4.1. The Influence of the Vortex on the Inlet Flow Field of the Impeller
Inlet flow fields have a direct effect on impeller performance. To quantitatively analyze the flow field state of the impeller inlet, the distribution uniformity of the axial velocity at the impeller inlet is denoted as
. A modified formula is proposed that ignores the influence of the grid area on the calculation results and improves the calculation accuracy as follows:
where
is the distribution uniformity of the axial velocity;
is the average axial velocity;
is the calculated cell grid area;
is the axial velocity of the calculated cell grid; and
is the area of the calculated section.
The axial velocity weighted average angle (
) is a common index to evaluate the angle of incidence. Its expression as follows:
where
is the tangential velocity at the inlet plane of the impeller. The closer
is to 90°, the more uniform the axial-flow velocity distribution at the inlet plane of the impeller.
Under the design flow rate, 5 measurement lines were taken before the impeller inlet to compare the differences in the radial velocity. The positions and velocities of each measurement line are shown in
Figure 12 and
Figure 13. The X-coordinate value in the figure is the horizontal distance between each point and the hub center.
As shown in
Figure 13, in the absence of VGs, the radial velocity of each measurement line gradually decreases from the hub to the shroud. In the main flow area, the radial velocity of each measurement line is basically the same, and the differences between values are small, indicating a better inlet flow pattern of the impeller. In the presence of VGs, the radial velocity of each measurement line obviously changes, and the differences between measurement lines are significant. When X = 0.11 m, the radial velocities of line 2 and line 5 increase by 1.7 m/s and 0.9 m/s, respectively. As the distance between a measurement line and the VGs increases, the intensity of the disturbance of the radial velocity decreases, which also indicates that the intensity of the vortex is decreasing.
In the inlet plane of the impeller,
and
under different flow rates were obtained, as shown in
Figure 14.
As shown in
Figure 14, without VGs,
and
increase with an increasing flow rate; with VGs,
increases with an increasing flow rate, while
first increases and then decreases. Overall, without VGs, the smaller the flow rate is, the flow pattern at the inlet plane is more disordered, which conforms to the characteristics of a general axial-flow pump. With VGs, the disturbance of the vortex generator to the flow state is significant, and presented the trend of the larger the flow, the more serious the disturbance. When the size of the VGs is fixed, with the increase of the flow rate, the effect of blocking water increases, the intensity of the generated vortex is stronger, and the damage to the flow field is greater.
4.2. Effect of the Vortex on the Pump Device Performance
When water passes through the flow parts, such as the inlet and outlet passages, friction, impact, vortices and backflow will occur [
27]. Such losses are called the hydraulic loss, which is an important factor affecting the performance of the pump device, expressed as follows:
where
P2 is the static pressure of the outlet sections;
Z1 is the water level in the inlet sections;
Z2 is the water level in the outlet sections;
u1 is the velocity of the inlet sections; and
u2 is the velocity of the outlet sections.
For the inlet passage with VGs, the loss is mainly divided into three parts, which can be described by the following expression:
where
is the hydraulic loss caused by vortex turbulence;
is the hydraulic loss caused by the water-blocking function of the VGs; and
is the friction loss between the water flow and the passage wall.
The hydraulic losses for each part of the inlet passage is shown in
Figure 15. With increasing flow rate, the hydraulic losses of each part of the inlet passage and the total hydraulic losses increase. Regarding the hydraulic losses of each part,
is closely related to the size of the inlet passage. In the optimization calculation of the inlet passage, this loss should be as small as possible, but it cannot be eliminated.
is the water-blocking function of the VGs and will not be produced in actual engineering.
is the unnecessary hydraulic loss caused by the vortex in the inlet passage and must be eliminated. After calculation,
. accounts for 25–30% of the total hydraulic loss in the inlet passage, and its influence othe efficiency of the pump device is 0.5–2.2%.
The inlet flow field directly affects the impeller performance. The impeller efficiency in different working conditions with and without VGs was obtained as shown in
Figure 16.
