CN108708875B - Design method for centrifugal pump impeller blade placement angle - Google Patents

Design method for centrifugal pump impeller blade placement angle Download PDF

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CN108708875B
CN108708875B CN201810416245.0A CN201810416245A CN108708875B CN 108708875 B CN108708875 B CN 108708875B CN 201810416245 A CN201810416245 A CN 201810416245A CN 108708875 B CN108708875 B CN 108708875B
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blade
inlet
impeller
angle
outlet
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CN108708875A (en
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张瑶瑶
唐铃凤
赵永涛
蒋志诚
闫志超
杨强楠
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Anhui Polytechnic University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/18—Rotors
    • F04D29/22—Rotors specially for centrifugal pumps
    • F04D29/24—Vanes
    • F04D29/242—Geometry, shape
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/66—Combating cavitation, whirls, noise, vibration or the like; Balancing
    • F04D29/669—Combating cavitation, whirls, noise, vibration or the like; Balancing especially adapted for liquid pumps

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Structures Of Non-Positive Displacement Pumps (AREA)

Abstract

The invention discloses a design method of a centrifugal pump impeller blade mounting angle, which specifically comprises the following steps: determining the direction of the absolute speed at the inlet of the blade by using a connecting line between an inlet a of a working surface molded line of the blade 1 and an outlet b of a back molded line of the blade 2, establishing a functional relation between an inlet mounting angle and an outlet mounting angle, searching the corresponding inlet mounting angle and outlet mounting angle when the pump efficiency is highest, taking a point b as a reference, taking four points c, d, e and f along the blade 2, respectively connecting the point a with the points c, d, e and f to further change the direction of the absolute speed, researching the influence of the inlet and outlet mounting angles on pump performance parameters, and aiming at improving the efficiency and the cavitation performance and searching the optimal position of the absolute speed on the impeller 2. The invention provides a method for determining a blade setting angle, which is characterized in that a mathematical model of the blade setting angle is established, a mathematical model between pump performance parameters and the blade setting angle is established, and theoretical guidance is provided for selection of the blade setting angle.

