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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 402 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 5415 * F.Stern1, J.Longo1, R.Penna2, A.Olivieri2, T.Ratcliffe3, H.Coleman4 (1Iowa Institute of Hydraulic Research, The University of Iowa, Iowa City, IA, USA; 2Italian Ship Model Basin, Rome, Italy; 3David Taylor Model Basin, Bethesda, MD, USA; 4Propulsion Research Center, University of Alabama in Huntsville, Huntsville, AL, USA) ABSTRACT Results are presented from overlapping towing tank tests between three institutes for resistance, sinkage and trim, wave profiles and elevations, and nominal wake using the same model geometry and conditions, including rigorous application of standard uncertainty assessment procedures. Two of the institutes used 5.7 m models whereas the third institute used a smaller 3 m model. Comparison variables were defined for data-reduction equations and data differences and data-difference uncertainties. Detailed descriptions were provided of facilities, measurement systems, data- acquisition and reduction procedures, and uncertainty assessment. Results were discussed with regard to levels and causes of data differences and data-difference uncertainties and to estimate facility/model geometry and scale effect biases. For same size 5.7 m models, data differences were in general oscillatory, and in many cases, larger in magnitude than data- difference uncertainties, which indicates unaccounted for bias and precision limits and that current individual facility uncertainty estimates are often too optimistic. Scale effects for the 3 m model are only evident for resistance and trim tests at high Fr. Facility/model geometry and scale effect bias are estimated based on comparisons. Uncertainty estimates including such biases may provide better estimates, especially for use in CFD validation, which is the recommendation of the present study along with efforts towards improvement of individual institute uncertainty estimates. Use of standard models and current ITTC efforts in providing standard quality manual procedures for towing tank tests and uncertainty estimates will also be helpful in this regard. INTRODUCTION Towing tank testing is undergoing change from routine tests for global variables to detailed tests for local variables for model development and computational fluid dynamics (CFD) validation, as design methodology changes from model testing and theory to simulation-based design. Such detailed testing requires that towing tanks utilize advanced modern instrumentation with complete documentation of test conditions, procedures, and uncertainty assessment. The requirements for levels of uncertainties are even more stringent than those required previously since they are a limiting factor in establishing the level of validation and credibility of simulation technology. Also, routine test data is more likely utilized in house, whereas detailed test data is more likely utilized internationally, which additionally requires use of standard procedures and establishment of benchmark levels of data uncertainties. Detailed testing offers new opportunities for towing tanks, as the amount and complexity of testing is increased. International collaborations are attractive from a resource perspective. The benchmark database for CFD validation for resistance and propulsion is fairly extensive with current focus on modern hull forms and detailed tests as reported by the Resistance Committee of the 22nd International Towing Tank Conference (ITTC, 1999). Tanker (KVLCC2), container ship (KCS), and surface combatant (DTMB 5415) hull forms were recommended for use and are currently being used as test cases in the Gothenburg 2000 Workshop on CFD for Ship Hydrodynamics (Gothenburg 2000; http://www.iihr.uiowa.edu/gothenburg2000/). KVLCC2 and KCS were conceived by the Korean Institute of Ships & Ocean Engineering (KRISO) specifically as test cases for modern tanker and container ship hull forms for CFD validation for ship hydrodynamics ca. 1997. KVLCC2 and KCS have bulbous bows and bulbous cruiser and transom sterns, respectively. The KVLCC2 and KCS data were procured by KRISO (Van et al., 1997 and 1998a, b) in collaboration with Pohang University of Science and the authoritative version for attribution. * 23rd Symposium on Naval Hydrodynamics, 17–22 September 2000, Val de Reuil, France

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 403 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 Technology, Korea (Lee et al., 1998) and Ship Research Institute, Japan, respectively. DTMB 5415 was conceived by David Taylor Model Basin, USA Navy as a preliminary design for a surface combatant ca. 1980 with a sonar dome bow and transom stern. The DTMB 5415 data were procured by DTMB (Ratcliffe, 1995; http://www50.dt.navy.mil/5415/) in collaboration with Istituto Nazionale per Studi ed Esperienze di Architettura Navale (INSEAN), Italy (Avanzini et al., 1998, Avanzini et al., 2000, Olivieri and Penna, 1999, Olivieri and Penna, 2000), and Iowa Institute of Hydraulic Research, USA (Longo and Stern, 1998, Gui et al., 1999, Longo et al., 2000, Stern, 2000: http://www.iihr.uiowa.edu/ ~towtank/). The present paper describes the international collaboration on DTMB model 5415 between DTMB, INSEAN, and IIHR. The collaboration was done at DTMB using 5415 (5.72 m, 1/24.8 scale model), at INSEAN using INSEAN model 2340 and 2340A (exact geosyms of 5415), and at IIHR using DTMB model 5512 (3.038 m, 1/46.6 scale geosym of 5415). Figure 1 shows models 5415, 2340A, and 5512. Between all three institutions many conditions and physics are under investigation. The conditions include bare hull without (all) and with appendages and propulsor (DTMB), and fixed and free model (all). The physics are comprehensive and include model size (IIHR), facility biases (all), Reynolds number (Re) effects (all), boundary layer and wake (INSEAN), stern flow (all), Froude number (Fr) effects (all), bow and transom flow (DTMB), wave breaking (INSEAN), and turbulence and head waves (IIHR). The uncertainty assessment procedures closely follow ITTC (1999) recommendations. Overlapping tests for resistance, sinkage and trim, wave profile, wave elevations, and nominal wake are included for evaluation between institutes of facilities; measurement systems; test procedures; uncertainty assessments; model size, offsets, and turbulence stimulation; and facility/model geometry and scale effect biases, through comparisons of both data and uncertainties. The results of the overlapping tests build on information provided by the Cooperative Experimental Program of the Resistance Committees of the 17–19 ITTC and the cooperative uncertainty assessment example for resistance test of the Resistance Committee of the 22nd ITTC. The former provided comparison between up to 22 institutes of global (resistance, sinkage and trim, wave profile, wave cut, wake survey, form factor, and blockage) and local (surface pressure and boundary layer traverses) data for a standard geometry (Series 60) of different sizes (1.2–9.6 m), but did not consider uncertainty assessment. The latter built on the former in providing comparison between 7 institutes of resistance test uncertainties following standard uncertainty assessment methodology, but for different model geometries and sizes (Series 60, container ships, and 5415). Present work builds on both in providing comparisons between 3 institutes of both data and uncertainties for the same model geometry of 2 sizes (3 and 5.72 m). Such comparisons between facilities is apparently relatively uncommon in other fields such as aerospace and mechanical engineering, which may be due to increased complexity of routine ship model testing due to viscous and free surface effects in comparison to routine testing in other fields. The results are timely with regard to the Gothenburg 2000 Workshop on CFD for Ship Hydrodynamics and should be taken into consideration in reaching conclusions regarding levels of CFD validation. The focus herein is on the overlapping tests; however, highlights are given of the overall test program. Sections describe, respectively: the overlapping test design, comparison variables, and conditions; facilities, measurement systems, and procedures; uncertainty assessments; CFD validation/complementary CFD; comparisons of results; highlights of the overall test program; and conclusions. OVERLAPPING TEST DESIGN, COMPARISON VARIABLES, AND CONDITIONS The most typical towing-tank tests were selected for the overlapping tests, i.e., resistance, sinkage and trim, wave profile, wave elevations, and nominal wake. Each institute followed their usual procedures; however, special consideration was given to integration of uncertainty assessment into all phases of the experimental process, CFD validation, and complementary CFD. Comparison variables were defined for total and residuary CR resistance, sinkage σ and trim τ, wave profile and elevations ζ, and nominal wake mean velocity and pressure Cp, as given by the following data-reduction equations: (1a) (1b) (1c) (1d) the authoritative version for attribution.

