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24th Symposium on Naval Hydrodynamics Fukuoka, JAPAN, 8-13 July 2002 Phase-Averaged PIV for Surface Combatant in Regular Head Waves J. Longo, J. Shao, M. Irvine, and F. Stern (Iowa Institute of Hydraulic Research, The University of Iowa, Iowa City, lA, USA) ABSTRACT Results are presented from towing-tank tests of the phase-averaged nominal wake velocities (U. V, W) and ~ . . . Reynolds stresses ~ uu, vv, ww, up, uw ~ for a surface combatant advancing in regular head waves, but restrained from body motions, i.e., forward-speed diffraction problem. The geometry is DTMB model 5512, which is an L=3.048 m, 1/46.6 scale geosym of DTMB model 5415. The experiments are conducted in a 3x3x100 m towing tank equipped with a plunger type wave maker. The measurement systems include a towed particle image velocimetry and servomechanism wave probe. Uncertainty assessment following standard procedures is used to evaluate the quality of the data. Comparisons steady and unsteady data indicate streaming effects in 0th-harmonic and phase- averaged turbulence, which are primarily observed at the location of a boundary layer bulge containing low- momentum fluid. Unsteady data is analyzed separately for its harmonic content and indicates clear trends in IS'- and 2n4-harmonic amplitudes and 1 St-harmonic phase patterns and phase leads and lags between velocity components. Animation of the nominal wake is achieved through Fourier-Series reconstruction of the velocity components. Comparison with forces and moment and wave elevation animations from previous study for same conditions indicates boundary layer contraction and expansion for local wave elevation increases and decreases, respectively. Unsteady heave force reaches maximum and minimum values when the nominal wake contracts and expands to its limiting values, respectively. The data will be used for validation of Reynolds-averaged Navier Stokes simulation of DTMB model 5512. INTRODUCTION Focus of engineering fluid dynamics research is moving into unsteady flows in support of computational fluid dynamics (CFD) code development for simulation-based design with numerous natural and forced unsteady flow applications for aerospace, turbo machinery, and marine and ship hydrodynamics industries. Meeting this challenge requires significant advances in both CFD and experimental fluid dynamics (EFD). Present interest is in unsteady viscous ship hydrodynamics in support of unsteady Reynolds- averaged Navier Stokes (RANS) code development. Authors have identified forward-speed diffraction problem, i.e., restrained body advancing in regular head waves (or incident waves), as building block problem towards ultimate goal of physical understanding and simulation of viscous nonlinear seakeeping and 6DOF maneuvering. Approach is complementary CFD, EFD, and uncertainty assessment (UA). CFD is used to guide EFD, EFD is used for validation and model development, and lastly CFD is validated and fills in sparse data for complete documentation and diagnostics of flow. Initial CFD study was conducted by Rhee and Stern (2001) and validated using Wigley hullform EFD data from Journee (1992) for investigation of unsteady forces and moments. A concurrent EFD study involving detailed measurement (Gui et al. 2001 b) and UA (Gui et al. 2001a) of the turbulent nominal wake boundary layer of naval combatant DTMB model 5415 geosym (5512) was completed for development and commissioning of a towed, particle image velocimetry (PIV) measurement system for the Iowa Institute of Hydraulic Research (IIHR) towing tank. Both CFD and EFD efforts were then initiated to investigate unsteady forces and moments, wavefield, and flowfield for model 5512 in regular head waves (Gui et al. 2001c; Gui et al. 2002; Wilson and Stern 2002) of which the EFD work was part of an international collaborative project between IIHR, INSEAN, and DTMB on EFD/CFD and uncertainty assessment for DTMB model 5415 (Stern et al. 2001~. The present study represents completion of the remaining EFD task, which is procurement of the
unsteady flowfield and UA for model 5512 at the nominal wake plane. Precursory work (Longo et al. 2002) has been completed for towed PIV measurements of a regular, two-dimensional (2D) progressive wave flowfield in order to (1) develop necessary data acquisition, reduction, and UA tools for conducting unsteady PIV experiments with ship models; and (2) evaluate the nature of the head wave flowfield which will be used to excite the nominal wake of model 5512. Progressive wave results have demonstrated effectiveness of newly developed, phase-averaging techniques for unsteady PIV. Results for wave elevation and flowfield velocities show dominant 1St- harmonic or linear response. Comparison of experimental results with 2D progressive wave theory for long wave, low-steepness waves indicate ~0.9% and 0.8-2.0% difference in 1 St-harmonic amplitude and phase, respectively, for axial and vertical velocity components. This paper provides detailed documentation of the test design with ship model including data-acquisition and reduction procedures, UA methodology for unsteady PIV, steady and unsteady results, and conclusions with future work. 2 TEST DESIGN 2.1 Facility and model The tests are conducted in the IIHR towing tank. The tank is 100 m long, 3.048 m wide and deep, and equipped with a drive carriage, plunger-type wavemaker, and moveable wave dampener system. The drive carriage houses a computer (PC) and data- acquisition instrumentation, and pushes a 5.5-m trailer which is used as a platform for the PIV system and point of attachment for models. The wavemaker is hydraulically driven and controlled with an MTS controller and LabView software. It is capable of producing a wide range of wavelengths (~0.5-6.0 m) and wave steepnesses (Ak=0.025-0.3) and can also generate irregular waves. The wave dampeners are raised and lowered from the carriage before and after runs and enable twelve- and twenty-minute intervals for steady and unsteady tests, respectively. A right-handed Cartesian coordinate system (x, y, z) is used for the tests (Fig. 11. The origin is at the intersection of the calm free surface and forward perpendicular (FP, x=O) of the model. The x, y, z axes are directed downstream, into the page, and upward, respectively. The coordinate system moves with the speed of the carriage, trailer, and PIV system Uc. PIV data is transformed into a wave-based coordinate system after defining the phase angle associated with each vector map. The geometry of interest is model 5512, a 1:46.6 scale, I'3.048 m, fiber-reinforced Plexiglas hull with block coefficient, CB=0.506, Fig. 2. The model has a forward-facing wedge-shaped bow above the waterline, a sonar bow dome below the waterline, and a transom stern. The model is unappended for the current tests, i.e., not equipped with shafts, struts, propulsors, or rudders. To initiate transition to turbulent flow, a row of cylindrical studs of 1.6 mm height and 3.2 mm diameter are fixed with 9.5 mm spacing on the model at x=0.05. The size and spacing of the studs is in accordance with standard practices. PIV measurements are made on the port side of the model where the hull surface is painted black for minimization of laser-sheet reflection. (a) n Servo-wave ~~ ~-~ (b) Fig. 1. Experimental setup: (a) wavemaker, PIV system, servo wave probe, model trailer, model 5512 and incident head wave (~4.572 m, Ak=0.0251; (b) coordinate system moving with camera. Fig. 2. Model 5512. 2.2 Data-reduction equations Measured variables are the steady and unsteady flowfield (U. V, W) and elevation (z). The data- reduction equation for steady or unsteady, instantaneous PIV measurements are expressed C _ obj k.i. j ~ Bi Li~ng atUC k=1,2,3; i=l' ,Nvm; j=l, tNcr (1)
