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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 PROPELLER WAKE ANALYSIS BY MEANS OF PIV 499 - The tip vortex vorticity diffusion is very strong up to x/R=1 as also shown in figure 12, where the mean vorticity of the tip vortex is plotted along the downstream distance. Such result is similar to those obtained by Jessup (1989) for the unskewed propeller 4119. - As soon as the blade wake is released and before it is dissipated, a strong deformation takes place. At about x/ R=1 the wake of the actual blade feels the action of the tip vortex of the previous one which starts to deform the wake. At x/R≈1.5 the wake of the actual blade interacts with the tip vortex of the previous one. For x/R>2 the wake of the actual blade looses the link with its tip vortex and is rolled up by the previous blade tip vortex. Figure 13 shows the distribution of the turbulence intensity σU and σV for the measured velocity components for θ=0°, while figure 14 shows the evolution of σV for θ=20°, 40°, 60°, 80°. Even if the confidence of the statistical estimator is limited, due to the fact that has been evaluated only over 65 samples, some important features of the wake can be recognised. The turbulent wake released by the blade is quickly dissipated and diffused downstream. The same process of wake deformation and broadening, due to the action of the tip vortices and of the hub vortex, observed in the vorticity plots, is also seen in the turbulence level distributions. Nevertheless, new information are obtained by this second order statistics: - The effect of hub vortex roll up in the wake is very important and at x/R=2 the blade wake, linking the tip vortex to the hub vortex, almost disappears especially for the σU distribution. - Turbulence diffusion from the hub vortex occurs in the longitudinal evolution especially for σV as expected due to the hub vortex orientation. - Some small scale turbulence, more evident in the σV distribution, generated probably at the leading edge of the blade, is quickly dissipated downstream within one propeller radius - The effect of noise in the images, due to the cavitating hub is pointed out by the intense spikes in the turbulence level distribution - Velocity fluctuations at the tip vortex core increase while this is convected downstream. This aspect is related to the vortex breakdown instability which affects the velocity fluctuations through spatial oscillations of the core. Furthermore, the pattern of the turbulence distribution suggests that the tip vortex oscillation occurs in some preferential directions. The tip vortex fluctuations, leading to the breakdown, can be pointed out also by evaluating the standard deviation of the spatial fluctuations of tip vortex core with respect to the mean at a given longitudinal position. The result, given in figure 15, shows that the amplitude of the spatial fluctuation is increasing downstream and that the amplitude of transversal fluctuations has a higher growth rate in respect to the longitudinal. This result is similar to those obtained by Cotroni et al. (1999) for a different propeller and seems to be a general feature of the helical vortex system behaviour. Another important feature of the tip vortex system instability, pointed out by PIV, is the separation of the four tip vortex trajectories after the section of maximum contraction. In figure 16 the evolution of the tip vortex trajectory for different revolution angles is shown. After the contraction, and approximately at the same location where the tip vortex interacts with the wake of the subsequent blade, there is a clear separation of the trajectory of the tip vortices due to the different blades. Furthermore, as pointed out in the same figure, the location of the tip vortices in the measurement plane at different angles points out the oscillation of the whole stream tube. This is loosing its axisymmetry and blade periodicity but in the first phase of the breakdown still maintains the phase with the propeller revolution. Such behaviour also provides an explanation of the blade sub harmonics pressure fluctuations sometime experienced by the hull. Such measurements are in perfect agreement with the flow visualisations obtained in incipient cavitation given in figure 17. The tip vortex trajectory separation is strictly related to the hub vortex deformation which moves from a line into a spiral. This behaviour is mainly due to mutual tip-hub vortex interaction as demonstrated by their simultaneous generation. The starting point of the instability could be the cross-blade wake interaction as proved by the fact that when reducing the loading conditions this interaction is shifted downstream as do the breakdown. CONCLUSIONS The PIV technique was used in a circulating water tunnel to investigate the spatial and temporal evolution of the wake of a four blade marine propeller in a uniform inflow. Both instantaneous and averaged velocity fields are achieved, the latter after phase sampling averaging over the same angular position of the propeller blade. The experimental results, in terms of velocity and vorticity fields, reveal some of the different contributions to the complex propeller flow field: 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 PROPELLER WAKE ANALYSIS BY MEANS OF PIV 500 1. The viscous part of the wake generated by the boundary layers on the blade surfaces. 