Twenty-Third Symposium on Naval Hydrodynamics (2001)

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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 HYDROFOIL TURBULENT BOUNDARY LAYER SEPARATION AT HIGH REYNOLDS NUMBERS 314 Hydrofoil Turbulent Boundary Layer Separation at High Reynolds Numbers D.Bourgoyne, S.Ceccico, D.Dowling (University of Michigan, USA) W.Brewer, S.Jessup, J.Park (Naval Surface Warfare Center, Carderock Division, USA) R.Pankajakshan (Mississippi State University, USA) ABSTRACT One of the main hydroacoustic noise sources from fully submerged lifting surfaces is the unsteady separated turbulent flow near the surface's trailing edge that produces pressure fluctuations on the surface and unsteady oscillatory flow in the near wake. However, the turbulent flow characteristics near boundary layer separation are largely undocumented at the high Reynolds numbers typical of many hydrodynamic applications. This paper describes results from the first phase of an experimental effort to identify and measure the dominant flow features near the trailing edge of a hydrofoil at chord-based Reynolds numbers approaching 108. The experiments are conducted at the US Navy's Large Cavitation Channel with a two-dimensional test-section-spanning hydrofoil (2.1 m chord, 3.0 m span) at flow speeds from 0.5 to 18 m/s. The foil section is a modified NACA 16 with a flat pressure side and an anti-singing trailing edge. The results presented here cover the first phase of experiments and emphasize LDV-measured mean flow velocities and turbulence statistics from the separating boundary layer flows near the hydrofoil's trailing edge at Reynolds numbers from 6 to 60 million. INTRODUCTION The flow at the trailing edge of lifting surfaces has received considerable attention and has been investigated by many researchers. Designers of ship propulsors and control surfaces have examined flows over two-dimensional hydrofoils and airfoils in order to understand how modification of the trailing edge geometry influences the production of lift and drag as well as the creation of flow generated noise. (Blake 1986). Similarly, researchers have attempted to compute both the flow field and the noise it generates (Wang et al. 1996, Arabshahi et al. 1999). Unfortunately highly controlled test data at operational scales is essentially non-existent. Thus, sea trials of actual hardware have been the only means of validating scaling laws or computational models of propeller performance. Many important flow phenomena are Reynolds number dependent between model and full scale. Controlled tests over a wide range of Reynolds numbers can result in improved scaling rules. An example of a Reynolds number dependant flow is that over the trailing edge of a hydrofoil. Interestingly, relatively small modifications to the trailing edge geometry can lead to substantial changes in the hydrodynamic and hydroacoustic performance of a hydrofoil (Blake 1986). The application of a chamfer or knuckle to the trailing edge of the hydrofoil can increase the transverse thickness of the wake and consequently modify the shedding of large-scale vorticity from the trailing edge. This, in turn, can substantially change the magnitude and spectrum of the acoustic energy generated near the trailing edge. The trailing edge flow near the hydrofoil is strongly related to the wall-bounded shear flows on the suction and pressure sides. These boundary layer flows separate and ultimately combine together to form the wake. The complexity of turbulent boundary layer separation—on either flat or curved surfaces—is substantial (Simpson 1989). Thus, significant changes in Reynolds number may lead to fundamental modification of the trailing-edge boundary layers (especially on the suction side of the foil) and near-wake flow. Typical wind and water tunnel tests of hydrofoils can achieve chord-based Reynolds numbers of up to 106 or so. However, full scale Reynolds numbers achieved on the lifting surfaces associated with naval vessels easily exceed 107. Consequently, examination of these flows is desirable at the highest Reynolds number that can be achieved the authoritative version for attribution. *Currently at Mississippi State University 