where Lobe iS the width of the camera view in the object plane, Limg iS the width of the digital image, Skid is the component of the particle image displacement, and At is the time between PIV images. The indices on C and S designate (1) velocity component: k=1, 2, 3 for U. V, W. respectively; (2) vector map number: i=1,...,NVm where NVm is the total number of vector maps in a single carriage run; and (3) carriage run number: j= 1, . . . ,NCr where NCr is the total number of carriage runs for a single position of the PIV measurement area. The data-reduction equation for incident wave elevation is Its zing For unsteady PIV measurements, vector-map phase angle is defined Hi j =_ + D 271 _ ti 2~ where Gil is the 1St-hamonic phase angle of the jeh- incident wave, D is the distance between the servo wave gage and middle of the PIV measurement area, is the wavelength of the incident wave, ti is the time stamp of ith vector map, and Te is the encounter period. Steady post-processed variables include mean values, normal stresses, and shear stresses expressed below in equations (4146), respectively. ck = 4,, AtU N ~ Skij = ~ MU Sk (4) | N. Aid 2 cock N ~ (Ck,ij Ck ) k = 1,2,3 My CmCn = N ~ (C'n if Ck Xcn ij Ck ) n=1,2,3; mean (6) NVa~ is the number of valid vectors at any given grid point in the measurement area which remain after applying one or more filters to NVm*Ncr data values. Unsteady post-processed variables include encounter frequency (fe), Nth-order Fourier series (FS) coefficients for PIV and wave elevation data, and phase-averaged turbulence. fe is computed with a standard fast-Fourier transform (FFT) of the butt time history. Next, FS analysis is performed on ~ bite to determine the phase of the incident wave at t=0 sec. The generalized N~-order FS for given variable X (X=(, U. V, W) is expressed X F (<t) =+ ~ Xn cOs (2=fet + In ) 2 no \ In In Hi Xn = Van + by in = tango b,' ~ Ida, J (10) an =~X(t~cos(2~nfet)dt for n = 0,1, 2, . . . (11) T 0 be =~ X(t)sin(2~nfet)dt for n = 0,1, 2, . . . (12) T 0 wherein XF is the reconstructed time history; Xn is the nth-order harmonic amplitude; On iS the corresponding phase; N is the order of the FS and chosen high enough (2) to include all important frequency components. In iS the harmonic phase adjusted with the incident wave. Time interval T is a multiple of the encounter wave period Te (=1/fe). Phase-averaged turbulence is `3' computed similarly as in equations (5) and (6), however, for the unsteady case, the FS reconstruction of U. V, W is substituted for the mean value, Ck, as per the equations below // ~ 1 NVaiid 2 lo kCk )FR N ~ (Ck,ij XF(tij )) k = 1,2,3 (13) (CInCn )FR = ~ (Cm,ij X F ( tip JXCn,ij XF( tij )) n = 1,2,3; m At n (14) tij is the time of the ith vector map in the Oh carriage run (between O see and Te) Fly indicates full-range phase-averaged turbulence where all valid data points through the full 0-2~ phase range are used in the computations. Sub regions such as 0-~/4, ~/4-~12, etc. can also be computed and analyzed but fewer valid points are utilized, and the sub-region turbulence in those phase ranges may not be converged. 2.3 Measurement systems The towed DANTEC PIV system combines hardware and software that are integrated into a single measurement system illustrated in Fig. 1. The PIV hardware components (hydrodynamic strut, laser, light- guiding arm, light-sheet optics, digital camera) are assembled with a massive 2D, computer-controlled traversing system capable of automated movement along the transverse (y) and vertical (z) axes. Movement in the x-coordinate is done manually. The strut is pressurized, partly submerged, and contains a 20 my, dual cavity Nd:Yag laser and light-guide arm for steering 532 nm beams through the light-sheet optics, which are housed in a submerged, streamlined torpedo. The digital camera is a lKxlK (1008x1018 pixels) cross-correlation camera fitted with a f/1.4 50 mm lens (8) that views the light sheet from a distance of 50 cm through a 90° mirror. The maximum object-plane size (9) or MA is 7.5x7.5 cm2, however, smaller areas can be
utilized to increase processor throughput. The camera is housed in a separate submerged, streamlined torpedo. Light-sheet and camera torpedoes are joined with a rigid, streamlined mini-strut such that the light sheet is orthogonal to the viewing axis of the camera. Fig. 1 shows the system configured to measure the vertical (xz) Mane wherein mean (U. W) and turbulent ~ uu, ww, uw ~ variables are acquired. Counter- clockwise rotation downward through 90° of the torpedoes and mini-strut about the light sheet torpedo longitudinal axis enables measurements in horizontal (xy) Planes wherein mean (U. V) and turbulent ~ uu, vv, uv ~ variables are acquired. Synchronization of the laser and camera, image processing, and acquisition of towing carriage speed are performed with the DANTEC PIV 2000 processor which is equipped with a four-channel, 12-bit analog-to-digital (AD) card. Data acquisition and parameter settings are facilitated with an IBM-compatible, Windows NT PC equipped with a National Instruments GPIB card and DANTEC v.3.11 Flowmanager software. Results in the form of vector maps are displayed virtually in real-time at a rate of 7.5 Hz. Unsteady data is phase-locked to the incident wave elevation by connection of a servo wave probe to the PIV AD board. The probe monitors the incident wave either directly above the MA or from some distance D upstream of the MA. The servo probe is a +5 cm, pre- calibrated Kenek wave probe with a resolution of 0.1 mm and maximum probe velocity of 700 mm/s. Silver- coated hollow glass spheres with a density of 1600 kg/m3 and an average diameter of 15 ,um are used as seed particles. These particles have demonstrated very good light-reflectance for PIV image capture and adequate suspension capability. Additionally, the particles are capable of following sinusoidal motions with frequencies up to 1375 Hz. The second measurement system is composed of a DOS PC and the IIHR speed circuit. This measurement system is used for monitoring and measuring the carriage speed for each data-acquisition run. The DOS PC also monitors the output from the servo wave probe. 2.4 Conditions Steady (without wave) and unsteady (with wave) tests are performed with forward speed, UC=1.S3 m/s. Steady tests are repeated from previous study (Gui et al, 2001b) in order to map a larger region of the nominal wake and facilitate comparisons between steady and unsteady measurements. The model is rigidly fixed to the carriage and towed at the dynamic sunk and trimmed condition, which is determined in calm water at Fr=0.28 (Longo and Stern 1999~. For unsteady cases, the head wave parameters including wavelength, frequency, and steepness are ~4.572 m, fW=0.584 Hz, and Ak=0.025, respectively, where fw and Ak are defined in equations (15) and (16), and A and g are wave amplitude and local gravity acceleration (g=9.8031 mls2), respectively. fw =127~ 21:A (15) (16) The wave parameters and non-zero forward speed cases combine to produce an encounter frequency fe = ~ 2~. + ~,c ~ 0.922 Hz (17) which is the dominant frequency of the unsteady response in the incident head wave flowfield. The above speed and wave conditions are based on Gui et al. (2001 b), Gui et al. (2001cy, and Gui et al. (20021. UC=1.S3 m/s produces a Froude number Fr=Uc/~=0.28 for testing with model 5512 which is the cruise speed for full-scale version. The wave parameters were selected following observation and analysis of unsteady forces and moment results because these parameters produced the most manageable linear response in the farf~eld of the ship model. 