A design method of a two-way flow channel pump station outlet flow channel based on dean vortex theory and a two-way flow channel pump station outlet flow channel

Abstract

The application provides a design method of a two-way flow channel pump station outlet flow channel based on Dean vortex theory and a two-way flow channel pump station outlet flow channel, and comprises the following steps: based on Dean vortex theory, defining the curvature ratio and width ratio of the two-way pump station in the geometric coordinate system respectively, and establishing a mathematical model of the outlet flow channel geometry about the curvature ratio and the width ratio; establishing a plane rectangular coordinate system in the outlet flow channel center line, obtaining the curvature ratio and the width ratio of the outlet flow channel center line; calculating the outlet flow channel center line curvature radius, and obtaining the outlet flow channel center line curvature radius range; calculating the change relationship of the outlet flow channel width with the horizontal axis coordinate; obtaining the function relationship of the curvature ratio and the width ratio about the outlet flow channel center line along the way respectively, and determining the outlet flow channel geometry based on the function relationship. The application optimizes the water flow characteristics in the flow channel by accurately controlling the curvature and width change of the flow channel center line, thereby reducing the energy loss and improving the operation efficiency of the pump station.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of hydraulic engineering, and particularly relates to a two-way flow channel pump station outlet flow channel design method based on Dean vortex theory and a two-way flow channel pump station outlet flow channel. BACKGROUND

[0002] According to the 2022 National Water Development Statistics Bulletin, a total of 522 water supply mechanical wells with daily water intake not less than 20m 3 or irrigation mechanical wells with inner diameter not less than 200mm have been built in China. A total of 94030 various pump stations with installed flow rate of 1m 3 / s or installed power of 50kW or more have been built in China, including 482 large pump stations, 4745 medium pump stations and 88803 small pump stations. With the increasing demand of social development and production, two-way pump stations have gradually developed and matured due to their characteristics of irrigation and drainage, and play an irreplaceable role in urban river water diversion and drainage, water quality protection and plain area drainage irrigation. However, with the continuous expansion of the practical application of two-way pump stations, the contradiction between application and design theory is increasingly prominent. Especially in the design of two-way pump station outlet flow channel, the designer needs to design and optimize the parameters of the water guide cone and the horn pipe profile, and the design and application process is complicated.

