27 th Symposium on Naval Hydrodynamics Seoul, Korea, 5-10 October 2008

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1 27 th Symposium on Naval Hydrodynamics Seoul, Korea, 5-10 October 2008 Cavitation Visualizes the Flow Structure in the Tip Region of a Waterjet Pump Rotor Blade H. Wu 1, F. Soranna 1, T. Micheal 2, J. Katz 1, S. Jessup 2 ( 1 Johns Hopkins University, 2 NSWC/Carderock) ABSTRACT In this paper, we examine the occurrence of cavitation in the tip region of a waterjet pump, and use the observations to identify key features of the flow structure. The rotor, stator and pump casing in our recently upgraded facility are made of acrylic, whose refractive index matches that of the working fluid, a concentrated aqueous solution of sodium iodide. Such matching makes the blades invisible, enabling flow structure visualization and optical measurements without any obstructions. Our initial tests with fresh water focus on cavitation in the vicinity of the tip region close to design conditions. Near the leading edge, cavitation inception near the tip corner of the pressure side causes accumulation of bubbles along the pressure side of the corner until mid blade. As roll-up of the tip leakage vortex (TLV) starts in the mid blade region, these bubbles travel across the tip-clearance to the suction side, and become nuclei for cavitation inception in the TLV. As the TLV migrates to the vicinity of the pressure side of the neighboring blade it bursts, generating a cloud of bubbles that spreads over most of the aft section of the passage. The leakage flow in the tip gap along the aft side of the blade is strong enough to cause sheet cavitation within the gap, starting from the pressure side corner. The paper also presents preliminary Particle Image Velocimetry (PIV) data concentrating on the roll-up of TLV. Results are consistent with observed cavitation phenomena. INTRODUCTION Design of Waterjet pumps for Naval jet propulsion requires computational tools for modeling and predicting the flow within them. Validation of CFD results need detailed experimental data on flow structure and turbulence over the entire machine. Furthermore, since most water-jet turbo-pumps operate near atmospheric pressures, inception of cavitation and its numerous adverse effects are also important issues that must be accounted for during design. The flow field in turbomachines is extremely complex due to simultaneous occurrence of multiple phenomena and interactions among them, e.g. tip and hub vortices, highly strained turbulence and turbulent boundary layers as well as turbulent wakes interacting with downstream blade rows, etc. In the tip region of a rotor blade, the focus of the present paper, the pressure difference between the pressure and suction sides, induces a leakage flow through the finite clearance between the moving blade and the casing wall. On the suction side, the leakage flow rolls up into a TLV whose complex configuration depends on the blade and casing geometry as well as flow conditions. This topic, associated turbulence and cavitation phenomena have been investigated extensively for many years (e.g. Lakshminarayana 1996, Inoue et al 1986, Li and Cumpsty 1991a, b, Oweis et al., 2006a, b, Palafox et al. 2008, Rehder and Dannhauer 2007, Liu et al 2006, Yu et al. 2007). It is well established that TLV affects the overall performance of a turbomachine, and plays a significant role in turbulence production and diffusion near the endwall (e.g. Li and Cumpsty 1991a, b). Due to the inherent low pressure in the vortex core, cavitation inception within turbomachines is usually coupled with vortex structures (Arndt, 2002, Farrel and Billet, 1994, Higashi et al. 2002, Gopalan et al 2004, Murayama et al. 2006). Consequently, occurrence of cavitation points out low pressure regions, and often visualizes the associated flow structures, e.g. tipleakage, trailing and hub vortices as well as turbulent eddies developing in regions of flow separation. Entrained bubbles tend to grow along the vortex core, becoming cylindrical, and as a result indicate the shape and location of vortices. When these vortices are stable, e.g. tip vortices, the cavitation within them persist for long periods, sometimes until the vortex breaks down. In addition to the tip region, other forms of cavitation occur near the blades surface, such as sheet cavitation, traveling bubble cavitation and cloud cavitation (Arndt 1991, Brennen, 1994). Due to the complex flow structure in pumps and physical processes involved with cavitation, many related questions are still open. In fact, except for empirical information, which is geometry-dependent, we do not 1

