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24th Symposium on Naval Hydrodynamics Fukuoka, JAPAN, 8-13 July 2002 Frontiers in Experimental Techniques Joseph Katz (The Johns Hopkins University, USA) INTRODUCTION This paper discusses several recent developments in experimental techniques in fluid mechanics and their applications in problems that are relevant to Naval Hydrodynamics. We are not presumptuous to cover all the recent advances. That would require at several books (e.g. Smits and Lim, 2000; Raffel et al., 1998~. Thus, this paper is confined to specific technologies, and is not free of the personal perspective of the author. Second, the sample data presented here has been obtained by many collaborators, graduate students, posdocs and colleagues. It is not practical to include all of them as co-authors, and I have no choice but to list their names in the acknowledgement. First and foremost, the advances of computer technology and consequently, the emergence of digital image acquisition, have led to the ever- increasing dominance of Particle Image Velocimetry (PIV). Early contributions to the development of this technique are summarized in Adrian (1991~. During the 1990's the use of PIV became wide spread and this technology is now available commercially in a variety of forms. PIV had enabled us to examine instantaneous two-dimensional flow structures, and with increasing computer power, also obtain the turbulence statistics. Subsequently, using two cameras focusing on the same plane from different angles, stereo PIV enables us to measure all three velocity components in the sample area (e.g. Prasad, 20004. Clearly, the simplicity and flexibility of 2-D and stereo PIV are the primary reason that they are overtaking/replacing all other velocity measurement techniques, especially in liquids. As demonstrated in this paper, PIV has already been implemented in our group for measuring the complex flow structure within multistage turbomachines, and for measuring the flow and turbulence structure in the bottom boundary layer of the coastal ocean. Full scale PIV measurements of flows around helicopter rotor have been performed by Raffel et al. (2001), and around a car by Wendt and Furll (2001~. However, at the present time PIV cannot provide the combined spatial and temporal resolution of hot wire measurements in air. A few specialized LDV systems also have higher spatial resolution. The gap will diminish with time, as computer and imaging technologies improves. The current digital cameras, containing typically 2kx2k pixels, limit the spatial resolution to the order of 1% of the total image size. The temporal resolution is limited by the currently available data acquisition technologies. Digital cameras recording 1000 frames per second and resolution of lkxlk are already available commercially. However, since the resulting acquisition rate, 1 GB/s, is beyond the present range of computer busses, the period of data acquisition is short and requires internal specialized storage capacity. There is no doubt however, that this limitation is temporary. Unlike the wide-spread use of planar velocimetry, there have been very few successful applications of methods for measuring the three dimensional velocity distribution in a finite volume. Holographic PIV (HPIV) is the only technique that has successfully measured the instantaneous 3-D velocity distribution within a sample volume (e.g. Barnhart et al., 1994; Meng and Hussain, 1995; Zhang et al., 1997~. The primary difficulty in implementing HPIV is the complex optical setup. We have already implemented HPIV to generate instantaneous distributions with 130x130x130 velocity vectors (Tao et al., 2002), and recent developments enabled us to increase the particle concentration to more than 200 per mm3 and 400x400x400 vectors (Sheng et al., 2002~. Defocused image velocimetry (Pereira and Gharib, 2002) has successfully measured the 3-D trajectory of particles/bubbles in a large volume. This technique is considerably simpler than HPIV, but is limited to a substantially lower particle concentration. PIV MEASUREMENTS IN TURBOMACHINES There have already been numerous applications of PIV to flows within turbomachines, including centrifugal pumps (Dong et al., 1992, 1997, Sinha et al., 2000a, b, 2001; Akin and Rockwell, 1994a, b), upstream and downstream of propellers, (e.g. Yoon
and Lee, 2002), as well as within and around compressor blades (e.g. Sanders et al., 1999; Goginenietel., 19973. Most applications of PIV in turbomachines suffer from limitations in optical access to the region of interest. The difficulties occur in part due to the presence of complex, multiple blades and blade rows. In addition, reflection of the laser sheet from boundaries overwhelms the particle traces, which severely reduce the quality of boundary layer data. The latter problem has been resolved in liquid flows by using fluorescent particle as tracers. The different (higher) wavelength of fluorescence can be separated from the illuminating laser sheet by inserting a filter in front of the camera, including the reflections from boundaries (e.g. Sinha et al., 2000a, b, 2002~. Overcoming the optical obstruction problem is a more complicated problem, and has resulted in partially obstructed views/data on the flow structure (Sanders et al., 1999~. However, addressing turbulence modeling issues, and examining the complex wake-blade and wake-wake interactions within turbomachines require complete views. To overcome the optical access problem we have constructed a facility that utilizes transparent blades and contains liquid that has the same optical index of refraction as the blades. The fluid is a concentrated solution, 62%- 64% by weight, of Nat in water. This fluid has a specific gravity of 1.8 and a kinematic viscosity of l.lx10-6 m2/s, i.e. very close to that of water. Consequently, the blades become almost invisible, allowing the laser sheet to pass through them undisturbed, and do not obstruct the field of view. There is also very little reflection when the laser sheet penetrates the blades. Information related to use and maintenance of the Nat solution can be found in Uzol et al. (2002a). As illustrated in Figure 1, the test facility consists of a two-stage axial turbomachine, and the experiments are performed within the second stage. Two setups with different blade geometries, with the characteristics shown in Figure 2 have