An Improved Diffuser Design Method Based on Matrix Transformation

Abstract

The present invention discloses an improved design method for a diffuser based on matrix transformation. First, the inlet and outlet position information of the diffuser is extracted, and then a double-coefficient adjustable polynomial is used to design the center line of the diffuser between the centroids of the inlet and outlet sections, as well as the variation law of each cross-sectional area of ​​the diffuser along the center line. In terms of the transition of the inlet and outlet shapes of the diffuser, after mapping the inlet and outlet sections to the ξ‑η space, an improved algorithm based on matrix transformation is used to find several transition shapes between the inlet and outlet sections. The inlet and outlet shapes and each transition shape together constitute the local cross-sectional shapes of the diffuser along the center line. Based on the above cross-sectional shape, cross-sectional area variation law and centerline variation law, the final three-dimensional geometry of the diffuser can be constructed in the o‑xyz three-dimensional coordinate system, and the flexible and controllable design of the three-dimensional geometric modeling of the diffuser can be realized.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft air inlets, and in particular relates to an improved design method for an air inlet diffuser. Background Art

[0002] As an important component of the aircraft propulsion system, the air inlet is located at the upstream of the aircraft engine, and is responsible for capturing flow and adjusting the airflow quality for the downstream engine. The diffuser is an important component of the air inlet. From the perspective of geometric characteristics, the diffuser is essentially a three-dimensional pipe with a gradually expanding cross-sectional area. It achieves deceleration and pressure increase of the subsonic airflow in the pipe by expanding the area.

[0003] There are currently two approaches to designing diffuser three-dimensional geometric surfaces: (1) One is to use commercial modeling software and the bridging function in the software to generate a smooth diffuser surface between given inlet and outlet sections; (2) The other is to design several two-dimensional transition sections and then arrange the transition sections in sequence to form the diffuser's three-dimensional surface.

[0004] The disadvantages of the first design approach are obvious. It is impossible to accurately control the bending law and area expansion law of the diffuser, which will make it difficult to control the flow in the diffuser and carry out subsequent surface optimization work.

[0005] The second design idea is widely used in aerospace engineering design ("A Design Method for Complex Variable Cross-Section Inlet", Journal of Aerospace Power, 2009, 24(06): 1357-1363), which takes into account the controllability and algorithm convenience of the shape transition between the given inlet and outlet. The specific implementation process of this idea is to first use a specific algorithm to algebraically represent the inlet and outlet cross-sections (i.e., algebraize the geometric shapes), for example, express them as a function ("Universal Subsonic Diffuser Design Method", CN201410187196.X), or a matrix ("A Stealth Serpentine Inlet Design Method Based on Matrix Transformation", CN202210241584.6), then interpolate between the algebraic quantities of the inlet and outlet cross-sections to generate several transition algebraic quantities, and then inversely calculate the transition cross-sections based on these transition algebraic quantities, and finally enlarge, rotate, and translate these transition cross-sections in three-dimensional space to finally form the three-dimensional surface of the diffuser.

[0006] However, as the requirements for aircraft radar stealth performance become higher and higher, the centerline of the diffuser is required to be bent in a more complex way in the air inlet, such as an "S" shape with a large offset, or even a "double S" shape. Under this technical requirement, the classic Lee centerline (CC Lee, "Subsonic diffuser design and performance for advanced fighter aircraf t", AIAA Journal, 1985.) used in the conventional design process is unable to meet the requirements. This method only provides three change rules: "fast at the beginning and slow at the end", "quite fast and slow" and "slow at the beginning and fast at the end". Since these three rules are monotonically increasing functions, it is impossible to directly generate a "double S" centerline. If the classic Lee centerline is used to design a "double S" diffuser with good stealth capability, the centerline must be designed in sections between the inlet and outlet sections, which increases the complexity of the design process. In addition, the centerline finally generated by this method has only 3×3=9 possibilities at most, and the design results lack diversity and sufficient flexibility. A stealth serpentine air inlet design method proposed by Nanjing University of Aeronautics and Astronautics ("A stealth serpentine air inlet design method based on matrix transformation", CN202210241584.6) uses a quintic polynomial to design the centerline, but faces a similar problem, that is, in order to produce a "double S" shaped centerline, the front and rear "single S" shaped centerlines must be designed separately in sections and then spliced ​​together.

[0007] In addition, the existing design methods ("Universal Subsonic Diffuser Design Method CN201410187196.X", "Improved Universal Subsonic Diffuser Design Method CN202110392258.0", "A Stealth Serpentine Inlet Design Method Based on Matrix Transformation C202210241584.6") are very inconvenient when designing left-right asymmetric diffusers. They all require the diffuser design process to be artificially divided into left half design and right half design. After completing the left and right half designs, they are spliced ​​into a complete diffuser.

[0008] In summary, the main problems of the existing diffuser design method are:

[0009] (1) The bending law of the diffuser centerline is either relatively simple, with only one of the three options: fast at the front and slow at the back, fast and slow equally, or slow at the front and fast at the back. Alternatively, a complex quintic polynomial is used. Although it is more flexible, the calculation process of the polynomial coefficients is relatively cumbersome. In addition, for the "double S" centerline, the above methods all require segmented design and then splicing, which makes the design process lengthy.

[0010] (2) For asymmetric diffusers, the transition between the inlet and outlet sections cannot be completed at one time during the design process. Usually, the inlet and outlet sections need to be artificially divided into two halves. The division process is arbitrary and needs to be designed separately and then spliced ​​together, resulting in a lengthy design process.

[0011] Therefore, a new technical solution is needed to solve the above technical problems. Summary of the invention

[0012] In view of the above problems, the present invention provides an improved design method for diffusers based on matrix transformation. The improved design method not only inherits the idea of ​​describing the cross-sectional contour line through a matrix, but also improves the centerline generation method and the cross-sectional transition method, avoiding the front and rear segmented design of the centerline and the left and right half-molding of the diffuser profile, and realizing the controllable and flexible design of the centerline and the one-time molding of the diffuser's three-dimensional geometric profile.