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Local fluid velocities in the regions of interest were measured with a traverse-mounted two-component LDV. This LDV system uses Dantec FO probes with 111 mm beam spacing and 1600 mm focal length for an in-water probe volume 0.17 mm in diameter and 6.5 mm in length. Laser wavelengths of 514.5 and 488.0 nm were used for the two LDV channels. Both velocity channels were Bragg-cell shifted to allow measurement of flow velocities with either sign. The flow components measured were streamwise mean (U) and fluctuating (u) velocities (positive downstream), and vertical mean (V) and fluctuating (v) velocities (positive upward). Reynolds shear stress, <uv>, was also measured. The LDV data processors were burst signal analyzers from Dantec, so flow statistics were determined from tabulations of individual particle passages through the LDV focal volume. Continuous time histories of flow velocity were not analyzed. Thus, turbulence spectra are not presented here. The LDV system was calibrated with a reference velocity from a spinning disk attached to a Compumotor SM32 motor driven by a Compumotor TQ10X Servo Controller. Bias error in this calibration is introduced through uncertainty in (1) disk rotational speed, (2) disk radius, and (3) the linear regression fit of the calibration curve. Disk speed uncertainty based on the manufacturer's spec is ±0.040 revolutions per second. The disk radius is 100 mm with an uncertainty of ±0.35 mm arising from the need to locate the disk center. The uncertainty introduced by the linear regression fit is no greater than ±30 mm/s. Based on these values, the maximum calibration bias in the LDV velocity measurement ranges from ±1.4% at a flow speed of 3 m/s to ±0.4% at 18.3 m/s. This translates into a maximum fractional bias error in the normalized mean velocities (dimensionless) of ±0.02 at 3 m/s to ±0.006 at 18.3 m/s. Through the normalization velocity, bias also enters the normalized mean squares of the velocity fluctuations, but is limited to a fraction of ±0.002 or less. Precision error is also present in the calibration, but 1000 LDV samples are taken to produce each calibration curve point, rendering this error negligible. In order to make proper use of facility time, a nominal sampling period of 0.6 min per coordinate location was chosen for collection of all data sets. Since the LDV data rate changed with survey location and flow speed, the collection period was controlled (when necessary) by varying the number of samples per coordinate location between 500 and 12,000. At some coordinates, fewer samples were acquired than sought either due to low data rate (timeout) or failed data acceptance criteria for the LDV bursts. In such cases, measurements from coordinate locations with fewer than 100 samples were discarded in post-processing. The main impact of this test-timing constraint was felt in the separated and reverse-flow near the foil's trailing edge at the 3 m/s test speed. Otherwise the 0.6-minute data-point interval was well matched to the experiment. The vortex-shedding oscillation time scale for the foil's wake was calculated (Blake 1986) to be 60 ms at 3 m/s and 10 ms at 18.3 m/s. Hence, the data point collection interval represents 600 to 3600 fundamental wake oscillations, so statistical uncertainty in the measured mean velocities and turbulence quantities should be merely a few percent. This contention is backed up by the relatively smooth measured profiles shown on Figs. 8–24. In all cases, the LDV's random fluctuation level (approx. 1% of the freestream speed) were incoherently subtracted from the reported u and v fluctuation levels. Scatter in the plotted data points is probably the best measure of the extent of statistical convergence. The two-component LDV measurements were made at five stations for a total of over 3,100 coordinate locations within the flow. The five stations are shown on Fig. 3 and are referred to as follows: (1) the inflow plane, with its normal along the flow direction; (2) the leading edge line, a vertical line of data just upstream of the hydrofoil; (3) the trailing edge region, a plane with its normal perpendicular to the flow and centered near the point of separation, (4) the near wake plane, a plane slicing through the trailing edge region with its normal along the flow direction; and (5) the far wake line, a vertical line of data further downstream of the trailing edge. the authoritative version for attribution. Figure 3. Location of LDV Surveys 