been tested to date. Test Setup No. 1 has 4 blade rows, forming two very similar stages. The rotors blades have a chordlength of 50 mm, span of 44.5 mm, thickness of 7.62 mm and camber varying from 2.54 mm at the hub to 1.98 mm at the tip. The Reynolds number based on the tip speed and rotor chordlength is 3.7x105 at 500 rpm, the speed of the present tests. The stators blades have chordlength of 73.2 mm, span of 44.5 mm, thickness of 11 mm and camber of 6.22 mm. Test Setup No. 2 has the same 1St stage, but the 2n~ stage consists of a a stator followed by a rotor. A honeycomb occupies the entire gap between the two stator-rows. The purpose of this honeycomb is to reduce the effect of large- scale turbulence generated at the upstream blade rows, and align the flow in the axial direction, consistent with the orientation of the 1St stage stator. The ultimate purpose of this arrangement is to study the stability of swirling wakes. The system is driven by a 25 HP rim-driven motor, which is connected directly to the 1St stage rotor, preventing the need for Transparen s Transparent Rotor Or ~ Stage Rotor ~~ . ~,,,,~,,,= (a) Laser sheet (b) Window Motor 25 HP Transparent 1 stagestator Transparent Rater Honeycomb No. of stoics No. of rotor blades No. of stator blades _ Hu~to tip ratio R2-S: anal gapIRotor =~1 chord S1-R2 ~1 gapJRotor anal chord Rotor pitc~to-chord ratio (kinsman) Stator pitch-to-chord redo (~ruckspan) Rotor chord (mm) Stator chord (rmn) Rotor and SteLor span (mm) Motor 25 HP Test SetuD _ Ne. 1 No. 2 2 12 ~17 1.92~ ~ ~1.95 ~~ ~1 .34~ 0.66 73.2 . ~1.471 . bUA 1.34 . ~~ ~0 97 . ~0 _ 44.S Second Stage of: Test Setup 1 Stator (S2) Rotor (R2) Test Setuo 2 Rotor (R2) Stator (S2) Figure 1: The axial turbomachine (a) Test setup No. 1; (b) Test setup No. 2; (c) Geometrical parameters for Test Setups No. 1 and No. 2. a stator followed by a rotor. A honeycomb occupies the entire gap between the two stator-rows. The
purpose of this honeycomb is to reduce the effect of large scale turbulence generated at the upstream blade rows, and align the flow in the axial direction, consistent with the orientation of the 1St stage stator. The ultimate purpose of this arrangement is to study the stability of swirling wakes. The system is driven by a 25 HP rim-driven motor, which is connected directly to the 1St stage rotor, preventing the need for a long shaft. The two rotors are connected by a common shaft and supported by precision bearings. A shaft encoder and a control system are used for synchronizing our PIV system with the rotor phase. Further details can be found in Uzol et al. (2002a, b) and Chow et al. (2002~. Optical access is provided by a window that extends from upstream of the rotor, covers the entire 2n~ stage and extends to the far wake downstream of the stator (Figures 1 and 2~. An additional transparent insert enables us to insert a probe containing the laser-sheet optics. Consequently, we can illuminate any desired plane with a laser sheet from the hub to the tip of the blades, including the tip-gap. The interrogated planes can be parallel or normal to the axis of the turbomachine. The corner window also provides us with an optical access to the interior of the rotor and the stator, which is essential for future, 3-D, HPIV measurements. u J Insert Sheet ~ ~ r Camera PIV optics Platform Figure 2: Optical access to the test section and the PIV system. The light source of the PIV system is a dual-head Nd- YAG laser whose beam is expanded to generate a 1 mm thick light sheet. The flow is seeded using 20% silver coated, hollow glass, spherical particles, which have a mean diameter of 13,um and an average specific gravity of 1.6, i.e. slightly below that of the working fluid. The images are recorded by a 2048x2048 pixels2, Kodak ES4.0 digital camera. The laser and the camera are synchronized with the orientation of the rotor using a shaft encoder that feeds a signal to a controller containing adjustable delay generators. Consequently, we can acquire data at any desired rotor phase. Typically, the sample area is 50x50 mm2, and as a result several (five) data sets at different axial locations with sufficient overlap have been recorded to cover the entire stage. Measurements of wake and boundary layer structures have been obtained at higher magnification, a total sample area of 15x15 cm, and vector spacing of 120 ~m. Data analysis includes image enhancement and cross-correlation analysis. Details can be found in Uzol et al. (2002a). The uncertainty in mean displacement in each interrogation window is about 0.3 pixels, provided the window contains at least 5-10 particle pairs. For the typical displacement between exposures of 20 pixels, the resulting uncertainty in instantaneous velocity is about 1.5%. Slip due to the difference between the specific gravity of the particle (1.6) and that of the fluid (1.8) may cause an error of less than 0.2%, i.e. much less than other contributors (Sridhar andKatz,1995). We have already recorded and process substantial amount of data, covering the entire second stages, and results have been presented in several publications (Oguz et al., 2002a, b; Chow et al., 2002~. The measurements have enables us to examine and quantify complex flow phenomena associated with blade-wake and wake-wake interactions. Phase- averaged data has been obtained at 10 rotor phases, every three degrees of blade orientation, which cover an entire rotor blade passage of 30 . For each condition (phase and location) at least one hundred instantaneous realizations have been recorded. For selected cases we record 1000 images in order to obtain converged statistics on the turbulence. The turbulence parameters are determined from ensemble averaging of data at the same phase. A detailed discussion on the flow structure within these turbomachines is beyond the scope of this paper. However, a few examples are selected to illustrate the flow complexity, and the ability of PIV measurements in the index matched facility to resolve them. Figure 3 shows velocity and turbulent kinetic energy distributions at three phases, positioned to match the relative orientation of the blades. Clearly and not surprisingly, the phase averaged velocity distributions and turbulence are highly non uniform, and the entire domain contains a lattice of interacting wakes. The wakes are dissected by the blades but their segments can be identified far downstream of their origins.