[0003] In a Chinese patent, a method of adding two external double-flow channels to a double-flow pump station is proposed to reduce the pump station's head pressure. Meanwhile, a channel is opened between the newly added external flow channel and the original pump operation flow channel, and the opening and closing of the channel are controlled by a gate, which weakens the dead water area in the existing double-flow pump station structure, effectively eliminates the vortex into the pump, and improves the efficiency of the pump station. However, this patent mainly focuses on the number of flow channels and the interaction between flow channels in a double-flow pump station, and does not specifically address the outlet flow channel of the pump station. To address issues such as the turbulent flow characteristics in the outlet flow channel of a double-flow pump station during actual operation, the unbalanced axial force causing pump shaft and system vibration, and other factors, a Chinese patent, a double vertical pump station outlet diffusion structure, designs the structure of the de-spiral chamber, outlet diffusion horn pipe, rear guide cone, and box culvert outlet chamber, and optimizes the size and shape of the outlet horn pipe and rear guide cone, improving the outlet flow pattern of the double-flow pump station, reducing vortex and hydraulic loss, and achieving improved hydraulic efficiency of the outlet flow channel. The design takes into account the characteristics of a double-flow pump station, providing a new type of outlet diffusion structure that helps improve the overall performance of the pump station. However, the patent may lack detailed analysis of the performance of the pump station under different flow conditions, and further verification of its adaptability under different operating conditions is needed. In addition, the design only improves the structural parameters, and lacks systematic theoretical guidance for the design of the outlet flow channel. In a Chinese patent, a design method for a bell-shaped inlet flow channel for a pump station, a detailed design formula for a bell-shaped inlet flow channel is provided, including several key geometric parameters of the flow channel, and the design takes into account the specific speed, head, and flow of the pump. The design method is more versatile and conducive to the optimization design of the flow channel and the stable and efficient operation of the pump station. The bell-shaped and elbow-shaped design methods for the inlet flow channel of the pump station are proposed, effectively improving the inlet flow pattern and greatly reducing the hydraulic loss of the inlet flow channel, improving the economic benefits of pump operation. In a Chinese patent, a design method for a bell-shaped inlet flow channel for a pump station, a set of detailed elbow-shaped inlet flow channel design formulas is provided, including key parameters such as the height from the impeller center to the inlet flow channel bottom plate and the inlet height of the inlet flow channel. These formulas help improve the stability and efficiency of pump station operation. In addition, the design method takes into account various operating parameters of the pump, such as flow, speed, and head, enabling parameterized design and facilitating computer-aided design and optimization. By optimizing the geometric shape of the flow channel, the service life of the pump and pump station is extended, and the economic benefits of the pump station are improved. Although the patent provides design formulas, it does not provide detailed derivation processes and theoretical bases for these formulas, which may require further experimental verification. For special conditions or unconventional sizes of pump stations, the design method in the patent may need to be adjusted, and its versatility needs further research. In a Chinese patent, a design method for a double-flow pump station inlet flow channel horn mouth, by establishing a coordinate system and solving a parabolic equation, the parameterized design of the horn mouth cross-sectional line is realized, improving the accuracy and convenience of the design.The section design is adopted, the horn section line is divided into straight line and parabolic line section, the line transition is smoother, and the water flow dynamics is improved. The geometric parameters of the horn are optimized, the hydraulic loss of water flow in the pump station inlet flow channel is reduced, and the operation efficiency of the pump station is improved. However, the design method may need professional software support to realize the establishment of the coordinate system and the solution of the equation, and the adaptability to the traditional design method is not strong. Most of the above patents are two-way pump station inlet flow channel design methods, and few of them are two-way flow channel pump station outlet flow channel. SUMMARY

[0004] In view of the deficiencies in the prior art, the present application provides a two-way flow channel pump station outlet flow channel design method based on Dean vortex theory and a two-way flow channel pump station outlet flow channel. The main design parameters of the outlet flow channel are used to design the flow channel centerline, and the variation law of the outlet flow channel width is given. The outlet flow channel is designed by combining the flow channel centerline curvature ratio and the outlet flow channel width ratio. The design of the guide cone profile and the horn pipe profile is unified, which greatly simplifies the parameter optimization process of the outlet flow channel. The innovation of the present application lies in that a mathematical model based hydraulic design method of the outlet flow channel is proposed. By accurately controlling the curvature and width variation of the flow channel centerline, the water flow characteristics in the flow channel are optimized, thereby reducing the energy loss and improving the operation efficiency of the pump station. Compared with the traditional design method, the present application 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 application achieves the above technical purposes through the following technical means.

[0006] A two-way flow channel pump station outlet flow channel design method based on Dean vortex theory, comprising the following steps:

[0007] Based on the Dean vortex theory, the curvature ratio and the width ratio of the two-way pump station in the geometric coordinate system are defined respectively, and the mathematical model of the outlet flow channel geometry about the curvature ratio and the width ratio is established ψ=f(C r ,A r ), wherein ψ represents the target function of the outlet flow channel geometry, C r is the curvature ratio, and A r is the width ratio;

[0008] A plane rectangular coordinate system is established in the outlet flow channel centerline, the curvature ratio and the width ratio of the outlet flow channel centerline are obtained, the outlet flow channel centerline curvature radius is calculated, and the outlet flow channel centerline curvature radius range is obtained, and the relationship between the outlet flow channel width and the horizontal axis coordinate is calculated.

[0009] The function relationship of the curvature ratio and the width ratio about the outlet flow channel centerline along the way is obtained, and the outlet flow channel geometry is determined based on the function relationship.

