A subsonic diffuser design method based on nonlinear weighted cross-sectional variation law
By using nonlinear weighted cross-sectional variation rules and piecewise spline control weights, the problem of inflexible design of the middle cross-sectional shape of the subsonic diffuser is solved, achieving a more flexible and precise diffuser design.
Patent Information
- Application Number
- CN202411947226.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-27
- Publication Date
- 2025-10-24
- Estimated Expiration
- 2044-12-27
AI Technical Summary
In the existing technology of subsonic diffuser design, the design of the middle cross-section shape is not flexible enough, lacks geometric intuitiveness, and cannot uniquely determine the cross-section shape between the inlet and outlet.
A design method based on the nonlinear weighted cross-section variation law is adopted. The discrete coordinates of the intermediate cross-section shape line are regarded as a weighted combination of the coordinates of the discrete points of the inlet and outlet cross-section shapes. The variation law of the weights is controlled by piecewise splines to realize the parametric design of the diffuser.
The flexibility and local adjustment of the diffuser cross-sectional shape are achieved, the design flexibility and accuracy are enhanced, and a more intuitive geometric design method is provided.
Smart Images

Figure CN119808312B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of aircraft inlet, and particularly relates to a novel design method of a subsonic diffuser. BACKGROUND
[0002] In the field of aircraft engines, the inlet is responsible for capturing the compression of the incoming flow, so that the airflow is decelerated and pressurized, and finally flows to the aircraft engine at a suitable speed. The subsonic diffuser refers to a pipe with gradually increasing cross-sectional area, and its cross-sectional shape is generally also changing, which can decelerate the subsonic airflow and increase the pressure. Therefore, the subsonic diffuser is an important part of the aircraft inlet.
[0003] The diffuser design method proposed by C.C.Lee in 1985 is a relatively classic method. He expressed the change law of the center line of the isolation section and the change law of the cross-sectional area of the pipe with a fourth-order polynomial. By taking different polynomial coefficients, three change laws of slow and rapid, slow first and rapid later, and rapid first and slow later are formed. However, the method proposed by C.C.Lee can only determine the center line shape and cross-sectional area change law of the diffuser, and cannot determine the shape of each cross section of the diffuser. Even if the inlet shape and outlet shape are specified, the cross-sectional shape between the inlet and outlet cannot be uniquely determined.
[0004] The general subsonic diffuser design method proposed in the patent No.CN201410187196.X calculates the curvature distribution of the inlet and outlet shape lines, and creates each intermediate cross-sectional shape line through the transition of the curvature distribution of the inlet and outlet shape lines. The improved general subsonic diffuser design method proposed in the patent No.CN202110392258.0 obtains a more accurate diffuser structure by dividing the inlet and outlet shape lines into multiple parts and one-to-one correspondence.
[0005] The technical solutions of the above two patents lack geometric intuition when generating intermediate cross-sectional shape lines, and the shape design of the intermediate cross section is not flexible enough.
[0006] Therefore, a new diffuser design method with more flexible cross-sectional shape change is needed. SUMMARY
[0007] To solve the above problems, the application provides a subsonic diffuser design method based on nonlinear weighted cross-section variation law.
[0008] To achieve the above purpose, the application can adopt the following technical solutions:
[0009] A subsonic diffuser design method based on nonlinear weighted cross-section variation law comprises the following steps:
[0010] (1) Discretize the inlet cross-section profile and the outlet cross-section profile of the diffuser into a plurality of point coordinates;
[0011] (2) Calculate the inlet cross-section area and the outlet cross-section area of the diffuser through the plurality of point coordinates, and then divide the point coordinates of the inlet cross-section profile and the outlet cross-section profile by the inlet cross-section area and the outlet cross-section area respectively, so as to scale the discretized inlet cross-section and outlet cross-section to unit area;
[0012] (3) Calculate the centroid of the scaled inlet cross-section and outlet cross-section, and then subtract the centroid coordinates from the point coordinates of the inlet cross-section profile and the outlet cross-section profile respectively, so as to translate the inlet cross-section profile and the outlet cross-section profile to the origin;
[0013] (4) Weight the point coordinates of the translated inlet cross-section profile and outlet cross-section profile with weights, control the variation law of the weights through piecewise spline, so as to control the cross-section shape variation law, and obtain the discrete point coordinates of the intermediate cross-section;
[0014] (5) Determine the cross-section area variation law, and scale the point coordinates of the inlet cross-section, the outlet cross-section and the intermediate cross-section according to the law;
[0015] (6) Determine the center line shape, translate the centroids of the inlet cross-section, the outlet cross-section and the intermediate cross-section to the same x position of the center line, and rotate each cross-section so that its surface is perpendicular to the center line;
[0016] (7) Smoothly connect the discrete points of each cross-section to form the final inner surface of the diffuser.
