A method for determining blade wrap angle of centrifugal pump based on numerical integration of fluid mechanics

Abstract

The present application relates to the technical field of centrifugal pump, in particular to a centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration. The centrifugal pump blade wrap angle determination method is a numerical integration method based on fluid mechanics equation. By combining differential equation and numerical integration, equidistant points are divided on the axial surface streamline in the axial surface projection diagram, and the arc length and radius between each adjacent two equidistant points are calculated. Based on one-dimensional flow theory, the axial surface fluid velocity v m is calculated m , and a curve changing along the axial surface streamline is drawn. According to Euler equation, a linear distribution model of tangential velocity moment v u r is established. After calculating the integral coefficient K, K·△s i is calculated point by point, and the integral is accumulated to directly obtain the centrifugal pump blade wrap angle value. The effectiveness of the centrifugal pump blade wrap angle value is verified by using an example verification method. The present application can realize the design of the centrifugal pump blade wrap angle through parameterization, and get rid of the condition that the centrifugal pump blade wrap angle can only be obtained by relying on experience.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of centrifugal pumps, in particular to a centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration. BACKGROUND

[0002] In the design of centrifugal pump blades, the blade wrap angle is an important geometric parameter of the blade, and the size of the wrap angle directly affects the performance of the centrifugal pump impeller. According to the existing centrifugal pump blade design theory, the square grid conformal transformation method and the twisted triangle method all need to estimate an initial wrap angle according to experience at the beginning before determining the centrifugal pump blade wrap angle, and then draw the stream line expansion line. When the shape of the stream line expansion line is not ideal, the position of the blade inlet edge, the inlet and outlet installation angle or the wrap angle should be modified, and the process is relatively cumbersome. In the square grid conformal transformation method and the twisted triangle method, the initial value of the wrap angle can only be selected according to experience, and it is not necessarily the final wrap angle value. The final wrap angle value is determined only according to the shape and smoothness of the stream line expansion line, and the size of the final wrap angle can be determined only when the stream line expansion line is drawn, and the size of the wrap angle cannot be determined according to the design requirements at the beginning. Therefore, these two traditional methods for determining the centrifugal pump blade wrap angle are too dependent on experience, and there are great deficiencies in quickly determining the centrifugal pump blade wrap angle. If a wrap angle determination method can be proposed to calculate a reasonable wrap angle value according to the design requirements of the centrifugal pump, the selection of the wrap angle according to experience can be avoided, and the influence of the change of the final wrap angle on the performance of the impeller can also be avoided.

[0003] After searching, there is no patent related to the present application, only in some literature, and the corresponding technical solution is mainly to determine the blade wrap angle according to the blade inlet and outlet installation angle, which is still based on the square grid conformal transformation method, and the final wrap angle is determined according to the shape and uniformity of the stream line expansion line. SUMMARY

[0004] The present application aims to provide a centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration to solve the problems in the background art.

[0005] In order to solve the above technical problems, the present application provides the following technical scheme: a centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration, the method comprising:

[0006] S1, equally spacing the points on the axial surface stream line in the axial surface projection drawing of the impeller, and calculating the arc length and radius between each adjacent two equally divided points;

[0007] S2, calculating the fluid velocity v m from the blade inlet to the blade outlet according to the axial surface projection drawing of the impeller and the one-dimensional flow theory m , and drawing the curve of v along the axial surface stream line.

[0008] 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 streamline import tangential velocity moment and the streamline export tangential velocity moment are combined to draw the curve of the tangential velocity moment along the axial surface streamline from the import to the export;

[0009] S4, the integral coefficient K of the i-th division point is calculated according to the blade profile differential equation i ;

[0010] S5, the blade wrap angle of the centrifugal pump is calculated by combining the arc length, the radius, the curve of the tangential velocity moment along the axial surface streamline, the curve of the tangential velocity moment along the axial surface streamline from the import to the export and the integral coefficient K m ; i obtained by steps S1-S4.

[0011] Further, the axial surface streamline in the axial surface projection drawing of the impeller in S1 is obtained according to CFD software numerical simulation; when the axial surface streamline is divided in the axial surface projection drawing of the impeller, the axial surface streamline is divided into A equally spaced division points, and the A is a preset constant.

[0012] 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.

[0013] 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 . v m The curve of the tangential velocity moment along the axial surface streamline is drawn wherein f() represents the fluid velocity from the blade inlet to the blade outlet v m with the relationship function between Δs i The calculation formula is as follows:

[0014]

[0015] wherein, is the arc length between the i-th and the i+1-th division point; r1 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 preset according to a theoretical model.

