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24th Symposium on Naval Hydrodinamics Fukuoka, JAPAN, 8-13 July2002 Propeller Wake Analysis Behind a Ship by Stereo PIV G. Calcagno, F. Di Felice, M. Felli, F. Cerebra iNSEAN (Istituto Nazionale di Studi ed Esper~enze di Architettura Navale) ABSTRACT An experimental investigation of a five blade MAU propeller wake behind a Series 60 Cb=0.6 ship model has been performed using Stereo Particle Image Velocimetry (Stereo-PIV) in a large free surface cavitation tunnel. The investigation of the wake at different longitudinal stations and its evolution in phase with the propeller has pointed out the capability of Stereo-PIV in resolving the complexity of the flow field. The blade viscous wake, which develops from the blade surface boundary layers, the trailing vortex sheets that are due to the radial gradient of the bound circulation, and the velocity fluctuation distributions are identified and discussed. The complex interaction between the hull wake and propeller is described through the evolution of the mean velocity components and the vorticity fields. In the near field the effects of turbulent diffusion and viscous dissipation, which cause a rapid decay of the velocity gradients in the trailing edge wake, are also examined. INTRODUCTION In the last 20 years the application of advanced optical measurement techniques like laser Doppler velocimetry (LDV) has provided a deep insight into complex flow fields like propeller flows. Most of the actual knowledge on propeller flow, especially regarding the turbulence characteristics, derives from the application of the LDV measurement technique (Min. 1978; Kobayashi, 1982; Cenedese et al., 1985; Jessup, 1989, Chesnack et al. 1998, Stella et al., 2000) and is today routinely used by the main research organizations in the world and in different fields. LDV will allow, also in the future, to obtain valuable information with high accuracy on the mean and fluctuating velocity fields in complex flows which is of relevance for their physical modeling and for the validation of computer codes. However, as any experimental technique, besides its undeniable advantages, LDV has some limitations: it can hardly give an idea of the spatial characteristics of large coherent structures which are generally encountered in complex and separated flows, due to its single point measurement nature; it can induce significant errors on the intensity of unsteady vertical structures, due to its fixed location and time averaging nature; it needs long periods of operation of the facility to get a whole velocity field, increasing the testing costs and leading to difficulties in unsteady flows or when the facility working characteristics have to be kept constant for long periods of time. This is the case of the experimental investigation of the propeller wake in a non-uniform inflow. This analysis requires a sufficiently dense grid into the whole measurement plane, for each different propeller angle, in order to resolve the flow structures during the propeller revolution (Fell) et al., 2000; Esposito et al., 2000; Di Felice et al., 2000~. From this point of view, Particle Image Velocimetry (PIV) technique, as it allows the instantaneous measurement of the velocity at a plane, offers many advantages over single point techniques: the experimental analysis could be fast and easily conducted by acquiring images at each angular position of the blade, drastically reducing the testing time. Over the past decade PIV technique has experienced a considerable progress and is today considered to be a powerful whole field measurement technique, continuously broadening its range of applications. The growth of the PIV technique due to the improvement of the hardware components is
clear: high-energy and nanosecond pulse duration lasers, high-resolution and low-noise CCD cameras, fast frame grabbers, as well as faster computers and large data storage hard disks are among the major factors that have raised the capabilities of the measurement approach. Recent literature demonstrates the applicability of the technique to the naval field, in particular in towing tank applications (Guj et al. 2001) and in the case of the propeller flow (Cotroni et al., 2000; Di Felice et al 2000) even if these investigations were limited only to the two velocity components in the measurement plane (planar PIV or 2C-PIV). However, it is apparent that this information is not always sufficient to characterize the flow field especially for propeller flows where the presence of strong three-dimensional flow structures with strong velocity gradients requires the knowledge of all the velocity components. Stereoscopic PIV, using two cameras to view the flow from two perspectives, is the obvious extension of planar-PIV for measuring all three velocity components in a plane. Two components of velocity nominally perpendicular to the camera optical axis are measured from each camera viewpoint. The pair of two-dimensional velocity vectors for a point in the flow are then combined to yield a three-dimensional velocity vector. By combining the vector fields from the two cameras, the