[0010] Further, a plane rectangular coordinate system is established in the water outlet flow channel center line, and coordinates of any point of the water outlet flow channel center line in the plane coordinate system are denoted as (x, y), and the curvature ratio C of any point of the water outlet flow channel center line is r (x) is:

[0011]

[0012] In the formula, R1 is the radius of the diffusion pipe at the inlet of the flow channel; p x is the curvature radius at the arbitrary point;

[0013] The width ratio A of any point of the water outlet flow channel center line is r (x) is:

[0014]

[0015] In the formula, R3 is the radius of the diffusion pipe and the water guide cone at the outlet of the flow channel; B x is the width of the flow channel at the arbitrary point.

[0016] Further, the curvature radius of the water outlet flow channel center line of the bidirectional flow channel pump station is calculated, and the range of the curvature radius of the water outlet flow channel center line is obtained, and specifically, the curvature radius of the water outlet flow channel center line is

[0017] The function of the water outlet flow channel center line in the plane rectangular coordinate system is determined, and is denoted as g(x);

[0018] The curvature radius of any point of the water outlet flow channel center line is

[0019] In the formula, g'(x) is the first-order derivative of g(x) at the point (x, y); and g''(x) is the second-order derivative of g(x) at the point (x, y);

[0020] The relationship ρ(x) between the curvature radius of the water outlet flow channel center line and the abscissa x is obtained;

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

[0022] According to the water outlet flow channel center line, the relationship between the width of the water outlet flow channel and the abscissa is calculated.

[0023] Further, the water outlet flow channel center line is an elliptical line, a plane rectangular coordinate system xoy is established with the horizontal direction at the inlet of the flow channel as the x-axis and the vertical direction at the outlet of the flow channel as the y-axis, and the function g(x) of the water outlet flow channel center line in the plane rectangular coordinate system is represented as

[0024]

[0025] wherein: a1 is the long semi-axis of the ellipse, a1 = (H1 + H2) / 2, H1 is the height of the diffuser pipe; H2 is the height of the draft tube; b1 is the short semi-axis of the ellipse, b1 = R3 - R1 - B0 / 2, R1 is the radius of the diffuser pipe at the inlet of the flow passage; R3 is the radius of the diffuser pipe and the draft tube at the outlet of the flow passage, B0 is the width at the inlet of the two-way pump station;

[0026] The radius of curvature of the center line of the outlet flow passage at an arbitrary point can be expressed as:

[0027]

[0028] wherein g'(x) and g''(x) are the first derivative and the second derivative of the ellipse curve g(x) at the point (x, y), respectively,

[0029]

[0030] The radius of curvature of the center line of the outlet flow passage at an arbitrary point is:

[0031]

[0032] Substituting the ellipse equation into the elimination of y, the relationship of the radius of curvature of the center line of the ellipse type flow passage is:

[0033]

[0034] wherein k = c1 / b1 = c1 / (R3 - R1 - B0 / 2), c1 is the focal distance of the ellipse;

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

[0036] When x = -b1, the radius of curvature at the inlet of the outlet flow passage is the maximum, and the maximum radius of curvature is p max = a1 2 / b1;

[0037] When x = 0, the radius of curvature at the outlet of the outlet flow passage is the minimum, and the minimum radius of curvature is p min = b1 2 / a1;

[0038] The range of the radius of curvature p(x) of the center line of the outlet flow passage is:

[0039]

[0040] Further, according to the center line of the ellipse type flow passage, the relationship between the flow passage width and the abscissa x is obtained:

[0041]

[0042] Wherein, B0 is the width of the two-way pump station entrance.

[0043] Further, the curvature ratio about the outflow passage center line along the course is obtained as a function:

[0044]

[0045] The width ratio about the outflow passage center line along the course is obtained as a function:

[0046]

[0047] Further, the outflow passage center line is a hyperbola, with the horizontal direction at the entrance of the flow passage as the x-axis, and the center axis of the water guide cone as the y-axis, to establish a plane rectangular coordinate system xoy, and the function g(x) of the outflow passage center line in the plane rectangular coordinate system is expressed as:

[0048]

[0049] Wherein, a2 is the real half axis of the hyperbola, a2 = R1 + B0 / 2, R1 is the radius of the diffuser pipe at the entrance of the flow passage, B0 is the width of the two-way pump station entrance; b2 is the imaginary half axis of the hyperbola, b2 = (H1 + H2) / 2, H1 is the height of the diffuser pipe; H2 is the height of the water guide cone;

