Since overlarge axial force can damage the pump, accurate calculation formula of axial force on pump is very significant. The traditional formula is based on the assumption that the leakage amount of the pump is zero and the angular speed of fluid in the pump chamber rotates at half the impeller rotation’s angular speed. In order to propose an accurate calculation formula, the whole flow fields of multistage pumps with three different ring clearances were calculated by using Computational Fluid Dynamics (CFD). The results indicate that the axial force on first-stage impeller is larger than that on the second. Along with the change of ring clearance, the static pressure distribution on the shroud of impeller changes at the same time, which leads to the value change of axial force. Meanwhile, angular speed of the fluid in the pump chamber is changing. Therefore, this research works out the reason why the error of traditional axial force calculation is large when the amount of leakage is relatively high. At last, an accurate calculation formula of axial force on pump is obtained through the verification of numerical simulation and experiment.
The sectional multistage pump and high-head pump will generate huge axial force when running. Although balance devices are usually installed on the pump, balancing devices still may be damaged during operation due to inaccurate calculation of axial force, which in severe cases even results in accidents such as motor burn-outs [
However, with the operation of the pump, the ring clearance expands, the leakage amount changes, and the pressure distribution in the pump chamber changes also, which will influence the axial force [
Figure
Distribution of axial force on one impeller.
The first recommended formula of axial force in the book of
dynamic reaction:
In the formulas,
The second formula of axial force recommended by Pfleiderer is as follows [
the axial forces outside the back shroud:
the axial force inside the front shroud:
the axial component due to the axial clearance pressure:
dynamic reaction:
In the formulas:
The above two formulas are based on the assumption that the angular speed of fluid in the pump chamber rotates at half the impeller rotation’s angular speed (
the axial force inside the front shroud:
the axial forces outside the back shroud:
the axial force outside the front shroud:
the axial force outside the ring:
dynamic reaction:
In the formulas
The axial force of one model pump will be calculated by using above three formulas, and the geometrical parameters of the pump are shown in Table
Geometrical parameters of pump.
Parameters |
Names | Values |
---|---|---|
|
Impeller outlet diameter of front shroud | 119 mm |
|
Average impeller outlet diameter | 113.5 mm |
|
Ring diameter | 53.7 mm |
|
Impeller inlet diameter | 48 mm |
|
Hub diameter | 22 mm |
|
Impeller outlet diameter of back shroud | 108 mm |
|
Included angle between the outlet axial velocity and axial direction | 66.78° |
At the rated condition, the rotation speed of pump
Calculated results.
Formula | First | Second | Third |
---|---|---|---|
|
268.86 | 59.87 | 154.09 |
Experiments were done in an open-type pump system, which have the identification from Jiangsu Province of China. The test rig is composed of two parts, namely, the data acquisition system and the water circulation system [
Test rig of open-type pump system.
Axial force test equipment.
Table
Experimental axial force of one impeller.
|
12 | 16 | 20 | 24 | 28 |
---|---|---|---|---|---|
|
213.82 | 205.10 | 178.38 | 124.74 | 52.79 |
The whole flowing parts of pump are composed of inlet section, ring, impeller, guide vane, and outlet section [
The two-stage pump.
The grid of impeller and guide vane.
In this paper, standard
Usually the traditional calculation formula for axial force only considers the axial force on the outer surface of the impeller, not including the axial force on the inner surface of the impeller. The axial force on inner surface of impeller is regarded as internal forces. And it is considered that the total force of internal force is zero. This is acceptable in theory but difficult to understand and analyze. In contrast, it is easier to understand and analyze that the axial forces are the total axial components of forces on inner and outer surface of impeller. Therefore, the inside and outside surfaces of impeller are divided into the following sections:
In the formulas, the axial force on the outer surface of the impeller front shroud
Figure
Axial force of first-stage impeller
Axial force of second-stage impeller
Figure
Comparison of experimental values and the numerical simulation values.
This paper focuses on analyzing the relationship between the axial force and the ring clearance. Table
Calculated value of each component of axial force on the impellers with three ring clearances.
Clearance |
|
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|---|
0.0 mm | First stage | 798.075 | −974.2899 | −0.4571 | 24.2695 | −0.2887 | 185.956 | 73.0531 |
Second stage | 1832.09 | −2017.003 | −57.217 | 48.0199 | −20.43 | 237.215 | 70.8216 | |
| ||||||||
0.25 mm | First stage | 790.095 | −842.824 | −1.0523 | 23.8369 | −0.3041 | 182.096 | 151.847 |
Second stage | 1807.82 | −1869.446 | −50.253 | 47.1561 | −19.965 | 232.105 | 147.418 | |
| ||||||||
0.5 mm | First stage | 782.72 | −770.935 | −0.2441 | 23.3823 | −0.0271 | 180.348 | 215.245 |
Second stage | 1791.75 | −1791.943 | −47.195 | 46.4717 | −19.759 | 230.165 | 209.487 |
Figure
Radial static pressure of front shroud of impeller.
This pump is a multistage pump. In order to reduce the maximum shaft power, the outlet placed angle of guide vane is usually less than 90 degree. When the liquid comes out from the first guide vane and goes into the second impeller, there is certain angular speed in the liquid. In other words, the liquid is preswirled before entering the second impeller. In this paper, because the flow field of the second-stage pump is more representative in multistage pump, only the angular speed of the liquid in the second-stage pump chamber is shown in Figure
Radial distribution of angular speed of the liquid in the second pump chamber.
In the front pump chamber
In the back pump chamber
The model pumps with three different ring clearances were simulated, respectively, through CFD. The results indicate that the axial force in the front shroud improves with the increase of ring clearance. The increase of static pressure in the front shroud on the same radius is the main reason enhancing axial force. When the ring clearance is 0 mm, the angular speed of liquid in the pump chamber is 0.4-0.5
This research was supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions, the Scientific and Technological Innovation team Project of College in Jiangsu Province (no.