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 404 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 (2) (3) (4) (5) (6) is selected as the comparison variable for resistance, since it calibrates all data to the same temperature T=15°C; thereby, enabling quantitative comparisons for similar tests and models at different institutes, as recommended by ITTC Quality Manual Procedure 4.9–03–03–01.2 1978 ITTC Performance Prediction Method. k is the form factor and CF is the flat-plate friction line. σ and τ are defined without Fr2 in the denominator. ζ, and Cp are normalized by model length L, carriage speed Uc, and dynamic pressure respectively. To facilitate the comparisons of data procured at the different institutes, data (A, B, C), data differences Di, and data differences uncertainty variables are defined as follows: (7) (8) (9) (10) (11) (12) (13) Data differences Di are attributed to differences in facility (size, water quality, carriage); model size (for C), offsets, and turbulence stimulation; and measurement systems and procedures. Comparison of two institutes is relatively straightforward. For (14) data between institutes agree at level Presumably, design sets the required level of agreement between institutes. Better agreement requires reduction of and possibly Di. For (15) data disagreement is attributed to model size (for C) and unaccounted for bias B(A, B, C) and precision P(A, B, C) limits. Comparison of three institutes is not straight forward as there are many combinations of equation (14) and (15). Various combinations were considered such as A=B-2C, A+C-2B, and B+C-2A; however, it was difficult to draw conclusions from these results. Presentations of comparisons are therefore limited to (A, B, C), Di, U(A, B, C), and The conditions at each institute for the overlapping tests are summarized in Table 1. For each test, the measurement system, Fr, Re, average temperature Tave, density, kinematic viscosity, surface tension, density of data, and model installation with displacements at bow (FP) and stern (AP), is indicated. FACILITIES, MEASUREMENT SYSTEMS, AND PROCEDURES Facilities. Experiments with 5415 are performed in basin no. 2 (575 m long, 15.5 m wide, 6.7 m deep). Basin no. 2 is equipped with an electro-hydraulically operated drive carriage and capable of speeds of 10.3 m/s. Sidewall and endwall beaches enable 20-minute intervals between carriage runs. Towing-tank water is supplied by the Washington Suburban Sanitation Commission. Experiments with 2340A are performed in towing tank no. 2 (220 m long, 9 m wide, 3.6 m deep). Towing tank no. 2 is equipped with a single drive carriage that is capable of speeds of 10 m/s. Sidewall and endwall beaches enable 20-minute intervals between carriage runs. Towing tank water is spring water. Experiments with 5512 are the authoritative version for attribution. performed in the IIHR towing tank (100 m long and 3.048 m wide and deep). The IIHR tank is equipped with an electric- motor operated drive carriage that is cable driven by a 15-horsepower motor and capable of speeds of 3 m/s. Sidewall and endwall beaches enable twelve-minute intervals between carriage runs. Towing-tank water is supplied by the city of Iowa City. Model geometry. 5415 was constructed at the DTMB model workshop in 1980 from a blank of laminated wood and a computerized numerical-cutting (CNC) machine. Turbulence stimulation is at x=0.05

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 405 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 with cylindrical studs having 3.2 mm diameter, 2.5 mm height, and spaced 5.0 mm. The geometry offset measurement system consists of twenty-five wooden templates. Fig. 1: Model geometries for the overlapping tests. 2340A was constructed in 1998 at the INSEAN model workshop from a blank of laminated wood and a CNC machine. Turbulence stimulation is at x=0.01 with cylindrical studs having 3.0 mm diameter, 3.0 mm height, and spaced 30.0 mm. The geometry offset measurement system consists of computer-aided design (CAD), hand-cut templates, level table, right angle, plumb, and rulers and feeler gauges. The data is reduced by computing crossplane and global average values for the error in the offsets for each coordinate and for S. 5512 was constructed in 1996 at the DTMB model workshop from molded fiber-reinforced Plexiglas. Turbulence stimulation is at x=0.05 with cylindrical studs having 3.2 mm diameter, 1.6 mm height, and 10.0 mm spacing. The measurement system and data-reduction procedures for determination of the errors in the geometry offsets and S are virtually the same as at INSEAN, however, the IIHR templates are CNC milled. Carriage speed. At each facility, carriage speed Uc is measured with encoder-based measurement systems and PC data acquisition. The operating principle is integer pulse (n) counting at a wheel-mounted (diameter=D) encoder in known time intervals (∆t). The data-reduction equations are of the form (16) where a=(520, 1000, 8000), respectively for (A, B, C). Pulse count data is either passed to a PC directly as a frequency or through an analog-to-digital (AD) conversion. DTMB utilizes a 520-pulse, magnetic encoder carriage speed measurement system that is calibrated periodically to monitor its accuracy. Linear resolution is 0.33 mm/pulse. Data acquisition is done through collection of 2000 discrete samples over 5 seconds at 400 Hz. Pulses are counted in ∆t and entered into the PC as a frequency. Data reduction is completed through statistical analysis of the sample population (average, standard deviation, minimums, maximums, outliers). Outliers are identified and deleted using Chauvenet's criterion. INSEAN utilizes a 1000-window, optical encoder carriage speed measurement system. Linear resolution is 1 mm/window. Data acquisition is done through a 16-bit AD card by collection of 300 samples over 10 seconds at 30 Hz. Digital output from the encoder is converted to velocity prior to being recorded by the PC AD card and/or digital recorder (DAT). Data reduction is similar as for DTMB. IIHR utilizes an 8000-window, optical encoder carriage speed measurement system that is calibrated periodically at IIHR to determine its voltage-frequency relationship. Linear resolution is 0.15 mm/window. Data acquisition is done through collection of 2000 samples over 10 seconds at 200 Hz. Pulses undergo two conversions (DA and AD) before entering the PC. The data-reduction processes are similar as for DTMB and INSEAN. For the resistance and sinkage and trim tests, the models are free to heave, pitch, and roll but restrained in surge, sway, and yaw. For all other tests, the models are restrained from heave, pitch, roll, surge, sway, and yaw but fixed at their dynamic sinkage and trim (Table 1). Resistance. Resistance CT15C is measured with loadcell-based measurement systems and PC data acquisition. The towing force in (kg) is converted to Newtons (N) by multiplication with g (gA=9.8009 m/s2; gB=9.8033 m/s2; gC=9.8031 m/s2) based on the local latitude (Halliday and Resnick, 1981). Towing tank water temperature is measured daily at the model mid draft using a digital thermometer from which density ρ and kinematic viscosity ν are linearly interpolated using fresh water values as recommended by ITTC Quality Manual Procedure 4.9–03–01–03 Density and Viscosity of Water. The form factor k=0.15 is calculated using Prohaska's method, as recommended by ITTC Quality Manual Procedure 4.9–03–03–01.2 1978 ITTC Performance Prediction Method. Data-reduction processes are the same as for the the authoritative version for attribution. carriage-speed tests. DTMB uses a variable reluctance, in-house manufactured loadcell, signal conditioner, and 16-bit AD card with carriage PC for the resistance tests. The loadcell, signal conditioner, and carriage PC AD card are statically calibrated on a DTMB test stand to determine the voltage-mass relationship. Data acquisition is done through collection of 2000 discrete samples over 5 seconds at 400 Hz. Data is filtered

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 406 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 through a 10 Hz low-pass filter. INSEAN uses a Hottinger Baldwin Messtechnik model U1, 50 kg loadcell, signal conditioner, and 16-bit AD card with PC for the resistance tests. The loadcell, signal conditioner, and carriage PC AD card are statically calibrated on a Kempf and Remmers precision test stand to determine the voltage-mass relationship. Data acquisition is done through collection of 300 discrete samples over 10 seconds at 30 Hz. Amplified analog voltages are converted to frequency (3000±2500Hz) for transmission to the AD card to reduce signal sensitivity to noise. Data is filtered through a 10 Hz low-pass filter. IIHR uses a Nisshio strain-gage type 20 kg loadcell, signal conditioner, and 12- bit AD card with PC for the resistance tests. The loadcell, signal conditioner, and carriage PC AD card are statically calibrated on an IIHR test stand to determine the voltage-mass relationship. Data acquisition is done through collection of 2000 discrete samples over 10 seconds at 200 Hz. Data is filtered through a 3 Hz low-pass filter. Sinkage and trim. Sinkage σ and trim τ are measured with potentiometer-based measurement systems and PC data acquisition. The potentiometers sense displacements of the model at the FP and AP which are converted to σ and τ with equations (2) and (3). Data-reduction processes are the same as for the resistance tests. DTMB employs linear potentiometers, signal conditioners, and a 16-bit AD card with PC for the sinkage and trim tests. The potentiometers, signal conditioners, and carriage PC AD card are statically calibrated on a DTMB test stand to determine the voltage- displacement relationship. Data acquisition is done through collection of 500 discrete samples over 5 seconds at 100 Hz. Data is filtered through a 10 Hz low-pass filter. INSEAN employs rotative potentiometers, signal conditioners, and a 16- bit AD card with PC for the sinkage and trim tests. Displacement measurements are made by conversion of vertical to angular displacements through weight-balanced, mechanical parallelograms. The potentiometers, signal conditioners, and carriage PC AD card are statically calibrated on an INSEAN test stand to determine the voltage-displacement relationship. Data acquisition is done through collection of 300 discrete samples over 10 seconds at 30 Hz. Data is filtered through a 10 Hz low-pass filter. IIHR employs linear potentiometers and a 12-bit AD card with PC for the sinkage and trim tests. The potentiometers and carriage PC AD card are statically calibrated on an IIHR test stand to determine the voltage-displacement relationship. Data acquisition is done through collection of 2000 discrete samples over 10 seconds at 200 Hz. Data is not filtered. Wave profile. Wave profiles ζ are measured with different measurement systems and normalized with model length L. DTMB utilizes a waterproof pencil and hull-based grid system for the wave profile tests. Wave profiles are marked on the model as it is towed through the basin. Vernier calipers are used to quantify the wave profile heights referenced to the full-load water line. INSEAN utilizes a photographic and digitizing measurement system with a hull-based grid system for the wave profile tests. Data acquisition is done by photographing the wave profile in sections (20% L) and digitizing the negatives with a high-resolution scanner. Wave heights are quantified at x-stations on the model with CAD software. IIHR utilizes adhesive markers, flexible ruler, level table, height gauge, and hull-based grid system for the wave profile tests. Data acquisition is done by fixing the adhesive markers at the top of the wave profile at each x-station. The model is removed from the tank and a flexible ruler is used to measure the wave profile distance along the girth of the model from the calm waterline. The above two steps are repeated three times. The model is inverted and mounted on a level table and the average wave height values are remarked along the girth of the model from the calm waterline. The height gauge is used to measure the wave height z. Far-field wave elevations. Far-field wave elevations ζFF are measured with either capacitance- or servo/acoustic- based measurement systems or PC data acquisition. A longitudinal-cut method is used to acquire the far-field data. Data- reduction is completed by conversion of longitudinal-cut time histories to a ship coordinate system and then normalizing elevations with model length. DTMB uses capacitance-wire probes suspended from an automated 2D traversing system, a 16-bit AD card, and shore-based PC for the far-field wave elevations tests. The probes and traversing system are cantilevered from the tank sidewall on a boom. The capacitance wires, 2D traversing system, and shore-based PC AD card are statically calibrated to determine their voltage-elevation relationships. Data acquisition is done through collection of 2000 and 3000 discrete samples over 20 and 30 seconds at 100 Hz for Fr=0.28 and 0.41, respectively. Data is filtered at 10 Hz. Data was collected at two longitudinal positions: y=0.097 and 0.324. INSEAN uses an array of four capacitance- wire probes, moveable slide, 12-bit AD card, and shore-based PC for the far-field wave elevation tests. The probes and traversing system are cantilevered from the tank sidewall on a boom. The capacitance wires, move able slide, and shore- based PC AD card are statically calibrated to determine their voltage-elevation relationships. Data acquisition is done through the authoritative version for attribution.