[0017] Further, in step (1), the inlet cross-section profile and the outlet cross-section profile are uniformly discretized, and if the inlet profile has an acute angle, the acute angle is taken as an additional point, while the number of discrete points of the outlet cross-section profile and the inlet cross-section profile is kept equal.
[0018] Further, in step (2), the inlet cross-section area and the outlet cross-section area are calculated by the following formula:
[0019]
[0020] wherein S is the inlet cross-sectional area or the outlet cross-sectional area,
[0021] When S is the inlet cross-sectional area, it is denoted as S in , z1, y1 are the z, y coordinates of the first point of the inlet cross-sectional profile in the xyz three-dimensional rectangular coordinate system, z n , y n are the z, y coordinates of the last point of the inlet cross-sectional profile in the xyz three-dimensional rectangular coordinate system, z i , y i are the z, y coordinates of the i-th point of the inlet cross-sectional profile in the xyz three-dimensional rectangular coordinate system.
[0022] When S is the outlet cross-sectional area, it is denoted as S out , z1, y1 are the z, y coordinates of the first point of the outlet cross-sectional profile in the xyz three-dimensional rectangular coordinate system, z n , y n are the z, y coordinates of the last point of the outlet cross-sectional profile in the xyz three-dimensional rectangular coordinate system, z i , y i are the z, y coordinates of the i-th point of the outlet cross-sectional profile in the xyz three-dimensional rectangular coordinate system.
[0023] Further, in step (2), the formula for scaling the inlet and outlet cross-sections after being discretized into a plurality of points to a unit area is:
[0024]
[0025] wherein Z i , Y i are the z, y coordinates of the points of the unit area inlet or outlet cross-section on the z, y axes.
[0026] Further, in step (3), the formula for calculating the centroid coordinates of the inlet cross-section and the centroid coordinates of the outlet cross-section is:
[0027]
[0028] (z c , y c ) is the centroid coordinates of the inlet cross-section or the centroid coordinates of the outlet cross-section.
[0029] Further, in step (4), to control the change rule of the weight, the discrete point coordinates of the intermediate cross-section are realized by using the following formula:
[0030]
[0031] w irepresents the weight of the i-th section coordinate along the way between the inlet and outlet sections; z i,j and y i,j They represent the coordinates of the jth point along the i-th cross-sectional line; z in,j and yin ,j They represent the coordinates of the jth point on the inlet cross-sectional line, zout ,j and yout ,j They respectively represent the coordinates of the jth point on the outlet cross-sectional line.