Description

Design method for centrifugal pump impeller blade placement angle
Technical Field
The invention relates to the field of fluid machinery design, in particular to a design method of a centrifugal pump impeller blade setting angle.
Background
The blade placement angle is a key structural parameter affecting performance parameters such as efficiency and cavitation margin, and has a large influence on the flow inside the pump. At present, the blade placement angle is usually designed by determining a liquid flow angle according to an impeller outlet and selecting an attack angle according to experience, so that the impeller blade inlet placement angle is calculated. The design method is a single working condition design method based on experience, has a large number of experience factors and does not have scientific theory and mathematical model as supports, so that the value of the blade installation angle has certain contingency, and the designed impeller cannot be guaranteed to have better hydraulic performance.
Disclosure of Invention
The invention aims to solve the technical problem of providing a design method of a centrifugal pump impeller blade setting angle, so as to solve the defect that the value of the blade setting angle is taken mainly by experience in the prior art.
In order to achieve the above purpose, the present invention provides the following technical solutions: a design method of a centrifugal pump impeller blade setting angle is characterized in that a connecting line between an inlet a of a working surface molded line of a blade 1 and an outlet b of a back molded line of the blade 2 is used for determining the direction of the absolute speed at the inlet of the blade, a functional relation between the inlet setting angle and the outlet setting angle is established, the inlet setting angle and the outlet setting angle corresponding to the highest pump efficiency are found, four points c, d, e and f are additionally taken along the blade 2 by taking the point b as a reference, the point a and the points c, d, e and f are respectively connected with the point a, the point d, the point e and the point f to further change the direction of the absolute speed, the influence of the inlet and outlet setting angles on pump performance parameters is researched, the efficiency is improved, the cavitation performance is improved, and the optimal.
Preferably, the design method for determining the placement angle comprises the following specific steps:
(1) designing basic parameters of the centrifugal pump impeller according to a speed coefficient method;
(2) determining the absolute speed direction, and ensuring that the direction is collinear with a connecting line of an inlet a of a molded line of the working surface of the impeller 1 and an outlet b of a molded line of the back surface of the impeller 2;
(3) establishing a solving model of the blade inlet and outlet placement angle;
(4) solving the blade inlet and outlet placement angle;
(5) changing the connecting line direction, constructing another four models, and respectively solving the sizes of the inlet placing angles according to the method;
preferably, the basic parameters of the centrifugal pump, including the impeller inlet diameter D, are designed using a speed coefficient method1Outside diameter D of impeller2Number of blades z, selected outlet setting angle β2Range of (d), inlet true thickness δ1True thickness of outlet delta2And a blade wrap angle phi.
Preferably, the specific method of determining the absolute velocity direction is:
the circumferential thickness at the impeller exit is:
Figure 541656DEST_PATH_IMAGE001
（1）
in the formula, the geometric relationship can be obtained:
Figure 631972DEST_PATH_IMAGE002
（2）
the included angle between every two adjacent blades is as follows:
Figure 220079DEST_PATH_IMAGE003
（3）
the distance between the inlet a of the working surface of the blade 2 and the outlet b of the molded line on the back surface of the blade 1 is as follows:
Figure DEST_PATH_IMAGE005AA
(4)
the angle between the absolute speed direction and the peripheral speed direction is:
Figure 331123DEST_PATH_IMAGE007
(5)
in the formula (I), the compound is shown in the specification,
Figure 293263DEST_PATH_IMAGE009
(6)
wherein λ is2Is the included angle between the axial surface streamline and the axial surface sectional line, tau is the central angle corresponding to the outlet circumference thickness, and z is the number of blades.
Preferably, the specific process of solving the placement angle is as follows:
(1) establishing the inlet circumference partial velocity u of the centrifugal pump blade1；
Figure 173888DEST_PATH_IMAGE011
(7)
(2) According to the displacement coefficient of the inlet of the centrifugal pump blade
Figure 803452DEST_PATH_IMAGE013
And blade inlet cross-sectional area F1Establishing the blade inlet axial surface velocity vm1；
Figure 977076DEST_PATH_IMAGE015
Figure 426512DEST_PATH_IMAGE017
Figure 107898DEST_PATH_IMAGE019
(3) Solving the absolute speed and the relative speed of the blade inlet;
Figure 60810DEST_PATH_IMAGE021
Figure 670914DEST_PATH_IMAGE023
(4) establishing centrifugal pump blade inlet placement angle β1The mathematical model of (2);
as can be seen from the velocity triangle, the velocity,
Figure DEST_PATH_IMAGE025
preferably, when the blade inlet and outlet placement angle is solved, the optimization is performed by using a loss extreme method, the efficiency and the cavitation are taken as optimization targets, and the objective function is as follows:
Figure DEST_PATH_IMAGE027
(a)
in the formula (a), the reaction mixture is,
Figure DEST_PATH_IMAGE029
-impeller energy loss;
Figure DEST_PATH_IMAGE031
-a cavitation margin.
Preferably, the energy loss of the impeller is hydraulic loss, and mainly comprises impeller outlet loss, impeller flow passage friction loss and impeller flow passage diffusion loss.
Preferably, the angular displacements of the points c, d, e and f with respect to the point b are 20 °, 40 °, 60 ° and 80, respectively, and may be increased or decreased as appropriate for the angular displacement according to the actual situation.
Preferably, centrifugal pump blade setting angle
Figure DEST_PATH_IMAGE033
The solution of the mathematical model is an iterative solution.
The invention has the beneficial effects that: the invention discloses a design method of a centrifugal pump impeller blade setting angle, and provides a method for determining the blade setting angle.
Drawings
FIG. 1 is a schematic diagram of a design method for a centrifugal pump impeller blade setting angle;
FIG. 2 is a schematic view of a velocity triangle corresponding to the inlet a;
FIG. 3 is a schematic diagram of an impeller hydraulic model for empirically selected inlet and outlet angles (where inlet 22, outlet 30);
FIG. 4 is a schematic diagram of an impeller water model corresponding to a selected inlet and outlet angle after the model is established;
FIG. 5 is a schematic diagram of an impeller water model corresponding to a change in the inlet placement angle;
FIG. 6 is a diagram of a full channel numerical simulation model.
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