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 HYDROFOIL TURBULENT BOUNDARY LAYER SEPARATION AT HIGH REYNOLDS NUMBERS 317 At stations 2, 3, and 4, a reference position for the LDV coordinate system was identified from a distinguished point on the foil (i.e. leading or trailing edge). The alignment of the LDV traverse with respect to this reference point was checked every time the tunnel speed was changed to correct for deflection of the foil caused by hydrodynamic loading. Nearly complete data sets at all five stations were taken at four channel velocities: 3.0, 6.0, 12.0, and 18.3 m/s with the bulk of the data (2,500 coordinate locations) being taken within the trailing edge region (station 3). The small amount of missing data is from the lower tunnel speeds at which data rates were too low to justify the requisite tunnel time. This limitation set 3 m/s as a minimum speed at which extensive measurements were practical, while 18.3 m/s represents the top flow speed for the LCC. Thus, these experiments spanned the largest possible Reynolds number range available under the experimental constraints. Throughout all data collection, tunnel pressure was held constant and sufficiently high to suppress cavitation that would alter the test. As mentioned above, the tests were all speed controlled and water temperature was monitored throughout the experiment. Unfortunately, the available heat exchanger capacity was not sufficient for full thermal control and tunnel water temperature increased as much as 1.3 °C/hr during tests a 18.3 m/s. Thus it was necessary to intersperse 18.3 m/s tests with tests at lower velocities throughout the course of the experiment to stay below the tunnel's maximum allowed water temperature of 40 °C. As a result, data at a single speed and a station can vary in temperature by as much as 9 °C, although water temperatures ranged from 24 °C to 40 °C for the entire experiment. The main impact of elevated water temperatures was to decrease water viscosity and thereby produce a higher Reynolds number for the same flow speed. Thus, the chord-based Reynolds numbers (Re) of the experiments reported here are as follows: 3 m/s implies Re=7 to 10 million; 6 m/s implies Re=16 to 20 million; 12 m/s implies Re= 29 to 39 million; and 18.3 m/s implies Re=46 to 61 million. EXPERIMENTAL RESULTS The model and its mounting scheme were designed to produce two-dimensional flow. However, determining the actual extent of spanwise flow uniformity was an important and necessary step for the subsequent measurements made at a single spanwise location. Thus, planes of LDV data-points perpendicular to the flow direction were collected to document spanwise flow uniformity far upstream of the foil (station 1) and in the near wake of the foil (station 4). Sample results at 18.3 m/s for the streamwise and vertical velocity components at stations 1 and 4 are shown in contour plots as Figures 4, 5, 6, and 7. The left edge of each of these figures lies in the center plane of the LCC (50% foil span). The right edge of each figure lies close to the test section windows (near 0% foil span). The top and bottom edges of these figures lie approximately 500 mm above and below the foil, respectively. The locations of data points from which the contours are drawn are shown as dots on the figures. For the streamwise flow results (Figs. 4 and 6), the velocity component is normal to the page. For the vertical Figure 5: Inflow Plane (Station 1), V/Uref Figure 4: Inflow Plane (Station 1), U/Uref the authoritative version for attribution. Figure 6: Wake Plane (Station 4), U/Uref 

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 HYDROFOIL TURBULENT BOUNDARY LAYER SEPARATION AT HIGH REYNOLDS NUMBERS 318 component results (Figs. 5 and 7), positive is upward parallel to the vertical edges of each figure. At station 1, the measured velocity has been normalized by the local free-stream, while at station 2 the measured velocity is normalized by the flow speed far-upstream of the foil. Figure 7: Wake Plane (Station 4), V/Uref Figures 4 through 7 illustrate several features of the flow over the hydrofoil and show the spanwise uniformity of the flow is good. Figures 4 and 5 show that the flow far upstream of the foil (1.8 chord lengths from the leading edge) is uniform to within 1.3% and predominantly horizontal. However, the contours on Fig. 4 also show that within 0.10 to 0.15 m (3 to 5% span) the LCC's sidewall boundary layer begins to degrade the flow's spanwise uniformity. Fig. 6 tells a similar story regarding the extent of spanwise uniformity, but the flow results are altered by the presence of the foil. In particular, the horizontal band of depressed streamwise velocity is the wake of the foil resulting from its drag while the increase in flow speed above the foil is caused by the foil's lift. The nearly uniform negative vertical velocity in Fig. 7 is the downwash and is also a result of the foil's lift. Measured results for stations 1 and 4 at the other test speeds are essentially identical and have been omitted for brevity. However, these omitted results and those shown on Figs. 4 through 7 were used to set the span location for the remainder of the LDV measurements. Although measurements at the center plane (50% foil span) of the LCC are clearly preferred by symmetry, LDV measurements are easier and more time-efficient—for optical and mechanical reasons related to water opacity, valid LDV burst data rate, and foil deflection—when the LDV focal volume is closer to the test section windows. To balance these two issues, the 25% span location was chosen for the remainder of the measurements at stations 2, 3, and 5. Velocity measurements from 26 mm upstream of the foil's leading edge (station 2) for flow speeds of 3, 6, 12, and 18.3 m/s are shown in Figs. 8 and 9. As before, the results at each speed are normalized by the free-stream speed measured far-upstream of the foil. Here, the y-coordinate increases in the vertical direction and y=0 lies at the nose of the foil. As expected, both streamwise (Fig. 8) and vertical (Fig. 9) velocity profiles upstream of the leading edge collapse well. The remaining small differences could be due to imprecision in the LDV calibration or are a mild manifestation of the effects of increasing Reynolds number. Figure 8. Leading-edge LDV measurements of Figure 9. Leading-edge LDV measurements of normalized streamwise mean velocity U/Uref. normalized vertical mean velocity V/Uref. the authoritative version for attribution. The trailing edge measurements were the main focus of this research effort and are shown on Figs. 10 through 14 for flow speeds of 3 and 18.3 m/s, and on Figs. 15 through 19 for 6 and 12 m/s. While some of these results may seem repetitive, these figures have been included for completeness. 

