Matrix transformation-based improved design method for diffuser

Abstract

Disclosed in the present invention is a matrix transformation-based improved design method for a diffuser. Firstly, inlet and outlet position information of a diffuser is extracted, and then a double-coefficient adjustable polynomial is used to design a central line of the diffuser between the centroid of an inlet section and the centroid of an outlet section, and a change rule of the area of each section of the diffuser along the central line. In the aspect of transition of the shapes of an inlet and an outlet of the diffuser, once the inlet section and the outlet section have been mapped to a ξ-η space, a plurality of transition shapes between the inlet section and the outlet section are obtained by using a matrix transformation-based improved algorithm. The shapes of the inlet and the outlet, and each transition shape jointly form the shape of each local section of the diffuser along the central line. On the basis of the shapes of the sections, the change rule of the sectional area, and the change rule of the central line, the final three-dimensional geometry of the diffuser can be constructed under an o-xyz three-dimensional coordinate system, and the three-dimensional geometric modeling of the diffuser can be flexibly and controllably designed.

Description

Improved design method of diffuser based on matrix transformation TECHNICAL FIELD

[0001] The application belongs to the technical field of aircraft inlet, and particularly relates to an improved design method of an inlet diffuser. BACKGROUND

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

[0003] There are two ideas for the design of the three-dimensional geometric surface of the diffuser at present: (1) one is to use the bridging function in the commercial modeling software to generate a smooth diffuser surface between the given inlet and outlet cross sections; (2) the other is to design several two-dimensional transition cross sections, and then arrange the transition cross sections to form the three-dimensional surface of the diffuser.

[0004] The disadvantages of the first design idea are obvious, which cannot 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 also difficult to carry out subsequent surface optimization work.

[0005] The second design idea is widely used in aerospace engineering design (A Design Method of Complex Variable Cross-section Inlet, Journal of Aerospace Power, 2009, 24(06): 1357-1363), which takes into account the controllability of shape transition between the given inlet and outlet and the convenience of algorithm. The specific implementation process of this idea is as follows: first, the inlet and outlet cross sections are algebraically expressed (i.e., geometric shape algebraization), such as a function (A General Design Method of Subsonic Diffuser, CN201410187196.X) or a matrix (A Design Method of Stealth Serpentine Inlet Based on Matrix Transformation, CN202210241584.6), then interpolation is performed between the algebraic quantities of the inlet and outlet cross sections to generate several transition algebraic quantities, then the transition cross sections are calculated according to the transition algebraic quantities, and finally the three-dimensional surface of the diffuser is formed by scaling, rotating and translating the transition cross sections in three-dimensional space.

[0006] However, with the increasing demand for radar stealth performance of aircraft, the centerline of the diffuser needs to be curved in a more complex way, such as a large offset "S" shape or even a "double S" shape. Under this technical requirement, the classic Lee centerline (C.C. Lee, "Subsonic diffuser design and performance for advanced fighter aircraft", AIAA Journal, 1985.) used in the conventional design process is not up to the task. This method only provides three change patterns: "fast in front and slow in back", "slow in front and fast in back", and "slow in front and fast in back". Since these three patterns are monotonically increasing functions, they cannot directly produce a "double S" centerline. If we want to use the classic Lee centerline to design a "double S" diffuser with good stealth capability, we need to design the centerline in segments between the inlet and outlet sections, which increases the complexity of the design process. In addition, this method can only produce a maximum of 3x3=9 possible centerlines, and the design results lack diversity and sufficient flexibility. A stealthy serpentine inlet design method proposed by Nanjing University of Aeronautics and Astronautics ("A stealthy serpentine inlet design method based on matrix transformation", CN202210241584.6) uses a quintic polynomial to design the centerline, but faces similar problems. In order to produce a "double S" centerline, the front and back "single S" centerlines need to be designed separately and then spliced together.

[0007] In addition, existing design methods ("General subsonic diffuser design method CN201410187196.X", "Improved general subsonic diffuser design method CN202110392258.0", "A stealthy serpentine inlet design method based on matrix transformation C202210241584.6") are very inconvenient when designing left-right asymmetric diffusers. They need to artificially divide the design process into left half design and right half design. After completing the left and right half design, the complete diffuser is spliced.

[0008] In summary, the main problems with existing diffuser design methods are:

[0009] (1) The bending pattern of the diffuser centerline is either relatively simple, with only three options: fast in front and slow in back, slow in front and fast in back, and slow in front and fast in back, or a complex quintic polynomial is used, which is more flexible but the polynomial coefficient calculation process is more complicated. In addition, for "double S" centerlines, the above methods need to be spliced after segment design, and the design process is lengthy.

[0010] (2) For the left-right asymmetric diffuser, the transition between the inlet and outlet sections cannot be completed at one time in the design process, and the inlet and outlet sections are usually artificially divided into left and right halves, the division process is arbitrary, and the inlet and outlet sections need to be designed separately and then spliced together, and the design process is long.

[0011] Therefore, there is a need for a new technical solution to solve the above technical problems. SUMMARY

[0012] To solve the above problems, the application provides an improved design method for a diffuser based on matrix transformation. The improved design method not only inherits the idea of describing the section contour line by matrix, but also improves the generation method of the center line and the transition method of the section, avoids the front and back segmentation design of the center line and the left and right half forming of the diffuser profile, and realizes the controllable and flexible design of the center line and the one-time forming of the three-dimensional geometric profile of the diffuser.

