Bidirectional flow channel pump station water outlet flow channel design method based on Dehn vortex theory and bidirectional flow channel pump station water outlet flow channel

Abstract

The invention provides a two-way flow channel pump station water outlet flow channel design method based on the Dean vortex theory and a two-way flow channel pump station water outlet flow channel The two-way flow channel pump station water outlet flow channel design method comprises the following steps that based on the Dean vortex theory, the curvature ratio and the width ratio of a two-way pump station in a geometric coordinate system are defined respectively; establishing a mathematical model of the geometrical shape of the water outlet flow channel about the curvature ratio and the width ratio; establishing a rectangular plane coordinate system on the midline of the water outlet flow channel to obtain the curvature ratio and the width ratio of the midline of the water outlet flow channel; the curvature radius of the midline of the water flow channel is calculated, and the curvature radius range of the midline of the water flow channel is obtained; calculating the change relation of the width of the water flow channel along with the horizontal axis coordinates; obtaining a function relation of the curvature ratio and the width ratio with respect to the midline of the water outlet flow channel along the path, and determining the geometrical shape of the water outlet flow channel based on the function relation. The characteristics of water flow in the flow channel are optimized by accurately controlling the curvature and width change of the center line of the flow channel, so that the energy loss is reduced, and the operation efficiency of the pump station is improved.

Description

Technical Field

[0001] The invention relates to the technical field of water conservancy engineering, and in particular to a design method for a water outlet flow channel of a two-way flow channel pump station based on Dean vortex theory and a water outlet flow channel of a two-way flow channel pump station. Background Art

[0002] According to the 2022 National Water Resources Development Statistical Bulletin, the country has built a total of 20,000 hectares of water supply per day. 3 There are 522 water supply mechanical and electrical wells or irrigation mechanical and electrical wells with an inner diameter of not less than 200mm. 3 / s or 94,030 pumping stations with installed power of more than 50kW, including 482 large pumping stations, 4,745 medium pumping stations and 88,803 small pumping stations. With the increasing demand for social development and production, bidirectional pumping stations have gradually developed and matured due to their dual-purpose characteristics of irrigation and drainage, playing an irreplaceable role in urban river drainage, water quality assurance, and drainage and irrigation in plain areas. However, with the continuous expansion of the practical application of bidirectional pumping stations, the contradiction between application and design theory has become increasingly prominent. Especially in the design of the outlet flow channel of the bidirectional pumping station, the designer needs to design and optimize the parameters of the water guide cone and the trumpet pipe profile, and the design application process is cumbersome.

