A Comparison of Full-Scale Experimental Measurements and Computational Predictions of the Transom-Stern Wave of the R/V Athena I
Donald C. Wyatt, Thomas C. Fu, Genevieve L. Taylor, Eric J. Terrill, Tao Xing, Shanti Bhushan, Thomas T. O'Shea, Douglas G. Dommermuth
227 th Symposium on Naval HydrodynamicsSeoul, KOREA, 5 – 10 October 2008
A comparison of full-scale experimental measurements andcomputational predictions of the transom-stern wave of theR/V Athena I
Donald C. Wyatt , Thomas C. Fu , Genevieve L. Taylor , Eric J. Terrill ,Tao Xing , Shanti Bhushan , Thomas T. O’Shea , andDouglas G. Dommermuth Science Applications International Corporation, USA Naval Surface Warfare Center - Carderock, USA Scripps Institution of Oceanography, USA University of Iowa, USA
ABSTRACT
Full-scale experimental measurements and numericalpredictions of the wave-elevation topology behind atransom-sterned vessel, the R/V Athena I, are comparedand assessed in this paper. The mean height, surfaceroughness (RMS), and spectra of the breaking stern-waves were measured in-situ by a LIDAR sensor over arange of ship speeds covering both wet- and dry-transomoperating conditions. Numerical predictions for this dataset from two Office of Naval Research (ONR) supportednaval-design codes, NFA and CFDship-Iowa-V.4, havebeen performed. Initial comparisons of the LIDAR datato the numerical predictions at 5.4 m/s (10.5 kts), awet-transom condition, are presented. This work repre-sents an ongoing effort on behalf of the ONR Ship WaveBreaking and Bubble Wake program, to assess, validate,and improve the capability of Computational Fluid Dy-namics (CFD) to predict full-scale ship-generated wavefields.
INTRODUCTION
Full-scale in-situ measurements of the free-surface el-evation in the transom region of the R/V Athena Iwere made in early June of 2005 by research groupsfrom the Marine Physical Laboratory, Scripps Institu-tion of Oceanography-UCSD and the Naval Surface War-fare Center, Carderock Division (Fu, Fullerton, Terrill& Lada 2006a). The objective of the experiment wasto obtain full-scale qualitative and quantitative breakingtransom-stern wave-field data from a naval combatant-like hull form for use in subsequent CFD code devel-opment and validation. Although high-resolution mea-surements of full-scale bow waves (Fu et al. 2004) andlow-resolution measurements of transom breaking waveshave been made in the past (Fu et al. 2006b), this was the
Figure 1:
The R/V Athena first set of high resolution measurements of the breakingtransom wave of a full-scale ship. This paper presentsthe first comparison of CFD to the transom-stern wavedata collected during this experiment.The vessel used in the experiment, the R/V Athena I,is a converted PG-84 class patrol boat built in 1969 andconverted to a research vessel in 1976. Her hull con-struction is aluminum with a fiberglass superstructure.The transom-stern of the Athena was used as a source ofbreaking stern waves for this study. The Athena’s sternhas a submergence similar to that of a full-scale DDG-51 class destroyer, making her a relevant selection fortransom-stern wave studies. A picture of the R/V Athenais shown in Figure 1, and the vessel particulars are out-lined in Table 1.Measurements of the free surface in the transom re-gion of the R/V Athena were made at various speeds.Table 2 lists these test conditions. The test set was de-signed to enable the examination of the transom-stern a r X i v : . [ phy s i c s . f l u - dyn ] O c t ake from fully wet to fully dry. During the experimentthe transom was observed to transition from wet to drytransom between 8 to 9 m/s (15 to 17 knots). This paperwill focus on the wetted-transom condition of 5.4 m/s(10.5 knots). Table 1 R/V Athena DetailsLength Overall 50.3 m (165 ft)Waterline Length 46.94 m (154 ft)Extreme Beam 7.3 m (24 ft)Draft 3.2 m (10.5 ft)Propulsion Twin screwSpeed 6.2 m/s (12 kts) (diesel)18 m/s (35 kts) (turbine)The sensors deployed for this experiment includedthe Quantitative