2 Figure 1: The new test loop. Top view with dimensions in mm. The pipe diameter is 304.8mm. Figure 2: The test loop corner showing the pump, settling chamber, corner with turning vanes and shaft. (unit: mm) have reliable tools for predicting cavitation inception in pumps. In the present paper, we demonstrate several forms of cavitation in the tip region of a waterjet pump. We start with a detailed description of our recently upgraded flow visualization facility, and then provide a series of images showing the results of our observations along with sample PIV measurement. Some of these results are quite similar to those mentioned above, e.g. cavitation inception within the TLV. However, the picture is considerably more complicated, starting with cavitation on the leading edge side of the tip corner, which feeds bubbles across the tip gap into the TLV. Bursting of this tip vortex within the blade passage generates a large bubble cloud, some of which become nuclei for cavitation within the tip gap, along the pressure side corner. EXPERIMENT SETUP The entire facility is illustrated in Figure 1. One the right bottom corner is the 60HP motor, which drives the pump through a long shaft, as shown in more detail Figure 2. Downstream of the pump, there are three cooling sections made of double-walled pipes. Cold water provided by the air-conditioning system of the building runs through the gap between the interior and exterior walls. A flow-control valve consisting of two perforated disks that can be rotated relatively to each other is located downstream of the cooling sections. Upstream of the pump section, there is a pressure control tank, which is kept half-filled with liquid, and its top is connected to a vacuum pump and to a high pressure Nitrogen source. The facility is designed to operate at absolute pressures ranging from very near vacuum up to 10 atm. To reduce secondary flows, the corner where the shaft penetrates contains turning vanes. Furthermore, a settling chamber containing two honeycombs is located just upstream of the pump. In the present setup, the shaft is located inside a stationary sleeve until the exit from the settling chamber, and is exposed further downstream. The axial waterjet pump consists of a seven blades rotor and an eleven blades stator, as shown in Figures 2-4. The hub of the rotor and stator has an ellipsoidal shape. The rotor tip diameter is mm, with the tip gap 0.7 mm. Starting from the beginning of the stator passage, the channel diameter gradually decreases from 305 mm to a 162 mm nozzle, as shown in Figures 3 and 6. At the exit of the nozzle, the channel suddenly expends back to 305 mm. Figure 7 compares the measured performance curve of this pump to the design predictions using a panel flow method (Kerwin 1994, Young 2006),. As is evident, results agree quite 2

3 well. The selected flow condition for subsequent tests at 900 RPM is a flow rate of 0.14 m 3 /s and total head rise in fresh water of 7 m. The entire rotor, stator and casing of the test section are made of acrylic, enabling us to observe the flow and cavitation almost everywhere. The outer surface of the casing contains several flat surfaces to accommodate imaging equipment. During velocity (PIV) measurements, the refractive index of the acrylic is matched with that of the fluid using a 62%~64% by weight solution of NaI in water. This fluid has specific gravity of 1.8 and kinematic viscosity of m 2 /s, i.e. very close to that of water. Within this fluid, the blades become almost invisible, enabling unobstructed velocity measurements essentially everywhere. As shown in Figures 3 and 6, the casing has several ports distributed throughout the test chamber, enabling us to insert kiel probes, pitot tubes, pressure transducers, hydrophones or inject air. As we assembled the new setup and tested it, we have performed observations on the occurrence of cavitation in the tip region of the rotor blade, and results are described in the following section. During these tests, we have used 2K x 2K pixels digital cameras to record images of the cavitation. For these observations, the camera is aligned normally to the outer surface of the casing, and we use a strobe light for illumination. For Two dimensional PIV measurements, we used a green (532 nm) Nd-YAG laser as a light source, the same cameras, and the optical setup illustrated in Figure 6. During stereo PIV measurements we attach a prism to the outer casing to keep the lens axis perpendicular to the window. In the future, Tomographic PIV, a relatively new technique (Elsinga 2005), will also be used to obtain the instantaneous 3-dimensional distributions of 3 velocity Figure 3: Photos of the rotor, stator and nozzle components, especially in the tip region. PRELIMINARY RESULT CAVITATION IN THE TIP REGION In this section we provide a series of images demonstrating the occurrence of cavitation in several locations near the tip region. For clarification, Figure 5 illustrates the locations of images. Region 1 covers the leading edge; region 2 is the mid chord area, covering both the suction and pressure sides; region 3 focuses on the area of TLV detachment, propagation and bursting in the mid chord area; and region 4 focuses on the tip clearance, slightly upstream of the trailing edge, but downstream of the point of TLV detachment. For defining the cavitation index, we use the mean pressure and velocity at the entrance to the pump, Figure4: Front illustration of the rotor and stator and definition of parts. Figure5: Definition and locations of regions examined during cavitation visualizations. 3