[0013] In order to achieve the above object, the present invention may adopt the following technical solutions:

[0014] A diffuser improvement design method based on matrix transformation comprises the following steps:

[0015] (1) Based on the overall constraint parameters of the engine, i.e., the given diffuser inlet and outlet cross sections, the diffuser inlet and outlet position information in the o-xyz three-dimensional coordinate system is extracted, and the engine inlet and outlet position information is algebraically converted;

[0016] (2) Based on the centroid coordinates of the diffuser inlet and outlet cross sections, the flow distances, longitudinal offsets, and spanwise offsets of the diffuser inlet and outlet cross sections are obtained;

[0017] (3) Design the diffuser centerline using a linear function or a double-coefficient adjustable polynomial;

[0018] (4) Mapping the three-dimensional discrete points of the diffuser inlet and outlet cross sections onto a virtual ξ-η two-dimensional plane;

[0019] (5) Design M central control sections in the ξ-η two-dimensional plane;

[0020] (6) Discretize the reference circle in the ξ-η two-dimensional plane to obtain the reference circle matrix

[0021] (7) Based on the reference circle matrix Obtain the coefficient matrix of the diffuser inlet cross section and the coefficient matrix of the diffuser outlet cross section

[0022] (8) Determine the number of transition sections K including the center control section and calculate the coefficient matrix of K transition sections by cubic spline interpolation

[0023] (9) Coefficient matrix based on transition section Calculate the matrix expression of each transition section in the ξ-η two-dimensional plane

[0024] (10) The matrix expression of the transition section is modified so that the cross-sectional area described by the matrix expression of the transition section is equal to the area of ​​the reference circle;

[0025] (11) Determine the area variation of the diffuser along the centerline using a linear function or a double-coefficient adjustable polynomial;

[0026] (12) Based on the area change law, the final two-dimensional figure of the transition section is obtained, that is, the matrix describing the section in three-dimensional space

[0027] (13) The matrix of each transition section in the o-xyz coordinate system Rotation and translation are performed to obtain the final three-dimensional shape of the diffuser.

[0028] Furthermore, in step (1), according to the overall constraint parameters of the engine, that is, the given diffuser inlet and outlet cross sections, N discrete points are extracted with equal arc lengths on the contour lines of the diffuser inlet cross section and the diffuser outlet cross section in the o-xyz three-dimensional coordinate system, and the three-dimensional coordinates of each point are obtained, and the three-dimensional coordinates of each point are placed in a matrix of N rows and 3 columns. and

[0029]

[0030] is a matrix composed of discrete points extracted from the diffuser inlet cross-section contour line, where the first column Indicates the x-axis coordinate of the point, the second column Indicates the y-axis coordinate of the point, the third column Indicates the z-axis coordinate of a point; the superscript in indicates that the point is located on the contour line of the diffuser inlet section, the subscripts 1, 2, ... N indicate the i-th discrete point, and N is the number of discrete points on each curve;

[0031] is a matrix composed of discrete points extracted from the diffuser outlet cross-sectional contour line, where the first column Indicates the x-axis coordinate of the point, the second column Indicates the y-axis coordinate of the point, the third column represents the z-axis coordinate of a point; the superscript out indicates that the point is located on the contour line of the diffuser outlet section, the subscripts 1, 2, ... N represent the i-th discrete point, and N is the number of discrete points on each curve;

[0032] Based on the coordinate matrix of each discrete point on the contour line and Calculate the normal vector of the diffuser inlet section and the normal vector of the diffuser outlet section At the same time, the centroid C of the inlet section is calculated in Coordinates and centroid C of the outlet section out The coordinates of

[0033] According to the normal vector and Determine the inclination information of the centerline at the inlet and outlet sections of the diffuser, where θ y-in yes The angle between the projection on the XY plane and the x-axis, θ y-out yes The angle between the projection on the XY plane and the x-axis; θ z-in yes The angle between the projection on the XZ plane and the z-axis, θ z-out yes The angle between the projection on the XZ plane and the z-axis;

[0034] The arithmetic mean method is used to define the center position of the diffuser inlet section and the diffuser outlet section, which is recorded as the centroid; the following formula is the centroid of the inlet section C in x c,in ,y c,in ,z c,in The coordinates of the solution expression and the x of the centroid of the outlet section c,out ,y c,out ,z c,out The coordinate solution expression of ; similarly, the centroid position of any discretized cross section can be solved according to the definition.

[0035]

[0036]

[0037] The above physical quantities θ y-in ,θ y-out ,θ z-in ,θ z-out , C in and C out That is the entry and exit location information.

[0038] Furthermore, in step (2), the centroid information of the inlet and outlet cross sections of the diffuser is obtained by algebraically converting the inlet and outlet position information in step (1); based on the centroid C of the diffuser inlet cross section in , the centroid C of the diffuser outlet section out The coordinates of the diffuser inlet and outlet sections are calculated according to the following formula to obtain the flow distance between the diffuser inlet and outlet sections, that is, the flow field length L of the diffuser is recorded as ΔX; the longitudinal and spanwise offsets of the diffuser inlet and outlet sections are obtained, recorded as ΔY and ΔZ;

[0039] Where ΔY, ΔZ and ΔX are solved as shown in the formula:

[0040]

[0041] Furthermore, in step (3), a parametric equation is used to describe the diffuser centerline, where f 0 (t),f 1 (t),f 2 (t) The specific form is a linear function, or a cubic polynomial with double adjustable coefficients, f 0 (t),f 1 (t),f 2 (t) Once determined, the centerline of the diffuser is uniquely determined;

[0042]

[0043] In the formula, x c,in ,y c,in and z c,in are the coordinates of the starting point of the diffuser's three-dimensional centerline, where x c,out ,y c,out and z c,out are the coordinates of the centroid of the diffuser outlet cross section in the rectangular coordinate system o-xyz;

[0044] The variable t in the parametric equation ranges from 0 to 1, and f 0 (t), f 1 (t) and f 2 (t) are all function expressions with parameter t as the independent variable, and their function values ​​also vary between 0 and 1. 0 (t) is a linear function, f 1 (t) and f 2 (t) are all double-coefficient adjustable polynomials and have similar forms, so only f is given. 1 (t) is a functional expression;

[0045]

[0046] Among them, a 1 、a2 、a 3 and a 4 is the unknown coefficient, which can be solved according to the given conditions; 0 (t), α 1 (t), β 0 (t) and β 1 (t) is the basis function of the double-coefficient adjustable polynomial, where and There are two adjustable coefficients. After the unknown coefficients are determined, the adjustable coefficients are uniquely determined to obtain the function distribution of various bending laws;

[0047]