[0016] 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 realizes the design of the blade wrap angle of the centrifugal pump through parameterization, and gets 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.

[0017] Further, the S3 is obtained according to the improved inlet circulation formula and the improved Euler formula, and the related 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:

[0018]

[0019] ;

[0020] wherein, is the blade inlet setting angle, is the magnitude of the incidence angle, 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 incidence angle 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 the 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 incidence angle correction; is the impeller inlet width; Q is the design flow rate; g is the acceleration of gravity, which is 9.81; v u2 is the outlet tangential velocity; r2 represents the outlet radius, which is the radius of the circular profile at the impeller outlet; v u1 The inlet tangential velocity; r 1 represents the inlet radius; the inlet radius is the radius of the circular profile at the impeller inlet. ω H is the impeller angular velocity; th To determine the theoretical head of the impeller; the tangential velocity v at the streamline inlet is obtained. u1 r1 and streamlined exit tangential velocity v u2 After r2, draw the tangential velocity moment v according to the formula. u The curve of r changing along the axial streamline from inlet to outlet. ;draw The relevant formulas are as follows:

[0021]

[0022] Among them, tangential velocity moment v u r The change in streamlines along the axial plane from inlet to outlet is a linear change; v u2 The exit tangential velocity; r 2 represents the export radius; v u1 The inlet tangential velocity; r 1 represents the import radius; ω H is the impeller angular velocity; th For impeller theory head; L is the arc length between the i-th division point and the (i+1)-th division point; L is the total arc length of the axial streamline.

[0023] Among them, the flow channel expansion of high specific speed pumps is a key factor affecting the hydraulic performance of centrifugal pumps. In the design of high specific speed pumps, significant flow channel expansion and large angle of attack correction are key technologies that are interrelated. When the flow channel expansion of a high specific speed pump is significant, it will lead to changes in the fluid flow state. At this time, large angle of attack correction is needed to deal with this change, optimize hydraulic performance, reduce impact loss, and widen the high efficiency zone.

[0024] Furthermore, 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; The arc length Δs between the dividing points i The corresponding tangential velocity, and According to Curve interpolation yields each component point The corresponding value; v m The arc length Δs between the dividing points icorresponding fluid velocity, and v m is obtained according to The integral coefficient of the i-th point is obtained by curve interpolation corresponding value; the integral coefficient of the i-th point is obtained by the blade profile differential equation ; wherein the blade profile differential equation is derived based on kinematics and dynamics principles of fluid in the blade passage.

[0025] The blade profile differential equation reflects the variation rule of the blade profile in geometry under the consideration of the rotation of the impeller and the flow of fluid, and is helpful to design and analyze the shape of the blade to meet specific fluid dynamics performance requirements; the integral coefficient of the i-th point is obtained by the blade profile differential equation , and the process is as follows:

[0026] The blade profile differential equation is transformed as: At the i-th point of the meridional streamline, the radius C i of the point and the corresponding velocity interpolation and are substituted, and the integral coefficient is obtained, which has the physical meaning of the angular change rate of the point i.

[0027] Further, the formula for calculating the blade wrap angle of the centrifugal pump in S5 is as follows:

[0028]

[0029] wherein, is the blade wrap angle of the centrifugal pump; and θ i is the sum of each Δ θ i corresponding to different values of i, and Δ θ i is the arc length corresponding to the central angle and ; wherein, is the arc length between the i-th point and the i+1-th point; is the integral coefficient of the i-th point, is the integral coefficient of the i+1-th point.

[0030] ​The application significantly improves the accuracy and efficiency of the wrap angle design by using step-by-step calculation and parameterized modeling in the process of determining the wrap angle of the centrifugal pump blade based on the fluid mechanics differential equation and the numerical integration theory. The method takes a theoretical model as the core, directly calculates the wrap angle value according to the design parameters such as the head and the rotating speed by establishing the blade profile differential equation , combining the Euler equation and the axial plane velocity distribution, and overcomes the defects of the traditional method that relies on the initial value of experience. The discretization of the split point and the point-by-point integral formula are used to form a tabular calculation process, so that the design cycle is shortened by more than 40%, and the calculation error is controlled within 3%, which is better than the experience adjustment mode of the traditional conformal transformation method. At the same time, through the definition of the integral coefficient , the tangential momentum, centrifugal force and velocity gradient are dynamically related, and the method has good adaptability to multiple working conditions, and is especially suitable for complex operating conditions such as high specific speed and large flow.

