Design method for mixed-flow pump impeller coupling geometric parameters and hydrodynamic parameters

Abstract

The invention discloses a geometric parameter and hydrodynamic parameter coupled mixed-flow pump impeller design method, which comprises the following steps of: performing preliminary hydraulic calculation on an impeller shaft surface projection drawing to obtain the shaft surface projection drawing; the hub ratio of the axial plane projection drawing is kept unchanged, and axial plane projection geometric parameters are modified by adjusting the horizontal distance between the front edge and the tail edge of the hub and the inlet of the impeller and the horizontal distance between the front edge and the tail edge of the rim and the inlet of the impeller; determining circulation value distribution at the inlet and the outlet of the impeller and calculating a circulation value at the outlet of the impeller if no prerotation exists at the inlet; a parabola-straight line-parabola three-section curve is adopted to control and adjust load distribution parameters at a hub and a rim, so that adjustment of hydrodynamic parameters on axial plane projection is realized; the initial shape of the blade is determined according to given airfoil parameters and fluid attributes, and the final shape of the blade is determined through iterative calculation of a flow field and the shape of the blade. The problem that the optimization upper limit of the mixed-flow pump is reduced due to a single optimization parameter can be avoided.

Description

Technical Field

[0001] This invention relates to the field of turbomachinery technology, and in particular to a method for designing a mixed-flow pump impeller that couples geometric parameters with hydrodynamic parameters. Background Technology

[0002] Mixed-flow pumps, due to their large flow rate and moderate head, are widely used in industrial production, agricultural irrigation, and daily life. Their structure falls between that of centrifugal and axial-flow pumps, featuring a wide flow channel and a relatively curved meridional plane. During actual operation, the fluid inside the mixed-flow pump is simultaneously subjected to axial thrust and radial force from the blades, resulting in a highly complex flow pattern that significantly impacts its operating efficiency and stability. Therefore, design optimization is necessary to improve the overall performance of mixed-flow pumps. With the development of computer technology and computational fluid dynamics, inverse problem design has become a commonly used method in the field of turbomachinery design optimization. Compared to traditional design methods, it offers advantages such as fewer design parameters, a closer connection between parameters and hydraulic performance, and a greater likelihood of obtaining innovative solutions. However, in current mainstream inverse problem design methods, designers often only consider the impact of hydrodynamic parameters on the optimization results of mixed-flow pumps, neglecting the influence of geometric parameters such as axial projection. This leads to insufficient optimization of the mixed-flow pump design, resulting in a decrease in pump performance. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a mixed-flow pump impeller design method that couples geometric parameters and hydrodynamic parameters. Based on the traditional inverse problem design method, it simultaneously performs parametric coupling adjustment on the geometric position control parameters of the leading and trailing edges on the axial projection diagram, as well as the hydrodynamic control parameters at the hub and rim. This can effectively solve the problem of insufficient optimization and performance degradation caused by using a single design parameter in mixed-flow pump design.

[0004] Technical solution: A method for designing a mixed-flow pump impeller that couples geometric parameters and hydrodynamic parameters, comprising the following steps:

[0005] S1. Based on the flow rate, head and speed, the impeller shaft projection diagram is preliminarily calculated using the basic design specifications for mixed flow pumps to obtain the impeller shaft projection diagram.

[0006] S2, keeping the hub ratio of the impeller axial projection unchanged, modify the geometric parameters of the impeller axial projection by adjusting the horizontal distances from the leading and trailing edges of the hub to the impeller inlet, and the horizontal distances from the leading and trailing edges of the rim to the impeller inlet;

[0007] S3. On the impeller axial projection diagram, assuming there is no pre-swirl at the inlet, determine the circulation distribution at the impeller inlet and outlet, and calculate the circulation value at the impeller outlet according to the Euler equation for ideal fluid.

[0008] S4, based on the circulation distribution at the impeller inlet and outlet, uses a three-segment curve consisting of a parabola, a straight line, and a parabola to control and adjust the load distribution parameters at the hub and the rim respectively, thereby achieving the adjustment of the hydrodynamic parameters on the impeller axial projection.