[0013] To achieve the above purpose, the technical scheme that can be adopted by the application is as follows:

[0014] An improved design method for a diffuser based on matrix transformation, comprising the following steps,

[0015] (1) According to the overall constraint parameters of the engine, that is, the given inlet and outlet sections of the diffuser, the position information of the inlet and outlet of the diffuser in the o-xyz three-dimensional coordinate system is extracted, and the position information of the engine inlet and outlet is algebraized;

[0016] (2) Based on the centroid coordinates of the inlet and outlet sections of the diffuser, the streamwise distance and the longitudinal and lateral offsets of the inlet and outlet sections of the diffuser are obtained;

[0017] (3) A one-time function or a double-coefficient adjustable polynomial is used to design the center line of the diffuser;

[0018] (4) The three-dimensional discrete points of the inlet and outlet sections of the diffuser are mapped to a virtual ξ-η two-dimensional plane;

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

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

[0021] (7) Based on the reference circle matrix The coefficient matrix of the inlet section of the diffuser is obtained And the coefficient matrix of the outlet section of the diffuser

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

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

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

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

[0026] (12) Based on the area variation law, obtain the final two-dimensional graph of the transition section, i.e. the matrix describing the section in three-dimensional space

[0027] (13) Rotate and translate the matrix of each transition section in the o-xyz coordinate system to obtain the final three-dimensional surface of the diffuser.

[0028] Further, in step (1), according to the overall constraint parameters of the engine, i.e. the given diffuser inlet and outlet sections, in the o-xyz three-dimensional coordinate system, N discrete points are extracted at equal arc length on the contour lines of the diffuser inlet section and the diffuser outlet section, respectively, to obtain the three-dimensional coordinates of each point, and the three-dimensional coordinates of each point are placed in an N-row 3-column matrix and

[0029] is a matrix composed of discrete points extracted on the contour line of the diffuser inlet section, wherein the first column represents the x-axis coordinate of the point, the second column represents the y-axis coordinate of the point, and the third column represents the z-axis coordinate of the point; the superscript in represents that the point is located on the contour line of the diffuser inlet section, and the subscripts 1, 2, …, N represent the i-th discrete point, and N is the number of discrete points on each curve;

[0030] is a matrix composed of discrete points extracted on the contour line of the diffuser outlet section, wherein the first column represents the x-axis coordinate of the point, the second column represents the y-axis coordinate of the point, and the third column The z-axis coordinate of the point is indicated; the superscript "out" indicates that the point is located on the diffuser outlet section profile line, and the subscripts 1, 2...N indicate the i-th discrete point, where N is the number of discrete points on each curve;

[0031] 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 Simultaneously calculate the centroid C of the inlet section. in Coordinates and centroid C of the exit section out The coordinates;

[0032] Based on the normal vector and Determine the inclination angle of the centerline at the diffuser inlet and outlet sections, where θ y-in yes The angle θ between the projection onto the XY plane and the x-axis. y-out yes The angle between the projection onto the XY plane and the x-axis; θ z-in yes The angle θ between the projection onto the XZ plane and the z-axis. z-out yes The angle between the projection onto the XZ plane and the z-axis;

[0033] The center positions of the diffuser inlet and outlet sections are defined using the arithmetic mean method, denoted as the centroid; the following formula is the centroid C of the inlet section. in x c,in ,y c,in ,z c,in The coordinate solution expression and the x-axis of the centroid of the exit section. c,out ,y c,out ,z c,out The coordinate solution expression is given; similarly, the centroid position of any discrete cross-section can be solved according to the definition.

[0034] The above physical quantities θ y-in θ y-out θ z-in θ z-out C in and C out This refers to the entry and exit location information.

[0035] Furthermore, in step (2), after algebraizing the inlet and outlet position information in step (1), the centroid information of the diffuser inlet and outlet sections is obtained; based on the centroid C of the diffuser inlet section... in, the centroid C of the diffuser outlet section out The flow direction distance of the diffuser inlet and outlet sections, i.e. the flow field length L of the diffuser, is calculated according to the following formula, and is denoted as ΔX; the offset distances of the diffuser inlet and outlet sections in the longitudinal and spanwise directions are denoted as ΔY and ΔZ;

[0036] wherein ΔY and ΔZ are in terms of ΔX and are solved according to the formula as shown below:

[0037] Further, in step (3), the parameter equation is used to describe the center line of the diffuser, wherein f0(t), f1(t) and f2(t) are in the form of a first order function or a third order polynomial with double adjustable coefficients, and after f0(t), f1(t) and f2(t) are determined, the center line of the diffuser is uniquely determined;

[0038] wherein x c,in , y c,in and z c,in are the coordinates of the starting point of the three-dimensional center line of the diffuser, wherein x c,out , y c,out and z c,out are the coordinates of the centroid of the diffuser outlet section in the rectangular coordinate system o-xyz;

[0039] The variable t in the parameter equation ranges from 0 to 1, and f0(t), f1(t) and f2(t) are all function expressions with the parameter t as the independent variable, and the function values thereof also vary between 0 and 1, wherein f0(t) is a first order function, and f1(t) and f2(t) are both double-coefficient adjustable polynomials and have similar forms, and therefore only the function expression of f1(t) is given;

[0040] wherein a1, a2, a3 and a4 are undetermined coefficients which can be solved according to given conditions; wherein α0(t), α1(t), β0(t) and β1(t) are base functions of the double-coefficient adjustable polynomials, and the two adjustable coefficients and in the base functions are to be determined, and after the undetermined coefficients are determined, the adjustable coefficients are uniquely determined, and a plurality of function distributions of the bending law are obtained;

[0041] The formula is converted into a matrix form, and f0(t), f1(t) and f2(t) are denoted as F(t), and the expression in the matrix form is as follows:

[0042] For the double-coefficient adjustable polynomial, the expression of the function F(t) is as follows:

[0043] For the undetermined coefficients a1, a2, a3, a4, the following constraint conditions are given for solving:

[0044] In the above equation set, y' is the first derivative of y; wherein θ y-in is the angle between the X-Y plane projection and the x axis, θ y-out is the angle between the X-Y plane projection and the x axis; θ z-in is the angle between the X-Z plane projection and the z axis, θ z-out is the angle between the X-Z plane projection and the z axis; y 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 section in the y axis direction;

[0045] The polynomial coefficients a1, a2, a3, a4 are solved from the above equation set, at this time, the variation law of the diffuser center line in the X-Y plane only depends on two adjustable coefficients and By adjusting the coefficients and , the X-Y plane diffuser center line can be made to vary according to a simple law or a complex law;

[0046] Similarly, the undetermined coefficients in the diffuser center line equation in the X-Z plane are determined, and the center line is adjusted by only two adjustable coefficients and ;

[0047] After the diffuser center line is determined, the total length S of the diffuser center line is obtained as the total arc length.