Matching all the appropriate rotor phases relative to the stator enables us to construct the entire flow field around the rotor blade in the rotor frame of reference, including its inlet and its wake. Figure 4 shows a sample distributions of phase-averaged velocity, flow angle and turbulent kinetic energy. The flow field is dominated by the interaction with the 1St stage stator and rotor wakes. In the sample shown, a stator wake, characterized by high k and low flow angle, is just starting to impinge on the rotor blade. The inclined region with elevated turbulent kinetic energy just above this stator wake is the 1St stage rotor wake. Another segmented wake can be identified, one part on the pressure side of the blade and the other near the trailing edge on the suction side. The discontinuity in wake trajectory is caused by the differences in velocities on the suction and pressure sides of the blade. Note also the low momentum zone accompanied by (mostly) high (negative) flow angle on the pressure side of the rotor blade. This region coincides with the intersection of the 1St stage stator and rotor wakes, illustrating the impact of upstream blades on the flow around the blade. The interaction of the stator wake segments with the 2n~ stage rotor wakes cause phase-dependent meandering of the rotor wake, evident for example, in the upper rotor wake. The non-uniformities in the horizontal velocity distributions, which are a direct result of the "discontinuities" in the trajectories of the stator wake, also shear the rotor wake. As illustrated in Figure 5, this shearing creates a kink in the lVl/utip l 0.00 0.07 0.13 0.20 0.27 0.33 0.40 OA7 0.53 0.60 _ - . . 1 ~ ~ _ 1 idol . 0.4 ~ ~ l ~ . ~ ~ : 1 ! . 1 ~ 1 0.3 n -0 1 -0.2 l_ _ ]_ 3_ __ _I I_ _@ 3~ 4~_ trajectory of the rotor wake, characterized by concentrated vorticity and high turbulence levels. We define these regions as "turbulent hot spots." Although the wakes diffuse, hot spots persist far downstream of their origins. In fact, every region of wake intersection has an elevated turbulence level (e.g. Figure 4~. The few examples shown here demonstrate the ability of PIV in the index-matched facility to elucidate the complex flow structure in multi-stage turbomachines. Further results, including turbulent spectra, estimates of dissipation rates, high magnification details of wake-boundary layer interactions, distributions of Reynolds and deterministic stresses, effects of wake- blade and wake-wake interactions on the performance of the turbomachine can be found in Oguz et al. (2002a, b) and Chow et al. (2002~. OCEANOGRAPHIC APPLICATION OF PIV The simplicity of PIV, on one hand, and the wealth of data that it provides makes it an attractive option for large-scale and field applications. In problems relevant to Naval hydrodynamics PIV has been used for measuring the structure of breaking bow waves (Dong et al., 1997; Roth et al., 1999), as well as the flow and turbulence in spilling breakers and in the wake behind ships (e.g. Gui et al., 2001). In these examples, the images were recorded in towing tanks k / U2tip x 105 0.00 0.45 0.65 0.86 0.91 1.08 1.67 2.78 3.89 5.00 _! ma_ 11_ ZEST 0.75 o.5 xJ Ls - 0.25 o 0.75 o.5 x ~ Ls Figure 3: Matched sets of phase averaged absolute velocity (|V|/UIjp, left side) and turbulent kinetic energy (k, right side) constructed from data obtained in several phases. Arrow shows the rotor direction.
|Vl / Utjp k / U2tjp x 10~ aR (degrees) _nnn nss nR4 nFs n7' n7.R n7s nR.R n~R 1 1n 0.45 0.4 0.35 0.3 ~n 0.25 0.2 0.15 0.1 0.05 O ~ . - . _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ r ~ ~ r - - l_ nnnnnnn4Rn7nnnnnsE 1lR2En~nn Hn nn 7n 27 -~9 77 -ER 12 -~ 62 27 En 0.3 0.2 0.1 0 0.3 0.2 0.1 0 0.3 0.2 0.1 0 xJLs xILs xJLs (a) (b) (c) Figure 4: (a) Sample phase averaged velocity in the rotor frame of reference; (b) Turbulent kinetic energy (c) Phase averaged flow angle in the rotor frame of reference around the rotor blade. (1Js) 300.00 251.02 213.54 1 65.31 1 1 6.33 87.89 73.61 52.45 43.04 30.15 14.43 -1 5 4.42 ~ -6.12 ~-20 -27.43 ~ - 0.69 >,,-25 -55.1 0 79 b9 -30 -96.70 -1 28.57 -1 65.31 -202.04 -251 .02 3nn nn 15 1n o -10 -40 -50 _ ~ ~ . :~ 1. ~ ~:: ~':~'l~:~-~-.~:. ~ 1 1 ~ 1 1 1 1 1 30 20 10 0 x (m m) o -10 -35 -40 -45 -50 ~_ ~_ . 1 1 1 ~ I ~ I,,,, 1 30 20 10 0 x~mm) k (m2ls2) · 027 ~ . 0.24 ~3 0.21 0.18 ~1 0.15 0.12 0.09 a 006 _ 0.03 0.00 Figure 5: Vorticity and turbulent kinetic energy in the near field of the rotor wake obtained by combining high magnification data sets (lSxlS mm2 each) in different areas. Location: mid-span; number of vector maps for each area: 1000.
