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EVALUATION OF SURFACE,SHIP RESISTANCE

AND PROPULSION MODEL.,SCALE DATABASE

FOR CFD VALIDATION

by

J. Longo and F. Stern

Sponsored by

Society of Naval Architects and Marine Engineers Purchase Order #0644

and

Office of Naval Research

Grant N00014-934-0052

IIHR Report No. 375

lowa Institute of Hydraulic Research The University of Iowa Iowa City, Iowa 52242

August 1995

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Unclassified

SECO-HIT* CLASSIFICATION OF TIHS PAGE (Man Dote Ilatoese0

DD iFJORMn 1473 EDITION OF 1 NOV 611 IS OBSOLETE

6/N 0102.0346601 I Unclassified

SECURITY CLABSIFICATION OF THIS PAGE (Masi Delo Ilbstoree

REPORT DOCUMENTATION PAGE BEFORE COUPLET= FORM', READ INSTRUCTIONS

I. REP 111 WI

IIHR Technical Report #375

O.

r

S. RECIPIENT'S CATALOG NUMBER

Evaluation of Surface-Ship Resistance and

Validation

S. TYPE OF REPORT 11 PERIOD

=yaw

Final Technical Report G. PERFORMING OWL REPORT NUMBER

575 '

7. AUTHOR(a)

J. Longo and F. Stern

_

IL CONTRACT OR GRANT NUIIIIIER()

1400014-931,0052 S. PERFORMING ORGANIZATION :NAME AND ADDRESS

The Univertity-ol Iowa institute of Hydraulic Res 300 South Riverside Drive

Iowa City, Iowa 52242-1585

10. PROGRAM ELEMENT. PROJECT. TASK AREA WORK UNIT HUMMERS

II. CONTROLLING OFFICE MAINE AND ADDRESS Office of Naval. Reserach

.

536 South Clark Street

Chicago IL 60605-1588

It. REPORT DATE August 1995 13. NuNGER OF PAGES

59

141. MONITORING.AGENCY NAME A ADDR(SS(1/ Wean& fraen Catero/Iffid Wham) 01. SECURITY CLASS. (al OdaAwl) Unclassified

IS& DECLASSIncknOWDOWNGRADING

SCHEDULE -

-IL DISTRIGUTION STATEMENT (al ado Napery Unclassified

17. DISTRIOUTION STATEMENT (OS Wm abalaml 0010,06 be Ohba ak ',Whim" ifou Ralmg)

Unlimited Distribution

IL SUPPLEMENTARY NOTES .

-IS. KEY WORDS (Cdottheno on tovoirla &de IS momegy sad Main* $p 6/oak abs)umr

Database for CFD Validation

-MI. ANSTRACT (Cowitnue on ravaroo side If w000mry mod MEW& by Weak aumlose

. . .

An evaluation is performed of the surface-ship.model-Scaie database for

Computational. fluid dynamics validation with regard to current status and

futur-requirements. The specific emphasis is on data of relevance to resistance and

propulsion and Validation Of Reynolds-averaged Navier-Stokes computer codes. The data was evaluated relative to criteria and requirements developed for

geo-metry and flow, physics:, and CFD validation as well as past uses. Conclusions

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TABLE OF CONTENTS

ABSTRACTH

ii

ACKNOWLEDGMENI'S

LIST OF SYMBOLS

INTRODUCTION 1

CRITERIA AND REQUIREMENTS 1

COLLECTION AND EVALUATION 3

CONCLUSIONS 5

RECOMMENDATIONS 5

REFERENCES 6

TABLES

Table 1: Database. 10

Table 2: Data ranking 11

Table 3: Summary of reported accuracies 12

Table 4: Summary of data quantities

14

APPENDICES

LETTER TO ITTC MEMBER ORGANIZATIONS 15

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ABSTRACT

An evaluation is performed of the surface-ship model-scale database for

computational fluid dynatnics validation with regard to current status and future

requirements. The specific emphasis is on data of relevance to resistance and propulsion

and validation of Reynolds-averaged Navier,Stolces computer codes. The data was

evaluated relative to criteria and requirements developed for geometry and flow, physics,

and CFD validation as well as past uses. Conclusions are made with regardto the available

data and past uses and recommendations provided for future uses of the available data and

futitre data prcicurement.

