3.1 Effects of air injection on the cavitation characteristic
Gas contents are dimensionless into Inlet Gas Volume Fraction (IGVF) for comparison, and its equation is defined as
$$IGVF=\frac{{Q}_{g}}{{Q}_{l}+{Q}_{g}}\times 100\%$$
1
where Qg is the gas flow rate and Ql is the liquid flow rate.
Net Positive Suction Head (NPSH) shows the tendency for cavitation in the pump and is defined as follows:
$$NPSH=\frac{{P}_{in}-{P}_{v}}{\rho g}+\frac{{v}_{in}^{2}}{2g}$$
2
where Pin is the inlet pressure, Pv is the saturated vapor pressure, ρ is the mixed density, vin is the inlet velocity and g is the gravity acceleration.
As shown in Fig. 2, taking the head and internal flow characteristics at IGVF = 0% as a reference, cavitation stages at different IGVFs are divided into five forms: none cavitation, incipient cavitation, sheet cavitation, cloud cavitation and super cavitation. When IGVF is 0% shown in Fig. 2(a), in the incipient cavitation, the cavity first occurs at the suction side of the inducer blade tip. The primary symptom of sheet cavitation, as shown in Fig. 2(b), is the development of an aperiodic triangular cavitation area on the suction side of the blade. Meanwhile, the head has decreased. As shown in Fig. 2(c), the periodic cloud cavitation that occurs when the NPSH drops cause the length and thickness of the cavitation area on the suction side of the blade to expand in the opposite direction of the inducer rotation, even spreading to the pressure side of the other blade, resulting in the further rapid head drop. When the whole blade surface is completely covered by cavity, super cavitation shown in Fig. 2(d) is formed and the head descends to the lowest point. It can be found that a large number of cavitation bubbles gather in the inducer outlet flow passage, indicating the impeller inlet has also suffered serious cavitation, triggering the cavitation surge backflow to the inducer outlet.
It is worth noting that head first rises slightly and then drops as the NPSH decreases, but descending slopes of IGVF = 0%, 0.1% and 0.5% are larger than that of IGVF = 1%, 1.5% and 2%. The initial and final broken head at different IGVFs are similar, even though the rate of head fall varies, the NPSH corresponding to the lowest point of head is basically around 2m. In other words, the NPSH for the first head drop increases with the increase of IGVF, indicating that the air in the passage makes the flow unsteady and causes cavitation to occur earlier in the pump, so the head is sensitive to the pressure drop and drops directly. When IGVF is 0%~0.5%, the head starts to fall in the sheet cavitation stage, but it has already fallen in the incipient cavitation stage at IGVF = 1%~2%. Although the inflection points of head curves at IGVF = 0% and 0.1% are close, the slopes of the head decline within the cloud and super cavitation stages are different. The slope of the head decline at IGVF = 0.1% is steeper, which suggests a more rapid head breakage. As the IGVF increases further, the slope of the head curve decreases and the breakage rate slows down, which is most obvious during the sheet and cloud cavitation stage. In brief, an increase in IGVF could accelerate the cavitation inception while inhibiting its further development to some extent.
3.2 Effects of air injection on cavitation and inlet pressure pulsation
Figure 3 shows that the ranges of the incipient and sheet cavitation decrease but that of the cloud cavitation and super cavitation increase significantly as the IGVF increases. The frequency range of the inlet pressure pulsation fluctuation at IGVF = 0% is 0-0.75 f/fn, but it narrows to 0-0.5 f/fn as IGVF is increased to 2%. When IGVF is 0%, the frequency fluctuation range becomes narrower as the NPSH decreases and the peak inlet pressure pulsation shifts to lower frequencies, indicating that cavitation makes the main frequency of inlet pressure pulsation transfer to the lower frequency. At IGVF = 0.1%, the frequency fluctuation range is basically unchanged compared to that at IGVF = 0%. However, the inlet pressure pulsation fluctuation of 0.2–0.75 f/fn is weaker and the peak value decreases, indicating that a tiny amount of air can alleviate the fluctuation of inlet pressure pulsation and reduce the peak value of pulsation. The frequency range of pressure fluctuations decreases at IGVF = 1%, but pressure fluctuations and amplitudes increase during the none cavitation and incipient cavitation stages. The frequency range shifts to the lower frequency as the NPSH decreases. As the IGVF increases to 2%, the inlet pressure amplitudes within the five cavitation forms increase and the degree of fluctuation has intensified. In particular, during the cloud cavitation and super cavitation stages, the inlet pressure pulsation accelerates and the fluctuation frequency range widens to 0.3 f/fn compared to small air IGVFs. It can be assumed that cavitation makes the fluctuations of inlet pressure pulsation shift to lower frequencies. The oscillations and amplitude of inlet pressure pulsation can be attenuated if a small amount of air is injected into the inlet, while excessive amounts of air can boost the fluctuations.