[0048] Further, in step (4), the N rows and 3 columns matrix and are transformed, so that the first column numbers in the transformed matrix are the same, that is, the coordinates in the x direction are the same, and similarly, the first column numbers in the transformed matrix are the same, and then and are mapped into a virtual ξ-η two-dimensional plane, and the diffuser inlet section is represented by an N row and 2 column matrix in the ξ-η plane, and the diffuser outlet section is represented by an N row and 2 column matrix ;

[0049] Furthermore, in step (5), the outline of the central control section is designed in the ξ-η plane, and the percentage of arc length s of the centroid of the central control section on the diffuser centerline is specified. m , 0 < s m <1, and the central control section contour line in the ξ-η plane is discretized into N points of equal arc length, and described by an N-row, 2-column matrix. Where m = 1, 2, ..., M;

[0050] Furthermore, in step (6), a full circle with a radius of 1m is used as the reference circle in the ξ-η two-dimensional plane, and the reference circle is discretized with equal arc lengths; using N discrete points, the coordinates of the reference circle in the ξ-η two-dimensional plane are obtained, forming an N+1 row and 2 column matrix. The first and last rows contain the same data; matrix This is called the reference circle matrix;

[0051] Furthermore, in step (7), the definition is... Let be the coefficient matrix of the diffuser inlet, which satisfies It is an N x N + 1 column matrix; matrix The specific expansion is as follows:

[0052] Expanded to:

[0053] The matrix can be solved based on the above equations. Similarly, the coefficient matrix at the diffuser outlet can be obtained. and the coefficient matrix of the central control section

[0054] Furthermore, in step (8), the total number of transition sections K is specified, and the percentage of arc length position 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 a central control section exists, then the central control section is one of the transition sections; s is the percentage of the arc length of the transition section. k As the independent variable, with the coefficient matrix For the variable to be interpolated, the cubic spline interpolation method is used to calculate... The value; if there is a central control section, then the calculation of the transition coefficient matrix needs to be performed in segments for interpolation, and the interpolation method still adopts cubic spline interpolation.

[0055] Furthermore, in step (9), according to The result obtained in step (6) and the result obtained in step (8) Calculate the matrix expressions for each transition section in the ξ-η two-dimensional plane.

[0056] 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, until the matrix corresponding to the last transition section is calculated. The following is the matrix expression for the transition section. The calculation formula:

[0057] Furthermore, in step (10), the matrix expression of the transition section is calculated based on step (9). Calculate the area enclosed by each transition section in the ξ-η two-dimensional plane, and evaluate the matrix expression. Make appropriate scaling and corrections to make The area enclosed in the ξ-η two-dimensional plane is ultimately equal to the area of ​​the reference circle. The matrix expressions for each transition section in the ξ-η two-dimensional plane after correction are still denoted as...

[0058] First, based on step (9), a discrete point matrix for describing the transition section profile has been obtained. Fit the graph, then calculate the area of ​​the transition section, and denote the area of ​​the Kth transition section as A. k Let the area of ​​the reference circle be A. base ;

[0059] Secondly, determine A k A base The ratio of areas yields the scale factor. Where r represents the ratio of the radius of the circle with the same area as the transition section to the radius of the reference circle;

[0060] Subsequently, on the matrix Make corrections, and the corrected matrix will still use... The expression is shown in the formula; the modified expression is as follows.

[0061] The above process is applied to all transition sections to obtain a series of transition sections with an area equal to that of the reference circle, as well as a discrete point matrix describing the transition sections.

[0062] Furthermore, the variation law of the diffuser cross-sectional area is specified as A. k =Ain +(A out -A in )·w(s k )

[0063] wherein A k represents the area of the kth transition cross section, w(s k ) is a linear function or a double coefficient adjustable polynomial; through the given inlet and outlet conditions of the diffuser, the undetermined coefficients are determined, at this time the area variation law is adjusted through two adjustable coefficients and .

[0064] The scaling coefficient G k of the transition cross section is determined, wherein k=1, 2, 3…K, and the specific expression is as follows:

[0065] In the formula, A k represents the area of the kth transition cross section, and A out is the outlet cross section area of the diffuser.

[0066] Further, in step (12), according to the kth transition cross section area determined in step (10), the matrix expression of the transition cross section is enlarged or reduced again according to the area variation law of step (11) to form the final matrix expression describing the transition cross section graph, and each graph is recorded as a matrix of N rows and 3 columns The first column of numbers in the matrix is 0, and the last two columns are the same as the enlarged or reduced , that is, the contour line information in the ξ-η two-dimensional plane is converted into the three-dimensional coordinate system o-xyz, but the normal vector and the x direction of the graph are still kept the same;

[0067] Further, in step (13), K discrete points are extracted on the center line determined in step (3) at equal arc length, and each transition cross section represented by is rotated and translated in the o-xyz coordinate system, after rotation and translation, the centroid of any kth transition cross section coincides with the kth point on the diffuser center line, and is perpendicular to the diffuser center line at the point, k=1, 2, 3…K. Subsequently, the required three-dimensional expansion pipeline, i.e. the inlet duct diffuser, is obtained.

