Effect of the difference in slit locations on the suppression of cavitation instabilities in an inducer.

Cavitation instabilities are caused by unsteady cavitation in the inducer in liquid rocket turbopumps. This phenomenon has a negative impact on pumps and must be suppressed. Our research group has proposed a method to suppress the instabilities by adding slits to the inducer blades, and previous studies was shown the effectiveness of this method. In this study, water experiments of inducers with slits at different locations were conducted. As a results, the vibration characteristics of cavitation in the slit inducers changed when the location of the slit was changed although the cavitation instabilities were successfully suppressed in all slit inducer. The visualized image of cylindrical surface of the axial flow pump was expanded into a two-dimensional plane to determine the time variation of the area of the tip leakage vortex cavitation generated in each blade. The suppression mechanism of cavitation instabilities in each slit location was discussed from the obtained unsteady image of cavity area in each blade in the slit inducers.


Introduction
In fluid machinery, when a flow accelerates and the local pressure drops roughly below the saturation vapor pressure of the liquid, a phenomenon called cavitation occurs, in which the liquid changes its phase to gas.Cavitation instability, an oscillation phenomenon of hydraulic machinery caused by cavitation, often occurs in liquid rocket turbopump inducers.Instability phenomena can be classified into cavitation surge (CS) [1] and rotating cavitation (RC) [2], and RC can be further classified into super-synchronous rotating cavitation (Super-S RC), synchronous rotating cavitation (Sync RC), and sub-synchronous rotating cavitation (Sub-S RC).RC and CS become a problem because RC causes axial whirling and CS causes pulsations of working fluid.
As methods to suppress cavitation instability, J-Groove [3] and the Backflow Restriction Step [4] have been studied, but while they are effective for certain instability phenomena, they have not been able to prevent them completely.In addition, issues remain from the viewpoints of simplicity of processing and miniaturization.Our research group has been working on the development of a simple method for the suppression in which slits are added to inducer blades.Three types of inducers with slits at different locations was investigated experimentally and numerically, and it was shown that vibration caused by cavitation instability was suppressed in each inducer [5][6][7][8].However, the suppression mechanism of the slit and the influence of the location of the slit on the instability phenomena are still unknown.
In this study, unsteady characteristics Super-S RC occurring in the three types of inducers with different slit locations and inducers without slits were compared experimentally.The frequency of cavitation and the cavity length in each inducer was compared and the suppression mechanism and the influence of the slit position were discussed.

Test Facility
The experiment was conducted using water cavitation tunnel at the Japan Aerospace Exploration Agency (JAXA) Kakuda Space Center.Figure 1 shows a schematic diagram of the experimental apparatus.The working fluid is water.The inducer is operated at a constant rotational speed by a 185 kW DC motor through a gearbox.The inlet pressure can be set optionally by a piston, and the flow rate  is regulated by a downstream flow control valve.The water temperature is maintained nearly constant by a heat exchanger.To visualize the inducer, the casing is made of acrylic resin, and a highspeed camera is used to capture images.Pressure fluctuations are measured at the inlet, outlet, and three points in between, as well as axial vibration using an axial displacement meter.In the present experiments, the rotational speed was set at 6000 rpm, the opening of the flow control valve was kept constant, and the inlet pressure was gradually reduced.The flow ratios /  were 1.15, 1.10, and 1.05.The parameters used in this study are shown below.Cavitation number is a dimensionless number that represents the ease of cavitation.The smaller the value is, the more likely cavitation occurs.
where   ,   , ,   present inlet static pressure, saturated vapor pressure, water density, and relative inflow velocity.The unsteady cavitation frequency   was used to evaluate the oscillatory characteristics of cavitation.This is the fluctuating frequency of individual cavitations as seen in the rotating system.  =   −   (2) where   ,   present rotation frequency of Super-S RC and inducer rotation frequency, respectively.

Test Inducer
The snapshot of an inducer without a slit (Inducer000) is shown in Figure 2 [9].The inducer used in the experiments is THK inducer which is modelled the inducer of a three-blade liquid oxygen turbopump and the diameter is 152 mm.An example of the slit inducer is shown in Figure 3.The locations of slits are different and slit shape has in common in each slit inducer.The different slit locations are shown in Figures 4 and 5, respectively.The location of the slit is divided into 5 equal sections of 120° from the leading edge of each blade tip to the throat.When the location is called 1 to 5 from upstream side, then Inducer035 has two slits at locations 3 and 5 on two blades among three.Inducer333 and Inducer555 are those with slits at locations 3 and 5 on all three blades, respectively.The slits are rectangular in shape with a width of 5 mm and a depth of 30 mm.