[0031] Compared with the prior art, the application has the beneficial effects that the application provides a method for determining the wrap angle of a centrifugal pump, which can finally obtain the blade flow line wrap angle value by applying the blade profile differential equation, dividing points along the axial flow line and integrating point by point according to the design requirements of the impeller, and can avoid selecting the wrap angle value according to experience and avoiding determining the final wrap angle value only according to the shape and smoothness of the flow line development line. BRIEF DESCRIPTION OF DRAWINGS

[0032] The accompanying drawings are used to provide a further understanding of the application, and constitute a part of the specification, together with the embodiments of the application, to explain the application, and do not constitute a limitation on the application. In the drawings:

[0033] Figure 1 is a flowchart of a centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration;

[0034] Figure 2 is a schematic diagram of equidistant point division and corresponding size on the front cover plate flow line of an impeller of a centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration;

[0035] Figure 3 is an axial plane velocity distribution curve of a centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration v m along the front cover plate axial flow line from the inlet to the outlet ;

[0036] Figure 4 is a distribution curve of the value of a centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration v u r along the front cover plate axial flow line from the inlet vu1 r 1 to exit v u2 r 2 distribution curve ;

[0037] Figure 5 A centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration K value along the front cover plate axial surface streamline from the inlet v u1 r 1 to exit v u2 r 2 curve

[0038] Figure 6 A centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration θ i along the front cover plate axial surface streamline from the inlet v u1 r 1 to exit v u2 r 2 curve

[0039] Figure 7 A centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration DETAILED DESCRIPTION

[0040] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of the present application.

[0041] Please refer to Figures 1-7 , the present application will be further described in combination with the drawings and design examples; as shown in Figure 1 A centrifugal pump blade wrap angle determination method based on fluid mechanics numerical integration, the method comprises:

[0042] S1, equally spaced points are made on the axial surface streamline in the impeller axial surface projection drawing, and the arc length and radius between each adjacent two equally divided points are calculated;

[0043] S2, the fluid velocity v m is calculated from the blade inlet to the blade outlet according to the impeller axial surface projection drawing and one-dimensional flow theory mA curve of the variation of the stream line along the axial surface;

[0044] S3, according to the improved inlet circulation formula and the improved Euler formula, obtaining the stream line inlet tangential velocity moment and the stream line outlet tangential velocity moment; and combining the stream line inlet tangential velocity moment and the stream line outlet tangential velocity moment, drawing a curve of the variation of the stream line tangential velocity moment along the axial surface from the inlet to the outlet;

[0045] S4, calculating the integral coefficient K of the i-th division point according to the blade profile differential equation i ;

[0046] S5, calculating the centrifugal pump blade wrap angle by combining the arc length, the radius, the v m variation curve of the stream line along the axial surface, the tangential velocity moment variation curve of the stream line along the axial surface from the inlet to the outlet and the integral coefficient K i obtained in steps S1-S4.

[0047] Taking the parameters of a design example as the flow rate Q =400m 3 , the head H =35m, the rotating speed n =1480r / min, and the specific rotating speed N S =125.1, the centrifugal pump cover plate stream line is taken as an example for illustration;

[0048] Combining Figure 2 the axial surface projection of the impeller, 13 points are equally divided along the front cover plate axial surface stream line, and the equal interval △Xi is measured as 0.0074m, Figure 2 wherein r represents the radius of the impeller circular contour corresponding to the position point of the axial surface stream line in the axial surface projection of the impeller, and the value range of r belongs to the interval constituted by r1 and r2; according to the formula

[0049]

[0050] the fluid velocity from the inlet to the outlet is obtained v m and the curve of the variation of the stream line along the axial surface is drawn v m ; Figure 3 ;

[0051] According to the improved inlet circulation formula and the improved Euler formula,

[0052] the stream line inlet tangential velocity moment

[0053] and the stream line outlet tangential velocity moment ;

[0054] are calculated, and then​

[0055] Plotting tangential velocity moment v u r The curve of the change of the axial surface streamline from the inlet to the outlet; wherein the centrifugal pump head H = 35m, the hydraulic efficiency of the estimated centrifugal pump is 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 according to linear change, as Figure 4 ; and the outlet boundary condition is determined by the Euler equation combined with the theoretical head, including the flow boundary condition, the pressure boundary condition, the velocity boundary condition and the free outflow boundary condition, after the boundary condition is clear, the working parameters of the centrifugal pump under specific working conditions can be determined, and whether the centrifugal pump meets the actual industrial demand can be evaluated through the working parameters.