[0003] In a Chinese patent for a two-way flow channel pump station structure and a two-way flow channel pump station, a method of adding two outer two-way flow channels to the two-way flow channel pump station is proposed to reduce the pressure of the pump station; at the same time, a channel is opened between the newly added outer flow channel and the original pump operation flow channel, and the opening and closing of the channel is controlled by a gate, which weakens the dead water area existing in the existing two-way flow channel pump station structure, can effectively eliminate the top plate pump vortex, and improve the operation efficiency of the pump station. However, this patent mainly focuses on the number of flow channels of the two-way pump station and the interaction between the flow channels, and does not specifically involve the outlet flow channel of the pump station. In order to solve the problems of the disordered flow characteristics in the outlet flow channel of the bidirectional flow channel pump station in actual operation, and the vibration of the pump shaft and the system caused by the unbalanced axial force of the pump shaft, etc., China patented a water outlet diffusion structure for a bidirectional vertical pump station. By designing the de-cyclone chamber, outlet diffusion trumpet, rear water guide cone and box culvert outlet chamber, and optimizing the size and shape of the outlet trumpet and rear water guide cone, the water outlet flow state of the bidirectional pump station is improved, the vortex and hydraulic loss are reduced, and the hydraulic efficiency of the outlet flow channel is improved. The design takes into account the characteristics of the bidirectional flow channel pump station and provides a new type of water outlet diffusion structure, which helps to improve the overall performance of the pump station. However, the patent may lack a detailed analysis of the performance of the pump station under different flow conditions, and its adaptability under different working conditions needs to be further verified. In addition, the design is only an improvement on the structural parameters, and lacks a systematic theoretical guidance for the design of the outlet flow channel. In a design method for a bell-shaped water inlet channel for a pumping station, a Chinese patent provides a detailed design formula for the bell-shaped water inlet channel, including multiple key geometric parameters of the channel. The design takes into account parameters such as the specific speed, head and flow rate of the pump. The design method is more universal and is conducive to the optimization design of the channel and the stable and efficient operation of the pumping station. The bell-shaped and elbow-shaped design methods of the pumping station water inlet channel are respectively proposed, which effectively improves the water inlet flow state, greatly reduces the hydraulic loss of the water inlet channel, and improves the economic benefits of the pump operation. In a design method for a bell-shaped water inlet channel for a pumping station, a set of detailed elbow-shaped water inlet channel design formulas are provided, including key parameters such as the height from the impeller center to the bottom plate of the water inlet channel and the inlet height of the water inlet channel. These formulas help to improve the stability and efficiency of the pumping station operation. In addition, the design method takes into account a variety of working parameters of the pump, such as flow rate, speed and head, realizes parametric design, and facilitates computer-aided design and optimization. By optimizing the geometric shape of the flow channel, hydraulic losses are reduced, the service life of the pump and pumping station is extended, and the economic benefits of the pumping station are improved. Although the patent provides design formulas, it does not explain in detail the derivation process and theoretical basis of these formulas, which may require further experimental verification. For pump stations with special working conditions or unconventional sizes, the design method in the patent may need to be adjusted, and its universality needs further study. In a Chinese patent invention patent, a method for designing the bell mouth of a bidirectional pump station inlet flow channel is used to establish a coordinate system and solve parabolic equations to achieve parametric design of the bell mouth profile line, thereby improving the accuracy and convenience of the design.The segmented design is adopted to divide the profile line of the bell mouth into straight lines and parabolic segments, making the transition of the profile smoother and helping to improve the dynamics of the water flow. The geometric parameters of the bell mouth are optimized, which helps to reduce the hydraulic loss of water flow in the water inlet channel of the pump station and improve the operating efficiency of the pump station. However, its design method may require professional software support to achieve the establishment of the coordinate system and the solution of the equation, and it is not adaptable to traditional design methods. Most of the above patents are design methods for the water inlet channel of a bidirectional pump station, and rarely involve the water outlet channel of a bidirectional flow channel pump station. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention provides a design method for the outlet flow channel of a two-way flow channel pump station based on the Dean vortex theory and a two-way flow channel pump station outlet flow channel. The center line of the flow channel is designed based on the main design parameters of the outlet flow channel, and the variation law of the width of the outlet flow channel is given. The outlet flow channel is comprehensively designed in combination with the curvature ratio of the center line of the flow channel and the width ratio of the outlet flow channel. The design of the water guide cone line and the trumpet tube line is coordinated, which will greatly simplify the optimization process of the outlet flow channel parameters. The innovation of the present invention lies in proposing a hydraulic design method for the outlet flow channel based on a mathematical model. This method optimizes the water flow characteristics in the flow channel by accurately controlling the curvature and width changes of the center line of the flow channel, thereby reducing energy loss and improving the operating efficiency of the pump station. Compared with traditional design methods, the present invention not only simplifies the design process and reduces the dependence on the designer's experience, but also improves the reliability and universality of the design through systematic design parameters.

[0005] The present invention achieves the above technical objectives through the following technical means.

[0006] A method for designing an outlet flow channel of a bidirectional flow channel pump station based on Dean vortex theory comprises the following steps:

[0007] Based on the Dean vortex theory, the curvature ratio and width ratio of the bidirectional pump station in the geometric coordinate system are defined respectively, and the mathematical model of the outlet flow channel geometry with respect to the curvature ratio and width ratio is established. r ,A r ), where ψ represents the objective function of the outlet channel geometry, C r is the curvature ratio, A r is the width ratio;

[0008] A plane rectangular coordinate system is established on the center line of the water outlet flow channel to obtain the curvature ratio and width ratio of the center line of the water outlet flow channel; the curvature radius of the center line of the water outlet flow channel is calculated, and the curvature radius range of the center line of the water outlet flow channel is obtained; and the relationship between the width of the water outlet flow channel and the horizontal axis coordinate is calculated;

[0009] The functional relationships of the curvature ratio and the width ratio along the center line of the outlet flow channel are obtained, and the geometric shape of the outlet flow channel is determined based on the functional relationship.