2.5 Data acquisition (DA) setup and procedures Measurement area dimensions are 192x1018 pixels (14.3x74.9 mm; Fig. 3d) or 18% of the total field of view. Advantages of above area include previous use by Gui et al. (2001 b), higher data throughput, and reduction of amplitude and phase errors for the unsteady tests (Longo et al. 20021. Interrogation areas are 32x32 pixels, 50% overlap in both coordinates, 8 pixels of offset in the axial coordinate, and a Gaussian window function is used in the correlations. With above settings, the measurement grid is l lx62. Measurements are performed in six zones with vertical (zones A,B,C) and horizontal (zones D,E,F) lightsheet orientations (Fig. 3 a,b,c). All zones are centered on the nominal wake plane and cover the region of interest in the yz-crossplane as predicted by a RANS solution for the current test conditions, i.e., x=0.935; -0.06=y=~0,ys); -0.06=Z=~0,ZS) where Ys, Zs are coordinates of the model for measurements bordering the hull surface. Zones are arranged to provide adequate overlap to check for measurement continuity across zones. Overlap is variable between zones A,B (28-80%), constant between zones B,C (28%), and constant between zones D,E,F (32%~. Zone A sets the nearest measurement locations to the model through
placement of the top interrogation area at x=0.935 adjacent to the hull surface. Fig. 3. Measurement locations: (a) model 5512 and nominal wake measurement region; (b) zones for xz-measurements; (c) zones for xy measurements; (d) typical measurement area in zone B; (e) final measurement grid at nominal wake. 0.04 nn2 . , . . , n .~ 6.0C .~ _ 3- . ~ tt,4.0C _0.03 ~ ~-. ,~ . ~ 2.0t .,,,,,,,,,. 0.02 0.00 _ 0 1000 2000 (a) Nv.ud (b) . · · · . ~0~0.e.~41 - ,~s~*~*~` -- -- - ¢- -- -- - (iD=(6,1 ); u, ~ ----- (i.D=(6,60);u, - ~ +---- (`D=(6,1);w, -- - - A- - -- (iD=(6,60); W. - 0 1000 2000 Nv.ud Fig. 4. Typical convergence histories of 1 St-harmonic amplitude (a) and 1St-harmonic phase for U. W at two grid points. This ensures a minimum distance of 1.2 mm between the closest measurement and the hull surface. For the unsteady cases, incident wave data is taken 4.42 m upstream of the measurement area midpoint. PIV image pairs are taken at 133 ms intervals, i.e., 7.5 Hz data rate and time between images is /`t=490,us. DOS data is sampled for 10 seconds over two analog channels at a rate of 410 Hz. For unsteady DA, first reference voltages for the servo probe and speed circuit are measured, then sidewall dampeners are raised, and the wavemaker is started and allowed to push a fully developed train of waves across the length of the tank. The carriage is started and reaches a steady speed after which PIV acquisition is initiated from the PC keyboard. The laser enters a free-running, 15 Hz mode. For each double image, the PIV processor makes one sweep across the analog inputs which includes the output from the servo wave probe (~) and correlates the digital images. The DOS computer runs in parallel with PIV windows machine, acquiring carriage speed and incident wave data. Vector maps are stockpiled over several carriage runs at a rate of 200 maps per carriage run. Convergence histories (Fig. 4) reveal that roughly 1200 and 2000 vector maps are required for steady and unsteady tests, respectively, for converged mean and turbulence variables and harmonics. For steady DA, same procedures apply except the wavemaker remains stationary. 2.6 Data reduction (DR) procedures Data is post-processed with unsteady and steady FORTRAN 90 source codes written and executed from a Windows PC. A flowchart (Fig. 5) illustrates the major steps in processing the unsteady data. For unsteady DR, data is phase averaged by processing batches of carriage runs. Datasets (PIV and DOS speed files) are grouped by elevation and read as input (Fig. 6a). Instantaneous PIV components are scaled up 1.2% with a scale-factor derived from uniform flow (i.e., no model condition) tests. fe is computed from DANTEC- sampled ~ for each carriage run and FS coefficients are then computed which yields first-harmonic phase at t=0 sec and wave amplitude. fe is then used in equation (3) to compute specific phase angle of all vector maps in each carriage run. The following procedures are completed at each grid point in the MA. Data is sorted on phase angle from 0-2~ (Fig. 6b) and then filtered with a two-stage range filter and 2D-median filter to remove spurious vectors (Fig. 6b,c). Rejected vectors are not replaced because the phase-averaging technique does not require this step. A 5'h-order least-squares curve is fit to the filtered data which represents the average unsteady response through one encounter
period. , If all precision ! locations processed ~ ! - comp. precision limits '~ \ - comp. total uncertainties / ~ , Linear interpolation for xy/xz data in TECPLOT to 1 50x150 standard grid -0<y<-0.06 -0<z<-0.06 ,~3 Read DANTEC PIV data and DOS Uc data Ck j j: k=1,2 or 1,3; i=1,...,N,,,,,; j=1~,NCr equ. (1), Fig. 6a Compute feand FS coefficients from DANTEC C(t) ecu. f7-12) Compute phase angle for each vector map ~I: i=1,...,N,,,,; j=1,...,NC, equ (3J So vector maps _ _ on phase angle /) (A 5th-order least-squares curve fit forall grid points: (i=1,11; j=1, 62) Fig. 6d FS coefficients for U,W or U,V for all grid points: (i=1,11; j=1, 62) Uo, U., U2, ~U1,tU2, Wo, W1, W2, ~YW1,YW2 or Uo' U1, U2, ~U1,~/U2, Vo, V1, V2, jv~,tv2 equ. (7-12), Fig. Ed | Full-and sub-region | | Check FS convergence | Iturbulence equ. (13-1~ L Fig. 4 l | If precision locations Write output data to file | - compute bias limits Zones. A,B;C,D,E,F Match data across zones -sort data on 'y' or 'z' -moving-average filter -interpolate to new 'y'or'z' Fig. (7) , ~ ,' Combine xy/xz steady , and unsteady data to , 3D dataset - ave. overlapping variables - steady/unsteady t.k.e ' - steady/unsteady data cliff. _ ~ - write steady data ,' `` - write unsteady data l ', aniCmeaatitons ~ · {~3 Fig. 5. Flowchart for unsteady PIV data processing. Dashed lines indicate final results. Then, a 2n0-order FS is computed of the least-squares curve fit to obtain the harmonic amplitudes and phases of the response (Fig. 6d). Turbulence quantities are computed for valid vectors by first taking differences between raw vector and FS reconstruction. Then, RMS values are obtained from statistics of these differences over all phase angles (0-2~) or in eight phase groups equally spaced in 0-2~ to test for phase-dependence of turbulence. Convergence histories for 0~ and 1St- harmonic amplitude and 1 St-harmonic phase are computed Nvali~-lO times at seven equally spaced locations on the center of the MA from top to bottom. n '~ 0.0` tic 0,5n ~ ~ 1 I! · 0 500 1000 1500 2000 n 1¢ n 1r 0.05 -o of -0 1C -0 15 " ~ ~ . . . . 0 90 ~ 80 270 360 (C) ~ ( ) 2.00 _ . 1.00 0.00 -~.00 -2.00 o 90 (b) 0.15 0.10 0.05 0.00 -0.05 -0.10 o,Jc (d) ~ 80 270 360 T(1 Range/medan fleed Sd, order best squares 2nd-orebr Fourier "rt" 2D~y Fig. 6. Typical unsteady PIV data and data-reduction processes: (a) unsorted, unfiltered data; (b) phase-sorted, unfiltered data and 1 St-stage range-filter limits; (c) 1 St-stage range-filtered data and 2n0-stage range-filter limits; (d) range- and median-filtered data and least- squares, FS, and 2D theory comparison data. 0.08 - 0.04 0.02 PAP' Zone AJB match: Zone B/C match ^, ~~ . 0.00 ~~ -0.06 ~0.04 -0.02 0.00 Raw, sorted data Average-filtered data 0 Interpolated data Fig. 7. Typical data matching across zones A, B. C.