Visualization (QViz) system (Furey &Fu 2002), and a Light Detection and Ranging (LIDAR)sensor (Fu et al. 2006b). Only measurements from theLIDAR will be compared to numerical predictions in thispaper. The LIDAR technique allows scanning of the free-surface at rates rapid enough to resolve the inherent un-steadiness of the breaking transom waves. The collectionof the LIDAR data and its data reduction and analysis areincluded in the Field Experiment section of this paper.The full-scale LIDAR data is compared to predic-tions from two CFD codes currently under developmentby ONR, Numerical Flow Analysis (NFA) and CFDship-Iowa-V.4. Numerical Flow Analysis is a Cartesian gridformulation of the Navier-Stokes equations utilizing acut-cell technique to impose the hull boundary condi-tions. A description of the code and its current capabili-ties can be found in Dommermuth, O’Shea, Wyatt, Rat-cliffe, Weymouth, Hendrikson, Yue, Sussman, Adams &Valenciano (2007). CFDship-Iowa-V.4 is an unsteadyReynolds-Averaged Navier-Stokes (URANS)/detachededdy simulation (DES) code that uses a single-phaselevel-set method, advanced iterative solvers, conserva-tive formulations, and the dynamic overset grid ap-proach for free-surface flows (Bhushan, Xing, CarricaTable 2 Experimental Test ConditionsShip Speed Ship Speed F r L F r transom (m/s) (kts)3.1 6 0.14 1.154.6 9 0.21 1.72 FIELD EXPERIMENT
An at-sea LIDAR-based wave measurement system, de-veloped and deployed by the Scripps Institution ofOceanography, was used to measure the time-varyingtransom wake at multiple distances aft of the vessel. Thescanning LIDAR system consists of a 2D scanning LI-DAR unit (2.5 cm range resolution), a pan/tilt unit tocontrol the measurement location to within ± . ◦ inelevation and azimuth, a bore-sighted camera for visu-alizing the field scanned by the LIDAR, a GPS for deter-mining vessel speed, and a time-synchronized 6-degreeof freedom motion sensor. The other transom measure-ment systems deployed during the field tests have beendescribed by Fu et al. (2006a). The LIDAR system wasmounted on top of a tower approximately 12 m abovethe free surface and 0.58 m port of the ship centerline.A drawing of the Scanning LIDAR System onboard theAthena is shown in Figure 2.The LIDAR enploys a Class I 900 nm wavelengthLaser (Riegl LMS-Q140i-80), with an 80-degree max-imum swath width, and a 20 Hz sampling rate. Thepan/tilt unit (QuickSet QPT-90IC) has an integrated con-troller which enabled remote control of the elevation andazimuth angles of the LIDAR. An inertial motion unit(Xbow motion sensor) was packaged with the LIDARhead unit at the top of the tower and sealed inside of aweatherproof housing (Figure 2). The unit was placedat the top of the tower to directly measure any potentialtower vibration that could not be recorded by the princi-pal ship-motion sensor, a higher grade GPS-6 DOF unit(CodaOctopus F180), affixed to the deck of the vessel.The LIDAR system was operated in two modes: 1)sweeping mode, in which the LIDAR was continuouslyswept along ship centerline from the transom to the aft-horizon, using the pan/tilt, effectively scanning a swathof the wake up to 12 m aft of the vessel; or 2) fixed an-gle mode, where the LIDAR scanned the free surface ata constant elevation and azimuth relative to the ship. Theprogrammable pan/tilt unit allowed data to be sequen-tially captured, typically gathering 60 seconds of data ata number of preset elevation angles. The flexibility ofthese deployment schemes allowed the interrogation ofdifferent regions within the wake. Positioned at almost12 m above the mean waterline, the LIDAR’s effectiveswath was approximately 20 m wide. Theoretically, thefield-of-view should increase further aft, but data returnsdecreased as the angle-of-incidence with the water sur-face increased. Thus 20 m was the effective maximumswath that the LIDAR could measure for the tower heightused in these studies.2 igure 2: The Scripps LIDAR System mounted to the transomof the R/V Athena I.
