradients were calculated using the least squares element basis method. A structured grid was used in the simulation. To improve resolution at the leading edge and shock wave, a pressure gradient-based adaptive grid method was employed. After two adaptive processing steps, the number of grid cells in each example was approximately 20 to 30 million. The incoming 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 A simulation cloud diagram of the inflator bulge according to a specific embodiment of the present invention is shown. Figure 12b A simulation cloud diagram of the voltage reduction bulge according to a specific embodiment of the present invention is shown. Figure 12c Simulation contour plots of a transverse pressure bulge according to a specific embodiment of the present invention are shown. Three contour plots compare the simulated pressure distribution with a preset pressure distribution. The contour plots represent the simulated pressure distribution, and the thick solid lines represent the preset values. It can be seen from the figures that the simulated pressure distribution basically matches the preset values ​​well, with only a slight difference at the rear of the transverse pressure bulge. Statistical analysis shows that the maximum error between the simulated bulge surface pressure and the preset pressure is approximately 4.9%, which meets the requirements of engineering practice. The above simulation results demonstrate that the three-dimensional flow field reverse solution method based on shock wave-driven surface iteration proposed in this application can realize the reverse design of bulges with arbitrary preset three-dimensional pressure distributions. This method will provide a solid foundation for related engineering explorations.

[0148] This application proposes a bulge design method with preset arbitrary three-dimensional pressure. It discretizes the three-dimensional space using artificially given flow surfaces and replaces the direct solution of the three-dimensional flow field with the solution of the flow field within each flow surface. When solving for each flow surface, it is assumed that the flow around each point on the flow surface is an axisymmetric flow with a different axis of symmetry at different points, ensuring a more accurate approximation to the original three-dimensional flow. Simultaneously, a shock-driven iterative method is used to solve for the shape of the flow surface in the discrete three-dimensional space, addressing the problem that flow field solution methods based on classical kissing theory cannot determine the shape of the kissing surface when pressure distribution is used as the design input. The shapes of the shock surface 1 and the iterative flow surface change in each iteration. After multiple iterations of the three-dimensional flow field, the shape of the flow surface tends to converge. At this point, integrating the flow fields in each flow surface yields the three-dimensional flow field and bulge surface corresponding to the design input.

[0149] The above description is merely a preferred embodiment of this application and an explanation 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 technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above 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, Includes the following steps: S1: Input a preset three-dimensional pressure distribution and leading edge line, generate an initial shock surface corresponding to the three-dimensional pressure distribution, and discretize the leading edge line into a number of discrete points to construct a number of initial flow surfaces corresponding to each of the discrete points; S2: Solve for the radius of curvature at each point within each initial flow surface and the flow surface pressure distribution corresponding to each initial flow surface, wherein the process of solving for the radius of curvature includes: S201: Divide each of the initial flow surfaces into several flow surface grids; S202: Determine the first grid point on the initial flow surface to be solved, and extract the second and third grid points on two adjacent initial flow surfaces that correspond to the first grid point; S203: Construct an arc that passes through the first grid point, the second grid point, and the third grid point simultaneously, wherein the radius of the arc is the radius of curvature corresponding to the first grid point; The solution process for the surface pressure distribution includes: S211: Project the wall line geometry parameters of the initial flow surface onto the plane where the preset three-dimensional pressure distribution is located to obtain the projection curve; 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; S213: Assign the pressure values ​​of each point on the projection curve to the corresponding points on the wall line, and integrate the pressure values ​​of each point on the wall line to obtain the flow surface pressure distribution corresponding to the initial flow surface; S3: Based on the radius of curvature and pressure distribution of each initial flow surface, the points on the initial flow surface are twisted to the virtual meridional surface, and the flow parameters of the points on each initial flow surface on the virtual meridional surface are obtained using the improved two-dimensional feature line method. S4: Construct the shock wave preset line of the initial shock wave surface. The shock wave preset line includes several meridians and several parallels. The meridians and parallels divide the initial shock wave surface into several shock wave grids, and generate several local cut surfaces of the initial flow surface corresponding to each shock wave grid. S5: Based on the shock wave preset line and the local tangent surface, the flow parameters on each initial flow surface are mapped to a 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 containing the iterative shock wave surface and the iterative bulge surface. 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 the initial shock surface with the iterative flow surface and the iterative shock surface obtained by the current iteration calculation and perform the next round of iteration calculation. Repeat steps S2-S6.