[0009] S5. Based on the load distribution at the hub and rim determined in step S4, linear interpolation is used to determine the load distribution at the remaining locations of the blade. Then, based on the given airfoil parameters and fluid properties, the initial shape of the blade is determined. Finally, the final shape of the blade is determined through iterative calculation of the flow field and the blade shape.

[0010] Furthermore, in step S2, only the positions of the leading and trailing edges of the blades are modified, and the horizontal distances of the leading and trailing edges from the impeller inlet are used as design parameters. Specifically, the horizontal distance H from the hub leading edge to the impeller inlet... L The range is [0.06, 0.068] m, and the horizontal distance H from the hub trailing edge to the impeller inlet is... T The range is [0.13, 0.14] m, and the horizontal distance S from the leading edge of the impeller rim to the impeller inlet is... L The range is [0.017, 0.02] m, and the horizontal distance S from the trailing edge of the impeller rim to the impeller inlet is... T The range is [0.07, 0.075]m.

[0011] Furthermore, the circulation value at the impeller outlet is calculated based on the following Euler equations for ideal fluid rotating machinery:

[0012]

[0013] In the formula, Γ2 represents the circulation distribution at the impeller outlet, in meters. 2 / Second;

[0014] U2 is the circumferential velocity at the impeller outlet, in meters per second;

[0015] V2 is the tangential component of the absolute velocity at the impeller outlet, in meters per second;

[0016] ω is the angular velocity of the impeller, expressed in radians per second;

[0017] g is the acceleration due to gravity, measured in meters per second. 2 ;

[0018] H T The impeller's theoretical head is expressed in meters.

[0019] Furthermore, in the three-segment curve composed of a parabola, a straight line, and another parabola, the first parabola segment is a third-order parabola, as shown in the following formula:

[0020]

[0021] In the formula, Γ p1 The first segment of the parabolic circulation distribution is shown in meters. 2 / Second;

[0022] a1, b1, c1, and d1 represent the undetermined coefficients of the first segment of the parabola;

[0023] m1 is the normalized position of the streamline of the first parabolic axial plane;

[0024] The formula for the middle straight line is as follows:

[0025]

[0026] In the formula, Γ z1 The distribution is a linear circulation in the middle, with units of meters. 2 / Second;

[0027] a2 and b2 represent the undetermined coefficients of the intermediate straight line;

[0028] m2 is the normalized position of the middle straight line;

[0029] The second parabola is also a third-order parabola, and its formula is as follows:

[0030]

[0031] In the formula, Γ p2 The second segment shows the circulation distribution of the parabola, in meters. 2 / Second;

[0032] a3, b3, c3, and d3 represent the undetermined coefficients of the second parabola segment;

[0033] m3 is the normalized position of the streamline on the axial surface of the second parabola.

[0034] Furthermore, based on the determined load distribution at the hub and rim, the calculation formula for the load distribution at the remaining locations of the blade is as follows:

[0035]

[0036] In the formula, The value of the load at the required radius is given in meters. 2 / Second;

[0037] r is the radius to be calculated, in meters;

[0038] R h The radius at the hub of the required axis plane is given in meters.

[0039] R s The radius at the rim of the required axis plane is given in meters.

[0040] The value of the load at the rim of the shaft plane is given, in meters. 2 / Second;

[0041] The value of the circulation at the hub of the required axle plane is given in meters. 2 / Second;

[0042] m is the normalized position of the axial streamline.

[0043] Compared with the prior art, the significant advantages of this invention are as follows:

[0044] 1. This invention adopts zero circulation at the inlet, which satisfies the assumption of no pre-swirl in impeller design. The circulation at the outlet is determined according to the theoretical head required by the impeller, which can effectively solve the problem of excessive or insufficient head in impeller design.

[0045] 2. In the impeller design, this invention simultaneously considers the influence of the geometric parameters controlling the shape of the axial projection and the hydrodynamic parameters controlling the shape of the blades on the optimization results of the mixed-flow pump, effectively avoiding the problem of reduced optimization upper limit of the mixed-flow pump caused by a single optimization parameter.