[0010] Furthermore, a plane rectangular coordinate system is established on the center line of the outlet flow channel. The coordinates of any point on the center line of the outlet flow channel in the plane coordinate system are marked as (x, y). Then the curvature ratio C of any point on the center line of the outlet flow channel is r (x) is:

[0011]

[0012] Where: R 1 is the radius of the diffuser at the inlet of the flow channel; ρ x is the radius of curvature at any point;

[0013] The width of any point on the centerline of the outlet channel is A r (x) is:

[0014]

[0015] Where: R 3 B is the radius of the diffuser and water guide cone at the outlet of the flow channel; x is the channel width at any point.

[0016] Furthermore, the curvature radius of the centerline of the outlet channel of the bidirectional flow channel pump station is calculated, and the curvature radius range of the centerline of the outlet channel is obtained, which is specifically:

[0017] Determine the function of the linear line of the outlet flow channel in the plane rectangular coordinate system, denoted as g(x);

[0018] The radius of curvature at any point on the centerline of the outlet channel is:

[0019] Where: g'(x) is the first-order derivative of g(x) at the point (x, y); g"(x) is the second-order derivative of g(x) at the point (x, y);

[0020] The relationship between the curvature radius of the outlet flow channel and the horizontal coordinate x is obtained as ρ(x);

[0021] According to the value of x in ρ(x), the maximum curvature radius is ρ max and the minimum radius of curvature is ρ min , determine the range of ρ(x);

[0022] The relationship between the width of the water outlet channel and the horizontal axis coordinate is calculated based on the centerline of the water outlet channel.

[0023] Furthermore, the centerline of the outlet flow channel is an ellipse, and the horizontal direction at the flow channel inlet is the x-axis, and the vertical direction at the flow channel outlet is the y-axis. A plane rectangular coordinate system xoy is established, and the function g(x) of the centerline of the outlet flow channel in the plane rectangular coordinate system is expressed as:

[0024]

[0025] Among them: a 1 is the major semi-axis of the ellipse, a 1 =(H 1 +H 2 ) / 2,H 1 is the height of the diffuser; H 2 is the height of the water guide cone; b 1 is the minor semi-axis of the ellipse, b 1 =R 3 -R 1 -B 0 / 2, R 1 is the radius of the diffuser at the inlet of the flow channel; R 3 B is the radius of the diffuser and water cone at the outlet of the flow channel, 0 is the width at the inlet of the bidirectional pump station;

[0026] The radius of curvature at any point on the midline of the outlet channel can be expressed as:

[0027]

[0028] Among them, g'(x) and g"(x) are the first-order derivative and second-order derivative of the elliptic curve g(x) at the point (x, y), respectively.

[0029]

[0030] The radius of curvature at any point on the centerline of the outlet channel is:

[0031]

[0032] Substituting the ellipse equation and eliminating y, the relationship between the curvature radius of the centerline of the elliptical flow channel and the change in curvature radius is:

[0033]

[0034] In the formula, k = c 1 / b 1 =c 1 / (R 3 -R 1 -B 0 / 2), c 1 is the focal length of the ellipse;

[0035] According to the value of x in ρ(x), the maximum curvature radius is ρ max and the minimum radius of curvature is ρ min , specifically:

[0036] When x=-b 1 When , the curvature radius at the inlet of the outlet channel is the largest, and the maximum curvature radius is ρmax =a 1 2 / b 1 ;

[0037] When x=0, the curvature radius at the outlet of the water flow channel is the smallest, and the minimum curvature radius is ρ min =b 1 2 / a 1 ;

[0038] The range of curvature radius ρ(x) of the outlet channel centerline is:

[0039]

[0040] Furthermore, according to the center line of the elliptical flow channel, the relationship between the flow channel width and the horizontal coordinate x is obtained:

[0041]

[0042] Among them, B 0 It is the width at the inlet of the bidirectional pump station.

[0043] Furthermore, the functional relationship of the curvature ratio along the centerline of the outlet flow channel is obtained:

[0044]

[0045] The functional relationship of the width ratio along the centerline of the outlet flow channel is obtained:

[0046]

[0047] Furthermore, the centerline of the outlet flow channel is a hyperbola, with the horizontal direction at the flow channel inlet as the x-axis and the central axis of the water guide cone as the y-axis, a plane rectangular coordinate system xoy is established, and the function g(x) of the centerline of the outlet flow channel in the plane rectangular coordinate system is expressed as:

[0048]

[0049] Among them, a 2 is the real semi-axis of the hyperbola, a 2 =R 1 +B 0 / 2, R 1 is the radius of the diffuser at the flow channel inlet, B 0 is the width of the bidirectional pump station inlet; b 2 is the imaginary semi-axis of the hyperbola, b 2 =(H 1 +H 2 ) / 2,H 1 is the height of the diffuser; H 2 is the height of the water cone;

[0050] The radius of curvature at any point on the midline of the outlet channel can be expressed as:

[0051]

[0052] Among them, g'(x) and g"(x) are the first-order derivative and second-order derivative of the hyperbola g(x) at the point (x, y), respectively.