Mean wake profiles were obtained by the LIDARsystem at 3.1, 4.6, 5.4, 9.3, and 13.4 m/s (6, 9, 10.5, 18,and 26 kts). In this paper the 5.4 m/s (10.5 kt) dataset ispresented and discussed.D
ATA P ROCESSING AND A NALYSIS
The post-processing scheme transforming the rawLIDAR data to wave height involved 1) conversion ofthe raw data to earth-based coordinates moving with the vessel, 2) correcting the free surface to mean sea level,and 3) compositing the surface at various locations aft ofthe vessel into a time-averaged 3D map.The scanning LIDAR outputs range and angle of therotating mirror. These data were converted to ship Carte-sian coordinates by using the elevation and azimuth an-gles of the pan and tilt. The vertical axes of the LIDARand the ship-fixed coordinate system were aligned, with x positive aft, z positive downward, and the origin atthe LIDAR. Measurements from the F180 (a combinedGPS/motion instrument that, in addition to GPS informa-tion, outputs acceleration in three axes, pitch, roll, yaw,and heave in real-time) was used to correct the data toa ground-fixed system. Real-time heave was calculatedfrom the acceleration data and simultaneously correctedfor drift using a Kalman filter.The registration of time within the LIDAR systemwas required for accurate motion correction of the data.The Xbow Dynamics Motion Unit (DMU) and LIDARwere synchronized by an external trigger which providedan accurate time registration in the data acquisition coin-cident with the reset of an internal clock within the LI-DAR. The clock reset trigger was typically used at leasttwice during an 11-minute data collection run. Upon ex-amining the timing synchronization between the LIDARand DMU clocks, it was found that the LIDAR clockdrifted less than 50 msec in any 11-minute period, i.e.the drift never exceeded the temporal spacing betweenLIDAR measurements. Due to the nature of the scan-ning mechanism, there is an along-track translation be-tween the first and last pixels of a single line scan. Thetime between the first and last pixel was 1.47 msec; fora maximum ship speed of 15 m/s, the longitudinal transitof a scan due to ship translation was 2.21 cm. The nomi-nal footprint of the laser on the ocean surface varies withdistance aft and distance away from the center scan, butit was generally 3-4 cm in diameter. Due to the smalltranslation distance relative to the footprint size, eachline scan was treated in post processing as an instanta-neous point measurement.During processing of data obtained when the wakeis scanned with the pan/tilt unit, careful attention is re-quire to register the time and position of the LIDAR headangle. The approach used relied upon the DMU’s x -axis (which was parallel to the LIDAR’s centerline mea-surement) acceleration, whose second derivative clearlyshows the start/stop times of elevation changes. In fixed-angle mode, a relatively constant x -acceleration was as-sumed to signify a constant elevation angle. In thesweeping mode, a linear rate of change in elevation wasassumed, which was a reasonable assumption for the an-gles used in this data collection.The DMU/LIDAR data also required time synchro-nized with an external GPS timestamp. The approachwas to cross-correlate x -axis data from the two mo-3ion packages to obtain the constant time-offset (typi-cally 1 second or less) between the LIDAR data and theF180/ship motion data. Once the timing of the LIDARmeasurement system with the F180 GPS time referencewas reconciled, now to an accuracy of O(0.01) second,the raw LIDAR measurements could be converted to anearth-based coordinate system using the F180 pitch androll angles.In the second post-processing step, the measuredfree surface was corrected to Mean Sea Level (MSL).MSL would ideally be measured when the boat was sta-tionary, but data was only collected at non-zero shipvelocities; so the average waterline measured approxi-mately 2 m aft of the transom at a ship speed of 1.0 m/s(2.0 kts) was used as the MSL vertical datum. Data wascollected for MSL over five minutes. In the final post-processing step, a 3D map of the mean surface wave fieldwas generated from elevation measurements at a varietyof LIDAR angles. A rectangular grid was created and thefield data were placed onto the grid and averaged withineach grid cell. The size of each grid cell was 0.1 m wideby 1 m long. Empty grid cells were linearly interpolated,and a 3-point median filter was applied along the wake’swidth to create the final images.LIDAR R ESULTS
Figure 3 shows mean wake profiles at locationsranging from 2.1 m aft to 11.5 m aft of the transom.Standard deviation is also included as the red dotted line.For this particular data set, the LIDAR system was setto collect data in time segments at fixed angles. Eleva-tions ranged between -80 to -45 in 5-degree increments.The aft location given was the mean location of the free-surface interrogated by the LIDAR at each angle. Sincethe along-scan resolution varies with time and elevationangle, the LIDAR data were gridded to 0.1 m resolutionin the port ( y -axis) and the mean and standard deviationof elevation were calculated for each grid cell. Only lo-cations within ±
