Huang Chen

Nick Doeller

Yuanchao Li

Joseph Katz
email: katz@jhu.edu

Measurements of the Flow and Pressure within an Axial Waterjet Pump during Cavitation Breakdown

Keywords:

The flow mechanisms causing cavitation breakdown in axial turbomachines have been a long-standing puzzle. Recently, observations in our laboratory have associated this phenomenon with blockage caused by perpendicular cavitating vortices (PCVs) in the blade tip region. In follow-up experiments, circumferential casing grooves (CGs) have been used to manipulate the tip leakage flow, intending to suppress the formation of PVCs. While the PCV formation is affected by a CG located near the trailing edge, it shows very little effect in alleviating the rapid performance deterioration during breakdown. Highspeed movies show that breakdown begins when a slight decrease in inlet pressure extends the attached/sheet cavitation on the blade suction side (SS) into the blade overlap region. At this phase, the area covered by the sheet cavitation initially fluctuates and then expands rapidly to cover a large portion of the surface. Stereoscopic particle image velocimetry (SPIV) measurements performed in noncavitating fractions of the passage show that this process involves a significant increase in liquid velocity and decrease in pressure along the blade pressure side (PS) in the overlap region. It appears that blockage caused by the cavitation on the SS accelerates the flow along the PS, which results in further reduction in pressure over the entire passage and further expansion of the cavitation on the SS. However, the pressure difference across the blade tip measured at mid span increases, compensating for the reduction in PS pressure. Hence, in some cases, the pump head increases slightly at the onset of breakdown. Further reduction in inlet pressure causes an increase in blockage in the tip region, but still a slight increase in velocity deeper in the passage. The reduced flowrate combined with a decrease in mid passage pressure results in a rapid drop in head as well. The CG is only partially effective in reducing the tip region blockage, presumed due to the inability of the shallow grooves to affect the cloud cavitation that fills the trailing edge tip region at this stage.

INTRODUCTION

Cavitation breakdown refers to the dramatic performance degradation of liquid handling axial turbomachines when working under inlet pressure conditions falling below some critical level. In spite of previous efforts, the mechanisms causing this phenomenon are still not understood. Theoretical analyses by Jakobsen [START_REF] Jakobsen | On the Mechanism of Head Breakdown in Cavitating Inducers[END_REF] concludes that the cavitation breakdown is related to a condensation shock caused by a rapid decrease in the speed of sound within the cloud cavitation. Based on experimental observations, Pearsall [START_REF] Pearsall | Design of Pump Impellers for Optimum Cavitation Performance[END_REF] shows that the performance breakdown happens when the attached cavitation on the SS surface extends into the blade overlap region "choking" the flow. Using RANS simulations, Lindau et al. [START_REF] Lindau | Modeling of Cavitating Flow through Waterjet Propulsors[END_REF] attribute the breakdown to choking that occurs when the attached cavitation reaches the blade trailing edge. More recently, Tan et al. [START_REF] Tan | Experimental Investigation of the Role of Large Scale Cavitating Vortical Structures in Performance Breakdown of an Axial Waterjet Pump[END_REF] show that the breakdown is related to the formation of large scale perpendicular cavitating vortices. These structures develop as the tip leakage vortex (TLV) entrains part of the cloud cavitation and reorients it in a direction that is perpendicular to the blade SS. When this interaction occurs in the blade overlap region, and the PCVs extend from the SS of one blade to the PS of the adjacent one, the passage is blocked in the tip region, causing the performance degradation.

Based on this perceived mechanism, preventing the formation of PCVs could presumably alleviate the rapid degradation during breakdown. Hence, we have tried to use circumferential casing grooves (CGs) to alter the trajectory of the TLV, and disengage it from the location of cloud cavitation. Circumferential casing grooves have already been used successfully to delay stall [START_REF] Takata | Stall Margin Improvement by Casing Treatment ---Its Mechanism and Effectiveness[END_REF][START_REF] Fujita | A Study on Configurations of Casing Treatment for Axial Flow Compressors[END_REF], and to suppress the instabilities associated with cavitation in axial turbomachines [START_REF] Kang | Suppression of Cavitation Instabilities in an Inducer by Circumferential Groove and Explanation of Higher Frequency Components[END_REF]. However, attempts by Choi et al. [START_REF] Choi | Suppression of Cavitation in Inducers by J-Grooves[END_REF] to use axial casing grooves to delay cavitation breakdown of an inducer have had limited success.

In ongoing experiments, performance tests and high-speed movies of cavitation are used for evaluating whether CGs affect the structure of cavitation and conditions for breakdown. Further insights are obtained by conducting velocity measurements in the non-cavitating part of rotor passage using SPIV under varying cavitation levels. The results are used for estimating the mean pressure distribution close to the entrance of the blade overlap region. The results confirm that cavitation breakdown process begins when the SS attached cavitation expands into the blade overlap region. Initially, the axial velocity increases and the pressure decreases along the blade PS, presumably due to the cavitation-induced blockage at the confined overlap zone. At this stage, rapid expansion of the SS cavitation compensates for the reduction in PS pressure, causing, in some cases, an increase in pump head [START_REF] Chesnakas | Performance Evaluation of the ONR Axial Waterjet 2 (AxWJ-2)[END_REF]. The flowrate and head starts to decrease after further reduction in cavitation index, which increase the cavitationinduced blockage in the tip region, and reduces the PS pressure deeper in the passage. The CGs fail to change the tip region blockage significantly, presumably due to the limited ability of the shallow groove to affect the cloud cavitation when it expands over the entire tip region of the passage.

EXPERIMENTAL SETUP

The axial waterjet pump (AxWJ-2) used in the current study has been designed by Michael et al. [START_REF] Michael | Design of the ONR AxWJ-2 Axial Flow Water Jet Pump[END_REF], and used already in several recent studies. Figure 1a provides a sketch of this pump and Table 1 summarizes the relevant parameters. It has 6 rotor blades with constant diameter of 305.2 mm and 8 stator blades, which taper to a 213.4 mm nozzle. Detailed descriptions of the pump and cavitation phenomena occurring in it can be found in [START_REF] Tan | Experimental Investigation of the Role of Large Scale Cavitating Vortical Structures in Performance Breakdown of an Axial Waterjet Pump[END_REF][START_REF] Chesnakas | Performance Evaluation of the ONR Axial Waterjet 2 (AxWJ-2)[END_REF][START_REF] Michael | Design of the ONR AxWJ-2 Axial Flow Water Jet Pump[END_REF][START_REF] Tan | The Three Dimensional Flow Structure and Turbulence in the Tip Region of an Axial Flow Compressor[END_REF][START_REF] Chen | Effects of Circumferential Grooves on the Cavitation and Performance of an Axial Waterjet Pump[END_REF]. When installed in the JHU closed-loop refractive index matched facility [START_REF] Tan | Visualization and Time Resolved PIV Measurements of the Flow in the Tip Region of a Subsonic Compressor Rotor[END_REF], the measured tip clearance without grooves is 0.7mm (0.0046R). The facility includes a half-full tank connected to high-pressure gas and a vacuum pump located above the loop to control the mean pressure. Cooling jackets surrounding some of the pipe sections of the main loop are used for controlling the liquid temperature. The working fluid is a concentrated aqueous sodium iodide solution, whose specific gravity is 1.8, its kinematic viscosity is 1.1×10 -6 m 2 s -1