[0068] Advantages: Compared with the prior art, the advantages of the present application are:

[0069] (1) The bending rule, area expansion rule and cross-section transition rule of the diffuser center line are more abundant. Not only can the traditional front slow and rear rapid, front rapid and rear slow and slow and rapid be realized, but also more change rules can be realized through adjusting the adjustable coefficient. For the "double S" type center line, there is no need to design in sections, which simplifies the design process.

[0070] (2) For the left-right asymmetric diffuser, the transition between the inlet cross-section and the outlet cross-section can be completed at one time, and there is no need to artificially divide into left and right halves for sectional design.

[0071] The design method provided by the application can be stored on a storage medium as a computer program, and includes the following technical solutions:

[0072] An electronic device includes:

[0073] One or more processors; and a storage device for storing one or more programs that, when executed by the one or more processors, cause the one or more processors to implement the above-mentioned improved design method for the diffuser based on matrix transformation.

[0074] And:

[0075] A computer-readable medium having stored thereon a computer program that, when executed by a processor, implements the above-mentioned improved design method for the diffuser based on matrix transformation. BRIEF DESCRIPTION OF DRAWINGS

[0076] Figure 1 is a schematic diagram of two complex "double S" center lines under different input conditions.

[0077] Figure 2 is a schematic diagram of common inlet cross-section, control cross-section and outlet cross-section profile lines.

[0078] Figure 3 is a two-dimensional plane schematic diagram and a three-dimensional scatter plot of the conversion of the ring-fan-shaped inlet cross-section to the circular outlet cross-section under the condition of no control cross-section.

[0079] Figure 4 is a two-dimensional plane schematic diagram and a three-dimensional scatter plot of the conversion of the trapezoidal inlet cross-section to the circular outlet cross-section under the condition of no control cross-section.

[0080] Figure 5 is a two-dimensional plane schematic diagram and a three-dimensional scatter plot of the conversion of the trapezoidal inlet cross-section to the circular outlet cross-section under the condition of control cross-section.

[0081] Figure 6 is a design flowchart.

[0082] Figure 7 is a schematic diagram of the input conditions, the designed center line and the adopted area change rule of the first specific implementation case.

[0083] Figure 8 is a front view of the three-dimensional diffuser generated in the first specific implementation case.

[0084] Figure 9 is a top view of the three-dimensional diffuser generated in the first embodiment.

[0085] Figure 10 is a side view of the three-dimensional diffuser generated in the first embodiment.

[0086] Figure 11 is a schematic diagram of the input conditions, the designed centerline and the adopted area variation law of the second embodiment.

[0087] Figure 12 is a three-dimensional view of the three-dimensional diffuser generated in the second embodiment.

[0088] Figure 13 is a front view of the three-dimensional diffuser generated in the second embodiment.

[0089] Figure 14 is a top view of the three-dimensional diffuser generated in the second embodiment.

[0090] Figure 15 is a side view of the three-dimensional diffuser generated in the second embodiment. DETAILED DESCRIPTION

[0091] In order to make the purpose, design process, technical method and advantages of the present application clearer, the present application will be further described in detail below in combination with the drawings.

[0092] Figure 6 in the drawings of the specification is a design process diagram of the present application, as shown in Figure 6, the general design method of the improved diffuser provided by the present application includes the following steps:

[0093] (1)

According to the overall constraint parameters of the engine, that is, the given inlet and outlet sections of the diffuser, the position information of the inlet and outlet in the o-xyz three-dimensional coordinate system is extracted

[0094] is a matrix composed of discrete points extracted on the profile line of the inlet section, wherein the first column represents the x-axis coordinate of the point, the second column represents the y-axis coordinate of the point, and the third column represents the z-axis coordinate of the point. The superscript in represents that the point is located on the profile line of the inlet section, and the subscript 1, 2, …, N represents the i-th discrete point, and N is the number of discrete points on each curve;

[0095] is a matrix composed of discrete points extracted from the profile line of the inlet section, wherein the first column represents the x-axis coordinate of the point, the second column represents the y-axis coordinate of the point, and the third column represents the z-axis coordinate of the point. The superscript out indicates that the point is located on the outlet profile line, and the subscripts 1, 2, …, N indicate the ith discrete point, and N is the number of discrete points on each curve;

[0096] Based on the coordinate matrix of each discrete point on the profile line and the normal vectors of the inlet section and the outlet section are calculated and The centroids C in and C out of the inlet section and the outlet section are calculated at the same time.

[0097] According to the normal vectors of the inlet section and the outlet section and the inclination information of the center line at the inlet section and the outlet section can be determined, wherein θ y-in is the included angle between the X-Y plane projection and the x-axis, θ y-out is the included angle between the X-Y plane projection and the x-axis; θ z-in is the included angle between the X-Z plane projection and the z-axis, and θ z-out is the included angle between the X-Z plane projection and the z-axis.

[0098] The centroid position of the inlet section and the outlet section is defined by the arithmetic mean, denoted as the centroid. Formula (1) is the coordinate solving expression of the x c,in , y c,in , and z c,in coordinates of the inlet section centroid C in . Similarly, the centroid position of any discrete section can be solved according to the defined manner, including the centroid C out of the outlet section.

[0099] The above physical quantities θ y-in , θ y-out , θ z-in , θ z-out , and C in are the “inlet and outlet position information”.

[0100] (2)

Calculate the length of the diffuser flow direction and the longitudinal and spanwise offset distance

[0101] wherein ΔY, ΔZ and ΔX are solved in the manner shown in equation (2):

[0102] (3)

Centerline design

[0103] In the formula, x c,in , y c,in and z c,in are the coordinates of the centroid C in of the inlet cross section, wherein x c,out , y c,out and z c,out are the coordinates of the centroid C out of the outlet cross section in the o-xyz coordinate system.