[0050] The curvature radius of the outflow passage center line at any point can be expressed as:

[0051]

[0052] Wherein, g'(x) and g''(x) are the first derivative and the second derivative of the hyperbola g(x) at the point (x, y), respectively,

[0053]

[0054] The curvature radius of the outflow passage center line at any point is:

[0055]

[0056] Substituting the hyperbola equation into the elimination of y, the curvature radius variation relationship of the hyperbolic flow passage center line is obtained as:

[0057]

[0058] In the formula, e2 is the eccentricity of the hyperbola, e2 = c2 / a2 = c2 / (R1 + B0 / 2), c2 is the focal distance of the hyperbola;

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

[0060] When x=R3, the curvature radius at the entrance of the water outlet channel is the maximum, and the maximum curvature radius is

[0061] When x=a2, the curvature radius at the exit of the water outlet channel is the minimum, and the minimum curvature radius is p min =b2 2 / a2;

[0062] The curvature radius p(x) of the center line of the water outlet channel varies in the range of:

[0063]

[0064] Further, according to the hyperbolic center line of the channel, the relationship between the channel width and the abscissa x is obtained:

[0065]

[0066] Wherein, B0 is the width of the inlet of the bidirectional pump station.

[0067] Further, the function relationship of the curvature ratio about the center line of the water outlet channel is obtained:

[0068]

[0069] The function relationship of the width ratio about the center line of the water outlet channel is obtained:

[0070]

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

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

[0073] The design method of the water outlet channel of the bidirectional channel pump station based on the Dean vortex theory starts from the type line category of the center line of the channel, based on the mathematical properties of the elliptic line and the hyperbolic line, respectively describes the channel design method based on the elliptic line and the hyperbolic line, and deduces the variation law of the curvature radius of the center line of the channel. On this basis, the variation law of the width of the water outlet channel is reasonably designed. Compared with the traditional design method, the design method of the present application can determine the shape of the channel by using the curvature ratio of the center line of the channel and the width ratio of the channel, which greatly simplifies the optimization work of the water outlet channel of the bidirectional pump station. The traditional design method of the water outlet channel of the bidirectional pump station is mainly determined by the water cone type line and the horn pipe type line, and the channel is determined by multiple parameters, and the parameter optimization work of the two type lines is relatively cumbersome. BRIEF DESCRIPTION OF DRAWINGS

[0074] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. The drawings in the following description are some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0075] Figure 1 The flow chart of the method for designing the outlet flow channel of the bidirectional flow channel pump station according to the present application based on the Dean vortex theory.

[0076] Figure 2 The main geometric parameter diagram of the outlet flow channel of the bidirectional flow channel pump station according to the present application.

[0077] Figure 3 The design diagram of the center line of the flow channel based on the elliptical line.

[0078] Figure 4 The design diagram of the center line of the flow channel based on the hyperbolic line.

[0079] Figure 5 The comparison of the external characteristics of the bidirectional pump station based on the elliptical line design method and the traditional design method. DETAILED DESCRIPTION

[0080] The embodiments of the present application will be described in detail below, and examples of the embodiments are shown in the drawings, wherein the same or similar notations represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary and are intended to explain the present application, and cannot be understood as a limitation of the present application.

[0081] In the description of the present application, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "axial", "radial", "vertical", "horizontal", "inner", "outer" and the like is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present application and simplifying the description, and therefore cannot be understood as indicating or implying that the device or element indicated must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation of the present application. In addition, the terms "first", "second" are only for the purpose of description, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the technical features indicated. Therefore, the features limited by "first", "second" can explicitly or implicitly include one or more of the features. In the description of the present application, the meaning of "multiple" is two or more, unless otherwise specifically limited.

