Centrifugal pump blade wrap angle determination method based on hydromechanics numerical integration

Abstract

The invention relates to the technical field of centrifugal pumps, in particular to a centrifugal pump blade wrap angle determining method based on hydromechanics numerical integration. The centrifugal pump blade wrap angle determining method is a numerical integration method based on a fluid mechanics equation, equal-interval point division is conducted on a shaft surface streamline in an impeller shaft surface projection drawing through combination of a differential equation and numerical integration, and the arc length and the radius between every two adjacent equal division points are calculated; after the axial surface fluid velocity vm is calculated based on the one-dimensional flow theory, a curve of vm changing along an axial surface streamline is drawn; establishing a linear distribution model of the tangential velocity moment vur according to an Euler equation; after the integral coefficient K is calculated, K.si accumulated integral is calculated point by point, the centrifugal pump blade wrap angle value is directly obtained, and the effectiveness of the centrifugal pump blade wrap angle value is obtained through verification with an example verification method; according to the method, the centrifugal pump blade wrap angle can be designed through parameterization, and the situation that the centrifugal pump blade wrap angle can only be obtained depending on experience is avoided.

Description

Technical Field

[0001] This invention relates to the field of centrifugal pump technology, specifically to a method for determining the blade wrap angle of a centrifugal pump based on numerical integration of fluid mechanics. Background Technology

[0002] In centrifugal pump blade design, the blade wrap angle is a crucial geometric parameter, directly impacting the impeller's performance. According to existing centrifugal pump blade design theories, both the grid conformal transformation method and the twisted triangle method require an initial estimate of the wrap angle based on experience before determining its size. Then, streamline development lines are drawn. If the shape of the streamline development lines is not ideal, modifications must be made to the blade inlet edge position, inlet / outlet angles, or the wrap angle itself, making the process quite cumbersome. Furthermore, in both the grid conformal transformation method and the twisted triangle method, the initial wrap angle value can only be selected empirically and is not necessarily the final value. The final wrap angle value is determined solely by the shape and smoothness of the streamline development lines, and its final size can only be determined when drawing the streamline development lines, not initially based on design requirements. Therefore, these two traditional methods for determining the wrap angle of centrifugal pump blades rely too heavily on experience and are far from sufficient for quickly determining the wrap angle of centrifugal pump blades. If a wrap angle determination method can be proposed that can calculate a reasonable wrap angle value based on the design requirements of the centrifugal pump, it can avoid selecting the wrap angle based on experience and also avoid the impact of changes in the final wrap angle on the impeller performance.

[0003] A search revealed that no patents related to this invention have been published yet. It is only mentioned in some literature, and the corresponding technical solutions mainly determine the blade wrap angle based on the blade inlet and outlet placement angles. This is still based on the grid conformal transformation method, and the final wrap angle is determined based on the shape and uniformity of the streamline development line. Summary of the Invention

[0004] The purpose of this invention is to provide a method for determining the wrap angle of centrifugal pump blades based on numerical integration of fluid mechanics, so as to solve the problems mentioned in the background art.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for determining the wrap angle of a centrifugal pump blade based on numerical integration in fluid mechanics, the method comprising: S1. Divide the streamlines of the impeller shaft into equally spaced points in the impeller shaft projection diagram, and calculate the arc length and radius between each two adjacent equally spaced points; S2. The fluid velocity v from the blade inlet to the blade outlet is calculated based on the impeller axial projection diagram and one-dimensional flow theory. m Then, draw v m A curve that varies along the streamlines of the axial plane; S3, according to the improved import circulation formula and the improved Euler formula, the streamline import tangential velocity moment and the streamline export tangential velocity moment are obtained; and the tangential velocity moment curve along the axial surface streamline from the import to the export is drawn in combination with the tangential velocity moment curve along the axial surface streamline from the import to the export; S4, the integral coefficient K of the i-th division point is calculated according to the blade profile differential equation i ; S5, the blade wrap angle is calculated after the arc length, the radius, the tangential velocity moment curve along the axial surface streamline from the import to the export, the tangential velocity moment curve along the axial surface streamline from the import to the export and the integral coefficient K obtained in steps S1-S4 are combined m i

[0006] Further, the axial surface streamline in the impeller axial surface projection drawing in S1 is obtained according to CFD software numerical simulation; when the axial surface streamline is divided in the impeller axial surface projection drawing, the axial surface streamline is divided into A equally spaced division points, and A is a preset constant.