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. at 3.0 and 18.3 m/s HYDROFOIL TURBULENT BOUNDARY LAYER SEPARATION AT HIGH REYNOLDS NUMBERS Figure 11. Trailing-edge LDV measurements of normalized vertical mean velocity V/Uref, taken at 3.0 and 18.3 m/s Figure 10. Trailing-edge LDV measurements of normalized streamwise mean velocity U/Uref, taken at 3.0 and 18.3 m/s Figure 12. Trailing-edge LDV measurements of normalized streamwise mean square velocity fluctuations <u2>/Uref2, taken 319 

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. 3.0 and 18.3 m/s HYDROFOIL TURBULENT BOUNDARY LAYER SEPARATION AT HIGH REYNOLDS NUMBERS Figure 14. Trailing-edge LDV measurements of normalized Reynolds Stress <uv>/Uref2, taken at 3.0 and 18.3 m/s Figure 15. Trailing-edge LDV measurements of normalized streamwise mean velocity U/Uref, taken at 6.0 and 12.0 m/s Figure 13. Trailing-edge LDV measurements of normalized vertical mean square velocity fluctuations <v2>/Uref2, taken at 320 

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. 6.0 and 12.0 m/s at 6.0 and 12.0 m/s HYDROFOIL TURBULENT BOUNDARY LAYER SEPARATION AT HIGH REYNOLDS NUMBERS Figure 16. Trailing-edge LDV measurements of normalized vertical mean velocity V/Uref, taken at 6.0 and 12.0 m/s Figure 18. Trailing-edge LDV measurements of normalized vertical mean square velocity fluctuations, <v2>/Uref2, taken at Figure 17. Trailing-edge LDV measurements of normalized streamwise mean square velocity fluctuations <u2>/Uref2, taken 321 