for the current temperatures, and the vapor pressure, 1.2 kPa, is slightly lower than that of the pure water [START_REF] Tan | Experimental Investigation of the Role of Large Scale Cavitating Vortical Structures in Performance Breakdown of an Axial Waterjet Pump[END_REF][START_REF] Patil | Thermodynamic properties of aqueous electrolyte solutions. 2. Vapor pressure of aqueous solutions of sodium bromide, sodium iodide, potassium chloride, potassium bromide, potassium iodide, rubidium chloride, cesium chloride, cesium bromide, cesium iodide[END_REF]. The refractive index of this solution matches that of the acrylic pump housing and inserts, allowing us to perform optical measurements in the rotor passage without distortions. The present rotor is made of Aluminum, the very same rotor discussed in [START_REF] Chesnakas | Performance Evaluation of the ONR Axial Waterjet 2 (AxWJ-2)[END_REF]. It should be noted that the rotor has been designed to delay cavitation breakdown by establishing a nearly uniform pressure distribution along the blade SS [START_REF] Michael | Design of the ONR AxWJ-2 Axial Flow Water Jet Pump[END_REF]. Circumferential casing grooves at varying locations are created by installing a combination of 6.35mm thick transparent acrylic inserts in slots surrounding the rotor, as illustrated in Fig. 1a. As shown in Fig. 1b, three CG configurations have been tested, with CG1 centered at the blade leading edge, CG2 located near the mid-chord, and CG3 covering the trailing edge. All grooves have the same width of 30.4mm (0.11c) and depth of 6.35mm (0.04R). Highspeed images of cavitation are recorded by a PCO ® dimax high-speed camera at 1800 frames per second, corresponding to 20 frames per blade passing when the rotor is operating at a constant speed of 900 rpm.

The setup for SPIV measurement is shown in Figs. 1 and2. The images are recorded by a pair of 2048×2048 pixels PCO ® 2000 interline transfer CCD cameras located on different sides of the laser sheet. Optical distortions are minimized by viewing the sample area through prisms with outer surface aligned perpendicularly to the lens axis. The flow is seeded with 13µm, silver-coated, hollow spherical particles that have a specific density of 1.6, slightly less than that of the fluid. To characterize the effect of cavitation on the pump performance, the SPIV measurements focus on the flow along PS deep inside the blade and the non-cavitating parts of tip region. The laser sheet is orientated to minimize the detrimental effects of light scattered by the cavitation. It is also almost perpendicular to the SS surface at the entrance to the blade overlap region. To define the orientation and location of this sheet, we use a general coordinate system (r, θ, z) that has an origin located at the pump center, and coincides with the plane of the leading edge of the blade. The coordinate system associated with the sample plane is (x', y', z'), where x' and y' are located within the illuminated area, and z' is inclined by β=40° to the z direction (Figs. 1a and2c). As illustrated in Figs. 2c andd, the origin of (x', y', z') is located at r/R=0.995, θ PIV =-37.5° (θ=0 is the vertical direction), and z=0. Figures 2a andb, which look at the sample area from the back, show that in this arrangement, the intersection of the bottom of the laser sample area with the blade PS is located more downstream of the LE than the top part. By maintaining the laser sheet in the same location, but recording data for different blade orientations, we can obtain data in different planes relative to the blade leading edge. The measurements have been performed in 4 planes. For each one, 200 images pairs have been record at a series of cavitation indices.

Calibration of the SPIV system follows a two-step process described by Wieneke [START_REF] Wieneke | Stereo-PIV Using Self-Calibration on Particle Images[END_REF]. As discussed in [START_REF] Chen | Visualizations of Flow Structures in the Rotor Passage of an Axial Compressor at the Onset of Stall[END_REF], the initial calibration step is performed by raising the entire system and traversing a target in a small chamber containing the same fluid. The second, a so-called self-calibration is carried out using particle images acquired in the actual sample area, after lowering the system back. Image pre-processing consists of applying background removal and modified histogram equalization algorithms [START_REF] Roth | Five Techniques for Increasing the Speed and Accuracy of PIV Interrogation[END_REF] to achieve uniform brightness of the particles. The FFT based cross-correlations performed using a commercial software package LaVision ® Davis, followed by application of the universal outlier detection algorithm [START_REF] Westerweel | Universal Outlier Detection for PIV Data[END_REF]. The sample area size is 75.3×114.8 mm 2 , and the vector spacing is 0.41 mm for 24×24 pixels 2 interrogation windows with 50% overlap. Due to obstruction by the TLV cavitation, only part of the PIV image is available, but it still allows us to examine the flow and pressure distributions along the pressure side of the blade, from the casing, r/R=1.0, down to r/R=0.66, which represents 50% of the rotor blade span. As shown in Fig. 2b, the "triangular" field of view (FOV) is bounded by the blade PS to the left and the casing wall on the top. The SPIV measurements have been performed on the baseline case without grooves and CG3 case, with the groove located near the blade trailing edge.

All the velocity components have been transformed from the laser sheet coordinate system (u, v, w) into the global cylindrical system (u r , u θ , u z ), with the corresponding ensemble averages components denoted as (U r , U θ , U z ). The coordinates and vectors transformations are as follows:

2 2 ( c o s ) ( c o s s i n s i n ) r P I V r P I V r x R y z R θ β β θ ʹ ʹ ʹ = + + + - (1)
1 cos sin sin tan cos

r P I V r P I V y z R x R β β θ θ θ - ʹ ʹ + - = ʹ + (2) sin cos z y z β β ʹ ʹ = - + (3) cos ( cos sin ) sin r u u v w θ β β θ = + + (4) sin ( cos sin )cos u u v w θ θ β β θ = - + + (5) sin cos z u v w β β = - + (6)
A sample distribution of axial velocity magnitude (|U z |/U T ) prior to cavitation breakdown is presented in Fig. 2b. It shows the axial velocity deficit near the tip occurring due to combined effects of the casing boundary layer, TLV cavitation induced blockage, and proximity to the blade leading edge, as well as the increase in velocity with increasing distance from the PS. In this case, the sample plane coincides with the leading edge of the blade tip. However, most of the data presented in this paper corresponds to a plane that intersects with the blade tip at s/c=0.065, i.e. inside the passage. Here, s is the distance from the leading edge along the blade tip chord.

RESULTS

Pump performance

Figure 3 shows the flowrate-head curves for all the tested cases. The test results conducted in NSWC [START_REF] Chesnakas | Performance Evaluation of the ONR Axial Waterjet 2 (AxWJ-2)[END_REF] using the same rotor are also included for comparison. Based on NSWC results, the pump efficiency peaks at 89% at φ=0.76, where φ is the flowrate coefficient, defined as

3 Q nD ϕ = (7)
Here, Q is the volumetric flowrate, n is the rotor angular speed in revolutions per second, and D is the diameter of the inlet. The flowrate is calculated by integrating the velocity profile acquired by translating a Pitot tube in the radial direction far downstream of the pump. The total head rise coefficient is defined as

2 2 ,2 ,1 2 1 2 2 2 s s Q Q p p A A n D ρ ψ ρ ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ ⎢ ⎥ - + - ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ = (8)
where, as illustrated in Fig. 1a, the subscripts 1 and 2 refer to the planes where the pressure taps are located, A is the through-flow area and p s is the measured static pressure. The static head rise, Δp S = p s,2 -p s,1 , is measured directly by a differential pressure transducer connected to the pressure taps. To account for the variations of the flow downstream of the stator, p s,2 is the average reading of five circumferentially distributed pressure ports. The absolute static pressure at the entrance to the pump (p s,1 at z/R=1. [START_REF] Chen | Visualizations of Flow Structures in the Rotor Passage of an Axial Compressor at the Onset of Stall[END_REF]) is measured by a monometer and used for calculating the cavitation index

where p v is the vapor pressure of the liquid. The uncertainties associated with the head rise and flowrate measurements are around 1.2% and 1.7%, respectively. As shown in Fig. 3, for φ=0.65-0.8, the casing grooves cause a 1%-2% reduction in total head rise compared to the baseline values. The untreated performance curve peaks at φ=0.61, suggesting that stall might occur under this condition. The present CGs do not seem to delay the onset of stall, and in fact, cause a maximum of about 4% decrease in performance at low flowrates. While other studies have shown that circumferential grooves cause a delay in the onset of stall [START_REF] Takata | Stall Margin Improvement by Casing Treatment ---Its Mechanism and Effectiveness[END_REF][START_REF] Fujita | A Study on Configurations of Casing Treatment for Axial Flow Compressors[END_REF], the present CGs do not, presumably due to their shallow depths.