2. The potential part of the wake deriving from the vortex sheet at the blade trailing edge. 3. The slipstream contraction of the wake along the downstream direction and the beginning of its broadening after the contraction 4. The cross-blade interaction which seems to be the starting point of the breakdown process. 5. The behaviour of the tip and hub vortex in the instability of the helical vortex system. The PIV technique, both for the careful control of the set-up adopted in the present experiment and for the image analysis algorithm implemented, allows a good spatial resolution (of the same order of magnitude as in LDV) to be obtained. PIV has proved to be a suitable means of investigating the complex flow field in the wake of a propeller giving additional and complementary information in comparison to the LDV technique. ACKNOWLEDGEMENTS. The authors are grateful to the CEIMM personnel and to Mr. Di Florio who supported the PIV measurements. This work was sponsored by Italian Ministero dei Trasporti e della Navigazione in the frame of INSEAN research plan 2000– 2002. REFERENCES Arndt, R., Maines, B. “Viscous effects in tip vortex cavitation and nucleation”, Proc. of the 20th Symposium on Naval Hydrodynamics, 1994. Biggers, J.C., Orloff, K.L., “Measurements of the helicopter rotor-induced flow field”, Journal of American Helicopter Society, Vol. 20, no. 1, 1975. Cenedese, A., Accardo, L., Milone, R. “Phase sampling techniques in the analysis of a propeller wake”, Proc. of the International Conference on Laser Anemometry Advances and Application, Manchester UK 1985. Chesnack C., Jessup S., (1998), Experimental characterisation of propeller tip flow, 22th Symposium on Naval Hydrodynamics, Washington D.C. Cotroni A., Di Felice, F., Romano, G.P., Elefante M. “Propeller Tip vortex Analysis by means PIV”, 3rd International Workshop on PIV, Santa Barbara CA, (1999) Hunter, WW, Nichols, CE., “Wind Tunnel Seeding Systems for Laser Velocimeters.” NASA Conference Publication 2393, Workshop, March 19–20, 1985, NASA Langley Research Jessup, S.D. “An experimental investigation of viscous aspects of propeller blade flow”. Ph.D. Thesis. 1989 The Catholic University of America, Washington D.C.. Keane R.D., Adrian R.J., “Theory of cross-correlation analysis of PIV images”, Applied Scientific Research, Vol. 49, 1992, pp. 191–215. Keane R.D., Adrian, R.J., “Optimization of Particle Image Velocimeteres”. Part 1: Double pulse system. Meas. Sci. Tech., 1, pp. 1202 1215, 1990 Kobayashi, S. “Experimental methods for the prediction of the effects of viscosity on propeller performance”. Dep. of Ocean Engineering, Rep. 81–7 MIT, 1981. Kobayashi, S., “Propeller wake survey by laser Doppler velocimeter”. Proc. of the International Symposium on the Application of laser-Doppler Anemometry to Fluid mechanics, Lisbon 1982. Koyama, K., Kagugawa, A, Okamoto, M. “Experimental investigation of flow around a marine propeller and application of panel method to the propeller theory”, Proc. of the 16th Symposium on Naval Hydrodynamics, 1986. Landgrebe, A.J., Johnson, B.V., “Measurement of model helicopter rotor flow velocities with a laser Doppler Velocimeter”, Journal of American Helicopter Society, 1974. Vol. 19, no. 3. Melling A., “Seeding Gas Flows for Laser Anemometry”. AGARD Conference on Advanced Instrumentation for Aero Engine Components, AGARD- CP 399, 1986. Min, K.S, “Numerical and experimental methods for prediction of field point velocities around propeller blades”. Dep. of Ocean Engineering, Report no. 78–12, MIT, 1978. Meyers, J.F., “Generation of Particles and Seeding”. Von Kárman Institute for Fluid Dynamics, Lecture Series 1991–05, Laser Velocimetry, Brussels, 1991 Raffel, M., Willert, C., Kompenhans, J., “Particle Image Velocimetry”, Springer ISBN 3–540–63683–8, 1998 Serafini, J.S., Sullivan, J.P., Neumann, H.E. “Laser Doppler flow-field measurements of an advanced turboprop”, 17th Joint Propulsion Conference, AIAA/SAE/ASME, Colorado Springs, Colorado, 1981. Stella, A., Guj, G., Di Felice, F., Elefante, M. “Propeller wake evolution analysis by LDV”, Proc. of the 22nd Symposium on Naval Hydrodynamics, Washington, 1998. Wang, M.H. “Hub effects in propeller design and analysis”, Dep. of Ocean Engineering., Rep. 85–14, MIT, 1985. the authoritative version for attribution.

