Experiment of cavitating flow characteristics of inducer with inflow entrained air

To study the effect of inflow entrained non-condensable LOX tank pressurization gas on cavitating flow inside inducer pumps, a series of experiment were performed. The cavitation head breakdown point and cavitation instability characteristics of an inducer pump under different inlet gas volume fraction(IGVF) were investigated. It was found that head breakdown occurred at higher cavitation number under higher IGVF condition. Analysis of low frequency pulsating pressure suggested that cavitation surge was supressed by extra compressibility provided by non-condensable gas at operating point near head breakdown.


Introduction
Turbopump is one of the key parts in a liquid rocket engine (LRE), rotating at high speed, responsible for providing pressurized fuel for the thrust chamber.Under condition of low entrance pressure, pump head breakdown can happen due to cavitation inside impeller, potentially resulting disastrous launch failure.To counteract this, an inducer is installed upstream of the main impeller [1] [2].Additionally the fuel tank is pressurized with non-condensable gas such as helium to improve cavitation performance [3] [4].However, these methods may raise some new issues.
On one hand, the cavitation flow inside the inducer is complex, and is prone to induce cavitation instabilities.Extensive researches have been conducted on this topic.Tsujimoto et al. [5] conducted comprehensive experiments on LE-7 turbopump inducer to identify various kinds of cavitation instabilities and their corresponding occurrence range, including cavitation surge, rotating cavitation and back flow vortices cavitation.Zoladz [6] studied the frequency relevance between rotating cavitation and cavitation surge in Fastrac LOX turbopump inducer.Letteri et al. [7] and Xiang et al. [8] investigated the circumferential velocity and phase difference of rotating cavitation cloud by installing transducer array on the inducer housing.Li et al. [9] and Kim et al. [10] studied the effect of tip clearance on rotating cavitation and concluded that a larger tip clearance can help suppress rotating cavitation.Kikuta et al. [11], Wang et al. [12] and Franc et al. [13] carried out experiments and obtained the thermal effect of liquid nitrogen, hot water, and R-114 on cavitation instabilities.Due to advantages in revealing the flow inside of inducer, researchers also conducted numerical simulation to study cavitation instability.Yamanishi [14] analyzed the periodic and large non-periodic backflow vortices structure of inducer based on LES method.Iga et al [15].and Li et al [16].simulated the inception and the convection of cavitation instability in 2-D cascade and 3-D inducer separately.
On the other hand, when non-condensable gas is used for tank pressurization, non-condensable gas can mix with fuel and flow into the turbopump in microgravity condition or when the fuel is depleted.It is known that the pump head may deteriorate under liquid-gas two-phase inflow conditions [17].However, there are few studies on the effect of inflow entrained non-condensable gas on inducer cavitation performance.The existing investigations on cavitating flow with non-condensable gas injection were mostly conducted in flow path with simple geometries such as hydrofoil [18] [19], converging-diverging channel [20] and rotating body [21].Nevertheless, the interaction between noncondensable gas and vapor is so complicated that there is still no conclusive conclusion how the noncondensable gas affects the cavitating flow.
Considering that the flow path characteristicd of an inducer is also quite different from those simple hydraulic models, we developed a new test facility and perform a series of tests on the effect of inflow entrained air on the cavitation characteristics of a model two-blade inducer.This paper discusses the cavitation performance of the inducer, the development of cavitation pattern and the characteristics of cavitation surge under inflow air entrained conditions.The working fluid of liquid phase is water and gas phase air. Figure 1 shows the schematic of the test facility.A water reservoir with internal capacity of 6 m 3 is employed to store degassed water.A vacuum pump is connected to the water reservoir to lower the pressure inside the reservoir and to reduce the air dissolved in the water.Before each experiment, the amount of dissolved oxygen is controlled to be around 4 ppm.Compressed air is supplied and mixed with water upstream of the inducer inlet.The inducer housing (see Figure 2) is made of transparent acrylic glass enabling visualization of flow patterns upstream and inside the inducer.A model pump is located downstream of the inducer to provide the desired volumetric flow.The water-air two phase mixture is discharged from model pump into an open water tank to achieve air-water separation.A gate valve is installed between the open water tank and water reservoir.During experiments, the gate valve is closed to keep water in the open water tank, which still contains a small amount of incompletely removed air, from mixing with water in water reservoir.The test inducer (see Figure 3) is a typical constant-pitch inducer, and its design parameters are presented in Table 1.

