Vur curve determination method for centrifugal pump point-by-point integration method

Abstract

The invention discloses a curve determination method for a centrifugal pump point-by-point integration method, and belongs to the technical field of centrifugal pumps. The curve determination method of the centrifugal pump point-by-point integration method is a parameterized modeling method based on an Euler equation and momentum conservation, the inlet and outlet boundaries of a vur curve are calculated according to design requirements, after a smooth transition curve is constructed in combination with runner geometry and attack angle constraint, the curve is constructed through nonlinear interpolation according to the dynamic correlation streamline arc length, and the curve is determined. The relation between the streamline arc length and the curve is established; according to the method, when the centrifugal pump blade molded line is designed, the curve can be quickly obtained through a parameterization method according to the given design condition and the streamline arc length s.

Description

Technical Field

[0001] This invention relates to the field of centrifugal pump technology, specifically to a method for point-by-point integration in centrifugal pumps. Curve determination method. Background Technology

[0002] In centrifugal pump blade design theory, commonly used blade drawing methods include the grid conformal transformation method, the twisted triangle method, and the point-by-point integration method. Among these, the point-by-point integration method utilizes the differential equation of the blade profile, applying it to a given axial velocity v. m and velocity circulation v u By observing the variation of r along the streamline, the axial angle Δθ corresponding to the radius r along the streamline is calculated point by point. Then, the plane projection of the streamline is plotted, yielding its profile. Since v m and v u Different variations of r along the streamline will result in blades with different performance characteristics; therefore, v can be obtained using the point-by-point integration method. m and v u The variation of r along the streamline is the most important. Currently, v m The changing pattern of v can be obtained through one-dimensional flow theory, while v u The variation of r along the streamline cannot be obtained quickly and relies on empirical assumptions, which are easily decoupled from design parameters. Therefore, if a method for plotting v could be proposed... u By understanding the variation of r along the streamline, we can apply the point-by-point integration method to adjust v. u By controlling the shape of the blades according to the streamline variation law, centrifugal pump impellers that meet different performance requirements can be designed. Summary of the Invention

[0003] The purpose of this invention is to provide a point-by-point integration method for centrifugal pumps. A curve determination method is proposed to address the problems mentioned in the background section.

[0004] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a point-by-point integration method for centrifugal pumps. Curve determination method, the method comprising: S1. Construct a dual Y-axis coordinate diagram with the axial streamline arc length as the X-axis, the inlet tangential velocity moment as the left Y-axis, and the outlet tangential velocity moment as the right Y-axis; S2. Determine the coordinate point B (0, v) on the right Y-axis of the dual Y-axis coordinate graph based on the parameters provided by the improved Euler formula and design requirements. u2 r2), and the coordinate point A (0, v) on the left Y-axis of the dual Y-axis coordinate diagram determined according to the flow regime at the blade inlet. u1 r1); S3, after determining the coordinates of point A of the left Y-axis and point B of the right Y-axis in the double-Y-axis coordinate diagram, a ray is drawn through point A, denoted as ray a, and the included angle between ray a and the X-axis is denoted as the impact angle value Δβ; a ray is drawn through point B, denoted as ray b, and ray b is parallel to the X-axis; S4, boundary conditions of the transition curve of the axial surface streamline arc length and the tangential velocity moment are constructed according to the double-Y-axis coordinate diagram through the coordinates of points A and B and the rays a and b; the axial surface streamlines in the axial surface projection diagram of the impeller are equally spaced to obtain the axial surface streamline arc length, the axial surface streamline arc length s is dynamically associated through an interpolation polynomial, and the transition curve of the axial surface streamline arc length and the tangential velocity moment is drawn in combination with the boundary conditions and the preset smooth transition constraint conditions between streamlines. S5, after the axial surface streamlines in the axial surface projection diagram of the impeller are equally spaced to obtain the axial surface streamline arc length s, the axial surface streamline arc length s is combined with the transition curve of the axial surface streamline arc length and the tangential velocity moment, and the transition curve is drawn. If the transition curve satisfies the boundary conditions, the transition function corresponding to the current streamline arc length s is determined. If the transition curve does not satisfy the boundary conditions, the axial surface streamline arc length s obtained by equally spacing the axial surface streamlines in the axial surface projection diagram of the impeller is adjusted, so that the transition curve satisfies the boundary conditions, and the transition curve at this time is the transition function. The v u r curve of each streamline is obtained according to the method described in S1-S5, and the smooth transition between streamlines is ensured through the constraint conditions.