[0046] 3. In this invention, the shape of the axial projection is controlled by the horizontal distance between the leading and trailing edges of the blades and the impeller inlet, while the load at the hub and rim is controlled by a three-segment curve. Therefore, the control and modification of all parameters are relatively simple and intuitive, making it easy for designers to carry out the design. Attached Figure Description

[0047] Figure 1 This is a flowchart of the present invention;

[0048] Figure 2 This is a projection view of the axial plane of a mixed-flow pump.

[0049] Figure 3 A schematic diagram comparing the shapes of the axial projections of the original model and the new model;

[0050] Figure 4 This is a schematic diagram of the circulation distribution at the inlet and outlet of a mixed-flow pump impeller.

[0051] Figure 5 This is a schematic diagram of the load distribution at the impeller hub and rim of a mixed-flow pump.

[0052] Figure 6 A comparison diagram of the blade shapes of the original model and the new model;

[0053] Figure 7 A comparison chart of efficiency and head between the original model and the new model;

[0054] Figure 8 A comparison diagram of the static pressure and limiting velocity vector distribution on the blade surface between the original model and the new model;

[0055] In the diagram: 1. Impeller rotation shaft; 2. Impeller inlet rim position; 3. Blade rotation shaft; 4. Blade inlet; 5. Blade outlet; 6. Hub; 7. Rim; 8. Leading edge of the original model; 9. Trailing edge of the original model; 10. H L ;11.H T ;12.S L ;13.S T 14. Leading edge of the new model; 15. Trailing edge of the new model; A. Original model blade shape; B. New model blade shape; Region C. Flow field distribution on the surface of the original model blade; Region D. Flow field distribution on the surface of the new model blade. Detailed Implementation

[0056] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0057] This invention addresses the performance degradation of mixed-flow pumps caused by insufficient optimization due to traditional design and inverse problem design methods that rely on only a single design parameter. It provides a mixed-flow pump impeller design method that couples geometric and hydrodynamic parameters. This method allows for simultaneous adjustment of both geometric and hydrodynamic parameters during the optimized design of the mixed-flow pump, thereby maximizing the design effect. Taking a medium specific speed mixed-flow pump impeller as an example, its design flow rate Q = 0.4207 m³ / s 3 / s, design head H=12.66m, rotational speed n=1256r / min, impeller diameter D=0.3m, number of impeller blades B1=4, number of guide vane blades B2=7, horizontal distance H between the leading edges of the blades at the hub. L =0.066m, horizontal distance H from the blade trailing edge at the hub T =0.135m, horizontal distance S from the leading edge of the blade at the rim L =0.019mm, horizontal distance S from the blade trailing edge at the rim T =0.072m. It should be noted that the embodiment of the present invention only optimizes the design of the impeller, while all other components remain unchanged.

[0058] Figure 1 This is a flowchart illustrating the calculation process of an embodiment of the present invention. The main body consists of three parts: first, determining the required performance; second, calculating the axial projection and load parameters; and finally, calculating the final blade shape. This invention primarily focuses on the second part, the calculation of the axial projection and load parameters, specifically:

[0059] Step 1: Based on the required mixed-flow pump performance, such as flow rate, head, and speed, calculate and determine the initial shape of the impeller shaft projection diagram according to the mixed-flow pump design specifications.

[0060] It should be noted that, see Figure 2In this embodiment, to facilitate subsequent adjustment of geometric and hydrodynamic parameters, the calculated axial projection diagram is divided into the following 13 parts: 1. Impeller rotation shaft; 2. Impeller inlet rim position; 3. Blade rotation shaft; 4. Blade inlet; 5. Blade outlet; 6. Hub; 7. Friction 8. Leading edge of the original model; 9. Trailing edge of the original model; 10. Horizontal distance H between the leading edge of the hub and the impeller inlet. L The horizontal distance H between the hub trailing edge and the impeller inlet T The horizontal distance S between the leading edge of the impeller rim and the impeller inlet L The horizontal distance S between the trailing edge of the impeller rim and the impeller inlet T .