three-dimensional velocity field for the plane in the fluid is computed. In the present work Stereo-PIV is applied to the analysis of a ship model with propeller in the large INSEAN Circulating Water Channel. The experiment is a partial replica of the Toda et al. (1990) experiments: measurements were performed By_ ,` ~ ' 1 tax in several cross-planes behind of a Series 60 Cb=0.6 ship model with a 5-blade MAU propeller. The Series 60 model was selected for the experiments to complement the many previous studies with this geometry. In the following sections, results of the wake survey are discussed pointing out to the measurement technique capabilities in resolving the wake structures and outlining the major problems in applying stereo PIV in a large facility . EXPERIMENTAL SET-UP Measurements were carried out at the INSEAN Circulating Water Channel, a free surface cavitation channel with a 10 m length, 3.6 m wide and 2.25 m depth test section which allows a 5.2 m/s water flow maximum speed. More information regarding the facilities capabilities can be found at http://www. in scan. it The ship-model was a Series 60 Cb=0.6, 6.096 m length, conforming to the standard offsets with some minor modification of the stern geometry to allow the propeller installation. The propeller was a 5- blade MAU propeller, with the following features: diameter D=22 1.9 mm, pitch-diameter ratio P/Do7=1.03 1, expanded area-disk area ratio AJAo=0.74. Tests are carried out at the propeller angular velocity of 6.7 rps with the tunnel water velocity set to 1.22 m/s, corresponding to a Froude number Fr = 0.16. In the presentation of the results and the discussion to follow, a Cartesian coordinate system is adopted in which the x,y,z axes are in the direction of the uniform flow, starboard side of the hull and upward, respectively. Measurements were Figure 1: Ship, propeller model and location of the measurement planes. The propeller is shown at ~ = 0° Figure 2: Experimental set-up
performed in three cross-planes orthogonal to the shaft and located downstream the propeller disk, respectively at x/L.= 0.9997, 1.0000, 1.0187 (figure 1) where L is the model length. In a reference frame with the propeller center, the above measurement planes are located at x/D= 0.59, 0.76 and 1.85 respectively. In the first plane, measurements without the propeller were also performed to have an estimate of the propeller inflow. The locations of the last two measurement planes are similar to the Toda et al. (1990) experiment while the first one is very close to the propeller and was selected to test the stereo-PIV capability of analyzing regions with stronger velocity gradients as expected in that plane. The experimental set-up is shown in Figure 2. The light sheet, generated by a two-head Nd-YaG laser was delivered to the measurement plane by means of underwater optics. The laser sheet generation rate was 10 Hz, with an energy output of 200 mJ per pulse. A rotary 3600-pulse/revolution encoder supplied the actual propeller position as an electrical trigger signal to the synchronizer. This in turn provided the trigger signals to the two flash lamps and two Q-switches of the double-head laser, as well as to both cameras. Therefore, the image acquisition was synchronized with the propeller angle. During the test campaign, 129 acquisitions at a given propeller angle were performed in order to obtain the mean velocity field. Propeller angles from 0° to 69° have been considered with a step of 3°. STEREO PIV SYSTEM SETUP In the present experiment the angular displacement method was adopted for the optical configuration of the stereo-PIV system. The setup consisted of two cameras with a resolution of 1280x1024 pixels each and a depth of 12 bits per pixel. The first one (left camera) was located 2 m downstream the ship model in an underwater housing, with an orthogonal view of the measurement plane, and the second one (right camera) outside the tunnel test section looking at the measurement plane through the tunnel access windows. To reduce the strong diffraction and aberrations due to the thick window and to the water/glass/air interfaces a prism filled with water has been placed in front of the right camera. The adopted configuration is not symmetric and has never been presented before in previous Stereo- PIV measurements. The main reasons that led to this choice are the following: . . a symmetrical configuration, with two cameras looking at the measurement plane through the windows on the opposite sides of the test section, which guarantees the maximum accuracy (Prasad, 1993; Weesterweel and Van Cord, 1999) because of the large angle between the cameras, was not practical. (size of the facility, limited length of the camera cables, need to control remotely the focus and Scheimpflug angle of the farther camera located in the opposite side of the test section with respect to the control room). with the adopted configuration the underwater camera was directly measuring the cross-flow components V and W. maximizing the accuracy on these components. Furthermore the Scheimpflug angle needs not to be remotely controlled which would increase the complexity with