[0005] Further, the axial surface streamline arc length in S1 is s; wherein the axial surface streamline arc length is the arc length between two adjacent equally spaced points after equally spacing the axial surface streamlines in the axial surface projection diagram of the impeller, and the value range of the axial surface streamline arc length s is 0≤s≤L; wherein L is the total streamline arc length calculated by the axial surface projection geometry.

[0006] Further, the blade inlet flow state includes a pre-rotation state and a non-pre-rotation state, when the blade inlet flow state is the pre-rotation state, the coordinates of point A are determined as (0, 0); when the blade inlet flow state is the non-pre-rotation state, the coordinates of point A (0, v u1 r1) on the left Y-axis are determined according to the improved Euler formula and the parameters provided according to the design requirements.

[0007] Further, the improved Euler formula for obtaining point B (0, v u2 r2) in S2 is ; when the blade inlet flow state is the pre-rotation state, the coordinates of point A (0, v u1 ​​​​​​The improved Euler formula for r1) is ;in The blade inlet placement angle, This is the angle of attack value; V is the impeller inlet width; Q is the design flow rate; g is the gravitational acceleration, taken as 9.81; v u2 r1 is the outlet tangential velocity; r2 is the outlet radius, which is the radius of the circular profile at the impeller outlet; v u1 r1 is the inlet tangential velocity; r1 is the inlet radius, which is the radius of the circular profile at the impeller inlet; ω is the impeller angular velocity; H th To provide impeller theory for head.

[0008] In centrifugal pumps, the coupling effect of flow channel expansion and angle of attack on mass distribution is a key factor affecting pump performance. Flow channel expansion leads to decreased fluid velocity and increased pressure, potentially causing boundary layer separation in low-velocity regions, resulting in reduced circulation. Consequently, the head decreases with decreasing circulation, significantly impacting centrifugal pump performance. This invention addresses this issue... The angle of attack correction term The coupling effect of flow channel expansion (r2 / r1) and angle of attack on circulation distribution was quantified to ensure that the outlet head matches the actual flow and improve pump efficiency.

[0009] Furthermore, in S3, the angle of attack value Δβ is divided into three types based on the different angles between ray a and the X-axis, and each type corresponds to one of the three types of ray a. Based on the angle between ray a and the X-axis, the angle of attack value Δβ is divided into three types: positive angle of attack, negative angle of attack, and 0 angle of attack. When the angle between ray a and the X-axis is a positive angle of attack, ray a travels from point A to the upper right, and is denoted as positive angle of attack ray a. When the angle between ray a and the X-axis is a negative angle of attack, ray a travels from point A to the lower right, and is denoted as negative angle of attack ray a. When the angle between ray a and the X-axis is 0 angle of attack, ray a is parallel to the X-axis, and is denoted as 0 angle of attack ray a. The magnitude of the angle of attack value Δβ is determined by design requirements. There is only one type of ray b.

[0010] In the embodiments of the present invention, Δβ=0 is designed; when the angle of attack is 0, boundary layer separation and impact eddies at the inlet can be avoided, which can minimize the flow loss of the centrifugal pump, achieve the design peak efficiency and stable head; high efficiency, low loss and stable operation are achieved through precise matching of flow and geometry.

[0011] Furthermore, in the process of dynamically associating the streamline arc length s through interpolation polynomials in S4, if the transition curve between the axial streamline arc length and the tangential velocity moment satisfies the boundary conditions, then the transition curve between the axial streamline arc length and the tangential velocity moment corresponding to this streamline arc length s is the desired result. If the transition curve between the axial streamline arc length and the tangential velocity moment does not satisfy the boundary conditions, then adjust the axial streamline in the impeller axial projection diagram by dividing it into equally spaced points to obtain the axial streamline arc length s, until the transition curve between the axial streamline arc length and the tangential velocity moment satisfies the boundary conditions. The transition curve between the axial streamline arc length and the tangential velocity moment that satisfies the boundary conditions is then taken as the desired curve. curve.