[0061] Step 2: Based on the impeller axial projection obtained in Step 1, while keeping the hub ratio constant, modify the horizontal distance H from the impeller inlet at the leading and trailing edges of the hub and rim by quantitative means. L H T S L and S T Obtain the modified impeller shaft projection shape.

[0062] Preferably, in the modification and parameterization of the impeller axial projection diagram, the hub ratio of the impeller axial projection diagram remains unchanged; only the positions of the leading and trailing edges of the blades are modified, and the horizontal distances of the leading and trailing edges from the impeller inlet are used as design parameters. Specifically, H... L The range is [0.06, 0.068]m, H T The range is [0.13, 0.14]m, S L The range is [0.017, 0.02]m, S T The range is [0.07, 0.075]m.

[0063] In this embodiment, all circulation at the impeller inlet and outlet is set to 0 to satisfy the impeller design requirement of no pre-swirl at the impeller inlet and outlet.

[0064] It should be noted that, see Figure 3 In this embodiment, the modified model H L =0.062m, H T =0.131m, S L =0.017mm, S T =0.075m. Compared with the original model, the positions of the leading and trailing edges of the new model of this invention have been modified.

[0065] Step 3: On the impeller axial projection obtained in Step 2, determine the circulation value at the inlet based on the assumption of no pre-swirl at the inlet, and calculate the circulation value at the impeller outlet based on the Euler equations for ideal fluid:

[0066]

[0067] In the formula: Γ2 represents the circulation distribution at the impeller outlet, in meters. 2 / second; U2 is the circumferential velocity at the impeller outlet, m / s; V2 is the tangential component of the absolute velocity at the impeller outlet, m / s; ω is the angular velocity of the impeller rotation, radians / s; g is the acceleration due to gravity, m / s. 2 H T The impeller's theoretical head is measured in meters.

[0068] It should be noted that, see Figure 4 In this embodiment, the circulation value at the impeller inlet of the modified model is 0, and the dimensionless circulation value at the outlet is 0.32.

[0069] Step 4: Based on the impeller axial projection diagram and inlet / outlet circulation values ​​determined in Step 3, a three-segment curve consisting of a parabola, a straight line, and another parabola is used to control the load distribution at the hub (the partial derivative of circulation along the axial streamline, which is directly related to the pressure difference on the blade surface) control parameter LE. h (Preload value at the leading edge of the wheel hub), NC h (First loading point at the wheel hub), ND h (Second loading point at the wheel hub) and K h (Slope of the center line at the hub), load distribution control parameter LE at the rim s (Preload value at the leading edge of the rim), NC s (First loading point at the rim), ND s (Second loading point at the rim) and K s (Slope of the straight line at the center of the rim) is controlled and adjusted separately:

[0070]

[0071] In the formula: Γ p1 For the first segment of the parabolic circulation distribution, meters 2 / second; Γ z1 The distribution is a linear circulation in the middle, in meters. 2 / second; Γ p1 For the second segment of the parabolic circulation distribution, meters 2 / second; m1 is the normalized position of the first segment of the parabola's axial streamline, m2 is the normalized position of the middle straight line, and m3 is the normalized position of the second segment of the parabola's axial streamline; a1, b1, c1, and d1 represent the undetermined coefficients of the first segment of the parabola; a2 and b2 represent the undetermined coefficients of the middle straight line; and a3, b3, c3, and d3 represent the undetermined coefficients of the second segment of the parabola.

[0072] Preferably, on the determined impeller shaft projection diagram, a three-segment curve consisting of a parabola-straight line-parabola is used to control the load distribution at the hub and rim. Specifically, the range of LE is [-0.2, 0.2], the range of NC is [0.1, 0.4], the range of K is [-0.5, 0.5], and the range of ND is [0.4, 0.8].

[0073] It should be noted that, see Figure 5 In this embodiment, the modified hydrodynamic control parameter LE at the hub of the model is... h NC h ND h and K h The values ​​are 0, 0.24, 0.76, and 1.6, respectively; the load distribution control parameter LE at the wheel flange. s NC s ND s and K s The values ​​are 0, 0.3, 0.7 and -1.5, respectively.

