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Controlled cavitation tests were performed after de-aerating the water in the tunnel and using electrolysis to generate cavitation nuclei. The experiments consisted of simultaneously detecting cavitation inception a 2000fps digital camera (visual) and two accelerometers (“acoustic”) mounted on the test-section windows. Good agreement between these methods was achieved when the visual observations were performed carefully. Portions of the signal containing cavitation noise were analyzed using Hilbert and Wavelet transforms. In order to obtain the time dependent spectra, rates of cavitation events as a function of the cavitation index (σ) for the 3 gap sizes (0.6, 1.4, 2.6mm) were measured. The observations clearly demonstrate that high amplitude noise spikes are generated when the bubbles are distorted and “shredded”—broken to several bubbles following their growth in the vortex core. Mere changes to bubble size and shape caused significantly lower noise. High resolution Particle Image Velocimetry (a vector spacing of 180µm) was used to measure the flow, especially to capture the slender tip vortices where cavitation inception was observed. Seventy instantaneous realizations for the 0.6mm gap and 65 for the 1.4mm gap were analyzed to obtain distributions of circulation of the leakage vortex. PIV experiments for the 2.6mm gap are presently underway and only instantaneous samples are presented. The vortex core diameter was found to be 3–4 vector spacings. Minimum pressure coefficients in the cores of these vortices were estimated using a Rankine model. These coefficients showed a very good agreement with the measured cavitation inception indices. INTRODUCTION Cavitation occurs in liquid flows when a nucleus (bubbles, particles etc.) is captured in a region where the pressure is lower or equal to the vapor pressure (Arndt 1981, Brennen 1995, Joseph 1998). Such low-pressure regions could be at the cores of vortical structures, which occur very frequently in shear flows (Katz & O'Hern 1986, O'Hern 1991, Ran & Katz 1994, Gopalan et al. 1999, Belahadji et al. 1995). In such cases inception of cavitation is marked by intermittent events. Experimental studies on tip vortex formation and cavitation have been addressed (for e.g.) by Maines and Arndt (1997), Higuchi et al. (1989) and a numerical study of steady-state tip vortex has been reported by Hsiao & Pauley (1998). Several papers in recent years have dealt with cavitation in tip leakage or tip clearance flows. As a result of the gap, a tip leakage vortex develops which is prone to cavitation (Farrell & Billet 1994, Boulon et al. 1999). Farrell and Billet (1994) examined the effect of gap size on tip leakage cavitation and found that the cavitation inception indices increased with decreasing gap sizes. They also found a cavitation inception index minima near λ≈0.2 (λ is the ratio of the tip gap size to the maximum tip thickness). Conversely, experiments performed by Boulon et al. (1999) do not show a minimum in the cavitation inception index. Their observations could be explained using a potential flow model (elaborated in Boulon et al. and briefly in section 4 of this paper). In the present study the following issues will be addressed- (i) cavitation inception measurements using both visual and acoustic techniques, (ii) bubble dynamics during cavitation using a high-speed camera, (iii) a comparison between the acoustic signal and the occurrence of cavitation, including detailed spectral analysis of the signal, (iv) structure of the leakage flow using Particle Image Velocimetry (PIV) and the effect of gap size on leakage flow characteristics. Plots of cavitation index, σ against rate of cavitation events (rc) are obtained in nuclei controlled conditions. Three gap sizes of 0.6, 1.4 and 2.6 were studied (λ=0.12, 0.28, 0.52). Cavitation events were recorded using accelerometers attached to windows of the test section. A high-speed camera at 2000fps was used to record the motion of bubbles as they interacted with the core of the tip vortex. The observations demonstrate clearly the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line ON THE FLOW STRUCTURE, TIP LEAKAGE CAVITATION INCEPTION AND ASSOCIATED NOISE 649 REFERENCES ARNDT, R.E.A. 1981 Cavitation in fluid machinery and hydraulic structures. Ann. Rev. Fluid Mech. 13, 273–328. BELAHADJI, B., FRANC, J.P. & MICHEL, J.M. 1995 Cavitation in the rotational structures of a turbulent wake. J. Fluid Mech., 287, 383–403. BOULON, O., CALLENAERE, M., FRANC, J.P., MICHEL, J.M. 1999 An