[0056] As shown in Figures 5 to 7 , the relevant data calculated after each streamline is calculated into the point-by-point calculation blade wrap angle calculation table;

[0057] Table 1: Point-by-point calculation of blade wrap angle calculation table

[0058]

[0059] And according to , the blade wrap angle of the centrifugal pump is calculated to be θ=22.43°; Through the method of example verification and comparison with traditional design, it is concluded that the error of the blade wrap angle of the centrifugal pump obtained by the present application is less than 3%, the design cycle is shortened by 40%, and the impeller efficiency is improved by 2%~5%, which reflects that the present application can eliminate the dependence on experience to obtain the blade wrap angle of the centrifugal pump by combining differential equation with numerical integration, and realize the parameterized design of the wrap angle; The defects that the wrap angle needs to be repeatedly adjusted in the traditional square grid conformal transformation method and the twisted triangle method are solved.

[0060] It is to be noted that, in the present text, relational terms such as first and second and the like can be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus.

[0061] Finally, it should be noted that the above-mentioned only constitutes preferred embodiments of the present application and is not intended to limit the present application. Although the present application has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications, equivalent replacements, improvements and the like of the technical solutions described in the foregoing embodiments can still be made. Any modifications, equivalent replacements, improvements and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for determining the wrap angle of centrifugal pump blades based on numerical integration in fluid mechanics, characterized in that, The method includes the following steps: 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; 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: in, r1 is the arc length between the i-th and (i+1)-th division points; r1 is the inlet radius, which is the radius of the circular profile at the impeller inlet; Q is the design flow rate, where the design flow rate Q is preset according to the theoretical model. 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. In step S3, the streamline inlet tangential velocity moment is obtained based on the improved inlet circulation formula and the improved Euler formula. v u1 r 1 and streamlined exit tangential velocity moment v u2 r The relevant formula for 2 is: in, The blade inlet placement angle, The size of the angle of attack and =0.8 (N S / 100) 0.6 ,in This is the specific speed of the impeller; V is the impeller inlet width; Q is the design flow rate; g is the gravitational acceleration, taken as 9.81; v u2 The exit tangential velocity; r 2 represents the outlet radius, which is the radius of the circular profile at the impeller outlet; v u1 The inlet tangential velocity; r 1 represents the inlet radius; the inlet radius is the radius of the circular profile at the impeller inlet. ω H is the impeller angular velocity; th To determine the theoretical head of the impeller; the tangential velocity v at the streamline inlet is obtained. u1 r1 and streamlined exit tangential velocity v u2 After r2, draw the tangential velocity moment v according to the formula. u The curve of r changing along the axial streamline from inlet to outlet. ;draw The relevant formulas are as follows: Among them, tangential velocity moment v u r The change in streamlines along the axial plane from inlet to outlet is a linear change; v u2 The exit tangential velocity; r 2 represents the export radius; v u1 The inlet tangential velocity; r 1 represents the import radius; ω H is the impeller angular velocity; th For impeller theory head; Let L be the arc length between the i-th division point and the (i+1)-th division point; L is the total arc length of the axial streamlines. 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.

2. The method for determining the wrap angle of a centrifugal pump blade based on numerical integration in fluid dynamics according to claim 1, characterized in that: The axial streamlines in the impeller axial projection diagram in S1 are obtained by numerical simulation using CFD software. When dividing the axial streamlines into points in the impeller axial projection diagram, the axial streamlines are divided into A equally spaced points, where A is a preset constant.

3. The method for determining the wrap angle of a centrifugal pump blade based on numerical integration in fluid dynamics according to claim 1, characterized in that: 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.

4. The method for determining the wrap angle of a centrifugal pump blade based on numerical integration in fluid dynamics according to claim 1, characterized in that: The relevant formula for calculating the centrifugal pump blade wrap angle for each streamline on the impeller axial projection diagram in S5 is as follows: in, This is the required centrifugal pump blade wrap angle; This represents the different values ​​of i. The sum of all, arc length The corresponding central angle and ;in, Let be the arc length between the i-th dividing point and the (i+1)-th dividing point; middle Let be the integral coefficient at the i-th division point. It is the integral coefficient of the (i+1)th division point.

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