[0082] In the present application, unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connecting", "fixing" and the like should be understood in a broad sense, for example, can be fixed connection, can also be detachable connection, or integrally connected; can be mechanical connection, or electrical connection; can be directly connected, or indirectly connected through an intermediate medium, or the internal communication of two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0083] As shown in Figure 1 The design method of the outflow channel of the bidirectional flow channel pump station based on the Dean vortex theory comprises the following steps:

[0084] Based on the Dean vortex theory, the curvature ratio and the width ratio of the bidirectional pump station in the geometric coordinate system are defined respectively, and a mathematical model of the geometric shape of the outflow channel about the curvature ratio and the width ratio is established ψ = f(C r ,A r ), wherein ψ represents the objective function of the geometric shape of the outflow channel, C r is the curvature ratio, and A r is the width ratio;

[0085] A plane rectangular coordinate system is established in the center line of the outflow channel, the curvature ratio and the width ratio of the center line of the outflow channel are obtained, the curvature radius of the center line of the outflow channel is calculated, the range of the curvature radius of the center line of the outflow channel is obtained, and the relationship between the width of the outflow channel and the horizontal axis coordinate is calculated.

[0086] The function relationship of the curvature ratio and the width ratio about the center line of the outflow channel is obtained, and the geometric shape of the outflow channel is determined based on the function relationship.

[0087] Figure 2 As shown in the figure, R1 is the radius of the diffuser pipe at the inlet of the flow channel, m; R2 is the radius of the water guide cone at the inlet of the flow channel, m; R3 is the radius of the diffuser pipe and the water guide cone at the outlet of the flow channel, m; B1 is the height of the diffuser pipe, m; B2 is the height of the water guide cone, m; B0 is the width of the flow channel at the inlet, m.

[0088] In the embodiment, R1 = 1.0 m, R2 = 1.6 m, R3 = 2.8 m, H1 = 2.0 m, and H2 = 3.6 m.

[0089] Embodiment 1 takes the center line of the outflow channel as an elliptical line as an example for specific description:

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

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

[0092]

[0093] The width ratio A of any point in the middle line of the outlet flow channel is r (x) is:

[0094]

[0095] In the formula, ρ x is the radius of curvature at the point; B x is the width of the flow channel at the point.

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

[0097]

[0098] In the formula, a1 is the long semi-axis of the elliptical line, a1 = (H1 + H2) / 2, H1 is the height of the diffuser pipe; H2 is the height of the water guide cone; b1 is the short semi-axis of the elliptical line, b1 = R3 - R1 - B0 / 2, R1 is the radius of the diffuser pipe at the inlet of the flow channel; R3 is the radius of the diffuser pipe and the water guide cone at the outlet of the flow channel, and B0 is the width at the inlet of the two-way pump station;

[0099] In the embodiment, a1 = R3 - R1 - B0 / 2 = 2.1 m, b1 = (H1 + H2) / 2 = 2.8 m, and B0 = (R1 + R2) / 2 = 0.3 m. Therefore, the equation g(x) of the middle line of the outlet flow channel can be represented as:

[0100]

[0101] The radius of curvature of any point in the middle line of the outlet flow channel can be represented as:

[0102]

[0103] In the formula, g'(x) and g''(x) are the first-order derivative and the second-order derivative of the elliptical curve g(x) at the point (x, y), respectively,

[0104]

[0105]

[0106] ​The curvature radius of the outlet flow channel center line at any point is:

[0107]

[0108] The curvature radius variation relationship of the outlet flow channel center line can be obtained by substituting the ellipse equation into eliminating y:

[0109]

[0110] In the formula, k = c1 / b1 = c1 / (R3-R1-B0 / 2), c1 is the focal length of the ellipse line, c1 = (a1 2 -b1 2 ) 1 / 2 = 1.852 m, k = c1 / b1 = 0.8819, so the curvature radius variation relationship of the outlet flow channel center line can be expressed as:

[0111]

[0112] When x = -b1, the curvature radius at the outlet flow channel inlet is maximum, and the maximum curvature radius is p max =a1 2 / b1 = 3.733 m;

[0113] When x = 0, the curvature radius at the outlet flow channel outlet is minimum, and the minimum curvature radius is p min =b1 2 / a1 = 1.575 m;

[0114] The curvature radius p(x) of the outlet flow channel center line varies in the range of:

[0115] 1.575 m ≤ p(x) ≤ 3.733 m.