Constant-y or-z data is then matched across zone boundaries and five passes of a moving-average filter is applied across the range of 'y' or 'z' values to remove high-frequency content (Fig. 71. The three-dimensional flowfield at the nominal wake plane is construct through linear interpolation to a standard grid of the final results from both xz and xy configurations. Animations of U. V, W are then generated with the FS harmonic content and equations (71-~121. For steady DR, data is also reduced by processing batches of carriage runs. Data is read and spurious vectors are removed with a two-stage range filter and a 3D median filter where the third dimension is time. Mean and turbulence results are computed with statistical analysis at each grid point from the full population of valid vectors. Convergence histories for each variable are computed NVa~i~-1 times at seven equally spaced locations on the center of the MA from top to bottom. 2.7 Uncertainty assessment The uncertainty assessment of the measurement results follows the ASME Test Uncertainty (19981. The UA procedures are based on separation and identification of systematic (bias) and random (precision) error sources, and combination with a root- sum-square (RSS) procedure to determine total uncertainty. 95% confidence levels are maintained for both bias and precision limits through judicious selection of individual bias error sources and small- sample (M=10) multiple test approach for precision errors. 2.7.1 Background Original development of UA procedures for steady PIV measurements were undertaken to commission the IIHR towed PIV system and document the quality of nominal wake data (Gui et al. 2001b). This effort produced a related study that assessed a technique for reducing the PIV cross-correlation evaluation bias with window functions (Gui et al. 2001a). UA for unsteady forces and moments and wavefield were then developed using same framework as for above PIV studies (Gui et al. 2001c; Gui et al. 2002~. Present study requires development of all-new software for unsteady PIV UA, combining many of the ideas and concepts from above three studies for completion. Since much of the bias and precision limit code for unsteady PIV UA overlaps with steady PIV UA, all-new subroutines were developed for steady PIV UA. These were tested satisfactorily on the previous steady PIV dataset to evaluate new software for accuracy. The steady UA is completed again on the current PIV dataset and presented in the next section with comparisons previous UA values from Gui et al. 2001b. The unsteady UA is then outlined at two levels including the FS harmonics and the FS-reconstructed time histories and includes the equations and methodology. The UA procedures for FS harmonics and FS-reconstructed time histories will be discussed, and a summary of results for current measurements is provided. 2.7.2 Steady UA Measurement uncertainties for the steady mean and turbulence variables are provided in Table 1 including previous values from Gui et al. (2001b). Bias and precision limit contributions are applicable to current results, only. Current results are considered satisfactory and show 1-3% reduced uncertainties over previous values for six of eight variables with ww and up moderately higher in magnitude than previous values. UA reductions are generally attributed to better repeatability of measurements, i.e., lower precision limits. For the mean quantities, more than half of the uncertainty is attributed to the bias limits, whereas, the precision limits are dominant in the Reynolds stress uncertainties. Table 1. UA summary for steady-flow results. Term Bx Px Ux tUx U 66.5% 33.5% 1 .6% 2.4% V 78.8% 21.2% 3.8% 7.7% W 94.5% 5.5% 3.2% 4.4% uu 42.6% 57.4% 2.6% 4.7% vv 35.3% 64.7% 3.1% 4.3% ww 47.3% 52.7% 5.3% 5.0% uv 25.3% 74.7% 5.9% 4.1 % uw 20.0% 80.0% 2.6% 5.8% t: results from Gui et al. 2001 b 2.7.3 Unsteady UA ln order to determine the bias limits for the FS harmonic amplitudes and phases, it is assumed that the measured value X deviates from the real value X' with a bias error p. When the random error is not considered, the real and measured value are related with X=X'+p (18) The bias error ~ is not a constant, and it is usually a function of the measurement value. For simplification, we assume the relation is linear, i.e. F=fo+^ (19) where K iS the bias gradient, and Q0 is the constant part of the bias error. The FS harmonic amplitudes and
phases (n=O) for the biased and unbiased cases are related as follows: an = , ~ (~1 + K\JX (`t~Jcos(~2~nit~J dt + , ~ ~Bo cos(~2mnitiJdt T 0 T 0 = (~1 + K) '; X (<t')cos(~2l~lft) dt + 0 = (1 + K)an (20) T 0 bn = (1 + K)bn Xn = Van + bn = (1 + K)X,~ (22) In = tan (if + K)~`2 )= tan (a' )= Al (23) Wherein a', b', Xn and it' are for the unbiased case. The bias errors for the FS harmonic amplitudes and phases can then be determined as Can Xn X,` = ~ Xn (24) /9Yn = rot In = 0 (25) The above deductions indicate that the bias error of the FS harmonic amplitude does not directly depend on the bias error, but on the bias gradient of the measured variable. Also, the bias error of the FS harmonic phase is independent of the bias error of the measured variable X. According to equation (24) The bias limits of the FS harmonic amplitudes can be determined as * Ben = * Xn for n ~ O (26) 1 + K where K* is the limit (maximal magnitude) of the bias gradient, which can be calculated with the data- reduction equation and elementary bias limits. The bias limit of the zeroth FS harmonic amplitude is determined as 2 T' _ Bx° = T. .[Bx dt = 2BX (27) According to equation (25) the bias limits of the FS harmonic phases equal zero, i.e. ~,=0. The bias limits of the adjusted phases (Bern) are then determined with equation (31. For example, the bias limits of the 1St- harmonic phases for U. V, W are written B~/U,n = B~Yv~n = BAYW~ = r ~ 4(0DBD ) + (LABS ) + (0tBt ) + (0TeBTe ) (28) The precision limits of the FS harmonics are determined with the multiple-test method. Ten converged steady and unsteady datasets are obtained at zone B. plane 05 (y=-30.48 mm; z=-53.34 mm) and zone D, plane 14 (y=0 mm; z-53.34 mm), two locations where the turbulent kinetic energy is high and moderate repeatability of the measured variables is expected. The datasets are spaced evenly in time through the course of the experiments to account for factors that influence the precision of the measured variables such ambient motions in the tank water, traverse errors in the y,z coordinates, laser-power variability, seeding variability, etc. The precision limits are computed with (21) p _ K StX x - ,~ (29) where K=2 is the coverage factor for 95% confidence level and StX is the standard deviation of the sample of M=10 realizations of variable X The total uncertainty for the measured variables Ux is defined as the RSS of the bias and precision limits and normalized with the dynamic range of the variable. UX=4B2+PX (30) Uncertainties in Tables 1, 2, and 3 represent average values from 62 grid locations at the nominal wake plane, i.e., x=0.935 (i=6, j=1-62) on the measurement grid. Values for Uu, Mu, fib, Us, U2, ~1, Up, UUUFR' UF(t) represent averages of xy and xz configuration values. The data-reduction equation for a FS-reconstructed time history can be represented as XF (to)= XF (XO, XI ~X2,- - -'XN,~/I ,~2, ,~IN,t)~31) For the reconstructed time history, time t is a given value, so it has neither bias nor precision errors. According to the data-reduction equation the bias and precision limits are determined with BXF = \|(0XOBXO ) + I(0XnBXn ) + £(~InBAIn ) (32) r ~ XF ; (0XO PRO ) + ~ (fain Pin ) + ~ (f9dY PAY ) (33) The sensitivity coefficients are `' OX F ~ OX F so ax ~ xn ax n amen aX F (34) Total uncertainties for the reconstructed time histories are computed as per the FS harmonics in equation (30~. Measurement uncertainties for the FS harmonics including oth, 1St, 2n~ harmonic amplitude, 1St, 2n~ harmonic phase, and full-range turbulence values are provided in Table 2. Comparisons of steady and 0~- harmonic uncertainties are close for U. W but Uvo is a factor of three higher than Uv because of poorer measurement repeatability for the unsteady case. First