[0048] The formula is converted into matrix form, and f 0 (t),f 1 (t),f 2 (t) is recorded as F(t), and the expression converted into matrix form is as follows:

[0049]

[0050] For a double coefficient adjustable polynomial, the expression of the F(t) function is as follows:

[0051]

[0052] For the unknown coefficient a 1 、a 2 、a 3 、a 4 , given the following constraints to solve:

[0053]

[0054] In the above equations, y' is the first-order derivative of y; where θ y-in yes The angle between the projection on the XY plane and the x-axis, θ y-out yes The angle between the projection on the XY plane and the x-axis; θ z-in yes The angle between the projection on the XZ plane and the z-axis, θ z-out yes The angle between the projection on the XZ plane and the z-axis; c,in is the coordinate of the centroid of the diffuser inlet section in the y-axis direction, y c,out is the coordinate of the centroid of the diffuser outlet cross section in the y-axis direction;

[0055] Solve the above equations to find the polynomial coefficient a 1 、a 2 、a3 、a 4 At this time, the change law of the diffuser centerline in the XY plane depends only on two adjustable coefficients and By adjusting the coefficient and The center line of the XY plane diffuser can be changed according to simple or complex rules;

[0056] Similarly, determine the unknown coefficients in the diffuser centerline equation on the XZ plane, and make the centerline consist of only two adjustable coefficients and adjust;

[0057] After the diffuser centerline is determined, the total length S of the diffuser centerline is obtained as the total arc length.

[0058] Furthermore, in step (4), the N-row and 3-column matrix and Transform so that the transformed The numbers in the first column of the matrix are the same, that is, the coordinates in the x direction are the same, and the transformed The numbers in the first column of the matrix are the same, and then and Mapped to a virtual ξ-η two-dimensional plane, and in the ξ-η plane a matrix with N rows and 2 columns To represent the diffuser inlet cross section, a matrix with N rows and 2 columns is To represent the diffuser outlet cross section;

[0059]

[0060] Furthermore, in step (5), the contour line of the center control section is designed in the ξ-η plane, and the arc length position percentage s of the center control section centroid on the diffuser centerline is specified. m , 0<s m <1, and the contour line of the central control section in the ξ-η plane is discretized into N points with equal arc length, and described by a matrix with N rows and 2 columns Where m = 1, 2, ... M;

[0061]

[0062] Furthermore, in step (6), a full circle with a radius of 1 m is used as a reference circle in the ξ-η two-dimensional plane and the reference circle is discretized with equal arc lengths; N discrete points are used to obtain the coordinates of the reference circle in the ξ-η two-dimensional plane to form a matrix with N+1 rows and 2 columns: The data in the first and last rows are the same; the matrix It is called the reference circle matrix;

[0063]

[0064] Furthermore, in step (7), define is the coefficient matrix at the diffuser inlet, which satisfies is a matrix with N rows and N+1 columns; the matrix The specific expansion is as follows:

[0065]

[0066] Expands to:

[0067]

[0068] According to the above equation, the matrix can be solved Similarly, the coefficient matrix of the diffuser outlet is obtained: and the coefficient matrix of the center control section

[0069] Furthermore, in step (8), the total number of transition sections K is specified, and the arc length position percentage s of the centroid of each transition section on the diffuser centerline is specified. k , 0<s k <1, where k = 1, 2, 3 ... K; if there is a center control section, then the center control section is one of the transition sections; the arc length percentage s of the transition section k is the independent variable, with the coefficient matrix is the variable to be interpolated, and the cubic spline interpolation method is used to calculate value; if there is a center control section, it is necessary to perform interpolation in sections during the calculation of the transition coefficient matrix, and the interpolation method still uses cubic spline interpolation.

[0070] Further, in step (9), according to Step (6) finds And the value obtained in step (8) Calculate the matrix expression of each transition section in the ξ-η two-dimensional plane

[0071] The matrix corresponding to the contour line of the first transition section is The matrix corresponding to the contour line of the second transition section is The matrix corresponding to the contour line of the third transition section is And so on, the matrix corresponding to the last transition section is calculated. The following is the matrix expression of the transition section: The calculation formula is:

[0072]

[0073] Furthermore, in step (10), the matrix expression of the transition section calculated in step (9) is Calculate the area enclosed by each transition section in the ξ-η two-dimensional plane, and use the matrix expression Appropriate scaling and correction are performed to make The final area enclosed in the ξ-η two-dimensional plane is equal to the area of ​​the reference circle. After correction, the matrix expression of each transition section in the ξ-η two-dimensional plane is still recorded as

[0074] First, based on step (9), a discrete point matrix for describing the transition section contour line has been obtained: Fit the graph, and then calculate the area of ​​the transition section. The area of ​​the Kth transition section is A. k ; Let the area of ​​the reference circle be A base ;

[0075] Next, determine A k , A base The ratio of the areas to obtain the scale factor Where r represents the ratio of the radius of the circle with the same area as the transition cross section to the radius of the reference circle;

[0076] Then, the matrix After correction, the corrected matrix still uses Represents; the modified expression is shown in the formula

[0077]

[0078] All transition sections are processed as above to obtain a series of transition sections with areas equal to the reference circle, as well as a discrete point matrix describing the transition sections.

[0079] Furthermore, the change law of the diffuser cross-sectional area is specified as

[0080] A k =A in +(A out -A in )·w(s k )

[0081] Among them A k represents the area of ​​the kth transition section, w(s k ) is a linear function or a double-coefficient adjustable polynomial; the coefficient to be determined is determined by the given diffuser inlet and outlet conditions. At this time, the area change law is expressed by two adjustable coefficients. and Make adjustments;

[0082] Determine the scaling factor G of the transition section k , where k = 1, 2, 3...K, the specific expression is as follows:

[0083]

[0084] Where A k represents the area of ​​the kth transition section, A out is the diffuser outlet cross-sectional area.