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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 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 the authoritative version for attribution. PROPELLER WAKE ANALYSIS BY MEANS OF PIV Figure 8: Longitudinal (U) and radial (V) component distribution for θ=0° Westerweel J., “Fundamentals of Digital Particle Image Velocimetry”, Meas. Science and Technology Vol. 8, pp. 1379–1392., 1997 Westerweel J., “Efficient detection of spurious vectors in particle image velocimetry data”, Experiments in Fluids, Vol. 16, pp. 236–247., 1994 501

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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 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 the authoritative version for attribution. PROPELLER WAKE ANALYSIS BY MEANS OF PIV Figure 9: Modulus of the inplane velocity with streamlines Figure 10: Non dimensional vorticity distribution and streamline in the frame moving with the upstream flow for θ=0° 502

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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 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 the authoritative version for attribution. PROPELLER WAKE ANALYSIS BY MEANS OF PIV Figure 11: Vorticity evolution for θ=20°.40°, 60°, 80° 503

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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 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 the authoritative version for attribution. PROPELLER WAKE ANALYSIS BY MEANS OF PIV Figure 13: Turbulence intensity distribution for =0° Figure 12: Mean tip vortex vorticity downstream evolution 504

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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 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 the authoritative version for attribution. PROPELLER WAKE ANALYSIS BY MEANS OF PIV Figure 14: σV distribution evolution at θ=20°, 40°, 60°, 80° 505

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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 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 the authoritative version for attribution. PROPELLER WAKE ANALYSIS BY MEANS OF PIV Figure 16: Tip vortex location at different revolution angle θ Figure 15: Tip vortex spatial fluctuation with respect the mean position 506

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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 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 the authoritative version for attribution. PROPELLER WAKE ANALYSIS BY MEANS OF PIV Figure 17: Flow visualitation in incipient cavitation of the propeller vortex system dispersion and hub vortex deformation 507