[0116] According to the ellipse line type flow channel center line, the relationship between the flow channel width and the abscissa x is obtained:

[0117]

[0118] S03: Obtain the function relationship of the curvature ratio about the outlet flow channel center line along the way:

[0119]

[0120] Obtain the function relationship of the width ratio about the outlet flow channel center line along the way:

[0121]

[0122] S04: Determine the outlet flow channel geometry based on the function relationship of the curvature ratio and the width ratio.

[0123] Embodiment 2 takes the hyperbola as an example to illustrate the case that the centerline of the outlet flow passage is a hyperbola: in order to distinguish from Embodiment 1, the coordinates of any point in Embodiment 2 are denoted as (x', y'),

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

[0125] A rectangular coordinate system is established in the centerline of the outlet flow passage, and the coordinates of any point in the centerline of the outlet flow passage are denoted as (x', y'). The curvature ratio C of any point in the centerline of the outlet flow passage is: r (x') is:

[0126]

[0127] The width ratio A of any point in the centerline of the outlet flow passage is: r (x') is:

[0128]

[0129] In the formula: p x′ is the radius of curvature at any point; B x′ is the width of the flow passage at any point.

[0130] S02: As shown in the formula, a rectangular coordinate system xoy is established with the horizontal direction at the inlet of the flow passage as the x-axis and the center axis of the water guide cone as the y-axis. The function h(x') of the centerline profile of the outlet flow passage in the rectangular coordinate system is represented as: Figure 4

[0131]

[0132] wherein a2 is the real half-axis of the hyperbola, a2 = R1 + B0 / 2, R1 is the radius of the diffuser pipe at the inlet of the flow passage, and B0 is the width at the inlet of the bidirectional pump station; b2 is the imaginary half-axis of the hyperbola, b2 = (H1 + H2) / 2, H1 is the height of the diffuser pipe; H2 is the height of the water guide cone; B0 is the width at the inlet of the bidirectional pump station;

[0133] In the embodiment, in this specific embodiment, the real half-axis of the hyperbola is a2 = R1 + B0 / 2 = 1.3 m; b2 = (H1 + H2) / 2 = 2.8 m, and the hyperbolic equation h(x') can be represented as:

[0134]

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

[0136] ​

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

[0138]

[0139] In Example 2, the focal length of the hyperbola is c2=(a2 2 +b2 2 ) 1 / 2 = 3.087 m, the eccentricity is e2=c2 / (R1+B0 / 2)=2.3747, and the hyperbolic equation is substituted to eliminate y' to obtain the relationship between the radius of curvature of the centerline of the hyperbolic flow channel:

[0140]

[0141] When x=R3, the radius of curvature at the inlet of the outlet flow channel is maximum, and the maximum radius of curvature is

[0142] When x=a2, the radius of curvature at the outlet of the outlet flow channel is minimum, and the minimum radius of curvature is min =b2 2 / a2=6.031 m;

[0143] The radius of curvature of the centerline of the outlet flow channel varies in the range of 6.031 m≤ρ(x')≤11.682 m.

[0144] According to the centerline of the hyperbolic flow channel, the relationship between the width of the flow channel and the abscissa x is obtained:

[0145]

[0146] S03: Obtain the function relationship of the curvature ratio about the centerline of the outlet flow channel:

[0147]

[0148] Obtain the function relationship of the width ratio about the centerline of the outlet flow channel:

[0149]

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

[0151] In the implementation of the present application, first of all, according to the specific working conditions and design requirements of the pump station, the main geometric parameters of the flow channel are determined, including the radius and height of the diffuser pipe and the water guide cone. Then, using the method provided by the present application, the elliptical or hyperbolic model of the flow channel center line is established, and the corresponding curvature radius and width variation law are calculated. In the calculation process, through iteration and optimization algorithm, it is ensured that the design parameters meet the predetermined performance indicators, such as the hydraulic efficiency and anti-swirl performance of the flow channel. Through computer aided design (CAD) software, according to the calculated parameters, the three-dimensional model of the flow channel is drawn, and detailed fluid dynamics analysis is carried out to verify the rationality and effectiveness of the design. In the model verification stage, computational fluid dynamics (CFD) simulation can be used to analyze the flow field in the flow channel in detail, 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 Comparing the external characteristics of the two-way 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 difference is not large, the pump operating efficiency designed based on the method is greater than that of the traditional method.