experimental insight into the effect of confinement on tip vortex cavitation of an elliptical hydrofoil, J. Fluid Mech., 390. BRENNEN, C.E. 1995 Cavitation and Bubble Dynamics. Oxford University Press. DONG, R., CHU, S., KATZ, J. 1992 Quantitative Visualization of The Flow Structure Within The Volute of a Centrifugal Pump, Part A: Technique, J. Fluids Eng., 114, 390–395. FARRELL, K.J. & BILLET, M.L. 1994 A correlation of leakage vortex cavitation in axial-flow pumps, Journal of Fluids Engineering, 116. GOPALAN, S., KATZ, J., KNIO, O. 1999 The flow structure in the near field of jets and its effect on cavitation inception, Journal of Fluid Mechanics; 398, 1–43. GOPALAN, S. & KATZ, J. 2000 Flow structure and modeling issues in the closure region of attached cavitation, Physics of Fluids, 12, 895–911. HIGUCHI, H., ARNDT, R.E.A., ROGERS, M.F., 1989 Characteristics of tip vortex cavitation noise, J. Fluids Engng., 111, 495–501. HUANG, N.E. et al. 1998 The empirical mode decomposition and the Hilbert spectrum for non-linear and non-stationary time series analysis. Proc. R. Soc. London 454, 903–995. HSIAO, C.T. & PAULEY, L.L. 1998 Numerical study of the steady-state tip vortex flow over a finite-span hydrofoil. Journal of Fluids Engineering, 120. JOSEPH, D.D. 1998 Cavitation and the state of stress in a flowing liquid. J. Fluid Mech. 366, 367–378. KATZ, J. & O'HERN, T.J. 1986 Cavitation in large-scale shear flows. J. Fluids Engng 108, 373–376. MAINES, B.H. & ARNDT, R.E.A. 1997 Tip vortex formation and cavitation, Journal of Fluids Engineering, 119. O'HERN, T.J. 1990 An experimental investigation of turbulent shear flow cavitation. J. Fluid Mech. 215, 365–391. RAN, B. & KATZ, J. 1991 The response of microscopic bubbles to sudden changes in ambient pressure. J. Fluid Mech. 224, 91–115. ROTH, G., HART, D. & KATZ, J. 1995 Feasibility of using the L64720 video motion estimation processor (MEP) to increase efficiency of velocity map generation for PIV, ASME/EALA Sixth International Symposium on Laser Anemometry, Hilton Head S.C. ROTH, G., & KATZ, J. Five techniques for increasing the speed and accuracy of PIV interrogation, submitted to Meas. Sci. Technol. (June 2000). SRIDHAR, G. & KATZ, J. 1995 Lift and drag forces on microscopic bubbles entrained by a vortex. Phys. Fluids 7, 389–399. the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line ON THE FLOW STRUCTURE, TIP LEAKAGE CAVITATION INCEPTION AND ASSOCIATED NOISE 650 DISCUSSION Georges L.Chahine and Chao-Tsung Hsiao DYNAFLOW, INC. We are grateful to Dr. Rood and the authors of the very interesting paper “On the Flow Structure, Tip Leakage Cavitation Inception and Associated Noise”, for requesting a discussion. The authors have conducted careful experiments to investigate cavitation inception in the gap region between a foil and a solid wall. They visualized the cavities in the vortical regions and detected the acoustic signal emitted during the dynamics. They generated bubble nuclei using electrolysis. They then modified the gap size and deduced trends in cavitation inception curves. We are particularly interested in two conclusions the authors draw: 1. “High amplitude noise during cavitation is primarily due to the growth, distortion and fragmentation of the bubbles”. 2. “The acoustical and visual detection of cavitation match reasonably well”. The first conclusion confirms our original early numerical predictions for bubble dynamics in a vortical structure [1]. Commonly used spherical bubble models predict that the bubble continuously grows during capture until it reaches the “vortex axis”, then collapses later when the vortex diffuses. To the contrary, our 3D BEM numerical simulations show that bubbles larger than some characteristic size significantly distort while being captured, form reentrant ‘jets', stretch, elongate, and get split into two or more smaller bubbles. This occurs when the pressure gradient the bubble sees is large and when various parts of its surface grow with differing velocities. At some point some parts see a pressure rise while the rest of the bubble is still growing. (See Fig. 1, 2). Once a bubble becomes centered on the vortex axis it can continue to elongate and subdivide [1] producing further noise. This leads to liquid-liquid impact on some part of the bubble that can be a significant noise source. Unfortunately, this part of the problem is difficult to compute, and is a subject of our on- going efforts for ONR. The conclusions in this paper give us further confidence in our simulations. Figure 1. Bubble shape at four instances. Initial bubble