Experiment method
In this study, two static pressure transducers with accuracy of ±0.5% full scale(0.1 Mpa) are located 2D upstream air-water mixer and 2D downstream volute outlet.Two electromagnet flow meter with uncertainty of ± 0.5% full scale(14 m 3 /h) are installed 10D upstream air-water mixer and 10D downstream volute outlet to measure the volumetric flow rate.In addition, two unsteady pressure transducer are placed 6D upstream air-water mixer and 6D downstream volute outlet to get unsteady characteristics.
Where, Q is the inlet total volumetric flow rate, Ω is the rotating speed of the inducer,   is the inducer blade tip diameter, pout and pin are static pressure measured by outlet and inlet pressure transducer, pv is the saturation vapor pressure ρ is the density of water.
Inlet gas volume fraction(IGVF) is used to determine the amount of air flow into the test section.
air air water Where, Qair and Qwater are volumetric flow rate of air and water at inducer inlet.The value of Qwater is given directly by inlet flow meter(range 16-160L/h accuracy ±2% of full scale).Due to pressure difference between air supplement and inducer inlet, Qair is calculated from reading of air flow meter Qm by universal gas law, where: Where, Tsup and psup are temperature and pressure of the compressed air; Tin and pin are temperature and pressure at the inducer inlet.
In order to record the flow pattern inside inducer, a high speed camera and high intensity LED lighting system is deployed, the movies are acquired at 4000 fps with resolution 1280×720 at exposure time of 1 μs.In this investigation, the rotational speed is set at Ω = 5000 r/min at which the feature Reynolds number of the inducer Re * = 9.2×10 5 >>10 5 ，and constant water reservoir temperature T = 28℃.In a single group cavitation experiment, the inlet mass flow rate and IGVF is kept constant and the suction pressure is decreased continuously.Especially the flow rate of compressed air is correspondingly adjusted as the suction pressure decreases.

No air-entrained cavitation performance
The cavitation performance curves of the model inducer without inlet entrained air are shown in Figure 4.As we can see, at higher cavitation number, the head coefficient remains unchanged for all three flow coefficients.When the cavitation number further decreases to less than about 0.3, the head coefficient slightly increases with the decrease of the cavitation number.However, when the cavitation number drops to a critical value, the head suddenly drops sharply, causing the inducer pump to experience head breakdown.The internal flow pattern under different flow coefficients and cavitation numbers captured by the high-speed camera are displayed in Figure 5.It is noticeable that the working fluid inside the inducer leaks through tip clearance from the pressure side to the suction side of the blade driven by pressure difference and that a tip leakage flow vortex is formed.Because of the low pressure at the vortex core, at relative high cavitation number operating point (Figure 5(a)(e)(i)), a rotating ribbon-shaped cavitation vortex is formed at blade tip.As the cavitation number decreases (Figure 5(b)(f)(j)), leakage vortex cavitation zone extends and connects with the shear layer cavitation zone, forming a triangular cavitation zone at the blade tip.As shown in Figure 5(c)(g)(k), when the cavitation number further decreases, the triangular cavitation zone at the blade tip further extends downstream.In addition, small-scale cavitation bubbles can be seen continuously detached from the tail of the cavitation zone.Although the cavitation number at those points (Figure 5(c)(g)(k)) is less than 0.1, there is no significant drop of pump head, and the cavitation zone inside the inducer appears as a white foam-like form.However, when the cavitation number further decreases to occurrence of pump head breakdown, as shown in Figure 5(d)(h)(l), signification flow pattern change is observed.The white foam-like leakage vortex cavitation and shear layer cavitation disappear, and meanwhile a clear and continuous interface appears between the cavitation zone and the liquid phase inside the inducer.The continuous cavitation area starts from leading edge, extends downstream along the inducer blade, and completely covers the inducer blade which is known as super-cavitation.At this point, the inducer outlet flow angle is changed by vapor phase covering inducer blade, and according to Euler equation in cascades, the head of the inducer drops.