[0012] The transition curve between the axial streamline arc length and tangential velocity moment in the dual Y-axis coordinate diagram is constructed based on the flow channel geometry and angle-of-attack constraints, and dynamically correlated with the streamline arc length and boundary conditions using an interpolation polynomial. The relevant formula for dynamically correlated with the streamline arc length using the interpolation polynomial is as follows: The relevant formulas for boundary conditions are: in, L is the total streamline arc length calculated from axial projection geometry. The streamline arc length at the exit point; The length of the streamlined arc at the inlet; Constructed transition function for: Among them, v u2 r2 is the exit tangential velocity; r2 is the exit radius; v u1 r1 is the inlet tangential velocity; r1 is the inlet radius; ω is the impeller angular velocity; H th s is the theoretical head of the impeller; s is the arc length between two adjacent equally spaced points after dividing the streamlines on the impeller axial projection diagram at equal intervals; L is the total arc length of the streamlines obtained from the geometric calculation of the axial projection; Δβ is the angle of attack value; it can be seen from the formula that when When it is 0, the transition function v u The function curve of r(s) is a standard S-curve.

[0013] This invention is in The first term represents the tangential velocity moment at the inlet, which is determined by the inlet flow state, including the presence of pre-swirl and guide vane influence; the second term describes the linear transition of the velocity moment from the inlet to the outlet, with the core being a cubic interpolation polynomial; the third term, the angle of attack correction term, reflects the influence of the angle of attack Δβ on the inlet flow direction, quantifying the asymmetric flow effect.

[0014] In this invention, since the data changes in the transition curve constructed in the dual Y-axis coordinate graph exhibit a non-linear pattern, linear interpolation would fail to capture the transition curve, resulting in data loss. Therefore, this invention utilizes non-linear interpolation to fit the data with a curve, which can more accurately capture the complex trends of the data, reduce the errors caused by linear approximation, and meet the requirements of high-precision engineering.

[0015] Furthermore, the function boundary conditions in S5 are as follows: The curve passes through point A and is tangent to ray a at point A. The curve smoothly transitions from point A to point B and At point B, the curve is tangent to ray b; the constraint condition ensuring a smooth transition between streamlines is... .

[0016] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: The present invention proposes a parametric modeling method based on Euler's equations and momentum conservation, which can calculate v according to the design requirements of centrifugal pump impeller head, efficiency, speed, inlet velocity circulation, inlet angle of attack, head, speed, and inlet conditions. u The inlet and outlet boundaries of the r-curve are used to construct a smooth transition curve by combining the flow channel geometry and angle of attack constraints. Nonlinear interpolation is achieved by dynamically associating the streamline arc length through the smooth transition curve to determine v. u r varies along the streamline curve; this invention can relatively easily determine v. u r varies along the streamline curve, and according to the determined v u The centrifugal pump blade profile designed along the streamline curve is smooth and the centrifugal pump blade wrap angle value is reasonable. Attached Figure Description

[0017] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 It is a point-by-point integration method used for centrifugal pumps. Flowchart of the curve determination method; Figure 2 It is a point-by-point integration method used for centrifugal pumps. v of the curve determination method u A schematic diagram illustrating the method for drawing the variation law of streamlines along the axial plane; Figure 3 It is a point-by-point integration method used for centrifugal pumps. An example of the curve determination method: a blade axial view; Figure 4 It is a point-by-point integration method used for centrifugal pumps. Example v of curve determination methodu The variation law of r along the axial streamline; Figure 5 It is a point-by-point integration method used for centrifugal pumps. The blade front cover plate profile plan view obtained from an embodiment of the curve determination method. 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 1-5 The present invention will be further described in conjunction with the accompanying drawings and design examples; like Figure 1 As shown, a point-by-point integration method for centrifugal pumps Curve determination method, the method comprising the following steps: S1. Construct a dual Y-axis coordinate diagram with the axial streamline arc length as the X-axis, the inlet tangential velocity moment as the left Y-axis, and the outlet tangential velocity moment as the right Y-axis; The axial streamline arc length in S1 is s; where the axial streamline arc length is the arc length between two adjacent equally spaced points after dividing the axial streamline into equally spaced points in the impeller axial projection diagram, and the range of the axial streamline arc length s is 0≤s≤L; where L is the total streamline arc length obtained by geometric calculation of the axial projection.