To test the effectiveness of the CGs on delaying cavitation breakdown, the mean pressure in the facility is gradually reduced, and the pump performance is measured after running the machine at the same condition for more than 40s. The results are summarized in Fig. 4. The tests are carried out at two different initial flowrates, one starting from φ=0.74-0.75 while the other one starting from φ=0.67-0.68. For all the cases and flowrates, the total head drops abruptly at around σ=0.17, indicating that the CGs do not change the breakdown cavitation index noticeably. Furthermore, the breakdown cavitation index is not affected by the flowrate, hence the blade load distribution. Tests performed by Kang et al. [START_REF] Kang | Suppression of Cavitation Instabilities in an Inducer by Circumferential Groove and Explanation of Higher Frequency Components[END_REF] for an inducer with CG at the LE have shown similar trends. In their study, although the primary goal of using the CGs to suppress the instabilities caused by cavitation is achieved, the grooves do not appear to have a significant impact on delaying the cavitation breakdown.

Apparence of cavitation

Detailed descriptions of the appearance of cavitation for the different CG cases are provided in [START_REF] Chen | Effects of Circumferential Grooves on the Cavitation and Performance of an Axial Waterjet Pump[END_REF], and only samples for CG3 are presented in this paper. Briefly, at high cavitation indices, well above breakdown, CG1&2 trap the TLV, altering its interactions with the cloud cavitation. However, upon further reduction in inlet pressure, but still before breakdown, part of the TLV "escapes" from the grooves, resulting in tip region cavitation phenomena that are similar to those associated with the baseline case. Figure 5 compares the evolution of cavitation for the baseline and CG3 cases with decreasing σ. The cavitation indices are chosen to represent the flow conditions that are just before and after cavitation breakdown. Before breakdown (Figs. 5a&d), the extent of TLV cavitation and the area covered by attached cavitation on the blade SS for the baseline and CG3 appear to be similar. In both cases, entrainment and re-orientation of the cloud cavitation by the TLV generate the small-scale PCVs indicated on the figure. Under this condition, the attached cavitation has not yet propagated into the blade overlap region. The only effect of CG3 is formation of an additional cavitating vortical structure inside the groove, close to the trailing edge. Similar phenomena have been observed for the other grooves, but at different locations. In contrast, once breakdown occurs, substantial fraction of the blade SS within the overlap region is covered by cavitation (Figs. 5b, c, e andf). A sample time sequence demonstrating the transition between these states is presented for the baseline case in Fig. 6. Here, the cavitation index (σ=0.171) is only slightly lower than that of Figure 5a (σ=0.186), corresponding of an absolute pressure difference of 2.8 kPa. The attached cavitation propagates into the blade overlap region and the fraction of SS area covered by it oscillates at high amplitude. All the images in Fig. 6 correspond to the same mean flow condition, but while a small area is covered by cavitation at t=t 0 and t=t 0 +3Δt (Figs. 6a&d), most of the lower blade is covered at t=t 0 +Δt and t 0 +2Δt (Figs. 6b &c). It should be noted that at this condition, which is referred to in the rest of this paper as "breakdown onset", the flowrate still has not changed, and the head rise increases slightly. 5b). While expansion of the attached cavitation into the overlap region occurs for the CG3 case as well, its chordwise extent is lower than that in the baseline case, and the formation of PCVs near the blade trailing edge is suppressed (Fig. 5e). Yet, the performance barely improves, as evidenced by the slightly higher head rise occurring at a lower cavitation index (σ=0.158) in Fig. 5e. This observation challenges the claim that the PCVs play primary roles in the cavitation breakdown, as proposed by Tan et al. [START_REF] Tan | Experimental Investigation of the Role of Large Scale Cavitating Vortical Structures in Performance Breakdown of an Axial Waterjet Pump[END_REF]. Further minor reduction in cavitation index causes substantial deterioration of both the flow and head coefficients for both the baseline and CG3 cases (Figs. 5c&f). Here, the PCVs form for the CG3 case as well, demonstrating that this groove is not effective in suppressing them.

Velocity and pressure distributions

SPIV measurements have been conducted at conditions corresponding to φ=0.74-0.75 prior to breakdown at five different cavitation indices. Figure 7 shows the distribution of axial velocity magnitude (|U z |/U T ) for the baseline case. The five conditions are: (i) high pressure when cavitation is suppressed (σ=0.77); (ii) close to, but before breakdown (σ=0.180); (iii) "breakdown onset", when attached cavitation oscillates and the head rise peaks (σ=0.170); (iv) "early breakdown" when the performance of the machine already deteriorates (σ=0.166); and (v) "deep breakdown" (σ=0.161), when the head coefficient is 9% lower than that without cavitation. For convenience, each velocity distribution is accompanied with the corresponding point on head coefficient plot.

At σ=0.77, |U z | is low near the endwall casing and along the PS, increasing with decreasing distance from the blade SS. The reduced velocity along the casing is associated with the casing boundary layer as well as other phenomena, such as tip leakage flows, TLV formation, etc. (e.g., [START_REF] Khalid | Endwall Blockage in Axial Compressors[END_REF][START_REF] Stauter | Measurement of the Three-Dimensional Tip Region Flowfield in an Axial Compressor[END_REF][START_REF] Bindon | The Measurement and Formation of Tip Clearance Loss[END_REF]). The low velocity along the PS is inherent. Due to partial visual blockage by the tip region cavitation, the FOVs for the other σ are smaller, as indicated by the dotted line. At σ=0.180, |U z | increases slightly essentially everywhere. Further reduction in pressure to σ=0.170 causes a substantial increase in velocity over almost the entire FOV, including the vicinity of the PS, but not in the tip region. For example, along the PS and at x'/R=-0.35, there is a 6% increase, from 0.395U T to 0.420U T . Since the overall flowrate in the machine remains essentially unchanged, the increase in axial velocity along the PS is likely to be a result of (cavitation-induced) blockage in other regions of the rotor passage, predominantly along the SS. Recall that the visual observations indicate that at σ=0.170, the attached cavitation oscillates and extends rapidly into the blade overlap region (e.g, Figs. 6a&d), supporting the argument about the effect of cavitation-induced blockage. Further slight decrease in cavitation index to σ=0.166, when the flowrate and the head rise start to drop, the axial velocity decreases in the outer parts of the PS and in the tip region, but keeps on increasing along inner parts of the PS, at x'/R<-0.2. When the cavitation index is lowered further to σ=0.161, there is a reduction in axial flow over the entire FOV, including the PS, but especially along the endwall casing. The latter is presumably associated with the cavitation, including the cavitating TLV, the cloud cavitation near the trailing edge, and the large PCVs evident in Figs. 5b &c.

Figure 8 shows the evolution of circumferential velocity for the baseline case at three different σ. The magnitude of U θ is much smaller than |U z |, but it decreases by about 50% at breakdown onset (σ=0.170), and keeps on decreasing as the cavitation index is reduced further. Note that a decrease in U θ implies higher velocity relative to the blade (less swirl). The corresponding evolution of the radial velocity component is shown in Fig. 9. The values are quite low almost everywhere, and decrease with decreasing cavitation index. During the transition from σ=0.180 to σ=0.170, the combined effects of rapidly increasing |U z | and decreasing U θ , the latter implying that in the rotor reference frame (Ωr-U θ ) increases, result in nearly unchanged flow angle relative to the blade (not shown). Hence, the phenomena occurring during breakdown onset do not involve substantial changes to the incidence angle.