using submerged cameras. Over the last decade, we have developed and deployed a submersible PIV system for measuring the flow structure and turbulence in the bottom boundary layer of the coastal ocean. Several generations of this system have been described in Bertuccioli et al. (1999), Doron et al. (2001) and Nimmo-Smith et al. (2002a, b). The present version of the system is illustrated in Figure 6. Predictions of the ocean dynamics, sediment transport, pollutant dispersal and biological processes require knowledge on the characteristics of turbulence in the bottom boundary layer. Modeling of the turbulence requires data for development/validation of closure models. Consequently our goal has been to measure the Reynolds stresses (free of wave contamination), velocity profile, dissipation rate, production, buoyancy flux and turbulent spectra in the coastal bottom boundary layer, and relate them to oceanographic parameters that represent the local environment (e.g. waves, currents, stratification, bottom topography). Due to potential future applications of LES for modeling oceanic flows, we have also examined the dynamics of sub-grid scale (SOS) stresses and SGS energy flux. Several field trips to acquire data have already taken place along the Atlantic coast. A schematic of the submerged components of the oceanic PIV system is shown in Figure 6a, and the platform is shown in Figure 6b. The laser (a pulsed dye laser generating pairs of 2 Us pulses) is located on the ship and the light is transmitted through optical fibers to submerged probes. Images are acquired using two, 2k x 2k CCD cameras. Each camera and associated light sheet can be aligned independently, in the same or different planes, near each other or apart. The data is recorded on mass data acquisition systems (one for each camera), allowing continuous sampling for many hours. The submersible components of the PIV system are mounted on a seabed platform, which can be rotated to align the sample areas with the mean flow direction, and extend vertically to sample at different elevations. The platform is a 5-stage telescopic hydraulic cylinder, with a vertical range of 9.75m. The system also contains a series of instruments or characterizing the local environment, including a CTD, transmissometer, dissolved oxygen sensor, precision pressure transducer (for sensing surface waves), clinometer, compass and video-microscope for sampling the particle distributions at high magnification. Fiber Optic Laser Probe \~' \ ,,,--~ Video ~ f Direction Vane / Mounting Point . - ..~ :..: Light Sheet Sample Area ~1 EXTENDED (Height 12.5m) ~ ^ r: ~ ~ ~ 4~ r Camera (x2) /' Light Sheet tx2) Smallest Moving _ Stage: 1 3cm Dia. 1 _ 5-Stage Double- ActingTelescopic Hydraulic Cylinder = ~r~ Largest Moving Stage: 25cm Dia. RETRACTED (Height 2.75m) ~3 l _ ~ 1 _ i 1U n I Li ~ ~~ I Weighted Tripod Base (2m Dia.) Figure 6. The oceanic PIV system.
In Nimmo-Smith et al. (2002b) we select and compare several data sets obtained at different depth to represent conditions of relatively high, intermediate and weak mean flows. They also represent substantially different turbulent Reynolds numbers. Table 1 summarizes the selected data series. To characterize the mean flow and amplitude of surface waves, we average the velocity over the vector map to obtain the instantaneous average velocity componen_ (U and W). The mean current is characterized by U and W. the overall average (over all distributions), whereas URMS is the RMS values, representing mostly the effect of surface waves but also turbulence at scales larger than the instantaneous distributions. The data of Runs A and B were obtained at the mouth of the Delaware Bay, at a mean near the bottom velocity of 38 cm s with little wave motion. Runs C to F were obtained of-shore, where the current is moderate to weak, but the region is exposed to oceanic swell. For Runs C and D the amplitude of the wave induced velocity is of the same magnitude as the mean flow. For Runs E and F. the mean current is very low, namely the flow consists almost entirely of wave-induced motion. Data were collected continuously for periods of 20 min. at 2-3.3 Hz, and at elevations up to 8.5 m above the seabed. Here we use data obtained at mean elevations (vector map center) of 0.55-2.5 m above the bottom. Figure 7 presents mean, one-dimensional energy spectra of u (E11) and w (<E33) integrated along the streamwise skit directions. In addition, each graph contains an insert containing the distributions of s~21 My Eii(k~) and (314~tF~kii Eii(ki). As is evident, the turbulence is anisotropic at all scales. In most cases the vertical velocity spectra have a range of wavenumbers with a -5/3 slope, but the horizontal velocity spectra do not. The horizontal spectra appear Run A B C D E F U cm/s 38.2 l 32.6 14.9 7.7 -0.5 , 0.9 . URMS cm/s 2.8 3.7 4.5 3.3 4.0 3.2 l ~ W cm/s -0.8 l -0.3 l -0.8 -0.2 0.1 l -0.1 cm/s 1.82 2.20 0.55 0.55 0.33 0.28 w' 1.80 1.86 0.55 0.50 0.26 0.20 Re 325 440 83 83 37 28 BLF X 1 0 m2ls3) 217 307 7.65 5.68 1.92 1.47 Table 1: The selected data sets showing mean velocity, to have 'bumps'. The magnitudes of these bumps are emphasized in the inserts that have a linear vertical axis. The existence of such bumps has been observed in previous measurements (e.g. Saddoughi and Veeravalli, 1994~. They are attributed to a "bottleneck" that occurs at the transition between the inertial and dissipative range of the turbulence spectrum. Since the spectra of the vertical velocity appear to have a more extended "inertial" range, we use E33(1c~) to estimate the dissipation rate, denoting this estimate as ELF. The results are summarized in Table 1. Having data that extends to wavenumbers in the dissipation range, enables us to obtain more "direct" estimate for the dissipation using all or some of the measured velocity gradients, ED = 3V~(~ + ~ _) + ~ _) + ~ HOW) + MU HOW 2 MU HOW ~ +2 ~ BOX + 3 AX LIZ ~] 15 /au\ in 2 ( dZ ) (1) The values of £3Z are commonly used by oceanographers to estimate the dissipation rate. Values are also presented in Table 1, along with the Kolmogorov scale, r' = (v3 / SD)~/4 . Errors associated with the data being under resolved are in the 25%-45% range. There are significant spatial variations between instantaneous distributions of ED, and car, but when averaged, SD and Fez are consistently very close to each other, supporting the validity of result that would be obtained from vertical profiling. The trends of StF differ significantly from the other methods and do not provide meaningful results for Runs C-F, the moderate and weak flows. - ED i; 10 (mossy) 109 127 14.7 15.0 8.78 _ 8.20 l 1 71 | mm 1 10.71 1 0.68, L1.33 1 1 1.35 mm 7.84 7.84 5.41 5.41 5.41 5.41 1 m2/s3 1 100 117 1 12.7 L 13.1 1 7.65 1 1 7.18 SG(~ )| x107 1 m2/s3 1 l 30.8 185 0.59 1 1.10 1 o.og 1 .os 1 SG(1~)| x107 1 m2/s3 1 61.5 273 1.15 1.79 1 0.14 1 1 -0.05 wave induced motion ( URMS ), RMS values of turbulent velocity fluctuations (u', w'), Taylor microscale and resulting Rex, dissipation rates, Kolmogorov Scale (a), vector spacing (~ and SGS dissipation ~ BSG ~
One can characterize the turbulence using the Taylor micro-scale Reynolds number, Red ~ u'7 /v, ZU#u'(l5v/~/2. To estimate ~ and w' without being contaminated by waves one can use the second order structure function, a method introduced by Trowbridge (22), and implemented using PIV data in Nimmo-Smith et al. (2002a, b). Averaged values of u' and w' and the corresponding Rex are also presented in Table 1. In Runs A and B Rem, is in the 300-400 range. However, Rex of the New Jersey coast are 68-83 at moderate flow, and 14-27 when the mean current is weak. Since Runs C-F represent typical calm weather conditions in coastal water, the results indicate that turbulence in the coastal bottom boundary layer in calm weather has a very low _~0-~ . Reynolds number. The moderate and low Rem, cases fall in the range where assumptions of universality of ~ the energy spectrum are invalid (Pope, 2000~. ~s up ~n~'` PIV data can also be used for evaluating models of the sub-grid scale (SOS) stresses, and for estimating the SGS dissipation (or energy flux) for Large Eddy Simulations (LES) (Liu et al., 1994, Tao et al., 2002~. In LES the Navier Stokes Equations are filtered spatially at a scale ~ and the resulting SGS stresses, {iSGS=UiUi-UiUi ("~" indicates spatial filtering) must be modelled (see example in Figure 8~. Associated with this stress is the SGS dissipation ~ ~ rate, ESG = _~`S~Gssii' Si; = 0.5(3Ui/ik j + ~Uj/3xi), which represents transfer of energy from the resolved to subgrid scales. Consequently, attempts to model the SGS stresses frequently focus on reproducing the correct levels of BSG. Unlike viscous dissipation, ESG can be both positive and negative. A positive U = 12.4 cm/s, W = -0.2 cm/s 60 45 4n 104 ,0-it _ t, 10-6 _ 10~8 . 10 A\ 2r 10 1X 1000 [~,,1 10 a~ 10 1X IWO _ __ 3 10 100 l00o 100 k1 (radium) :1~- \, 1000 100 1000 Figure 7. Spatial energy spectra. Solid lines: E/l(kl9, Dashed lines: 3/4E33(kl). Inset figures are spectra of ~ Y sky Eii(k~) . a - f correspond to Runs A - F. value indicates flux of energy from large to small scales whereas a negative value indicates "backscatter" of energy from small to large scales. Reviews are available in Lesieur and Metais (1996), Piomelli (1999) and Meneveau and Katz (2000~. When the filter is in the inertial range of isotropic, homogeneous turbulence, the mean SSG is (almost) equal to the viscous dissipation rate. However, -15 -10 -5 0 5 10 15 X (cm) Figure 8: Instantaneous distributions of: a. Sample velocity distribution, NJ coast, 2001; b. The same velocity field filtered at A=86; and c. The corresponding distributions of tl3, contoured at intervals of Sx10-6 m2/s2. Negative values are shaded gray.