[0085] Furthermore, in step (12), according to the area of ​​the Kth transition cross section determined in step (10), the matrix expression of the transition cross section is enlarged or reduced again according to the area change rule of step (11): The final matrix expression describing the transition section graph is formed, and each graph is recorded as a matrix with N rows and 3 columns. The first column of numbers is 0, and the last two columns are the same as the numbers after enlarging or reducing The same is to convert the contour information in the ξ-η two-dimensional plane into the three-dimensional coordinate system o-xyz, but still keep the normal vector and x direction of the figure the same;

[0086]

[0087] Further, in step (13), K discrete points are extracted with equal arc length on the center line determined in step (3), and the coordinate system is Each transition section represented by the transition section is rotated and translated. After rotation and translation, the centroid of any k-th transition section coincides with the k-th point on the centerline of the diffuser, and is perpendicular to the centerline of the diffuser at this point, k = 1, 2, 3 ... K. Subsequently, a three-dimensional expansion duct that meets the requirements, namely the inlet diffuser, is obtained.

[0088] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are:

[0089] (1) The bending law, area expansion law and cross-sectional transition law of the diffuser centerline are more abundant. Not only can the traditional three types of change laws, namely, slow at the beginning and fast at the end, fast at the beginning and slow at the end, and slow and fast equally, be realized, but more change laws can also be realized by adjusting the adjustable coefficient. For the "double S" centerline, segmented design is not required, which simplifies the design process.

[0090] (2) For diffusers that are asymmetric on the left and right, the transition between the inlet section and the outlet section can be completed in one go, and there is no need to artificially divide the diffuser into left and right halves for segmented design.

[0091] The design method provided by the present invention can be stored in a storage medium as a computer program, and includes the following technical solutions:

[0092] An electronic device, comprising:

[0093] One or more processors; and a storage device for storing one or more programs, when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned improved diffuser design method based on matrix transformation.

[0094] as well as:

[0095] A computer readable medium stores a computer program, which, when executed by a processor, implements the above-mentioned improved diffuser design method based on matrix transformation. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 Schematic diagram of two complex “double S-shaped” center lines under different input conditions.

[0097] Figure 2 It is a schematic diagram of the common inlet section, center control section and outlet section contour lines.

[0098] Figure 3 It is a two-dimensional plane schematic diagram and a three-dimensional scatter plot of the transformation of the annular fan-shaped inlet section to the circular outlet section without a central control section.

[0099] Figure 4 It is a two-dimensional plane schematic diagram and a three-dimensional scatter plot of the transformation of the trapezoidal inlet section to the circular outlet section without a central control section.

[0100] Figure 5 It is a two-dimensional plane schematic diagram and a three-dimensional scatter plot of the transformation of the trapezoidal inlet cross-section to the circular outlet cross-section under the condition of a central control section.

[0101] Figure 6 It is a design flow chart.

[0102] Figure 7 It is a schematic diagram of the input conditions, designed center line and area change law adopted for the specific implementation case one.

[0103] Figure 8 It is a front view of the three-dimensional diffuser generated in the specific implementation case one.

[0104] Fig. 9 It is a top view of the three-dimensional diffuser generated in the specific implementation case one.

[0105] Fig.10 It is a side view of the three-dimensional diffuser generated in the specific implementation case one.

[0106] Fig.11 It is a schematic diagram of the input conditions, designed center line and area change law used in the specific implementation case 2.

[0107] Fig.12 It is a three-dimensional view of the three-dimensional diffuser generated in the specific implementation case 2.

[0108] Fig.13 It is a front view of the three-dimensional diffuser generated in the specific implementation case 2.

[0109] Fig.14 It is a top view of the three-dimensional diffuser generated in the specific implementation case 2.

[0110] Fig.15 It is a side view of the three-dimensional diffuser generated in the specific implementation case 2. DETAILED DESCRIPTION

[0111] In order to make the purpose, design process, technical method and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings.

[0112] In the drawings of the specification Figure 6 This is the design flow chart of the patent of this invention, such as Figure 6 As shown, the improved diffuser general design method provided by the present invention comprises the following steps:

[0113] (1) [According to the overall constraint parameters of the engine, i.e., the given diffuser inlet and outlet cross sections, extract the inlet and outlet position information in the o-xyz three-dimensional coordinate system] According to the overall constraint parameters of the engine, i.e., the given diffuser inlet and outlet cross sections, in the o-xyz three-dimensional coordinate system, extract N discrete points of equal arc length on the contour lines of the inlet and outlet cross sections, obtain the three-dimensional coordinates of each point, and place them in a matrix of N rows and 3 columns and

[0114]

[0115] is a matrix composed of discrete points extracted from the inlet cross-section contour line, where the first column Indicates the x-axis coordinate of the point, the second column Indicates the y-axis coordinate of the point, the third column Indicates the z-axis coordinate of a point. The superscript in indicates that the point is located on the inlet section contour line, and the subscripts 1, 2, ... N indicate the i-th discrete point, where N is the number of discrete points on each curve;

[0116] is a matrix composed of discrete points extracted from the inlet cross-section contour line, where the first column Indicates the x-axis coordinate of the point, the second column Indicates the y-axis coordinate of the point, the third column Indicates the z-axis coordinate of a point. The superscript out indicates that the point is located on the exit section contour line, and the subscripts 1, 2, ..., N indicate the i-th discrete point, where N is the number of discrete points on each curve;

[0117] Based on the coordinate matrix of each discrete point on the contour line and Calculate the normal vectors of the inlet and outlet sections and Simultaneously calculate the centroid C of the inlet and outlet sections in and C out The coordinates of .

[0118] According to the normal vector of the inlet and outlet sections and The inclination information of the centerline at the inlet and outlet sections can be determined, where θ y-in yes The angle between the projection on the XY plane and the x-axis, θ y-out yes The angle between the projection on the XY plane and the x-axis; θ z-in yes The angle between the projection on the XZ plane and the z-axis, θ z-out yes The angle between the projection on the XZ plane and the z-axis;

[0119] The arithmetic mean is used to define the center position of the inlet section and the outlet section, which is recorded as the centroid. Formula (1) is the centroid of the inlet section C in x c,in ,y c,in ,z c,in Similarly, according to the definition, the centroid position of any discretized cross section can be solved, including the centroid C of the outlet cross section. out .

[0120]

[0121] The above physical quantities θ y-in ,θ y-out ,θ z-in ,θ z-out and C in That is, "entry and exit location information".

[0122] (2) [Calculate the diffuser flow length and longitudinal and spanwise offsets] Based on the centroid coordinates C of the inlet and outlet sections in and C out, obtain the flow distance of the inlet and outlet sections, that is, the flow length L of the diffuser is recorded as ΔX; obtain the offset distance of the inlet and outlet sections of the diffuser in the longitudinal and span directions, recorded as ΔY and ΔZ.