harmonic amplitude uncertainties are judged satisfactory in consideration of smaller dynamic ranges for 1 St-harmonic quantities. Second harmonic uncertainties are larger due to small dynamic range of these quantities but later results will show repeatable coherent patterns in second harmonics. First-harmonic phase uncertainties are moderate but elevated for UP due to high precision limits. Roughly 95% of the bias limit for these variables is associated with the bias limit in Te. Second-harmonic phase uncertainties are increased as measured values are smaller and near limiting resolution of PIV system. Precision limit contributions for these uncertainties are nearly 100%. Uncertainties for full-range, phase-averaged turbulence are larger for 3 of 5 variables than for the steady case. As with the steady case, precision limits are weighted more heavily for the unsteady turbulence quantities. Interestingly, many of the y-coordinate uncertainties are elevated in comparison with the other coordinates. This may result from conducting the multiple tests in a region that has high natural unsteadiness. Additionally, the 1St-harmonic amplitude and phase are very small in this region and near the resolution of the PIV system which makes accurate measurement more difficult. Table 2. UA summary for FS harmonics. Term Bx Px Ux Uo 44.0% 56.0% 2.0% Vo 30.9% 69.1 % 13.4% Wo 94.3% 5.7% 3.2% Hat 6.1 % 93.9% 4.4% V1t 2.8% 97.2% 8.2% W1t 3.9% 96.1 % 2.1 % U2t 0.7% 99.3% 4.5% V2t 0.4% 99.6% 4.4% W2t 0.3% 99.7% 5.5% JU1t 83.9% 16.1 % 6.2% W1t 11.3% 88.7% 16.8% Act 92.0% 8.0% 6.0% U2t 61.2% 38.8% 13.7% V2t 21.0% 79.0% 12.6% N2t 67.2% 32.8% 19.9% US FR 36.1 % 63.9% 4.1 % VV FR 27.9% 72.1 % 5.1 % WW FR 50.4% 49.6 3.6% TV FR 3.2% 96.8% 8.7% UW FR 2.8% 97.2% 2.3% t normalized with X1; t: normalized with 2~ Measurement uncertainties for the FS- reconstructed time histories are provided in Table 3. These values combine influences of uncertainties in ash, 1St, 2n~ harmonic amplitudes and 1St, 2n~ harmonic phases. All uncertainties are judged satisfactory with highest accuracy in the axial coordinate as expected since signal-to-noise ratios for this measurement are consistently higher than for V,W. Precision limits are weighted higher than bias limits for UF(t),VF(t) and visa versa for WF(t). Table 3. UA summary for reconstructed time histories of U,V,W. Term BXF PXF UXF UF(t) 38.0% 62.0% ~ .7% VF(t) 25.4% 74.6% 5.6% W F(t) 90.7% 9.3% 4.7% 3. RESULTS AND DISCUSSION Steady and unsteady PIV results are presented at the nominal wake for Fr=0.28 and Fr=0.28, Ak=0.025, ~4.572, respectively. The results are organized with initial discussions of the 5512 steady flow including comparisons previous and current PIV results. Then, the incident wave elevation and flowfield measurements for Ak=0.025, ~4.572 m are discussed to evaluate the nature of the inflow for unsteady PIV. Previous unsteady forces and moment and wavefield for current incident wave parameters are then summarized to aid in later discussion of unsteady PIV results. Finally, the unsteady flow is discussed with regard to comparisons 0~-harmonic and steady, FS harmonics, and FS-reconstructions of the flowfield. 3.1 Steady flow The complete IIHR dataset for 5512 steady-flow experiments at Fr=0.28 includes Longo and Stern (1999~: resistance, sinkage and trim, wave profile, nominal wake with five-hole pitot probe; Gui et al. (2001b): nominal wake with PIV; and Gui et al. (2001 c) and Gui et al. (20021: wave elevations. The current steady PIV measurements replicate the data from Gui et al. (2001b) in order to check the quality of present data and facilitate comparisons of steady and unsteady flowfield variables. Additionally, current PIV measurements cover a larger area, which results because unsteady effects in the flow are present further from the hull centerplane and free surface for the unsteady case. Fig. 8 is a sample comparison of previous and current xy-configuration mean (U. V) and turbulence ~ uu, vv, up ~ PIV data at z=-0.025. Evaluation of new data-reduction software for steady
PIV is facilitated by plotting reprocessed data with new code and published results from Gui et al. 2001b. Current data represents processed results from zones D, E, F prior to data-matching procedures illustrated in Fig. 7 and allows evaluation of data overlap between common areas in adjacent zones. Comparisons of reprocessed data and published results show favorable agreement but trends and magnitudes of the five variables are not replicated everywhere which are likely due to small differences in the range and 3D-median filtering that was applied to the dataset. Tests have shown modest levels of sensitivity in the mean and turbulence variables for some data with different filter settings and techniques. It was judged that most of the data differences were within the noise of the data such that the present steady PIV code performance was satisfactory. 1.0C O.9C 0.8C 0.7C 0.60 0.5C 0.4 nnn~ a' ' ' I ' ' ' . ~ - - - ~ ~ - ~~ IF`' : ~ "? Zone D - 0 Zone E o Zone F Gui: zone A new processing Gui: zone B new processing Gui et al. 2001 b 0.2( 0.1' 0.1( 0.0! n n' 0.00( -0.06 -0.04 -0.02 0.00 y -0.06 -0.04 -0.02 0.00 y A AD ...... ? 0 001 ' ' ' ~ ~ I -0.06 -0.04 -0.02 0.00 i ? ~ Fig. 8. Comparison previous (Gui et al. 2001b) and current xy-configuration data at z=-0.025. ? Qualitative agreement between the previous and current data in Fig. 8 appears very good, however, there are some differences in uu and vv in high-gradient regions that are significant. These differences may be due to differences in model-roughness, laser intensity and seeding density, camera focus, or Neat between previous and current experiments. Finally, the closeness of overlap between zones D and E and E and F is generally good for U. V, uv but degraded somewhat for uu and vv in the outer flow where transition between high- and low-turbulence areas occurs. This effect is currently unexplained but may be caused by digital-image distortion or interaction between the submerged part of the PIV system and the free surface and or hull surface. Overlap regions in the data are treated with a matching technique illustrated in Fig. 7. Summary of current steady mean and turbulent PIV measurements is shown in Fig. 9 as contours U. V, W a d VW vectors and Fig. 10 as contours ks,___ uu, vv, ww,uv,uw, respectively. ~3 ~ Elf :g =1 0. ~ . '. ~~t 2 '~0, ~ ;. . ~ REV ~:~,~ ,,, ,........ Fig. 9. Summary of current steady-flow mean measurements. 1 6~j' ~'~2 o~ .. O:~ DOE25 ~Y=16 . y =st 1 ~ | Amp' A ~ = ~3 Q`~ ~ Am: ~ ~:4 0.DOf2 D.~ Y . ~ ~ ' _ 0,it, . .~:~j~: . ~ j i: ~ ~ i. ~ ~ ~.~1 3 Or - ' 2 bat! Q bole . t~ : 0.~ O.~ . O. 0 0 q:~ t: 0~ i ~ ~ - it :t . '??'' : 'i ~ i: :. I, ,, j ,, ~ ~~ ? v? ~ eat ,. l ~ ~ <~?~ ~4 0,~ i ~a.~3~ At ~ 1~ 4~ G. !I'4:~14 1, ~ ~ _- ~ 0,~ 1111 5135:~3 I I ~ _ .1 1111 at · ~ l' ~f~0 ~4 l ~ 1~ ~ ~ ~~?g ° f ~ l ~ ~ ~ .~` ? . l ~ I _ .? . ¢.~ ., I. ~~ ~~ ~~ i, , ,? ??~?~~9 Fig. 10. Summary of current steady-flow turbulence measurements.