[0020] The flow regime at the blade inlet includes a pre-swirling state and a non-pre-swirling state. When the flow regime at the blade inlet is in the pre-swirling state, the coordinates of point A are determined to be (0, 0). When the flow regime at the blade inlet is in the non-pre-swirling state, the coordinates of point A on the left Y-axis are determined to be (0, 0) based on the improved Euler formula and the parameters provided by the design requirements. u1 The coordinates of point r1).

[0021] S2. Determine the coordinate point B (0, v) on the right Y-axis of the dual Y-axis coordinate graph based on the parameters provided by the improved Euler formula and design requirements. u2 r2), and the coordinate point A (0, v) on the left Y-axis of the dual Y-axis coordinate diagram determined according to the flow regime at the blade inlet. u1 r1); In S2, point B(0, v) is obtained. u2 The improved Euler formula for r2) is When the flow regime at the blade inlet is pre-swirling, point A(0, v) is obtained. u1 The improved Euler formula for r1) is ;in is the blade inlet angle of attack, is the value of the angle of attack; is the blade 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; r2 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; r1 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.

[0022] S3, after determining the coordinates of point A of the left Y-axis and point B of the right Y-axis in the double-Y-axis coordinate graph, a ray is drawn through point A, denoted as ray a, and the angle between ray a and the X-axis is denoted as the angle of attack value Δβ; a ray is drawn through point B, denoted as ray b, and ray b is parallel to the X-axis; in S3, the angle of attack value Δβ is divided into three types according to the size of the angle between ray a and the X-axis, and the three types correspond to three types of rays a respectively; the angle of attack value Δβ is divided into three types of positive angle of attack, negative angle of attack and 0 angle of attack according to the size of the angle between ray a and the X-axis; when the angle between ray a and the X-axis is a positive angle of attack, ray a is directed to the upper right from point A, and ray a is denoted as a positive angle of attack ray a; when the angle between ray a and the X-axis is a negative angle of attack, ray a is directed to the lower right from point A, and ray a is denoted as a negative angle of attack ray a; when the angle between ray a and the X-axis is a 0 angle of attack, ray a is parallel to the X-axis, and ray a is denoted as a 0 angle of attack ray a; wherein the size of the angle of attack value Δβ is determined by design requirements; the ray b is only one type.

[0023] S4, boundary conditions of the transition curve of the axial surface streamline arc length and the tangential velocity moment are constructed according to the coordinate points A and B, and the rays a and b in the double-Y-axis coordinate graph; the axial surface streamlines in the axial surface projection graph of the impeller are equally spaced to obtain the axial surface streamline arc length, the axial surface streamline arc length s is dynamically associated through an interpolation polynomial, and the transition curve of the axial surface streamline arc length and the tangential velocity moment is drawn by combining the boundary conditions and the preset smooth transition constraint conditions between streamlines. in S4, in the process of dynamically associating the axial surface streamline arc length s through the interpolation polynomial, if the transition curve of the axial surface streamline arc length and the tangential velocity moment satisfies the boundary conditions, then the transition curve of the axial surface streamline arc length and the tangential velocity moment corresponding to the current axial surface streamline arc length s is determined as the sought curve; if the transition curve of the axial surface streamline arc length and the tangential velocity moment does not satisfy the boundary conditions, then the axial surface streamline arc length s obtained by equally spacing the axial surface streamlines in the axial surface projection graph of the impeller is adjusted until the transition curve of the axial surface streamline arc length and the tangential velocity moment satisfies the boundary conditions, and the transition curve of the axial surface streamline arc length and the tangential velocity moment when satisfying the boundary conditions is taken as the sought curve. ​

[0024] Wherein, the transition curve of the meridian streamline arc length and the tangential velocity moment is constructed in the double Y-axis coordinate graph, and is constructed according to the flow passage geometry and the angle of attack constraint, and the streamline arc length and the boundary condition are dynamically associated through the interpolation polynomial; wherein, the related formula of the interpolation polynomial dynamically associated with the streamline arc length is: The related formula of the boundary condition is: Wherein, L is the total streamline arc length calculated by the meridian projection geometry; Lout is the meridian streamline arc length at the outlet; Lin is the meridian streamline arc length at the inlet; The transition function v r(s) constructed is: Wherein, v u2 out is the outlet tangential velocity; r2 is the outlet radius; v u1 in is the inlet tangential velocity; r1 is the inlet radius; ω is the impeller angular velocity; H th is the theoretical head of the impeller; s is the arc length between adjacent two equally spaced points after equally spacing the meridian streamline in the impeller meridian projection graph; L is the total streamline arc length calculated by the meridian projection geometry; Δβ is the angle of attack value; according to the formula, when v u r(s) is the standard S curve.

