A turbine draft tube based on a common spherical tangent

Abstract

This invention discloses a turbine draft tube based on a common tangent sphere, relating to the field of hydraulic engineering technology. It includes a tube body defined by multiple common tangent spheres arranged sequentially along the flow direction of the draft tube with gradually changing radii. The center coordinates, radius, and center-to-center distance of each common tangent sphere are determined through correlation calculations using inlet and outlet parameters of the draft tube. The inner wall profile of the tube body is composed of multiple tapered tube sections. These tapered tubes are formed by rotating 360° around their axis via a symmetrical waistline and then being divided by a partition plate. The turbine draft tube designed in this invention achieves continuous gradual change in the inner wall profile and optimization of hydraulic characteristics through a collaborative control method of geometric construction. This solves the technical problems of traditional turbine draft tube design relying on empirical formulas or local optimization, as well as the complex design process, long cycle, and limited flexibility. Simultaneously, it simplifies the design process and enhances the flexibility and scalability of the design.

Description

Technical Field

[0001] This invention relates to the field of water conservancy and hydropower engineering technology, and in particular to a turbine tailrace pipe based on a common tangent ball. Background Technology

[0002] The draft tube, a core hydraulic component of the turbine unit, is installed at the runner outlet. Its core function is to recover the residual kinetic and potential energy of the water discharged from the runner, reduce the outlet velocity, improve the turbine's energy conversion efficiency, and guide the water flow smoothly out of the unit, preventing equipment vibration caused by turbulent flow. Its structure directly affects the turbine's operating efficiency, vibration characteristics, and cavitation performance. Traditional draft tube designs often rely on empirical formulas or local optimizations, making it difficult to achieve good hydraulic matching across the entire flow path.

[0003] The existing design of turbine draft tubes has the following problems: Traditional designs rely on empirical formulas or iterative optimization using finite element analysis, making it difficult to accurately control the continuous and gradual changes in the inner wall profile. This leads to flow separation, backflow, and vortex phenomena within the tube, resulting in significant energy loss and reduced overall turbine efficiency. Under varying operating conditions, the fixed geometry of the draft tube has poor adaptability and is prone to pressure pulsation and vibration. In traditional designs, the optimization and adjustment of various parameters are independent and lack a collaborative mechanism, resulting in poor flow channel adaptability and difficulty in balancing flow stability and energy recovery efficiency under different operating conditions. Traditional design methods are complex and time-consuming, making it difficult to quickly respond to personalized design needs under different head and flow conditions, limiting flexibility and scalability. Therefore, a turbine draft tube based on a common tangent sphere is proposed. Summary of the Invention

[0004] The purpose of this invention is to solve the problems in the prior art by proposing a turbine tailrace pipe based on a common spherical tangent.

[0005] A turbine draft tube based on a tangent sphere includes a tube body determined by multiple tangent spheres. The multiple tangent spheres are arranged sequentially along the flow direction of the draft tube and their radii are gradually changed. The center coordinates, radius, and center-to-center distance of each tangent sphere are determined by correlation calculation of the inlet and outlet parameters of the draft tube. The inner wall profile of the tube is composed of multiple sections of tapered tubes, which are formed by rotating 360° around the axis of the tapered tubes via symmetrical waistlines and then being divided by partition plates. Each section of the conical tube is a segment between two adjacent common tangent spheres. The line connecting the centers of the two adjacent common tangent spheres is the axis of the conical tube. All the axes of the conical tubes are on the same plane, i.e., the axial plane. The common tangent line between two adjacent common tangent spheres on the axial plane and near the inner bend of the tailpipe is the axial plane common tangent line. The intersection of the axial plane common tangent line of the conical tube and the axial plane common tangent line of the next section of the conical tube is the waistline outlet. The line connecting the waistline outlet of the conical tube and the waistline outlet of the previous section of the conical tube is the waistline of the conical tube. The symmetrical waistline on each conical tube is obtained symmetrically through the axis of the conical tube.