[0123] The solution of ΔY, ΔZ and ΔX is shown in formula (2):

[0124]

[0125] (3) [Centerline design] The centerline is described using the parametric equation shown in formula (3), where f 0 (t),f 1 (t),f 2 (t) The specific form is a linear function, or a cubic polynomial with double adjustable coefficients, f 0 (t),f 1 (t),f 2 Once (t) is determined, the centerline of the diffuser is uniquely determined.

[0126]

[0127] In the formula, x c,in ,y c,in and z c,in They are the centroid of the inlet section C in The coordinates of x c,out ,y c,out and z c,out are the outlet cross-section centroid C out Coordinates in o-xyz.

[0128] The variable t in the parametric equation ranges from 0 to 1, and f 0 (t), f 1 (t) and f 2 (t) are all function expressions with parameter t as the independent variable, and their function values ​​also vary between 0 and 1. 0 (t) is a linear function, f 1 (t) and f 2 (t) are all double-coefficient adjustable polynomials and have similar forms, so only f is given. 1 The functional expression of (t) is shown in formula (4):

[0129]

[0130] Among them, a 1 、a 2 、a 3 and a 4 is the unknown coefficient, which can be solved according to the given conditions. 0 (t), α1 (t), β 0 (t) and β 1 (t) is the basis function of the double-coefficient adjustable polynomial, where and There are two adjustable coefficients. After the unknown coefficients are determined, the adjustable coefficients can be uniquely determined to obtain the function distribution of various bending laws.

[0131]

[0132] Therefore, the above formula (3) can also be converted into a matrix form. For the convenience of writing, f 0 (t),f 1 (t),f 2 (t) is denoted as F(t), and the specific matrix expression of formula (3) is as follows:

[0133]

[0134] For a double coefficient adjustable polynomial, the expression of the F(t) function is as follows:

[0135]

[0136] For the unknown coefficient a 1 、a 2 、a 3 、a 4 , given the following constraints to solve:

[0137]

[0138] In the above equations, y' is the first-order derivative of y. y-in yes The angle between the projection on the XY plane and the x-axis, θ y-out yes The angle between the projection on the XY plane and the x-axis; θ z-in yes The angle between the projection on the XZ plane and the z-axis, θ z-out yes The angle between the projection on the XZ plane and the z-axis; c,in and c,out They are the coordinates of the centroid of the inlet and outlet sections in the y-axis direction respectively.

[0139] The polynomial coefficient a is obtained by solving the above equations. 1 、a 2 、a 3 、a 4 At this time, the change law of the center line of the XY plane depends only on two adjustable coefficients and Usually, by adjusting the coefficients, the center line of the XY plane can be changed according to a simple rule.

[0140] Similarly, the unknown coefficients in the centerline equation on the XZ plane can be determined, and the centerline is composed of only two adjustable coefficients and adjust.

[0141] The drawings of this patent specification Figure 1 Gives different and When taking values, center lines with different bending patterns can be formed at one time between the starting point and the end point, including a "double S-shaped" center line with a more complex bending pattern.

[0142] After the center line is determined, the total length S (total arc length) of the center line can be obtained.

[0143] (4) [Map the three-dimensional discrete points of the inlet and outlet sections to the virtual ξ-η two-dimensional plane] The N-row and 3-column matrix obtained by discretizing the inlet and outlet sections in the o-xyz coordinate system and Transform them so that the numbers in the first column of the transformed matrices are the same, that is, the coordinates in the x direction are the same, and then map them to a virtual ξ-η two-dimensional plane, and use a matrix with N rows and 2 columns in the ξ-η plane and To represent the inlet and outlet cross-sections. Common two-dimensional schematic diagrams of inlet and outlet cross-sections and discrete point schematic diagrams of half-side contour lines are shown below: Figure 2 As shown, even for irregular shapes, a schematic diagram of the entire contour obtained by discretizing it in an equal arc length manner can also be given.

[0144]

[0145] (5) [Design of center control section] In general, when designing a diffuser, a smooth transition is usually made from the inlet section to the outlet section. However, the transition of the profile can also be controlled by designing M center control sections. In the ξ-η plane, the contour of the center control section is designed, and the arc length percentage s of the center control section centroid on the diffuser centerline is specified. m (0<s m <1), and the contour line of the central control section in the ξ-η plane is discretized into N points of equal arc length, and a matrix with N rows and 2 columns is used to describe Where m=1,2,…M.

[0146]

[0147] (6) [Discrete the reference circle in the ξ-η two-dimensional plane] In the ξ-η two-dimensional plane, define a full circle with a radius of 1 m as the reference curve (referred to as the reference circle). Extract N discrete points on the reference circle and their coordinates in the ξ-η plane with equal arc lengths to form a matrix with N+1 rows and 2 columns. The first and last rows of data are the same. is the reference circle matrix.

[0148]

[0149] (7) [Calculation of coefficient matrix for import and export] Definition is the coefficient matrix of the import, which satisfies is a matrix with N rows and N+1 columns. The specific expansion is as follows:

[0150]

[0151] Therefore Can be expanded to:

[0152]

[0153] According to the above equation, the matrix can be solved Similarly, the coefficient matrix of the export can be obtained and the coefficient matrix of the center control section

[0154] (8) [Calculate the coefficient matrix of transition sections] Specify the total number of transition sections K (including inlet and outlet sections) and the percentage s of the arc length of the centroid of each transition section on the diffuser centerline k (0<s k <1), where k=1,2,3……K. If there is a center control section, it is one of the transition sections. The arc length percentage s of the transition section k is the independent variable, with the coefficient matrix is the variable to be interpolated, and the cubic spline interpolation method is used to calculate The value of .

[0155] (9) [Inversely calculate the matrix expression of each transition section in the ξ-η two-dimensional plane] according to Step (6) finds And the value obtained in step (8) Calculate the matrix expression of each transition section in the ξ-η two-dimensional plane

[0156] For the first section, the matrix corresponding to its contour line is For the second section, the matrix corresponding to its contour line is For the third section, the matrix corresponding to its contour line is And so on, until the last section is calculated. The following is the matrix expression of the transition section: The calculation formula is:

[0157]

[0158] (10) [Modify the matrix expression of each transition section in the ξ-η two-dimensional plane] According to the matrix Calculate the area enclosed by each transition section in the ξ-η two-dimensional plane, and Appropriately scale it so that the area it finally encloses in the ξ-η two-dimensional plane is equal to the area of ​​the reference circle. After scaling correction, its matrix expression is still recorded as The detailed steps for scaling correction are as follows:

[0159] First, based on step (9), a discrete point matrix for describing the transition section contour line has been obtained: Through the discrete point matrix, the graph is fitted and then its area is calculated. The area of ​​the Kth transition section is recorded as A k ; Let the area of ​​the reference circle be A base .