[0007] CFD software numerical simulation is one of the most commonly used methods for obtaining axial surface streamline at present; compared with other methods for obtaining axial surface streamline, CFD software numerical simulation can obtain axial surface streamline distribution more quickly, realize visualization and optimization of outlet edge shape, and balance accuracy and efficiency; the axial surface streamline obtained by CFD software numerical simulation in the application can minimize errors and realize accurate design of the blade wrap angle of the centrifugal pump.

[0008] Further, after the arc length between each adjacent two division points obtained in S2, the arc length between the i-th division point and the i+1-th division point is recorded as Δs i , and the arc length Δs i is combined with the integral coefficient K i to obtain Δs i corresponding to Δ θ i , wherein Δ θ i is the central angle corresponding to the arc length Δs i ; for the radius between each adjacent two division points obtained, the radius between the i-th division point and the i+1-th division point is recorded as C i ; and the fluid velocity from the blade import to the blade export is obtained according to the related formula v m , and the curve v m along the axial surface streamline is drawn , wherein f() represents the fluid velocity from the blade import to the blade export v m and Δs i ​​The relationship function between the two is as follows: wherein, is the arc length between the i-th and the i+1-th division point; r1 is the inlet radius, the inlet radius being the radius of the circular profile at the impeller inlet; Q is the design flow rate, wherein the design flow rate Q is preset according to a theoretical model.

[0009] The design flow rate of a centrifugal pump is one of the core parameters of the design of the centrifugal pump, and the size change of the design flow rate will affect important geometric parameters such as the impeller inlet diameter and the flow passage width; since the present application is to realize the design of the blade wrap angle of the centrifugal pump through parameterization, and to get rid of the method of relying on experience to obtain the blade wrap angle of the centrifugal pump, the presetting of the design flow rate according to the theoretical model in the present application avoids the blindness of the experience-based design, and realizes the unity with the core technology of the present application.

[0010] Further, the relevant formula for obtaining the streamline inlet tangential velocity moment v u1 r 1 and the streamline outlet tangential velocity moment v u2 r 2 is as follows: ; wherein, is the blade inlet setting angle, is the magnitude of the angle of attack, and = 0.8 (N S / 100) 0.6 ; wherein is the specific speed of the impeller; the present application increases the specific speed because the formula dynamically correlates the angle of attack with the specific speed Ns, and reflects the influence of the specific speed on the inlet flow direction through the exponential form (0.6) and the coefficient (0.8), the flow passage of a high specific speed pump (large flow rate, low head) expands significantly, and the inlet flow is easy to deviate from the design direction, and needs a larger angle of attack correction; is the impeller inlet width; Q is the design flow rate; g is the acceleration of gravity, taken as 9.81; v u2 is the outlet tangential velocity; r 2 is the outlet radius, the outlet radius being the radius of the circular profile at the impeller outlet; u1 is the inlet tangential velocity; r 1 is the inlet radius; the inlet radius being the radius of the circular profile at the impeller inlet; ω is the angular velocity of the impeller; H this the theoretical head of the impeller; after v u1 r1and v u2 r2are obtained, the tangential velocity moment v u ris drawn according to the formula ; the related formula is as follows: wherein, the tangential velocity moment v v u r the change along the axial surface streamline from the inlet to the outlet is linear change; v u2 is the outlet tangential velocity; r 2is the outlet radius; v u1 is the inlet tangential velocity; r 1is the inlet radius; ω is the angular velocity of the impeller; H th is the theoretical head of the impeller; is the arc length between the i th equal point and the i+1 th equal point; L is the total arc length of the axial surface streamline.

[0011] Wherein, the flow passage expansion of the high specific speed pump is a key link affecting the water conservancy performance of the centrifugal pump, and in the design of the high specific speed pump, the flow passage expansion is significantly associated with the large cam angle correction, which is a key technology. When the flow passage expansion of the high specific speed pump is significant, the fluid flow state changes; at this time, the large cam angle correction is needed to cope with the change, optimize the water conservancy performance, achieve the purpose of reducing the impact loss and widening the high efficiency area.

[0012] Further, the integral coefficient of the i th equal point in S4 is calculated as ; wherein, C i is the radius of the i th equal point and the i+1 th equal point; is the arc length Δs i corresponding to the tangential velocity, and is the value of each point corresponding to the curve according to the interpolation; v is the value of each point corresponding to the curve according to the interpolation; v is the value of each point corresponding to the curve according to the interpolation; v m is the arc length Δs i corresponding to the fluid velocity, and v m is the value of each point corresponding to the curve according to the interpolation; the integral coefficient of the i th equal point is obtained through the blade profile differential equation ; wherein, the blade profile differential equation is obtained through the blade profile differential equation ; wherein, the blade profile differential equation ​Is based on the kinematics and dynamics of fluid in the blade passage derived.