[0104] The variable t in the parametric equation has a value range of 0 to 1, f0(t), f1(t) and f2(t) are all function expressions with the parameter t as the independent variable, and the function values also vary between 0 and 1, wherein f0(t) is a first order function, and f1(t) and f2(t) are both double-coefficient adjustable polynomials and have similar forms, so only the function expression of f1(t) is given, as shown in equation (4):

[0105] wherein a1, a2, a3 and a4 are undetermined coefficients, which can be solved according to given conditions. α0(t), α1(t), β0(t) and β1(t) are base functions of the double-coefficient adjustable polynomials, wherein and are two adjustable coefficients, and after the undetermined coefficients are determined, the adjustable coefficients can be uniquely determined to obtain a variety of function distributions of bending rules.

[0106] Therefore, the above equation (3) can also be converted into a matrix form, and in order to facilitate writing, f0(t), f1(t), f2(t) are recorded as F(t), and the specific matrix expression of equation (3) is as follows:

[0107] For the double coefficient adjustable polynomial, the expression of F(t) function is as follows:

[0108] For the undetermined coefficients a1, a2, a3, a4, the following constraint conditions are given for solving:

[0109] In the above equation group, y' is the first derivative of y. Where θ y-in is the included angle between the X-Y plane projection and the x axis, θ y-out is the included angle between the X-Y plane projection and the x axis; θ z-in is the included angle between the X-Z plane projection and the z axis, θ z-out is the included angle between the X-Z plane projection and the z axis; y c,in and y c ,out are the coordinates of the centers of the inlet and outlet sections in the y axis direction.

[0110] Solve the polynomial coefficients a1, a2, a3, a4 from the above equation group, at this time, the center line variation law of the X-Y plane only depends on two adjustable coefficients and Usually, the adjustment coefficient can make the center line of the X-Y plane change according to a simple law.

[0111] Similarly, the undetermined coefficients in the center line equation of the X-Z plane can be determined, and the center line is adjusted by only two adjustable coefficients and .

[0112] Figure 1 of the drawings of the present patent specification shows that when different and values are taken, the center line with different bending laws can be formed between the starting point and the ending point at one time, including the "double S-type" center line with relatively complex bending mode.

[0113] After the center line is determined, the total length S (total arc length) of the center line can be obtained.

[0114] (4)

Map the three-dimensional discrete points of the inlet and outlet sections to a virtual ξ-η two-dimensional plane

[0115] (5) Designing the control section Generally, when the diffuser is designed, the inlet section is smoothly transitioned to the outlet section, but the transition of the profile can also be controlled by designing M control sections. In the ξ-η plane, the profile line of the control section is designed, and the arc length position percentage s of the centroid of the control section on the center line of the diffuser is specified m (0 < s < 1). m <1), and the profile line of the control section in the ξ-η plane is discretely equal-arc-length to N points, which is described by an N-row 2-column matrix where m = 1, 2, …, M.

[0116] (6) Discretizing the reference circle in the ξ-η two-dimensional plane In the ξ-η two-dimensional plane, the whole circle with a radius of 1 m is defined as the reference curve (referred to as the reference circle), and N discrete points on the reference circle and their coordinates in the ξ-η plane are extracted according to the equal arc length, to form an N+1-row 2-column matrix where the first row and the last row of data are the same, and are referred to as the reference circle matrix.

[0117] (7) Calculating the coefficient matrix of the inlet and outlet Define as the coefficient matrix of the inlet, which satisfies is an N-row N+1-column matrix. The specific expansion of the matrix is as follows:

[0118] Therefore, can be expanded as:

[0119] According to the above equation, the matrix can be solved. Similarly, the coefficient matrix of the outlet and the coefficient matrix of the control section can be obtained.

[0120] (8) Calculating the coefficient matrix of the transition section The total number K of the transition sections (including the inlet and outlet sections) is specified, and the arc length position percentage s of the centroid of each transition section on the center line of the diffuser is specified k (0 < s < 1). k<1), where k = 1, 2, 3...K. If a central control section exists, then the central control section is one of the transition sections. The percentage of the transition section arc length s... k As the independent variable, with the coefficient matrix For the variable to be interpolated, the cubic spline interpolation method is used to calculate... The value of .

[0121] (9) [Calculate the matrix expressions of each transition section in the ξ-η two-dimensional plane] Based on The result obtained in step (6) and the result obtained in step (8) Calculate the matrix expressions for each transition section in the ξ-η two-dimensional plane.

[0122] 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 cross-section is calculated. The following is the matrix expression for the transition section. The calculation formula:

[0123] (10) [Correct the matrix expression of each transition section in the ξ-η two-dimensional plane] Based on the matrix Calculate the area enclosed by each transition section in the ξ-η two-dimensional plane, and then apply the matrix... By scaling it appropriately so that the area it ultimately 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 denoted as The detailed steps for scaling correction are as follows:

[0124] First, based on step (9), a discrete point matrix for describing the transition section profile has been obtained. The figure is fitted using a discrete point matrix, and its area is then calculated. Let A be the area of ​​the Kth transition section. k Let the area of ​​the reference circle be A. base .

[0125] Secondly, determine the ratio of their areas to obtain the scaling factor. Where r represents the ratio of the radius of the circle with the same area as the transition section to the radius of the reference circle.