4 σ = p inlet p v 1 2 ρ(u tip )2 where U tip is the impeller tip speed and p inlet is the mean pressure at the inlet plane. In region 1, cavitation inception occurs at on the pressure side of the tip corner, as Figure 8 demonstrates. Note that only one of the bubbles is in focus since they are located at different depth. Consistent appearance of bubble cavitation on the pressure side indicates that in this region, the pressure on the pressure side is lower than that on the suction side. In addition to the large bubbles, a train of smaller bubbles forms along the tip corner, and some bubbles appear in the tip gap. There are two possible explanations for the latter phenomenon. The first involves formation of a corner vortex due to interaction of the blade with the casing wall. The second, which seems to be more likely, is that the lower pressure on the pressure side generates a leakage flow and rollup of a small leakage vortex along the pressure-side tip corner. This process is reversed further downstream. The pressure side tip corner traps a train of bubbles that extends to the mid chord region of the pressure side, as shown in Figure 9, this time at the same pressure (σ=0.26). Such persistence indicates that in this region, there is very little or even no leakage flow across the tip to the suction side, i.e. the pressure along the pressure side corner is either equal or lower than that on the suction side. The shape of this train of bubbles strongly suggests that they are trapped within a vortex core, which is located near but clearly separated from the corner. As the TLV start rolling up on the suction side of the tip corner at mid chord. Figure 10 shows that the trapped bubbles occasionally start crossing from the pressure to the suction side with the tip leakage flow, and are subsequently entrained into the developing vortex, forming cylindrical cavitation along the vortex core. The location of bubble crossing Figure 6: The casing of the test section (top), a cross section showing the ports (bottom left) and illustration of 2-D PIV measurement setup (bottom right) (Unit: mm) 4

5 bubbly core becomes initially helical, and then breaks up into a cloud of bubbles. With further reduction in pressure, e.g. at σ =0.26, the breakup process of the cavitating core becomes more violent, and fills the entire aft part of the blade passage with a large cloud of bubbles (Figure 12). This flow pattern suggests that vortex bursting (breakdown) occurs in the blade passage, presumably due to the adverse pressure Figure 7: Pump performance compared with CFD prediction. Symbols: measured data; pink solid line and blue squares: CFD results at 1190rpm; dashed lines: predictions at 300rpm rpm (as indicated) using standard pump scaling based on the CFD results. and number of bubbles being entrained vary, and with it, the initial appearance of TLV cavitation. As the tip leakage flow increases past the mid chord, all the bubbles trapped along the pressure side corner are forced through the tip gap to the suction side and are entrained into the TLV. TLV detaches from the blade shortly after its initial rollup, and it propagates towards pressure side of the neighboring blade. In the vicinity of the neighboring blade, at about mid-passage, several kinks appear in the shape of this vortex. At a relatively high cavitation index ( σ =0.33), Figure 11 shows that the 5mm Figure 9: Bubbles along the pressure side tip corner. The image shows the lower part of Region 2; σ =0.26 5mm Figure 8: Inception of cavitation along the pressure side, near the leading edge of the tip. Image shows Region 1 (See Figure 5 for definition of regions). Figure 10: Bubbles crossing the tip clearance to the suction side and entrained into the TLV (Region2); σ =