ACKNOWLEDGMENTS

This research was sponsored by the Society of Naval Architects and Marine Engineers Purchase Order #0644 and Office of Naval Research Grant N00014-934-0052.

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AP after perpendicular

beam

CB block coefficient

-LppBT

CI) pressure coefficient

LIST OF SYMBOLS

Cr 8 5* FP Fr

(

R.

total resistance coefficient = --a7-, .5pU;S boundary-layer thickness displacement thickness forward perpendicular

Froude number--,___

(

-N/gLpp) gravitational constant

length between perpendiculars

kinematic viscosity density U,Lpp Re Reynolds number I = -RT total resistance surface area draft

U,V,W mean velocities in ship coordinate system

U, carriage speed

ujui Reynolds stresses

av

w

(ot axial vorticity - Ty-)

x,y,z axial,transverse,vertical coordinate directions

wave height: profiles or elevations

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I.

INTRODUCTION

Rapid advancements in the development of computational fluid dynamics (CFI)) has created the need to evaluate the surface-ship model-scale database for validation with regard to current status and future requirements. This is the goal of the present study with specific emphasis on data of relevance to resistance and propulsion and validation of Reynolds-averaged Navier-Stokes (RANS) computer codes. The approach taken was: (1) candidate data was collected through literature review and solicitation from International

Towing Tank Committee (ITT'C) member organizations; (2) criteria and requirements were

developed for geometry and flow, physics, and CFD validation; (3) the data was evaluated

relative to the criteria and requirements as well as past uses; and (4) conclusionsare made

with regard to the available data and past uses and recommendations provided for future uses of the available data and future data procurement. This report provides the overall results from the study.

II. CRITERIA AND REQUIREMENTS

In order to evaluate the data with regard to current status and future requirements, criteria and requirements were developed for geometry and flow, physics, and CFD

validation as follows.

Geometry and flow

The geometry is restricted to practical model-scale surface-ship hull forms (tanker,

cargo/container, and combatant). The flow is restricted to conditions of interest to

resistance and propulsion in distinction from seakeeping and maneuvering.

Physics

The physics of interest include: forces and moments, sinkage, trim, heel, and ballast conditions, surface pressure and shear stress, wave profiles and elevations, mean velocity and pressure, turbulence, wave-boundary layer and wake interaction, bow flow, near free-surface flow, wave breaking, bubble entrainment and distribution, wave-induced

separation, scale-effects, off-design (e.g.,

yaw and unsteady flow), propeller-hull

interaction, appendages, roughness, and shallow water.

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2

CFD Validation

The quality, quantity, and documentation of the data should be sufficient for

validation of RANS CFD computer codes.

Qua lity

The quality of the data is measured by uncertainty analysis and accuracy. Only

recently have rigorous standards and guidelines been set forth for experimental uncertainty

analysis (Rood and Telionis, 1991). Thus, many studies do not include uncertainty analysis and there is no general consensus as to accuracy standards and guidelines. Herein, studies are accepted without uncertainty analysis if the equipment, operation, and

data are of established high quality. The evaluation of the data includesa table of reported

accuracies, which may be useful in determining standards and guidelines.

Quantity

The quantity of data is measured with regard to resolution of the flow physics. For this purpose, the data should be sufficiently dense for evaluation of the dominant terms in the governing RANS and auxiliary (turbulence model, etc.) equations and other variables of interest (e.g., vorticity); however, equipment limitations and cost and time constraints are limiting factors such that this is practicably impossible. Therefore, only data providing less than partial mapping and coarse measurement locations was excluded. Making such a

judgment is difficult as is a complete literature review; however, the studies consideredare

felt to be sufficiently complete and representative to

support the conclusions and

recommendations.

Documentation

The documentation of the data is measured by the level of the detailed reporting of

the geometry and conditions, analysis of the data with regardto the physics of interest, and

availability/usability. Although many of the studies were motivated both for explication of

the flow physics and CFD validation, the documentation varies considerably. Herein,

studies are accepted even with limited documentation, i.e., sufficient reporting of geometry

and conditions, minimal analysis, and proprietary, i.e., not approved for public release

with unlimited distribution. Proprietary datawas accepted in order to determine and justify

its need for release and distribution.