[0006] Preferably, the radius of the common tangent sphere gradually increases according to a preset multiplier, and the formula for calculating the radius of the common tangent sphere is:

[0007] in, For the first One common tangent sphere radius; For the first +1 common tangent sphere radius; For the first +1 factor of the common tangent sphere radius, ; For segment number =1,2,3,…,n, where n is the number of sections in the tapered tube. .

[0008] Preferably, the distance between the centers of adjacent common tangent balls is calculated as follows: It has a semi-cone apex angle and axis turning angle The apex angle of the semi-cone The angle between the cone tube axis and the cone tube waistline is set segment by segment along the water flow direction. The axis turning angle The angle between the axis of the conical tube and the axis of the previous conical tube is set segment by segment along the direction of water flow. ; The distance between the centers of two adjacent common tangent spheres is determined by the radius of the adjacent common tangent spheres and the apex angle of the semicone. Jointly determined:

[0009] in, For the first The semi-cone apex angle of the conical tube .

[0010] Preferably, the coordinates of the center of the common tangent sphere are obtained through iterative calculation in the following manner: Using the coordinates of the center of the greatest common tangent sphere as the origin, iterate segment by segment in the reverse direction of water flow:

[0011]

[0012]

[0013] In the axial plane, For the first The coordinates of the center of each common tangent sphere For the first +1 coordinates of the center of the common tangent sphere, For the first The distance between the centers of the two common tangent spheres in the conical tube. For the first The axis turning angle of the tapered tube , For the first Inlet angle of the tapered pipe The water inlet angle The angle between the axis of the tapered tube and the axis of the inlet is denoted as , and .

[0014] Preferably, the horizontal angle of the waistline of the tapered tube is... The calculation method for the vertex of the horizontal cone is as follows: No. The common tangent of the axial plane of the tapered tube and the first The straight line containing the center of the common tangent sphere. The intersection point is the first The vertex of the horizontal cone, the common tangent of the axial plane and the straight line The included angle is the horizontal angle of the waistline. ; The horizontal angle of the waistline The angle is equal to the inlet angle of the corresponding cone pipe. With the apex angle of the semi-cone The sum of ; The coordinates of the vertex of the horizontal cone are calculated as follows:

[0015]

[0016] in, The first The x and y coordinates of the vertex of the horizontal cone in the conical tube. For the first Horizontal angle of the waistline of the tapered tube , For the first The radius of the tangent sphere.

[0017] Preferably, the waistline exit coordinates are calculated as follows: The coordinates of the waistline exit are solved by simultaneously solving the equations of the two adjacent tapered tube waistlines. Let the equation of the line containing the tapered tube waistline be:

[0018] Let the ordinates of the equations of two adjacent lines be... If they are equal, solve for the x-coordinate of the point where the waistline exits. Substituting into any equation, we obtain the ordinate of the point where the waistline exits. .

[0019] Preferably, the starting point of the pipe body 1 is the inlet of the first waistline, and the formula for calculating the coordinates of the inlet of the first waistline is:

[0020]

[0021] in, , These are the x and y coordinates of the entrance to the first waistline section, respectively. , These are the x and y coordinates of the vertex of the first horizontal cone, respectively. The horizontal angle of the waistline of the first tapered tube ; The x-coordinate of the vertex of the first horizontal cone is determined using the coordinates of the center of the first common tangent sphere and the horizontal angle of the waistline of the first conical tube. The vertical axis is the coordinate of the center of the first common tangent ball, which is:

[0022] in, , Let x and y be the coordinates of the center of the first common tangent sphere.

[0023] Preferably, the formula for calculating the exit coordinates of the last waistline is:

[0024]

[0025] in, , These are the x and y coordinates of the exit point of the last waistline section. The radius of the largest common tangent sphere, and The slope and intercept of the line equation containing the last waistline; The equation of the straight line containing the last waistline is determined by the coordinates of the vertex of the last horizontal cone and the exit coordinates of the penultimate waistline.