6 we present data for three planes, which are numbered as I II III in Figure 14, are located at 45%, 50%, 55% of the chord length downstream of the leading edge, respectively. Techniques associated with image processing in this facility are described in Chow (2002), and the PIV cross correlations are calculated using Lavision commercial PIV software, Davis 7.4. The average velocity fields based on 200 samples for each of the three planes are shown in Figure 15.The results show the TLV beginning to roll up at the first plane, and rapidly detaching from the blade in the next planes. The horizontal distances from the core of TLV to the blade suction side corner in plane I II III are 1.95mm, 4.10mm, 5.59 mm respectively, which means the TLV detaching the blade. These results are consistent with those of the cavitation visualizations. Figure11: Bursting of a cavitating TLV generated by the blade located on the left side near the pressure side of a neighboring blade, which is located on the right side; region3, σ =0.33. The cloud of bubbles on the left side of the picture results from bursting of a vortex in that passage. gradients in aft section of blade passage, especially along the pressure side of the blade. This well-known phenomenon frequently occurs in aerodynamic flows and combustion chambers (Leibovich 1978, Maxworthy et al. 1985, Ragab and Sreedhar 1995, Sotiropoulos et al. 2001). A fraction of the bubbles generated by the vortex breakup is entrained into the tip leakage flow, and subsequently by the TLV on the other side of the blade, as shown in Figure 12. As the flow across the tip gap becomes stronger in the rear part of the rotor passage, attached sheet cavitation inception occurs within the tip gap, starting from the pressure side corner of the blade tip. At intermediate cavitation indices, the process is intermittent, but as Figure 13 demonstrates, at σ =0.26, sheet cavitation covers substantial fractions of the tip gap. Figure 12: Bubbles generated by bursting of a TLV provide nuclei for the TLV of the following blade; region3, σ =0.26. PRELIMINARY RESULT PIV MEASUREMENT AND QUALITATIVE DISCUSSION In region 2, where the TLV rolls up, we have performed planar PIV measurements using sodium iodide aqueous solution as working fluid. The setup of laser illumination plane and camera is shown in Figure 14. By adjusting time delay of the laser pulses relative to the shaft encoder signal, which corresponds to a fixed angle of the shaft, we are able to capture planes at different locations within the blade passage. These measurements are presently in progress. In this section, Figure 13: Sheet cavitation inside the tip clearance; region 4, σ =

7 Figure14: Locations of PIV planes. Acquisition of PIV data over the entire blade passage is presently in progress. SUMMARY AND CONCLUTION The optically index-matched flow visualization facility has been upgraded and modified for testing of Naval Waterjet pumps. Cavitation phenomena occurring within the first totally transparent model have been examined, and PIV measurements are presently in progress. Several types of cavitation occur simultaneously in the tip region of the rotor blade under the selected flow conditions. Close to the leading edge, cavitation first develops near the tip corner of the pressure side, both as bubble cavitation on the blade surface as well as within a vortex that forms along the tip corner. Both indicate that near the leading edge, the pressure on the pressure side of the blade is lower than that on the suction side. Accumulation of bubbles within the vortex along the pressure side corner presists to mid chord, and tip tip leakage flow to the suction side does not start until mid blade, as confirmed by PIV measurement. When the direction of pressure gradient across the tip gap is reversed at mid chord region, tip leakage flow from the pressure to suction side forces the bubbles trapped within the pressure side corner to cross the tip gap to the suction side, and become the nucleation sites for cavitation inception within the tip leakage vortex. On-going PIV measurements in the mid chord region, samples of which are provided, clearly show the exact location of TLV rollup. As the TLV develops, it detaches from the suction side surface and propagates towards the pressure side of the neighboring blade. There, the initially thin and almost straight bubbly core expands rapidly and becomes helical, followed by breakup into a large cloud of small bubbles. With decreasing pressure, this process becomes more violent. Some of these bubbles are forces to the suction side by the tip leakage flow of the neighboring blade, and are subsequently entrained by its tip leakage vortex. These observations suggest that TLV breakdown occurs within the rotor passage, presumably due to exposure to adverse pressure gradients along the pressure side. As the flow across the tip gap increases in the rear part of the blade, Figure 15: Mean velocity in PIV Planes I, II and III. 7