As was the case for accuracy standards and

guidelines, there is no general consensus as to documentation standards and guidelines,

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Di COLLECTION AND EVALUATION

The data was collected through literature review and solicitation from ITTC membef

organizations (Appendix A). Table 1 provides a list of the database considered for detailed Study. The data was evaluated using summary tables with regard to the criteria and requirements as provided in Appendix B along with figures showing typical results. To aid

the evaluations, the data was ranked for physics and CFD validation as indicated in table 2.

Table 3 provides a summary of the reported accuracies. The detailed and total rankingsare

provided in the sturunary tables and table 1, respectively. The datawas also evaluated with

regard to past uses. It proved impossible, as originally intended, to specifically evaluate the data with regard to its value for providing insight on the physics of interest and effects

of hull forms and appendages and usefulness for design due to the magnitude and non

uniform presentation of the data and complexity of the design methodology.

Evaluation: Criteria and Requirements

Many hull forms have been investigated ranging from idealized Wigley and semi-practical Series 60 CB=.6 to semi-practical tanker, container/cargo, and combatant geometries.

Also, many physics of interest have been investigated, although in many cases the quantity

of the data is limited (i.e., turbulence, bow flow, hear free-surface flow, wave breaking, scale effects, appendages, roughness, and shallow water). Data is completely lacking for bubble entrainment and distribution, wave-induced separation, and unsteady flow. Database entries [1,2,5,6] and [3,4,7,8,9,10,11] are ranked limited and comprehensive, respectively, for physics.

As already noted, most studies lack rigorous uncertainty analysis and accuracy

standards and guidelines are nonexistent; thus, the quality of the data is difficult to measure

by the current standard. In consideration of the data and institutions and researchers

involved, the quality of the data is, in fact, excellent. However,

to emphasize this

requirement, the data is ranked for uncertainty analysis and the ranking for accuracy is retained, although all database entries were given an excellent ranking. Database entries [1,10], [4,5,6,8,9], and [2,3,7,11] are ranked none, partial, and rigorous for uncertainty analysis, respectively. Based on the highest ranked and other recent (e.g., Ratcliffe and

Fisher, 1993; Z,ierke et al., 1993; Jessup, 1994; Stem et a., 1994b) studies, there still

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4

presentation of the results for experimental uncertainty analysis. Table 3 provides a

summary of the reported accuracies. The accuracies for the various quantities vary somewhat between the different studies. Also, the accuracies for the mean velocity and Reynolds stresses are difficult to compare due to the already noted differences in practice and presentation for uncertainty analysis. Note that for sufficiently high speeds the

accuracies for forces and moments are close to 1%, which has been stated as the

requirement for designl.

The quantity of the data varies considerably.

Database entries [1,2,9],

[3,5,6,7,10], and [4,7,8,11] are ranked partial mapping and dense and large mapping and coarse and dense, respectively. Only relatively few studies are of the highest ranking.

Table 4 summarizes the quantities for coarse and dense rankings.

The documentation of the data also varies considerably. Database entries [5,9,10],

[1,2,3,6,7], and [4,8,11] are ranked limited, partial, and detailed documentation,

respectively. Here again, only relatively few studies are of the highest ranking. Although some of the studies were apparently planned for use for CH) validation, none describe the

consideration given or use of CFD for this purpose.

The database entries total rankings vary between 9-15. The database entries with

lower rankings are considered marginally useful for CFD validation due to the limited

physics of interest, quality, quantity, and/or documentation such that it is difficult to justify

the effort required in performing CFD validation. The database entries with higher rankings are considered useful for CFD validation; however, even in these cases none of

the studies can truly be considered complete. The proprietary data [3,7] is of high ranking

such that it would be useful for CFD validation.

Evaluation: Past Uses

Similarly as for experimental uncertainty analysis and data quality, only recently have rigorous standards and guidelines been set forth for computational uncertainty

analysis (Freitas, 1993) such that past usesare difficult to measure by the current standard.