ks is the steady turbulent kinetic energy, uu, vv, ww are the axial, transverse, and vertical normal stresses, respectively, and up, uw are the measurable shear stresses. Contours U show a low-velocity bulge ~ U ~ 65%Uc ~ near mid girth and relatively thin boundary layer near the center plane. Cross plane velocity vectors are generally upward with a region of weak out board rotation in region of bulge and thin boundary layer. Contours ks correlate with U contours, but with largest values compressed in a narrow, horizontal band closer to the hull (ail;: ~ 5%Uc ). The normal Reynolds stresses show similar patterns as ks. Values are not isotropic; since, axial stress is two to tom times cros,~plane stresses ~ largest values ,,/uu ~ 6%Uc, Jvv ~ 4~oUc, and ,|ww ~ 4%Uc . The Reynolds shear stress uv is negative in regions of increasing au / by and positive in regions of decreasing O~Dy with largest values where gradient is largest (~/uv~3%Uc). uw is spar but correlates with Ou/&z with largest value ,/uw ~ 3%Uc . 3.2 Incident wave elevation and flowfield For the unsteady tests, time histories of the incident head wave Czar are fundamentally important for establishing the phase angle of each PIV vector map. Fig. 11 shows a sample measured time history presented for Fr=0.28, Ak=0.025, ~ =4.572 m, where the incident wave frequency is fW=0.584 Hz and the encounter frequency fe is 0.922 Hz. 2.54 ~ 0.0 . N . -2.5 . \~ ~ 0,- 5.0 t (SeC) Fig. 11. Typical incident wave elevation time history for unsteady PIV tests. In Fig. 11, incident wave elevation time history represents a nearly perfect linear response. FS analysis shows that the O'h-harmonic amplitude is less than 1% of the 1 St-harmonic amplitude and the super harmonic amplitudes are two-orders-of-magnitude smaller than the 1 St-harmonic amplitude. The uncertainty in wave frequency fw and wave amplitude Aw is 0.7% and 2.7%, respectively, which is determined from multiple tests (M=10) and estimates of the bias limits. Also, the uncertainty of the encounter frequency ~ is determined as 0.4%. More details on the incident wave elevation and uncertainty are found in Longo et al. (1999) and Gui et al. (20021. Unsteady PIV measurements of the incident wave flowfield with no model have been conducted and documented in detail (Longo et al. 20021. Experimental results were evaluated through comparison with 2D progressive wave theory. Results using the same measurement area size and data acquisition and reduction processes as in present study yield satisfactory comparisons of theory and experiment. Fig. 12 shows differences theory and experiment of harmonic amplitudes (uorUoE, worwoE; UIT-UIE, W~rW~E) and the 1 St-harmonic phase (YUI~YUIE, Twos ]/WlE) for three elevations z=-25.0, -53.34, and - 110.45mm where the latter two elevations are coincident with zones B and C in the test program with ship model. Average departure from theory is 1.2%,0.10% for oth harmonic amplitude U. W. 0.9% for 1St harmonic amplitude U. W. and 0.8%,2.0% for 1St- harmonic phase U. W._Full-range, phase-averaged turbulence is 0.01% for UUFR,WWFR and negligible for UWFR . Note that differences theory and experiment for Oth-harmonic amplitude U is same as for uniform flow tests in calm water and used as scale factor for instantaneous PIV measurements previously mentioned in section 2.6. Wav:, uc' 1 -0. 02 X I Y 1 - ~ U1T U1E (%) ·50 .04 1.20 ~ 0.60 B 0.45 11 o,o ~ ~ ~ o.o, 935 (h) Ann Wave luc'2' ~ ]4.02 X4Y 1 1 8 | OT UOE (%) 311 I 1 50 J11 1~04 '2305 _ . .9 l _ I 0.75 ; I 0.60 i ·1 045 I 1 ~ ~ 015 ~ ~ Do." ooo 1 _._ J- _1 ~ ~ 0.00 ,pO.t _ 935 (a) ~O.Ot ~ --a V/ Hi-- Wav:, ' ha Z .91 1 ~ n n7 ~~`v _ ~ - 811-0.02 X1v Fig. 12. Comparison theory and experiment for ash and 1St harmonic amplitude U. W and 1St harmonic phase U. W for case with no model. 3.3 Summary unsteady forces and moment and wave field Unsteady resistance, heave force, pitch moment, and free surface elevations for 5512 at steady forward speed and in regular head waves were investigated and
documented in Gui et al. (2001c) and Gui et al. (20021. The test program included a wide range of conditions: low (0.19), medium (0.28), mid-high (0.34), and high (0.41) Froude numbers; small (0.025), small-median (0.05, 0.075), and median (0.10) wave steepnesses; and short (1.524m), median (3.048m), and long (4.572m) wavelengths. The encounter frequency fe varied from low (0.8 Hz) to high (2.5 Hz). For seakeeping, the corresponding HIX covered very small (1/125), small (1/60), median (1/40) and mid-large (1/30) values. The total number of test cases was 42. After observation and analysis of the forces and moment results, a test case of median Fr (0.28), long ~ (4.572m) and low Ak (0.025) was selected for the unsteady free-surface elevations, because this condition produces the most manageable linear response, especially, in the farfield region. A summary of results for this specific case follows. Using the first-order FS harmonics for above case, the time histories of incident wave, resistance coefficient (CT), heave coefficient (CH), and pitch moment coefficient (CM) are reconstructed and presented in Fig. 13. ..00 0 50 flu ~=0° \ ~ SteadY7/~~ 1.00 ,.................... 0.010 / \ Unsteady / \ ~ Steady 0.000 \ -0.50 0.00 0.2\\`'/~.75 -1.00 day ooo 0.25 Cure 0~75 0.00 .02 nit ~_06 (C) 0.00 0.25 era o.olt O.OOt L <,)~0.00C ~.005 Unsteady ----- Steady -0.01C ~dy woo 0.25 OUT 075 1.00 Fig. 13. Reconstructed time histories of forces and moments for Fr=0.28, Ak=0.025, ~4.572 m. The steady results are also plotted in the figure for comparison. At t~e=O, a wave crest is coincident with the FP of the model. For CT, CT O/CT St and CT I/CT S' are 1.05 and 0.69, respectively. The added resistance CT a~=CT D/2-CT s~=4~02e-04 which is about 9% of CT S[. For CH, CHO/CHSt and CHI/CHS' are 1.05 and 0.69, respectively. CM is nearly perfectly symmetric about CM St. Interestingly, the exciting forces for surge, heave, and pitch are the first harmonics of resistance, heave force, and pitch moment, respectively, and the long wavelength (~4.572 m) cases in the test program produced the highest exciting force amplitudes. CT, CH, and CM lead the incident wave phase by 70.0°, 140.0°, and 60°, respectively. CH leads CT by 70° and CM lags CT and CH by 10° and 80°, respectively. These phase lags and leads will be shown important in explaining the time-varying nature of the flowf~eld later. Maximum values of CT, CH, and CM occur when an incident wave crest reaches 0.30L, 0.57L, and 0.25L, respectively. Although not shown, the local unsteady wavefield at x=0.935 is decreasing, increasing, increasing, and decreasing for t/Te=O, 1/4, 1/2, and 3/4, respectively. These trends will also be important in explaining the unsteady nominal wake behavior. 3.4 Unsteady flow 3.4.1 oth harmonic versus steady Differences between oth harmonic and steady mean and turbulence variables are facilitated through data acquisition of steady and unsteady datasets at the same locations. Percent-difference contours and data- difference vectors are shown in Fig. 14. Contours of UO-U reveal a sizeable curved region close to the hull but off of the centerplane where the unsteady effect accelerates flow by 3.0-3.5%. Smaller regions are also visible for VO-V and WO-W where streaming effect is evident but peak values are about 33% of UO-U peak l 1.4 1 1 .;.- at 4., 42~ ~ 44 - .3 ~ .1. Fig. 14. Differences in O'h-harmonic and steady mean measurements.