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 HYDROFOIL TURBULENT BOUNDARY LAYER SEPARATION AT HIGH REYNOLDS NUMBERS 322 Figure 19. Trailing-edge LDV measurements of normalized Reynolds Stress <uv>/Uref2, taken at 6.0 and 12.0 m/s The unconventional grouping of the data was chosen to ease the comparisons between the lowest and highest Reynolds number measurements. In both figures, the foil's trailing edge appears as an outline within the left half of each frame. The vertical and horizontal axes show the spatial coordinates normalized by the foil chord. Here x/C= 1 lies at the tip of the foil's trailing edge, and y/C=0 corresponds to the vertical location of the flat pressure side of the foil. The vertical lines within each frame correspond to the location where the various flow quantities were measured. The horizontal distance from these vertical lines to the measured data points represents the measured field values. A scale that allows numerical determination of the field values is provided inside the foil outline of each figure. Negative measured values appear to the left of their vertical location lines while positive values appear to the right. For example, consider the measurements at x/C=1 on Figs. 10 and 11 for the normalized mean velocity components, U and V. On both frames, U and V go to zero at the tip of the foil and the measured data touch the vertical location line that passes through the tip of the foil. Using this as a reference point on Fig. 10, U above the foil tip is seen to have a weak reverse flow region and then a smoothly increasing value as y/C increases. Below the foil, U appears to change discontinuously to a positive value. The discontinuity occurs because the finite- size LDV focal volume can only be centered about one or two focal volume diameters from the foil's surface on closest approach because of optical constraints. In addition, the measurements near the topside (underside) of the foil must be made from above (below) with the LDV optics tilted slightly downward (upward). Thus, all the profiles for x/C≤1 (and some for x/C>1) are constructed from two or more separate traverses of the LDV system. Perhaps the most important feature of the data shown on Figs. 10 through 19, is the Reynolds number dependence. This is most clearly seen in the profiles of the turbulence quantities for the newly separated suction-side boundary layer (see Figs. 12, 13, and 14). Here, the peak values in the turbulence quantities are interpreted as lying at the center of the developing shear layer and the height of this shear layer above the foil surface is clearly different for the 3 m/s and 18.3 m/ s tests. Thus, the vertical extent of the near-wake is slightly larger at the lower flow speed, and this increased wake width extends out past the right edge of each figure. The mean velocity profiles are consistent with this trend. On Fig. 10, the streamwise velocity profile is clearly inflected at x/C=0.986 (−30 mm) for the 3 m/s data while the same profile is fuller and not inflected for the 18.3 m/s measurements. Similarly, the vertical velocity at the same location (Fig. 11) is less negative close to the foil surface at 3 m/s than at 18.3 m/s. Taken together these mean-flow findings and those for the turbulence quantities, all suggest that the suction side boundary layer separates closer to the foil's trailing edge at the higher speed. Thus, a simple interpretation of the suction side flow emerges. For the fixed geometry of the foil, increasing the Reynolds number through increases in tunnel speed act to thin the suction side boundary layer. A thinner boundary layer better is able to resist separation in the adverse pressure gradient that exists on the aft half of the suction surface. Thus at higher Reynolds number, the suction side boundary layer makes it further past the knuckle and separates closer to the trailing edge and the authoritative version for attribution. 

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 HYDROFOIL TURBULENT BOUNDARY LAYER SEPARATION AT HIGH REYNOLDS NUMBERS 323 thereby alters the size of the reverse flow region and the characteristics of the near wake. This phenomena is believed to be similar to the Reynolds number dependence found for the maximum lift coefficient of subsonic airfoils for chord-based Reynolds numbers of 2 to 12 million (see McCormick 1979). Several compelling reasons exist why the observed Reynolds number differences are genuine. First of all, the data shown on Figs. 10–19 were collected over a three week period and most if not all of the plotted profiles were pieced together from measurements made at different times on different days at (unfortunately) slightly different water temperatures. Yet, where the various profile pieces overlapped the agreement between pieces was good (typically better than ±1%). Second, the Reynolds number trend is monotonic. Although this is difficult to ascertain from the figures, the measured Reynolds number variations march in a consistent manner with increasing flow speeds in the proper ordering to match the conjectured simple interpretation described in the previous paragraph. Thirdly, the measured variations cannot be explained by alignment or positioning problems. The downward shift in suction side separated shear flow is approximately 1 cm as the flow speed increases from 3 to 18.3 m/s. This shift is far larger than the positioning error of the LDV system (±0.1 mm) or the lift-induced deflection of the foil at 25% span (2 to 3 mm). And finally, the measured results are consistent with classical measurements of turbulent shear flows. Although the flow near the trailing edge is more complicated than any simple free-shear flow, the turbulent fluctuation levels found in this study are in reasonable agreement with classical shear layer characteristics. For example, measurements in the attached pressure-side boundary layer upstream of the trailing edge nearly match classical results (provided in {,}-braces below) from the smooth-wall zero-pressure-gradient flat-plate boundary layer (see Hinze, 1975). The measured normalized peak <u2> is 0.0065±0.001 {0.0067}, the measured normalized peak <v2> is 0.0016±0.0002 {0.0016}, and the measured normalized peak Reynolds shear stress <uv>=0.0010±0.0001 {0.0014}. Likewise, the measured turbulence characteristics in the region downstream of both suction- and pressure-side boundary-layer separation are reasonably well matched to classical free shear layer measurements. For comparison, the results of Wygnanski and Fiedler (1970) are provided in {,}-braces below. The measured normalized peak <u2> is 0.025 ±0.002 {0.031}, the measured normalized peak <v2> is 0.017±0.002 {0.020}, and the measured normalized peak Reynolds shear stress <uv>= ±0.009±0.001 {0.009}. Although not conclusive in themselves, these comparisons suggest that there are no major problems with the current measurements, and the observed Reynolds number dependence is genuine. The final measuring station (5) was one half of a chord length downstream of the foil. Figures 20 through 24 present mean flow and turbulence results from station 5 for flow speeds of 3, 6, 12, and 18.3 m/s. Here, the data from the four speeds collapse reasonably well although some results do display weak trends with increasing Reynolds number. However, whatever variations are apparent here (like the decrease in vertical velocity fluctuations with increasing flow velocity, see Fig. 23) are much less pronounced than those found in the trailing edge data. This is especially true for the normalized Reynolds shear stress (Fig. 24) which collapses well in the wake even though it did not collapse near the foil's trailing edge (Fig. 14). Figure 20. Station 5 (Far Wake), U/Uref the authoritative version for attribution. 