[0026] Preferably, the tapered tube is formed by rotating it 360° around its axis via a symmetrical waistline and then dividing it into sections by a partition plate, specifically including: The partition plates are spaced apart along the axis of the tapered tube. The partition plates are stretched and formed by dividing lines in a direction perpendicular to the axis of the tapered tube. The intersection point of two adjacent symmetrical waistlines is the exit point of the symmetrical waistline. The starting coordinates of the dividing line are consistent with the exit coordinates of the waistline, and the ending coordinates are consistent with the exit coordinates of the symmetrical waistline. The stretching length of the dividing line is four times the radius of the maximum common tangent sphere.

[0027] Compared with existing technologies, the advantages of this invention are: The turbine draft tube designed in this invention achieves continuous gradual change of the inner wall profile and optimization of hydraulic characteristics through a collaborative control method of geometric structure. This solves the technical problems of traditional turbine draft tube design relying on empirical formulas or local optimization, as well as the complex design process, long cycle, and limited flexibility. At the same time, it simplifies the design process and enhances the flexibility and scalability of the design. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the two-dimensional structure of the tailrace pipe based on the common tangent sphere of the present invention (in the axial plane coordinate system).

[0029] Figure 2 This is a schematic diagram of the distribution structure of the conical tube in the tailwater pipe of the present invention.

[0030] Figure 3 This is a schematic diagram of the arrangement and core parameters of the common tangent ball of the present invention.

[0031] Figure 4 This is a schematic diagram of the first part of the structure of the present invention.

[0032] Figure 5 This is a schematic diagram of the structure of the tailwater pipe terminal section of the present invention.

[0033] Figure 6 This is a schematic diagram of the partition plate arrangement structure of the present invention.

[0034] Figure 7 This is a flowchart of the tailwater pipe design using software in this invention.

[0035] Figure 8 This is a rendering of the tailwater pipe created using software according to the present invention.

[0036] In the diagram: 1. Pipe body; 2. Conical pipe; 3. Inlet axis; 4. Radius of the first tangent sphere; 5. Conical pipe axis; 6. The... The radius of the common tangent sphere, the 7th... +1 common tangent radius, 8th... The center of the cut ball, the 9th +1 Common tangent sphere center, 10 Common tangent line of axial plane, 11 Waistline exit, 12 Horizontal cone vertex, 13 Conical tube waistline, 14 Semi-cone apex angle 15 axis turning angle 16 Waistline Horizontal Angle 17. First common tangent ball center; 18. First waistline inlet; 19. First horizontal cone vertex; 20. Maximum common tangent ball radius; 21. Maximum common tangent ball center; 22. Last waistline; 23. Penultimate waistline outlet; 24. Last waistline outlet; 25. Last horizontal cone vertex; 30. Symmetrical waistline; 31. Symmetrical waistline outlet; 32. Dividing line; 33. Inlet angle. 34. Divider plate. Detailed Implementation