Fig. 1 and 2 show a specific embodiment of the present invention: a design method of a centrifugal pump impeller blade setting angle is characterized in that a connecting line between an inlet a of a working surface molded line of a blade 1 and an outlet b of a back molded line of the blade 2 is used for determining the direction of an absolute speed at the inlet of the blade, a point b is used as a reference, four points c, d, e and f are additionally taken along the blade 2 and respectively connected with the point a and the points c, d, e and f to further change the direction of the absolute speed, the influence of the relative speed on the impact loss at the inlet of the blade is researched, and the optimal position of the absolute speed on the impeller 2 is found.
In this embodiment, the design method for determining the placement angle specifically includes the steps of:
(1) designing basic parameters of the centrifugal pump impeller according to a speed coefficient method;
(2) determining the absolute speed direction, and ensuring that the direction is collinear with a connecting line of an inlet a of a molded line of the working surface of the impeller 1 and an outlet b of a molded line of the back surface of the impeller 2;
(3) establishing a solving model of the blade inlet mounting angle;
(4) solving a blade inlet mounting angle;
(5) changing the connecting line direction, constructing another four models, and respectively solving the sizes of the inlet placing angles according to the method;
in the embodiment, basic parameters of the centrifugal pump are designed by using a speed coefficient method, wherein the basic parameters comprise the diameter D of an impeller inlet1Outside diameter D of impeller2Number of blades z, selecting an appropriate outlet setting angle β2True inlet thickness delta1True thickness of outlet delta2And a blade wrap angle phi.
In this embodiment, the specific method for determining the absolute velocity direction is as follows:
the circumferential thickness at the impeller exit is:
Figure 109111DEST_PATH_IMAGE034
（1）
in the formula, the geometric relationship can be obtained:
Figure 344920DEST_PATH_IMAGE036
（2）
the included angle between every two adjacent blades is as follows:
Figure DEST_PATH_IMAGE038
（3）
the distance between the inlet a of the working surface of the blade 2 and the outlet b of the molded line on the back surface of the blade 1 is as follows:
Figure DEST_PATH_IMAGE040
4)
the angle between the absolute speed direction and the peripheral speed direction is:
Figure 533763DEST_PATH_IMAGE007
(5)
in the formula (I), the compound is shown in the specification,
Figure 564036DEST_PATH_IMAGE041
(6)
wherein λ is2Is the included angle between the axial surface streamline and the axial surface sectional line, tau is the central angle corresponding to the outlet circumference thickness, and z is the number of blades.
In this embodiment, the specific process of solving the placement angle is as follows:
(1) establishing the inlet circumference partial velocity u of the centrifugal pump blade1；
Figure DEST_PATH_IMAGE042
(7)
(2) According to the displacement coefficient of the inlet of the centrifugal pump blade
Figure 535534DEST_PATH_IMAGE043
And blade inlet cross-sectional area F1Establishing the blade inlet axial surface velocity vm1；
Figure DEST_PATH_IMAGE044
Figure DEST_PATH_IMAGE045
Figure DEST_PATH_IMAGE046
(3) Solving the absolute speed and the relative speed of the blade inlet;
Figure 761985DEST_PATH_IMAGE021
Figure DEST_PATH_IMAGE047
(4) establishing centrifugal pump blade inlet placement angle β1The mathematical model of (2);
as can be seen from the velocity triangle, the velocity,
Figure 4004DEST_PATH_IMAGE025
wherein D is1aIs the diameter at the inlet interface a, RcThe radius of the water passing section at the blade inlet, the length of a forming line of the water passing section b and the rotating speed n.
In this embodiment, the specific process of solving the placement angle is as follows: optimizing by using a loss extreme method when solving the blade inlet and outlet placement angles, taking efficiency and cavitation as optimization targets, wherein an objective function is as follows:
Figure DEST_PATH_IMAGE048
(a)
in the formula (a), the reaction mixture is,
Figure 221490DEST_PATH_IMAGE029
-impeller energy loss;
Figure 867235DEST_PATH_IMAGE031
-a cavitation margin.
In this embodiment, the energy loss of the impeller is hydraulic loss, and mainly includes impeller outlet loss, impeller flow passage friction loss, and impeller flow passage diffusion loss.
In this embodiment, the angular displacements of the points c, d, e and f with respect to the point b are 20 °, 40 °, 60 ° and 80, respectively, and may be increased or decreased according to the actual situation.
In this embodiment, centrifugal pump blade setting angle
Figure DEST_PATH_IMAGE050
The solution of the mathematical model is an iterative solution.
The invention will be further described with reference to the following figures and specific examples, but the scope of the invention is not limited thereto.
Specific numerical examples given according to the above method are as follows:
centrifugal pump with a specific speed of 61.5 and a design flow rate of Q20 m3/h，H＝30m，n ＝ 2900r/min。
(1) A hydraulic model of the centrifugal pump is designed by utilizing a speed coefficient method, and basic parameters of the centrifugal pump are as follows: d1=58mm，D2=164mm, z =6, and since the pump with a low specific speed selects a larger outlet setting angle, the outlet setting angle of the present embodiment is selected to be in the range of 28 ° -40 °, δ2=9mm, wrap angle phi =90 °.
(2) Taking the exit angle of 30 as an example, the absolute velocity direction is determined, knowing2=84 °, the circumferential thickness at the impeller exit is solved as: su2=18.0901mm，τ=12.64°，θ=60°，L12=63.768mm，γ=119.42°，α1=150.5824。
(3) Establishing the inlet circumference partial velocity u of the centrifugal pump blade1=8.807m/s, blade inlet cross-sectional area F1=0.004m2Inlet axial surface velocity vm1=3.63m/s, absolute velocity at inlet v1=7.39m/s and the relative velocity is w1=15.67m/s。
The optimal outlet placement angle and the optimal inlet placement angle are obtained by taking a loss extreme method as an optimization target, and the correspondence of partial outlet angles is shown in table 1.
TABLE 1
Outlet setting angle (degree) 28 30 35 40
Import placed angle (degree) 13.2 13.33 13.58 13.75
The impellers corresponding to the four models are shown in figure 4.
(4) And performing flow field analysis on the established models, selecting the inlet and outlet placement angle combination with the highest efficiency, changing the absolute speed direction, and establishing four groups of models to obtain the inlet placement angles corresponding to the models, wherein the inlet placement angle is 13.4 degrees, and the outlet placement angle is 30 degrees. The inlet placement angle changes are shown in table 2.
TABLE 2
By angle of deflection (°) 20 40 60 80 100 120
Inlet placement angle β1（°） 15.2 16.34 17.34 18.45 20.12 24.16
And then, analyzing the models again by using CFX to find the inlet and outlet placement angles with the best efficiency, wherein the four groups of model impellers are shown in figure 5.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various changes and modifications can be made without departing from the inventive concept of the present invention, and these changes and modifications are all within the scope of the present invention.