[0152] Therefore, the embodiments of the present application not only provide an efficient water outlet flow channel design method, but also provide important theoretical basis and technical support for the design and reconstruction of pump stations.

[0153] The two-way flow channel pump station water outlet flow channel of the present application is designed based on the two-way flow channel pump station water outlet flow channel design method of the present application.

[0154] It should be understood that although the present specification is described in terms of various embodiments, not every embodiment contains only one independent technical solution, and the description of the specification is only for clarity, and those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be combined to form other embodiments that can be understood by those skilled in the art.

[0155] The above series of detailed descriptions are only specific descriptions of feasible embodiments of the present application, and are not intended to limit the protection scope of the present application. Any equivalent embodiments or changes made without departing from the spirit of the present application should be included in the protection scope of the present application.

Claims

1. A method for designing a water outlet flow channel of a bidirectional flow channel pump station based on the theory of Dean vortex, characterized in that, The method comprises the following steps: Based on the theory of Dean vortex, the curvature ratio and width ratio of the two-way channel pump in the geometric coordinate system are defined respectively, and the mathematical model of the water outlet channel geometry about the curvature ratio and width ratio is established where ψ represents the objective function of the water outlet channel geometry, C r is the curvature ratio, A r is the width ratio; A plane rectangular coordinate system is established in the center line of the outlet flow channel, and the curvature ratio and the width ratio of the center line of the outlet flow channel are obtained; the curvature radius of the center line of the outlet flow channel is calculated, and the range of the curvature radius of the center line of the outlet flow channel is obtained; the change relationship of the width of the outlet flow channel with the horizontal axis coordinate is calculated; and the specific steps are as follows: In the water outlet flow channel line to establish a plane rectangular coordinate system, water outlet flow channel line in the plane coordinate system at any point coordinates marked (x, y), then the water outlet flow channel line in the curvature of any point C r (x) is: ； where: R1 is the radius of the diffuser at the inlet to the flow passage; R is the radius of curvature at any point; The width ratio A of any point on the center line of the water outlet flow channel r (x) is: ； where: R3 is the radius of the diffuser and the draft tube at the outlet of the flow passage; W is the flow passage width at any point; The curvature radius of the center line of the outlet flow channel of the bidirectional flow channel pump station is calculated, and the range of the curvature radius of the center line of the outlet flow channel is obtained, and the specific steps are as follows: The function of the center line of the outlet flow channel in the plane rectangular coordinate system is determined and is denoted as g(x); The radius of curvature at any point of the outlet water flow channel center line is: , wherein: is the first derivative of g(x) at the point (x,y); is the second derivative of g(x) at the point (x,y). The relationship between the radius of curvature of the linear line in the water outlet channel and the abscissa x is obtained ; According to the value of x in , the maximum curvature radius is ρ max and the minimum curvature radius is ρ min , the range of is determined; The change relationship of the width of the outlet flow channel with the horizontal axis coordinate is calculated according to the center line of the outlet flow channel; The center line of the outlet flow channel is an elliptic line or a hyperbolic line, the function relationship of the curvature ratio and the width ratio with the center line of the outlet flow channel along the path is obtained, and the geometric shape of the outlet flow channel is determined based on the function relationship.