Knowledge of the velocity magnitude upstream and within the rotor passage enables us to use the Bernoulli equation to estimate the pressure distributions along the blade PS. Neglecting effects of viscous and Reynolds stresses and assuming a steady flow in the rotor reference frame, along a streamline

2 2 ( ) 2 2 p r W const ρ Ω + - = ( 10
)
where W is the speed of the fluid in the rotor reference frame [START_REF] Lyman | On the Conservation of Rothalpy in Turbomachines[END_REF][START_REF] Lakshminarayana | Fluid Dynamics and Heat Transfer of Turbomachinery[END_REF]. In the current case, considering that U r is very small (Fig. 9), the radial displacement of the streamlines is negligible, and the (Ωr) 2 /2 is cancelled. Hence, the timeaveraged pressure in the passage is where U z,in is the measured axial velocity at z/R=0.65, well upstream of the rotor LE [START_REF] Tan | Common Features in the Structure of Tip Leakage Flows[END_REF]. Since the inlet condition have only been recorded at φ=0.76, the U z,in profiles at other flowrates are estimated by assuming the same radial distributions far upstream of the rotor, and scaling the velocity magnitude accordingly. Since the present analysis focuses on the effect of cavitation on the performance of the machine, in addition to σ, we also define the local cavitation index Its distribution along the PS of the blade will be used as a representative of the pressure difference across the blade when the SS is covered by attached cavitation. The distributions σ local for the baseline case are shown in Fig. 10.

As is evident, the slight decrease in σ from 0.18 to 0.17 (breakdown onset) causes an order of magnitude larger decrease in σ local everywhere in the passage. This drastic reduction in pressure is associated with the increase in velocity magnitude in the rotor reference frame. Further reduction in cavitation index to σ=0.166 causes further significant decrease in pressure along the inner part of the PS, but not as the same rate as that occurring between σ=0.18 to 0.17. In the rest of the passage, especially in the tip region, the pressure hardly changes. Between σ =0.166 to 0.161, the latter corresponding "deep breakdown", the pressure distribution changes very little across the FOV, but there is a decrease in the PS pressure at low x'/R. downstream, as shown in Fig. 5e. Figure 13 shows three sample distributions of σ local for CG3. Accounting for the differences in σ, the pre-breakdown and breakdown-onset pressure distributions are not significantly different from those of the baseline in Fig. 10. Accordingly, the pressure coefficients are also marginally different. However, there is a difference at early breakdown (σ=0.164), where the pressure over the entire area is higher than that at σ=0.166 or 0.161 for the baseline data. The difference is significant, being higher by e.g. 0.04-0.06 along the PS of the CG3 distribution. Accordingly, the corresponding overall pressure coefficient of the CG3 setup is markedly higher, by 0.1-0.24, for similar flowrates. Hence, once the exact conditions are compared, adding the casing groves delays the rapid deterioration of PS pressure slightly and the overall performance in a more significant manner. However, this advantage is limited to a narrow range of flow coefficients and cannot be maintained as σ is decreased further (Figs. 4 and5). The implications of these findings are addressed in the following discussion.

Sample comparisons between the baseline and CG3 flow fields

DISCUSSION

In this section, we combine the present and previous findings about cavitation breakdown to introduce a plausible explanation for the mechanisms involved. The precursor for cavitation breakdown, referred as breakdown onset in the current paper, occurs when the attached cavitation on the blade SS starts to expand into the blade overlap region, and the area covered by it fluctuates with large amplitudes (Fig. 6). This phenomenon has been observed for all the tested cases, and is consistent with the condition for breakdown observed for other machines by Pearsall et al. [START_REF] Pearsall | Design of Pump Impellers for Optimum Cavitation Performance[END_REF]. At this cavitation index (σ=0.170 for the baseline case), the pump flowrate does not change, and the head increases slightly. The latter trend is consistent with simulations performed for the same pump geometry [START_REF] Lindau | Modeling of Cavitating Flow through Waterjet Propulsors[END_REF] and for different machines [START_REF] Guinard | An Experimental Study of Axial Flow Pump Cavitation[END_REF][START_REF] Stripling | Cavitation in Turbo Pumps-Part 1[END_REF]. Yet, the SPIV measurements show that during breakdown onset, the mean axial velocity increases by 5-6% (Figs. 7&11) and the mean pressure decreases by more than 25% along the PS of the blade near the entrance to the overlap region (Fig. 10). The increase in axial velocity without a change in flowrate is presumably associated with a reduction in the through-flow area caused by the attached cavitation along the SS of the neighboring blade. The decrease in pressure over the entire entrance area is likely to reduce the pressure along the SS as well, resulting in a rapid expansion of the attached cavitation deep into the overlap region.

While the decrease in PS pressure concurrently with an increase in total head appears to be puzzling, it can be explained as follows: Measurements of pressure distributions on the surface of a cavitating 2D hydrofoil by Shen & Dimotakis [START_REF] Shen | The Influence of Surface Cavitation on Hydrodynamic Forces[END_REF] show that the pressure inside the cavitation area on the SS is very close to the vapor pressure, and recovers to the fully wetted values only downstream of the cloud cavitation. Hence, in parts of the SS, the pressure is lower than that in a fully wetted flow. For this isolated foil, the pressure along the PS is not effected significantly by the cavitation, at least as long as the SS cavitation does not reach the foil trailing edge. Consequently, partial cavitation actually increases the lift force. In the current pump, although PS pressure drops, it is accompanied by a rapid expansion of the SS cavitation, and area where the pressure is equal to the vapor pressure. Hence, the blade loading might still increase in spite of the decreases in PS pressure. Evidence supporting this argument can be obtained from the endwall casing pressure measurements in the same machine by Tan et al. [START_REF] Tan | Experimental Investigation of the Role of Large Scale Cavitating Vortical Structures in Performance Breakdown of an Axial Waterjet Pump[END_REF] using two, fixed, flush-mounted piezoelectric transducers. The location of these transducers is indicated in Fig. 14a Figure 14c shows the effect of reducing σ on the pressure difference across the blade for both transducers along with the corresponding pump performance. As is evident, near the LE (transducer No. 1), the pressure difference decreases with decreasing σ, with ∂ΔC p /∂σ~1 at 0.175<σ<0.25. Under these conditions, the SS attached cavitation already extends to Transducer No. 1, hence the SS pressure is expected to be nearly constant and close to the vapor pressure. The slope of the ΔC p line implies that the PS pressure decreases at the same rate as the inlet pressure, i.e. p ps -p in remains unchanged. The corresponding performance and flowrate remain nearly unchanged at 0.175<σ<0.25, indicating that the decrease of blade loading near the LE must be compensated by an increase in blade loading somewhere else along the blade. According to Shen & Dimotakis [START_REF] Shen | The Influence of Surface Cavitation on Hydrodynamic Forces[END_REF], the decrease in blade loading near the leading edge is compensated by an increase in pressure difference across the blade at higher chord fractions, where the pressure in the cavitation-covered SS remains low. Indeed, as the SS cavitation expands to Transducer no. 2 at the breakdown onset conditions, ΔC p (blade loading) increases at mid-chord, while drastically decreasing near the leading edge, consistent with the present observations. Figure 14b indicates that the increase in ΔC p2 is mostly attributable to the decrease in SS pressure. In Tan et al. [START_REF] Tan | Experimental Investigation of the Role of Large Scale Cavitating Vortical Structures in Performance Breakdown of an Axial Waterjet Pump[END_REF], this decrease is associated with formation of PCVs at the same location. The rapid decrease in ΔC p1 is attributed in this paper to cavitation-induced blockage once the attached cavitation reaches the blade overlap region. Considering that breakdown onset involves rapid expansion of the SS area covered by cavitation, i.e. has a vapor pressure, a similar increase in ΔC p most likely occurs over a broad fraction of the blade. This process might be the primary reason for the brief increase in total head at σ=0.17. Although the cavitationinduced blockage reduced the PS pressure near the leading edge, the corresponding rapid expansion of the SS cavitation appears to make up for it.