a larger underwater case to host all the necessary equipment. In such way, all the errors, in the stereo reconstruction, are confined to the estimate of the longitudinal component only. the adopted configuration, with an angle between the right and left cameras ranging from 36° to 40°, depending on the measurement plane, is the most accurate in the evaluation of the out-of-plane component, among all possible optical configurations having the cameras on the same side of the test section. This result has been assessed on a test bench by measuring a known displacement of a reference object placed on a translation stage. IMAGE ANALYSIS AND STEREO RECONSTRUCTION As the first step toward the determination of the three velocity components at the measurement plane, the images are processed to obtain the vector fields viewed by the left camera and the right camera. The acquired images were analyzed using an algorithm in which the window offset correlation method has been implemented (Westerweel 1997). Furthermore a recursive processing method was used by implementing a hierarchical approach in which the sampling grid was continually refined and also the size of the interrogation windows was reduced during the iterations. During the iteration the interrogation window was also weighted by using a Gaussian function that was stretched in the direction of the window offset to further improve the signal to noise ratio of the correlation function (Di Florio et
al., 2001~. In the last iteration the windows were also overlapped to obtain a better reconstruction of the whole flow field especially in the regions with strong gradients. This procedure has the added capability of Figure 3: Image preprocessing: a) original image; b) mean image over 129 acquisitions; c) final image with propeller removed in the background obtained subtracting (b) from (a) applying interrogation windows with size smaller than the particle image displacement increasing both the dynamic range and the spatial resolution. To eliminate the remaining spurious vectors, each data set was subjected to a validation procedure to detect and replace spurious displacement vectors (Keane and Adrian, 1992~. For the results presented in the following sections, a final window size of 32x32 pixels, with 75% overlap between two adjacent windows, has been adopted as the best compromise in terms of spurious vector reduction and spatial resolution. This window size was equivalent to 7 x 7 mm2 in real space. In the stereo reconstruction the procedure described by Soloff et al. (1997) is used. The camera views were calibrated using a special target providing a mesh of 20X20 dots in two planes. This calibration was required to determine the transformation function needed to reconstruct the 3 velocity components from the two separate planar Figure 4: Longitudinal mean velocity component obtained by stereo reconstruction without (a) and with (b) image preprocessing
PIV measurements. Besides the geometrical correction of the perspective, this non-linear transformation took also into account the optical distortions introduced by the presence of multiple interfaces (air, glass and water). In the adopted configuration, the measurement area was defined by the overlapping region between the separate views and had a dimension of about 250 mm X 200 mm that was sufficient for investigating the whole propeller disc. The analysis of the acquired images presented some difficulties due to the fact that both left and right cameras were imaging the rotating propeller in the background of the measurement plane. The propeller, even if black painted with care, was scattering the light diffused by the particles, especially for the plane x/L=.9997 closer to the propeller masking the particles and locking the velocity at the propeller speed especially in the regions in proximity of the hub and at the blade edges. This led to the erroneous evaluation of the 3 components of the velocity field in the region extending along an horizontal radius from the hub. To overcome this problem the images have been pre-processed: a mean image (figure 3b) has been calculated by using all the acquired images at a given angle and this reference image has been subtracted from the actual image before the analysis (figure 3b). This procedure allows the elimination of the background propeller image (figure 3c) and drastically improves the final result. A comparison of the mean field obtained with and without such procedure at x/L = 0.9997 for ~ = 0° is shown in figure 4. The preprocessing procedure was used only in the analysis of the measurement plane closer to the propeller. For the planes at x/L = 1.000 and 1.018 the preprocessing of the images was not necessary because of the larger distance between the propeller and the measurement planes. Moreover the small depth of field of the camera objectives reduced the occurrence of the above problem. MEASUREMENT UNCERTAINTY A comprehensive discussion on the uncertainty and the accuracy of the PIV technique, especially for stereo-PIV, is out of the goal of the present work and this aspect is a complex topic with many open points. A detailed analysis can be found in Prasad (20001. In the following, the main assessments necessary to qualifier the present results and to outline the major problems are reported. 1100 1 000 900 800 700 .X 600 >500 400 300 con 1100 1 nnn 900 In _ 700 ·~600 >500 400 300 200 100 U (mars) 1~ I. do.~ oa - lo* camera field 5W 10W X trim - l 5W 10W X pixel Istantaneous 3D vector field (3 = 0° Vd Mag -;; ' if I; "A 5 44075 .~, , . - .i , ., . : ,., :: .:+ A ,.,. in,. ,,, I,,>,TSAR 2~ .S : 4.3526 ant ~ . 1 ~815 O Figure 5: Left (a) and right (b) camera instantaneous field with the 3 D stereo reconstruction (c)