[0032] Furthermore, in step (4), the weight w i The acquisition method is:
[0033] First provide the piecewise cubic spline expression of weight w:
[0034]
[0035] The piecewise cubic spline represented by the above formula consists of three first-connected and smoothly transitioned cubic curves A, B, and C. The expression of the piecewise cubic spline is determined as follows:
[0036] The expression for piecewise cubic spline is is the independent variable, i.e. the dimensionless x-coordinate of the diffuser length L, with a value range of [0,1]; the x-coordinate of the centroid of the diffuser inlet section x c,in is 0, the corresponding dimensionless coordinate Specify the coordinate weight w of the point on the diffuser inlet cross-section line c,in 1, which is the starting point of the spline That is, P1(0,1); the x coordinate of the centroid of the diffuser outlet section is x c,out is L, the corresponding dimensionless coordinate Specify the coordinate weight w of the point on the diffuser outlet cross-section line c,out 0, which is the end point of the spline That is, P1(1,0); In addition, the expression for determining the piecewise cubic spline also requires two spline control points, namely the connection points between the cubic curves A and B and the connection point between cubic curves B and C The spline starting point P1, the spline ending point P2 and the two spline control points CP1 and CP2 divide the segmented cubic spline into three segments, namely cubic curves A, B and C;
[0037] a1, b1, c1, d1, a2, b2, c2, d2, a3, b3, c3, d3 are unknown coefficients; is the coordinate of the spline starting point P1 in the x-axis direction, is the coordinate of the spline control point CP1 in the x direction, is the coordinate of the spline control point CP2 in the x direction; is the coordinate of the spline end point in the x direction,
[0038] is the non-dimensional x coordinate of the i-th section centroid along the path is substituted into the expression of the piecewise cubic spline, i.e. The weight w of the point coordinate on the section centroid line is obtained i ,
[0039] Further, the weight w of the point coordinate on the section centroid line is obtained i is substituted into The point coordinate of the intermediate section centroid line is obtained, i.e. the shape of all intermediate sections is determined.
[0040] Advantages: Compared with the prior art, the advantages of the present application are:
[0041] The piecewise spline is used to control the shape change rule of the diffuser, and the piecewise spline can locally change the shape by controlling the points, so as to locally correct the area change rule of the diffuser, and increase the flexibility on the basis of the conventional cross section change rule.
[0042] The design method provided by the present application can be stored on a storage medium as a computer program, and comprises the following technical scheme: an electronic device comprising one or more processors and a storage device for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned matrix transformation-based improved design method of a diffuser.
[0043] and
[0044] A computer readable medium having a computer program stored thereon, wherein the program is executed by a processor to implement the above-mentioned matrix transformation-based improved design method of a diffuser. BRIEF DESCRIPTION OF DRAWINGS
[0045] Figure 1 is a weight distribution graph of different forms in the present application.
[0046] Figure 2 is a cross section area change rule graph used in case 1 and case 2.
[0047] Figure 3 is a center line change rule graph used in case 1 and case 2.
[0048] Figure 4 is a comparison graph of section centroid lines under different weighting modes.
[0049] Figure 5 is the diffuser inner surface in linear weighting mode.
[0050] Figure 6 is the diffuser inner surface obtained in case 1.
[0051] Figure 7 is the diffuser inner surface obtained in case 2. DETAILED DESCRIPTION
[0052] In order to make the purpose, design process, technical method and advantages of the present application more clear, the present application will be further explained in detail below with the help of the accompanying drawings.
[0053] A subsonic diffuser design method based on nonlinear weighting cross-section variation law, comprising the following steps:
[0054] (1) Establish a rectangular coordinate system with the flow direction as the x-axis, the diffuser height direction as the y-axis, and the spanwise direction as the z-axis. Discretize the diffuser inlet and outlet cross-section profile into n ordered points, and mark their coordinates as z i , y i , i∈1, 2, 3,..., n. If the profile has cusps, each cusp is regarded as a point, and the total number of points at the inlet and outlet must be equal during the discretization process.
[0055] (2) Calculate the inlet and outlet cross-section areas S in , S out , respectively, by the polygon area calculation method shown in formula (1.1), where z and y represent the z and y coordinates of the discrete point coordinates on the corresponding cross-section profile, and the subscript represents the order of the point. Then, divide the point coordinates of the inlet and outlet cross-section profiles by the inlet and outlet areas, respectively, according to formula (1.2), so as to scale the inlet and outlet cross-sections to unit area.
[0056]
[0057] (3) Calculate the center of gravity coordinates z c , y c of the scaled inlet and outlet cross-sections according to formula (1.3), and then subtract the center of gravity coordinates from the point coordinates of the inlet and outlet cross-section profiles according to formula (1.4), so as to translate the inlet and outlet cross-section profiles to the coordinate origin.