[0126] Subsequently, on the matrix Make corrections, and the corrected matrix will still use... The modified expression is shown in equation (7)

[0127] The matrix expression of K transition sections in the ξ-η two-dimensional plane is obtained by processing all the transition sections as above

[0128] (11) Specifying the area variation law

[0129] In steps (1) to (10), only the shape of each cross section of the intake passage is determined, and the size of each cross section area is adjusted to be equal to the area of the reference circle. However, the diffuser of the intake passage requires the area of the pipe cross section to gradually increase, so it is necessary to further adjust the size of each cross section so that the area of each cross section increases according to a certain law. Therefore, the variation law of the diffuser cross section area is specified as A k = A in +(A out -A in )·w(s k )

[0130] where A k represents the area of the kth transition section, and w(s k ) can be a first-order function or a double-coefficient adjustable polynomial. The form of the double-coefficient adjustable polynomial is similar to that of the center line variation law f1(t). By given inlet and outlet conditions, the undetermined coefficients can be determined, and at this time the area variation law can be adjusted by two adjustable coefficients and .

[0131] The scaling factor G k of the transition section is determined, where k = 1, 2, 3, …, K, and the specific expression is as follows:

[0132] where A k represents the area of the kth transition section, and A out is the outlet cross section area.

[0133] (12) Obtaining the final transition section

[0134] The obtained in step (10) is enlarged or reduced (k = 1, 2, 3, …, K), and the scaling factor G k is determined in step (11), to obtain the final transition section, and the matrix expression is a matrix of N rows and 3 columns The first column of the matrix is 0, and the last two columns are the same as the enlarged or reduced , 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 the x direction of the figure are still the same.

[0135] (13)【In the o-xyz coordinate system, rotate and translate each of the rotated and translated, the centroid of any K-th section after rotation and translation 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 diffuser (i.e. inlet passage diffuser) that meets the requirements is obtained.

[0136] Based on steps (1) to (13), the three-dimensional center line design and transition section design of the diffuser are finally realized. This design method realizes universality, and can achieve smooth transition from the inlet section to the outlet section under different inlet section shapes, with or without a control section.

[0137] Figure 3 shows a two-dimensional plane schematic and a three-dimensional scatter plot of the conversion of a ring-fan-shaped inlet to a circular outlet without a control section;

[0138] Figure 4 shows a two-dimensional plane schematic and a three-dimensional scatter plot of the conversion of a trapezoidal inlet to a circular outlet without a control section;

[0139] Figure 5 shows a two-dimensional plane schematic and a three-dimensional scatter plot of the conversion of a trapezoidal inlet to a circular outlet with a control section.

[0140] Two specific implementation cases are provided below to verify the effectiveness of the design method.

[0141] Specific implementation case one (without control section):

[0142] According to the above design method, a diffuser design program is written using Matlab software. Taking the shape shown in Figure 3 as the inlet and outlet sections of the inlet passage, the diffuser is designed, and other design parameters are shown in the following table:

[0143] Table 1

[0144] The design parameters and the center line and area variation are shown in Figure 7.

[0145] A total of 24 sections (including the inlet section and the outlet section) are taken in the design, and the program calculation results are exported to generate an inlet passage model in UG. The front view, top view and side view are shown in Figures 8, 9 and 10 respectively.

[0146] ​Design case two (with the middle control section):

[0147] According to the above algorithm, the design program of the general subsonic inlet (diffuser) is compiled by using the Matlab software. Taking the inlet with the expansion ratio of 1.5 and the area variation law of the equivalent of slow and fast as an example, the inlet section, the middle control section and the outlet section adopt the shape shown in Fig. 2, and the geometric input conditions are shown in the following table:

[0148] Table 2

[0149] The design parameters and the center line of the design are shown in Fig. 11, wherein the area variation law is still equivalent of slow and fast.

[0150] A total of 24 sections (including the inlet section, the middle control section and the outlet section) are taken in the design,

[0151] The program calculation results are exported, and the three-dimensional inlet model generated in UG is shown in Fig. 12, and the front view, top view and side view are shown in Figs. 13, 14 and 15 respectively.

[0152] The improved design method of the diffuser based on the matrix transformation described above is compiled as a program language by using the Matlab software, and can be stored in the processor or the computer readable medium, so the embodiments of the electronic device and the computer readable medium are also given.

[0153] An embodiment of an electronic device includes:

[0154] One or more processors; and a storage device for storing one or more programs, which, when executed by the one or more processors, cause the one or more processors to implement the improved design method of the diffuser based on the matrix transformation described above.

[0155] An embodiment of a computer readable medium has a computer program stored thereon, which, when executed by a processor, implements the improved design method of the general inlet based on the matrix transformation described above.

[0156] In addition, there are many specific implementation methods and ways of the present application, and the above description is only the preferred embodiment of the present application. It should be noted that for ordinary skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can also be made, which should be considered as the protection scope of the present application.