10 m from the centerline are shown be-cause the data drop-out rate was much higher outside thisregion leads to unreliable measurement statisticsIn general, wake elevations are higher towards shipcenterline and decrease away from the center. The localmaximum to either side of the centerline is the wake’s”shoulder.” Notice a slight depression in height betweenthe two shoulders. Just outside the shoulder, the wake el-evation decreases sharply, and continuing outward fromthe center, the surface remains fairly constant (as at 6.6and 8.0 m aft) or rises gradually (3.1, 4.2, 5.4 m aft).Standard deviation is fairly constant across this regionof the wake except approximately ± Figure 3:
Mean (blue) and standard deviation (red) of the wakesurface at various aft locations. which is characteristic of a ship’s V-shaped wake.The elevation data at all tilt angles were insertedinto a regularly-spaced 2D grid to composite the free sur-face. The V-shape of the wake is well-defined in the data(Figure 4a) and in the photograph from the LIDAR sys-tem’s camera (Figure 4c). The trough outside the shoul-ders and the slight centerline depression can also be ob-served. Figure 4b is a reconstruction of the average nor-malized signal return (on logarithmic scale) to the LI-DAR. This figure is instructive because the brightness ofthe signal return is dependent on the optical scatteringefficiency of the free surface, which is dependent on theconcentrations of bubbles and foam at the surface. Thedata from this active optical technique shows the bubblesare mostly found at the shoulders and along the center-line, consistent with the passive imaging provided by theblack/white photograph. Additionally, within 7 m aft ofthe transom, a streak of bubbles can be seen at 5 - 6 mport and starboard of the centerline. This was also ob-served in the video footage (Figure 4c). These bubbleswere created either at the bow or along the side hull ofthe vessel and were being swept aft to the transom region.With the time-series of surface elevation havingbeen obtained at multiple port locations, the spectral con-tent across the wake was computed, and it was found that4 igure 4: (a) Mean wake surface, (b) logarithmic signal returnamplitude, and (c) photograph at 5.4 m/s (10.5 kts). the most energetic portion of the wake was in a region of ± Figure 5: (a) Frequency spectra of the wake elevation at vari-ous aft locations. Spectra were averaged spatially between 1 mport and 1 m starboard of ship centerline. (b) Pitch, roll spectra.(c) Peak of the frequency spectrum vs. aft distance. gion at multiple distances aft of the vessel are shown inFigure 5a. The peaks in the spectra are close to 1 Hz. Aslight linear relationship is observed between distance aftand peak frequency (Figure 5c). The absence of a corre-sponding peak at 1 Hz in the pitch/roll spectra, Figure 5b,suggests that this peak is a characteristic of the inherentunsteadiness of the wake, and not due to ship motions.5
IELD D ATA D ISCUSSION
Figure 3 illustrates that the central region of thewake’s surface is the most variable, while the regionsoutside the shoulders have relatively low variability. Thisvariability is found to result from a narrowband wavespectrum (Figure 5) in the frequency range between 0.8- 1.1 Hz. Time series analysis of the LIDAR data, andqualitative observations from bore-sighted video cameraindicate that breaking shoulder waves traveling to thevessel centerline collide. When the opposing waves meetin the center, a peak in the surface profile forms (Fig-ure 7). Subsequently there is a depression in the cen-ter of the profile as the water falls away from the center.Thus a standing wave is observed that occurs betweenthe wake’s shoulders with a fundamental frequency of0.8 - 1.1 Hz. Analysis of the square of the vertical ve-locity along the cross-track of the wake (computed usingthe time derivative of the elevation measurements) indi-cates there is a spike in kinetic energy just outside of thewake shoulders and near the centerline (Figure 6)wherebreaking is most active. Consistent with observations ofa standing wave, it appears that the nodes of the stand-ing wave are approximately ± ± Figure 6:
Mean elevation, logarithmic normalized signal am-plitude, and square velocity at 3.1 m aft of the transom, 5.4 m/s(10.5 kts).
NUMERICAL PREDICTONS
Initial comparisons of the experimental LIDAR measure-ments are made to predictions from NFA and CFDship-
Figure 7:
Instantaneous wake elevations every 0.1 sec. Twowaves from the shoulders are traveling in opposite directions.
Iowa-V.4 in the following sub-sections.In the previous section, a significant amount of dy-namic heave, roll, and pitch was removed from the LI-DAR data to register the data to MSL. The fact that sucha small final standard deviation was achieved suggeststhis registration was applied successfully (see Figure 3).However, the data in that figure displays both a higherthan expected (or predicted) mean height in addition toa clear roll dependence. It was therefore deemed neces-sary to remove these last biases before making the quan-titative comparisons.In the following sections, the LIDAR mean-heightdata has been de-trended in the following manner: Themean elevation data has been reduced in height by 0.08m, and a roll of 0.28 degrees has been removed. The re-sulting heave correction of -0.08 m is of the same orderas the dynamic heave difference measured at model-scalefrom the 0 m/s to 5.4 m/s (10.5 kts) operation (-0.05 mto -0.075 m). Although the F180 could measure ship re-sponse to most ocean waves, it is surmised that the heavedue to steady ship dynamics may have been incorrectlyinterpreted as sensor drift and therefore not taken into ac-count. The 0.28 degree tilt could also have arisen froma small alignment difference between the sensor with theboat hull.6FA P