The uncertainty on velocity measurements by each single camera is mainly due to the error on the particle displacement evaluation which can be normally considered less than 1/lOth of a pixel for the present image analysis algorithm (Raffel et al., 1998), which is equivalent to approximately 4 cm/s in terms of velocity. This error is essentially present in the measurement of the instantaneous flow field, in particular in the evaluation of the cross flow components which are directly measured by the underwater camera as explained before. The error in the measurement of the longitudinal component is related mainly to the stereo reconstruction. In the present case test bench results pointed out errors around 5%, but in the facility with a longer focal length of the objectives and the window aberration the previous number could be underestimate. This error, which seems to be relatively large, is a typical value for a stereo-PIV measurement and is depending on many factors such as the adopted optical configuration (angle between the cameras), optics aberrations, numbers of dots in the calibration target, numbers of planes used in the calibration, etc. The errors due to light reflections from the hub and from the blade edges were important in flow field regions mapped in the right or left camera in proximity of reflection spots. The moving propeller mean Held ~ = 0° ~ e,~f,~~ 4, ~ ~,~/~~ ~ ~ I. J (mIs) 1.E 1.24 o. in the background of the measurement plane is another source of error. Even if pre-processing the images mostly removes the propeller image and reduces this effect, the correlation peak is still locked at the propeller velocity, in the regions where there is a lack of particle traces. In the post-processing phase, the validation procedure is very effective to detect such spurious vectors due to the large difference between the flow and the blade velocity especially at the tip of the blade. Detected erroneous vectors are eliminated and replaced by interpolation. Nevertheless, spurious vectors might also be validated biasing the statistics especially in the proximity of the hub where the flow and propeller velocity become closer. This effect is relevant especially for the second order statistics. The accuracy of the mean velocity field definitely depends on the number of acquired samples and on the shape of the velocity probability distribution function. The probability density fimction in the tip vortex core and in the blade wake markedly differs from the Gaussian. Furthermore, a lack of data and less samples available for statistics have been observed in these regions. However by using the t- Student distribution (for which the confidence interval at 95%, is +1.96*rms /NI(N-1), with N=129), it is possible to estimate the uncertainty on a velocity ~1 100 , .' r ~ . ~ ~ }, ~ ~ ~ ~ ~ t ,' ~ ,' , ,' `, :, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ~ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 _ -100 -50 0 50 100 150 Y (mm) Figure 6: Mean field over 129 acquisitions. O -50 1
component to be about 1/6th of the measured velocity rms. RESULTS Instantaneous Flow Field An example of an instantaneous flow field obtained in the first measurement plane for the angular position O=0° is shown in figures 5a and Sb. For graphical reasons vectors were skipped by a factor of four. From the led and the right field, the 3D velocity field can be evaluated, as shown in figure 5c. The reconstructed flow field shows many missing vectors due to the fact that the number of spurious vectors is approximately the union of the right and left ones. During the mean values calculation, performed using only validated vectors and not the interpolated ones, the holes in the reconstructed mean field were recovered as shown in figure 6 where the 3D field is shown after averaging over 129 . . . acquisitions. Hull Wake And Propeller Inflow Before going into the details of the propeller wake, and to better understand the behavior of the flow field during the propeller rotation, the mean field and the vorticity field at x/L=0.9997 measured without the propeller are shown in figure 7 and 8. The mean field has been obtained averaging over 500 acquisitions. Although in the present case measurements of the propeller inflow were not exhaustive due to limited optical access with the Stereo-PIV set-up, this information can give an idea of the nominal wake and of the propeller inflow, even if obtained slightly downstream the propeller plane. The mean velocity field is characterized by a sharp and strong axial velocity defect due to the diminishing cross