Effect of inflow entrained air on Cavitation performance.
Figure 6, Figure 7, and Figure 8 respectively show the cavitation performance curves of the inducer pump at different IGVF and flow coefficients of Φ = 0.083, Φ = 0.071, and Φ = 0.059.It can be seen that at higher cavitation number, the head coefficient of the inducer pump significantly decreases when IGVF increases to higher than 2% to 2.5%.It is obvious that, at this operating point, there is no cavitation inside the centrifugal pump.According to previous studies [17] [22], due to the accumulation of non-condensable gas, gas pockets inception happens in the centrifugal pump, resulting in a sudden drop in the head of the centrifugal pump.That is to say, a gas lock phenomenon occurs at IGVF higher than 2.5%~3%.
Comparing the cavitation performance curves at different IGVF, it can be found that, the injection of non-condensable gas at the inlet will cause an increase in the head breakdown critical cavitation number, except for the condition of Φ = 0.059 and IGVF = 1%.This also means that the inflow entrained non-condensable gas reduces the erosion resistance performance of the inducer pump.In addition, for the two operating conditions of flow coefficient Φ = 0.083 and Φ = 0.071, there are two stepped increases in the head breakdown critical cavitation number, with the critical points being the first injection of non-condensable gas and the IGVF exceeding 2.5% to 3% respectively.
To further clarify this phenomenon, Figure 9 illustrates the relationship between the critical cavitation number (defined here as the point where the head drops by 20%, which is reasonable for LRE applications [23] ) and IGVF.The critical head breakdown cavitation number of each operating point is normalized based on the operating point without non-condensable gas at inlet.It is evident that the introduction of a small amount (1-2%) of inflow non-condensable gas results in an approximate 30~40% increase in the the critical head breakdown cavitation number.This phenomenon has not been extensively discussed in the literature.The author hypothesizes that the air enters the inducer in form of bubbles serving as cavitation nuclei for cavitation inception.Additionally, the entrained noncondensable gas expands at the low pressure zone in the vicinity of the leading edge.The combined effect of these factors increases the volume of the cavities (the sum of gas and vapor phase) inside inducer and promotes the flow pattern transition to super-cavitating flow, ultimately leading to premature head breakdown of the pump.In the case of IGVF surpassing about 2.5%-3% and the aforementioned inception of gas pockets inside the centrifugal pump, a second sharp increase in the critical cavitation number occurs.Analysis of the pressure fluctuations indicates system surging triggered by gas pocket inception.It is believed that the increase and discrete distribution of the critical cavitation number at high IGVF can be attribute to the hysteresis in the cavitation curve under inlet pressure pulsation.For investigation of the effect of non-condensable gas, high-speed visualization results were taken under different IGVF condition at flow coefficient Φ = 0.083, as shown in Figure 10.At cavitation number of points (a)(e)(i) in Figure 10, compared with operating point without inlet entrained air, the leakage vortex cavitation is prolonged and widened.This is due to the non-condensable gas being sucked into the vortex core.Since the non-condensable gas does not condense, it continues to extend downstream the leakage vortex until it spreads outwards under the effect of turbulent dispersion and the swinging of the leakage vortex tail.Similarly, at operating points with smaller cavitation numbers, as shown in Figure 10 (b)(f)(j), the cavitation cloud further extends downstream, and under the effect of the jet flow at the tail of the cavitation cloud, the mixed cavity is shedding more violently in the form of small bubbles [19].When the cavitation number drops further to below critical head breakdown cavitation number, the leakage vortex cavitation and shear layer cavitation inside the inducer disappear and transit to super-cavitation flow.This transition process is the same as the condition without inflow entrained non-condensable gas.This indicates that the inflow entrained non-condensable gas does not change the mechanism of head breakdown of the inducer, but promotes cavitation and leads to earlier head breakdown.