While we cannot provide a substantiated explanation for the oscillation in the area covered by cavitation, once could still postulate about possible reasons. The rapid expansion of the SS cavitation is most likely a result of the cavitationinduced blockage, and the presently-observed corresponding increase in velocity and decrease in pressure over the entire wetted fraction of the passage (Fig. 10). However, the expansion of the SS cavitation increases the pump performance, i.e. the pressure in the vicinity of the blade trailing edge. This increase is likely to shrink the area covered by cavitation, hence, reduce the total head and pressure in the passage. Consequently, the area covered by cavitation oscillates.

Upon further reduction in cavitation index, the head rise drops sharply, consistent with the blade loading reduction both at the LE and at mid chord (Fig. 14c). At deep breakdown, i.e. σ=0.161, the attached cavitation of the baseline case reaches the blade trailing edge (Fig. 5b) and stops oscillating, while the pressure along the LE PS remains nearly unchanged (Fig. 10). This trend is consistent with the plateau in ΔC p1 at σ<0.165 in Fig. 14c. However, the blade loading near mid chord keeps on decreasing, at least in the tip region, contributing to the performance loss. In Tan et al. [START_REF] Tan | Experimental Investigation of the Role of Large Scale Cavitating Vortical Structures in Performance Breakdown of an Axial Waterjet Pump[END_REF], the latter trend is attributed to the cavitation-induced blockage as the entire tip region becomes occupied by the PCVs (Fig. 5c). The increased tip blockage is consistent with the persistent decrease in |U z | near the LE, as shown in Fig. 7.

Finally, one has to answer why the grooves have a limited effect on the breakdown process (consistent with [START_REF] Choi | Suppression of Cavitation in Inducers by J-Grooves[END_REF]), in spite of the fact that they suppress the formation of PCVs and improve the machine performance during early phases of breakdown (σ ≥0.158), as shown in Figs. 5b&e. The PCVs reappear and the performance deteriorates rapidly upon further reduction in cavitation index, reaching conditions that are similar to those of the machine without grooves (Figs. 4, and5e&f). The groove does reduce the blockage in the tip region under deep breakdown (Fig. 12), but apparently, this effect is not sufficient for causing a significant delay the cavitation index corresponding to the breakdown. There are several possible reasons for this observation. First, away from the tip, the increase in axial velocity, decrease in PS pressure, and rapid expansion of the attached cavitation caused by cavitation-induced blockage when it reaches the blade overlap region during cavitation breakdown onset can be seen in both cases (Figs. 10111213). Hence, the effect of the groove is limited to the tip region. Second, for σ<0.16, the reappearance of the PCVs indicates that the present groove is no longer effective, resulting in a growing tip region blockage. Larger or different geometry grooves might have been more effective, but it is not clear to what extent. It should be noted that in addition to the PCVs, the SS tip near the trailing edge under the PCVs is occupied by cloud cavitation as well. Hence, suppressing the PCVs might not be sufficient, requiring additional means to alleviate the effect of the cloud cavitation.

CONCLUSIONS

Performance tests, high-speed imaging and SPIV measurements have been carried out to study the flow structures and pressure within the rotor passage of an axial waterjet pump during cavitation breakdown. Prior study [START_REF] Tan | Experimental Investigation of the Role of Large Scale Cavitating Vortical Structures in Performance Breakdown of an Axial Waterjet Pump[END_REF] in our lab has attributed this phenomenon to the formation of large scale perpendicular cavitating vortices, which block the flow in the tip region. In recent experiments, we have tried to use circumferential grooves placed in several axial locations to manipulate the tip leakage flow, hoping to affect the PCV formation. These observations show that when the CG is located near the blade trailing edge, using the so-called CG3, the PCV formation is delayed. However, it causes only a limited effect on the conditions for cavitation breakdown, in agreement with previous studies [START_REF] Choi | Suppression of Cavitation in Inducers by J-Grooves[END_REF]. Consistent with Pearsall [START_REF] Pearsall | Design of Pump Impellers for Optimum Cavitation Performance[END_REF], the onset of breakdown occurs when the attached cavitation on the blade SS reaches the blade overlap region, with or without casing grooves, and at all flowrates. Just before the rapid performance degradation, the attached cavitation expands rapidly with large oscillations in the SS area covered by it. Blockage to the through-flow area at the entrance to the overlap region accelerates the flow in the remaining area, causing a significant (~25%) reduction to the pressure along the blade PS. This pressure reduction presumably causes further expansion of the attached cavitation on the SS. At this stage, the performance is not degraded yet, and in-fact the pump head even increases slightly, consistent with RANS simulations of the same pump performed by Kim and Schroeder [START_REF] Kim | Numerical Study of Thrust-Breakdown Due to Cavitation on a Hydrofoil , a Propeller , and a Waterjet[END_REF] and Lindau et al. [START_REF] Lindau | Modeling of Cavitating Flow through Waterjet Propulsors[END_REF] as well as numerous studies performed in other machines. From the measurements of pressure difference across the blade tip at mid passage, it appears that reduction in the SS pressure as the attached cavitation expands rapidly compensates for the reduction in PS pressure, causing an increase in overall performance. The resulting increase in pressure rise across the blade passage might oppose the expansion of the SS cavitation area, causing the high amplitude oscillation.

Further slight reduction in cavitation index causes rapid deterioration in flowrate and head, increased tip region blockage, but a slight increase in velocity and decrease in PS pressure at mid span. The SS cavitation expands to the vicinity of the blade trailing edge, and the oscillations in coverage diminish. At mid span, with the SS maintained at the vapor pressure, and the PS pressure decreasing, the pump performance deteriorates. In the tip region, PCVs extending from the SS of one blade to the PS of the neighboring one occupy most of the tip region in the overlap area. Cloud cavitation also appears under the PCVs, but only near the SS. Both structures appear to contribute to the tip region blockage. While the trailing edge casing groove delays the PCV formation, it has a limited effect on the cloud cavitation. Hence, the groove is only partially effective in reducing the tip region blockage. During early phases of breakdown, suppression of the PCVs by CG3 indeed causes a limited improvement to the tip blockage and performance of the pump. However, with further slight reduction in cavitation index, the PCVs reappear.

Figure 1 .

 1 Figure 1. (a) The AxWJ-2 with casing groove (CG3) installed and the imaging setup for SPIV measurement. (b) The circumferential groove configurations.

Figure 2 .

 2 Figure 2. (a) A perspective view of the laser sheet coincides with the LE tip. (b) A magnified view of the SPIV plane with sample |U z | distributions. (c & d) Top and section views of the SPIV setup.

Figure 3 .

 3 Figure 3. Pump performance curves 2.2 Apparence of cavitationDetailed descriptions of the appearance of cavitation for the different CG cases are provided in[START_REF] Chen | Effects of Circumferential Grooves on the Cavitation and Performance of an Axial Waterjet Pump[END_REF], and only samples for CG3 are presented in this paper. Briefly, at high cavitation indices, well above breakdown, CG1&2 trap the TLV, altering its interactions with the cloud cavitation. However, upon further reduction in inlet pressure, but still before breakdown, part of the TLV "escapes" from the grooves, resulting in tip region cavitation phenomena that are similar to those associated with the baseline case. Figure5compares the evolution of cavitation for the baseline and CG3 cases with decreasing σ. The cavitation indices are chosen to represent the flow conditions that are just before and after cavitation breakdown. Before breakdown (Figs. 5a&d), the extent of TLV cavitation and the area covered by attached cavitation on the blade SS for the baseline and CG3 appear to be similar. In both cases, entrainment and re-orientation of the cloud cavitation by the TLV generate the small-scale PCVs indicated on the figure. Under this condition, the attached cavitation has not yet propagated into the blade overlap region. The only effect of CG3 is formation of an additional cavitating vortical structure inside the groove, close to the trailing edge. Similar phenomena have been observed for the other grooves, but at different locations. In contrast, once breakdown occurs, substantial fraction of the blade SS within the overlap region is covered by cavitation (Figs.5b, c, e and f). A sample time sequence demonstrating the transition between these states is presented for the baseline case in Fig.6. Here, the cavitation index (σ=0.171) is only slightly lower than that of Figure5a(σ=0.186), corresponding of an absolute pressure difference of 2.8 kPa. The attached cavitation propagates into the blade overlap region and the fraction of SS area covered by it oscillates at high amplitude. All the images in Fig.6correspond to the same mean flow condition, but while a small area is covered by cavitation at t=t 0 and t=t 0 +3Δt (Figs. 6a&d), most of the lower blade is covered at t=t 0 +Δt and t 0 +2Δt (Figs.