[0058]
[0059] (4) Determine the variation pattern of the cross-sectional shape. Weight the coordinates of the points on the translated inlet and outlet lines to obtain the coordinates of the discrete points of the middle cross-section. Use piecewise cubic splines to control the variation pattern of the weights. By changing the relative coordinates of the spline control points, the weights can be changed within a small range, thereby locally changing the variation pattern of the cross-sectional shape and making the cross-sectional shape change more flexible.
[0060] In formula (1.5), w i represents the weight of the coordinates of the i-th cross-section line along the path starting from the inlet; z i,j and y i,j They represent the coordinates of the jth point along the i-th cross-sectional line; z in,j and y in,j They represent the coordinates of the jth point on the inlet cross-sectional line, z out,j and y out,j They respectively represent the coordinates of the jth point on the outlet cross-sectional line.
[0061] z i,j =(1-w i )z in,j +w i z out,j
[0062] y i,j =(1-w i )y in,j +w i y out,j (1.5)
[0063] The weighted piecewise cubic spline curve expression is determined as follows:
[0064] The expression for piecewise cubic spline is is the independent variable, i.e. the dimensionless x-coordinate of the diffuser length L, with a value range of [0,1], as shown in formula (1.6). The x-coordinate x of the centroid of the diffuser inlet section is c,in is 0, the corresponding dimensionless coordinate Specify the coordinate weight w of the point on the cross-section line c,in 1, which is the starting point of the spline That is, P1(0,1). The x-coordinate of the centroid of the diffuser outlet section is x c,out is L, the corresponding dimensionless coordinate Specify the coordinate weight w of the point on the cross-section line c,out 0, which is the end point of the spline That is, P1(1,0). In addition, the expression for determining the piecewise cubic spline also requires two spline control points, namely the connection points between the cubic curves A and B. and the connection point between cubic curves B and C The spline starting point P1, the spline ending point P2 and the two spline control points CP1 and CP2 divide the piecewise cubic spline into three segments, which are cubic curves A, B and C respectively; the cubic curve expression is in the form of where a, b, c and d are undetermined coefficients, and the equation group of the three curves is shown in formula (1.7), where a1, b1, c1, d1, a2, b2, c2, d2, a3, b3, c3 and d3 are undetermined coefficients.
[0065]
[0066] There are 12 undetermined coefficients in the equation group (1.7), and 12 constraint conditions are needed. According to the C0 continuity condition of the spline curve, the spline A should pass through the starting point P1 and the control point CP1, the spline B should pass through the control point CP1 and CP2, and the spline C should pass through the control point CP2 and the ending point P2. By substituting the coordinates of each point into the corresponding equation, the following six equations can be obtained.
[0067]
[0068] is the coordinate of the spline starting point P1 in the x-axis direction, is the coordinate of the spline control point CP1 in the x direction, is the coordinate of the spline control point CP2 in the x direction; is the coordinate of the spline ending point in the x direction,
[0069] According to the C1 continuity condition of the spline curve, the slopes of the adjacent curve segments constituting the spline curve should be equal at their intersection points. The derivative of the cubic curve equation group (1.7) with respect to the independent variable is formula (1.8). At the control point CP1, the slopes of the cubic curves A and B should be equal, and at the control point CP2, the slopes of the cubic curves B and C should be equal, that is, formula (1.10). Combining formula (1.9) and substituting the coordinates of the points CP1 and CP2 into formula (1.10) and rearranging, two equations shown in formula (1.11) can be obtained.
[0070]
[0071] According to the C2 continuity condition of the spline curve, the curvatures of each spline curve segment should be equal at the intersection points, that is, the second derivatives should be equal. The derivative of the cubic curve equation group (1.7) with respect to the independent variable Taking the second derivative yields equation (1.12). At control point CP1, the second derivatives of cubic curves A and B should be equal. At control point CP2, the second derivatives of cubic curves A and B should be equal, i.e., equation (1.13). Combining equation (1.12) and substituting the coordinates of points CP1 and CP2 into equation (1.13) and sorting them out, we obtain the two equations shown in equation (1.14).