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 407 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 collection of 552 discrete samples over 12 seconds at 92 Hz. Data is filtered at 20 Hz. Data is collected at a total of 136 longitudinal cuts that are spaced at ∆y=0.0026 between the maximum beam of the model and y=0.433. IIHR uses a Kenek servo-type wave probe and signal conditioner, a Keyence acoustic-type wave probe and signal conditioner, 2D traversing system, 12-bit AD card, and shore-based PC for the far-field wave elevation tests. The probes and traversing system are cantilevered from the tank sidewall on a 1.0 m boom. The servo and acoustic probes, signal conditioners, 2D traversing system, and shore-based PC AD card are statically calibrated to determine their voltage-elevation relationships. Data acquisition is done through collection of 2700 discrete samples over 13.3 seconds at 202.5 Hz. Data is not filtered. Data is collected at a total of 32 longitudinal cuts that are spaced at ∆y=0.01 between the maximum beam of the model and the sidewall wave dampeners (y=0.392). Near-field wave elevations. Near-field wave elevations ζNF are measured with servo-based measurement systems and PC data acquisition at DTMB and IIHR. A transverse-cut method is used to acquire the data at the bow, stern, and wake regions which are inaccessible with the longitudinal-cut method. Data-reduction processes are similar as for the carriage speed tests. DTMB employs four DTMB whisker probes, signal conditioners, 2D traversing system, 16-bit AD card and carriage PC for the near-field wave elevation tests. The whisker probes, signal conditioners, and carriage PC AD card are statically calibrated on the traverse system to determine its voltage-elevation relationships. Data acquisition is done at 100 Hz and the data is filtered at 10 Hz. Data is collected at a total of 20 transverse cuts that are spaced at ∆x=0.0088 in bow and stern regions. Data is collected with a continuous traversing method in the y (transverse) coordinate with ∆y~0.0009. IIHR employs a Kenek servo wave probe, signal conditioner, 2D traversing system, 12-bit AD card and carriage PC for the near-field wave elevation tests. The servo probe, signal conditioner, and carriage PC AD card are statically calibrated on the traverse system to determine its voltage-elevation relationship. Data acquisition is done through collection of 4096 discrete samples over 9 seconds at 455 Hz. Data is not filtered. Data is collected at a total of 46 transverse cuts that are spaced at ∆x=0.05 in bow and stern/wake regions. Data is acquired with a point-to-point method with ∆y=0.005 between measured points. Nominal wake. Nominal wake data (U, V, W, Cp; x=0.935) are measured with multihole probe/differential pressure transducer-based measurement systems and PC data acquisition. DTMB utilizes a five-hole (3.2 mm tip), boundary layer pitot probe, pitot-static probe, five differential pressure transducers and signal conditioners, 16-bit AD card, and carriage PC for the nominal wake tests. The five-hole probe is calibrated before acquisition of the nominal wake data. Pitot tube calibration pressure coefficient matrices are determined from the calibration measurements, performed on a calibration rig towed in calm water with no ship model present. The calibration is expressed in coefficient form as: pitch angle (Cp pitch) versus yaw angles (Cp yaw), and axial velocity (Cp vel) versus yaw angle. Data acquisition for these experiments was done in a rectangular coordinate frame through collection of 500 samples over 5 seconds at 100 Hz. Data is collected at 358 points on 18 horizontal cuts with variable spacing in y and z. Data reduction is done with the calm-water calibration matrices. INSEAN utilizes a port-side, five-hole, boundary layer pitot probe (3.2 mm tip), pitot-static probe, five differential pressure transducers and signal conditioners, 16-bit AD card, and carriage PC for the nominal wake tests. Three calibrations are used for the nominal wake tests: (1) five-hole pitot probe is calibrated in the IIHR 1.07-m open throat wind tunnel. (2) differential pressure transducers and signal conditioners are statically calibrated with water head to establish the voltage-pressure relationships; and (3) calibration is made for the five-hole pitot probe preset angles by taking initial data at each x-station with the probe located at sufficient (y, z) that uniform-flow conditions prevail. Data acquisition is done through collection of 2000 samples over 2 seconds at 1000 Hz. Data is collected at a total of 32 horizontal cuts that are spaced ∆z=0.0025. Transverse spacing of data is ∆y=0.0025. Data reduction is done in five steps: (1) AD card output is statistically analyzed; (2) the average value is converted to mm H2O using the voltage-pressure calibration with linear interpolation; (3) velocity vector angles and probe calibration coefficients (M, P) are obtained with local linear interpolation; (4) correction for five-hole pitot probe preset angle from calibration for and (5) U, V, W, and Cp are calculated. Density is calculated as described for the resistance test. IIHR utilizes the same equipment and procedures as INSEAN except: (1) IIHR uses a proportionately smaller five-hole pitot probe which has the same size probe tip; (2) IIHR measures starboard-side nominal wake data; and (3) IIHR collects 1500 samples over 12 seconds at 125 Hz with a 12-bit AD card. UNCERTAINTY ASSESSMENT All three institutes followed ITTC Quality Manual Procedures 4.9–03–01–01 Uncertainty Analysis the authoritative version for attribution.