REDICTIONS
The objective of the numerical predictions is to as-sess the capability of NFA to predict unsteady transomflows of model-scale and full-scale ships.A description of the NFA and its current capabili-ties can be found in Dommermuth et al. (2007). NFAsolves the Navier-Stokes equations utilizing a cartesian-grid formulation to model the free surface and a ship hull.An interface capturing technique is used to resolve thefree surface. The interface capturing of the free surfaceuses a second-order accurate, volume-of-fluid technique.A cut-cell method is used to enforce free-slip boundaryconditions on the hull. The free-slip boundary conditiondoes not resolve the ship’s boundary layer. Away fromthe hull, NFA uses a Smargorinsky turbulence modelbased on a large-eddy formulation. A surface represen-tation of the ship hull is all that’s required as input. Rel-ative to methods that use a body-fitted grid, the potentialadvantages of NFA’s approach are significantly simpli-fied gridding requirements and greatly improved numer-ical stability due to the highly structured grid.As an initial step in evaluating the capability ofNFA to model the wake of the full-scale Athena, a grid-density convergence study was performed. Two simula-tions have been performed with medium and high griddensities for the Athena moving with constant forwardspeed at 5.4 m/s (10.5 kts) ( F r = 0 . ), and one sim-ulation has been performed with medium resolution for9.3 m/s (18 kts) ( F r = 0 . ). The medium-resolutionsimulations used 1024x192x256=50,331,648 grid points,and the high-resolution simulation used 1280x384x384= 188,743,680 grid points. The length scales were nor-malized by the ship length ( L = 46 . m), and the ve-locity scales were normalized by the ship speed (U=5.4m/s (10.5 kts) & 9.3 m/s (18 kts)). Grid stretching wasused along the cartesian axes. Grid points were clus-tered near the stern region, along the sides of the ship,and the mean free-surface. The minimum grid spacing, ∆ , for the high-resolution simulation ( ∆ = 0 . )was about half the medium simulation ( ∆ = 0 . ).For the high-resolution simulation, the grid spacing nearthe edges of the domain was ( ∆ = 0 . ), which dueto more stretching was slightly higher than the medium-resolution simulation ( ∆ = 0 . ). For all simula-tions, the length, width, water depth, and air height ofthe computational domains were respectively 3.0, 1.0,1.0, and 0.5 ship lengths. The non-dimensional timesteps were ∆ t = 0 . . , and the numeri-cal simulations run 28,000 and 32,000 time steps for themedium and high-resolution simulations, respectively.This corresponds to seven ship lengths for the medium-resolution simulations and four ship lengths for the high-resolution simulation. An adjustment procedure wasused to bring the ship up to full speed. The adjustmentperiod was 0.5. The results of the medium-resolution simulation were output every 20 time steps. Due to filesize consideration, the high-resolution simulation wasonly output every 100 time steps. The sampling ratesfor the medium and high-resolution simulations were re-spectively 23.0137 Hz and 9.2055 Hz in dimensionalunits. The medium and high-resolution simulations re-spectively used 384 and 720 subdomains. For each sim-ulation, each subdomain was assigned to a single nodeon a Cray XT3. The medium and high-resolution simu-lations respectively take 46.7 and 122 wall-clock hours,which corresponds to 6.0 and 13.8 cpu seconds per timestep.For this investigation: symmetry boundary condi-tions were imposed across the centerplane of the ship,appendages and propulsors were not modeled, and thehull was fixed in sinkage and trim. The sinkage and trimconditions were established based upon high-density DasBoot (Wyatt 2000) predictions. At 5.4 m/s (10.5 kts) thesinkage was set at − . − (in non-dimensional units),and trim was set at . ◦ . At 9.3 m/s (18 kts), thesinkage was − . − (non-dimensional), and the trimwas . ◦ . Model-Scale Predictions and Comparisons
Figure 8 compares NSWCCD model-scale bare-hullmeasurements and NFA predictions of wave cuts for the5.4 m/s (10.5 kt) and 9.3 m/s (18 kt) cases. Resultsare shown for medium grid resolutions. The agreementbetween measurements and predictions is better for the9.3 m/s case than for the 5.4 m/s case. Apparently, thedry-transom flow at 9.3 m/s (18 kts) is predicted betterby NFA than the wetted-transom flow at 5.4 m/s (10.5kts). In fact, for 5.4 m/s (10.5 kts) the transom is dryas predicted by NFA, whereas a wet transom is observedat model-scale. Figure 9 compares NSWCCD bare-hullmeasurements and NFA predictions of free-surface con-tours for the two speed cases. Results are shown formedium grid resolutions. Once again, the agreement be-tween measurements and predictions is better for the 9.3m/s (18 kt) case than for the 5.4 m/s (10.5 kt) case. Thecontour plots show no evidence of numerical dissipationaway from the ship model.