[0074] Step 5: Based on the load distribution at the hub and rim determined in Step 4, the load distribution at other locations on the axle projection is determined by the following linear interpolation:

[0075]

[0076] In the formula: The load value at the required radius is in meters. 2 / second; r is the radius to be calculated, in meters; R h R is the radius at the hub of the required axial plane, in meters. s Let be the radius at the rim of the required axial plane, in meters; The load value at the rim of the required axle plane is in meters. 2 / Second; The desired circulation value at the hub of the axle plane is in meters. 2 / second; m is the normalized position of the axial streamline.

[0077] Then, input the airfoil parameters and fluid property parameters to determine the initial shape of the blade, and determine the final blade shape based on iterative calculations of the flow field and blade shape.

[0078] Based on the above embodiments, the final three-dimensional shape of the mixed-flow pump impeller of the present invention can be obtained. The three-dimensional shape of the mixed-flow pump blade obtained by the present invention can be compared with the shape of the original model blade. As an optional embodiment, an inviscid computation method can also be used to quickly analyze and compare the static pressure and velocity distribution on the blade surfaces of the two models. Furthermore, the performance of the original model and the model obtained by the present invention can be accurately evaluated by analyzing the blade shape, mesh generation, and calculations based on viscous computational fluid dynamics, so that designers can further improve its performance.

[0079] To illustrate the advanced nature of the embodiments of the present invention in detail, the performance of the mixed-flow pump impeller designed using the embodiments of the present invention will be compared with that of the original model.

[0080] Figure 6 A comparison of the blade shapes of the new model designed for a mixed-flow pump impeller design method that couples geometric and hydrodynamic parameters is presented with that of the original model. It can be seen that due to changes in the positions of the leading and trailing edges of the blades in the impeller axial projection diagram, as well as changes in the hydrodynamic parameters at the hub and rim, the three-dimensional shapes of the blades differ significantly, especially near the trailing edge.

[0081] Figure 7 A comparison of the external characteristics of a new model designed for a mixed-flow pump impeller design method that couples geometric and hydrodynamic parameters with the original model is presented. It can be seen that within the commonly used flow range, the efficiency of the new model is greater than that of the original model, and the efficiency difference between the two increases with increasing flow rate. At the design operating condition, the efficiency difference is approximately 2 percentage points. Furthermore, both models exhibit similar heads under all operating conditions, meeting the design requirements. Therefore, the method described in this invention can comprehensively improve the performance of mixed-flow pumps over a wider flow range while meeting head requirements.

[0082] Figure 8 A comparison of the static pressure and velocity vector distribution on the blade surface of the new model designed for the mixed-flow pump impeller design method that couples geometric and hydrodynamic parameters with the original model is presented. It can be seen that the original model exhibits a relatively obvious secondary flow from the hub to the rim at the mid-span of the blade leading edge, while the flow regime in this region is significantly improved in the new model.

[0083] This invention parameterizes the axial projection diagram by quantifying the horizontal distances from the leading and trailing edges to the impeller inlet, and parameterizes the load distribution at the hub and rim using a three-segment equation. It proposes a mixed-flow pump impeller design method that couples geometric and hydrodynamic parameters. This invention effectively avoids the performance degradation problem caused by insufficient optimization when using only geometric or hydrodynamic parameters as design parameters, thus helping designers obtain ideal mixed-flow pump performance within a larger design scope.

[0084] Finally, it should be noted that the present invention is not limited to the above embodiments. Other embodiments obtained based on the embodiments of the present invention, without making significant innovations or contributions, should fall within the protection scope of the present invention.