Cavity length
In this study, image processing developed by our group was used to investigate cavitation behaviour.Figure 6 shows the image processing procedure.The images visualized in this study show distortion from the actual dimensions as the distance from the axis center increases.Therefore, a development of the rotating cylindrical surface was created by cropping the axis center at an arbitrary width for each frame and arranging them in frame order.Binarization was performed to determine the area of cavitation.Cavitation was further extracted by processing to remove those caused by light reflection.Although the gray level threshold procedure [10] and other methods are used to determine the threshold for binarization, in this study, the cavity interface was defined by binarization with a threshold determined on the luminance value.
A narrow frame was set up along the blade of the development created by the image processing.The trailing edge of cavitation on the blade was extracted from the leading edge within the frame, and this was used as the cavity length in this study.

Occurrence of cavitation instabilities
Fast Fourier transform (FFT) analysis was performed for measured pressure on the casing in the middle of inducer and shaft vibration.The example of FFT analysis results for pressure fluctuations are shown in Figure 7 at higher flow condition /  = 1.15 because the difference between the inducer is most clear in the flow rate condition.In Figure 7, x-axis is frequency, y-axis is , and z-axis is the spectrum amplitude.The classification of the instability can be determined using the results of the FFT analysis.The rotational frequency of the shaft is 100 Hz, since the shaft rotational speed is 6000 rpm in the experiment.Super-S RC, Sync RC, and Sub-S RC are phenomena in which cavities appear to propagate at 1.1 ~ 1.3 times, 1 time, and 0.8 ~ 0.9 times the inducer rotation speed, respectively, when observed from a stationary frame.Therefore, the FFT analysis results show periodic pressure fluctuations at 110 ~ 130 Hz, 100 Hz, and 80 ~ 90 Hz, respectively in each RC.The RC also causes whirling motion so that not only the casing pressure but also the shaft vibration component appears.CS does not propagate because the cavities grow and contract in phase in all blades, but when severe CS occurs, it causes vibration of the entire system, and a component of 10 to 40 Hz is observed in the pressure fluctuations.
In the pressure fluctuations in Figure 7, the three slit inducers, especially Inducer333, have smaller overall spectrum amplitude than Inducer000.Additionally, in Inducer000 and Inducer035, Super-S RC, Sync RC, and CS occur, while Super-S RC and Sync RC occur in Inducer555, and only Super-S RC occurs in Inducer333 at /  = 1.15.The result indicates that Inducer333 is able to reduce the type of instabilities and suppress the fluctuation at higher flow rate condition.

Unsteady characteristics of cavitation
For each inducer, the range where Super-S RC occurs, as determined with respect to σ by the results of the FFT analysis of axial vibration, was extracted and compared in respective flow rate /  = 1.15, 1.10 and 1.05, as shown in Figure 8.For /  = 1.15,Inducer333 has the narrowest range of occurrence compared to the other inducers; Inducer035 also has a narrower range of occurrence than Inducer000; and Inducer555 has a range of occurrence not much different from that of Inducer000.For /  = 1.10 and 1.05, the range of the slit inducer is not much different from that of Inducer000 for the three types of slit inducers.The above results suggest that slit inducers are effective in suppressing the occurrence range of RC under higher flow conditions, especially Inducer333 has the greatest suppression effect.