Piomelli et al., (1991) shows that near the wall of channel flows, the mean BSG iS small and even negative. Evaluation of turbulence models requires data on the SGS energy flux, estimated as 2 ~ ~ ~ ~ ~ 33 533 t! IS33{33 S} ~ + 1 2[ ~ 3 S! 3 ~ Measured averaged values of ESG are presented in Table 2 for three filter sizes, a=4, 8 and 16 vector spacings (d, Table 1). At high flow (A-B) ESG iS of the same order as ED, whereas in the moderate and weak mean flow conditions, the SGS dissipation Is more than an order of magnitude lower than SD, decreasing to negligible levels as the flow diminishes. Considering that cases C-F represent typical calm weather conditions in coastal waters, the results bear significant implications for applications of LES to coastal flows. Further details, including detailed evaluation of typically used SGS stress models are presented in Nimmo-Smith et al. (2002b). Clearly, PIV can be applied to characterize large- scale flows and in difficult field conditions. The same technology with appropriate adjustments can be used for studying boundary layers on full-scale models. 3-D VELOCITY MEASUREMENTS USING HPIV Stereo-PIV systems, capable of measuring the all three velocity components in a plane are already available commercially and used extensively. However, as noted in the introduction, HPIV is the only technique that can measure the 3-D velocity distribution in a finite volume. Several HPIV systems have been implemented over the years. Barnhart et al (1994) introduced a phase- conjugate off-axis recording system, and were the first to use it as a 3-D velocity measurement technique. Meng and Hussain (1995) proposed a simplified in-line recording and off-axis viewing method, which combines the simplicity of in-line recording, and the high signal-to-noise ratio of off- axis holography. Since in-line holography involves a reference beam passing through the sample volume, the particle concentration is limited, limiting the spatial resolution of the measurement. Zhang et al. (1997) and subsequently Tao et al. (2000, 2002) increased the measurement accuracy and data density using (see Figure 9) near-forward scattering, high- pass filtering, off-axis reference beams and two simultaneous, orthogonal views of the same flow field. The two views are essential for overcoming the inherent "depth of focus" problem of holography, i.e., the substantially larger measurement uncertainty, typically in the 200~m - 1.5mm range, along the depth direction (the light propagation direction), compared to about 10mm in the other two directions. This method was used for measuring the flow within a square duct provided the first set of spatially resolved, 3-D instantaneous velocity distributions that were used as a research tool. The resulting maps containing 130x130x130 vectors were used to study geometric and scaling relationship of SGS stresses and their models in a high Reynolds number turbulent flow Tao et al. (2000, 2002~. Another approach, introduced by Pu and Meng (1999), consisted of a wide-angle side-scattering, off- axis HPIV system, and promised to achieve both high resolution and accuracy. Although their 90° side- scattering is substantially weaker than near-forward scattering, the wider scattering angle (larger numerical aperture) reduces but does not eliminate the depth-of-focus problem. In the Zhang et al. ( 1997) approach (Figure 9) this problem is circumvented, at the cost of added complexity, by recording two orthogonal views of the same flow field. Furthermore, they require four windows, an arrangement that is rarely available in typical test facilities. Sheng et al. (2002) recently resolved this constraint by introducing the "Single Beam Two Views" (lB2V) HPIV system. M M B2E M B3 M~ ~ VOLUME ~=7 . L B1 M t- / LL R / R ~F ~ R [B.C. ~ FILM DRIVE ~ R4/ 'Yll FILM DRIVE [~ B ~ Beam splitter B.C. t Beam collimator H.F. ~ High pass filter L ~ Lens M: Mirror R; Relay lens Figure 9: The HPIV setup of Zhang et al. (1997). It consists of recording two perpendicular off- axis holograms. The principles of the Sheng et al. (2002) approach are sketched in Figure 10. In the recording phase, a mirror is inserted in the flow field and as a result each particle is illuminated in two different directions.