Figure 16 shows that the change trends of the efficiency of the two impellers with the flow rate are the same; however, with increasing flow rate, the difference between the impellers increases. The larger the flow rate is, the more serious the decrease in impeller efficiency with VGs and the greater the influence of the vortex on the performance of the impellers. According to the comparison and analysis of
Figure 14, the variation trend of distribution uniformity of the axial velocity is consistent with that of the impeller efficiency. For
Qd,
is reduced by 0.6% and the corresponding impeller efficiency is reduced by 0.7%; for 1.2
Qd, the value of
is reduced by 1.2% and the corresponding impeller efficiency is reduced by 1.8%.
The influence of the vortex on the flow patterns of the impeller, the guide vane and the outlet passage was qualitatively analyzed under the design condition. The velocity contour of the impeller center section was obtained, as is shown in
Figure 17.
When no vortex occurs, the velocity distribution inside the impeller presents a stepped shape, gradually rising from the blade inlet to the outlet, and the velocity is small near the hub and large near the shroud. In the presence of a vortex, the velocity distribution in the impeller is similar to that in the absence of a vortex. The disturbance of the inlet flow field of the blade due to the vortex is evident, and this disturbance disrupts the velocity distribution in the impeller, reducing the ability of the impeller to work.
As an important part of the pump device, the guide vane can recover the loop amount of high-speed rotating water flowing out of the impeller and convert the kinetic energy into pressure energy. The dynamic and static interactions between the impeller and the guide vane have been the focus of research [
28]. After the rectification of the guide vane, the axial velocity at the outlet of the guide vane should be uniform.
Figure 18 shows that in each channel of the guide vane there is a low axial velocity zone in the back of the blades. An uneven velocity distribution and a large velocity gradient can easily cause flow instabilities. When an inlet vortex occurs, the zone of low axial velocity near the hub decreases, and a few channels appear low axial velocity near the shroud. According to Equation (8), the calculated values of
for
Figure 18a,b are 74.5% and 76.1%, respectively. This indicates that the inlet vortex will influence the interior flow fields of the guide vane; however, the effect is limited. In addition, appropriate flow pattern interference may improve the inner backflow of the guide vane, and this effect is also worth further study.
The outlet passage is an important part of the pump device, and its internal flow pattern directly affects the efficiency and stability of the pump device [
29]. The pressure contour of the middle section of the outlet passage was obtained, as shown in
Figure 19. The pressure cloud diagram of the outlet passage shows that the lateral pressure is high in the turn section, while the internal pressure is low. The pressure gradually increases from the inlet to the outlet of the outlet channel, indicating that the energy of the flow is converted from kinetic energy to pressure energy. The pressure distribution trends with and without an inlet vortex are basically the same, but the pressure values are slightly different, which may be caused by the different abilities of the impeller to work. The inlet vortex has little effect on the performance of the outlet passage.
4.3. Shape Changes of the Vortex
The pressure contour diagram, velocity vector and vortex diagram in the water guide cone were obtained under the design condition. This paper studies the vortex according to the
q criterion [
30,
31], when
q = 6 × 10
4 s
−2, the shape of the vortex is shown in
Figure 20.
In the absence of VGs, the overall pressure of the section is high, and the pressure distribution is relatively uniform; no vortex appears. Influenced by the water guide cap, the water tends to flow from the hub to the shroud and is influenced by the blade, forming four high-speed zones. With the VGs, four pairs of counter-rotating vortices are formed in the water guide cone. A low-pressure area correspondingly occurs at the vortex positions, and the pressure distribution is uneven. Influenced by the elbow inlet passage, the shapes of the four groups of vortices are slightly different. The shapes of the vortices are greatly different on the left and right sides, and the left low-pressure area is evident. The shape of the low-pressure area at the upper and lower positions is the same as that of the vortices. Although the VGs can produce a continuous vortex and its position is relatively fixed, the shape of the vortex will also twist due to the disturbance of the rotating blades.
Because the impeller is the core part of the pump, exploring the propagation of the vortex and its influence on the performance of the impeller is very important. When q = 6 × 104 s−2, the vortex is identified using the isosurface and the vortex surface is expressed by the velocity.