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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 PROPELLER WAKE ANALYSIS BY MEANS OF PIV 508 DISCUSSION R.Arndt University of Minnesota, USA I would assume that the propeller tip vortex interaction would be a function of advance coefficient. Is this true? Have you investigated vortex breakdown? AUTHOR'S REPLY The propeller tip vortex and wake blade interaction as well as the vortex breakdown are function of the advance coefficient as expected. In the present paper results regarding only the case of advance coefficient J=.74 has been presented but measurements for J=.88 and J=1.02 have also been performed. In figure is shown the comparison of the vorticity field for the above higher and lower advance coefficients for the same propeller revolution angle. At higher J due to the higher pitch of the wake, the interaction of the actual blade wake with the tip vortex of the previous one is shifted downstream. Furthermore at higher advance coefficients, a weaker wake and tip vortex, reduce the cross-interaction resulting in a more stable helical vortex system as observed in incipient cavitation flow visualization (Stella et al 2000) REFERENCES Stella, A., Guj, G:, Di Felice, F., Elefante, M. “Propeller wake analysis by LDV and Flow Visualitations”, September 2000, Journal of Ship Research, Vol 44, N 3, pp. 155–169 Figure: Comparison of the vorticity field at two different values of the advance coefficient J 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 PROPELLER WAKE ANALYSIS BY MEANS OF PIV 509 DISCUSSION G.Bark Chalmers University of Technology, Sweden First of all I would like to thank the authors for a very interesting paper demonstrating the potential of the PIV technique for the study of aspects of propeller wakes that can be of interest to understand propeller operation as well as cavitation. For understanding the cavitation process a thorough knowledge of the unsteady flow field of the non-cavitating flow is important also if the actual flow can be significantly influenced by the cavitation. The recording of the velocity as a function of time in a point is limited by the frame rate of the cross correlation camera, in this case 15 Hz. This frame rate is too small to generate a relevant time series at typical conditions. Thinking of the frame rates of high speed digital video cameras, being typically some thousands frames per second, my question is whether it is possible with present technology to increase the frame rate in the PIV-application and record a time series of significantly higher resolution in time? Or do we have to relay on the periodicity of the flow and construct the time series from measurements from different revolutions with different displacements relative the propeller? (Due to the tangentially induced velocity a material point will however move slowly out of the axial plane in which it was originally observed). For a steady homogeneous inflow the quasi steady method for tracing the vortex development downstream the blade is adequate. In the more or less unsteady wake of a ship, where the so called tip vortex bursting sometimes occurs in the cavitating vortex, it can however be of interest to follow the development of a particular vortex. Is a study of an unsteady motion of such a time scale possible with the needed requirements on the accuracy? With the present questions in mind, what is then the exact meaning of the term “instantaneous” in Figure 7? AUTHOR'S REPLY To reply to the interesting points raised by Prof. Bark, we would like to refer to the images given in the figure. They represent the near-wall region of a turbulent water channel flow acquired with a high-speed video camera (up to 2000 images/s) at the University “La Sapienza” in Rome. A continuous sequence of up to 1000 images as those showed can be acquired and stored on a PC. At present, this device is used to acquire PIV images and to derive the time evolution of the whole PIV field in different flows (1). The information from these plots are used to detect flow structures (as that at x +≈150÷220, y+≈50 in the figure, where the+is used to indicate wall variables) and to follow their evolution and interactions. With a similar system it is possible to compute cross-correlation functions between successive frames and to obtain the velocity field with a rather high temporal resolution (similar to that obtained with an LDA system). Therefore, the answer is definitely yes, it is possible to achieve a resolution in time as high as 1 kHz. In this way, vortices can be followed also in unsteady and inhomogeneous flow conditions (as in the wake of a ship or propeller). It is not strictly necessary to average over different propeller revolutions, unless this was required by the user. Problems arise in respect to the spatial resolution of the system when high frame rates are required (as in the case of large flow velocity). It should also be noticed that, with the PIV measurement system employed in the paper, although the velocity time history is not derived, the velocity field is almost instantaneous. Indeed, the time interval between the two laser exposures (used to compute the cross-correlation function) is rather small (100 µs). The term “instantaneous” must be considered as an average over a time interval of such an order of magnitude. REFERENCES (1) Ciraolo G., Romano G.P. “Investigation on wall structures in a turbulent channel flow using stereo PIV”, Proceedings of the 8th European Turbulence Conference, Barcelona, 2000. the authoritative version for attribution.

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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 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 the authoritative version for attribution. PROPELLER WAKE ANALYSIS BY MEANS OF PIV Figure. Velocity vectors in the near-wall region of a water channel recorded at time intervals equal to 1/250s. 510