[0013] Blade profile differential equation ; Reaction in the case of considering the rotation of the impeller and fluid flow, the change rule of blade profile in geometry, help to design and analyze the shape of the blade to meet the specific requirements of fluid dynamics performance; through the blade profile differential equation Integral coefficient of the i-th point of equal division The process is as follows: From the blade profile differential equation Transformed as: At the i-th point of equal division of the meridional streamline, the radius C i And the corresponding velocity interpolation And Substitute, that is, the integral coefficient , the physical meaning of which is the angular rate of point i .

[0014] Further, the related formula for calculating the blade wrap angle of the centrifugal pump in S5 is: Wherein, The blade wrap angle of the centrifugal pump is obtained; the cumulative sum of Δ θ i Corresponding to each Δ θ i When i is different, Δ θ i The arc length Corresponding to the central angle and ; wherein, The arc length between the i-th point of equal division and the i+1-th point of equal division; In the formula The integral coefficient of the i-th point of equal division, The integral coefficient of the i+1-th point of equal division.

[0015] In the process of determining the blade wrap angle of the centrifugal pump based on the fluid mechanics differential equation and the numerical integral theory, step-by-step calculation and parameterized modeling are adopted, which significantly improves the accuracy and efficiency of the wrap angle design. The method takes the theoretical model as the core, and directly calculates the wrap angle value according to the design parameters such as head and speed by establishing the blade profile differential equation , combined with Euler equation and meridional velocity distribution, which overcomes the defects of relying on empirical initial value in traditional methods. The discrete points and point-by-point integral formula , form tabular calculation process, make design cycle shorten more than 40%, and the calculation error is controlled within 3%, which is better than the empirical adjustment mode of traditional conformal transformation method. Through the definition of integral coefficient , tangential momentum, centrifugal force and velocity gradient are dynamically related, and good multi-working condition adaptability is achieved, especially for complex operating conditions such as high specific speed and large flow.

[0016] Compared with the prior art, the beneficial effects achieved by the present application are: the present application proposes a determination method of the wrap angle of a centrifugal pump, which can obtain the blade streamline wrap angle value according to the design requirements of the impeller, by applying the blade profile differential equation, dividing points along the axial surface streamline and integrating point by point, so that the wrap angle value can be selected according to experience and the final wrap angle value can be determined only according to the shape and smoothness of the streamline development line. BRIEF DESCRIPTION OF DRAWINGS

[0017] The accompanying drawings are included to provide a further understanding of the present application, and constitute a part of the specification, and are used together with embodiments of the present application to explain the present application, and do not constitute a limitation on the present application. In the drawings: Figure 1 It is a flowchart of a centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration; Figure 2 It is a schematic diagram of equidistant point division and corresponding size on the front cover plate streamline of an impeller of a centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration; Figure 3 It is an axial surface velocity v m Distribution curve of the value along the front cover plate axial surface streamline from the inlet to the outlet ; Figure 4 It is a distribution curve of the value along the front cover plate axial surface streamline from the inlet to the outlet v u r of a centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration v u1 r 1 to the outlet v u2 r 2 of a centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration ; Figure 5 It is a distribution curve of the value along the front cover plate axial surface streamline from the inlet to the outlet K of a centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration v u1 r 1 to the outlet v u2r The curve of 2; Figure 6 Δ is a method for determining the vane wrap angle of a centrifugal pump based on numerical integration in fluid mechanics. θ i Along the axial streamline of the front cover from the inlet v u1 r 1 to the exit v u2 r The curve of 2; Figure 7 It is a planar shape of the streamline of the front cover plate of a centrifugal pump obtained by calculation based on a method for determining the wrap angle of centrifugal pump blades using numerical integration in fluid mechanics. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Please see Figures 1-7 The present invention will be further described in conjunction with the accompanying drawings and design examples; for example... Figure 1 As shown, a method for determining the wrap angle of a centrifugal pump blade based on numerical integration in fluid dynamics is described, the method comprising: S1. Divide the streamlines of the impeller shaft into equally spaced points in the impeller shaft projection diagram, and calculate the arc length and radius between each two adjacent equally spaced points; S2. The fluid velocity v from the blade inlet to the blade outlet is calculated based on the impeller axial projection diagram and one-dimensional flow theory. m Then, draw v m A curve that varies along the streamlines of the axial plane; S3. Based on the improved inlet circulation formula and the improved Euler formula, obtain the streamline inlet tangential velocity moment and the streamline outlet tangential velocity moment; and combine the streamline inlet tangential velocity moment and the streamline outlet tangential velocity moment to draw the curve of the streamline tangential velocity moment changing along the axial streamline from the inlet to the outlet. S4. Calculate the integral coefficient K of the i-th division point based on the differential equation of the blade profile. i ; S5. By obtaining the arc length, radius, and v from steps S1-S4... m The curve showing the variation of streamlines along the axial plane, the curve showing the variation of tangential velocity moment from inlet to outlet along the axial plane streamline, and the integral coefficient K. i By combining these methods, the wrap angle of the centrifugal pump blades can be calculated.