Since there are four impeller blades, an impeller rotation of 90° is identified as a cycle to analyze the change in the vortex in the impeller, as shown in
Figure 21. On the suction surface side of the blade, the blade sweeps the vortex, cutting it off, and the vortex is closely attached to the blade. When the blade rotates to different angles, the vortex position remains unchanged. On the pressure surface side of the blade, after the vortex is cut off by the blade, the shape of the vortex is destroyed, the strength of the vortex is weakened, and the vortex tends to follow the movement of the blade.
To analyze the vortex inside the impeller more intuitively, when
q = 6 × 10
4 s
−2, the vortex is identified by the isosurface. The vortex in a single channel is shown in
Figure 22 as an example.
Figure 22 shows the shape of the vortex in the impeller. As the impeller rotates at a constant speed, the position of the vortex entering the impeller remains the same, and the vortex is cut into two parts by the impeller. The two resulting vortices remain in the shape of straight pipes. The vortex near the pressure surface moves forward a certain distance with the rotating blade, where the longer the blades sweep through the vortex, the greater that certain distance. The vortex on the suction side clings to the blade surface, and the vortex at the tail is broken up, while the vortex at the bottom is still tubular. When a blade passes by, the vortex will connect for a short time, and then be cut off by the next blade.
4.4. Vortex-Induced Pressure Fluctuation
The frequency-domain diagrams of pressure pulsation at inlet points 1, 2, 3, 7, 8, and 9 and outlet points 10, 11, and 12 of the impeller were obtained under the design flow condition, as shown in
Figure 23.
As shown in
Figure 23a, the amplitude of the pressure fluctuation increases from the hub to the shroud. Without VGs, the main frequencies of the three measurement points are all the blade frequency, and the maximum amplitude of point 3 is 542 Pa. With VGs, the result of point 1 is the same as that without VGs. At point 2, the low-frequency pulsation with an amplitude near that of the blade frequency is increased. At point 3, the dominant frequency caused by the vortex is not the blade frequency but the rotating frequency of the impeller, and the maximum amplitude is 2870 Pa, which is 5.3 times the amplitude without VGs. When the low-frequency pressure pulsation caused by the vortex is consistent with the vibration of the unit, it will threaten the stable operation of the pump device. As shown in
Figure 23b, the main frequency is the blade frequency, and the pulsation amplitudes at measurement points 7, 8 and 9 are significantly larger than those at measurement points 1, 2 and 3. The main frequencies are all the blade frequency, and the values are the same. At point 9, with VGs, low-frequency pulsations still appear, but the amplitude is smaller, only one-fifth of the blade frequency amplitude. As shown in
Figure 23c, the main frequencies of the three measurement points are still the blade frequency, and they all have low-frequency pulsations. At point 10, the main frequency with VGs is four times that without VGs. At point 11, the main frequency with VGs is nearly the same as that without VGs. At point 12, the main frequency with VGs is two times that without VGs. The above analysis shows that the pressure pulsation amplitude at the impeller inlet is larger closer to the blade position. At the outlet of the impeller, the main frequency amplitude of the pressure pulsation decreases, but the low-frequency pressure pulsation increases, which indicates that the interference effects of the rotor and the stator are strengthened and that the internal flow field becomes complicated. The above phenomenon is in accord with the general regularity of axial-flow pump pressure pulsation.
Because the low-frequency pressure fluctuation is evident near the impeller inlet sidewall, the time-domain diagrams at measurement points 3, 6 and 9 with and without VGs were obtained, as shown in
Figure 24.