Full-Scale Predictions and Comparisons
Figure 10 compares LIDAR measurements and NFApredictions of the free-surface elevation in the stern re-gion for the 5.4 m/s (10.5 kt) case. Mean and RMSfree-surface elevations are shown for medium and high-resolution simulations. For the mean free-surface ele-vation, the high-resolution prediction are in slightly bet-ter agreement with field measurements than the medium-resolution prediction. The opposite is true for the RMSfluctuations in the free-surface elevation. Both the pre-dicted mean and RMS free-surface elevations attenuate7a) − − − − − − − − − − − − − − − − − − − − − − − − (b) − − − − − − − − − − − − − − − − − − − − − − − − Figure 8:
Model 5365 (Athena) wave cuts at four trans-verse offsets. NSWCCD measurements and NFA predictionsare respectively denoted by black and blue lines. The fore per-pendicular is located at x/L=0 and the aft perpendicular is lo-cated at x/L=-1. For each set of plots, the transverse offsetsare y/L=0.1067, 0.1861, 0.2482, and 0.31023. (a) 5.4 m/s (10.5kts), full-scale equivalent. (b) 9.3 m/s (18 kts), full-scale equiv-alent. more rapidly downstream than the field measurements.The predicted RMS fluctuations are higher than the mea-surements along the centerplane. This is where sym-metry has been imposed in the NFA simulations. Wealso note that the background RMS fluctuations are muchhigher in the field measurements than the numerical pre-dictions. Due to the collection of measurements in anunsteady environment, some background level of RMSsurface roughness is to be expected.In Figure 11 the power spectra of the wave elevationtime series for medium-resolution simulation and the LI-DAR measurements are plotted for several aft transomlocations (2.1, 3.1, 4.2, 5.4, 6.6, 8.0, 9.6, and 11.5 me-ters). These spectra have been averaged over the center-line region within ± Figure 9:
Model 5365 (Athena) free-surface contours.NSWCCD measurements and NFA predictions are respectivelyplotted in the bottom and top halves of each plot. (a) 5.4 m/s(10.5 kts), full-scale equivalent. (b) 9.3 m/s (18 kts), full-scaleequivalent. iments (as was observed for both the predicted mean andthe RMS free-surface elevations). The predicted spectrallevels then attenuate more rapidly downstream than thefield measurements. A dominant frequency at 1.3 Hz isobserved for all aft transom locations for the predictions,which is above the dominant frequency of the field data(1.0 Hz), but the peak spectral amplitudes appear to bewell-predicted.
NFA Predictions Discussion
NFA predicts the location of the onset of breakingwell. NFA predicts slightly greater mean wave heightsthan both the model-scale and full-scale measurements.The overprediction by NFA is significantly less at 9.3 m/s(18 kts), a dry transom with less turbulence, than for the5.4 m/s (10.5 kt) case - suggesting that NFA does notaccurately model the amount of dissipation due to turbu-lence caused by the breaking observed in this region. Atfull-scale NFA successfully captures the trend and peaklocations for wave elevation, RMS, and spectral distri-bution, but over-predicted the initial magnitudes, and ex-hibited much greater attenuation aft. The transom wasdry in the 5.4 (10.5 kt) simulation. It may be that boththe over-prediction and the rapid attenuation of the waveamplitude is partially due to the dry transom prediction.Appendages and propellers were not included inthe NFA simulations, so their absence may have con-tributed to the dry transom result. The effects of thefinite-difference operators that are used in NFA also re-quires investigation. The predicted RMS fluctuations andthe dominant frequency peak are high along the cen-terplane where symmetry is imposed in the NFA sim-ulations. Future work should investigate whether no-symmetry boundary conditions would alleviate these ef-fects.8a) (b)(c) (d)
Figure 10:
NFA versus experiments in the stern region at 5.4 m/s (10.5 kts). NFA predictions and LIDAR measurements arerespectively plotted in the top and bottom halves of each plot. (a) Wave height (medium resolution, correlation coefficient=0.81).(b) RMS height (medium resolution, correlation coefficient=0.88). (c) Wave height (high resolution, correlation coefficient=0.84).(d) RMS height (high resolution, correlation coefficient=0.85). −2 −1 −4 −3 −2 −1 Frequency (Hz) (b) −2 −1 −4 −3 −2 −1 Frequency (Hz)
Figure 11:
NFA versus experiments in the stern region at5.4 m/s (10.5 kts). (a) NFA predictions and (b) LIDAR mea-surements are respectively plotted in this figure. The averagedwave frequency spectra for the wake centerline region within ± CFD
SHIP -I OWA -V.4 P
REDICTIONS
The objective of this study is to evaluate the capabil-ity of CFDship-Iowa-V.4 version 4 to predict unsteadytransom flows of Athena R/V in both model- and full-scale Reynolds numbers. This objective is in contrast tothe grid-density sensitivity performed in the NFA study.The general-purpose solver CFDShip-Iowa-V.4solves the unsteady Reynolds averaged Navier-Stokes(RANS) or detached eddy simulation (DES) equations inthe liquid phase of a free-surface flow (Carrica, Wilson &Stern 2007). The free surface is captured using a single-phase level-set method and the turbulence is modeled byisotropic or anisotropic turbulence models. Numericalmethods include: advanced iterative solvers, second andhigher-order finite-difference schemes with conservativeformulations, parallelization based on a domain decom-position approach using the message passing interface(MPI), and dynamic overset grids for local grid refine- ment and large amplitude motions.
Figure 12:
Model-scale results for: (a) mean free-surface ele-vation for bare-hull predictions and measurements, (b) fully-appended prediction of mean free surface is compared withmodel-scale bare-hull measurements, and (c) the RMS of thefree-surface wave elevation is compared for the bare hull andfully-appended simulations.