2. The bulge design method according to claim 1, characterized in that, In step S1, the process of constructing the initial flow surface includes: S101: Determine the direction of the kissing surface corresponding to the discrete point based on the shape of the leading edge; S102: Determine the pressure value of the discrete point by interpolation based on the preset three-dimensional pressure distribution; S103: Substitute the pressure values ​​at the discrete points into the Rankine-Hugoniot shock transition equation to obtain the corresponding shock angle and wall deflection angle. Determine the wall line and shock line of the tangent surface based on the shock angle and the wall deflection angle. Integrate the wall line and the shock line to obtain the initial flow surface.

3. The bulge design method according to claim 1, characterized in that, In S3, the flow around the point on the initial flow surface is approximately an independent axisymmetric flow. Starting from the second round of iteration calculation, the flow parameters obtained from the previous round of iteration calculation are used to perform two-dimensional interpolation on the radius of curvature.

4. The bulge design method according to claim 1, characterized in that, In S4, each meridian corresponds to an initial flow surface, and the meridian intersects the initial flow surface at a point on the leading edge. The points corresponding to each meridian are connected to form the parallels of latitude. The meridian is composed of several meridian grid lines connected end to end. The meridian grid lines are the intersection lines of the initial shock surface and the local tangent surface.

5. The bulge design method according to claim 4, characterized in that, S4 further includes: S401: Determine the intersection point of the initial flow surface and the leading edge line as the first intersection point, and obtain the coordinates of the first intersection point and the coordinates of each vertex of the shock mesh corresponding to the first intersection point; S402: Calculate the normal vector of the mesh plane formed by the lines connecting the vertices using the cross product method; S403: Combining the normal vector and the free flow velocity vector, the local tangent surface corresponding to the initial flow surface within the shock wave grid range is obtained, and 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 cutting surface and the grid plane as the 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; S405: Using the second intersection point as the starting intersection point of the next shock wave grid, solve for all the meridian grid lines and the local cross-sections corresponding to the initial flow surface in sequence.

6. The bulge design method according to claim 1, characterized in that, In step S5, the initial flow surface reconstruction process includes: S501: Reconstruct the shock line of the initial flow surface onto the mapped shock line on the virtual meridian, and deflect the mapped shock line according to the direction determined by the meridian corresponding to the initial flow surface and the local tangent surface to obtain the real shock line; S502: The points mapped from the initial flow surface onto the virtual meridional surface are layered along a direction away from the real shock line, wherein the points located outside the real shock line are all interior points of the initial flow surface; S503: Perform layer-by-layer interior point reconstruction on the initial flow surface. Based on the reconstructed real shock line and the flow parameters of the interior points on the virtual meridional surface, solve the position of the interior points in the three-dimensional Cartesian coordinate system of each layer, and generate the reconstructed iterative surface.

7. The bulge design method according to claim 6, 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 meridional plane. S503 further includes: S5031: The position of the interior point in the three-dimensional Cartesian coordinate system is obtained based on the axial position ξ, radial position ζ, flow angle θ of the interior point on the virtual meridional plane and the coordinates of the reconstructed real shock line; S5032: Decompose the velocity V of the interior point on the virtual meridional 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 meridional plane to the corresponding point in the three-dimensional Cartesian coordinate system.

8. The bulge design method according to claim 1, characterized in that, In step S6, the three-dimensional flow field obtained from the initial flow surface iteration calculation is not subject to error judgment. Error judgment begins from the three-dimensional flow field obtained from the second iteration calculation. The condition for error judgment is... Where E is the relative error of the Cartesian coordinates of any point within the three-dimensional flow field. As the preset error value, E is calculated as follows: ； Among them, X cur Y cur and Z cur X is the Cartesian coordinate of the point obtained in this iteration. last Y last and Z last These are the corresponding grid coordinates calculated in the previous iteration.

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