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 408 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 in EFD, Uncertainty Analysis Methodology; 4.9–03–01–02 Uncertainty Analysis in EFD, Guideline for Towing Tank Tests; and 4.9–03–01–01 Uncertainty Analysis, Example for Resistance Test. The Example for Resistance Test is based on results from most members of the 22nd ITTC Resistance Committee, including the present results from INSEAN and IIHR. Bias limits are estimated with consideration to significant elemental error sources for individual variables, whereas precision limits are estimated end-to-end for experimental results based on multiple tests at the same conditions. Total uncertainties are estimated with a root-sum-square (RSS) and normalization with the range of the result. Table 2 summarizes the uncertainty assessment results for the overlapping tests. Model geometry. Precision limits are not considered in the analyses, thus, all of US is from the bias limit. For DTMB and INSEAN, 100% of the bias limit is associated with the errors in the model geometry offsets (x, y, z) which are averaged over 25 x-stations with templates. For IIHR, inaccuracies in loading the model to the correct draft account for 78% of US, and the remaining 22% are associated with the errors in the model geometry offsets which are averaged over 31 x-stations with templates. The error in the geometry offsets is small (Bx, y, z=0.8 mm), but US is relatively high because the model is comparatively small, having 3.5-times less wetted surface area than 5415 and 2340A. Carriage speed. Uncertainty in Uc at DTMB is very small (0.03%) for low and medium Fr. Bias errors stemming from measurement of D and n are major contributors to the bias limit. Precision limits contribute moderately and increase with increasing Fr. Uncertainty in Uc at INSEAN is one order of magnitude larger than at DTMB and decreases with increasing Fr. As per DTMB, measurement uncertainty in D and n are significant and account for most of the bias limits. Precision limits are relatively low and not Fr-dependent which suggests that the drive motor for INSEAN towing tank no. 2 is stable at all speeds in the test matrix. Uncertainty in Uc at IIHR is somewhat higher than at INSEAN due to the lower range of speeds for the smaller model. UUc also decreases with increasing Fr as per INSEAN. For all Fr, bias limits dominate (82–94%) UUc and decrease with increasing Fr. Measurement of n occurs twice in the data stream and accounts for 95–100% of the bias limits. Contributions from measurement of D are 0.2–3.5% and errors in the AD timebase are negligible as per DTMB and INSEAN. PUc increases with increasing Fr indicate reduced ability of the drive motor to maintain constant Uc for increasing speeds, i.e., for increasing load on the motor. at DTMB is of same order as values presented by 22nd ITTC Resistance Resistance. Uncertainty in Committee, 4.9–03–01–01 Uncertainty Analysis, Example for Resistance Test. Uncertainty in the loadcell calibration weight standard produces high and moderate contributions of bias limit to total uncertainty for Fr=0.10 and 0.28, respectively. Precision limit contributions are relatively high which is possibly due to residual tank motions between runs. Uncertainty in at INSEAN is moderately higher than at DTMB and decreases with increasing Fr. Biases in the measurement of Fx contribute 70%–10% of BCT15 for increasing Fr and are attributed to the standardized calibration weights and scatter in the calibration data. Other significant factors in BCT15 are US which contributes 10%–65% for increasing Fr and UUc which contributes 5%–15% for increasing Fr. The uncertainties in the water temperature measurement are negligible for all Fr as per DTMB and IIHR. Precision limit contributions are relatively high as per DTMB which also may be possibly due to residual tank motions between runs. Uncertainty in at IIHR is roughly similar as for INSEAN except for low Fr where IIHR is 46% lower than INSEAN. The bulk of UCT15 is bias related with UUc and US contributing 62%–29% to BCT15 for increasing Fr and 9%–71% to BCT15 for increasing Fr, respectively. Effects of scatter in loadcell calibration data account for 100% of BFx. Precision limit contributions are relatively low for all Fr which may be due to less residual tank motions between runs as compared with DTMB and INSEAN. Sinkage and trim. Uncertainty in σ and τ at DTMB is somewhat large for Fr=0.10 but decreases significantly with increasing Fr as the range of the measurements increase, i.e., the potentiometers operate further from their limiting resolution for higher Fr. Bias limit contributions for both variables are mainly affected by the scatter in the potentiometer calibrations and decrease with increasing Fr. Conversely, precision limit contributions increase with increasing Fr which may indicate elevated carriage vibration for higher Fr and or residual tank motions. Uncertainty in σ and τ at INSEAN is large for Fr=0.10 but decreases significantly to values comparable with DTMB with increasing Fr. Bias limits are negligible for both variables and all Fr due to dominance of precision limits whose elevated values are attributed to residual tank motions between carriage runs. Uncertainty in σ and τ at IIHR is somewhat large for Fr=0.10 but decreases significantly with increasing Fr as per DTMB and INSEAN. Bias limit contributions for σ are high to moderate for Fr=0.10 and Fr=0.28/0.41, respectively, with no Fr-dependence. Bias limit contributions for τ are high at Fr=0.10 and decrease with increasing Fr as the authoritative version for attribution.

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 409 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 per DTMB. Bias limit magnitudes originate from scatter in the calibration data. Precision limit contributions are mostly high for both variables and all Fr and caused by residual tank motions and heave/pitch oscillations at the model mount as the model seeks its hydrodynamic equilibrium. This ‘porpoising' of the model is likely present at all facilities. Wave profile. Uncertainty in ζ is less than 5% for all facilities and both Fr and decreases with increasing Fr. For DTMB and both Fr, bias limits account for 64.5% of Uζ and are composed of error estimates for marking the wave profile at the exact air-water interface (85%) and measuring the distance from draftline to measurement with a vernier caliper (15%). Precision limits account for 35.5% of Uζ and are based on three measurements of the wave profiles and estimates of the contact-line unsteadiness. For INSEAN precision limits are not considered in the analysis. Contributions to the bias limits are associated with the uncertainties in the hull-gridline thickness (40%), optical distortion for the camera (50%), scanner resolution (5%), and interpolation error (5%). For IIHR and both Fr, bias and precision limit contributions to Uζ are roughly 80% and 20%, respectively. Contributions to the bias limits are associated with uncertainties in the adhesive marker placement on the hull (50%), placement of the draft and x-station lines on the model (23%), reapplication of the wave profile marks on the hull after the test when the model is removed from the tank (23%), and height-gauge readings from draftline to measurement (4%). Precision limit contributions to Uζ are relatively low and computed for N=3 multiple tests. Far-field wave elevations. Uncertainty in ζFF at DTMB is better than 4% for Fr=0.28 and 0.41. A longitudinal cut at y=0.082 is chosen for detailed assessment of measurement uncertainty. For both Fr, bias limits are main contributor to UζFF and are composed mainly of scatter in the calibration data. Precision limits are estimated from N=9 multiple tests and increase with Fr which may be due to elevated levels of free-surface turbulence with increasing Fr and “snapshot”- like feature of the longitudinal-cut method. Uncertainty in ζFF at INSEAN is 3% or better for Fr=0.28 and 0.41. Longitudinal cuts at y=0.082, 0.172, 0.259, and 0.347 are chosen for detailed analysis of measurement uncertainty. The majority of UζFF is bias-limit related. The uncertainty in Uc accounts for 70% of BζFF with a 10%–15% contribution from the uncertainty in (x, y) probe position in the test region. Uncertainty in the distance measurement D between the wave probes and the FP of the model at t=0 accounts for 5% of BζFF. Uncertainty in the time lag between switch engagement and data acquisition is negligible. Precision limits are estimated with N=10 multiple tests, contribute moderately to UζFF, and decrease with Fr in opposition to those at DTMB. Uncertainty in ζFF at IIHR is better than 3.5% for Fr=0.28. A longitudinal cut at y=0.082 is chosen for detailed analysis of measurement uncertainty. The majority of UζFF is bias-limit related. The uncertainty in carriage speed accounts for 79% of BζFF with 6%–8% contribution from the uncertainty in (x, y) probe positioning in the test region. Uncertainty in the distance measurement D between the wave probes and the FP of the model at t=0 accounts for 6% of BζFF. Uncertainty in the time lag between switch engagement and data acquisition is negligible. Precision limits are estimated with N=10 multiple tests and contribute significantly to UζFF as per DTMB and INSEAN. Near-field wave elevations. For DTMB, low-turbulence LTR and high-turbulence HTR (x, y) regions are identified for detailed analysis. In the HTR, precision limit contributions to UζNF are elevated (85.5%) from large fluctuations in the free surface and air entrainment into the flow. This produces comparatively high uncertainty in the near-field measurements. For the LTR, contributions of bias and precision limits are more balanced and the uncertainty is less than 5%. For this case, the scatter in the whisker probe calibration governs bias limit magnitude. For IIHR, LTR (x, y=0.05, 0.07) and HTR (x, y=1.075, 0) regions are identified in the wavefield for detailed analysis. Bias limits contribute (25– 50%) to UζNF which is mainly (~100%) due to scatter in the servo-probe calibration data. Relatively high PζNF is due to free-surface turbulence at the multiple-test conditions. Note that PζNF is three-times greater in the HTR than the LTR. Nominal wake. For DTMB, LTR (x, y, z=0.9346, 0.04, −0.065) and HTR (x, y, z=0.9346, 0.02, −0.02) regions are identified in the flowfield for detailed assessment of the measurement uncertainty. In both HTR and LTR, bias limit contributions to total uncertainties are dominant for U and Cp but somewhat evenly matched with precision limit contributions for V and W. Uncertainties in the five-hole calibration accounts or 23% of the bias limit with the remaining portion due to probe position uncertainty in the flowfield and pressure stabilization during a carriage run. Precision limits are estimated from N=10 multiple tests and are moderate for V, but 15–35% of the total uncertainty for U, W, and Cp which may be a result of high free-surface turbulence/probe vibration. For INSEAN, LTR (x, y, z=0.9346, 0.06, −0.0602) and HTR (x, y, z=0.9346, −0.0025, −0.0602) regions are identified in the flowfield for detailed assessment of the measurement uncertainty. Bias and precision limit contributions to total uncertainties of all variables are the authoritative version for attribution.