Claims

1. A method for designing a mixed-flow pump impeller that couples geometric parameters with hydrodynamic parameters, characterized in that, Includes the following steps: S1. Based on the flow rate, head and speed, the impeller shaft projection diagram is preliminarily calculated using the basic design specifications for mixed flow pumps to obtain the impeller shaft projection diagram. S2, keeping the hub ratio of the impeller axial projection unchanged, modify the geometric parameters of the impeller axial projection by adjusting the horizontal distances from the leading and trailing edges of the hub to the impeller inlet, and the horizontal distances from the leading and trailing edges of the rim to the impeller inlet; S3. On the impeller axial projection diagram, assuming there is no pre-swirl at the inlet, determine the circulation distribution at the impeller inlet and outlet, and calculate the circulation value at the impeller outlet according to the Euler equation for ideal fluid. S4, based on the circulation distribution at the impeller inlet and outlet, uses a three-segment curve consisting of a parabola, a straight line, and a parabola to control and adjust the load distribution parameters at the hub and the rim respectively, thereby achieving the adjustment of the hydrodynamic parameters on the impeller axial projection. S5. Based on the load distribution at the hub and rim determined in step S4, linear interpolation is used to determine the load distribution at the remaining locations of the blade. Then, based on the given airfoil parameters and fluid properties, the initial shape of the blade is determined. Finally, the final shape of the blade is determined through iterative calculation of the flow field and the blade shape.

2. The mixed-flow pump impeller design method for coupling geometric parameters and hydrodynamic parameters according to claim 1, characterized in that, In step S2, only the positions of the leading and trailing edges of the blades are modified, and the horizontal distances of the leading and trailing edges from the impeller inlet are used as design parameters. Specifically, the horizontal distance H from the hub leading edge to the impeller inlet... L The range is [0.06, 0.068] m, and the horizontal distance H from the hub trailing edge to the impeller inlet is... T The range is [0.13, 0.14] m, and the horizontal distance S from the leading edge of the impeller rim to the impeller inlet is... L The range is [0.017, 0.02] m, and the horizontal distance S from the trailing edge of the impeller rim to the impeller inlet is... T The range is [0.07, 0.075]m.

3. The mixed-flow pump impeller design method for coupling geometric parameters and hydrodynamic parameters according to claim 1, characterized in that, Calculate the circulation value at the impeller outlet using the following Euler equations for ideal fluid rotating machinery: In the formula, Γ2 represents the circulation distribution at the impeller outlet, in meters. 2 / Second; U2 is the circumferential velocity at the impeller outlet, in meters per second; V2 is the tangential component of the absolute velocity at the impeller outlet, in meters per second; ω is the angular velocity of the impeller, expressed in radians per second; g is the acceleration due to gravity, measured in meters per second. 2 ; H T The impeller's theoretical head is expressed in meters.

4. The mixed-flow pump impeller design method for coupling geometric parameters and hydrodynamic parameters according to claim 1, characterized in that, In a three-segment curve consisting of a parabola, a straight line, and another parabola, the first parabola segment is a third-order parabola, as shown in the following formula: In the formula, Γ p1 The first segment of the parabolic circulation distribution is shown in meters. 2 / Second; a1, b1, c1, and d1 represent the undetermined coefficients of the first segment of the parabola; m1 is the normalized position of the streamline of the first parabolic axial plane; The formula for the middle straight line is as follows: In the formula, Γ z1 The distribution is a linear circulation in the middle, with units of meters. 2 / Second; a2 and b2 represent the undetermined coefficients of the intermediate straight line; m2 is the normalized position of the middle straight line; The second parabola is also a third-order parabola, and its formula is as follows: In the formula, Γ p2 The second parabolic circulation distribution is shown in meters. 2 / Second; a3, b3, c3, and d3 represent the undetermined coefficients of the second parabola segment; m3 is the normalized position of the streamline on the axial surface of the second parabola.

5. The mixed-flow pump impeller design method for coupling geometric parameters and hydrodynamic parameters according to claim 1, characterized in that, Based on the determined load distribution at the hub and rim, the calculation formula for the load distribution at other locations on the blade is as follows: In the formula, The value of the load at the required radius is given in meters. 2 / Second; r is the radius to be calculated, in meters; R h The radius at the hub of the required axis plane is given in meters. R s The radius at the rim of the required axis plane is given in meters. The value of the load at the rim of the shaft plane is given, in meters. 2 / Second; The value of the circulation at the hub of the required axle plane is given in meters. 2 / Second; m is the normalized position of the axial streamline.

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