section of the hull at the stern. The cross flow generally is directed upwards and towards the hull center-plane where it tends to roll up generating a diffused circulation well resolved by the vector field and vorticity field. For the considered measurement plane, data from Toda et al., obtained by using Pilot tubes are available for comparison. Figure 9 shows the axial wake profiles performed at the same Froude number. The differences between the velocity profiles is rather apparent with a larger thickness of the velocity defect in Toda et al. (1990~. The difference can be related to the difference in the Reynolds number, which in the present experiment is almost double, as well as to the different characteristics of the facilities. Near Propeller Wake Evolution In the following discussion the evolution of the wake in phase with the propeller angular position at x/L=.9997 will be presented. In figure 10 the evolution of the longitudinal component U is shown for the propeller angles ranging from 0° to 63° with a step of 9° (this range corresponds to a blade passage). The main characteristics of a propeller wake working with non Figure 7: Mean velocity field at x/L=0.9997. Left side axial component. Right side cross-flow components Figure 8: Velocity modulus (right) and vorticity field (left)
uniform inflow due to the hull wake can be pointed out: the propeller wake loses the axisymmetrical morphology typical of an isolated propeller and the largest longitudinal velocity are achieved in the lower part of the propeller disc and at radial positions r/R=0.6-0.7 (R propeller radius) . the thin wake released by each blade can be recognized in the longitudinal component plots even if the wake thickness is approximately of the same order of magnitude of the spatial resolution of the PIV measurement. This leads to an underestimation of the velocity defects due to the smoothing effect of the interrogation window the tip vortex are visible in the velocity map and are pointed out by the strong velocity gradients at different angular positions at about r/R= 0.9. -1 oo -150 _ -20D _ 1 1 O.g N _ ~ O.8 o ~ 0.6 0.5 ~0.9 I;-'' X (mm) Figure 9: Ship model wake without propeller at x/L=.9997. Comparison with Toda et al. (1990) Tip vortices and blade wake are more evident in the V and W contour plots shown in figure 11 where the evolution of the cross-flow components is shown for a blade passage with a step of 18°. The above figures clearly show the strong circulation generated by the hub vortex that characterize the propeller slipstream. The passage of the blade in the narrow wake of the hull at 12 o'clock generates strong three- dimensional effects. In the axial velocity contour plots, when the blade is in the range of 18°< ~ < 36°, two parallel stripes of maximum and minimum velocity near the blade tip can be noticed. This phenomenon points out to the presence of a strong vortex structure having the axis parallel to the measurement plane. The strong three-dimensional effects due to the blade passage in the sharp hull wake can also be noticed in the vorticity evolution shown in figure 12. From the previous figure the following considerations can also be done: - the trailing vorticity, shed from the blade trailing edge, is well identified and consists of two layers of opposite sign which overlap at about r/R =0.7, in the blade section of maximum loading. - the link of the tip vortex with the blade trailing vorticity is more apparent with respect to the mean velocity field where this information is almost confused or lost; - the vorticity field provides information of the radial distribution of the blade loading and points out to the differences between the five blades due to the different respective inflow conditions; - the wake at 6 and 12 o'clock position is strongly distorted and fragmented as a consequence of the strong inflow variations in these angular positions. An example of the important modifications of the shape and intensity of the wake released by the blade during the revolution, is shown in figure 13. The location of the wake, identified by the vorticity field, is reported for the five blades for the propeller angle = 0°. The strong modification of the wake shape stresses the importance of considering the angular variation of the propeller inflow, which most of the time is ignored in some CFD calculations by integrating the nominal wake along the circumference at a given radius. Figure 14 shows the evolution of the total turbulence intensity distribution ~I(ui)2 +(V)2 +(W)2 where U7' V' and w' are the standard deviations of the velocity components. Even if the confidence interval on this second order statistical estimator is rather limited, due to the fact that only 129 samples have been evaluated, some important features of the turbulent wake can be outlined: - the maximum values of turbulent intensity are achieved in the tip and hub vortex cores;
~- F: `~.i ~.-iiN .~.~.~ i - ~.~. \~;i \.~;,,;~..~ - , .~..~...~... - :J - ....-}i~ i6.. :~ni ;.~.i. ~ 7.i ~d ., v~r ~ .~..~-i ~ :; Hi, :'.,~j~A Figure 10: Longitudinal velocity U (m/s) at different angles (0°,9°,18°,27°,36°,45°,54°,63°) for plane x/L=O.