[0053]

[0054] The radius of curvature at any point on the centerline of the outlet channel is:

[0055]

[0056] Substituting the hyperbolic equation and eliminating y, the relationship between the curvature radius of the centerline of the hyperbolic flow channel is:

[0057]

[0058] In the formula, e 2 is the eccentricity of the hyperbola, e 2 =c 2 / a 2 =c 2 / (R 1 +B 0 / 2), c 2 is the focal length of the hyperbola;

[0059] According to the value of x in ρ(x), the maximum curvature radius is ρ max and the minimum radius of curvature is ρ min , specifically:

[0060] When x = R 3 When , the curvature radius at the inlet of the outlet channel is the largest, and the maximum curvature radius is

[0061] When x=a 2 When , the curvature radius at the outlet of the water flow channel is the smallest, and the minimum curvature radius is ρ min =b 2 2 / a 2 ;

[0062] The range of curvature radius ρ(x) of the outlet channel centerline is:

[0063]

[0064] Furthermore, according to the center line of the hyperbolic flow channel, the relationship between the flow channel width and the horizontal coordinate x is obtained:

[0065]

[0066] Among them, B 0 It is the width at the inlet of the bidirectional pump station.

[0067] Furthermore, the functional relationship of the curvature ratio along the centerline of the outlet flow channel is obtained:

[0068]

[0069] The functional relationship of the width ratio along the centerline of the outlet flow channel is obtained:

[0070]

[0071] A water outlet flow channel of a bidirectional flow channel pump station, wherein the water outlet flow channel is designed according to the water outlet flow channel design method of a bidirectional flow channel pump station based on Dean vortex theory.

[0072] The beneficial effects of the present invention are:

[0073] The method for designing the outlet flow channel of a bidirectional flow channel pump station based on Dean vortex theory described in the present invention starts from the category of the centerline profile of the flow channel, and based on the mathematical characteristics of the ellipse and the hyperbola, respectively explains the flow channel design methods based on the ellipse and the hyperbola, and derives the law of change of the radius of curvature of the centerline of the flow channel. On this basis, the law of change of the width of the outlet flow channel is reasonably designed. Compared with the traditional design method, the design method of the present invention can determine the shape of the flow channel by using the curvature ratio of the centerline of the flow channel and the flow channel width ratio, which greatly simplifies the optimization work of the outlet flow channel of the bidirectional pump station. The traditional design method of the outlet flow channel of a bidirectional pump station is mainly determined by the design of the water guide cone profile and the trumpet tube profile. The flow channel is determined by multiple parameters, and the workload of optimizing the parameters of the two profiles is relatively cumbersome. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. The drawings described below are some embodiments of the present invention. For ordinary technicians in this field, it is obvious that other drawings can be obtained based on these drawings without paying any creative work.

[0075] Figure 1 The present invention is a flowchart of the method for designing the outlet flow channel of a bidirectional flow channel pump station based on Dean vortex theory.

[0076] Figure 2 It is a schematic diagram of the main geometric parameters of the outlet channel of the bidirectional flow channel pump station described in the present invention.

[0077] Figure 3 Schematic diagram of flow channel centerline design based on elliptical line.

[0078] Figure 4 Schematic diagram of the flow channel centerline design based on hyperbola.

[0079] Figure 5 This paper compares the external characteristics of a bidirectional pump station based on the elliptical profile design method and the traditional design method. DETAILED DESCRIPTION

[0080] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0081] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "axial", "radial", "vertical", "horizontal", "inner", "outer" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first" and "second" are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.

[0082] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0083] like Figure 1 As shown, the method for designing the outlet flow channel of a bidirectional flow channel pump station based on the Dean vortex theory of the present invention comprises the following steps:

[0084] Based on the Dean vortex theory, the curvature ratio and width ratio of the bidirectional pump station in the geometric coordinate system are defined respectively, and the mathematical model of the outlet flow channel geometry with respect to the curvature ratio and width ratio is established. r ,A r), where ψ represents the objective function of the outlet channel geometry, C r is the curvature ratio, A r is the width ratio;

[0085] A plane rectangular coordinate system is established on the center line of the water outlet flow channel to obtain the curvature ratio and width ratio of the center line of the water outlet flow channel; the curvature radius of the center line of the water outlet flow channel is calculated, and the curvature radius range of the center line of the water outlet flow channel is obtained; and the relationship between the width of the water outlet flow channel and the horizontal axis coordinate is calculated;

[0086] The functional relationships of the curvature ratio and the width ratio along the center line of the outlet flow channel are obtained, and the geometric shape of the outlet flow channel is determined based on the functional relationship.