However, unfortunately in this case, consensus is lacking such that the standards and guidelines are controversial (Shyy and Sindir, 1994; Vanka, 1994; Freitas, 1994; Roache, 1994; Ferziger, 1994; Leonard, 1995; Karniadakis, 1995; Freitas, 1995; Vanka, 1995).

Past uses include partial (Mang et al., 1991; Raven, 1993; Fanneret al., 1993; Carnpana et

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al., 1993; Chen et al., 1993; Weems et a., 1994) and complete (Fry and Kim, 1988; Stern et al., 1994a; Tahara and Stern, 1994) usages and national (Lindenmuth et al., 1991) and international (CFD Workshop Tokyo, 1994) workshops. Based on the references and Workshops, even partial use of the data enables a useful assessment of the state-of-the-art

of CFD for resistance and propulsion. Complete use of the data additionally enablesa

more thorough assessment, including analysis of the physics of interest. In general, the

standards and guidelines are not used and the uncertainty analyses are deficient with regard to documentation of the grid dependence and convergence characteristics.

IV. CONCLUSIONS

Information is available for many hull forms, but there isa need to identify specific

modern practical tanker, container/cargo, and combatant geometries for future study. This need is due to the requirement for data of relevance to future designs and the large amount

of data required in conjunction with the desirability of contributions from many institutions.

Many physics of interest have been investigated, but information 'is lacking to support the

most crucial future developments in CFD, i.e., turbulence and unsteady-flow data are

needed. The quality, quantity, and documentation of the data needs improvement. The data has not been fully utilized due to lack of rigorous computational uncertainty analysis and proprietary restrictions. The data has not been archived for general dissemination.

Accuracy and archiving and general dissemination standards and guidelines are needed.

V. RECOMMENDATIONS

The recommendations are as follows:

The current and future data should be fully utilized throughapproval for public release

with unlimited distribution of proprietary data and through complete usages with rigorous

computational uncertainty analysis.

The ITTC and the United States Navy should identify specific modern practical tanker, Container/cargo, and combatant geometries for future study.

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6

The ITTC and the United States Navy should set standards and guidelines for accuracy

and documentation (including, archiving and dissemination) of the data and identify

specific institutions for this purpose.

Complete data should be procured for the designated geometries with emphasis on

turbulence and unsteady flow in support of the most crucial future developments in CFD.

The quality, quantity, and documentation of future data should include careful consideration of experimental and computational uncertainty analysis standards and guidelines. Also, the standards and guidelines and CFD should be used in planning the

experiments.

REFERENCES

Bertram, V., Chao, K.-Y., Lammers, G., and Laudan J., (1994), "Experimental

Validation Data of Free-Surface Flows for Cargo Vessels," Proc. CFD Workshop Tokyo, Vol. 1, pp. 311-320.

Campana, E., Di Mascio, A., Esposito, P.G., and Lalli, F., (1993), "Domain

Decomposition in Free Surface Viscous Flows," Proc. Sixth International Conf. on

Numerical Ship Hydrodynamics, Iowa City, IA., pp. 329-340.

CFD Workshop Tokyo, (1994), Proc. Vol. 1 and 2, Ship Research Institute Ministry of

Transport Ship & Ocean Foundation.

Chen, H.-C., Lin, W.-M., and Weems, K.M., (1993), "Interactive Zonal Approach for

Ship Flows Including Viscous and Nonlinear Wave Effects," Proc. Sixth International Conf. on Numerical Ship Hydrodynamics, Iowa City, IA., pp. 341-363.

Farmer, J., Martinelli, L., and Jameson, A., (1993), "A Fast Multigrid Method for Solving the Nonlinear Ship Wave Problem with a Free Surface," Proc. Sixth International Conf. on Numerical Ship Hydrodynamics, Iowa City, IA., pp. 155-172.

Ferziger, J.H., (1994), "Comments on the Policy Statement on the Control of Numerical Accuracy," ASME J. Fluids Eng., Vol. 116, p. 396.

Forgach, K.M., (1994), "Measurement Uncertainty Analysis of a Ship Model Resistance

Test," Technical Memorandum, David Taylor Research Center, Bethesda, MD.

Freitas, C.J., (1993), "Policy Statement on the Control of Numerical Accuracy," ASME J. Fluids Eng., Vol 115, No. 3, pp. 339-340.