Primary streaming effect is associated with the low- momentum flow in the boundary layer bulge but secondary cells for all three velocity components are near the region of highest turbulent kinetic energy at the hull/centerplane juncture. Difference vectors reveal broad regions of increased upflow in the measurement region whereas transverse flow increases and decreases are more balanced. Differences between the phase-averaged (unsteady) turbulence and steady turbulence variables are shown in Fig. 15 as data-difference contours, i.e., unsteady- steady. Average turbulent kinetic energy increases by 11.5% from steady to unsteady cases. Largest increases are confined to a small regions at the hull/centerplane (primary) and hull/free surface (secondary) junctures. Away from the hull outside the boundary layer, data d fferences are very small or slightly negative. For uv~2 - us, modest increases occur near the hull/freesurface juncture. The broad positive and negative regions that are side-by-side in up are decreased and increased, respectively. UWFR - uw are mostly positive everywhere with largest increases in a small region close to hull/centerplane juncture. 3 I' 80~ L,] ~ ~~~ ~ emit S ' 0,~ _ a.r~: _ ~4 _ ~~U _ At _ ~ : _ : ~~= _ -4:~:34 Fig. 15. Data differences in phase-averaged and steady turbulence measurements. 3.4.2 FS harmonics Contours of 1St- and 2nd-harmonic amplitude for U. V, W are shown in Fig. 16. Ul shows distinct patterns with highest values centered on the bulging portion of the boundary layer. Peak value of Ul is 9% or roughly 6% higher than harmonic content of incident wave flowfield with no model at this elevation. Two small regions close to the hull/centerplane and hulVfreesurface junctures have large Ul values. The former is centered on the location of peak unsteady turbulent kinetic energy and together with the largest region of Us bracket a modest area where unsteady effects are largely absent in Ul. In the outer flow, Ul decreases with increasing depth and is constant for all y at deepest elevations as per 2D progressive wave theory prediction. Vl also shows distinct patterns, which are similar to those for mean V (Fig. 9) and oth harmonic VO. Vl is highest in a broad, curved region near the hull/free surface juncture with peak values of about 3.5% which is a sole unsteady effect as Vl is O everywhere for case with no model. Vat is O on the centerplane as expected since V is asymmetric and tends to O as y?O. Here again, Wl also shows distinct patterns with highest values in a broad region beginning near the hull/free surface juncture and extending downward with decreasing values. Peak values of Wl are present in this region and close to Vat peak values of 3.5%. 3 _ f 3 ~ ~ 3 3 3 1 ~ 3 Ire' 33 ~ 2 1 - Date 0..~. O~ ~ . Q~3 0 - 3 R3. '. · _ f~ 2'~,, ",: ~ ~: ~~ .' 1~;,>~< Gaff c Ales ~ O. Crl', A... Q- O.~ } b~0 it. O-, :~:.~. ~~ ~ . Qua 0.~ a 0~4 . dig 0 O~7 o~ : 0~ Ark . amen ~ . Fig. 16. Summary of 1St- and 2nd-harmonic amplitudes of U,V,W. This region is close to the outer flow which suggests that most of Wl is from the head wave flowfield. Close to the hull and centerplane, Wl effects are minimal which suggests that the interaction of head wave flowfield and hull boundary layer serves to dampen the unsteady effects for W component. In the outer flow,
We decreases with increasing depth and is constant for all y at deepest elevations as per 2D progressive wave theory prediction. Second-harmonic amplitude content in U. V, W is generally insignificant in terms of magnitude but exhibits interesting, repeatable trends, nonetheless. Trends in U2 are dominated by two cells that bracket the region of maximum Us. Average U2 values through the measurement region are 0.4%, an order-of- magnitude smaller than Us. Peak value is centered on the dividing line between cells of maximum and minimum Us. Smaller, secondary cells of U2 are also present near the hull/centerplane and hull/free surface junctures. IT is nearly zero in the outer flow. V2 has one cell of interest coincident with largest U2 cell. Average V2 values through the measurement region are 0.2%. Peak value is centered at the location of peak U2. V2 is nearly zero in the outer flow. W2 has one cell of interest near the hulVcenterplane juncture. Average W2 values through the measurement region are 0.2%. Peak value is centered at the location of a secondary 1~ cell. W2 is nearly zero in the outer flow. First-harmonic phase angle and phase leads and lags are presented in Fig. 17. Phase-angle contours for U. V, W are presented with ranges of t7r,-~] except for Owl which is presented for f~,-1.5~. Trends and patterns within the boundary layer are unique for each phase component. Fig. 17. Summary of 1 St-harmonic phase angle and phase leads and lags for U. V, W at the nominal wake plane. But includes two notable features including a wide cell of 1.0~ close to the hull and free surface and a narrow region close to the hull/centerplane juncture that follows the boundary layer periphery where Cut experiences a sharp, horizontal discontinuity and phase sign change. As y,z? -8, but tends to the limiting value (0~) for the external head wave flowfield. Eve also exhibits a region close to the centerplane but starboard of the boundary-layer bulge where a sharp, horizontal discontinuity and phase sign change is present. As y? - 8, Eve tends to 2/3lrV but as z? -8, no trend in Eve is evident. Apparently, the measurement region is not large enough to observe Eve tend to its limiting value far from the model. Owl is dominated by two, large regions of negative phase angle, side-by-side beneath the transom and offset toward the centerplane. A dividing line between the cells is vertically oriented. As y,z? - 8, yew tends to the limiting value (-1.5~) for the external head wave flowfield. Phase lags and leads are also present in Fig. 17 as contours of Yu~-7v~, Yu~-yw~, and ~v~-yw~. Positive and negative regions are interpreted as second component phase lead and lag over first component, respectively. Results show that Tv~ leads but in a narrow, horizontal region centered on the But phase discontinuity. The remainder of the measurement area indicates that Eve lags Bun. In the outer flow, Owl leads yu~ by roughly 1.5~ as per 2D progressive wave theory prediction. Inside the boundary layer Owl lags But in a region initiating on the hull/centerplane juncture and moving diagonally away from the hull and then downward. Finally, in the outer flow, Owl leads Eve by roughly 2.5~, however, Awl lags Eve in a narrow horizontal area centered on the Eve phase discontinuity. 3.4.3 FS-reconstructed time histories FS-reconstructed time histories are generated for UF(t), VF(t), WF(t) using equations (7~-~12) and presented in Fig. 18 at four instances in one encounter period, i.e., t/Te=°, 1/4, 1/2, 3/4. FS reconstructions include effects of oth-, lo-, 2n~-harmonic amplitudes and 1St- and 2n6-harmonic adjusted phase angle. Phase- angle adjustments are made such that zero phase angle (or t/Te=O) corresponds to an incident wave crest at the FP. The phase delay from the FP to the nominal wake plane is roughly 224°. Although only four instances are shown, relative changes of contours reveal time-varying behavior of the boundary layer. At t/Te=O, incident wave trough is ~J4 upstream of the nominal wake plane, i.e., the local free surface elevation at x=0.935 is decreasing with time and the boundary layer is undergoing expansion. Subplot for UF(t) at t/Te=0 indicates boundary layer thickening while VF(t) and WF(t) indicate reduction in flow toward centerplane and
lax a:: - G~U A. 0.~1 0 O~ ~4 O.:~; ~1 0.~) _ _ _ _ _UT=0.50~ ,,= ~ W91w'' ~ .~ O.~. _ b45i 0~' ....... _ _ _ ~ (a) ~ M. ,-~ n: an ,~ t~ ~ . ... ~ ~ . . ~ ~ ~0~54 1.a 0. u O 0.A~ O~ a: 046{ ¢~01 ~ _ : _: :~ :: ~ `: anon ~ _ foci :~m,: ~.~1 t..~t ~ I. I AGE {~ ~017 4.~t 'Am ~ ' '~11 ~ :~= <. _ _ : i.~1 2:='RS ma. 6#:~. my.: waU ''2.~= i,01' Arty ~ _ _ _F (b) .~ _ ~ . ~d A.. - i a. - it? .-~13. I,. airs I. :07 ~33 .~H, l=~ '. ^047 '. ~~ ' . _i l' ~ ~ _ l ~ ~ l . ~ 11 V -~u 1 _ 1 _~1 l ~ 1 _ 1 _1 1 _ __ am_ 1 tm 1 ~.1 d:~¢ 1 g I Q0~! 011 ~C" 1 -}Lot! i DA=1 W: O.~ :~. - 0.~4 1 c~ o.= 1 ~~' 4~ 1 decor; 1 ;~1 ' 1 ~~ 11_ ~ An Gus r ," ~ ~1= ~ ~ 11* , ~1 t1, DOT Pat! f~P ' OUT ~3 b OC7 Q" bO,0 - _~_~s _ _ _~ ~~ ::~. ~ 1_~. _~ ~ _ . em 81 J ~ ~ ~ rid ~1 0,1~ 1tO o.~m For ~ lo', dig= it Ill, t1, C8,T ~ Cur ~ I _r '' Fig. 18. FS reconstructions of the time-varying nominal wake at four instances in one encounter period: (a) UF(t); (b) VF(t); and (c) WF(t). At t/Te=1/4, CT and CM have recently passed maximum values (Fig. 13) and incident wave trough has traveled :,~'~' ~/4 downstream of the nominal wake plane, i.e., local 4~' free surface elevation at x=0.935 is increasing with time and the boundary layer is starting to contract. At ~ O=' tlTe=1/2, CH has recently passed its maximum value |~45$~ (Fig. 13). Incident wave trough has traveled ~/2 L. ~~ downstream of the nominal wake plane, i.e., local free __ surface elevation at x=0.935 continues to increase with t~ time and the boundary continues to contract. Note that subplots for UF(t) at t/Te=1/4 and 1/2 indicate boundary ~ layer contraction, and VF(t) and WF(t) show evidence of || increased flow toward centerplane and model, respectively, especially near the free surface and centerplane, respectively. Apparently, the boundary layer contraction and attending fluid flow toward the model is associated with the heave force peak in Fig. 13. Finally, at t/Te=3/4, another incident wave trough is approaching the nominal wake plane from ~/2 upstream. The local wave elevation is decreasing in ~ time as per t/Te=0 and the boundary layer is in I expansion mode with rapid thickening occurring. VF(t) shows increased strength near the free surface moving fluid toward the centerplane, and WF(t) indicates global reduction of upward flow. l 4. CONCLUSIONS AND FUTURE WORK Results are presented from towing-tank tests of the phase-averaged nominal wake velocities (U. V, W) and Reynolds stresses ~ uu, vv, ww, us, uw ) for a surface combatant advancing in regular head waves, but restrained from body motions, i.e., forward-speed diffraction problem. The geometry is DTMB model 5512, which is an L=3.048 m, 1/46.6 scale geosym of DTMB model 5415. The experiments are conducted in a 3x3x100 m towing tank equipped with a plunger type wave maker. The measurement systems include a towed particle image velocimetry and servomechanism wave probe. Uncertainty assessment following standard procedures is used to evaluate the quality of the data. The incident head wave elevation and flowfield (no model) have been measured and conform closely with 2D progressive wave theory. Current steady flow mean and turbulence results are within the measurement uncertainties of previous steady PIV measurements which validates current data acquisition and data-reduction procedures where the latter were developed specially for the current steady and unsteady tests. Comparison of steady mean and 0th-harmonic indicates small to moderate areas mostly near the low- momentum, boundary layer bulge where streaming occurs at the level of 3.5%, 0.7%, 1.5% for U. V, W.