[0087] Figure 2 The figure shows the main geometric parameters of the bidirectional flow channel pump station. 1 is the radius of the diffuser at the inlet of the flow channel, m; R 2 is the radius of the water guide cone at the flow channel inlet, m; R 3 is the radius of the diffuser and water cone at the outlet of the flow channel, m; B 1 is the height of the diffuser, m; B 2 is the height of the water cone, m; B 0 is the channel width at the channel inlet, m.

[0088] In an embodiment, R 1 =1.0m, R 2 =1.6m, R 3 =2.8m, H 1 =2.0m, H 2 =3.6m.

[0089] Example 1 takes the outlet flow channel center line as an ellipse line as an example for specific description:

[0090] S01: Based on the Dean vortex theory, the curvature ratio and width ratio of the bidirectional pumping station in the geometric coordinate system are defined respectively, where:

[0091] A rectangular coordinate system is established on the center line of the outlet flow channel. The coordinates of any point on the center line of the outlet flow channel in the plane coordinate system are marked as (x, y). Then the curvature ratio C of any point on the center line of the outlet flow channel is r (x) is:

[0092]

[0093] The width of any point on the centerline of the outlet channel is A r (x) is:

[0094]

[0095] Where: xis the radius of curvature at any point; B x is the channel width at any point.

[0096] S02: Figure 3 As shown, with the horizontal direction at the flow channel inlet as the x-axis and the vertical direction at the flow channel outlet as the y-axis, a plane rectangular coordinate system xoy is established. The function g(x) of the linear line of the outlet flow channel in the plane rectangular coordinate system is expressed as:

[0097]

[0098] Among them: a 1 is the major semi-axis of the ellipse, a 1 =(H 1 +H 2 ) / 2,H 1 is the height of the diffuser; H 2 is the height of the water guide cone; b 1 is the minor semi-axis of the ellipse, b 1 =R 3 -R 1 -B 0 / 2, R 1 is the radius of the diffuser at the inlet of the flow channel; R 3 B is the radius of the diffuser and water cone at the outlet of the flow channel, 0 is the width at the inlet of the bidirectional pump station;

[0099] In an embodiment, a 1 =R 3 -R 1 -B 0 / 2=2.1m,b 1 =(H 1 +H 2 ) / 2=2.8m,B 0 =(R 1 +R 2 ) / 2 = 0.3m, so the equation of the centerline of the outlet flow channel g(x) can be expressed as:

[0100]

[0101] The radius of curvature at any point on the midline of the outlet channel can be expressed as:

[0102]

[0103] Among them, g'(x) and g"(x) are the first-order derivative and second-order derivative of the elliptic curve g(x) at the point (x, y), respectively.

[0104]

[0105]

[0106] The radius of curvature at any point on the centerline of the outlet channel is:

[0107]

[0108] Substituting the ellipse equation and eliminating y, the relationship between the curvature radius of the centerline of the elliptical flow channel and the change in curvature radius is:

[0109]

[0110] In the formula, k = c 1 / b 1 =c 1 / (R 3 -R 1 -B 0 / 2), c 1 is the focal length of the ellipse, in the embodiment c 1 =(a 1 2 -b 1 2 ) 1 / 2 =1.852m, k=c 1 / b 1 =0.8819, then the relationship between the curvature radius of the centerline of the elliptical flow channel can be expressed as:

[0111]

[0112] When x=-b 1 When , the curvature radius at the inlet of the outlet channel is the largest, and the maximum curvature radius is ρ max =a 1 2 / b 1 =3.733m;

[0113] When x=0, the curvature radius at the outlet of the water flow channel is the smallest, and the minimum curvature radius is ρ min =b 1 2 / a 1 =1.575m;

[0114] The range of curvature radius ρ(x) of the outlet channel centerline is:

[0115] 1.575m≤ρ(x)≤3.733m.