The first beam (Ray 1) illuminates the particle before it is refelcted by the mirror. The second beam (Ray 2) is reflected by the mirror first, and then illuminates the particle. Consequently, two spatially separated particle images, one being the "real image" (solid lines); and the other being the "mirror image" (dotted lines) are recorded on the same hologram. During reconstruction both views are reconstructed simultaneously but at a different locations in space. Due to the depth of focus problem, both views are elongated along the direction of the optical axis of the reconstructed wave. However, since the two views are perpendicular to each other, exact information on the location of the particle can be obtained by combining the data provided by these views. Figure 10 also shows the optical setup for recording (solid lines) and reconstructing (dashed lines) the holograms. The single-beam two-views method has several advantages. First, since the mirror is placed inside the facility, the test facility requires only one window instead of four. Second, having to record only one hologram requires considerably fewer optical components compared to the Zhang et al. (1997) setup. However, the required window is larger and the sample volume has a triangular shape. Third and most important, the known 3-D coordinates of the particles enable us to quadruple the spatial resolution of the velocity distributions, and significantly increase the accuracy in velocity measurements. A reconstructed flow field containing more than 200 particles/mm3 enables us to calculate the 3-D velocity distribution using an interrogation volume of 220x154x250 ~m, and a vector spacing of half this distance. To obtain the 3-D velocity vectors from the two different holographic images, Zhang et al. (1997) and Tao et al. (2001, 2002) scan the reconstructed field, record 2-D slices of particle traces and use 2-D PIV techniques to compute the velocity. The 3-D vector field is obtained by combining the two 3-D distributions of two velocity components. Due to the depth of focus effect, each 2-D section through the reconstructed field contains traces of particles that are located within about 1 mm from this plane. Consequently, the velocity is effectively low-pass filtered in the depth (axial) direction. In the lB2V approach, data processing consists of two steps. The first, determines the 3-D location of particle centroids, and the second, calculates the 3-D velocity vectors using the known particle locations. The measured centroids are used for trimming the elongated particle traces in the original scanned Ax (Recording Phase) ax ~ s ~ OR SH: Shutter PBS: Polarized Beam Splitter VBE: Variable Beam Expander PH: Pinhole RLA: Relay Lens Assembly L1: Plano-Concave Lens (f=1") L2: Plano-Convex Lens (f=4") L3: Plano-Convex Lens (f=1.5m) L4: Plano-Convex Lens (f=10") L5: Plano-Convex Lens (fed") L6: Doublet Relay Lens (f=10") M1: 3" Mirror M2: 3" Mirror Domed line: Reconstruction Optics Setup 1: Reconstructed First View 2: Reconstructed Second View ~ Mirror ,, RB: Reference Beam 1 : Particle of 1st view 1' : Mirrored view 2 : Particle of 2nd view (b) / L6\ A> / <' I \ _, ~ L6 1 1 ~z Reconstructed I I Mirror Overlap do, ~ Region .1 COD Camera Figure 10: a. Placing an inclined mirror causes illumination of the same particle in perpendicular directions; b. The two views during reconstruction; c. Optical setup of a single beam two views HPIV system. images. The velocity is calculated from the trimmed traces. Sample cross sections of an elongated particle trace are presented in Figure 11. In subsequent calculation, each 3-D particle trace is replaced by a cylinder, least square fitted through the measured centers of the 2-D traces, and a mean radius, which is equal to the mean particle diameter. The original and mirror views generate two perpendicular fitted cylinders for each particle. The two views are matched, and the centroid of the particle is positioned at the center of the line defined by the shortest distance between the two traces. Once the centroid is determined, the particle traces are erased form all scanned planes whose
distance from the calculated centroid location exceeds a prescribed distance. In the examples shown, the reconstructed field is scanned every 250 ~m, and particles with centroids located more than ~125 Em from the scanned plane that is closest to the centroid are erased. The resulting effect on an interrogation window is illustrated in Figure 12. Repeating this procedure for all the particles effectively eliminates the adverse, low-pass filtering effect of the elongated traces. Then, 2-D PIV analysis is performed on the trimmed images, and by combining the data from the two perpendicular views, one obtains the 3-D vector for each interrogation volume (220x 1 54x250 ,um3~. As discussed in Sheng et al. (2002), the uncertainty depends on accurate determination of the mirror orientation, along with the typical uncertainties associated with PIV. Experiments show that the uncertainty in determining the particle centroid is about 7 ~m, sufficient for trimming the elongated traces. Velocity measurements in the wake behind rising bubbles are used for determining the accuracy of the 3-D velocity distributions. The analysis is performed using an interrogation window of 220x 154 ,um, with 50% overlap between windows. To check the accuracy of our measurement, one can examine how well the results satisfy the continuity equation. Following Zhang et al. (1997), one can calculate the normalized divergence, _ _, ( /x + /Y + Liz) 3 ~ ( ~/X )2 + ( By ) + ~ a W/z ) where the "over bar" denotes spatial averaging of the velocity using a 3-D box filter over a certain length scale. The average of ~ over an entire sample volume varies from zero, when the continuity equation is satisfied at every point, to 1.0 for random data. Figure 12 shows the cumulative distributions of or using the lB2V approach and compares them to the data of Zhang et al. (1997~. Clearly, trimming the elongated traces improves the data substantially. In fact, at the both percentile, the present car is five times smaller. The results in Sheng et al. (2002) demonstrate that HPIV can be implemented in a facility with one window and with a reduced number/complexity of optical elements Furthermore, with a vector spacing of 125 ~m, it is possible to obtain 3-D velocity distributions containing 400x400x400 vectors in a sample volume of 50x50xS0 mm. At this resolution, HPIV is a unique tool for characterizing complex, 3- . . - E - ~, I ~ to 9'. ~ ~ Hi , ,, i. In. - i., ~.~ .. ~ ,.,'.~i7.4 1 an'"' 4~ ~'' 478 29~ ~ Any 10.9~ me-' 48 Z x -10~ 14~ Figure 11: a. Line fitting through the centroid of particle traces; b. matched perpendicular elongated particle tracers determine the centroid location; c. Original and filtered interrogation window. D turbulent flows. Recently, we have also developed the technology for in-line, digital HPIV (Malkiel et al., 2002~. This technique provides a simpler tool for 3-D velocity measurements, but at a lower resolution, and a smaller sample volume. SUMMARY AND CONCLUDING COMMENTS This paper provides two examples demonstrating that 2-D PIV can be implemented for probing a wide variety of complex flows. Stereo-PIV enables