Simulations using CFDShip-Iowa-V.4 are summa-rized in Table 3. The ship simulations were performedfor fixed sinkage and trim. Sinkage and trim valueswere established based upon previously predicted val-ues of sinkage and trim obtained for the bare-hull ge-ometry at the same Froude number. The grid consistsof 14.5 M grid points, portioned into 105 blocks to runon parallel processors (Table 4). For convection termsin momentum, a hybrid scheme was applied, which usesthird-order upwind biased for the separation region andswitches to second-order very close to the wall. Asecond-order Euler backward difference scheme is usedfor the time derivative. A blended k-omega based DESmodel was used for turbulence modeling. Model-scalesimulation was performed using a near-wall turbulencemodel, whereas a multi-layer wall-function (y+=100)was used for the full-scale calculation.10able 3 Simulations using CFDShip-Iowa-V.4 for fully-appended Athena at 10.5 knot.Table 4 Fully-Appended Athena Fine Grid Particulars.Simulations were performed for six ship lengths (i.e.52 seconds). Averaging of the free-surface elevation andspectra were obtained using the last two ship lengths oftime (i.e, 2000 samples), which was sufficient enoughas evident from the running mean. The sampling periodalso corresponds to 15 turn-over times of the transomvortex shedding.
Model-Scale Predictions and Comparisons
In the absence of model-scale data for the fully-appended Athena, model-scale simulation results arecompared with model-scale measurements and predic-tions for the bare-hull geometry. Figures 12a and 12bcompare the mean free-surface wave elevation obtainedfrom the fully-appended geometry with the previousbare-hull results (Wilson, Carrica & Stern 2006) andthe bare-hull data (Fu, Karion, Pence, Rice, Walker &Ratcliffe 2005). Figure 12c compares the predicted RMSof the free-surface wave elevation for the bare hull andfully-appended hull. In Figure 13, the predicted free-surface elevation wave-cut profiles are compared at sev-eral spanwise locations with model-scale data.
Figure 13:
Wave cuts at different spanwise positions at model-scale using CFDShip-Iowa-V.4 (bare hull and fully-appendedgeometries) are compared with the EFD data .
Figure 14:
Simulations versus experiments in the stern region at 5.4 m/s (10.5 kts) for wave elevation mean and RMS. Lidarmeasurements and predictions are respectively plotted in the bottom and top halves of each plot; (a) wave elevation by CFDShip-Iowa-V.4, (b) RMS by CFDShip-Iowa-V.4, (c) wave elevation by NFA, (d) RMS by NFA.
Figure 15:
CFDship-Iowa-V.4 versus experiments in the sternregion at 5.4 m/s (10.5 kts). (a) CFDship-Iowa-V.4 predictionsand (b) LIDAR measurements are respectively plotted in thisfigure. The averaged wave frequency spectra for the wake cen-terline region within ± Full-Scale Predictions and Comparisons
The CFDship-Iowa-V.4 results have been shiftedvertically by 0.1 m to better match the full-scale waveelevation in the far-field. Results are presented in di-mensional units (using ship length of 46.94 m, and ve-locity U=5.4 m/s (10.5 kts). Figure 14 shows the free-surface elevation and RMS of the free-surface wave ele-vation for full-scale simulations that are compared withthe LIDAR measurements. NFA (unaltered) results arealso presented for comparison. In Figure 15 the center-line wave elevation time series FFT spectra for full-scalesimulations are plotted at several aft transom locations(2.1, 3.1, 4.2, 5.4, 6.6, 8.0, 9.6, and 11.5 meters). De-tails of the vortical structures and associated instabilitieswill be presented in a separated study (Bhushan, Xing &Stern 2008).