[0160] Secondly, determine the ratio of the two areas to obtain the scaling factor Where r represents the ratio of the radius of a circle with the same area as the transition cross section to the radius of the reference circle.

[0161] Then, the matrix After correction, the corrected matrix still uses The corrected expression is shown in formula (7):

[0162]

[0163] All transition sections are processed as above to obtain the matrix expression of K transition sections in the ξ-η two-dimensional plane:

[0164] (11) [Specify the area change rule]

[0165] In steps (1) to (10), we only determine the shape of each cross section of the inlet duct and adjust the size of each cross section to be equal to the area of ​​the reference circle. However, the inlet diffuser requires the area of ​​the pipe cross section to gradually increase, so we need to further adjust the size of each cross section so that the area of ​​each cross section increases according to a certain rule. Therefore, the change rule of the diffuser cross section area is specified as follows:

[0166] Ak =A in +(A out -A in )·w(s k )

[0167] Among them A k represents the area of ​​the kth transition section..., w(s k ) can be a linear function or a double-coefficient adjustable polynomial. The form of the double-coefficient adjustable polynomial and the law of center line change f 1 (t) is similar in form. By given inlet and outlet conditions, the unknown coefficient can be determined. At this time, the area change law can be obtained through two adjustable coefficients and Make adjustments.

[0168] Determine the scaling factor G of the transition section k , where k = 1, 2, 3...K, the specific expression is as follows:

[0169]

[0170] Where A k represents the area of ​​the kth transition section, A out is the outlet cross-sectional area.

[0171] (12) [Obtain the final transition section]

[0172] The obtained step (10) Zoom in or out (k=1,2,3...K), zoom factor G k The final transition cross section is determined in step (11) and its matrix expression is a matrix with N rows and 3 columns: The first column of numbers is 0, and the last two columns are the same as the numbers after enlarging or reducing The same is true, that is, the contour line information in the ξ-η two-dimensional plane is converted to the three-dimensional coordinate system o-xyz, but the normal vector and x direction of the figure are still kept the same.

[0173]

[0174] (13) [In the o-xyz coordinate system, Rotate and translate to obtain the final diffuser three-dimensional surface. Extract K discrete points of equal arc length on the center line determined in step (3) and calculate the final diffuser three-dimensional surface in the o-xyz coordinate system. The represented cross sections are rotated and translated. After the rotation and translation, the centroid of any K-th cross section coincides with the K-th point on the center line and is perpendicular to the center line at this point (k = 1, 2, 3 ... K). Subsequently, a three-dimensional expansion duct (i.e., an inlet diffuser) that meets the requirements is obtained.

[0175] Based on steps (1) to (13), the diffuser three-dimensional centerline design and transition section design are finally realized. This design method realizes universality and can achieve a smooth transition from the inlet section to the outlet section under different inlet section shapes, regardless of whether there is a center control section or not.

[0176] Figure 3 The two-dimensional plane diagram and three-dimensional scatter plot of the transformation from annular sector inlet to circular outlet without central control section are given;

[0177] Figure 4 The two-dimensional plane diagram and three-dimensional scatter plot of the transformation from a trapezoidal inlet to a circular outlet without a center control section are given;

[0178] Figure 5 A two-dimensional plane diagram and a three-dimensional scatter plot of the transformation from a trapezoidal inlet to a circular outlet with a center control section are given.

[0179] The following two specific implementation cases are provided to verify the effectiveness of this design method.

[0180] Specific implementation case 1 (no central control section):

[0181] According to the above design method, the diffuser design program was written using Matlab software. Figure 3 The shapes shown are the inlet and outlet cross-sections of the air inlet. The diffuser design is carried out and other design parameters are shown in the following table:

[0182] Table 1

[0183]

[0184]

[0185] Design parameters, design center line and area change rules are as follows Figure 7 shown.

[0186] A total of 24 sections (including inlet and outlet sections) were selected in the design. The calculation results of the program were exported. The front view, top view and side view of the inlet duct model generated in UG are as follows: Figure 8 , Fig. 9 and Fig.10 shown.

[0187] Design case 2 (with central control section):

[0188] According to the above algorithm, this project uses Matlab software to write a design program for a general subsonic inlet (diffuser). Here, an inlet with an expansion ratio of 1.5 and a cross-sectional area change law of equal speed is taken as an example. The inlet cross section, center control cross section and outlet cross section are Figure 2 The geometric input conditions for the shape shown are shown in the following table:

[0189] Table 2

[0190]

[0191]

[0192] Design parameters and the design center line are as follows Fig.11 As shown, the pattern of area change is still that of slowness and speed being equal.

[0193] A total of 24 sections were selected in the design (including the inlet section, the center control section and the outlet section).

[0194] The calculation results of the program are exported, and the three-dimensional intake duct model generated in UG is as follows Fig.12 As shown, its front view, top view and side view are respectively as shown in Fig.13 , Fig.14 and Fig.15 shown.

[0195] The above-mentioned improved diffuser design method based on matrix transformation is written as a program language through software such as Matlab, and can be stored in a processor or a computer-readable medium. Therefore, the present invention also provides embodiments of an electronic device and a computer-readable medium.

[0196] An embodiment of an electronic device includes:

[0197] One or more processors; and a storage device for storing one or more programs, when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned improved diffuser design method based on matrix transformation.

[0198] An embodiment of a computer-readable medium stores a computer program, which, when executed by a processor, implements the above-mentioned improved general air intake duct design method based on matrix transformation.