1 0.8 0.6 1~ - I_ ~ ~ i nil ~~ Lit/' ~ _ ~ : -, 0.4 _ 0.2 · 0~25=n · U. · 11an ~ Lynn ~B.93mm Zhang et al. ~ ,.~'r~n Zhang et al. O 1 1 1 0 0.2 0.4 0.6 0.8 1 Figure 12: Cumulative distributions of car obtained with the lB2V HPIV system (Sheng et al., 2002), compared to the data of Zhang et al. (1997~. measurements of all three velocity measurements in a plane. These techniques are simple to implement, and their present limitations are caused by constraints of the present computer technology. These limitations will diminish as higher resolution cameras and faster data transfer rates become available. Cameras with resolution of Skx5k (currently available, but not as "cross-correlation," interline transfer systems) and 10kx10k will enable us to increase the size of vector maps to 300x300 and 600x600 vectors, respectively. Acquisition rates of several KHz (1 KHz cameras with limited resolution and acquisition time are already available) will enable us to examine unsteady flows. Such technologies are already around the corner. Seeding is also an issue, especially in high-speed, compressible gas flows. Advancements are still needed in molecular tagging and associated/required camera sensitivity to address these issues (see Smits and Lim, 2000 for background). Global Doppler Velocimetry (e.g. Roehle and Willert, 2001; Reinath, 2001), which measures the velocity from the frequency (Doppler) shift at every point/pixel, is also a promising technology that would substantially increase the resolution limits. However, this technique presently suffers from technical limitations, mostly in the resolution of the frequency shift. HPIV is presently the only technique that can measure the 3-D velocity distribution in a finite volume. Holographic films have a resolution that is more than an order of magnitude higher than that of any digital recording medium. This resolution is essential for resolving the fringe spacing of off-axis holograms. As a result, reconstructed images can be scanned at a resolution that is substantially higher than that of typical digital cameras. For example, in Tao et al. (2002), each plane is converted to 10kx10k image, and in Sheng et al. (2002), the corresponding equivalent resolution is 20kx20k. This higher resolution enables us to obtain 400x400x400 vectors. However, the optical setup of HPIV is considerably more complex than 2-D PIV, limiting its range of applications. Nevertheless, HPIV is the only tool that be used for measuring/examining the structure of high Reynolds number turbulence. As we gain experience in implementing this technique, its range of application will expand. Digital HPIV would serve as an intermediate method, providing data at a lower resolution and a smaller sample volume, but the technology is considerably simpler to implement. ACKNOWLEDGEMENT The material presented in this paper is a result of experiments performed by numerous post-does and graduate students, as well as collaboration with several colleagues. The measurements in turbomachines have been performed by Oguz Uzol and Yi-Chih Chow. The oceanic measurements have been performed by Alex Nimmo-Smith, and he has worked together with P. Atsavaprani, Luksa Luznik and Weihong Zhu. The earlier HPIV measurements have been performed by Z. Zhang and Bo Tao, and the recent lB2V HPIV system has been developed by Jian Sheng and Ed Malkiel. My colleagues, C. Meneveau and T. Osborn have also been critical for the success of these projects. The turbomachinery work has been funded by ONR and AFOSR, the oceanic PIV measurements have been funded by ONR and NSF, and development of the HPIV system has been funded by ONR and NSF. REFERENCES Adrian R J., "Particle Imaging Techniques for Experimental Fluid Mechanics", Annual Review of Fluid Mechanics Vol.23 1991 pp. 261-304. , , Akin, O., and Rockwell, D., "Actively Controlled Radial Flow Pumping System: Manipulation of Spectral Content of Wakes and Wake-Blade Interactions", Journal of Fluids Engineering, Vol. 1 16, 1994, pp. 528-537. Akin, O., and Rockwell, D., "Flow Structure in A Radial Flow Pumping System Using High Image
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DISCUSSION L.P. Purtell Office of Naval Research, USA What is your estimate of uncertainty for the "three-image" PIV approach to pressure measurement? AUTHOR'S REPLY The technology and data analysis procedures for determining the unsteady pressure distribution from the material acceleration is presently being developed. Inherently, the uncertainty depends on these procedures. Thus, at this stage we cannot provide a quantitative response to this question. However, the uncertainty is adversely affected by having to subtract two large quantities (velocities) with similar magnitudes. Thus, even with sub-pixel accuracies in velocity, the relative uncertainty in acceleration can become substantial. Overcoming this problem requires us to circumvent the phase of determining the velocity. For example, PIV is based on cross-correlation of two images, and finding the correlation peak. To overcome the uncertainty in finding the correlation peak, one can directly cross-correlate the two cross- correlation maps (associated with the two velocities being compared), and determine the acceleration directly from the "cross-correlated correlation." Similarly, other sources of uncertainty must by carefully assessed and minimized (if possible), including issues related to spatial resolution, effect of viscosity, etc. Our current effort to develop the new pressure measurement technique includes a detailed uncertainty analysis.