center location is at 0.2 core radius. The second conclusion could be misinterpreted if one does not underline that optical and acoustical criteria for cavitation inception lead to the same answer only when one uses sophisticated techniques such as used in the paper, involving appropriately triggered micro-photography. Since this is rarely the case in practice, the acoustic criterion gives higher values for s. In addition, the authors have used an additional factor to call inception, which is the use of the number of events per second. We believe this to be a very useful approach. Figure 2. Bubble wire-frame shapes during its capture by a vortex. Figure 3. Normalized frequency spectra for various bubble sizes in a line vortex. An additional comment to add is the great importance of the initial nuclei size on the bubble dynamics in a vortex and on the generated acoustic signals and spectra. Our study [2] shows, albeit for spherical bubbles, that it is difficult to find a simple scaling to describe all bubble sizes. Instead, there appears to exist for a given vortex flow field several families of behaviors (see Fig. 3). We would like the authors to discuss this aspect of the problem since they have the authoritative version for attribution. restricted themselves to relatively large nuclei. REFERENCES 1. G.L.Chahine, “Bubble Interactions with Vortices,” Chapter 14, Vortex Flows Ed., S.Green Kluwer Academic, 1995. 2. C-T Hsiao, G.L.Chahine, and H.L.Liu, “Scaling Effects on Bubble Dynamics in a Line Vortex Flow: Prediction of Cavitation Inception and Noise,” DYNAFLOW, INC. Technical Report 98007–1, Aug, 2000.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line ON THE FLOW STRUCTURE, TIP LEAKAGE CAVITATION INCEPTION AND ASSOCIATED NOISE 651 AUTHOR'S REPLY We thank the discussers for reading the paper and offering several comments and suggestions. It is also nice to see that some of their numerical simulations showed similar results as observed in our experiments. In response to specific questions: First the discussers are correct to point out that the optical and acoustical detection of cavitation match well only when appropriately triggered, high-speed, high magnification photography is used. In this study we intentionally focus on bubbles that require little tension to cause cavitation inception (~100µm diameter). These initial bubble sizes are smaller than the vortex core (about 1/5th of the core diameter). We have not looked at the effect of various initial bubble sizes on bubble dynamics during cavitation. But as indicated by Chahine we agree that various bubble sizes will behave differently. For very small bubbles the critical pressure leading to cavitation inception is dependent on bubble size. Larger bubbles will be deformed, distorted and fragmented by the local pressure non-uniformities. In the present study we use bubbles that require little tension to initiate cavitation, but are still significantly smaller than the core. Once cavitation starts the bubble grows substantially leading to odd shapes, fragmentation etc. the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line ON THE FLOW STRUCTURE, TIP LEAKAGE CAVITATION INCEPTION AND ASSOCIATED NOISE 652 DISCUSSION K.J.Farrell and W.A.Straka Pennsylvania State University, USA I want to thank the authors for contributing this most interesting paper to the Naval Hydrodynamics symposium. The collection of detailed PIV flow field measurements, visual observations of individual bubble dynamics, and corresponding transient acoustic measurements are comprehensive and unprecedented at this small scale. It is interesting that the higher amplitude noise peaks were associated with bubble distortion and fragmentation rather than shape or size change. In my opinion, the intended relevance of the subject investigation to the “effect of gap size on the flow structure and on the inception of tip leakage cavitation” is limited and somewhat misleading due to the omission of several important features of tip leakage flows. First, the relative motion of the tip and end-wall is omitted. In a pump, the relative motion augments the leakage flow; in a turbine the motion opposes it. The so-called scraping vortex contributes vorticity to the leakage vortex; and this contribution is certainly a function of gap size. Additionally, centrifugal forces contribute to secondary flows, which can interact with the leakage vortex at the tip. Furthermore, the contemporary practice of unloading the blade tip is not a feature of the test hydrofoil. Rather, the lower half of the span is linearly