~ - ~= non Moo -also .0,40 -0.30 o.2o "o.1o O.OO O.lo 0.20 0.30 0.40 0.50 O.60 0.70 t.: jr Figure 11: Cross-flow V,W (m s) at different angles (0°,18°,36°,54°) for plane X/L=0.999
Figure 12: Vorticity ( s-l) at different angles (0°,9°,18°,27°,36°,45°,54°,63°) for plane x/L=0.999
60 _ 40 _ _ _ ~ _ ~5 - {D _ 20 o - ~ 5= = /J 0.4 U.b O.8 rl R Figure 13: Shape of the trailing vorticity wake for each blade for propeller angle O= 0° - the trace of the hull wake, represented by a vertical stripe of turbulence, can still be noticed in the measurement plane; · the passage of the blade in the hull wake produces a strong turbulence generation due to the interaction of the hull wake with the blade tip vortex; · the intense spikes in the turbulence level distribution located at the blade trailing edge, near the hub and at different propeller angles are due to the erroneous inclusion in the statistical calculation of some spurious vectors locked at the blade velocity. This effect is attributed to the background motion of the propeller which was not completely removed by the image preprocessing and by the vector post-processing validation not able to completely filter spurious measurements as explained previously. Longitudinal Wake Evolution The description of the wake longitudinal evolution will be limited only to the propeller angle ~ = 0° due to the restricted space. The distribution of the mean velocity field at the three measurement planes is shown in figure 15 where the longitudinal component U and cross-flow are reported The evolution along the longitudinal axis of the axial velocity component U shows: the wake contraction between the first two planes (they are very close together and also close to the propeller plane) that causes an axial acceleration as pointed out by the higher axial velocity achieved in the second measurement plane; the smoothing effect due to turbulent diffusion and strong dissipation between the first two planes and the last one which is farther downstream as also pointed out by the stronger radial gradients of the axial velocity component for the first two planes comparing with the last one; · the rapid decay of the tip vortex with respect to the hub vortex which is still characterizing the flow in the last measurement plane A better description of the vortices evolution is provided by the vorticity field shown in figure 16. The following features on the three different transversal planes can be noticed · a very strong distortion of the wake structure due to the different pitch of the wake shed from the trailing edge and the pitch of the tip vortices can be noticed from the first to the second plane; very strong diffusion and dissipation of the blade wake, which is spreading very quickly Dom the first to the second measurement plane. In the latter, the hub and the tip vortices are still present, even if very attenuated, while the blade wake is almost totally dissipated; The trace of the tip and hub vortices are still apparent in the last measurement plane pointing out that the wake is still in phase with the propeller far downstream. In figure 17 the turbulence distribution of the V component is reported as an example of the turbulence field evolution because the fluctuating field of the other components shows a similar behavior. 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. The high level of turbulence generated by the blade passage at 12 o'clock is convected downstream and dissipated even if a trace is present in the far downstream plane. CONCLUSIONS The analysis of a propeller wake behind a Series 60 ship model, in a large water channel, has been performed by using stereo-PIV. Both instantaneous and averaged velocity fields are achieved, the latter after phase sampling averaging over the same
Figure 14: Total turbulence (m/s) at different angles (0°,9°,18°,27°,36°,45°,54°,63°) for plane x/L=O.99