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 410 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 evenly distributed in the LTR and HTR. BU and BCp are influenced mostly by uncertainties in wind tunnel coefficients, M and P, respectively. For crossflow velocities, BV and BW are mainly affected by uncertainties in velocity vector pitch and yaw angles (α, ). Contributions from uncertainties in Uc to all variables are less than 3.5%, and uncertainties in measurement of pressures at the probe tip are negligible, except for the center hole where roughly 12% and 2% contributions to BU and BCp are computed. Precision limits are estimated from N=10 multiple tests and are moderate and high for U and V, respectively, but 10–30% for W and Cp which may be caused as per DTMB. For IIHR, LTR (x, y, z=0.9346, 0.1, −0.01375) and HTR (x, y, z=0.9346, 0, −0.02125) regions are identified in the flowfield for detailed assessment of the measurement uncertainty. Bias limit contributions to total uncertainties of all variables are dominant in the LTR and HTR. In the LTR, BU and BCp are influenced mostly by uncertainties in wind tunnel coefficients, M and P, respectively. BV and BW are mainly affected by uncertainties in velocity vector pitch and yaw angles (α, ). In the HTR, BU, BV, BW, and BCp are mainly influenced by uncertainties in the measurement of water head at the five-hole probe tip since the size of the tip is large with respect to the shear-flow gradients. BV and BW are also still affected significantly by uncertainty in the pitch and yaw angles in the HTR. Precision limits are estimated from N=10 multiple tests and are very small in relation to the bias limits, which maybe due to lack of free-surface turbulence/pitot-probe vibration. CFD VALIDATION/COMPLEMENTARY CFD The conditions and data locations and densities (Table 1) were selected with consideration to use of data for CFD validation. Cruise (Fr=0.28) and flank (Fr=0.41) speeds were selected for detailed validation with most extensive tests for former condition. No specific requirement was placed on experimental uncertainties UD, but rather considered an important quantity to be estimated at each facility with final estimates based on collective results, as discussed below. Additionally, previous experience and complementary CFD was used for determining data densities. COMPARISON OF RESULTS The focus of the discussions is on the comparison between institutes of facilities, model geometry, and overlapping test results for evaluation of facility/model geometry and scale effect biases. Comparisons are made of measurement systems and procedures and data (A, B, C) [equation (7)], data differences Di [equations (8), (10), (12)], data uncertainties U(A, B, C), and data-difference uncertainties [equations (9), (11), (13)]. Data differences for all variables are computed after interpolation of two data sets onto standard dependent variable values and subtraction. Average data differences are expressed as percentages by normalizing the average difference with the average range (all institutes) of the variable. Facilities. Facility locations are different as manifest by latitude, climate, and zone. Yearly average high/low/dew point temperatures are 66.6°/48.8°/44.4°, 68.0°/51.9°/52.8°, and 59.8°/39.7°/39.5°, respectively, at A, B, C. A and B have similar mild yearly climates, whereas C experiences harsher climate, especially during the fall and winter months. Zones for A and B are on outskirts of large cities, whereas C is in the center of a small city. Such differences in ambient conditions are partially accounted for by using values of g and density and viscosity based on local values of latitude and water temperature, respectively. Water quality is also different at each facility. A and C use local tap water and B uses local spring water; however, no account is made for water quality since as already mentioned all institutes base values of density and viscosity on water temperature only and fresh water values from standard tables. The tanks at each facility have different dimensions with the largest to smallest being A, B, and C, respectively, which affects both blockage and residual tank water motions between carriage runs. The blockage values (ratio of beam/ draft product and tank cross-sectional area) at A, B, and C are 0.0017, 0.0042, and 0.0055, respectively, which are all nearly at or below the recommended maximum value of 0.005. It is also recommended that model length should not be greater than tank depth or more than half-as-long as tank width. Thus only A satisfies all three requirements and B and C each violate one. Effects of blockage are partially accounted for through correction to carriage speed. Tank size and side and end wall wave damping affect residual tank water motions (free and sub surface) and required time intervals between carriage runs. A and B require 20 minutes between carriage runs and C 12 minutes all based on visual observations. In spite of waiting times, low frequency motions are still evident especially in the larger tanks (as mentioned above with regard to large precision limits for sinkage and trim measurements). Carriage speed affects all results, although not always included directly in data-reduction equations. Although each institute measures carriage speed with similar instrumentation (encoders and pulse counters), they have different resolutions. A has the lowest angular resolution in their magnetic encoder (520 the authoritative version for attribution.

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 411 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 pulses/rev) but the lowest uncertainty, while C has the highest resolution but the highest uncertainty. The uncertainty differences are due to the procedures for transferring pulse count into the data-acquisition PC (frequency for A and two AD conversions for C) and the speed range for the uncertainty assessment. Since A and B operate at nearly twice the carriage speed for a given Fr, and speed range is the normalizing factor for determination of UUc, A and B have less uncertainty in measured Uc. UUc can be further reduced through implementation of a closed-loop feedback system that constantly assesses and updates Uc with respect to a desired value. Currently, B is adopting this capability, however, none of the facilities had this capability during the overlapping tests. Carriage ride affects results through carriage vibration; however, such effects were not considered. Model geometry. Model geometry offsets, bow details (leading-edge radius), turbulence stimulation, surface roughness, and installation also surely affect all results, although, here again, not always directly through data-reduction equations. For each institute, US is estimated to be 0.5% which is near the level of US reported by the participating members of the 22nd ITTC uncertainty assessment example for resistance test. The method for determination of the uncertainties in the offsets is crude as templates are used at a limited number of stations and error estimation is tedious, involving moderate and low accuracy at low- and high-points on the hull surface, respectively. Accounting for twisting or sagging of a model in the estimation of the offset errors is a very difficult, if not impossible task with templates. Also complicating the issue is changes to the model offsets over time with changes in ambient temperature and humidity or by long-term water-immersion. Leading-edge radius on each model is 3.2 mm for A and B and 1.6 mm for C. Turbulence stimulation is different at each facility in terms of tripping location, however, results in suggest that the turbulence stimulation was effective for all three models. Model surfaces were finished using usual procedures at each facility and assumed hydraulically smooth. All models were installed according to draft line, which is presumed the best method for CFD validation purposes. However, it was noted by 22nd ITTC uncertainty assessment example for resistance test that installation according to ballast weight reduces uncertainty in surface area by partially accounting for inaccuracy of design offsets. Tow points are also different for each model, but have not yet been compared. Resistance. For resistance tests, measurement systems, procedures, and data uncertainty estimates (Table 2) are similar for all three institutes. Figure 2 displays the results. Figure 2a compares the resistance data and Figures 2b, c, d compare the data difference and data-difference uncertainties between institutes AB, AC, and BC, respectively. Trends in Figure 2a for all three institutes are typical for high-speed combatant, i.e., limited humps and hollows for low and medium Fr and sharply increasing resistance for high Fr. For low and medium Fr results for A, B, and C are very consistent with C usually between A and B, whereas for high Fr C is consistently lower than A and B. Fig. 2: Resistance results and data differences. For AB (Figure 2b), data differences are oscillatory with Fr and intermittently greater/less than or within data- difference uncertainty, which suggests the authoritative version for attribution.

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 412 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 unaccounted for bias and precision limits. Average data difference is 2.2%, whereas average data-difference uncertainty is only 1.5%. Fig. 4: Trim results and data differences. Fig. 3: Sinkage results and data differences. For AC (Figure 2c) and low and medium Fr, trends are similar (i.e., data differences are oscillatory and intermittently greater/less than or within data-difference uncertainty), whereas for high Fr the trend is evident that data difference increases nearly linearly and is much greater than data-difference uncertainty. Average data difference and data- difference uncertainty are 3.4% and 1.1%, respectively. Former is considerably larger than for AB and latter is somewhat smaller. Clearly the differences for AC compared to AB for larger Fr are due to scale effects. Trends for BC (Figure 2d) are very similar as for AC with average data differences and data-difference uncertainties of 3.9% and 1.6%, respectively. Results are important in showing that for same size model (5.72 m) a better estimate for uncertainty in resistance test is 2.2%, which is considerably larger than individual facility estimates, especially for medium and high Fr. Results also show that scale the authoritative version for attribution.

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 413 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 effects for 3 m model are significant for Fr>0.26, which is likely due to differences in wave breaking as will be discussed later with regard to wave elevation measurements. For resistance, average facility/model geometry and scale effect (Fr>0.26) biases are estimated as 0.5% and 5.8%, respectively, as summarized in Table 3. Note that averages are based on all three facilities and Fr ranges as given in Table 3, and that facility and model geometry biases are combined as they cannot be separated without use of a standard model. Table 3: Summary of facility/model geometry and scale effect biases. Fac./model geometry (UF/MG) Scale (USE) Result AB AC BC AC BC CR 0.7% 0.9%† 0%† 4.9%? 6.7%? σ 0% 0% 0% 0% 0% τ 0% 0%‡ 0%‡ 11.6%? 12.7%? ζ0.28 1.0% 0% 0% 0% 0% ζ0.41 2.6% 1.9% 0% 0% 0% ζFF 2.9% 1.1% 0% 0% 0% U 0% 0% 0% 0% 0% V 0.2% 0% 2.3% 0% 0% W 13.0% 0% 11.7% 0% 0% †: Fr0.26; ? : Fr>0.33 Sinkage and trim. For sinkage and trim tests, measurement systems and procedures are similar for all three institutes. However, data uncertainties are fairly large and show some differences (Table 2). Uncertainties for B at low Fr are very large. Figures 3 and 4 display the results. Figures 3a and 4a compare the sinkage and trim data and Figures 3b, c, d and 4b, c, d compares the data difference and data-difference uncertainties between institutes AB, AC, and BC, respectively. Trends in Figures 3a and 4a for all three institutes are also typical for high-speed combatant, i.e., increasing sinkage and bow down than up trim for increasing Fr. In general, results between institutes are consistent, however, for trim and high Fr, C is consistently lower than A and B. For AB (Figures 3b and 4b), data differences are oscillatory and mostly within the data-difference uncertainties. Average data differences are 4% and 2.5%, whereas average data-difference uncertainties are 14.1% and 18.3%, respectively, for sinkage and trim. In this case, data differences are fairly small but with large data-difference uncertainties. For AC (Figures 3c and 4c), trend for sinkage is similar as AB although percentage values are lower, whereas trend for trim is different for high Fr wherein as with resistance test data difference increases nearly linearly and is much greater than data-difference uncertainty. Average data difference and data-difference uncertainty are 5.5% and 7.8%, respectively. Former is larger than for AB and latter is smaller. Clearly for trim test, as with resistance test, the differences for AC compared to AB for larger Fr are due to scale effects. Trends for BC (Figures 3d and 4d) are very similar as for AC with average data differences and data-difference uncertainties of 2.6% and 16.9% and 5.5% and 13.5%, respectively, for sinkage and trim. Fig. 5: Wave profile results and data differences (Fr=0.28). Results are important in showing that for same size model (5.72 m) data differences are fairly small (i.e., similar the authoritative version for attribution. level as resistance test) and for low Fr considerably less than data-difference uncertainties. All institutes (especially B) need to reduce uncertainties for low Fr. Results also show that scale effects for 3 m model are significant for trim and Fr>0.33. Facility/model geometry biases are not evident for both sinkage and trim. Scale effect biases are not evident for sinkage and estimated as 12.2% for trim (Table 3).