[0199] In addition, there are many specific implementation methods and approaches of the present invention, and the above is only a preferred implementation of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A method for improving diffuser design based on matrix transformation, characterized in that: The following steps are included: (1) Based on the overall constraint parameters of the engine, i.e., the given diffuser inlet and outlet cross sections, the diffuser inlet and outlet position information in the o-xyz three-dimensional coordinate system is extracted, and the engine inlet and outlet position information is algebraically converted; (2) Based on the centroid coordinates of the diffuser inlet and outlet cross sections, the flow distances, longitudinal offsets, and spanwise offsets of the diffuser inlet and outlet cross sections are obtained; (3) Designing the diffuser centerline using a linear function or a polynomial with two adjustable coefficients; using a parametric equation to describe the diffuser centerline, where f0(t), f1(t), and f2(t) are linear functions or polynomials with two adjustable coefficients. Once f0(t), f1(t), and f2(t) are determined, the diffuser centerline is uniquely determined. In the formula, x c,in ,y c,in and z c,in are the coordinates of the starting point of the diffuser's three-dimensional centerline, where x c,out ,y c,out and z c,out are the coordinates of the centroid of the diffuser outlet cross section in the rectangular coordinate system o-xyz; In the parametric equation, the variable t ranges from 0 to 1, and f0(t), f1(t) and f2(t) are all function expressions with parameter t as the independent variable, and their function values ​​also vary between 0 and 1. Among them, f0(t) is a linear function, and f1(t) and f2(t) are both double-coefficient adjustable polynomials; f1(t) and f2(t) have similar forms, so only the function expression of f1(t) is given; Among them, a1, a2, a3 and a4 are unknown coefficients, which can be solved according to given conditions; among them, α0(t), α1(t), β0(t) and β1(t) are the basis functions of the double-coefficient adjustable polynomial, among which and There are two adjustable coefficients. After the unknown coefficients are determined, the adjustable coefficients are uniquely determined to obtain the function distribution of various bending laws; The formula is converted into matrix form, f0(t), f1(t), f2(t) is recorded as F(t), and the expression converted into matrix form is as follows: For a double coefficient adjustable polynomial, the expression of the F(t) function is as follows: For the unknown coefficients a1, a2, a3, and a4, the following constraints are given for solution: In the above equations, y' is the first-order derivative of y; where θ y-in yes The angle between the projection on the XY plane and the x-axis, θ y-out yes The angle between the projection on the XY plane and the x-axis; c,in is the coordinate of the centroid of the diffuser inlet section in the y-axis direction, y c,out is the coordinate of the centroid of the diffuser outlet cross section in the y-axis direction; The polynomial coefficients a1, a2, a3, and a4 are solved from the above equations. At this time, the change law of the diffuser centerline in the XY plane depends only on the two adjustable coefficients and By adjusting the coefficient and The center line of the XY plane diffuser can be changed according to simple or complex rules; Similarly, determine the unknown coefficients in the diffuser centerline equation on the XZ plane, and make the centerline consist of only two adjustable coefficients and adjust; (4) Mapping the three-dimensional discrete points of the diffuser inlet and outlet cross sections onto a virtual ξ-η two-dimensional plane; (5) Design M central control sections in the ξ-η two-dimensional plane; (6) Discretize the reference circle in the ξ-η two-dimensional plane to obtain the reference circle matrix (7) Based on the reference circle matrix Obtain the coefficient matrix of the diffuser inlet cross section and the coefficient matrix of the diffuser outlet cross section (8) Determine the number of transition sections K including the center control section and calculate the coefficient matrix of K transition sections by cubic spline interpolation (9) Coefficient matrix based on transition section Calculate the matrix expression of each transition section in the ξ-η two-dimensional plane (10) The matrix expression of the transition section is modified so that the cross-sectional area described by the matrix expression of the transition section is equal to the area of ​​the reference circle; (11) Use a linear function or a double-coefficient adjustable polynomial to determine the area variation law of the diffuser along the center line; specify the variation law of the diffuser cross-sectional area as A k =A in +(A out -A in )·w(s k ) Among them A k represents the area of ​​the kth transition section, w(s k ) is a linear function or a double-coefficient adjustable polynomial, A out is the cross-sectional area of ​​the diffuser outlet; the coefficient to be determined is determined by the given diffuser inlet and outlet conditions. At this time, the area change law is determined by two adjustable coefficients and Make adjustments; Determine the scaling factor G of the transition section k , where k = 1, 2, 3...K, the specific expression is as follows: Where A k represents the area of ​​the kth transition section, A out is the diffuser outlet cross-sectional area; (12) Based on the area change law, the final two-dimensional figure of the transition section is obtained, that is, the matrix describing the section in three-dimensional space (13) The matrix of each transition section in the o-xyz coordinate system Rotation and translation are performed to obtain the final three-dimensional shape of the diffuser.

2. The design method according to claim 1, characterized in that: In step (1), according to the overall constraint parameters of the engine, that is, the given diffuser inlet and outlet cross sections, N discrete points are extracted with equal arc lengths on the contour lines of the diffuser inlet cross section and the diffuser outlet cross section in the o-xyz three-dimensional coordinate system, and the three-dimensional coordinates of each point are obtained, and the three-dimensional coordinates of each point are placed in a matrix with N rows and 3 columns. and is a matrix composed of discrete points extracted from the diffuser inlet cross-section contour line, where the first column Indicates the x-axis coordinate of the point, the second column Indicates the y-axis coordinate of the point, the third column Indicates the z-axis coordinate of a point; the superscript in indicates that the point is located on the contour line of the diffuser inlet section, the subscripts 1, 2, ... N indicate the i-th discrete point, and N is the number of discrete points on each curve; is a matrix composed of discrete points extracted from the diffuser outlet cross-sectional contour line, where the first column Indicates the x-axis coordinate of the point, the second column Indicates the y-axis coordinate of the point, the third column represents the z-axis coordinate of a point; the superscript out indicates that the point is located on the contour line of the diffuser outlet section, the subscripts 1, 2, ... N represent the i-th discrete point, and N is the number of discrete points on each curve; Based on the coordinate matrix of each discrete point on the contour line and Calculate the normal vector of the diffuser inlet section and the normal vector of the diffuser outlet section At the same time, the centroid C of the inlet section is calculated in Coordinates and centroid C of the outlet section out The coordinates of According to the normal vector and Determine the inclination information of the centerline at the inlet and outlet sections of the diffuser, where θ y-in yes The angle between the projection on the XY plane and the x-axis, θ y-out yes The angle between the projection on the XY plane and the x-axis; θ z-in yes The angle between the projection on the XZ plane and the z-axis, θ z-out yes The angle between the projection on the XZ plane and the z-axis; The arithmetic mean method is used to define the center position of the diffuser inlet section and the diffuser outlet section, which is recorded as the centroid; the following formula is the centroid of the inlet section C in x c,in ,y c,in ,z c,in The coordinates of the solution expression and the x of the centroid of the outlet section c,out ,y c,out ,z c,out The coordinate solution expression of ; similarly, the centroid position of any discretized cross section can be solved according to the definition; The above physical quantities θ y-in ,θ y-out ,θ z-in ,θ z-out , C in and C out That is the entry and exit location information.