[0116] According to the center line of the elliptical flow channel, the relationship between the flow channel width and the horizontal coordinate x is obtained:

[0117]

[0118] S03: Get the functional relationship of the curvature ratio along the center line of the outlet flow channel:

[0119]

[0120] The functional relationship of the width ratio along the centerline of the outlet flow channel is obtained:

[0121]

[0122] S04: Determine the geometric shape of the water outlet flow channel based on the functional relationship between the curvature ratio and the width ratio.

[0123] Example 2 is specifically described by taking the middle line of the outlet flow channel as a hyperbola as an example: In order to distinguish from Example 1, the coordinates of any point in Example 2 are marked as (x', y'),

[0124] S01: Based on the Dean vortex theory, the curvature ratio and width ratio of the bidirectional pumping station in the geometric coordinate system are defined respectively, where:

[0125] A plane rectangular coordinate system is established on the center line of the outlet flow channel. The coordinates of any point on the center line of the outlet flow channel in the plane coordinate system are marked as (x', y'). Then the curvature ratio C of any point on the center line of the outlet flow channel is r (x') is:

[0126]

[0127] The width of any point on the centerline of the outlet channel is A r (x') is:

[0128]

[0129] Where: x′ is the radius of curvature at any point; B x′ is the channel width at any point.

[0130] S02: Figure 4 As shown, with the horizontal direction at the inlet of the flow channel as the x-axis and the central axis of the water guide cone as the y-axis, a plane rectangular coordinate system xoy is established. The function h(x') of the linear line of the outlet flow channel in the plane rectangular coordinate system is expressed as:

[0131]

[0132] Among them, a 2 is the real semi-axis of the hyperbola, a 2 =R 1 +B 0 / 2, R 1 is the radius of the diffuser at the flow channel inlet, B 0 is the width of the bidirectional pump station inlet; b 2is the imaginary semi-axis of the hyperbola, b 2 =(H 1 +H 2 ) / 2,H 1 is the height of the diffuser; H 2 is the height of the water cone; B 0 is the width at the inlet of the bidirectional pump station;

[0133] In the embodiment, in this specific embodiment, the real semi-axis of the hyperbola is a 2 =R 1 +B 0 / 2=1.3m; b 2 =(H 1 +H 2 ) / 2=2.8m, the hyperbola equation h(x') can be expressed as:

[0134]

[0135] The first and second derivatives of the hyperbola h(x') at a point (x',y') are h'(x') and h"(x') respectively.

[0136]

[0137] The radius of curvature at any point on the centerline of the outlet channel is:

[0138]

[0139] In Example 2, the focal length of the hyperbola is c 2 =(a 2 2 +b 2 2 ) 1 / 2 =3.087m, eccentricity is e 2 =c 2 / (R 1 +B 0 / 2)=2.3747. Substituting the hyperbolic equation and eliminating y', we can get the relationship between the curvature radius of the center line of the hyperbolic flow channel as follows:

[0140]

[0141] When x = R 3 When , the curvature radius at the inlet of the outlet channel is the largest, and the maximum curvature radius is

[0142] When x=a 2 When , the curvature radius at the outlet of the water flow channel is the smallest, and the minimum curvature radius is ρ min =b 2 2 / a2 =6.031m;

[0143] The range of curvature radius ρ(x′) of the centerline of the outlet flow channel is: 6.031m≤ρ(x′)≤11.682m.

[0144] According to the center line of the hyperbolic flow channel, the relationship between the flow channel width and the horizontal coordinate x is obtained:

[0145]

[0146] S03: Get the functional relationship of the curvature ratio along the center line of the outlet flow channel:

[0147]

[0148] The functional relationship of the width ratio along the centerline of the outlet flow channel is obtained:

[0149]

[0150] S04: Determine the geometric shape of the water outlet flow channel based on the functional relationship between the curvature ratio and the width ratio.

[0151] When implementing the present invention, first determine the main geometric parameters of the flow channel, including the radius and height of the diffuser and water guide cone, according to the specific working conditions and design requirements of the pump station. Then, using the method provided by the present invention, establish an elliptical or hyperbolic model of the centerline of the flow channel, and calculate the corresponding curvature radius and width variation law. During the calculation process, through iteration and optimization algorithms, ensure that the design parameters meet the predetermined performance indicators, such as the hydraulic efficiency and anti-vortex performance of the flow channel. Through computer-aided design (CAD) software, draw a three-dimensional model of the flow channel according to the calculated parameters, and perform detailed fluid dynamics analysis to verify the rationality and effectiveness of the design. In the model verification stage, computational fluid dynamics (CFD) simulation can be used to perform a detailed analysis of the flow field in the flow channel to ensure that the flow channel design can achieve the expected hydraulic performance. According to the simulation results and actual engineering requirements, the design parameters are fine-tuned to achieve the optimal flow channel design. Figure 5 By comparing the external characteristics of the bidirectional pump station based on the elliptical line design method and the traditional design method, it can be seen that, under the premise of ensuring that the pump head is not much different, the pump operating efficiency designed based on this method is greater than the operating efficiency under the traditional method.