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 414 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 Wave profile. For wave profile tests, measurement systems and test procedures are very different between institutes. However, data uncertainties have similar values (Table 2). Figures 5 and 6 display the results. Figures 5a and 6a compare the wave profile data for Fr=0.28 and 0.41 and Figures 5b, c, d and 6b, c, d compare the data difference and data- difference uncertainties between institutes AB, AC, and BC, respectively. Trends in Figures 5a and 6a for all three institutes are also typical for high-speed combatant for medium and high Fr, i.e., display bow, shoulder and stern waves and increasing transverse wavelength with increasing Fr. Fig. 6: Wave profile results and data differences (Fr=0.41). Results between institutes are fairly consistent, although A seems to show consistently smaller values especially for shoulder and stern waves. For AB (Figures 5b and 6b), data differences are oscillatory and mostly less than data-difference uncertainties. Average data differences are 6.4% and 5.7%, whereas average data-difference uncertainties are 5.4% and 3.1%, respectively for Fr=0.28 and 0.41. Results for AC (Figures 5c and 6c) and BC (Figures 5d and 6d) are fairly similar; however, in these cases data differences are mostly within data-difference uncertainties. Fig. 7: Far-field wave elevation results at Fr=0.28: (a) Fig. 8: Far-field wave elevation differences at Fr=0.28: DTMB 5415; (b) INSEAN 2340A; (c) IIHR 5512. (a) DTMB-INSEAN; (b) DTMB-IIHR; (c) INSEAN- IIHR. Results are important in showing that a better estimate for uncertainty in wave profile test is about 5–6%, which is larger than individual facility estimates, especially for high Fr. Results also show that scale effects for the 3 m model are insignificant. Average facility/model geometry and scale effect biases are estimated as 0.9% and not evident, respectively (Table 3). the authoritative version for attribution.

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 415 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 Wave elevations. For wave elevation tests, measurement systems and test procedures are different between institutes. However, data uncertainties have similar values (Table 2). Figures 7–10 display the results for the far field tests for Fr=0.28. Comparisons for the near field tests are not included. Figure 7 and 8 compare the wave pattern data and data differences, respectively. Figures 9 and 10 compare the data and data differences for two cuts y=0.324 and 0.082, respectively. Figures 8a, b, c and 9b, c, d are for AB, AC, and BC, respectively. Figure 10b is for BC. Trends in wave patterns for all three institutes are typical for high-speed combatant, i.e., show diverging and transverse wave systems originating from bow, shoulder, and stern. Overall patterns for all three institutes are very similar, although resolution for A appears less than that for B and C. Figure 9a shows fairly large differences between A, B, and C at this distance from the hull, whereas Figure 10a shows small differences between B and C close to the hull. Fig. 9: Far-field wave cut data and differences at y=0.324, Fr=0.28: (a) interpolated wave cuts; (b) DTMB-INSEAN; (c) DTMB-IIHR; (d) INSEAN-IIHR. Data differences (Figure 8) are largest for the diverging waves at crests and troughs. For AB, AC, and BC average data differences are 6.5%, 5.5%, and 2.5%, respectively, whereas average data-difference uncertainties for AB, AC, and BC are about 4%. Detailed comparisons at y=0.324 show that data differences are oscillatory and average data differences of about 4–5% and data-difference uncertainties of about 4% for AB, AC, and BC. Here again, largest differences are at crests and troughs. Trends are similar at y=0.082, except average data difference is only 0.6% and data-difference uncertainty is 2.8%. In this case uncertainty estimates include dependency on x. Fig. 10: Far-field wave cut data and differences at y=0.082, Fr=0.28: (a) data; (b) INSEAN-IIHR. Fig. 11: Nominal wake results at Fr=0.28. Results are important in showing that wave elevation differences are fairly small and close to the the authoritative version for attribution.

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 416 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 uncertainty estimates. Also, scale effects are not evident. However, visual observation of wave patterns especially for higher Fr shows differences in wave breaking, i.e., wave breaking is considerably reduced for the 3 m model in comparison to the 5.7 m models presumably due to differences in Weber number and also some differences between wave breaking patterns for larger models presumably due to water quality differences between facilities A and B. Average facility/model geometry and scale effect biases are estimated as 1.3% and not evident, respectively (Table 3). Fig. 12: Nominal wake data differences at Fr=0.28. Nominal wake. For the nominal wake tests, measurement systems and test procedures are similar between facilities. However, data uncertainties are fairly large and show some differences (Table 2). Figures 11 and 12 display the results for the mean velocity components (U, V, W) data and data differences, respectively, for Fr=0.28. Trends for nominal wake for all three institutes are typical for high-speed combatant, i.e., relatively thin boundary layer near keel and free surface and thick boundary layer near mid girth due to effects of sonar dome vortex. V and W show influences of sonar some vortex and upward/inward stern flow. Flow patterns for all three institutes are similar, although differences in resolution are apparent. For C, scale effects are not obvious. For AB, data differences are less than data difference uncertainties for U, whereas they are larger for V and W. However, data-difference uncertainties (and data differences, except U) are fairly large. Interestingly, results for AC and BC are similar, i.e., scale effects are mostly lost in noise, although pattern for data differences for both AC and BC are nearly same, which may be an indication of scale effects. Results are important in showing that the data differences and data uncertainty are reasonable close albeit with fairly large values. All institutes need to reduce uncertainties. Average facility/model geometry and scale effect biases are estimated for (U, V, W) as (0%, 0.8%, 8.2%) and 0%, respectively (Table 3). Fig. 14: INSEAN 2340A flow mapping at Fr=0.28. Fig. 13: DTMB 5415 axial velocity (U) contours and crossflow vectors for the w/propeller condition: Fr=0.28, x=0.9603, 436 rpm. the authoritative version for attribution. HIGHLIGHTS OF OVERALL TEST PROGRAM Although the emphasis herein has been on the overlapping tests, the collaborative effort also consists of focus studies at each institute. These studies were

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 417 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 designed to address a variety of important physics and expand the surface-ship database with quality datasets and uncertainty assessment. At A, model 5415 was used in a series of propeller-hull interaction tests. Shafts and struts were added to the model and data was obtained with and without the propellers operating. The measurements include free surface topographies of the transom wave field, longitudinal wave cuts (Ratcliffe, 2000), and velocity measurements in the nominal wake plane and both upstream and downstream of the operating propulsors. The velocity measurements were obtained with three-component laser-doppler velocimetry (LDV). Fig. 13 is a sample of results for the latter. At B, model 2340A was used for a comprehensive flow mapping of the boundary layer and wake flow at eleven cross planes with multi-hole probes and pressure transducers. The axial velocity results are plotted in Fig. 14. Results from this study as well as the overlapping tests and the near field bow and stern wave elevations from A will be used at the Gothenburg 2000 workshop on CFD in ship hydrodynamics. At C, model 5512 is currently being used for unsteady-flow testing in regular head waves. Measurements include unsteady forces and moment with a load cell, far-and near-field wave elevations (Fig. 15) with servo and acoustic probes, and mean and turbulent flow field with a towed particle-image velocimetry (PIV) system. The latter measurements are ongoing and will be archived with the rest of the unsteady data at http://www.iihr.uiowa.edu/-towtank. Figures 11 and 12 also include comparisons of nominal wake data for 5512 and pitot and PIV measurement systems. Data differences are similar to data-difference uncertainties. CONCLUSIONS Results are presented from overlapping towing tank tests between three institutes for resistance, sinkage and trim, wave profiles and elevations, and nominal wake using the same model geometry and conditions, including rigorous application of standard uncertainty assessment procedures as per the 1999 ITTC Quality Manual. Two of the institutes used 5.7 m models whereas the third institute used a smaller 3 m model. Comparison variables were defined for data- reduction equations and data differences and data-difference uncertainties. Detailed descriptions were provided of facilities, measurement systems, data-acquisition and reduction procedures, and uncertainty assessment. Results were discussed with regard to levels and causes of data differences and data-difference uncertainties and to estimate facility/ model geometry and scale effect biases. For same size 5.7 m models, data differences were in general oscillatory, and in many cases, larger in magnitude than data-difference uncertainties, which indicates unaccounted for bias and precision limits and that current individual facility uncertainty estimates are often too optimistic. Scale effects for the 3 m model are only evident for resistance and trim tests for Fr>0.26 and Fr>0.33, respectively. Facility/model geometry and scale effect bias are estimated based on comparisons, as summarized in Table 3. Uncertainty estimates including such biases may provide better estimates, especially for use in CFD validation, which is the recommendation of the present study along with efforts towards improvement of individual institute uncertainty estimates. Use of standard models and current ITTC efforts in providing standard quality manual procedures for towing tank tests and uncertainty estimates will also be helpful in this regard. Fig. 15: IIHR 5512 unsteady wave field at four instances in the encounter period: Fr=0.28, Ak=0.025, λ=4.572 m. ACKNOWLEDGEMENTS The research at IIHR and a portion of the research at INSEAN and at UAH were sponsored by the Office of Naval Research under Grants N00014–98–1–0156 and N00014–97–1–0014, respectively, under the administration of Dr. the authoritative version for attribution. E.P.Rood. The research at