[0020] The parameter of the design example is flow rate Q =400m 3 / h, head H =35m, rotational speed n =1480r / min, specific speed N S The streamline of the cover plate of a centrifugal pump with a specific speed of 125.1 is taken as an example for illustration; In combination with Figure 2 Thirteen points are equally spaced along the front cover plate in the axial plane, and the equally spaced interval ΔXi is 0.0074m, Figure 2 In the formula, r represents the radius of the circular profile of the impeller corresponding to the position point of the axial streamline in the axial projection of the impeller, and the value range of r belongs to the interval constituted by r1 and r2; according to the formula The fluid velocity from the inlet to the outlet is calculated v m The curve of the change of the tangential velocity moment along the axial streamline from the inlet to the outlet is plotted v m , as Figure 3 ; According to the improved inlet ring momentum formula and the improved Euler formula, the tangential velocity moment of the inlet of the streamline is calculated And the tangential velocity moment of the outlet of the streamline is calculated ; According to The tangential velocity moment v u r of the curve of the change of the tangential velocity moment along the axial streamline from the inlet to the outlet is plotted; wherein the head of the centrifugal pump H =35m, the hydraulic efficiency of the centrifugal pump is estimated to be 90%, so the theoretical head is about H th =39m, the inlet v u1 r 1=0, so the outlet v u2 r 2=2.46, The curve is plotted in a linear manner, as Figure 4 ; and the outlet boundary conditions are determined through the Euler equation combined with the theoretical head, including the flow rate boundary condition, the pressure boundary condition, the velocity boundary condition and the free outflow boundary condition. After the boundary conditions are determined, the working parameters of the centrifugal pump under specific working conditions can be determined, and whether the centrifugal pump meets the actual industrial requirements can be evaluated through the working parameters.

[0021] As​Figures 5 to 7 As shown, the relevant data after calculating each streamline are included in the point-by-point calculation table for blade wrap angle. Table 1: Calculation Table of Blade Wrap Angle Point by Point And according to The calculated wrap angle of the centrifugal pump blade is θ = 22.43°. Through example verification and comparison with traditional design methods, it is found that the wrap angle calculation error of the centrifugal pump blade obtained by the present invention is less than 3%, the design cycle is shortened by 40%, and the impeller efficiency is improved by 2% to 5%. This demonstrates that the present invention can eliminate the reliance on experience to obtain the wrap angle of the centrifugal pump blade by combining differential equations and numerical integration, and realize the parameterized design of the wrap angle. It also solves the defects of the traditional grid conformal transformation method and twisted triangle method, which require repeated adjustment of the wrap angle.

[0022] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0023] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for determining a blade wrap angle of a centrifugal pump based on numerical integration of fluid dynamics, characterized by, The method comprises the following steps: S1, equally spacing the points of the axial surface flow line in the axial surface projection diagram of the impeller, and calculating the arc length and radius between each adjacent two equally divided points; S2, fluid velocity v from blade inlet to blade outlet calculated according to blade axial surface projection diagram and one-dimensional flow theory m Afterwards, draw v m Curve of variation of axial surface streamline S3, obtaining the tangential velocity moment of the flow line inlet and the tangential velocity moment of the flow line outlet according to the improved inlet circulation formula and the improved Euler formula; and combining the tangential velocity moment of the flow line inlet and the tangential velocity moment of the flow line outlet, drawing a curve of the change of the tangential velocity moment of the flow line from the inlet to the outlet along the axial surface flow line; S4. Calculate the integral coefficient K of the i-th division point according to the blade profile differential equation i ; S5、by the arc length, radius, v m curve of tangential velocity moment along the meridional line from the inlet to the outlet along the meridional line and the integral coefficient K i In combination, the blade wrap angle of the centrifugal pump is calculated.