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 HYDROFOIL TURBULENT BOUNDARY LAYER SEPARATION AT HIGH REYNOLDS NUMBERS 324 Figure 22. Station 5 (Far Wake), <u2>/Uref2 Figure 21. Station 5 (Far Wake), V/Uref Figure 24. Station 5 (Far Wake), <uv>/Uref2 Figure 23. Station 5 (Far Wake), <v2>/Uref2 As with the near-trailing edge measurements, these wake measurements can be compared to classical results. The measured peak Reynolds shear stress <uv> normalized by the wake deficit velocity is 0.06±0.01, and this compares well to the range of values (0.04 to 0.08) found by Narasimha and Prabhu (1972) although 0.06 is somewhat above their equilibrium peak value of 0.045. Likewise the measured peak streamwise and vertical velocity fluctuations are approximately the same and this matches the expectation for two-dimensional wake flows (Townsend 1976). However the measured fluctuations levels in the foil's wake are a factor of two higher than those in a classical two- the authoritative version for attribution. 

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 HYDROFOIL TURBULENT BOUNDARY LAYER SEPARATION AT HIGH REYNOLDS NUMBERS 325 dimensional wake flow. This difference may arise because the hydrofoil's wake has both wake-deficit and shear-flow characteristics that are produced by the drag and lift loads on the foil, respectively. PRELIMINARY COMPARISONS TO CALCULATIONS Computations of the flow over the foil were made using Mississippi State's UNCLE flow solver (UNsteady Computation of FieLd Equations) which is based on the Reynolds-averaged Navier-Stokes (RANS) equations (Arabshahi et al. 1999). Time and resource limitations only allowed calculations at the 3 m/s and 6 m/s to be completed. The computations were run as a two-dimensional model, and did not include the tunnel walls in the simulation. A C-type grid containing 170,000 points was used for the computation. As shown in Fig. 25, the point distribution was densely packed near the foil surface and in the trailing edge region; y+ values near the surface are less than 0.5. Figure 25. Computational Grid In order to correct the computed data for the effects of the test-section walls and the boundary layers developing on them, a free-stream velocity correction was computed in the following manner: at the location where the computed surface pressure is zero, measured velocities equidistantly located above and below the foil are averaged. The computed surface pressure was zero at x/C=0.98. This method is based on experimental results by Jiang et al., (1990) who determined that the axial location where the surface pressure is zero is least affected by tunnel walls, and best represents what the unbounded velocity should be. This value was computed to be 1.065 for the 3 m/s case and 1.064 for the 6 m/s case. Comparisons between the computed results and the experimental measurements were performed at x/C locations of 0.978, 0.992, 1.0, and 1.028 as shown in Figures 26–33. Computations were completed at Reynolds numbers of 9 and 16 million and the results match favorably with the experimental measurements of the mean flow. The q-ω turbulence model gave more favorable results than the k-ε model in matching velocity profiles at the trailing edge region. Figure 26. Normalized mean streamwise velocity at x/ Figure 27. Normalized mean streamwise velocity at x/ the authoritative version for attribution. C=0.978, 3.0 m/s C=0.992, 3.0 m/s 