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 418 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 DTMB was sponsored by the Office of Naval Research with 6.2 Funding, administered by Dr. E.P.Rood. The research at INSEAN was also sponsored by the Italian Ministry of Transportation and Navigation in the frame of Research Plan 1997–1999. REFERENCES Avanzini, G., Bennedetti, and Penna, R., 1998, “Experimental Evaluation of Ship Resistance for RANS Code Validation,” ISOPE '98, Montreal, Canada, May. Avanzini, G., Benedetti, and Penna, R., 2000, “Experimental Evaluation of Ship Resistance for RANS Code Validation,” Journal of Offshore and Polar Engineering, Vol. 10, No. 1, March 2000 (pp. 10–18). G2K, 2000, http://www.iihr.uiowa.edu/gothenburg2000 Gui, L., Longo, J., and Stern, F., 1999, “Towing Tank PIV Measurement System and Data and Uncertainty Assessment for DTMB Model 5512,” 3rd International Workshop on PIV, Santa Barbara, CA, 16–18 September. Haliday, D. and Resnick, R., 1981, “Fundamentals of Physics”, John Wiley and Sons, New York, 816 pp. ITTC, 1999, “Report of the Resistance Committee,” Proceedings International Towing Tank Conference, Seoul, Korea & Shanghai, China, 5–11 September. Lee, J., Lee, S.J., and Van, S.H., 1998, “Wind Tunnel Test on a Double Deck Shaped Ship Model,” 3rd International Conference on Hydrodynamics, Seoul, Korea. Longo, L., Gui., L., Metcalf, B., and Stern, F., 2000, “Naval Surface Combatant in Regular Head Waves,” abstract submitted 23rd ONR Symposium on Naval Hydrodynamics, Val de Reuil, France, 17–22 September. Longo, J. and Stern, F., 1998, “Resistance, Sinkage and Trim, Wave Profile, and Nominal Wake and Uncertainty Assessment for DTMB Model 5512,” Proc. 25th ATTC, Iowa City, IA, 24–25 September. Olivieri, A. and Penna, R., 1999, “Uncertainty Assessment in Wave Elevation Measurements,” ISOPE '99, Brest, France, June. Olivieri, A. and Penna, R., 2000, “Detailed measurements of wave-pattern and nominal wake of a fast displacement ship model”, AFM Conference, Montreal, May 2000. Principles of Naval Architecture, 1967, The Society of Naval Architects and Marine Engineers, New York, N.Y., 827 pp. Ratcliffe, T., 1995, http://www50.dt.navy.mil/5415/ Ratcliffe, T., 2000, “An Experimental and Computational Study of the Effects of Propulsion on the Free-Surface Flow Astern of Model 5415,” 23rd ONR Symposium on Naval Hydrodynamics, Val de Reuil, France, 17–22 September. Stern, F., 2000, http://www.iihr.uiowa.edu/~towtank/ Van, S.H., Yim, G.T., Kim, W.J., Kim, D.H., Yoon, H.S., and Eom, J.Y., 1997, “Measurement of Flows Around a 3600TEU Container Ship Model,” Proceedings of the Annual Autumn Meeting, SNAK, Seoul, pp. 300–304 (in Korean). Van, S.H., Kim W.J., Kim, D.H., Yim, G.T., Lee, C.J., and Eom, J.Y., 1998a, “Flow Measurement Around a 300K VLCC Model,” Proceedings of the Annual Spring Meeting, SNAK, Ulsan, pp. 185–188. Van, S.H., Kim, W.J., Yim, G.T., Kim, D.H., and Lee, C.J., 1998b, “Experimental Investigation of the Flow Characteristics Around Practical Hull Forms,” Proceedings 3rd Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form Design, Osaka, Japan. the authoritative version for attribution.

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 419 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 Table 1: Summary of overlapping test conditions for DTMB, INSEAN, and IIHR. EXPERIMENT DTMB (A) INSEAN (B) IIHR (C) MODEL GEOMETRY Templates Templates Templates CARRIAGE SPEED Magnetic encoder Optical encoder Optical encoder RESISTANCE Loadcell Loadcell Loadcell 0.05–0.45 0.05–0.45 Fr 0.05–0.44 0.93–8.41e06 0.21–1.92e07 Re 0.21–1.92e07 25.1 22.1 Tave (°C) 17.8 ρ (kg/m3) 997.0720 997.7200 998.6960 ν (m2/s) 0.8925e–06 0.9547e–06 1.0638e–06 0.0727 0.0732 σ (N/m) 0.0738 ∆Fr=0.01 ∆Fr=0.01 Data density ∆Fr=0.013 free free Model installation ∆FP, ∆AP free - - - SINKAGE/TRIM Linear pots Rotative pots Linear pots Fr 0.05–0.45 0.05–0.45 0.05–0.44 Re 0.86–7.72e–06 0.21–1.92e07 0.21–1.92e07 Tave (°C) 21.5 22.1 17.8 ρ (kg/m3) 997.9400 997.7200 998.6960 ν (m2/s) 0.9708e–06 0.9547e–06 1.0638e–06 0.0733 0.0732 σ (N/m) 0.0738 ∆Fr=0.01 ∆Fr=0.01 Data density ∆Fr=0.013 free free Model installation ∆FP, ∆AP free - - - WAVE PROFILE Wax pencil Photography Adhesive marker Fr 0.28, 0.41 0.28, 0.41 0.28, 0.41 Re 4.47, 6.54e06 1.19, 1.75e07 1.19, 1.75e07 Tave (°C) 18.5 22.1 20.6 ρ (kg/m3) 998.5700 997.7200 998.1560 ν (m2/s) 1.0448e–06 0.9547e–06 0.9907e–06 0.0733 0.0732 0.0735 σ (N/m) 40 pts 41 pts 23pts, 25pts Data density fixed fixed fixed Model installation ∆FP, ∆AP (−0.0031L, −0.00079L), (−0.0027L, −0.00086L), (−0.0027L, −0.00086L), (−0.0015L, −0.0079L) (−0.00054L, −0.0083L) (−0.00054L, −0.0083L) NEAR-FIELD WAVES Whisker probe Servo probe Fr 0.28 0.28, 0.41 Re 3.81e06 1.19, 1.75e07 Tave (°C) 12.5 20.6 ρ (kg/m3) 999.5000 998.1560 ν (m2/s) 1.224e–06 0.9907e–06 0.0745 σ (N/m) 0.0735 46 cuts, ∆x=0.05, ∆y=0.005 Data density 20 cuts, ∆x=0.09L, ∆y=0.0009L fixed Model installation ∆FP, ∆AP fixed (−0.0031L, −0.00079L) (−0.0027L, −0.00086L), (−0.00054L, −0.0083L) FAR-FIELD WAVES Capacitance probes Capacitance probes Servo/acoustic probes Fr 0.28 0.28, 0.41 0.28, 0.41 Re 4.48e06 1.19, 1.75e07 1.19, 1.75e07 Tave (°C) 18.6 13.3 20.6 ρ (kg/m3) 998.5520 999.4000 998.1560 ν (m2/s) 1.0421e–06 1.1923e–06 0.9907e–06 0.0737 0.0743 σ (N/m) 0.0735 32 cuts, ∆x=0.001, ∆y=0.01 136 cuts, ∆x=0.016, ∆y=0.003 Data density 2 cuts at y=0.097L and 0.324L fixed fixed Model installation ∆FP, ∆AP fixed (−0.0031L, −0.00079L) (−0.0027L, −0.00086L), (−0.0027L, −0.00086L), (−0.00054L, −0.0083L) (−0.00054L, −0.0083L) NOMINAL WAKE 5-hole probe 5-hole probe 5-hole probe Fr 0.28, 0.41 0.28 0.28, 0.41 Re 1.19, 1.75e07 1.19e07 3.83, 5.61e–06 Tave (°C) 20.6 11.0 12.7 ρ (kg/m3) 998.1560 999.6800 998.7140 ν (m2/s) 0.9907e–06 1.2692e–06 1.2173e–06 the authoritative version for attribution. 0.0735 0.0744 0.0744 σ (N/m) 18 cuts, 358 points, variable 32 cuts, ∆y=∆z=0.0025 27 cuts, ∆y=∆z=0.0025 Data density fixed fixed fixed Model installation ∆FP, ∆AP (−0.0027L, −0.00086L), (−0.0027L, −0.00086L), (−0.0031L, −0.00079L), (−0.00054L, −0.0083L) (−0.00054L, −0.0083L) (−0.0015L, −0.0079L)