Claims

1. A method for improved design of a matrix- transformation-based diffuser, characterized by, The method comprises the following steps: (1) according to the engine overall constraint parameters, i.e. given diffuser inlet and outlet sections, extracting the diffuser inlet and outlet position information in the o-xyz three-dimensional coordinate system, and algebraizing the engine inlet and outlet position information; (2) based on the centroid coordinates of the diffuser inlet and outlet sections, obtaining the streamwise distance of the diffuser inlet and outlet sections and the longitudinal and spanwise offsets; (3) the central line of the diffuser is designed by using a linear function or a double-coefficient adjustable polynomial, and the central line of the diffuser is described by a parameter equation, wherein the specific form of f0(t), f1(t) and f2(t) is a linear function or a polynomial with double adjustable coefficients, and after f0(t), f1(t) and f2(t) are determined, the central line of the diffuser is uniquely determined; where x c,in , y c,in and z c,in are the coordinates of the origin of the three-dimensional centerline of the diffuser, respectively, and x c,out , y c,out and z c,out are the coordinates of the centroid of the outlet section of the diffuser in the Cartesian coordinate system o-xyz, respectively. The variable t in the parametric equation ranges from 0 to 1, f0(t), f1(t) and f2(t) are all function expressions with the parameter t as the independent variable, and the function values thereof also vary between 0 and 1, wherein f0(t) is a linear function, f1(t) and f2(t) are both polynomials with double coefficients; f1(t) and f2(t) have similar forms, and therefore only the function expression of f1(t) is given; wherein a1, a2, a3 and a4 are undetermined coefficients that can be solved according to given conditions; wherein a0(t), a1(t), b0(t) and b1(t) are base functions of the double-coefficient adjustable polynomial, wherein a0(t) and a1(t) are the first-order polynomial functions of t, and b0(t) and b1(t) are the second-order polynomial functions of t. and are two adjustable coefficients, after the undetermined coefficients are determined, the adjustable coefficients are uniquely determined, and a function distribution of various bending rules is obtained; The formula is converted into a matrix form, and f0(t), f1(t), and f2(t) are denoted as F(t). The expression converted into a matrix form is as follows: For the double-coefficient adjustable polynomial, the expression of the F(t) function is as follows: For the undetermined coefficients a1, a2, a3, a4, the following constraint conditions are given for solving: In the above set of equations, y' is the first derivative of y; where θ y-in is The angle between the x-axis and the projection of the X-Y plane, θ y-out is angle between the x-axis and the projection of the X-Y plane after the diffuser; y 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 section in the y-axis direction; Solving the above equations, the polynomial coefficients a1, a2, a3, a4 are obtained, at this time, the variation law of the diffuser centerline in the X-Y plane only depends on two adjustable coefficients and By adjusting the coefficient and The X-Y plane diffuser centerline can be changed according to a simple rule or a complex rule; The undetermined coefficients in the equation of the centerline of the diffuser on the X-Z plane are determined in the same way, and the centerline is made to be determined by only two adjustable coefficients and Adjustment; (4) mapping the three-dimensional discrete points of the diffuser inlet and outlet sections to a virtual ξ-η two-dimensional plane; (5) designing M control sections in the ξ-η two-dimensional plane; (6) Discretize the reference circle in the ξ-η two-dimensional plane to obtain a reference circle matrix (7) Based on a matrix of reference circles Obtaining a coefficient matrix for a diffuser inlet section and coefficient matrix of diffuser exit section (8) determine the number K of transition sections including the control section and calculate the coefficient matrix of the K transition sections by cubic spline interpolation (9) Coefficient matrix based on transition section The matrix expression of each transition section in the ξ-η two-dimensional plane is calculated (10) correcting the matrix expression of the transition section so that the sectional area described by the matrix expression of the transition section is equal to the area of the reference circle; (11) determining the area variation rule of the diffuser along the centerline by using a linear function or a two-coefficient adjustable polynomial; the variation rule of the diffuser sectional area is specified as A k = A in + (A out - A in ) · w(s k ) where A k represents the area of the kth transition cross section, w(s k ) is a linear function or a two-coefficient adjustable polynomial, A out is the area of the diffuser outlet cross section; by given diffuser inlet and outlet conditions, the undetermined coefficients are determined, and at this time the area variation law is determined through two adjustable coefficients and Adjustment; Determination of the scaling factor G of the transition section k where k = 1, 2, 3...K, with the specific expression as follows: wherein A k represents the area of the kth transition cross-section, A out is the diffuser exit cross-sectional area; (12) Based on the area change rule, the final transition cross-section two-dimensional graph is obtained, that is, the matrix describing the cross-section in the three-dimensional space (13) Matrix of each transition section under o-xyz coordinate system Rotation and translation are performed to obtain the final diffuser three-dimensional profile.

2. The design method of claim 1, wherein: In step (1), according to the overall constraint parameters of the engine, i.e. the given diffuser inlet and outlet sections, N discrete points are extracted on the profile lines of the diffuser inlet section and the diffuser outlet section in the o-xyz three-dimensional coordinate system at equal arc lengths, respectively, to obtain the three-dimensional coordinates of each point, and the three-dimensional coordinates of each point are placed in an N-row-by-3-column matrix and is a matrix composed of discrete points extracted on the profile line of the diffuser inlet section, wherein the first column x-coordinate of a point, second column y-coordinate of the point, third column z-axis coordinate of the point; the superscript in indicates that the point is located on the diffuser inlet section contour line, and 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 on the profile line of the diffuser outlet section, where the first column x-coordinate of a point, second column y-coordinate of the point, third column z-axis coordinate of the point; the superscript out indicates that the point is located on the diffuser outlet section contour line, and the subscripts 1, 2, …, N indicate the i-th discrete point, and N is the number of discrete points on each curve; a matrix of coordinates of each discrete point on the contour line and Normal vector to the diffuser inlet section and the normal vector of the diffuser outlet section The centroid C of the inlet cross-section is calculated simultaneously in The coordinates of the centroid C of the outlet cross-section out The coordinates of the centroid C of the outlet cross-section According to the normal vector and The inclination angle information of the center line at the inlet and outlet sections of the diffuser is determined, where θ y-in is angle between the x-axis and the projection of the vector on the X-Y plane, θ y-out is Angle between the X-Y plane projection and the x-axis; Θ z-in is The angle between the X-Z plane projection and the z axis, θ z-out is The angle between the X-Z plane projection and the z-axis; The center positions of the diffuser inlet and outlet sections are defined using the arithmetic mean method, denoted as the centroid; the following formula is the centroid C of the inlet section. in x c,in ,y c,in ,z c,in The coordinate solution expression and the x-axis of the centroid of the exit section. c,out ,y c,out ,z c,out The coordinate solution expression is given; similarly, the centroid position of any discretized 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 are the in and out position information.