[0025] S5, after obtaining the meridian streamline arc length s by equally spacing the meridian streamline in the impeller meridian projection graph, combining the meridian streamline arc length s with the transition curve of the meridian streamline arc length and the tangential velocity moment, and drawing the v curve; if the v curve satisfies the boundary condition, the transition function v corresponding to the meridian streamline arc length s is determined as the solution. curve; if the v curve does not satisfy the boundary condition, the meridian streamline arc length s obtained by equally spacing the meridian streamline in the impeller meridian projection graph is adjusted, so that the v curve satisfies the boundary condition, and the v curve at this time is the solution. curve; the v uThe r-curves are all obtained according to the methods described in S1-S5, and the smooth transition between streamlines is ensured by constraint conditions.

[0026] The function boundary conditions in S5 are as follows: The curve passes through point A and is tangent to ray a at point A. The curve smoothly transitions from point A to point B and At point B, the curve is tangent to ray b; the constraint condition ensuring a smooth transition between streamlines is... .

[0027] The parameters for the design example are flow rate Q = 400m³. 3 / h, head H=35m, speed n=1480r / min, specific speed n s Taking a centrifugal pump cover plate of 125.1 as an example for explanation; Figure 2 The drawing shown is v u The transition curve representing the variation of r along the axial streamline, where... Figure 1 The figures show v when the inlet is at a positive angle of attack. u The transition curve of r and v when the inlet is a negative angle of attack u The transition curve of r; such as Figure 3 The image shown is a axial projection of the blade in a design example. Only the profile of the front cover plate of the blade is drawn, and the axial streamline arc length is divided into 13 equal points at equal intervals. Figure 3 To implement this embodiment, the v obtained by the present invention u The variation law of the streamline along the front cover plate along the axis, where the arc length of the front cover plate streamline is s = 0.0888m, the inlet angle of attack Δβ = 0, and the inlet velocity circulation is v. u1 r1=0, exit velocity circulation v u2 r2=2.46. Figure 5 For the purposes of this embodiment Figure 4 The v shown u The final blade front cover profile obtained from the r variation curve is 148.1° (blade inlet placement angle), 0.176 (radial coordinate of the starting point of the front cover profile), and 0.1024 (axial coordinate of the starting point of the front cover profile). Its profile is smooth and the wrap angle is reasonable.

[0028] 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.

[0029] Finally, it should be noted that the above-mentioned only constitutes the 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 point-by-point integration method for centrifugal pumps The curve determination method is characterized by, The method includes the following steps: S1. Construct a dual Y-axis coordinate diagram with the axial streamline arc length as the X-axis, the inlet tangential velocity moment as the left Y-axis, and the outlet tangential velocity moment as the right Y-axis; S2. Determine the coordinate point B (0, v) on the right Y-axis of the dual Y-axis coordinate graph based on the parameters provided by the improved Euler formula and design requirements. u2 r2), and the coordinate point A (0, v) on the left Y-axis of the dual Y-axis coordinate diagram determined according to the flow regime at the blade inlet. u1 r1); S3. After determining the coordinates of point A on the left Y-axis and point B on the right Y-axis in the dual Y-axis coordinate graph, draw a ray through point A and denote it as ray a. Denote the angle between ray a and the X-axis as the angle of attack Δβ. Draw a ray through point B and denote it as ray b. Ray b is parallel to the X-axis. S4. Based on coordinate points A and B, and rays a and b in the dual Y-axis coordinate diagram, construct the boundary conditions for the transition curve between the axial streamline arc length and tangential velocity moment. Divide the axial streamlines in the impeller axial projection diagram into equally spaced points to obtain the axial streamline arc length. Dynamically correlate the streamline arc length s using interpolation polynomials, and combine the boundary conditions of the transition curve between the axial streamline arc length and tangential velocity moment with the preset smooth transition constraints between streamlines to draw the curve. curve; S5. Obtain the v of each streamline through steps S1-S4. u r-curve.