2. The method for determining blade wrap angle of a centrifugal pump based on numerical integration of fluid dynamics according to claim 1, characterized in that: The axial surface flow line in the axial surface projection diagram of the impeller in S1 is obtained according to numerical simulation of CFD software; when the axial surface flow line is divided in the axial surface projection diagram of the impeller, A equally spaced points are divided on the axial surface flow line, and A is a preset constant.

3. The method for determining blade wrap angle of a centrifugal pump based on numerical integration of fluid dynamics according to claim 1, characterized in that: After obtaining the arc length between each pair of adjacent equally divided points in S2, the arc length between the i-th equally divided point and the (i+1)-th equally divided point is denoted as Δs. i and the arc length Δs i With integral coefficient K i Combining these methods, we can obtain Δs. i The corresponding Δ θ i , where Δ θ i Let Δs be the arc length. i The corresponding central angle; for the radius between each pair of adjacent equally spaced points, the radius between the i-th equally spaced point and the (i+1)-th equally spaced point is denoted as C. i The fluid velocity from the blade inlet to the blade outlet is then calculated using relevant formulas. v m And draw v m Curves that vary along the axial streamline Where f() represents the fluid velocity from the blade inlet to the blade outlet. v m With Δs i The relationship function involves the following calculation formulas: wherein, is the arc length between the ith and (i+1)th point; ri is the inlet radius, which is the radius of the circular profile at the impeller inlet; Q is the design flow rate, wherein the design flow rate Q is predetermined according to a theoretical model.

4. The method for determining blade wrap angle of a centrifugal pump based on numerical integration of fluid dynamics according to claim 1, characterized in that: The S3 is according to the improved import circulation formula and the improved Euler formula, and the streamline import tangential velocity moment v u1 r 1 and the related formula of the streamline export tangential velocity moment v u2 r 2 is obtained as follows: wherein is the blade inlet setting angle, is the magnitude of the angle of attack and = 0.8 (N S / 100) 0.6 wherein is the specific speed of the impeller; is the impeller inlet width; Q is the design flow rate; g is the gravitational acceleration taken as 9.81 ; v u2 is the outlet tangential velocity; r 2 is the outlet radius, which is the radius of the circular profile at the outlet of the impeller; v u1 is the inlet tangential velocity; r 1 is the inlet radius, which is the radius of the circular profile at the inlet of the impeller; ω is the angular velocity of the impeller; H th is the theoretical head of the impeller; after obtaining the stream inlet tangential velocity moment v u1 r1 and the stream outlet tangential velocity moment v u2 r2, the curve of the tangential velocity moment v u r is drawn from the inlet to the outlet along the axial surface stream; ; the related formulae for drawing are as follows: where, tangential velocity moment v u r The change of the meridian streamline from the inlet to the outlet is linear change; v u2 is the outlet tangential velocity; r 2 is the outlet radius; v u1 is the inlet tangential velocity; r 1 is the inlet radius; ω is the impeller angular velocity; H th is the impeller theoretical head; is the arc length between the ith and (i+1)th division points; and L is the total arc length of the meridian streamline.

5. The method for determining blade wrap angle of a centrifugal pump based on numerical integration of fluid dynamics according to claim 1, wherein: In S4, the integral coefficient of the i-th division point is calculated as follows: Among them, C i Let be the radius between the i-th dividing point and the (i+1)-th dividing point; Let be the instantaneous value of the tangential velocity at the i-th equally divided point, and According to Curve interpolation yields each component point The corresponding value; v m Let v be the instantaneous value of the axial surface velocity at the i-th equally divided point, and v m According to Curve interpolation yields each component point The corresponding value.

6. A method for determining blade wrap angle of a centrifugal pump based on numerical integration of fluid dynamics according to claim 1, characterized in that: The related formula for calculating the blade wrap angle of the centrifugal pump for each axial surface flow line divided in the axial surface projection diagram of the impeller in S5 is: wherein, is the blade wrap angle of the centrifugal pump; denotes each of the respective cumulative sum of the is the arc length corresponding to the central angle and ; wherein, is the arc length between the i-th and the i+1-th point of division; is the integration coefficient of the i-th point of division, is the integration coefficient of the i+1-th point of division.​

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