[0152] Therefore, the embodiments of the present invention not only provide an efficient method for designing a water outlet flow channel, but also provide an important theoretical basis and technical support for the design and modification of a pump station.

[0153] The outlet flow channel of the bidirectional flow channel pump station described in the present invention is designed by the outlet flow channel design method of the bidirectional flow channel pump station based on Dean vortex theory.

[0154] It should be understood that although this specification is described according to various embodiments, not every embodiment contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

[0155] The series of detailed descriptions listed above are only specific descriptions of feasible embodiments of the present invention. They are not intended to limit the scope of protection of the present invention. All equivalent embodiments or changes that do not deviate from the technical spirit of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for designing the outlet flow channel of a bidirectional flow channel pump station based on Dean vortex theory, characterized in that: The steps include: Based on the Dean vortex theory, the curvature ratio and width ratio of the bidirectional pump station in the geometric coordinate system are defined respectively, and the mathematical model of the outlet flow channel geometry with respect to the curvature ratio and width ratio is established. r ,A r ), where ψ represents the objective function of the outlet channel geometry, C r is the curvature ratio, A r is the width ratio; A plane rectangular coordinate system is established on the center line of the water outlet flow channel to obtain the curvature ratio and width ratio of the center line of the water outlet flow channel; the curvature radius of the center line of the water outlet flow channel is calculated, and the curvature radius range of the center line of the water outlet flow channel is obtained; Calculate the relationship between the width of the water channel and the horizontal axis coordinate; The functional relationships of the curvature ratio and the width ratio along the center line of the outlet flow channel are obtained, and the geometric shape of the outlet flow channel is determined based on the functional relationship.

2. The method for designing the outlet flow channel of a bidirectional flow channel pump station based on Dean vortex theory according to claim 1 is characterized in that: A rectangular coordinate system is established on the center line of the outlet flow channel. The coordinates of any point on the center line of the outlet flow channel in the plane coordinate system are marked as (x, y). Then the curvature ratio C of any point on the center line of the outlet flow channel is r (x) is: Where: R1 is the radius of the diffuser at the inlet of the flow channel; ρ x is the radius of curvature at any point; The width of any point on the centerline of the outlet channel is A r (x) is: Where: R3 is the radius of the diffuser and water guide cone at the outlet of the flow channel; B x is the channel width at any point.

3. The method for designing the outlet flow channel of a bidirectional flow channel pump station based on Dean vortex theory according to claim 2 is characterized in that: Calculate the curvature radius of the centerline of the outlet channel of the two-way flow channel pump station, and find the curvature radius range of the centerline of the outlet channel, specifically: Determine the function of the linear line of the outlet flow channel in the plane rectangular coordinate system, denoted as g(x); The radius of curvature at any point on the centerline of the outlet channel is: Where: g'(x) is the first-order derivative of g(x) at the point (x, y); g"(x) is the second-order derivative of g(x) at the point (x, y); The relationship between the curvature radius of the outlet flow channel and the horizontal coordinate x is obtained as ρ(x); According to the value of x in ρ(x), the maximum curvature radius is ρ max and the minimum radius of curvature is ρ min , determine the range of ρ(x); The relationship between the width of the water outlet channel and the horizontal axis coordinate is calculated based on the centerline of the water outlet channel.