[0037] To facilitate understanding of this application and to make the aforementioned objectives, features, and advantages of this application more apparent, a detailed description of specific embodiments of this application is provided below in conjunction with the accompanying drawings. Numerous specific details are set forth in the following description to provide a thorough understanding of this application, and preferred embodiments are shown in the accompanying drawings. However, this application can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of this application. This application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application; therefore, this application is not limited to the specific embodiments disclosed below. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified. In the description of this application, "several" means at least one, such as one, two, etc., unless otherwise explicitly specified. It should be noted that when an element is referred to as being "fixed to" another element, it can be directly attached to the other element or there may be an intervening element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or there may be an intervening element. The terms "vertical," "horizontal," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible implementations. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is only for describing particular implementations and is not intended to limit the scope of this application. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0038] Reference Figure 1-6 As shown, a turbine draft tube based on a tangent sphere includes a tube body 1 defined by multiple tangent spheres. The multiple tangent spheres are arranged sequentially along the flow direction of the draft tube and their radii gradually change. The center coordinates, radius, and center-to-center distance of each tangent sphere are determined by correlation calculation using the inlet and outlet parameters of the draft tube. The inner wall profile of the pipe body 1 is composed of multiple sections of tapered pipe 2. Each section of tapered pipe 2 is a pipe segment between two adjacent common tangent spheres. The line connecting the centers of the two adjacent common tangent spheres is the tapered pipe axis 5. All tapered pipe axes 5 are on the same plane, namely the axial plane (the subsequent coordinates and straight line equations are all based on the axial plane as the coordinate system plane). The common tangent line of two adjacent common tangent spheres on the axial plane and close to the inner bend of the tailwater pipe is the axial plane common tangent line 10. The intersection of the axial plane common tangent line 10 of tapered pipe 2 and the axial plane common tangent line 10 of the next section of tapered pipe 2 is the waistline outlet 11. The line connecting the waistline outlet 11 of tapered pipe 2 and the waistline outlet 11 of the previous section of tapered pipe 2 is the tapered pipe waistline 13.

[0039] The radius of the common tangent sphere gradually increases according to a preset multiplier. The formula for calculating the radius of the common tangent sphere is:

[0040] in, For the first The radius of the tangent sphere is 6; For the first +1 common tangent sphere radius 7; For the first +1 multiple of the radius of the common sphere of 7, ; For segment number =1,2,3,…,n, where n is the number of sections in tapered tube 2. .

[0041] It has a semi-cone apex angle 14 and axis turning angle 15. Aperture of a semi-cone 14 is the angle between the cone tube axis 5 and the cone tube waistline 13, which is set segment by segment along the water flow direction. ; Axis turning angle 15 is the angle between the axis 5 of the conical tube and the axis 5 of the previous conical tube 2, and is set segment by segment along the water flow direction. .

[0042] The distance between the centers of two adjacent common tangent spheres is determined by the radius of the adjacent common tangent spheres and the apex angle of the semicone. 14. Jointly determined:

[0043] in, For the first The semi-cone apex angle of section cone tube 2 14.

[0044] The coordinates of the center of the common tangent sphere are obtained through iterative calculation as follows: Using the coordinates of the center of the greatest common tangent sphere 21 as the origin, the calculation is performed segment by segment in the reverse direction of water flow:

[0045]

[0046]

[0047] In the axial plane, For the first The coordinates of the center of the common tangent sphere, 8. For the first +1 coordinates of the center of the common tangent sphere, 9. For the first The distance between the centers of the two common tangent spheres in the conical tube 2 For the first The axis turning angle of the tapered tube 2 15, For the first The inlet angle of the cone pipe 2 33, inlet angle 33 is the angle between the axis 5 of the tapered tube and the axis 3 of the inlet, determined by the turning angle of each section's axis. 15 accumulated, and .

[0048] No. The common tangent 10 of the axial plane of the tapered tube 2 and the first The straight line containing the center of the common sphere at coordinate 8 The intersection point is the first The vertex of the horizontal cone is 12, and the common tangent line 10 on the axial plane intersects the straight line. The included angle is the horizontal angle of the waistline. 16.

[0049] Waistline horizontal angle Angle 16 is equal to the inlet angle of the corresponding cone 2. 33 and the apex angle of the semi-cone The sum of 14 is .

[0050] The coordinates of the vertex 12 of the horizontal cone are calculated as follows:

[0051]

[0052] in, The first The x and y coordinates of the horizontal cone vertex 12 in the conical tube 2. For the first Horizontal angle of the waistline of section cone tube 2 16, For the first The radius of the tangent sphere is 6.