As shown in Fig. 4, the ranges of incipient cavitation, cloud cavitation and super cavitation change most significantly, so the air and cavitation evolution of the inducer at IGVF = 0.1%, 1% and 2% are analyzed in depth as follows. As the IGVF increases, the number of air in upstream of the inducer increases, changing from discrete bubbles to continuously aggregated bubbles. Also, it is evident that each cavitation stage occurs earlier with the increase of IGVF. The transition time for the development of each cavitation stage increases, and differences in NPSHs increase along with it.
The incipient cavitation at IGVF = 0.1% is similar to that at IGVF = 0%, with the smoky air and cavitation flow at the blade tip. The triangular cavitation area on the suction side of the blade, which is identical to the cloud cavitation at IGVF = 0.1%, forms during the incipient cavitation stage at IGVF = 2%. This accounts for the early drop in the head at IGVF = 2% and the sharp fluctuations in inlet pressure pulsation during the incipient cavitation stage. In the cloud cavitation stage, cavitation has been fully developed on the suction side and is growing and spreading in the opposite direction of rotation. Air and cavity have spread downstream of the inducer, resulting in a head drop and strong pressure pulsation fluctuations. During the super cavitation stage, the suction side of the blade is completely covered by air and cavity, resulting in significant air and cavitation blockage in the inducer downstream. In this case, the inducer cannot provide enough energy for the impeller, causing the increased head drop and pressure pulsation amplitudes. It is conceivable that the presence of air could aggravate cavitation but delay the transition time for the development of various cavitation stages. The presence of air makes the complex cavitation flow in the inducer passage more turbulent and to some extent enhances fluctuations and amplitudes of the inlet pressure pulsation.
3.3 Effects of air injection on cavitation and inlet vibration
In order to better characterize the physical phenomenon of vibration, the Vibration Acceleration Level (VAL) is defined as:
$$VAL=20lg\frac{{V}_{r}}{{V}_{0}}$$
3
where Vr is the root mean square value of the vibration acceleration, and V0 is the reference vibration acceleration taken as 1×10− 9mm/s2.
According to Fig. 5, the horizontal axis represents the NPSH, and the vertical axes are the normalized frequency f/fn (fn is the shaft speed frequency) in the top figures and the normalized head H/H0 (H0 is the head at IGVF = 0%) in the bottom figures, respectively. The main frequency of vibration acceleration is at f/fn=1.0 under different IGVFs and NPSHs, and the harmonic frequencies are f/fn=2.0 and f/fn=4.0, which is affected by the number of inducer blades. When IGVF is 0%, fluctuations in vibration acceleration appear around f/fn=3.0 ~ 4.0 in the incipient cavitation stage, as shown in Fig. 5(a) Ⅱ. During the cloud and super cavitation stages, as shown in Fig. 5(a) Ⅳ and Ⅴ, the amplitude of vibration acceleration increases at f/fn=2.0 and f/fn=4.0, while the head drop rises greatly. This is because severe cavitation enhances the unsteady disturbance in the inlet inducer channel, causing strong vibration excitation. However, after air content of 0.1% is injected, as shown in Fig. 5(b), the fluctuations around 2–4 times the main frequency are all significantly decreased, indicating that a small amount of air can effectively mitigate the fluctuations in vibration acceleration triggered by the cavitation. In Fig. 5(c), when IGVF is increased to 1%, the fluctuations around 2–4 times the main frequency decrease at the low cavitation level, as shown in Fig. 5(c) Ⅰ and Ⅱ. However, at low NPSH, that is, at the sheet, cloud and super cavitation levels shown in Fig. 5(c) Ⅲ, Ⅳ and Ⅴ, the vibration fluctuations near f/fn=3.0 ~ 4.0 have enhanced and their amplitudes have also increased, whereas just as the head also happens to drop, indicating that the head drop and vibration are positively correlated. When IGVF is 2%, the head drop and an increase in vibration fluctuations around f/fn=3.0 ~ 4.0 occurs early in the incipient and sheet cavitation stages, as shown in Fig. 5(d) Ⅰ and Ⅱ, showing that if the percentage of air exceeds a certain value, the combined effect of the air and the cavitation will make the head drop earlier, thus inducing vibration fluctuations and amplitude increase earlier.
As shown in Fig. 6(a), NPSH0 is the definition of NPSH at the beginning pressure. When the head rises for the final time, the NPSH is regarded as the first net positive suction head (NPSHⅠ). The corresponding NPSH for the first head drop is the breakage (second) net positive suction head (NPSHb(Ⅱ)) and that for the minimum head point is the third net positive suction head (NPSHⅢ).