[0072]
[0073]
[0074] Finally, we need to consider the endpoint constraints. Given that the slope of spline A at the starting point P1 is s1, and the slope of spline C at the ending point P2 is s2, that is, equation (1.15), substituting the coordinates of points P1 and P2 into equation (1.15) yields the two equations shown in equation (1.16).
[0075] s1=A′(P1)
[0076] s2=C′(P2)(1.15)
[0077] s1=b1
[0078] s2=b3+2c3+3d4(1.16)
[0079] There are 12 simultaneous equations (1.8), (1.11), (1.14), and (1.16), which can be written in matrix form as the system of equations shown in (1.17). Solving this system of equations gives the expression (1.18) for the spline curve, which is a piecewise function consisting of three first-connected cubic curves A, B, and C.
[0080]
[0081] The dimensionless x-coordinate of the centroid of the i-th section along the path is Substitute it into formula (1.18) and we get The weight w of the coordinates of the points on the cross-sectional line can be obtained i ,
[0082] Then, according to formula (1.5), the point coordinates of the middle section shape line are obtained, which means the shapes of all middle sections are determined.
[0083] (5) Determine the law of cross-sectional area change and scale the coordinates of the inlet and outlet sections and the intermediate section points according to the law.
[0084] (6) Determine the shape of the center line, translate the centroids of the inlet and outlet sections and the middle section to the same x position on the center line, and rotate each section so that its surface is perpendicular to the center line.
[0085] (7), the discrete points of each section are smoothly connected to form the final inner profile of the diffuser.
[0086] The design method adopts a piecewise cubic spline with control points to represent the weight w of the cross section shape change i , and the relative coordinates of the control points can be changed to achieve arbitrary control of the cross section change rule, which can be used for parametric study and local profile optimization of the diffuser.
[0087] The specific implementation of the method will be given below in combination with the drawings:
[0088] Case 1:
[0089] (1), assuming that the inlet is a rectangle with a length of 1 m and a width of 3 m, and the outlet is a standard circle with a radius of 1.5 m. The inlet and outlet profiles are uniformly discretized to obtain ordered point coordinates (x i ,y i ) in the zy plane, a total of 48 points.
[0090] (2), the areas S in 、S out of the discretized inlet and outlet are calculated according to formula (1.1), and the inlet and outlet point coordinates are divided by S in 、S out , respectively, to obtain the discretized coordinates of the unit area inlet and outlet profiles.
[0091] (3), given control point coordinates CP1(0.4,0.75), CP2(0.7,0.43), starting point slope s1=0, and ending point slope s2=-1.428, the weight w distribution along the dimensionless x coordinate can be calculated by solving the linear equation system (1.17), and the specific expression is given by formula (1.19), Figure 1 The dashed line in formula (1.19) is the curve corresponding to the nonlinear expression. As can be seen from the figure, compared with the linear weighting in the prior art, the nonlinear weighting distribution in this example has the characteristics of slow in front and rapid in back, which makes the cross section shape of the diffuser in the first half transition slowly to the outlet shape, and in the second half transition quickly. Any form of change rule can be specified as needed.
[0092]
[0093] (4), given the length of the diffuser L=10 m, and 34 cross sections are uniformly distributed in the x direction, the dimensionless x coordinate of the cross section shown in formula (1.6) is brought into formula (1.18) to obtain the weight w i of the i-th cross section. According to formula (1.5), the profile point coordinates of the intermediate cross section can be calculated, that is, the change rule of the intermediate cross section shape is determined.
[0094] (5),Figure 2 The cross-sectional area variation law is shown in expression (1.20), where x c is the centroid coordinate of an arbitrary intermediate cross section (including the inlet and outlet cross sections), S is the area of the cross section, S in , S out are the areas of the inlet and outlet, respectively, and the point coordinates of the intermediate cross section profile are scaled by expression (1.20).