Freitas, C.J., (1994), "Response: To the Comments by Drs. W. Shyy and M. Sindir,"

ASME J. Fluids Eng., Vol. 116, p. 198.

Freitas, C.J., (1995), "The End of Justification, The Beginning of Implementation," ASME J. Fluids Eng., Vol. 117, p. 9.

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Okuno, T., Tanaka, N., and Hasegawa, Y., (1989), "Flow FieldMeasurement around Ship Hull at Incidence," J. Kansai Society of Naval Architects, No. 212, pp. 67-74.

7

Fry, D.J. and Kim, Y.H. (1988), "Bow Flow Field of Surface Ships," Proc. 17th ONR Sluwosillmon_Nayallydradyagniga, The Hague, pp. 319-346.

Hasegawa, Y., Okuno, T., Yamasaki, R., Nakanishi, Y., and Tanaka, H., (1989),

"Investigation into Flow Field around Fore Bottom of a High Speed Ship at Incidence," J.Kansai Society of Naval Architects, No. 211, pp. 41-46.

Hoekstra, M. and Ligtelijn, Jr. J. Th., (1991), "Macro Wake Features of

a Range of

Ships," MARIN Report 410461-1-PV, Maritime Research Institute Netherlands,

Wagenningen, The Netherlands.

ITTC, (1987), "Report of the Resistance and Flow Committee," 18th International Towing Tank Conference, Kobe, Japan, pp. 47-92.

ITTC, (1990), "Report of the Resistance and Flow Committee," 19th International Towing Tank Conference, Madrid, Spain, pp. 56,105.

ITTC, (1993), "Report of the Resistance and Flow Committee," 20th International Towing Tank Conference, San Francisco, CA., pp. 17-61.

Jessup, S.D., (1994), "Propeller Blade Flow Measurements Using LDV," ASME Fluids

Engineering Division Summer Meeting, Lake Tahoe, NV.

Karniadakis, G.E., (1995), "Toward a Numerical Error Bar in CFD," ASME J. Fluids Eng., Vol. 117, pp. 7-8.

Leonard, B.P., (1995), "Comments on the Policy Statement on Numerical Accuracy,"

AaME_LELdas_ngtiiE Vol. 117, pp. 5-6.

Lindenmuth, W. and Fry, D., (1995), "Viscous Macro-Wake Behind a Twin-Screw High Speed Surface Ship," Report No. DTRC/SHD-1273-01 (in preparation), David Taylor

Research Center, Bethesda, MD.

Lindenmuth, W.T., Ratcliffe, T.J., and Reed, A.M., (1991), "Comparative Accuracy of Numerical Kelvin Wake Code Prediction - Wake-Off," Report No. DTRC-91/004, David

Taylor Research Center, Bethesda, MD.

Longo, J., (1995), "Mean-Flow Measurements in the Boundary Layer and Wake and

Wave Field of a Yawed Series 60 CB=.6 Ship Model," Department of Mechanical

Engineering, The University of Iowa, Ph.D. Thesis (in preparation).

Longo, J., Stern, F., and Toda, Y., (1993), "Mean-Flow Measurements in the Boundary Layer and Wake and Wave Field of a Series 60 CB=.6 Ship Model - Part 2: Scale Effects on Near-Field Wave Patterns and Comparisons with Inviscid Theory," J. Ship Research, Vol. 37, No. 1, pp. 16-24.

Ogiwara, S., (1994), "Stern Flow Measurements for the Tanker 'Ryuko-Maru' in Model Scale, Intermediate Scale, and Full Scale Ships," Proc. CFD Workshop Tokyo, Vol. 1, pp. 341-349.

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8

Ratcliffe, T.J. and Fisher, S., (1993), "Nominal and Total Wake Measurements Performed on the Initial Contract Design Hull Form of the DDG 51 (Represented by Model 5422) Outfitted with the 18-foot Diameter Propeller Appendage Suit,"

CRDICNSWC-HD-0200-02, David Taylor Research Center, Bethesda, MD.