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 of a propeller working behind a ship: 1. The viscous part of the wake generated by the boundary layers on the blade surfaces. 2. The potential part of the wake deriving Dom the vortex sheet at the blade trailing edge. The varying loading conditions of the blade during the revolution which causes a strong wake deformation. 4. The complex and three-dimensional behavior of the tip vortex when passing through the narrow hull wake. The rapid spreading of the propeller wake in the downstream flow where the wake is faded and smoothed by turbulent diffusion and viscous dissipation. From the experimental setup point of view and with regards to the fitture implementation in standard ship model testing procedures, the stereo-PIV has shown a number of advantages compared to the well assessed LDV technique. In particular, and considering the limited time usually given to these tests combined with the management and technical difficulties typical of a large testing facility, the PIV technique can provide results within a short period. Instead, the LDV technique requires up to three-four times more testing time to obtain he same information, which consequently translates into additional costs of facility occupancy. The measurement time is drastically reduced with the stereo-PIV method, where the plane of measurement is mapped instantaneously and provides all three velocity components in one single step, while the LDV technique requires a long scanning of the interrogation domain. In this sense, the PIV approach offers the Deedom of extending the wake survey to a larger number of areas of interest, with very limited setup changes. The major drawbacks of the PIV technique are a reduced accuracy with respect to the LDV technique and a huge quantity of information generated both at the measurement and at the processing time (about 200 Gb in the case of the presented results): one must address the critical problem of storing, managing and processing this information without compromising the tests costs by extended data processing time. Acknowledgements The authors are grateful to the INSEAN Circulating Water Channel personnel and to Mr. Tiziano Costa who supported the PIV measurements. This work was sponsored by the Italian Ministero dei Trasporti e delta Navigazione in the frame of the [NSEAN 2000-2002 research plan. REFERENCES Cenedese, A.., Accardo, L., Milone, R., "Phase sampling in the analysis of a propeller wake", Experiments in Fluids, Vol. 6, 1988, pp. 55-60. Chesnack C., Jessup S.D., "Experimental characterization of propeller tip flow", Proceedings of the 22th Symposium on Naval HvdrodYnamics, Washington D.C., 1998. Cotroni, A., Di Felice, F., Romano, G.P., Elefante, M., "Investigation of the near wake of a propeller using particle image velocimetry', Experiments in Fluids, 2000, pp. 227 - 236. Esposito, P., Salvatore, F., Di Felice, F., Ingenito, G., Caprino, G., "Experimental and Numerical Investigation of the un steady Flow around a Propeller", Proceedings of the 23th Symposium on Naval Hydrodynamics, Val De Reuil, France, 1998. Di Felice, F., Romano, G.P., Elefante, M., "Propeller Wake Analysis by Means of PIV", Proceedings of the 23th Symposium on Naval Hydrodynamics, Val De Reuil, France, 1998. Di Felice, F., Felli, M., Ingenito, G., "Propeller wake analysis in non uniform inflow by LDV", Proceedings of the Propeller and Shafting Symposium, Virginia Beach, 2000. Di Florio, D., Di Felice, F., Romano, G.P., "Windowing and Deformation of PIV Images for the Investigation of Flow with Large Velocity Gradients", Proceedings of the 4th International SYmposium on Particle Image Velocimetrv, Gottingen, Germany, 2001. Felli M.. Di Felice. F.. Romano. G.P. Installed , , ~ 7 ~ Proneller wake analysis by LDV: phase sampling technique", Proceedings of the gth International Symposium on Flow Visualisation Edimburgh, 2000. Guj, L., Longo, J., Stern, F., "Towing Tank PIV Measurement System, Data and Uncertainty Assessment for DTMB Model 5512", Experiments in Fluids, Vol.31, 2001, pp. 336-346. Jessup, S.D., "An experimental investigation of viscous aspects of propeller blade flow". Ph. D. Thesis, The Catholic University of America, Washington D.C., 1989. Keane R.D., Adrian R.J., "Theory of cross-correlation analysis of PIV images", Applied Scientific Research. Vol.49, 1992,pp.191-215. Kobayashi, S., "Propeller wake survey by laser Doppler velocimeter". 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Figure 15: Mean flow field evolution: longitudinal component (m/s) (left) and cross-flow W. V (m/s) at 0° propeller angle for planes X/L=0.999, 1.00, 1.018 an orthogonal view of the measurement plane Vol 15, 1993, pp. 49-60 Prasad, A.K., "Stereoscopic Particle Image Velocimetry", Experiments in Fluids, Vol.29, 2000, pp. 103-116. Rafael, M., Willert, C., Kompenhans, J., "Particle hnage Velocimetry", Springer ISBN 3-540-63683-8, 1998. Soloff, S.M., Adrian, R.J., Liu, Z.C., "Distortion Compensation for Generalized Stereoscopic Particle Image Velocimetry", Meas. Sci. Technol., Vol.8, 1997, pp. 1441- 1454. Stella, A., Guy, G., Di Felice, F., "Propeller flow field analysis by means of LDV phase sampling techniques", Experiments in Fluids, Vol.28, 2000, pp. 1-10. Toda, Y., Stern, F., Tanaka, I., Patel, V.C., "Mean Flow measurements in the boundary layer and wake of a series