Claims (6)

1. A design method of a centrifugal pump impeller blade setting angle is characterized by comprising the following steps: determining the direction of the absolute speed at the inlet of the blade by using a connecting line between an inlet a of a working surface molded line of the blade I and an outlet b of a back molded line of the blade II, establishing a functional relation between an inlet mounting angle and an outlet mounting angle, searching the inlet mounting angle and the outlet mounting angle corresponding to the highest pump efficiency, taking a point b as a reference, taking four additional points c, d, e and f along the blade 2, respectively connecting the point a with the point c, d, e and f to further change the direction of the absolute speed, researching the influence of the inlet and outlet mounting angles on pump performance parameters, improving the efficiency and the cavitation performance as targets, and searching the optimal position of the absolute speed on an impeller II, wherein the specific step of the design method for determining the mounting angle is as follows:
(1) designing basic parameters of the centrifugal pump impeller according to a speed coefficient method;
(2) determining the absolute speed direction, and ensuring that the direction is collinear with a connecting line of an inlet a of the molded line of the working surface of the blade I and an outlet b of the molded line of the back surface of the blade II;
(3) establishing a solving model of the blade inlet and outlet placement angle;
(4) solving the blade inlet and outlet placement angle;
(5) and changing the connecting line direction, constructing another four models, and respectively solving the sizes of the inlet placing angles according to the method.
2. The design method of centrifugal pump impeller blade setting angle of claim 1, characterized in that: design of basic parameters of centrifugal pump by speed coefficient method, including inlet diameter D of impeller1Outside diameter D of impeller2Number of blades z, selected outlet setting angle β2Range of (d), inlet true thickness δ1True thickness of outlet delta2And a blade wrap angle phi.
3. The design method of centrifugal pump impeller blade setting angle of claim 1, characterized in that: optimizing by using a loss extreme method when solving the blade inlet and outlet placement angles, taking efficiency and cavitation as optimization targets, wherein an objective function is as follows:
min f(X)＝[ΔP(X),Δhr(X)]T(a)
in the formula (a), the reaction mixture is,
Δ P — impeller energy loss;
Δhr-a cavitation margin.
4. A design method for centrifugal pump impeller blade setting angles according to claim 3, characterized in that: the energy loss of the impeller is hydraulic loss and mainly comprises impeller inlet loss, impeller outlet loss, impeller flow passage friction loss and impeller flow passage diffusion loss.
5. The design method of centrifugal pump impeller blade setting angle of claim 1, characterized in that: the angular displacements of the points c, d, e and f relative to the point b are respectively 20 degrees, 40 degrees, 60 degrees and 80 degrees, and the angular displacements can be increased and decreased appropriately according to actual conditions.
6. The design method of centrifugal pump impeller blade setting angle of claim 1, wherein the centrifugal pump blade inlet setting angle β1The solution of the mathematical model is an iterative solution.
CN201810416245.0A 2018-05-03 2018-05-03 Design method for centrifugal pump impeller blade placement angle Expired - Fee Related CN108708875B (en)

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