unloaded from a constant lift coefficient along the upper half-span of the hydrofoil. Given these omitted features of a tip leakage flow, the study is more relevant to the effect of confinement on tip vortex cavitation inception and associated noise. This is important distinction relative to the observation of a cavitation inception index minimum at some value of normalized clearance. The authors correctly point out that Boulon et al. (1) do not observe a cavitation minimum, while Farrell and Billet (2) and Gearhart and Ross (3) do. On the basis of total pressure loss, an optimum clearance exists when the scraping, secondary, and leakage sources of circulation at the tip have a zero net sum (4) or are identically zero [the motivation of the compressor “squealer” tip, e.g. (5)]. Conversely, the data of Figure 14 suggest higher loss with the smaller clearance. From the measured cavitation event rates plotted in Figure 6, it would appear that for very low event rates that gap size may not be a significant discriminator in cavitation performance. The observation begs the often-asked question— what is the definition of cavitation? The ITTC round-robin tests clearly identified both flow and water quality as contributors to scale effects, but certainly the threshold of inception is important as well in collapsing data. Can the authors comment on this generally and on the very low event rate behavior observed in their experiment? The statistical nature of cavitation rests significantly on the probability of an appropriately sized nucleus entering the low-pressure zone in the vortex. Accordingly, would the aurthors comment on the uniformity of the nuclei distribution and the method and location of measurement? 1. Boulon, O., Callenaere, M., Franc, J.P., and Michel, J.M. “An Experimental Insight into the Effect of Confinement on Tip Vortex Cavitation of an Elliptical Hydrofoil,” J. Fluid Mechanics, Vol. 390, 1999. 2. Farrell, K.J. and Billet, M.L. “A Correlation of Leakage Vortex Cavitation in Axial-Flow Pumps,” J. Fluids Engineering, Vol. 116. 3. Gearhart, W.S. and Ross, J.R., “Tip Leakage Effects,” Applied Research Laboratory Penn State TM 83–20, 28 February 1983. 4. Lakshminarayana, B., “Methods of Predicting the Tip Clearance Flow in Axial Flow Turbomachinery,” J. Basic Engineering, September 1970, 467– 482. 5. Wisler, D.C., “Advanced Compressor and Fan Systems,” General Electric Aircraft Engine Business Group,” presented at the VKI/Penn State Short Course on “Tip Clearance Effects in Axial Turbo-Machines,” April, 1986. AUTHOR'S REPLY We thank the discussers for reading the paper and offering several comments and suggestions. The discussers are correct to point out that several features of a tip leakage flow in a rotating turbomachine are omitted—the motion of the tip relative to the end wall, effect of centrifugal forces and unloading of the tip (ours is intentionally loaded). The differences may explain why some investigators observe a minimum in cavitation index while some don't. To answer specific questions of the discussers: First the water in the test facility is deaerated and we record accelerometer signals without generating any nuclei. Under such conditions we may observe one or two cavitation events in a ten second period, the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line ON THE FLOW STRUCTURE, TIP LEAKAGE CAVITATION INCEPTION AND ASSOCIATED NOISE 653 indicating that the free stream nuclei are almost eliminated. Then we “flood” the tip region with bubbles (~100µm diameter—size distribution and details are provided in the paper) at approximately 2500 bubbles/s. The measurements were made just upstream of the leading edge and had a field of view of about 3mm. The images were analyzed using a blob analysis software. Bubbles in good focus were used for size distribution. All the traces including those that are not exactly in focus were used for computing the bubble flux. Bubble with diameters of 100µm require little tension to initiate cavitation, thus bubble size is not a critical issue in the present study. Also generation of 2500 bubbles per second makes cavitation inception less sensitive to bubble populations. However, being a very turbulent flow with large coherent structures, infrequent cavitation events (less than 2 per second) are a result of “extreme” flow conditions and not typical of the flow. With increasing events per second a trend can be correctly identified. Thus, the slope of the cavitation event rate curve is important in addition to its absolute values. the authoritative version for attribution.