respectively. Comparison of steady and phase- averaged turbulence reveals 11.5% increase in unsteady versus steady turbulence kinetic energy. Turbulence increases for the unsteady case are mostly confined to regions near the hull/centerplane or hull/free surface junctures. First-harmonic amplitudes peak at 9%, 3.5%, 3.5% for U. V, W. respectively, inside the boundary layer and tend to the 2D progressive wave theory in the external flow. Second-harmonic amplitudes are order-of-magnitude lower than first- harmonic amplitudes and occur near locations of first- harmonic amplitude peaks. First-harmonic phase angles have sharp phase changes near the boundary layer bulge and tend to head wave flowfield values in the external flow. In general, Owl leads Eve and But through most of measurement region and Eve lags But through most of measurement region. FS- reconstructions of U. V, W reveal expansions and contractions of the boundary layer when the local wave elevation is decreasing and increasing, respectively. In general, boundary layer expansion is accompanied by reductions in flow toward the centerplane and model while boundary layer contraction is accompanied by increased flow toward the centerplane and model. Heave force maximums and minimums correlate with limiting values of nominal wake contraction and expansion, respectively. The steady and unsteady uncertainties are presented and judged satisfactory such that current test case can be used for CFD validation. The final paper will include expanded discussion of the FS harmonic amplitudes and phase angles through subtraction of the incident head wave (no model) flowfield. In addition, subregion turbulence for the unsteady case will be presented in terms of its harmonic content. Future work includes roll-damping experiments for model 5512 including motions testing, unsteady forces and moments, unsteady wave elevations, and unsteady flowfield measurements. For the unsteady measurements, data acquisition will be phase-locked to the roll-motion of the hull similarly as the current tests are phase-locked to the incident wave elevation. The data and UA from the current tests will be archived at www.iihr.uiowa.edu/~towtank. ACKNOWLEDGEMENTS This research was sponsored by Office of Naval Research under Grants N00014-96-1-0018 under the administration of Dr. E.P. Rood and N00014-01-1-0073 under the administration of Dr. Pat Purtell whose support is greatly appreciated. Special thanks are extended to University of Iowa mechanical engineering undergraduates Tanner Kuhl and Ben Orozco for their efforts in data acquisition phases of this study. REFERENCES ASME, "Test Uncertainty," ASME PTC 19.1-1998, The American Society of Mechanical Engineers, 1998,112pp. Gui, L., Longo, J., and Stern, F., "Biases of PIV Measurement of Turbulent Flow and the Masked Correlation-Based Interrogation," Experiments in Fluids, Vol. 30, 2001a, pp. 27-35. Gui, L., Longo, J., and Stern, F., "Towing Tank PIV Measurement System, Data and Uncertainty Assessment for DTMB Model 5512," Experiments in Fluids, Vol. 31, 2001 b, pp. 336-346. Gui., L., Longo, L., Metcalf, B., Shao, J., and Stern, F., "Forces, Moment, and Wave Pattern for Surface Combatant in Regular Head Waves-Part 1: Measurement Systems and Uncertainty Assessment," Experiments in Fluids, Vol. 31, 2001c, pp. 674-680. Gui., L., Longo, L., Metcalf, B., Shao, J., and Stern, F., "Forces, Moment, and Wave Pattern for Naval Combatant in Regular Head waves-Part 2: Measurement Results and Discussions," Experiments in Fluids, Vol. 32, 2002, pp. 27-36. Journee, J.M.J., "Experiments and calculations on four Wigley hullforms,". Report No. 909, Delft University of Technology, Ship Hydromechanics Lab, The Netherlands. Longo, J., Rhee, S.-H., Kuhl, D., Metcalf, B., Rose, R., and Stern, F., "IIHR Towing-Tank Wavemaker," Proceedings of the 25th ATTC, Iowa City, Iowa, 1999. Longo, J., Shao, J., Irvine, M., Gui, L., and Stem, F., "Phase-Averaged Towed PIV Measurements for Regular Head Waves in a Model Ship Towing Tank" Proceedings PIV and Modeling Water Wave Phenomena, Cambridge, UK, 2002, (to appear). Longo, J. and Stern, F., "Resistance, Sinkage and Trim, Wave Profile, and Nominal Wake Tests and Uncertainty Assessment for DTMB Model 5512," Proceedings of the 25th ATTC, Iowa City, Iowa, 1999. Rhee, S.H. and Stern, F., "Unsteady RAN S Method For Surface Ship Boundary Layer And Wake And Wave Field," Int. J. Num. Meth. Fluids, Vol. 37, 2001, pp. 445-478. Wilson, R. and Stern, F., "Unsteady RANS Simulation of a Surface Combatant in Regular Head Waves," Journal of Fluid Mechanics, 2002, (in preparation). Stern, F., Longo, J., Penna, R., Oliviera, A., Ratcliffe, T., and Coleman, H., "International Collaboration on Benchmark CFD Validation Data for Naval Surface
Combatant," Proceedings of the 23 ONR Em on Naval Hydrodynamics. National Academy Press, 2001, pp. 402-422.
DISCUSSION Robert Beck University of Michigan, USA How did you translate the phase of the wave from the wave probe ahead of the model to the PIV measuring plane? Assuming you used linear translation, what effect would the actual phase translation have on your results? AUTHORS' REPLY Thank you for your question. The phase of the incident wave at the PIV measuring plane is computed with equation (3~. The wavelength value (~) in the second term on the right-hand side is measured at the halfway mark in the towing tank with two servo wave gages. This measured value (~=4.654 m) is underpredicted (~=4.572 m) by 1.8% with the first-order dispersion relation in equation (15~. We avoid significant post-processing phase errors related to this difference in ~ by using the measured value in equation (3~. The departure of ~ from linear theory may be a consequence of nonlinearities arising from the facility (plunger, tank sidewalls, or tank bottom) or finite-amplitude effects. Nonlinearities in the wave amplitudes appear to be insignificant based on FS analysis, i.e., higher-harmonic amplitudes are typically one- to two-orders of magnitude smaller than for the 1 St-harmonic amplitude. The dispersion relation relating wave frequency to wavelength is valid to second order. A third- order correction for wavelength is derived by Borgman and Chappelear (1958) that is qualitatively consistent with observed increases in X, however, the correction has not been evaluated quantitatively. REFERENCE Borgman, L. E. and Chappelear, J. E. , "The Use of Stokes-Struik Approximation for Waves of Finite Height," Proc. 6th Conf. Coastal Eng., ASCE, Council on Wave Research, Berkeley, CA., 1958.