Effect of inflow entrained air on Cavitation instabilities.
During cavitation performance experiments, periodic back flow vortex cavitation is observed as shown in Figure 11.The power spectrum density of inlet pulsating cavitation and raw inlet pulsating pressure signal are shown in Figure 12 and Figure 13.The frequency f is normalized by frequency rotational speed 1/f0.Two peaks relating respectively to cavitation surge and backflow vortex cavitation are pointed out.As we can see, the 10 Hz peak corresponds to the low-frequency periodic evolution of flow pattern, and the 117 Hz peak corresponds to the 5-element backflow vortex cavitation which rotates at about 1400 rpm.It is believed that cavitation surge of 10 Hz results in the periodic evolution of flow pattern.It is interesting to find that the inlet pressure fluctuation and system vibration is suppressed under inflow air entrained condition.As it can be seen in Figure 13, the peak-to-peak value of pulsating pressure decreases by about 50% at IGVF = 1% compared to the condition without inflow entrained air under operating point Φ = 0.083, σ = 0.090.The main pulsation frequency at IGVF = 1% also decreases significantly.To further demonstrate this effect, the power spectrum density of inlet pulsating pressure at different IGVF is shown in Figure 14.As illustrated, at Φ = 0.083, σ = 0.090, as IGVF increases, the main frequency of cavitation surge shifts from 10 Hz at IGVF=0% to 8.5 Hz at IGVF = 1%, and further to 3 Hz at IGVF = 2%.Moreover, with the injection of non-condensable gas, the corresponding power spectral density of cavitation surge decreases to 0.1% of the condition without inflow entrained air.This corresponds to the aforementioned decrease in pulsating pressure peak to peak value.Similarly, under the condition of Φ = 0.071, σ = 0.068, the frequency of cavitation surge also decrease from 7.5 Hz to 2 Hz.These two phenomena indicate that the cavitation surge of the inducer pump is significantly suppressed when non-condensable gas is present at the inlet.This effect is quite similar to the effect of gas injection on suppressing instabilities in the draft tube of a hydraulic turbine [24] [25].However, gas injection in the draft tube of a hydraulic turbine does not shift the frequency of surge.This may indicate that the mechanism of gas injection suppressing instabilities in inducer pump is different from that in hydraulic turbine.The author believes that the inflow entrained non-condensable gas provides extra cavitation compliance and thus changes the frequency and strength of cavitation surge.To further illustrate the hypothesis, the system dynamic equation [26] [27] for cavitation surge is present.
Where, j is unit imaginary.ω is normalized complex frequency, whose real part stands for angular frequency of cavitation surge and imaginary part for decaying rate, h is the width of inducer cascade, L is the length of inlet pipe, ζ1 denotes loss coefficient of the inlet pipe, 1 Φ is average inlet flow coefficient, M and K are mass flow gain factor and cavitation compliance respectively defined as : Where, Vc is the cavity volume inside the inducer and i is the angle of attack at the inlet of inducer.It is obvious that mass flow gain factor M stands for changes in cavity volume with respect to the change of angle of attack or, we can say, flow coefficient and cavitation compliance K stands for changes in cavity volume withrespect to the change of inlet pressure.
Analysis points out that cavitation occurs when: As the loss coefficient ζ1 stays unchanged and cavitation number σ << 1.It can be concluded that the occurrence of cavitation surge is dominated by left hand side of the equation M/K.The variation of mass flow gain factor M, cavitation compliance K and steady state cavity length lcs/h and steady state cavity volume Vcs * /i with respect to variation of σ/2i in a two dimensional cascade is given in reference [28], as shown in Figure 16.It can be seen from Figure 16, when σ/2i < 0.2, the absolute values of the slopes of the two curves of lcs/h and Vcs * /i have increased significantly.This indicates that the length of cavity inside the cascade increases sharply as the inlet pressure slightly changes.This corresponds to the head breakdown process of inducer, during which the cavity extends to form a super-cavitating flow pattern.
Meanwhile, the value of M/K decreases sharply to below the value of   In addition, the sudden increase of cavitation compliance directly to leads to the sharp decrease of M/K, since the value of M increased at this procedure.This indicates that the cavitation surge is suppressed in the vicinity of head breakdown by the sudden increase of cavitation compliance K.
As aforementioned discussion, the inflow entrained non-condensable gas provides extra compressibility (or cavitation compliance K) and promotes cavitation, it can be concluded that the injected non-condensable gas can suppress the cavitation surge at certain cavitation number slightly higher than the critical head breakdown cavitation number.
In addition, the frequency n of cavitation surge is given in reference [26] [27]: Where, 1  is the average inlet flow angle, ut is the circumferential velocity of blade tip .From this equation, it is obvious that the injection of non-condensable gas can frequency of cavitation surge, which is consistent with the experiment result shown in Figure 14 and Figure 15.

Figure 2 .
Figure 2. Photograph of transparent test section.

Figure 4 .
Figure 4. Cavitation performance curve without inflow air entrained at different flow coefficient.

Figure 5 .
Figure 5. Cavity development under different cavitation number and flow coefficient.

Figure 16 .
Figure 16.Steady characteristics of partial cavity on two dimensional cascade.[28]4.ConclusionIn the present study, we performed a series of experiment on a new cavitation test rig compatible with air injection to investigate the effect of inflow entrained non-condensable gas on cavitation flow in a two blade inducer.The cavitation performance of the inducer pump under different IGVF condition was recorded.The cavitation pattern evolution was documented by high-speed visualization system.In addition, the steady and unsteady cavitation characteristics of the inducer with inflow air injection are carefully discussed in this paper.(a)The critical head breakdown cavitation number increases significantly under inflow noncondensable gas entrained condition.(b) The non-condensable gas gathers in the low pressure region driven by pressure divergence, resulting in the elongation of the leakage vortex cavitation zone and shear layer cavitation Regardless of the presence of non-condensable gas, head breakdown in the inducer pump is always accompanied by the transition of cavity pattern from foam-like cavity to super-cavity.(c) At low cavitation number approaching head breakdown, non-condensable gas significantly increases the cavitation compliance K, thereby reducing the frequency and intensity of possible cavitation surge.

Table 1
Main parameters of model inducer.