2. The method of claim 1, wherein the method is characterized by: The center line of the outlet flow channel is an elliptic line, a plane rectangular coordinate system xoy is established with the horizontal direction of the flow channel inlet as the x-axis and the vertical direction of the flow channel outlet as the y-axis, and the function g(x) of the center line of the outlet flow channel in the plane rectangular coordinate system is represented as - b1 < x < 0, a1 > b1 Wherein, a1 is the long semi-axis of the elliptic line, a1=(H1+H2) / 2, H1 is the height of the diffuser pipe; H2 is the height of the water guide cone; b1 is the short semi-axis of the elliptic line, b1=R3-R1-B0 / 2, R1 is the radius of the diffuser pipe at the flow channel inlet; R3 is the radius of the diffuser pipe and the water guide cone at the flow channel outlet, and B0 is the width at the inlet of the bidirectional pump station; The curvature radius of the center line of the outlet flow channel at any point is represented as ， wherein and are the first and second derivatives of the elliptic curve g(x) at the point (x, y), respectively, ， ， The curvature radius of the center line of the outlet flow channel at any point is ， The change relationship of the curvature radius of the elliptic type flow channel center line is obtained by substituting the elliptic equation into eliminating y as ， In the formula, k=c1 / b1=c1 / (R3-R1-B0 / 2), c1 is the focal distance of the elliptic line; according to The value of x in the equation is used to obtain the maximum radius of curvature ρ. max and the minimum radius of curvature is ρ min Specifically: When x = -b1, the curvature radius at the outlet water channel entrance is the maximum, and the maximum curvature radius is p max = a1 2 / b1; When x = 0, the curvature radius at the outlet of the water outlet passage is the smallest, and the minimum curvature radius is p min = b1 2 / a1; Curvature radius of outlet water flow channel center line Varies in the range: 。 3. The method of claim 2, wherein the method is characterized by: According to the elliptic line type flow channel center line, the relationship between the flow channel width and the horizontal coordinate x is obtained as ， Wherein, B0 is the width at the inlet of the bidirectional pump station.

4. The method of claim 3, wherein the method is characterized by: The function relationship of the curvature ratio with the center line of the outlet flow channel along the path is obtained as ； The function relationship of the width ratio with the center line of the outlet flow channel along the path is obtained as 。 5. The method of claim 1, wherein the method is characterized by: The center line of the outlet flow channel is a hyperbolic line, a plane rectangular coordinate system xoy is established with the horizontal direction of the flow channel inlet as the x-axis and the central axis of the water guide cone as the y-axis, and the function g(x) of the center line of the outlet flow channel in the plane rectangular coordinate system is represented as a2≤ x ≤ R 3； Wherein, a2 is the real semi-axis of the hyperbolic line, a2=R1+B0 / 2, R1 is the radius of the diffuser pipe at the flow channel inlet, and B0 is the width at the inlet of the bidirectional pump station; b2 is the virtual semi-axis of the hyperbolic line, b2=(H1+H2) / 2, H1 is the height of the diffuser pipe; H2 is the height of the water guide cone; The curvature radius of the center line of the outlet flow channel at any point is represented as ， wherein and are the first and second derivative of the hyperbolic curve g(x) at the point (x,y), respectively, ， ， The curvature radius of the center line of the outlet flow channel at any point is ， The change relationship of the curvature radius of the hyperbolic type flow channel center line is obtained by substituting the hyperbolic equation into eliminating y as ， In the formula, e2 is the eccentricity of the hyperbolic line, e2=c2 / a2=c2 / (R1+B0 / 2), c2 is the focal distance of the hyperbolic line; according to The value of x in the equation is used to obtain the maximum radius of curvature ρ. max and the minimum radius of curvature is ρ min Specifically: When x = R3, the curvature radius at the entrance of the water outlet channel is the largest, and the maximum curvature radius is ; When x = a2, the curvature radius at the outlet of the water outlet passage is the smallest, and the minimum curvature radius is p min = b2 2 / a2; Curvature radius of outlet water flow channel center line Varies in the range: 。 6. The method of claim 5, wherein the method is characterized by: According to the hyperbolic line type flow channel center line, the relationship between the flow channel width and the horizontal coordinate x is obtained as ， Wherein, B0 is the width at the inlet of the bidirectional pump station.

7. The method of claim 6, wherein the method is characterized by: The function relation of the curvature ratio with respect to the length of the center line of the outlet flow channel is obtained: ； The function relation of the width ratio with respect to the length of the center line of the outlet flow channel is obtained: 。 8. A two-way flow channel pump station water outlet flow channel, characterized in that, The outlet flow channel is designed according to the design method of the two-way flow channel pump station outlet flow channel based on the Dean vortex theory in any one of claims 1-7.

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