[0095] (6) The eccentricity H = 10 m is specified, and the control point coordinates CP1(0.4, 0.35) and CP2(0.7, 0.13) are selected. Figure 3 The centerline variation law is shown in expression (1.21), where y c is the y-coordinate of the centroid of an arbitrary intermediate cross section (including the inlet and outlet cross sections), the discrete points of each cross section profile are translated so that the cross-sectional centroid coordinates satisfy expression (1.21), and the discrete points are then rotated so that each cross section is perpendicular to the centerline. The cross section profiles are obtained by connecting adjacent discrete points on the same cross section with straight line segments. Figure 4 The green lines and points represent the cross section profiles and discrete points, respectively. For ease of comparison, the linearly weighted cross section profiles and discrete points are shown in red lines and points.
[0096]
[0097] (7) The cross section profiles are connected to form the diffuser inner surface, Figure 6 The three-dimensional view of the diffuser inner surface obtained under the nonlinear weighting condition of this case is shown. As a comparative example of the prior art, Figure 5 The three-dimensional view of the diffuser inner surface obtained under the linear weighting condition of the prior art is shown.
[0098] Case 2
[0099] According to the steps of Case 1, the other parameters are kept unchanged, and the control point coordinates CP1(0.4, 0.35) and CP2(0.7, 0.13) are adjusted, the initial point slope s1 = -1.732, and the terminal point slope s2 = -0.466. The specific expression of the cubic piecewise spline is shown in expression (1.22), Figure 1 The dashed line in (1.22) is the weight distribution piecewise spline curve corresponding to this nonlinear expression. Compared with linear weighting, the nonlinear weighting distribution in this example has the characteristics of being sharp in the front and slow in the back, making the cross-sectional shape of the diffuser transition quickly to the outlet shape in the first half, and the transition slows down in the second half. Figure 4 The blue points in (1.22) represent the discrete points of the cross section profile, and the blue lines show the inlet, outlet, and part of the intermediate cross section profiles obtained in this case. Figure 7 The three-dimensional view of the diffuser inner surface obtained in this case is shown.
[0100]
[0101] An embodiment of an electronic device includes:
[0102] one or more processors; and a memory 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 above-mentioned subsonic diffuser design method based on nonlinearly weighted cross-sectional variation law.
[0103] An embodiment of a computer readable medium having stored thereon a computer program, which when executed by a processor, implements the above-mentioned subsonic diffuser design method based on nonlinearly weighted cross-sectional variation law.
[0104] In addition, there are many specific implementation methods and approaches of the present application, and the above description is only the preferred embodiment of the present application. It should be noted that for those 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 designing a subsonic diffuser based on a nonlinearly weighted cross-sectional variation law, characterized in that, The method comprises the following steps: (1) discretizing the inlet section profile and the outlet section profile of the diffuser into a plurality of point coordinates; (2) calculating the inlet section area and the outlet section area of the diffuser through the plurality of point coordinates, and then dividing the point coordinates of the inlet section profile and the outlet section profile by the inlet section area and the outlet section area respectively, so as to scale the discretized inlet section and outlet section to unit area; (3) calculating the centroid of the scaled inlet section and outlet section, and then subtracting the centroid coordinates from the point coordinates of the inlet section profile and the outlet section profile respectively, so as to translate the inlet section profile and the outlet section profile to the origin; (4) weighting the point coordinates of the translated inlet section profile and outlet section profile by weight, and controlling the variation law of the weight through piecewise spline, so as to control the variation law of the section shape and obtain the discrete point coordinates of the intermediate section; The variation law of the weight is controlled to obtain the discrete point coordinates of the intermediate section by using the following formula: ; w i represents the weight of the i-th coordinate along the section between the inlet and outlet section;z i,j and y i,j respectively represent the coordinates of the j-th point on the i-th section profile along the section;z in,j and y in,j respectively represent the coordinates of the j-th point on the inlet section profile,z out,j and y out,j respectively represent the coordinates of the j-th point on the outlet section profile. Weights w i The acquisition method is: First, a piecewise cubic spline expression of the weight w is provided: ; The piecewise cubic spline represented by the above formula is