Comparison by cavitation vibration characteristics
Figure 9 shows the results for /  = 1.15, 1.10, and 1.05, organized with frequency of unsteady cavitation   on the vertical axis and σ on the horizontal axis in the case in which Super-S RC occurs.At /  = 1.15, the slope of Inducer333 is steeper than that of Inducer000, indicating that   drops early according to decrease of σ and the Super-S RC ends earlier.In Inducer555 and Inducer035,   appears to be flat around σ = 0.040 ~ 0.055 and 0.050 ~ 0.055, respectively., then the end of Super-S RC delays in Inducer555 because of the standstill.Even at /  = 1.10, the slope of Inducer333 is steeper than that of Inducer000, indicating that   drops early and the Super-S RC ends.Similarly, Inducer555 and Inducer035 also showed a region where   is flat.At /  = 1.05, the frequency profile of Inducer333 and Inducer000 is almost the same, and Inducer555 has a slower but gradual change in the end of Super-S RC than Inducer000.
Although Inducer035, Inducer333 and Inducer555 were the fluctuation of Super-S RC was able to suppressed also in Inducer555, it was not so much as in Inducer333, pressure fluctuation of cavitation instabilities as shown in Figure 7, the mechanism of suppression is considered to be different between in Inducer333 and Inducer555 because of the different unsteady characteristics of cavitation are different between them as shown in Figure 9.Then, the cavity length in the case in which Super-S RC occurs is picket up and analyse in detail in next section.

Oscillation of cavity length
The cavity length in Super-S RC was determined using the image processing.Figure 10 shows the cavity length results for each inducer.For the slit inducers, the front and rear cavities were determined which occurs from around the leading edge of the blade and occurs from around the rear side of the slit, respectively.The location of the center of the slit was added to the graph by dashed line.For Inducer000, the cavity length oscillated with a phase difference in the order of Blade3, Blade2, Blade1 and again Blade3, which is the order of propagation of Super-S RC.In Inducer555, cavitation was found to grow just beyond the slit, and the front and rear cavities seem to oscillate continuously as one cavity, and the amplitude of oscillation is not suppressed.In Inducer333, it seems that the front and rear cavities oscillate independently in each blade, because the steady part of the rear cavity is large.Additionally, the amplitude of the oscillation of front cavity is drastically suppressed compared to that in Inducer555.Inducer035 has a slit at location 3 on blade 1, a slit at location 5 on blade 2, and no slit on blade 3.In Blade1 in Inducer035, front cavity disappears completely to the leading edge at a certain moment, which is the difference in Inducer333 although the slit location is same at 3. It means that the suppression effect of cavity oscillation by slit location 3 appears only until slits are opened on all blades at 3. Additionally, the oscillation of front and rear cavities are seems to independently in front and rear, which is a common feature of the slit location at 3 as observed in Inducer333.In Blade2 in Inducer035, the oscillation of the front cavity is suppressed compared to that in Inducer555.And the cavity length at the shortest moment in Blade 2 is longest among the three blades, it means that the slit location at 5 has larger suppression effect of cavity oscillation than that in location 3 in the asymmetric arrangement of the slits.
In the consequence, above results suggest that the symmetric location of slit at 3 is the most effective for the suppression of amplitude of cavity oscillation, and the mechanism of suppression of oscillation of Super-S RC in Inducer333 is that the front and rear cavities behave as independent short cavity, steady remained part of the unsteady cavity appears in both front and rear cavities and then the amplitude of oscillation of front and rear cavity length become small.However, it should be note that the slit location at 3 is not effective for the suppression of the cavity oscillation in the case of asymmetric arrangement of slits in the combination at 0, 3 and 5.

Conclusion
In this study, to elucidate the suppression mechanism of slit inducers on cavitation instability phenomena and the effect of the location of the slit on the instability phenomena, Super-S RC was compared with the experimental results using three types of inducers with different slit locations and an inducer without a slit.The results are summarized as follows.Firstly, inducer333was able to reduce the type of instabilities at higher flow rate condition.Secondly, slit inducers were effective in suppressing the occurrence range of super-S RC under higher flow rate conditions, especially Inducer333 has the greatest suppression effect.And lastly, the symmetric arrangement of slit at 3 was the most effective for the suppression of amplitude of cavity oscillation, and the mechanism of suppression of oscillation of Super-S RC in Inducer333 was clarified that the front and rear cavities behaved as independent short cavity and then the amplitude of oscillation of the cavity length became small.However, the slit location at 3 was not effective for the suppression of the cavity oscillation in the case of asymmetric arrangement of slits in the combination at 0, 3 and 5.
In the future, combinations with backflow reversal [4], which is effective in controlling backflow in low flow conditions, should be considered.

Figure 1 .
Figure 1.Water Cavitation Tunnel Test Facility at Kakuda Space Center of JAXA.

Figure 4 .
Slit location for each slit inducer.

Figure 8 .
Occurrence rang of Super-S RC.