[0053] The intersection of the common tangents 10 on all axial planes is the waistline exit 11. The coordinates of the waistline exit 11 are solved by simultaneously solving the equations of the two adjacent tapered tube waistlines 13. Let the equation of the line containing the tapered tube waistline 13 be:

[0054] Let the ordinates of the equations of two adjacent lines be... Equal to each other, solve for the x-coordinate of the point where the waistline exit 11 is located. Substituting into any equation, we obtain the ordinate of the point where the waistline exit 11 is located. The calculation formula is as follows:

[0055] Calculated and The results are as follows

[0056]

[0057] in, The first The x and y coordinates of the horizontal cone vertex 12 in section 1 of the tapered tube 2. For the first +1 section tapered tube 2 waistline horizontal angle 16.

[0058] The starting point of pipe body 1 is the inlet 18 of the first waistline. The coordinate calculation formula for the inlet 18 of the first waistline is:

[0059]

[0060] in, , These are the x and y coordinates of the first section waistline entrance 18, respectively. , These are the x and y coordinates of vertex 19 of the first horizontal cone. The horizontal angle of the waistline of the first tapered tube 2 16, = ; The x-coordinate of the first section of the horizontal cone vertex 19 is determined using the coordinates of the center 17 of the first common tangent sphere and the horizontal angle of the waistline of the first section of the conical tube 2. 16 is introduced, with the vertical coordinate being the center of the first common tangent ball. 17 is the vertical coordinate, which is:

[0061] in, , The x and y coordinates are the center point 17 of the first common tangent sphere.

[0062] Let the equation of the line containing the last waistline 22 be... Take the radius of the largest common tangent sphere, 20, as the ordinate of the vertex of the last waistline 22.

[0063] The formula for calculating the coordinates of the exit point 24 of the last waistline is:

[0064]

[0065] in, , These are the x and y coordinates of the exit 24 of the last waistline section. The maximum common tangent radius is 20. and Let be the slope and intercept of the line equation containing the last waistline 22.

[0066] The equation of the straight line containing the last waistline 22 is determined by the coordinates of the last horizontal cone vertex 25 and the penultimate waistline exit 23.

[0067] The tapered tube 2 is formed by rotating 360° around the axis 5 of the tapered tube through the symmetrical waistline 30 and then being divided by the partition plate 34. The symmetrical waistline 30 on each tapered tube 2 is obtained symmetrically by the tapered tube waistline 13 through the axis 5 of the tapered tube. The two adjacent symmetrical waistlines 30 intersect at the symmetrical waistline exit point 31.

[0068] After the symmetrical waistline 30 is rotated, the tube body 1 is divided into multiple tapered tubes 2 by the partition plate 34. The partition plate 34 is distributed at intervals along the direction of the tapered tube axis 5. The partition line 32 is stretched and shaped in a direction perpendicular to the tapered tube axis 5. The starting end coordinate of the partition line 32 is consistent with the coordinate of the waistline outlet 11, and the ending end coordinate is consistent with the coordinate of the symmetrical waistline outlet 31.

[0069] The stretching length of separator line 32 is four times the radius of the maximum common tangent ball, 20.

[0070] To verify the effectiveness of this software in rapidly modeling turbine draft tubes based on a common tangent sphere, a 3D parametric design of the turbine draft tube based on a common tangent sphere was performed and implemented step by step using PYCATIA. The specific steps are as follows: Figure 7 As shown. Taking a turbine draft tube with an inner radius of 1467mm at the main inlet as an example, a three-dimensional parametric model is performed, and the design parameters are set as follows: List of apex angles of a semi-cone: [5.737, 4.855, 0.663, 4.696, 4.381, 4.381, 4.381, 4.381, 4.381, 4.381, 2.223, 1.892, 4.788, 4.381, 4.638, 4.812, 4.769, 4.451, 4.986] (unit: degrees); List of radius enlargement factors: [1.225,1.028,1.004,1.02,1.02,1.02,1.02,1.02,1.02,1.02,1.02,1.02,1.02,1.02,1.02,1.02,1.02,1.069,1.092,1.105,1.095,1.1,1.101]; List of axis turning angles: [0,0.335,6.341,13.657,20.38,27.787,34.669,41.739,48.098,55.385,62.465,69.616,76.432,83.253,90.509,96.683,96.725,97.106,97.641,98] (unit: degrees).