composed of three cubic curves A, B and C which are connected at the beginning and smoothly transitioned; the piecewise cubic spline expression is determined in the following manner: The expression for piecewise cubic spline is is the independent variable, i.e. the dimensionless x-coordinate of the diffuser length L, with a value range of [0, 1]; the x-coordinate of the centroid of the diffuser inlet section is 0, the corresponding dimensionless coordinate , specify the coordinate weight of the point on the diffuser inlet cross-section line 1, which is the starting point of the spline ,Right now ; x-coordinate of the centroid of the diffuser outlet section is L, the corresponding dimensionless coordinate , specify the coordinate weight of the point on the diffuser outlet cross-section line 0, marked as the end point of the spline ,Right now ; In addition, the expression for determining the piecewise cubic spline also requires two spline control points, namely the connection points between the cubic curves A and B and the connection point between cubic curves B and C The spline starting point P1, the spline ending point P2 and the two spline control points CP1 and CP2 divide the segmented cubic spline into three segments, namely cubic curves A, B and C. a1, b1, c1, d1, a2, b2, c2, d2, a3, b3, c3, d3 are undetermined coefficients; is the coordinate of the spline start point P1 in the x-axis direction, = , is the coordinate of the spline control point CP1 in the x direction, is the coordinate of the spline control point CP2 in the x direction; is the coordinate of the spline end point in the x direction, = ; The dimensionless x coordinate of the centroid of the i-th cross section along the path is The dimensionless y coordinate of the centroid of the i-th cross section along the path is Substituting into the expression for the piecewise cubic spline, i.e. = The weight w of the point coordinate on the cross section profile is obtained i , w i= ; The weight w of the point coordinate on the cross-section shape line is obtained i After that, the following is obtained The point coordinate of the intermediate cross-section shape line is obtained, that is, the shape of all intermediate cross-sections is determined (5) determining the variation law of the section area, and scaling the point coordinates of the inlet section, the outlet section and the intermediate section according to the law; (6) determining the shape of the center line, translating the centroids of the inlet section, the outlet section and the intermediate section to the same x position of the center line, and rotating each section to make its surface perpendicular to the center line; (7) smoothing and connecting the discrete points of each section to form the final inner surface of the diffuser.
2. The design method according to claim 1, characterized in that: In step (1), the inlet section profile and the outlet section profile are uniformly discretized, and if the inlet profile has an acute angle, the acute angle is taken as an additional point, while the number of discrete points of the outlet section profile and the inlet section profile is kept equal.
3. The method of claim 1, wherein: In step (2), the inlet section area and the outlet section area are calculated by the following formula: ; where S is the inlet section area or the outlet section area, When S is the inlet cross-sectional area, it is denoted as S in , z1, y1 are the z, y coordinates of the first point of the inlet cross-sectional profile in the xyz three-dimensional rectangular coordinate system, z n , y n are the z, y coordinates of the last point of the inlet cross-sectional profile in the xyz three-dimensional rectangular coordinate system, z i , y i are the z, y coordinates of the i-th point of the inlet cross-sectional profile in the xyz three-dimensional rectangular coordinate system; When S is the outlet cross-sectional area, it is denoted as S out , z1, y1 are the z, y coordinates of the first point of the outlet cross-sectional profile in the xyz three-dimensional rectangular coordinate system, z n , y n are the z, y coordinates of the last point of the outlet cross-sectional profile in the xyz three-dimensional rectangular coordinate system, z i , y i are the z, y coordinates of the i-th point of the outlet cross-sectional profile in the xyz three-dimensional rectangular coordinate system.
4. The method of claim 1, wherein: In step (2), the formula for scaling the discretized inlet section and outlet section to unit area is: ; wherein Z i , Y i are the point coordinates on the z, y axes of the import or export section per unit area, respectively.
5. The method of claim 1, wherein: In step (3), the centroid coordinates of the inlet section and the centroid coordinates of the outlet section are calculated by the following formula: ; (z c , y c ) are the center of area coordinates of the inlet section or the center of area coordinates of the outlet section.
6. 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 5.
7. 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 5.
Citation Information
Patent Citations
Universal design method for subsonic diffuser
CN103950544B
Universal design method for subsonic diffuser
CN103950544A
Improved general subsonic diffuser design method
CN113212771A