Figure 4 .

 4 Figure 4. Cavitation breakdown curves: (a) Flow rate coefficient, and (b) total head coefficient.

Figure 5 .

 5 Figure 5. Comparisons of cavitation phenomena at three different cavitation numbers before (a & d) and after (b-c & e-f) cavitation breakdown for the baseline case (top row) and the CG3 case (bottom row). Solid red lines in (d-f) indicate the boundaries of CG3 and the dashed lines in (a-c) show the same location, but without a groove.

Figure 6 .

 6 Figure 6. Rapid oscillations of attached cavitation at breakdown onset for the Baseline. Δt=0.022s or 2 blade passing periods Further slight reduction of the inlet pressure of the baseline rotor to σ=0.160, a change of 2 kPa, already causes a significant reduction (8.5%) in head rise. The attached cavitation stabilizes in the overlap region, and distinct PCVs form near the blade trailing edge (Fig.5b). While expansion of the attached cavitation into the overlap region occurs for the CG3 case as well, its chordwise extent is lower than that in the baseline case, and the formation of PCVs near the blade trailing edge is suppressed (Fig.5e). Yet, the performance barely improves, as evidenced by the slightly higher head rise occurring at a lower cavitation index (σ=0.158) in Fig.5e. This observation challenges the claim that the PCVs play primary roles in the cavitation breakdown, as proposed by Tan et al.[START_REF] Tan | Experimental Investigation of the Role of Large Scale Cavitating Vortical Structures in Performance Breakdown of an Axial Waterjet Pump[END_REF]. Further minor reduction in cavitation index causes substantial deterioration of both the flow and head coefficients for both the baseline and CG3 cases (Figs. 5c&f). Here, the PCVs form for the CG3 case as well, demonstrating that this groove is not effective in suppressing them.

Figure 7 .

 7 Figure 7. Evolution of |U z | for the baseline case with σ at s/c=0.065 inside passage: σ=0.77 (without cavitation), σ=0.180 (just before breakdown), σ=0.170 (breakdown onset), σ=0.166 (early breakdown), and σ=0.161 (deep breakdown). Dotted line in σ=0.77 indicates the boundary of the field of view in σ=0.180-0.161.

Figure 8 .

 8 Figure 8. Evolution of U θ for the baseline case: σ=0.180 (just before breakdown), σ=0.170 (breakdown onset), and σ=0.166 (early breakdown).

Figure 9 .

 9 Figure 9. Evolution of U r for the baseline case: σ=0.180 (just before breakdown), σ=0.170 (breakdown onset), and σ=0.166 (early breakdown)

Figure 10 .

 10 Figure 10. Evolution of σ local for baseline case: σ=0.180 (just before breakdown), σ=0.170 (breakdown onset), σ=0.166 (early breakdown), and σ=0.161 deep breakdown.

Figure 11 .

 11 Figure 11. Changes in |U Z | with decreasing σ for (a) the baseline case (|U z, σ=0.170 | -|U z, σ=0.180 |) and (b) the CG3 case (|U z, σ=0.173 | -|U z, σ=0.187 |). Partially masked area in (a) is not available in (b).

Figure 12 .

 12 Figure 12. Changes in |U Z |/U T with decreasing σ for (a) the baseline case ((|U z, σ=0.161 |-|U z, σ=0.180 |) /U T ) and (b) the CG3 case ((|U z, σ=0.158 |-|U z, σ=0.187 |) /U T ).

  Figures 11 compare the changes to |U z | as the cavitation index is reduced from pre-breakdown to breakdown-onset conditions for the baseline and CG3 cases. For the baseline case, we present (|U z, σ=0.170 |-|U z, σ=0.180 |), and for the CG3 cases, ((|U z, σ=0.173 |-|U z, σ=0.187 |). The differences in the values of σ are caused by slight (<1 kPa) changes in the inlet pressure during the tests. The CG3 data also has a smaller field of view, which is indicated by the mask superimposed on the baseline figures. For both cases, the breakdown onset in characterized by an increase in axial velocity and decrease in pressure along the blade PS. The differences between the two cases along the PS are quite small, but the increase in |U z | along the tip of the blade with CG3 is lower than that of the baseline flow.

  Figure 12 provides a similar comparison between the baseline and CG3 cases, but this time the cavitation index is changed from pre-breakdown to deep breakdown conditions. Here, the area with decreasing |U z | indicating blockage, and the magnitude of the decrease in the CG3 data are smaller than those of the baseline. This trend might be associated with the suppression of the PCVs further

Figure 13 :

 13 Figure 13: Evolution of σ local for CG3 case: σ=0.187 (just before breakdown), σ=0.173 (breakdown onset) and σ=0.164 (early breakdown).

  . Transducer no. 1 is located near the blade LE (s/c=0.175), and Transducer no. 2, at the mid-chord (s/c=0.488). Sample ensemble-averaged pressure signals of Transducer no. 2 normalized by 0.5ρU T 2 (C p =p(θ)/0.5ρU T 2 )) for different σ are presented in Fig. 14b. The sharp decrease in pressure occurs as the blade passes by the transducer, peaking on the PS, and reaching a minimum value along the SS, with the difference between them (ΔC p =C p , PS -C p , SS ) representing the pressure difference across the blade. Hence, this difference can be used as a surrogate for the local loading near the blade tip. Note the sharp decrease in SS pressure at σ=0.171, the breakdown onset condition.

Figure 14 :

 14 Figure 14: (a) Illustration of transducer locations. (b) Casing wall pressure variations near the mid-chord. (c) Pressure differences across the blade measured at casing wall at two different axial locations for the baseline case. (Adapted from Tan et al. 2015)

NOMENCLATURE A =

  through flow area c = rotor blade tip chord h = width of the rotor blade tip gap p s,1 , p in = static pressure at pump inlet (z/R=1.16) p s,2 = static pressure at stator outlet p v = vapor pressure of NaI solution Q = volumetric flow rate R = casing radius r, z, θ = radial, axial and circumferential coordinates s = rotor blade chordwise coordinate u r , u z , u θ = radial, axial and circumferential velocity U r , U z , U θ = ensemble-averaged radial, axial and circumferential velocity u, v, w = velocity components in laser sheet coordinate system U T = rotor blade tip speed U z,in = axial velocity at inlet W = fluid speed in the rotor reference frame x', y', z' = laser sheet coordinate system ρ = NaI solution density φ = flow coefficient θ PIV = circumferential location of the laser sheet coordinate system σ = cavitation index σ local = local cavitation index ψ = total head rise coefficient Ω = rotor angular velocity

Table 1 .