CFDShip-Iowa-V.4 Predictions Discussion
The comparison between measurements, the model-scale bare-hull measurements versus the full-scale fully-appended LIDAR measurements, shows that the wave el-evation peak for the appended hull is 38.5% higher thanthat of bare hull. The region of significant wave eleva-tion for the appended hull is also much larger than thatfor bare hull. Unfortunately, similar observations for sur-face roughness can not be made, because measurementsfor RMS for the bare-hull configuration at model-scaleare not available.In comparing the model-scale bare-hull measure-ments with the bare-hull CFDShip-Iowa-V.4 simulations,the simulations predicted the mean wave crest and troughamplitudes well, but showed slightly shorter wavelengthand a smaller angle for the Kelvin wave pattern. Whenthe model-scale bare-hull predictions of Wilson et al.(2006) were compared with the current model-scaleappended-hull simulations, the current simulations pre-dicted the same Kelvin wave angle but slightly under-predicted wave crest and trough, significantly under-predicted RMS, and exhibited a different flow pattern es-pecially near the centerline. It is believed that the dif-ferences between the two CFD simulations is due to theeffect of appendages. Another possible factor are the dif-ferent grid design; Wilson et al. (2006) applied transomrefinement grids that are not used in the current study.For full-scale/appended-hull comparisons with theLIDAR measurements, CFDShip-Iowa-V.4 successfullycaptures the trend and peak locations for wave elevationand RMS but with under-predicted magnitudes. Thisdeficiency of magnitudes increases downstream, and islikely due to the coarser grid resolution farther awayfrom the ship hull. Power spectra analysis reveals a dom-inant frequency at 1 Hz for all aft transom locations,which agrees well with the LIDAR spectral analysis butwith amplitude under-predicted.A wetted transom was observed for both model andfull-scale simulations. Within the simulations, the un-steadiness of the wave elevations aft of the transom canbe directly related to the Karman-like vortex sheddingfrom the transom corner below the free surface. Fig-ure 16 shows one complete cycle of this shedding pe-riod. The corresponding Strouhal number (St) based onthe ship velocity and wetted transom height is reportedin Table 3.Future work will be to increase the grid resolution inthe transom region, add a propeller model, and evaluatethe effects of fixed motions versus predicted motions.13 igure 16:
Phases of transom vortex shedding usingCFDShip-Iowa-V.4 (full-scale simulation).
CONCLUSIONS
An initial set of full-scale LIDAR measurements and nu-merical predictions of the wave-elevation topology be-hind a transom-sterned vessel, the R/V Athena I, havebeen compared and assessed in this paper. Comparisonsof the mean height, surface roughness (RMS), and spec-tra of the breaking stern-waves at 5.4 m/s (10.5 kts), awet-transom condition, have been made. These analy-ses represent (perhaps the very first) comparisons of highdensity in-situ data with numerical predictions of break-ing stern-waves, and although preliminary, the results arereasonably encouraging.From a naval-design perspective, where mean waveheight is often the most important parameter, the nu-merical predictions compared reasonably well withthe LIDAR data. Both codes indicated the positionof the onset of breaking well, with NFA somewhatover-predicting and CDFShip-Iowa somewhat under-predicting the breaking wave heights. It is likely that,with additional effort, both codes will converge moreclosely to the measurements. For NFA this means theabsence of the centerplane-symmetry assumption em-ployed in this analysis, the addition of appendages, andfinally the addition of propulsors. For CFDship-Iowa-V.4, this additional work includes increased grid density,and the modeling of the propulsors.From a design-analysis perspective, where detailsof the flow become more significant, both numericaltechniques displayed an over-suppression of the surfaceroughness in the late wake after the initial onset of break-ing. While both codes displayed good spectral frequencydistribution with respect to the measurements, it was ev-ident that issues remain. At the onset of breaking, NFAhad initially higher spectral content but attenuated toorapidly aft. CFDship-Iowa-V.4 exhibited weaker attenu-ation aft, but at breaking onset initially had suppressedspectral content when compared to the measurements.While in both cases the attenuation aft may be due solelyto a lack of adequate grid resolution, it is also true thatun-modeled turbulent processes play a very importantrole in this region. For example, unsteady interactionof the propulsors and appendages may set up large or-ganized turbulent structures that affect the dissipationof surface roughness. Detailed analysis of the vorticalstructures and associated instabilities found in the CFDpredictions needs to be performed. These vertical struc-ture are closely connected with the time-history of tran-som wave elevation and resistance/pressure coefficients.Additionally, it is likely that the significant bubble en-trainment (observable at full-scale) plays an importantrole in the dissipation rates of turbulence in the late wakeregion, which neither code currently models.The LIDAR-based wave measurement systemproved itself to be a new and extremely useful tool for14he understanding of wavebreaking physics in these anal-yses. The LIDAR measurements have provided infor-mation and detail that have heretofore been unavailable.However, it was necessary to de-trend the data prior tomaking comparisons to the predictions. It may thereforebe inappropriate to attribute all the differences betweenthe simulations and measurements to the CFD codes.The full-scale measurements will require additional testsfor confidence before final conclusions can be properlymade.This paper represents a work in progress. While thisinitial comparison of the numerical predictions and full-scale measurements has generally shown good agree-ment, it has also revealed areas of necessary improve-ment. Significantly more analysis will be required tocomprehend and model the physics observed and avail-able in this full-scale data set. Fortunately, this full-scale measurement effort represents only one small por-tion of the ONR Ship Wave Breaking and Bubble Wakeprogram. It will be necessary to include data from allsources within this program to put any newly identifiedquestions introduced by these first comparisons into con-text: including examination of the other sensors (QViz,capacitance probes, and Void-Fraction sensors), and theother experiments (the large Transom-Stern model test,and the Athena model tests).
ACKNOWLEDGEMENTS
References