[0071] The final design rendering is as follows Figure 8 As shown.

[0072] The turbine draft tube designed in this invention achieves continuous gradual change of the inner wall profile and optimization of hydraulic characteristics through a collaborative control method of geometric structure. This solves the technical problems of traditional turbine draft tube design relying on empirical formulas or local optimization, as well as the complex design process, long cycle, and limited flexibility. At the same time, it simplifies the design process and enhances the flexibility and scalability of the design.

[0073] As is known from common technical knowledge, this invention can be implemented through other embodiments that do not depart from its spirit or essential characteristics. Therefore, the disclosed embodiments described above are merely illustrative in all respects and are not the only ones. All modifications within the scope of this invention or its equivalents are included in this invention.

Claims

1. A turbine draft tube based on a common tangent sphere, characterized in that: The pipe body (1) is determined by multiple tangent spheres. The multiple tangent spheres are arranged sequentially along the flow direction of the tailwater pipe and their radii are gradually changed. The center coordinates, radius, and center-to-center distance of each tangent sphere are determined by correlation calculation of the tailwater pipe inlet and outlet parameters. The inner wall profile of the tube body (1) is composed of multiple sections of tapered tubes (2). The tapered tubes (2) are rotated 360° around the axis (5) of the tapered tube by a symmetrical waistline (30) and then divided by a partition plate (34). Each section of the conical tube (2) is a pipe segment between two adjacent tangent spheres. The line connecting the centers of the two adjacent tangent spheres is the axis of the conical tube (5). All the axes of the conical tube (5) are on the same plane, namely the axial plane. The tangent line of the two adjacent tangent spheres on the axial plane and close to the inner bend of the tailpipe is the axial plane tangent line (10). The intersection of the axial plane tangent line (10) of the conical tube (2) and the axial plane tangent line (10) of the next section of the conical tube (2) is the waistline outlet (11). The line connecting the waistline outlet (11) of the conical tube (2) and the waistline outlet (11) of the previous section of the conical tube (2) is the waistline (13) of the conical tube. The symmetrical waistline (30) on each conical tube (2) is obtained symmetrically by the waistline (13) of the conical tube through the axis of the conical tube (5).

2. The turbine draft tube based on a common tangent sphere according to claim 1, characterized in that: The radius of the common tangent sphere gradually increases according to a preset multiplier, and the formula for calculating the radius of the common tangent sphere is as follows: in, For the first The radius of the common tangent sphere is (6); For the first +1 common tangent radius (7); For the first +1 times the expansion factor of the common tangent sphere radius (7), ; For segment number =1,2,3,…,n, where n is the number of sections in the conical tube (2). .

3. The turbine draft tube based on a common tangent sphere according to claim 2, characterized in that: The distance between the centers of adjacent common tangent balls is calculated as follows: It has a semi-cone apex angle (14) and axis turning angle (15), the apex angle of the semi-cone (14) is the angle between the cone tube axis (5) and the cone tube waistline (13), set segment by segment along the water flow direction. The axis turning angle (15) is the angle between the axis (5) of the conical tube and the axis (5) of the previous conical tube (2), and is set segment by segment along the water flow direction. ; The distance between the centers of two adjacent common tangent spheres is determined by the radius of the adjacent common tangent spheres and the apex angle of the semicone. (14) Jointly determined: in, For the first The semi-cone apex angle of the conical tube (2) (14).

4. A turbine draft tube based on a common tangent sphere according to claim 3, characterized in that: The coordinates of the center of the common tangent sphere are obtained through iterative calculation in the following manner: Using the coordinates of the center of the greatest common tangent sphere (21) as the origin, the calculation is performed segment by segment in the reverse direction of water flow: In the axial plane, For the first The coordinates of the center of the common tangent sphere (8) For the first The coordinates of the center of the +1 common tangent sphere (9) For the first The distance between the centers of the two common tangent spheres in the conical tube (2), For the first The axial turning angle of the conical tube (2) (15) For the first The inlet angle of the conical pipe (2) (33), the water inlet angle (33) is the angle between the axis of the conical tube (5) and the axis of the inlet (3), and .