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. C=0.978, 6.0 m/s C=1.000, 3.0 m/s Figure 30. Normalized mean streamwise velocity at x/ Figure 28. Normalized mean streamwise velocity at x/ C=0.992, 6.0 m/s C=1.028, 3.0 m/s HYDROFOIL TURBULENT BOUNDARY LAYER SEPARATION AT HIGH REYNOLDS NUMBERS Figure 31. Normalized mean streamwise velocity at x/ Figure 29. Normalized mean streamwise velocity at x/ 326 

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 HYDROFOIL TURBULENT BOUNDARY LAYER SEPARATION AT HIGH REYNOLDS NUMBERS 327 Figure 32. Normalized mean streamwise velocity at x/ Figure 33. Normalized mean streamwise velocity at x/ C=1.000, 6.0 m/s C=1.028, 6.0 m/s SUMMARY AND CONCLUSIONS Controlled tests of a two-dimensional hydrofoil at chord-based Reynolds numbers from 6 to 60 million have been performed. Two-component Laser-Doppler Velocimetry measurements have been made upstream of the foil, near the foil's leading and trailing edges, and in the wake of the foil. Spanwise uniformity of the flow over the foil was verified. Results for mean flow and turbulence quantities have been presented. Although this investigation will continue, the present results lead to three conclusions. First, the foil's near wake flow features appear to be Reynolds number dependent. This is shown most prominently in Figs. 12–14 where all of the profiles of the normalized Reynolds stress components on the suction side of the foil near its trailing edge show clear differences between test results at 3.0 m/s and 18.3 m/s. Second, the observed Reynolds number dependence is consistent with suction side boundary layer separation occurring closer to the trailing edge at higher Reynolds number. Support for this conclusion can be found in measurements of the mean flow and the turbulence quantities. And finally, classical RANS-based turbulence models appear to hold some promise for simulating the mean flow over this hydrofoil. However, the results presented here in Figs. 26 through 33 should be considered preliminary. ACKNOWLEDGEMENTS The authors of this paper wish to the acknowledge the contributions of Paul Tortora and Ronnie Bladh of the University of Michigan; William Blake, Ken Edens, Bob Etter, Ted Farabee, Jon Gershfeld, Joe Gorski, Tom Mathews, David Schwartzenberg, Jim Valentine, Phil Yarnall, and the LCC crew from the Naval Surface Warfare Center— Carderock Division; Lafe Taylor, Min-Yee Jaing, and David Whitfield from Mississippi State University; and Pat Purtell and Candace Wark from the Office of Naval Research. In addition, the authors wish to thank the Office of Naval Research for supporting this research effort under contract nos. N00014–99–1–0341, and N00014–99–1–0856. REFERENCES Arabshahi, A., Beddhu, M., Briley, W., Chen, J., Gaither, A., Janus, J., Jaing, M., Marcum, D., McGinley, J., Pankajakshan, R., Remotigue, M., Sheng, C., Sreenivas, K., Taylor, L., Whitfield, D. (1999) “A perspective on naval hydrodynamic flow simulation,” 22nd Symposium on Naval Hydrodynamics (National Academy Press, Washington DC), pp. 920–934. Blake, W.K. (1986) Mechanics of Flow Induced Sound and Vibration, Vol. II. (Academic Press, Orlando). Crighton, D.G. (1985) “The Kutta condition in unsteady flow,” Annual Review of Fluid Mechanics, Vol. 17, 411–445. the authoritative version for attribution. 