4. The method for designing the outlet flow channel of a bidirectional flow channel pump station based on Dean vortex theory according to claim 3 is characterized in that: The centerline of the outlet flow channel is an ellipse. With the horizontal direction at the flow channel inlet as the x-axis and the vertical direction at the flow channel outlet as the y-axis, a plane rectangular coordinate system xoy is established. The function g(x) of the centerline of the outlet flow channel in the plane rectangular coordinate system is expressed as: Where: a1 is the major semi-axis of the ellipse, a1=(H1+H2) / 2, H1 is the height of the diffuser; H2 is the height of the water cone; b1 is the minor semi-axis of the ellipse, b1=R3-R1-B0 / 2, R1 is the radius of the diffuser at the inlet of the flow channel; R3 is the radius of the diffuser and the water cone at the outlet of the flow channel, and B0 is the width at the inlet of the bidirectional pump station; The radius of curvature at any point on the midline of the outlet channel can be expressed as: Among them, g'(x) and g"(x) are the first-order derivative and second-order derivative of the elliptic curve g(x) at the point (x, y), respectively. The radius of curvature at any point on the centerline of the outlet channel is: Substituting the ellipse equation and eliminating y, the relationship between the curvature radius of the centerline of the elliptical flow channel and the change in curvature radius is: In the formula, k = c1 / b1 = c1 / (R3-R1-B0 / 2), c1 is the focal length of the ellipse; According to the value of x in ρ(x), the maximum curvature radius is ρ max and the minimum radius of curvature is ρ min , specifically: When x=-b1, the curvature radius at the inlet of the outlet channel is the largest, and the maximum curvature radius is ρ max =a1 2 / b1; When x=0, the curvature radius at the outlet of the water flow channel is the smallest, and the minimum curvature radius is ρ min =b1 2 / a1; The range of curvature radius ρ(x) of the outlet channel centerline is:

5. The method for designing the outlet flow channel of a bidirectional flow channel pump station based on Dean vortex theory according to claim 4 is characterized in that: According to the center line of the elliptical flow channel, the relationship between the flow channel width and the horizontal coordinate x is obtained: Among them, B0 is the width at the inlet of the bidirectional pumping station.

6. The method for designing the outlet flow channel of a bidirectional flow channel pump station based on Dean vortex theory according to claim 5 is characterized in that: The functional relationship of the curvature ratio along the centerline of the outlet flow channel is obtained: The functional relationship of the width ratio along the centerline of the outlet flow channel is obtained:

7. The method for designing the outlet flow channel of a bidirectional flow channel pump station based on Dean vortex theory according to claim 3 is characterized in that: The centerline of the outlet flow channel is a hyperbola. With the horizontal direction at the flow channel inlet as the x-axis and the central axis of the water guide cone as the y-axis, a plane rectangular coordinate system xoy is established. The function g(x) of the centerline of the outlet flow channel in the plane rectangular coordinate system is expressed as: Among them, a2 is the real semi-axis of the hyperbola, a2=R1+B0 / 2, R1 is the radius of the diffuser at the inlet of the flow channel, and B0 is the width at the inlet of the bidirectional pump station; b2 is the imaginary semi-axis of the hyperbola, b2=(H1+H2) / 2, H1 is the height of the diffuser; H2 is the height of the water guide cone; The radius of curvature at any point on the midline of the outlet channel can be expressed as: Among them, g'(x) and g"(x) are the first-order derivative and second-order derivative of the hyperbola g(x) at the point (x, y), respectively. The radius of curvature at any point on the centerline of the outlet channel is: Substituting the hyperbolic equation and eliminating y, the relationship between the curvature radius of the centerline of the hyperbolic flow channel is: Where, e2 is the eccentricity of the hyperbola, e2=c2 / a2=c2 / (R1+B0 / 2), c2 is the focal length of the hyperbola; According to the value of x in ρ(x), the maximum curvature radius is ρ max and the minimum radius of curvature is ρ min , specifically: When x=R3, the curvature radius at the inlet of the outlet channel is the largest, and the maximum curvature radius is When x=a2, the curvature radius at the outlet of the water flow channel is the smallest, and the minimum curvature radius is ρ min =b2 2 / a2; The range of curvature radius ρ(x) of the outlet channel centerline is:

8. The method for designing the outlet flow channel of a bidirectional flow channel pump station based on Dean vortex theory according to claim 7, characterized in that: According to the center line of the hyperbolic flow channel, the relationship between the flow channel width and the horizontal coordinate x is obtained: Among them, B0 is the width at the inlet of the bidirectional pumping station.

9. The method for designing the outlet flow channel of a bidirectional flow channel pump station based on Dean vortex theory according to claim 8, characterized in that: The functional relationship of the curvature ratio along the centerline of the outlet flow channel is obtained: The functional relationship of the width ratio along the centerline of the outlet flow channel is obtained:

10. A water outlet channel of a two-way flow channel pump station, characterized in that: The outlet flow channel is designed according to the method for designing the outlet flow channel of a bidirectional flow channel pump station based on Dean vortex theory according to any one of claims 1 to 9.

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