8 attached cavitation develops within the tip gap, starting from the pressure side corner of the tip. With decreasing pressure, this cavitation seems to fill substantial fractions of the gap. ACKNOWLEDGMENTS This project is sponsored by the Office of Naval Research under grant number N The program officer is Ki-Han Kim. Funding for the upgrades to test facility was provide by ONR DURIP grant No. N We would like to thank Yury Ronzhes and Stephen King for their major contributions to the construction and maintenance of the facility. REFERENCES Arndt, R. E.A., Cavitation in Fluid Machinery and Hydraulic Structures Ann. Rev. Fluid Mech pp Arndt, R. E.A., Cavitation in Vortical Flows Ann. Rev. Fluid Mech pp Brennen, C. E., Hydrodynamics of pumps, Oxford Press Chow Y.C., Uzol, O., Katz J., 2002, "Flow Non- Uniformities and Turbulent "Hot Spots" Due to Wake- Blade and Wake-Wake Interactions in a Multistage Turbomachine", ASME Journal of Turbomachinery, Vol. 124, No. 4, pp Elsinga, G.E., Scarano, F., Wieneke, B., Van Oudheusden, B.W., "Tomographic Particle Image Velocimetry", 6th International Symposium on Particle Image Velocimetry Pasadena, California, USA, 2005 Gopalan, S., Abraham, B., Katz, J. "Effect of Velocity Ratio on the Structure of a Jet in Cross Flow" Physics of Fluids, pp Higashi, S., Yoshida, Y., and Tsujimoto, Y., Tip Leakage Vortex Cavitation From the Tip Clearance of a Single Hydrofoil JSME Int. J., Ser. B, 45, 2002 pp Inoue, M., Kuroumaru, M., Fukuhara, M., Behavior of Tip Leakage Flow Behind an axial Compressor Rotor J. of Engineering For Gas Turbines and Power, 108, pp 7-14, 1986 FARRELL, K. J. & BILLET, M. L. "A correlation of leakage vortex cavitation in axial-flow pumps", Journal of Fluids Engineering, 1994 vol 116 Kerwin, J. E., Keenan, D. P., Black, S. D., Diggs, J. G., "A coupled viscous/potential flow design method for wake-adapted, multi-stage, ducted propulsors using generalized geometry" SNAME 1994,102, pp Lakshminarayana, B. Fluid dynamics and heat transfer of turbomachinery, John Wiley & Sons, 1996 Leibovich, S., "The structure of vortex breakdown" Annu Rev Fluid Mech, 1978, 10, pp Li, Y. S., Cumpsty, N. A. Mixing in Axial Flow Compressors: Part I-Test Facilities and Measurements in a Four-Stage Compressor J. of Turbomach, pp Li, Y. S., Cumpsty, N.A. Mixing in Axial Flow Compressors: Part II-Measurements in a Single-Stage Compressor and a Duct J. of Turbomach, pp Liu, B. J., Yu, X. J., Liu, H. X., Application of SPIV in Turbomachinery Experiment in Fluids, 2006, vol 40: 4 pp Maxworthy, T., Hopfinger, E. J., Redekopp, L. G., "Wave motions on vortex cores" J Fluid Mech, pp Murayama, M., Yoshida, Y., Tsujimoto, Y., Unsteady Tip Leakage Vortex Cavitation Originating from the Tip Clearance of an Oscillating Hydrofoil J. of Fluids Eng pp Oweis, G., D. Fry, C. J. Chesnakas, S. D. Jessup, and S. L. Ceccio, "Development of a Tip-Leakage Flow: Part 1- The Flow Over a Range of Reynolds Numbers," Journal of Fluids Engineering, vol.128, 2006, pp Oweis, G., D. Fry, C. J. Chesnakas, S. D. Jessup, and S. L. Ceccio, "Development of a Tip-Leakage Flow: Part 2- Comparison Between the Ducted and Unducted Rotor," Journal of Fluids Engineering, Vol.128, 2006, pp Palafox, P., Oldfield, M.L.G., LaGraff, J.E., Jones, T.V., "PIV Maps of Tip Leakage and Secondary Flow Fields on a Low-Speed Turbine Blade Cascade With Moving End Wall" Journal of Turbomachinery, 2008, v. 130, Ragab, S., Sreedhar, M., "Numerical simulations of vortices with axial velocity decits" Phys. of Fluids, 1995, 7, pp

9 Rehder, H. J., Dannhauer, A., "Experimental Investigation of Turbine Leakage Flows on the Three- Dimensional Flow Field and Endwall Heat Transfer" Journal of Turbomachinery, 2007, Vol. 129, pp Sotiropoulos, F., Ventikos, Y., Lackey, T. C., "Chaotic advection is stationary vortex breakdown bubbles: Silnikov's chaos and the devil's staircase" Journal of Fluid Mechanics, , pp Young, Y. L., Michael, T. J., Seaver, M., Trickey, S. T., Numerical and Experimental investigation of composite marine Propellers 26th Symposium on Naval hydrodynamics, Sep 2006, Rome, Italy Yu, X.J., Liu, B.J., Jiang, H.K., Characteristics of the tip leakage vortex in a low-speed axial compressor AIAA Journal, 2007, vol 45: 4 pp