 1 Relevant rotor geometry data

	Number of rotor blades		6
	Number of stator blades	8
	Tip profile chord length c	274.3mm
	Tip profile axial chord length cA	127.4mm
	Rotor radius R r			151.9mm
	Casing radius R			152.6mm
	Casing diameter D1			305.2mm
	Circumferential groove width	30.4mm (0.11c)
	Circumferential groove depth	6.35mm (9.1h)
	Outflow section diameter D2	213.4mm
	Pipe inner diameter downstream of	304.8mm
	the pump D
	Tip clearance h			0.7mm
	Tip clearance ratio 2hD	-1	4.6×10	-3
	Tip profile pitch ζ			159.1mm
	Tip profile solidity cζ	-1		1.72
	Tip profile stagger angle γ	27.7º
	Rotor angular velocity Ω (n)	94.2rad s	-1
				(900rpm)
	Tip speed UT			14.3ms	-1
	Tip profile Reynolds number Rec	3.6×10	6

ACKNOWLEDGMENTS

This project is sponsored by the Office of Naval Research. Ki-Han Kim is the Program Officer. The authors would like to thank Yury Ronzhens for his contributions to the construction and maintenance of the test facility.


Lu Jinling
email: jinling_lu@163.com

Zhang Xin

Zhang Jie

Luoxingqi

A Experimental Research On The Anti-erosion Material For Hydraulic Machinery

Keywords: Dynamic parameters, Particle size, Interactive wear, Erosion, SEM

Hydraulic machinery used in many fields was badly eroded, but it was found that not enough has been done on the erosion mechanism and the anti-erosion material. By using a rotating jet erosion testbed, four kinds of materials were tested under different dynamics parameters. At the same time, aluminum bronze was tested under different size of sand particle. Some conclusions can been obtained after observing material surface by SEM. With the increase of Impacting velocity , the damage of material surface became serious and weight loss got bigger. With the increase of the impacting angle, the weight loss first increased and then decreased. At the same dynamics parameters, because surface damages of 06Cr19Ni10 and 45Cr are small, so 06Cr19Ni10 and 45Cr had the better anti-erosion performance. However, Q235 had worse anti-erosion performance. With the increase of sand size, the erosion of material surface got worse, and weight loss had an obviously change between 0.4mm and 0.5mm.

INTRODUCTION

Hydraulic machinery is widely used in many fields, and plays a significant role in social economy. At the moment of creating huge economic benefits, the problems of erosion in hydraulic machinery also should be attention. In hydraulic machinery field, the interaction between cavitation and impacting wear caused by sand are defined erosion. It leads the blades wear seriously and make the efficiency fallen. As a result, it shortens the repair cycle and increases the operating costs, moreover it was not avoided in the operation of the hydraulic machinery [START_REF] Plesset | The growth of vapor bubbles in superheated liquids[J][END_REF] . So new technologies or measures were used to reduce erosion damage by researching its mechanisms. Erosion can be influenced by many factors, such as the material performance, dynamics parameters and the characters of the sediment [START_REF] Hong | Microstructure and cavitation-silt erosion behavior of high-velocity oxygen-fuel (HVOF) sprayed Cr 3 C 2-NiCr coating[END_REF][START_REF] Romo | Cavitation and high-velocity slurry erosion resistance of welded Stellite 6 alloy[END_REF] .

A lot of researches have been carried out on the anti-erosion of hydraulic machinery. Researchers from SEW and Voith companies think that the content, characteristic of sediment and the pattern of flow decide damage degree of the hydraulic turbine [START_REF] Zhang | Recent progress in liquidsolid two phase flow pump research[END_REF][START_REF] Freym | Surfaee Coating[END_REF] . According to studying the influence of velocity and content of the sand on erosion, Liang considers that anti-erosion performance of material was related to sand velocity and content. Erosion mechanisms were investigated by scanning erosion location [START_REF] Liang | Investigation on Cavitationabrasion of Metal Materials[END_REF] . A way to optimize runner of hydraulic turbine through researching runner cavitation and wear in the flow with sands was presented by Romeo and Gabriel [START_REF] Susan-Resiga | Analysis of the swirling flow downstream a Francis turbine runner[END_REF] . In this paper, by using the testbed which was built for researching the influence of rotating spray on material erosion [START_REF] Pang | The influence of sediment concentration and particle size on the erosion wearing characteristics of QT500[END_REF] , four kinds of materials on erosion were investigated under different dynamics parameters. Meanwhile, the anti-erosion performance of material was also studied under different sand particle sizes. At last, the surface morphology can be observed using SEM ( scanning electron microscope) and the weight loss can be measured by electronic scale.

METHODS

Testbed

As the Fig. 1(a) and (b) show, the testbed consists of adjustable speed motor, diaphragm pump, mixed water tank, steady voltage system, air compressor, refrigeration system and rotary table room. In the testbed, with the help of diaphragm pump, the flow with sands went through steady voltage system into rotary table room, and impact rotary table surface by using nozzles where the velocity could be set. Furthermore, rotary table was driven by motor and in high speed, it made the rotating centre pressure decrease and formed pressure gradient, and created opportunity for cavitation. Flow pattern at the back of the hole was damaged owing to cavitation hole. The area in low pressure produced gas nucleus and the gas nucleus were broken in the high pressure area, which lead the phenomenon of cavitation damage. Moreover, the flow with sands in high speed impacted material surface through nozzles and lead wear damage. Cavitation and wear could affect each other and formed erosion. Eventually, the flow with sands returned to mixed water tank.

Figure 1. Rotary spray erosion testbed

To keep the temperature of the water in the mixed water tank below 50 degree centigrade, so the cooling system used to absorb energy from rotary table was been set. Besides, the impacting velocity and impacting angle were regulated by changing flow and rotational speed of the rotary table. Other functions could be achieved on the control cabinet. Fig. 2(a) and (b) show the diagram of rotary table. Eight test materials were installed in the rotary table. In present paper, same materials were installed at the opposite angle, so four kinds of materials could be tested at the same time.

. Rotary table structure diagram and photo

Each test material was set a hole used to evoke cavitation. During the test, material weight loss was weighed by an electronic scale whose precision reached 0.1 mg after cleaning and drying every 2 hours. Aluminum bronze QAL9-4 was measured every 3 hours. In order to simulate the truth of the erosion, sands in the flow must be replaced every 6 hours. Finally, the result of this test was analyzed by using the SEM, it could clearly observe wear scratch and cavitation pits of the material surface.

Parameters setting

In this paper, two tests were finished. One was under different dynamics parameters, and the other was under different sand particle sizes. Four kinds of materials were used in the test to research influence of dynamics parameters on erosion and dynamics parameters included the impacting velocity and the impacting angle. Table1 shows the specific test parameters. Test time(h) 10 10

Aluminum bronze QAL9-4 was used to research the influence caused by different sand particle sizes on erosion [START_REF] Liao | Study on the erosion behavior of Aluminum bronze and design of test device in multiphase flow[END_REF] . Table . 2 shows the specific test parameters. Table 2.

Test result and analyze 3.1 Weight loss

After the test, four kinds of materials weight loss curves were shown in the fig. 3. The impacting velocity was set at 35 m/s, and impacting angle was set to 24 degree, 32 degree and 40 degree, respectively.

Impacting angle(degree) 32

Impacting velocity (m/s) 30

Sand particle sizes (mm) 0.1-0.2, 0.2-0. As Fig. 3 shows, the four kinds of materials show the same rules of erosion weight loss under three kinds of impacting angle. The accumulated weight loss of Q235 was the maximum and the one of 06Cr19Ni10 was the minimum. According to the material weight loss curves under three different impacting angles, the anti-erosion performance of the four kinds of materials could be obtained. The accumulative weight loss of 06Cr19Ni10 was the smallest, so the anti-erosion performance was best. The accumulative weight loss of Q235 was the largest and the anti-erosion performance was poor. The curves in Fig3 also show that weight loss of the erosion material included the incubation period, the rising period and the stabilization period [START_REF] Preece | Treatise on materials science and technology[END_REF][START_REF] Morch | Cavitation nuclei and bubble formationa dynamic liquid-solid interface[END_REF] . During the incubation period (from 0 to 2 hours), the surface of the material was damaged mainly by impacting wear. During the rising period (from 2 to 6 hours), due to wear and cavitation interaction, the material damage increased quickly. During stable period (6 hours later), wear and cavitation damage entered the relatively stable. Within the allowable range of test error, the trend of weight loss curve of four kinds of materials was almost the same. Comparing the erosion weight loss curves under three kinds of angles, it could be seen that the gradient of the weight loss curves of four materials was larger than that of the other two angles when the angle of impacting was 32 degree. Therefore, it could be concluded that the wear damage of the material was the most serious when the impacting angle was about 32 degree.