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 420 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 Table 2: Summary of uncertainties for DTMB, INSEAN, and IIHR overlapping tests. DTMB (A) INSEAN (B) IIHR (C) RESULT Fr B P U B P U B P U All Fr 100% 0% 100% 0% 100% 0% S 1.2% 0.5% 0.5% 0.10 78.0% 22.0% 99.1% 0.9% 94.2% 5.8% Uc 0.03% 0.18% 0.66% 0.28 68.2% 31.8% 93.7% 6.3% 85.9% 14.1% Uc 0.03% 0.13% 0.25% 0.41 NA NA NA 99.5% 0.5% 82.3% 17.7% Uc 0.12% 0.18% 0.10 76.3% 23.7% 69.4% 30.6% 87.6% 12.4% CT15/CR 1.49% 2.68% 1.46% 0.28 45.5% 54.5% 80.0% 20.0% 89.2% 10.8% CT15/CR 0.33% 0.64% 0.63% 0.41 NA NA NA 66.3% 33.7% 80.5% 19.5% CT15/CR 0.61% 0.60% σ 0.10 75.6% 24.4% 0% 100% 82.2% 17.8% 12.2% 42% 8.72% σ 0.28 68.4% 32.6% 0% 100% 30.4% 69.6% 5.6% 4.71% 1.40% σ 0.41 56.3% 44.7% 0% 100% 42.8% 57.2% 2.5% 2.93% 0.61% τ 0.10 64.5% 35.5% 0% 100% 50.8% 49.2% 14.4% 32% 10.22% τ 0.28 54.7% 46.3% 0% 100% 36.1% 63.9% 2.8% 4.70% 1.83% τ 0.41 38.1% 61.9% 0% 100% 4.1% 95.9% 1.5% 0.87% 1.76% ζ 0.28 64.5% 35.5% 100% 0% 83.7% 16.3% 3.52% 4.18% 3.43% ζ 0.41 64.5% 35.5% 100% 0% 81.6% 18.4% 1.84% 2.59% 2.00% ζNFHTR 0.28 14.5% 85.5% NA NA NA 25.2% 74.8% 14.6% 3.38% ζNFLTR 0.28 56.7% 44.3% NA NA NA 52.6% 47.4% 4.6% 4.75% ζNF 0.41 32.4% 67.6% NA NA NA NA NA NA 2.9% ζFF 0.28 76.5% 23.4% 64.9% 35.1% 59.0% 41.0% 2.73% 2.40% 3.42% ζFF 0.41 66.4% 33.6% 78.5% 21.5% NA NA NA 3.54% 3.00% UHTR 99.2% 0.8% 60.4% 39.6% 26.5% 0.28 74.5% 3.11% 0.38% 12.5% 93.3% 6.7% 15.9% 84.1% 56.5% P 43.5% 3.76% 2.71% 6.5% V 99.2% 0.8% 87.9% 12.1% I 44.6% 35.4% 4.48% 0.86% 3.7% W 100% 0% 81.8% 18.2% 15.5% T 84.5% 36.21% 9.03% 2.4% Cp ULTR 99.8% 0.2% 47.8% 52.2% O 65.4% 34.4% 1.20% 0.42% 1.6% 99.7% 0.3% 21.2% 78.8% T 54.3% 46.7% 5.54% 1.87% 2.9% V 99.9% 0.1% 79.1% 20.9% 65.3% 34.7% 4.08% 0.95% 6.5% W 100% 0% 70.2% 29.8% 88.7% 21.3% 29.29% 9.11% 1.2% Cp 0.28 42.1% 57.9% U 2.35% P 72.4% 27.6% V 7.73% I 62.4% 37.6% W 4.37% V 20.8% 79.2% u 4.72% 34.9% 65.1% v 4.31% 37.3% 62.7% w 4.99% 13.0% 87.0% uv 4.09% 30.1% 69.9% uw 5.80% the authoritative version for attribution.

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 421 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 DISCUSSION B.Beck University of Michigan, USA Since you apparently were doing fixed model tests, was any account taken of the standing waves that develop in a towing tank after a long day of testing? AUTHOR'S REPLY Please see the discussion in section “COMPARISONS OF RESULTS…Facilities.” No special accounting was taken of standing waves in the towing tanks due to extended periods of testing. Carriage-run intervals were twenty minutes at DTMB and INSEAN and twelve minutes at IIHR to minimize free-surface effects from previous carriage runs. Standing- wave effects at each facility were assumed small due to effective wave damping. DISCUSSION L.Doctors The University of New South Wales, Australia I would like to congratulate the authors on their very carefully controlled experiments, which must certainly constitute the most precise experiments on surface ships ever done. It would be interesting to estimate the wave reflection effects due to finite width and finite depth of the towing tanks. These effects would be different for all three towing tanks and could be computed reasonably accurately with linearized wave-resistance theory. It might then be possible to bring the residuary resistance, for example, into better alignment for the three models. In Figure 2(A), we notice a divergence of the results for the residuary resistance at low froude number. Plotting specific residuary resistance, rather than residuary resistance coefficient, might therefore be advised. AUTHOR'S REPLY Thank you for your kind remarks. Differences and scatter in data for low Fr are largely due to limited resolution of the measurement system for low towing speeds and marginally due to selection of amplifier gain setting which was optimum for medium and high Fr measurements. The results are presented and discussed as nondimensional coefficients to facilitate comparisons between facilities. DISCUSSION G.Jensen Hamburg Ship Model Basin, Germany 1) How can the form factor be determined for a ship with wetted transom according to Prohaskas method? 2) Did you consider shallow water effects in analyzing the data or is that part of the “facility bias”? The INSEAN tank is relatively shallow compared to the model length. Therefore, at high Froude Number some shallow water effect is expected. AUTHOR'S REPLY The form factor is used only for data reduction as per ITTC, 1978. The k values are small, i.e., ~0.15 for each facility. Shallow-water effects are included in the blockage correction to carriage speed for each facility through the following equation (Tamura's formula): where Am is the midship sectional area of the model, AT is the sectional area of the tank, Lm is the length of the model, BT is the tank width, and Frh is the Fr based on the tank depth h. DISCUSSION D.Murdoy Institute for Marine Development, Canada Would the authors please comment on the possibility that the differences in resistance at higher Fn may be associated with the different trims of the three models which, in turn, may be associated with different tow points? What were the tow points? the authoritative version for attribution. Some of the variability in the data may be due to differences in the order of test runs. Was the order (for example, lowest to highest Fn, followed by highest to lowest to fill in gaps) specified? What was the order used for the tests?

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INTERNATIONAL COLLABORATION ON BENCHMARK CFD VALIDATION DATA FOR SURFACE COMBATANT DTMB MODEL 422 lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line 5415 AUTHOR'S REPLY The towing points were all close to the model CG. Each facility used (x=0.5, y=0) but towing height (z) varied somewhat. In spite of the differences in towing height, the sinkage and trim data was very uniform in magnitude for all models outside of the Fr range where scale effects are important, i.e., Fr<0.33. Therefore, it is not felt that towing point position was a significant factor in the measured resistance differences, rather, the differences are likely due to wave breaking. The order of tests at each facility in terms of Fr was random. DISCUSSION K.Tamura Prof. Nagasaki Institute of Applied Science, Japan Thanks very much for your presenting the fundamental studies on resistance tests. I would like to ask 3 questions. 1) In page 9 of the text, you mentioned blockage effect, and I would like to ask you whether you correct the effect or not? It is common in Japan to correct it due to the difference of tank size. 2) How do you compensate the effect of current in the tank? In other words, do you measure water speed directly? 3) Do you consider the effect of standing wave of the tanks used for tests, which may be caused by towing a model repeatedly in a tank? AUTHOR'S REPLY The blockage correction is taken into account through Tamura's formula (see above) which adjusts the measured towing speed of the model. There is no compensation for the effect of current in the towing tanks as only the carriage speed is measured and not also the water speed directly. No special accounting was taken of standing waves in the towing tanks due to extended periods of testing. Carriage-run intervals were twenty minutes at DTMB and INSEAN and twelve minutes at IIHR to minimize free-surface effects from previous carriage runs. Standing-wave effects at each facility were assumed small due to effective wave damping. the authoritative version for attribution.