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 HYDROFOIL TURBULENT BOUNDARY LAYER SEPARATION AT HIGH REYNOLDS NUMBERS 328 Hinze, J.O. (1975) Turbulence, 2nd Ed. (McGraw Hill, New York), pp. 638–643. Jiang, C.W., Liu, H.L., and Huang, T.T. (1990) “Determination of wind tunnel wall effects and corrections”. In Proceedings of the 19th International Towing Tank Conference, held in Madrid, Spain, Vol. 2, PS-2.4, 310–317. McCormick, B.W. (1979) Aerodynamics, Aeronautics, and Flight Mechanics (John Wiley & Sons, New York), pp. 76–82. Narasimha, R., and Prabhu, A. (1972) “Equilibrium and relaxation in turbulent wakes,” J. Fluid Mech., Vol. 54, Pt. 1, 1–17. Simpson, R.L. (1989) “Turbulent boundary layer separation,” Annual Review of Fluid Mechanics, Vol. 21, 205–234. Townsend, A.A. (1976) The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge), pp. 202, 217. Wang, M., Lele, S.K., and Moin, P. (1996) “Computation of Quadrapole Noise Using Acoustic Analogy,” AIAA Journal, Vol. 34. 2247–2254. White, F.M. (1991) Viscous Fluid Flow, 2nd Ed. (McGraw Hill, Inc., New York), pp. 433–435. Wygnanski, I. And Fiedler, H.E. (1970) “The two-dimensional mixing region,” J. Fluid Mech., Vol. 41, 327–361. the authoritative version for attribution. 

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 HYDROFOIL TURBULENT BOUNDARY LAYER SEPARATION AT HIGH REYNOLDS NUMBERS 329 DISCUSSION S.Cordier Bassin d'Essais des Carenes, France Ship propeller finish tends to be degraded as the ships are in service. Could you discuss the influence of surface finish on the type of results you are presenting? AUTHOR'S REPLY Surface roughness can lead to premature transition to turbulence in the boundary layer and disrupt the flow within the boundary layer. The surface of the HIFOIL has been highly polished to an RMS surface roughness of 0.25 micrometers or less, and at the Reynolds numbers of interest, the hydrofoil can be considered hydrodynamically smooth (k +<0.5). Consequently, natural boundary layer transition is expected to occur near the leading edge, and the exact location of transition may vary somewhat with Reynolds number. However, the boundary layer has completely undergone transition by the time it reaches the trailing edge, and we do not expect that small variation in upstream transition location to influence the trailing edge flow. For fully rough flows (k+ >30), the surface roughness can significantly affect the developed boundary layer flow. It is possible that a propeller blade in service could exhibit such roughness (>25 micrometers RMS, say). Its effect on the flow would depend not only on the RMS level, but the topology of the roughness elements and their location on the blade surface. Since the focus or our experiments was scientific in nature we choose to study the simplest case (i.e. smooth) first. However, we are interested in investigating the effects of roughness in the future. DISCUSSION F.Di Felice Instituto Nazional per Studi ed Experienze di Architettura Navale (INSEAN), Italy LDV provides velocity measurement at a point and results are shown on a reference frame referred to the model. Did you take into account the model deformations? If yes, how? Measurements show find points near the surface. How do you solve the problem of the liquidation of the optical access when measuring the velocity component normal to the profile surface (vortical)? AUTHOR'S REPLY An experimental procedure was devised to measure velocities close to the surface of the hydrofoil. With the probe volume located in the area of interest, the LDV head was tilted to the minimum angle from horizontal at which all four LDV beams cleared the hydrofoil. Since this angle is known, its effect on the measured stream wise and transverse velocities could be taken into account. However, in all cases the angle effect was negligible in comparison with other sources of error and so was disregarded. The channel flow was then set on condition so that the hydrofoil assumed its lift-loaded shape. At this time the sharp tip of the trailing edge was located and used as the spatial reference point for the LDV measurements. (The point was located by observing the appearance and disappearance of the surface laser flare as the LDV probe volume was scanned vertically across the tip of the trailing edge.) Using this reference point with the hydrofoil's known angle of attack and surface contour, any given spatial coordinate for the LDV data may be related to any point on the hydrofoil surface. The LDV spatial coordinates were arranged in vertical columns rising from the hydrofoil surface. In order to ensure that data was acquired as close to the surface as conditions allowed, each column began with a coordinate just inside the hydrofoil surface and marched outward from the surface at increments of 0.2 mm. (Probe volume diameter was 0.17 mm.) Coordinates below the surface and so near to the surface as to be affected by surface flare timed-out before producing data. Such data dropouts were discarded in post-processing. the authoritative version for attribution.