Figure 6 shows the comparison of inlet vibration acceleration levels (VAL) at typical NPSH points under different IGVFs. For each IGVF, as shown in Fig. 6(b), the VAL shows the trend of decreasing first and then increasing with the decline in NPSH, which is contrary to the trend in the head in Fig. 6(a). NPSHI is where VAL has the smallest value and where the head reaches its highest point. The VALs from NPSH0 to NPSH1 have decreased by 0.61% at IGVF = 0%, 0.66% at IGVF = 0.1%, 0.99% at IGVF = 1% and 0.52% at IGVF = 2%, respectively, indicating that it is possible to somewhat mitigate the vibration instability by adding the proper amount of air. It is worth noting that the value of VAL at NPSHb is lower than that at NPSH0 for small air fractions (IGVF = 0%,0.1%,1%), although the head has dropped at this point. The VAL drop ratios between NPSH0 and NPSHb at IGVF = 0.1% (decreased by 0.51%) and 1% (decreased by 0.54%) are more than that at IGVF = 0% (decreased by 0.30%), demonstrating that the degree of vibration mitigation is enhanced with little increasing air. However, when IGVF is 2%, the VAL at NPSHb is higher than that at NPSH0 (increased by 0.38%), which is contrary to the low IGVFs. This indicates that excessive air will likely result in vibration deterioration instead. The VAL at NPSHⅢ for each IGVF reaches the highest value due to the further development of cavitation, which has caused the large cavity in the flow channel to increase the inlet vibration.
The drop in VALs at NPSH0 that occurs with a rise in IGVF suggests that the increase of air in the none cavitation stage may be able to lessen inlet vibration. In the case of the cavitation development, it is evident that VALs at NPSH1 and NPSHb fall as IGVF increases from 0–1% but rise as IGVF increases to 2%. During the cavitation deterioration stage, VALs at NPSHⅢ display the tendency of dropping to the minimum value as IGVF is from 0–0.1% and rising to the maximum value as IGVF is from 0.1–2%. This is due to the fact that while a tiny percentage of air might dampen vibrations, a large amount of air can induce serious cavitation surge and gas blockage in the inducer flow passage. This can be summarized that at the stage of cavitation development, there is a critical threshold for the impact of air on vibration. The percentage of air has a beneficial influence on vibration suppression when it is less than a particular value but a negative effect when it is greater than that value. In most cases, the increase of air can mitigate vibration, but when cavitation is particularly severe, the presence of air will undoubtedly make the cavitation vibration at the pump inlet intense.
According to the head curve in Fig. 6(a), the inducer flow field at NPSHb, where the head begins to decrease, was selected for further analysis and comparison. Figure 7 depicts the processes of cavity formation, development and shedding that occur in the visualization region of a single inducer blade during the course of a half rotation cycle with different IGVFs. Due to the limitation of shooting angle of the high-speed camera, only the cavitation evolution of one inducer blade can be observed simultaneously. The time taken for the inducer to rotate for one cycle is defined as T.
It can be observed that the cavity on a single blade gradually increases with the rotation of the inducer during 0 ~ 1/4T, and the cavitation region occupies from the top to the middle and bottom flow passage. The cavitation shedding occurs during 3/8T ~ 1/2T. When IGVF is 0%, the cavitation shedding region was mainly located in the middle and bottom flow passage. However, as the IGVF increases, the cavitation shedding expands to the top flow passage, indicating that the presence of gas could extend the cavitation shedding duration. Furthermore, with the increase of IGVF, the cavitation shedding transitions from locally fractured small-scale cavitation clusters to continuous large-scale cavitation clusters.
As shown in Fig. 8, the probability density analysis is conducted for the time frequency data of inlet vibration acceleration at NPSHb under IGVF = 0%, 0.1%, 1% and 2%, which accords with the normal distribution. The probability density peak of the inlet vibration acceleration first decreases and then increases with the increase of IGVF, with the minimum peak at IGVF = 1% and the maximum peak at IGVF = 0%. However, the broadband characteristics first increase and then decrease with the increase of IGVF. The broadband characteristic is most obvious at IGVF = 1%, indicating the most dispersed energy.
Above conclusions can be explained by Fig. 7. Small bubble flow, which is primarily distributed in the top area of the flow passage, characterizes the gas flow pattern at IGVF = 0.1%. When IGVF increases to 1%, the flow pattern in the inlet flow passage of the inducer transfers into a mixed flow of small bubble flow and small gas pocket flow. The flow pattern is currently in an unstable transition state, which makes the characteristic frequency of vibration complicated and the broadband characteristic obvious. In addition, the large cavity clusters on the suction side of the inducer blade are dispersed by the unstable gas-liquid mixed flow, shedding in the form of locally fractured small-scale cavity clusters. Therefore, the probability density peak of vibration acceleration at IGVF = 1% is the smallest and the energy is the most dispersed. However, when IGVF is 2%, the flow pattern in the inducer changes to the stable big gas pocket flow. The presence of high concentration gas increases the thickness of the cavity on the inducer blades, resulting in the continuous large-scale cavity cluster shedding. This causes the vibration characteristic frequency to concentrate and the peak probability density to increase at IGVF = 2%.