2. The point-by-point integration method for centrifugal pumps according to claim 1 The curve determination method is characterized by: The axial streamline arc length in S1 is s; the axial streamline arc length is the arc length between two adjacent equally spaced points after dividing the axial streamline into equally spaced points in the impeller axial projection diagram, and the range of the axial streamline arc length s is 0≤s≤L; where L is the total streamline arc length obtained by geometric calculation of the axial projection.

3. The point-by-point integration method for centrifugal pumps according to claim 1 The curve determination method is characterized by: The flow regime at the blade inlet includes a pre-swirling state and a non-pre-swirling state. When the flow regime at the blade inlet is in the pre-swirling state, the coordinates of point A are determined to be (0, 0). When the flow regime at the blade inlet is in the non-pre-swirling state, the coordinates of point A on the left Y-axis are determined to be (0, 0) based on the improved Euler formula and the parameters provided by the design requirements. u1 The coordinates of point r1).

4. The point-by-point integration method for centrifugal pumps according to claim 1 The curve determination method is characterized by: In S2, point B(0, v) is obtained. u2 The improved Euler formula for r2) is When the flow regime at the blade inlet is pre-swirling, point A(0, v) is obtained. u1 The improved Euler formula for r1) is ;in The blade inlet placement angle, This is the angle of attack value; V is the impeller inlet width; Q is the design flow rate; g is the gravitational acceleration, taken as 9.81; v u2 r1 is the outlet tangential velocity; r2 is the outlet radius, which is the radius of the circular profile at the impeller outlet; v u1 r1 is the inlet tangential velocity; r1 is the inlet radius, which is the radius of the circular profile at the impeller inlet; ω is the impeller angular velocity; H th To provide impeller theory for head.

5. The point-by-point integration method for centrifugal pumps according to claim 1. The curve determination method is characterized by: In S3, the angle of attack value Δβ is divided into three types based on the angle between ray a and the X-axis, and each type corresponds to one of three types of ray a. The angle of attack value Δβ is further divided into positive angle of attack, negative angle of attack, and 0 angle of attack based on the angle between ray a and the X-axis. When the angle between ray a and the X-axis is a positive angle of attack, ray a travels from point A to the upper right, and is denoted as positive angle of attack ray a. When the angle between ray a and the X-axis is a negative angle of attack, ray a travels from point A to the lower right, and is denoted as negative angle of attack ray a. When the angle between ray a and the X-axis is 0 angle of attack, ray a is parallel to the X-axis, and is denoted as 0 angle of attack ray a. The magnitude of the angle of attack value Δβ is determined by design requirements. There is only one type of ray b.

6. The point-by-point integration method for centrifugal pumps according to claim 1 The curve determination method is characterized by: In S4, the boundary condition for the function is that the transition curve between the axial streamline arc length and the tangential velocity moment passes through point A, and at point A, the function curve is tangent to ray a. The curve smoothly transitions from point A to point B and At point B, the curve is tangent to ray b.

7. The point-by-point integration method for centrifugal pumps according to claim 1 The curve determination method is characterized by: The preset smooth transition constraint condition between streamlines in S4 is as follows: .

8. The point-by-point integration method for centrifugal pumps according to claim 1 The curve determination method is characterized by: In the process of dynamically associating the streamline arc length s using interpolation polynomials in S4, if the transition curve between the axial streamline arc length and the tangential velocity moment satisfies the boundary conditions, then the transition curve between the axial streamline arc length and the tangential velocity moment corresponding to this streamline arc length s is the desired result. If the transition curve between the axial streamline arc length and the tangential velocity moment does not satisfy the boundary conditions, then adjust the axial streamline in the impeller axial projection diagram by dividing it into equally spaced points to obtain the axial streamline arc length s, until the transition curve between the axial streamline arc length and the tangential velocity moment satisfies the boundary conditions. The transition curve between the axial streamline arc length and the tangential velocity moment that satisfies the boundary conditions is then taken as the desired curve. curve.

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