5. A turbine draft tube based on a common tangent sphere according to claim 4, characterized in that: The horizontal angle of the waistline of the tapered tube (2) The calculation methods for (16) and the vertex (12) of the horizontal cone are as follows: No. The common tangent (10) of the axial plane of the tapered tube (2) and the first The straight line containing the center of the common tangent sphere (8) with its ordinate on the line... The intersection point is the first The apex of the horizontal cone (12), the common tangent of the axial plane (10) and the straight line The included angle is the horizontal angle of the waistline. (16); The horizontal angle of the waistline (16) The angle is equal to the inlet angle of the corresponding cone (2). (33) and the apex angle of the semi-cone The sum of (14) is ; The coordinates of the vertex (12) of the horizontal cone are calculated as follows: in, The first The x and y coordinates of the horizontal cone vertex (12) in the conical tube (2), For the first Horizontal angle of the waistline of the tapered tube (2) (16) For the first The radius of the common tangent sphere is (6).

6. A turbine draft tube based on a common tangent sphere according to claim 5, characterized in that: The coordinates of the waistline exit (11) are calculated as follows: The coordinates of the waistline exit (11) are solved by solving the equations of the two adjacent tapered tube waistlines (13) simultaneously. Let the equation of the line containing the tapered tube waistline (13) be: Let the ordinates of the equations of two adjacent lines be... Equal to each other, solve for the x-coordinate of the point where the waistline exit (11) is located. Substituting into any equation, we obtain the ordinate of the point where the waistline exit (11) is located. .

7. A turbine draft tube based on a common tangent sphere according to claim 6, characterized in that: The starting point of the pipe body (1) is the inlet (18) of the first waistline, and the coordinate calculation formula for the inlet (18) of the first waistline is: in, , These are the x and y coordinates of the entrance (18) of the first waistline, respectively. , Let x and y be the x and y coordinates of the vertex (19) of the first horizontal cone, respectively. The horizontal angle of the waistline of the first tapered tube (2) (16); The x-coordinate of the first horizontal cone vertex (19) is determined using the coordinates of the center of the first common tangent sphere (17) and the horizontal angle of the waistline of the first conical tube (2). (16) The vertical axis is the center of the first common tangent ball. (17) The vertical axis is: in, , Let x and y be the coordinates of the center of the first common tangent sphere (17).

8. A turbine draft tube based on a common tangent sphere according to claim 7, characterized in that: The formula for calculating the coordinates of the exit (24) of the last waistline is: in, , These are the x and y coordinates of the exit (24) of the last waistline, respectively. The maximum common tangent radius is (20). and The slope and intercept of the line equation containing the last waistline (22); The equation of the line containing the last waistline (22) is determined by the coordinates of the vertex (25) of the last horizontal cone and the coordinates of the exit (23) of the penultimate waistline.

9. A turbine draft tube based on a common tangent sphere according to claim 1, characterized in that: The tapered tube (2) is rotated 360° around the axis (5) of the tapered tube by a symmetrical waistline (30) and then divided by a partition plate (34) to form the shape, specifically including: The partition plates (34) are spaced apart along the direction of the tapered tube axis (5). The partition plates (34) are stretched and formed by the dividing lines (32) in a direction perpendicular to the tapered tube axis (5). The intersection point of two adjacent symmetrical waistlines (30) is the symmetrical waistline exit point (31). The starting end coordinates of the dividing line (32) are consistent with the waistline exit (11) coordinates, and the ending end coordinates are consistent with the symmetrical waistline exit (31) coordinates. The stretching length of the dividing line (32) is four times the radius of the maximum common tangent ball (20).

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