3. The method of designing according to claim 2, characterized in that: In step (2), the centroid information of the inlet and outlet sections of the diffuser is obtained after the algebraization of the inlet and outlet position information in step (1); based on the coordinates of the centroid C in of the inlet section of the diffuser and the centroid C out of the outlet section of the diffuser, the flow direction distance of the inlet and outlet sections of the diffuser, i.e. the flow field length L of the diffuser, is obtained according to the following formula, and is denoted as ΔX; the offset distances of the inlet and outlet sections of the diffuser in the longitudinal direction and the spanwise direction are obtained, and are denoted as ΔY and ΔZ; where ΔY, ΔZ in terms of ΔX and solved as shown in the equation:

4. The method of designing 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 method of designing according to claim 4, characterized in that: In step (4), the N-row, 3-column matrix is... and Perform a transformation so that the transformed If the numbers in the first column of the matrix are the same, that is, the coordinates in the x-direction are the same, then the transformed matrix will also have the same values. If the numbers in the first column of the matrix are the same, then... and Mapped into a virtual ξ-η two-dimensional plane, and expressed as an N x 2 matrix in the ξ-η plane. To represent the diffuser inlet cross-section, use an N x 2 matrix. To represent the diffuser outlet cross section; 6. The method of designing according to claim 5, characterized in that: In step (5), the profile line of the control section in the ξ-η plane is designed, and the arc length position percentage s of the centroid of the control section on the center line of the diffuser is specified m , 0 < s m < 1, and the profile line of the control section in the ξ-η plane is equi-arc length discretized into N points, which is described by an N-row 2-column matrix where m = 1, 2, …, M; 7. The method of designing according to claim 6, characterized in that: In step (6), a whole circle with a radius of 1 m is taken as a reference circle in the ξ-η two-dimensional plane, and the reference circle is discretized with equal arc length; N discrete points are adopted to obtain the coordinates of the reference circle in the ξ-η two-dimensional plane, to form an N+1 row and 2 column matrix where the data of the first row and the last row are the same; the matrix is called a reference circle matrix; 8. The method of designing according to claim 7, characterized in that: In step (7), define A coefficient matrix for the diffuser inlet, which satisfies is an N by N+1 matrix; the matrix A specific expansion of the matrix Unfolded is: From the above equation, the matrix The coefficient matrix of the diffuser outlet is obtained in the same way and the coefficient matrix of the central control section 9. The method of designing according to claim 8, characterized in that: In step (8), the total number of transition sections K is specified, and the percentage of arc length position 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 a central control section exists, then the central control section is one of the transition sections; s is the percentage of the arc length of the transition section. k As the independent variable, with the coefficient matrix For the variable to be interpolated, the cubic spline interpolation method is used to calculate... The value of ; in the process of calculating the transition coefficient matrix of the central control section, it is necessary to perform interpolation in segments, and the interpolation method is still cubic spline interpolation.

10. The method of claim 9, wherein: In step (9), the matrix expression of the transition section is calculated from In step (6), the matrix expression of the transition section is calculated from In step (8), the matrix expression of the transition section is calculated from The matrix expression of each transition section in the ξ-η two-dimensional plane is calculated The matrix corresponding to the profile line of the first transition section is The matrix corresponding to the profile line of the 2nd transition section is The matrix corresponding to the profile line of the 3rd transition section is And so on, up to the matrix corresponding to the last transition section The following is the matrix representation of the transition section the calculation formula of the second parameter is:

11. The method of designing according to claim 10, characterized in that: In step (10), the matrix expression of the transition cross section calculated in step (9) is scaled The area enclosed by each transition cross section in the ξ-η two-dimensional plane is calculated, and the matrix expression of each transition cross section is modified as The area enclosed by each transition cross section in the ξ-η two-dimensional plane is calculated, and the matrix expression of each transition cross section is modified as Finally, the area enclosed by each transition cross section in the ξ-η two-dimensional plane is equal to the area of the reference circle, and the matrix expression of each transition cross section in the ξ-η two-dimensional plane after modification is still denoted as First, based on step (9) the matrix of discrete points has been obtained for describing the profile line of the transition cross section The figure is fitted, and then the area of the transition section is calculated, and the area of the Kth transition section is denoted as A k ; the area of the reference circle is denoted as A base ; Second, determine A k , A base the ratio of the areas, obtaining a scale factor Wherein r represents the ratio of the radius of a circle with the same area as the transition section to the reference circle radius; Subsequently, the matrix The matrix is modified, and the modified matrix is still used Indicates that The modified expression is as shown in the equation All the transition sections are processed as above to obtain a series of transition sections with equal area and base circle, and a discrete point matrix describing the transition sections 12. The method of claim 1, wherein: In step (12), the matrix expression of the transition section is enlarged or reduced again according to the area change rule of step (11) based on the Kth transition section area determined in step (10) The final matrix expression describing the transition section pattern is formed, each pattern being recorded as a matrix of N rows and 3 columns The first column of numbers in the matrix is 0, and the last two columns are the same as the enlarged or reduced That is, the profile line information in the ξ-η two-dimensional plane is converted into the three-dimensional coordinate system o-xyz, but the normal vector and the x direction of the pattern are still kept the same; 13. The method of designing according to claim 12, characterized in that: In step (13), K discrete points of equal arc length are extracted on the centerline determined in step (3), and the points are analyzed in the o-xyz coordinate system. Each 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 diffuser centerline and is perpendicular to the diffuser centerline at that point, k = 1, 2, 3... K. Subsequently, a three-dimensional expansion duct that meets the requirements, namely the intake diffuser, is obtained.

14. An electronic device, comprising: One or more processors; and a storage device for storing one or more programs, which, when executed by the one or more processors, cause the one or more processors to implement the design method of any one of claims 1 to 13.

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

Images