Fig. 4 shows that the accumulative weight loss of four kinds of materials changed with test time when impacting angle was 32 degree and the impacting velocity were 30m/s, 35 m/s and 40 m/s, respectively. It had a positive proportion relation between the weight loss and the test time under the erosion damage. At the same impacting velocity, the weight loss of Q235 was the largest; the damage of 45Cr was close to the one of 06Cr19Ni10.

When the impacting velocity of Q235 was set at 30 m/s, 35 m/s, and 40 m/s, the accumulative weight loss was 65.45 mg, 117.3 mg,143.95 mg respectively after test. The weight loss of the largest is 2.19 times bigger than the smallest. Other materials had the same rules. According to these curves and experimental data, it could be concluded that the increasing of impacting velocity caused the sand particle momentum increase continuously. Which leaded material damage serious, and the weight loss of erosion increased quickly. Aluminum bronze used in marine propellers was considered as study object to investigate the influence of sand particle diameter on erosion. Fig. 5(a) shows that the accumulative weight loss of aluminum bronze changed with the test time under different sand particle sizes. The accumulative weight loss of erosion was proportional to the increase of time, and the larger of the particle size, the greater of the weight loss. The weight loss of materials had a big difference between the biggest particle size (from 0.4 mm to 0.5 mm) and other particle sizes at the beginning of the test. As Fig. 5(b), when the sand particle size was less than 0.4 mm, the increasing of accumulative weight loss of erosion was relatively slow. However, when the sand particle size was exceeded than 0.4 mm, the accumulative weight loss of erosion increased suddenly.

Surface topography analysis

To analyze easily, the original surface topographies of four materials which were not been tested after polishing were shown in Fig. 6. After polishing, the surfaces of the materials were relatively smooth without obvious scratches. Due to the defects of Q235, there were many pores in the surface of the material, but the influence of these pores was relatively small on test results, so it could be ignored. The Q235 was chosen as the study object, Fig. 7 shows the surface topography after 10 hours of erosion under 24 degree, 32 degree and 40 degree, respectively. The surface damage of the material mainly concentrated in the back of the cavitation hole, and the surface appeared furrow, fish scales lip, small cracks and small pit. When the impacting angle was small, the interaction between cavitation and wear was mainly micro cutting and the second was the effect of cavitation damage. The velocity of the sands in the process of movement was constituted by horizontal component and vertical component. The vertical component determined the sand into the material surface depth. The horizontal component completed the micro-cutting on the material surface [START_REF] Finnie | Proceedings of the 3th national congress of Applied Mechanics[END_REF][START_REF] Oh | On the location of fracture in brittle solids-I[J][END_REF] . It formed a lamellar deformation layer after many times of impacting on the material surface. Subsequently, the layer at the edge cracked and formed some concaves and convex lips. Eventually it leaded the surface micro volume shedding. When impacting angle was large, the wear loss was mainly decided by sand kinetic energy, the influences vertical impact and cavitation effect of the flow with sands on the material destroyed structure of the surface layer, causing fatigue spalling and leaving the pitting on the surface of the material. When the impacting angle was 24 degree, the surface of material were mainly large lips and also appeared small amount of cavitation pits and furrows. Direction of the furrow was neat, and depth was shallow. When the impacting angle was 32 degree, the cutting of sands made the surface plastic deformation seriously. At same time, the direction of lips and furrow are more chaos, and lip flanging was more serious. When the impacting angle was 40 degree, material surface damage was mainly based on vertical impact and cavitation damage, furrow trip was short and the lips appeared as small patches.

Also, Q235 was chose as the study object. In the erosion test, , the wear scar of the material surface was shallow and deep with the increasing of the impacting velocity, and the wear degree was also gradually increased . When the impacting velocity was 30 m/s, wear scar on the surface caused by sand were short and disorderly, the damage concentrated mainly in the surface layer. When the impacting velocity was 35 m/s, the surface cutting degree of the sand particles increased continually, and the furrow wear marks became longer and the wear direction was gradually neat. When the impacting velocity was 40 m/s, the cutting marks on the surface of the material were further increased and the furrow wear was deepened, and the damage of cavitation was further promoted.

The Fig. 9 shows the aluminum bronze surface morphology caused by erosion under four different particle sizes. The damage of the material surface became seriously with the increasing particle sizes of sand. The surface morphology of the material mainly included furrow, scaly lips and pits which came from lips spalling [START_REF] Stella | Cavitation-erosion of 3Y-TZPs obtained at different sintering temperatures[END_REF][START_REF] Sato | Basic study of coupled damage caused by silt abrasion and cavitation erosion[C[END_REF] . As the hit of the sands again and again, the furrow overlap became serious, and lips fatigue loss increased quickly. The shedding lips from outside to inside and furrow leaded the material loss. As the Fig. 9(a) and (b) show, aluminum bronze surface was worn seriously. The cutting effect of the sands made the material surface produce plastic deformation and leaded to accumulation of materials, as well as appeared lips and short furrows whose width was a small, however it distributed uniform. As Fig. 9(c) and(d) show, with the increase of the particle sizes, the furrow width increased and the furrow length also increased correspondingly. The damage of the furrow between(d)and others had a clear difference, it kept consistent with the test date when the size of from 0.4 mm to 0.5 mm, whose weight loss increased suddenly.

Conclusion

1 The erosion of materials became seriously with the increasing of the velocity. Impacting velocity had positively correlated with the weight loss. Moreover, the cumulative weight loss of erosion increased firstly and then decreased with increasing of the impacting angel. 2 06Cr19Ni10 and 45 Cr had better anti-erosion performance, followed by 45 steel, and Q235 had the Article Title -6 worst erosion performance. 3 The interaction between cavitation and impacting wear leaded the damage of material surface. Cavitation damage leaded to the uneven surface of the material, which promoted the impacting wear of sands. Conversely, the impacting wear of sands aggravated the cavitation damage. According to impacting angle, impacting wear of the sands was divided into micro cutting caused by horizontal direction and repeated impacting caused by vertical direction. 4 When the particle size of sands were in the range of 0.5 mm, The damage of the material surface became seriously with the increasing particle size of sands The material weight loss had a clear difference when the particle size of the sands from 0.4 mm to 0.5 mm.

Figure 2

 2 Figure 2. Rotary table structure diagram and photo

Figure 3 .

 3 Figure 3. Variation curves of weight loss of specimen under different erosion angle

Figure 4 .

 4 Figure 4.The variation curves of the weight loss of specimen under different erosion velocity

Figure 5 .

 5 Figure 5. The variation curves of the weight loss of specimen under different sand particle sizes

Figure 6 .

 6 Figure 6. Original specimen appearance

Figure 7 .

 7 Figure 7. SEM images with erosion angle 24degree, 32 degree, 40 degree .(5000x)

Figure 8 .

 8 Figure 8. SEM images of erosion velocity 30 m/s 35 m/s, 40 m/s .(5000x)

Figure 9 .

 9 SEM images of different particle sizes. (5000x)

Table 1 .

 1

Impacting angle(degree) 24, 32 ,40 32 Impacting velocity (m/s) 35 30, 35, 40 Sand particle sizes (mm) 0.2-0.3 0.2-0.3 Sand content (kg/m 3 ) 5 5

Acknowledgements

This work was supported by the National Natural Science Foundation of China [Grant numbers:51279160]. The supports are gratefully acknowledged.