As shown in
Figure 24a, without VGs, the pressures at these three measurement points change uniformly with time. The peaks and troughs generated by the passage of blades occur at the same times. The average pressures of monitoring points 3, 6 and 9 are 87,300 Pa, 84,075 Pa and 80,794 Pa, respectively, and the differences between the pressure trough minimum and the average value are 1282, 3645 and 11,860 Pa, respectively. The average pressure difference between point 6 and point 3 is 3225 Pa, while the average pressure difference between point 9 and point 6 is 3281 Pa; the two values are nearly equal. The amplitudes of the three points vary greatly. The amplitude of point 6 is 2.7 times that of point 3, and the amplitude of point 9 is 3.3 times that of point 6. When a measurement point is closer to the impeller inlet, the average pressure of the measurement point is smaller, and the amplitude of the pressure fluctuation is larger. As shown in
Figure 24b, with VGs, the pressure is lower because the velocity is higher at the back of the VGs, obviously; this change is caused by more than the increase of velocity because the changes in the pressures at these three measurement points with time are complex. At point 3, the shapes of the peaks and troughs are not symmetric. The peak and trough values in different periods are also very different. At points 6 and 9, the pressure changes more regularly than at point 3. The average pressures of monitoring points 3, 6 and 9 are 77,286 Pa, 81,559 Pa and 79,724 Pa, respectively, and the differences between the pressure trough minimum and the average value are 13,603 Pa, 9794 Pa and 21,975 Pa, respectively. The average pressure values of points 3, 6 and 9 first increase and then decrease, and the amplitudes of the pressure fluctuation first decrease and then increase. Comparing the two figures, with VGs, the amplitudes of the pressure fluctuation at the three points are 10.6, 2.7 and 1.8 times those without VGs. The influence of the vortex on the amplitude of the pressure fluctuation is weakened as the position of a measurement point approaches the inlet of the impeller. Additionally, the minimum pressure and the maximum pressure fluctuation amplitude occur at measurement point 9. The closer the impeller is to the inlet, the more dangerous the pressure pulsation caused by the vortex will be to the stable operation of the axial-flow pump device.
Considering that the pressure fluctuation of a monitoring point may be related to the vortex position, along with
Figure 23 and
Figure 24, the vortex diagram for
q = 6.0 × 10
4 s
−2 was obtained, as shown in
Figure 25. To verify this conjecture, three monitoring points 3′, 6′ and 9′ were added inside the vortex, and the
Z-axis coordinates of these three points correspond to those of points 3, 6 and 9, respectively. The positions of the points relative to the vortex are also shown in
Figure 25. The VGs produces a lot of very disordered vortices, but they are not fully displayed due to their low intensity. In addition, many vortices disappeared before they entered the impeller but the disturbance of the convection field does not disappear. Because this paper focuses on the interaction between the vortices and the impeller, the mechanism of the VGs is not studied in depth here.
The pressure fluctuations at points 3′, 6′ and 9′ were obtained, as shown in
Figure 26.
As shown in
Figure 26, at point 3′, the pressure greatly varies in different calculation periods, and a superposition of large and small wave periods occurs. At point 6′, 32 peaks and troughs can be distinguished, but some average values are not between the peaks and troughs. At point 9′, the effect of the blade on the pressure fluctuation is very strong; however, differences still exist between the peak and trough values. As a measurement point moves toward the impeller, the pressure fluctuation at that point significantly increases, indicating that the pressure pulsation caused by the vortex is lower than that caused by the impeller.
To quantitatively analyze the pressure fluctuations induced by the vortex, the results at points 3′, 6′ and 9′ are shown in
Figure 27, where the pressure with VGs is less than that without VGs.
As shown in
Figure 27, large periodic fluctuations occur in the pressures at the three points. As the position of a measurement point moves toward the impeller, the absolute value of the pressure fluctuation caused by the vortex decreases, and peaks and troughs influenced by the blades gradually appear. The data shown in
Figure 27 were transformed by the FFT method, and the frequency-domain diagram is shown in
Figure 28.
As shown in
Figure 28, the amplitudes at 0–1 times the rotation frequency caused by the vortex are larger. The maximum values at points 3′, 6′ and 9′ are 1632 Pa, 1961 Pa and 1547 Pa, respectively. When a measurement point is closer to the impeller, the blade frequency of the pressure fluctuation caused by the vortex significantly increases, and the number of low-frequency pressure fluctuations is greater. The vortex at the inlet can be inferred to interact with the impeller; although the intensity of the vortex weakens near the impeller, the influence of the impeller rapidly increases.