- i Figure 16: Vorticity (s A) for 0° angle at planes x/L=0.999, 1.00, 1.018 60 Cb=0.6 model ship with and without propeller", Journal of Ship Research, 34, 4, pp. 225-252, 1990. Westerweel J., Van Oord, J., "Stereoscopic PIV measurements in a turbulent boundary layer", Particle Image Velocimetrv: progress toward industrial application Kluwer, Dordrecht, 1999. Figure 17: Turbulence intensity of the V component (m/s) for O° angle at planes x/L=0.999, 1.00, 1.018 Westerweel, J., "'Fundamentals of Digital Particle Image Velocimetryll, Meas. Science and Technology Vol.8, 1997, pp. 1379-1392
DISCUSSION S. Nishio Kobe University of Mercantile Marine, Japan 1) The Stereo-PIV technique enables us to obtain the three-component of the velocity field on a plane, but the three-component of vorticity distribution cannot be obtained with a single plane velocity distribution. In mean time, the authors have measured on one pair of plane at x/L=0.9997, 1.0000, which are very close and parallel. It may possible to obtain three component of vorticity using those data, and it would be interesting to see the change of three-dimensional vorticity field. AUTHORS' REPLY This would be very interesting to compute and we will do in a future work. At the moment it is possible to notice that there is a very strong component of the vorticity with axes in the measurement plane as you can see in the axial velocity contour plot, fig. 10. When the blade is in the range of 18°< ~ < 36° two parallel stripes of maximum and minimum velocity near the blade tip can be noticed. This phenomena points out the presence of a strong vortex structure having the axis parallel to the measurement plane. DISCUSSION S. Nishio Kobe University of Mercantile Marine, Japan 2) The authors have applied a pre-processing on the original image to extract the background image effects, and it seems to work appropriately. By the way, the original image Fig.3 (a) has large gradient of illumination from left to right. The discusser is afraid if the gradient of illumination still remains on the final image Fig.3 (c), and it affects on the uncertainty of final velocity distribution. AUTHORS' REPLY 2) Actually subtracting the mean image seems to eliminate most of the gradients of illumination of the final image. This is due to the fact that gradients of illumination are also in the mean image and then they are subtracted. In any case adopting this procedure there has been a tremendous improvement in the quality of analyzed images and then in the uncertainty of final velocity distribution. DISCUSSION B.-G Paik Pohang University of Science and Technology, Korea I think the ship wake is important for the understanding of propeller wake. Because the ship wake connects the propeller wake behind a ship with the propeller wake in P.O.W. I think the measurement of ship wake at the propeller plane will be helpful for your better understanding of propeller wake. AUTHORS' REPLY Actually we did those measurements in the propeller plane. You can find the plot in figures 7 and 8. DISCUSSION B.-G Paik Pohang University of Science and Technology, Korea Another question regarding the perspective error defined by (IJ2D-U3D)/Uo in longitudinal wake measurements: In my case for measuring longitudinal wake using stereoscopic PIV, maximum two percent error has occurred. So, if you let me know the maximum perspective error. It will be helpful for my future research. Thank you for your exciting research. AUTHORS' REPLY We did a systematic analysis on the cameras relative positions to evaluate the perspective error. With the adopted configuration the error in the measurement of the longitudinal component is less than 5%.