3. The design method according to claim 2, characterized in that: In step (2), the centroid information of the inlet and outlet sections of the diffuser is obtained by algebraically converting the inlet and outlet position information in step (1); based on the centroid C of the diffuser inlet section in , the centroid C of the diffuser outlet section out The coordinates of the diffuser inlet and outlet sections are calculated according to the following formula to obtain the flow distance between the diffuser inlet and outlet sections, that is, the flow field length L of the diffuser is recorded as ΔX; the longitudinal and spanwise offsets of the diffuser inlet and outlet sections are obtained, recorded as ΔY and ΔZ; Where ΔY, ΔZ and ΔX are solved as shown in the formula:

4. The design method according to claim 3, characterized in that: In step (3), after the diffuser centerline is determined, the total length S of the diffuser centerline is obtained as the total arc length.

5. The design method according to claim 4, characterized in that: In step (4), the N-row and 3-column matrix and Transform so that the transformed The numbers in the first column of the matrix are the same, that is, the coordinates in the x direction are the same, and the transformed The numbers in the first column of the matrix are the same, and then and Mapped to a virtual ξ-η two-dimensional plane, and in the ξ-η plane a matrix with N rows and 2 columns To represent the diffuser inlet cross section, a matrix with N rows and 2 columns is To represent the diffuser outlet cross section; 6. The design method according to claim 5, characterized in that: In step (5), in the ξ-η plane, the contour line of the center control section is designed, and the arc length position percentage s of the center control section centroid on the diffuser centerline is specified. m , 0<s m <1, and the contour line of the central control section in the ξ-η plane is discretized into N points with equal arc length, and described by a matrix with N rows and 2 columns Where m = 1, 2, ... M; 7. The design method according to claim 6, characterized in that: In step (6), a full circle with a radius of 1 m is used as a reference circle in the ξ-η two-dimensional plane and the reference circle is discretized with equal arc lengths; N discrete points are used to obtain the coordinates of the reference circle in the ξ-η two-dimensional plane to form a matrix with N+1 rows and 2 columns: The data in the first and last rows are the same; the matrix It is called the reference circle matrix; 8. The design method according to claim 7, characterized in that: In step (7), define is the coefficient matrix at the diffuser inlet, which satisfies is a matrix with N rows and N+1 columns; the matrix The specific expansion is as follows: Expands to: According to the above equation, the matrix can be solved Similarly, the coefficient matrix of the diffuser outlet is obtained: and the coefficient matrix of the center control section 9. The design method according to claim 8, characterized in that: In step (8), the total number of transition sections K is specified, and the arc length position percentage s of the centroid of each transition section on the diffuser centerline is specified. k , 0<s k <1, where k = 1, 2, 3 ... K; if there is a center control section, then the center control section is one of the transition sections; the arc length percentage s of the transition section k is the independent variable, with the coefficient matrix is the variable to be interpolated, and the cubic spline interpolation method is used to calculate value; in the process of calculating the transition coefficient matrix of the central control section, it is necessary to perform interpolation in sections, and the interpolation method still uses cubic spline interpolation.

10. The design method according to claim 9, characterized in that: In step (9), according to Step (6) finds And the value obtained in step (8) Calculate the matrix expression of each transition section in the ξ-η two-dimensional plane The matrix corresponding to the contour line of the first transition section is The matrix corresponding to the contour line of the second transition section is The matrix corresponding to the contour line of the third transition section is And so on, the matrix corresponding to the last transition section is calculated. The following is the matrix expression of the transition section: The calculation formula is:

11. The design method according to claim 10, characterized in that: In step (10), the matrix expression of the transition section calculated in step (9) is Calculate the area enclosed by each transition section in the ξ-η two-dimensional plane, and use the matrix expression Appropriate scaling and correction are performed to make The final area enclosed in the ξ-η two-dimensional plane is equal to the area of ​​the reference circle. After correction, the matrix expression of each transition section in the ξ-η two-dimensional plane is still recorded as First, based on step (9), a discrete point matrix for describing the transition section contour line has been obtained: Fit the graph, and then calculate the area of ​​the transition section. The area of ​​the Kth transition section is A. k ; Let the area of ​​the reference circle be A base ; Next, determine A k , A base The ratio of the areas to obtain the scale factor Where r represents the ratio of the radius of the circle with the same area as the transition cross section to the radius of the reference circle; Then, the matrix After correction, the corrected matrix still uses express; The corrected expression is shown in the formula All transition sections are processed as above to obtain a series of transition sections with areas equal to the reference circle, as well as a discrete point matrix describing the transition sections.

12. The design method according to claim 1, characterized in that: In step (12), according to the area of ​​the Kth transition cross section determined in step (10), the matrix expression of the transition cross section is enlarged or reduced again according to the area change rule of step (11): The final matrix expression describing the transition section graph is formed, and each graph is recorded as a matrix with N rows and 3 columns. The first column of numbers is 0, and the last two columns are the same as the numbers after enlarging or reducing The same is to convert the contour information in the ξ-η two-dimensional plane into the three-dimensional coordinate system o-xyz, but still keep the normal vector and x direction of the figure the same; 13. The design method according to claim 12, characterized in that: In step (13), K discrete points are extracted with equal arc length on the center line determined in step (3), and the coordinate system is The transition sections represented are rotated and translated. After the rotation and translation, the centroid of any k-th transition section coincides with the k-th point on the centerline of the diffuser and is perpendicular to the centerline of the diffuser at this point, k = 1, 2, 3...K; then, a three-dimensional expansion duct that meets the requirements, namely the inlet diffuser, is obtained.

14. An electronic device comprising: one or more processors; And the storage device is used to store one or more programs, when the one or more programs are executed by the one or more processors, the one or more processors implement the design method described in any one of claims 1 to 13.

15. A computer readable medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the design method according to any one of claims 1 to 13 is implemented.

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