Ratcliffe, T.J. and Lindenmuth, W.T., (1990), "Kelvin Wake Measurements Obtained on

Five Surface Ship Models," DTRC-89/038, David Taylor Research Center, Bethesda, MD.

Raven, H.C., (1993), "Nonlinear Ship Wave Calculations Using the RAPID Method,"

Proc. Sixth International Conf. on Numerical Ship Hydrodynamics, Iowa City, IA.,pp.

95-118.

Roache, P.J., (1994), "Response: To the Comments by Drs. W. Shyy and M. Sindir," ASME J. Fluids Eng., Vol. 116, pp. 198-199.

Rood, E.P. and Telionis, D.P., (1991), "J. of Fluids Engineering Policy on Reporting

Uncertainties in Experimental Measurements and Results," ASME J. Fluids Eng., Vol. 113, pp. 313-314.

Shyy, W. and Sindir, M., (1994), "Comments on the Policy Statement on the Control of Numerical Accuracy," ASME J. Fluids Eng., Vol. 116, pp. 196-197.

Stern, F., Kim, H.T., Zhang, D.H., Toda, Y., Kerwin, J., and Jessup, S., (1994a),

"Computation of Viscous Flow Around Propeller-Body Configurations: Series 60 CB=.6

Ship Model," Journal of Ship Research, Vol. 38, No. 2, pp. 137-157.

Stern, F., Parthasarathy, R.N., Huang, H.P., and Longo, J., (1994b), "Effects of Waves

and Free Surface on Turbulence in the Boundary Layer of a Surface-Piercing Flat Plate,"

ASME Symposium on Free-Surface Turbulence, Invited Speaker, Lake Tahoe, NV.,pp.

37-51.

Tahara, Y. and Stern, F., (1994), "Validation of an Interactive Approach for Calculating

Ship Boundary Layers and Wakes for Nonzero Froude Number," J. Computers and

Fluids, Vol. 23, No. 6, pp. 785-816.

Toda, Y., Stern, F., and Longo, J., (1991), "Mean-Flow Measurements in the Boundary

Layer and Wake and Wave Field of a Series 60 CB=.6 Ship Model for Froude Numbers

.16 and .316," Iowa Institute of Hydraulic Research, The University of Iowa, Iowa City, MIR Report No. 352, 188 pp.

Toda, Y., Stern, F., and Longo, J., (1992), "Mean-Flow Measurements in the Boundary

Layer and Wake and Wave Field of a Series 60 CB=.6 Ship Model - Part 1: Froude

Numbers .16 and .316," J. Ship Research, Vol. 36, No. 4, pp. 360-377.

Toda, Y., Stern, F., Tanaka, I., and Patel, V.C., (1988), "Mean-Flow Measurements in

the Boundary Layer and Wake of a Series 60 CB=.6 Model Ship With and Without

Propeller," Iowa Institute of Hydraulic Research, The University of Iowa, [MRReport

No. 326, 100 pp.

Toda, Y., Stern, F., Tanaka, I., and Patel, V.C., (1990), "Mean-FlowMeasurements in

the Boundary Layer and Wake of a Series 60 CB=.6 Model Ship With and Without Propeller," J. Ship Research, Vol. 34, No. 4, pp. 225-252.

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9

Vanka, P., (1994), "Response: To the Comments by Drs. W. Shyy and M. Sindir," ASME J. Fluids Eng., Vol. 116, pp. 197-198.

Vanka, P., (1995), "Comment on "Toward a Numerical Error Bar in CFD" by G.

Karniadakis," ASME WE, Vol. 117, p. 9.

Weems, K., Korpus, R., Lin, W.M, and Fritts, M., (1994), "Near-Field Predictions for Ship Design," Proc. 20th ONR Symposium on Naval Hydro., Santa Barbara, CA.,

August 1994.

-Zhang, D.-H., Broberg, L., Larsson, L., and Dyne, G., (1991), "A Method for

Computing Stern Flows With an Operating Propeller," Royal Institution Naval Architects.

Zierke, W.C., Straka, W.A., and Taylor, P.D., (1993), "The High Reynolds Number Flow Through an Axial-Flow Pump,' Applied Research Laboratory, Technical Report No TR 93-12.

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Table

Database:

FIF- F FM SP WP

WE: MV:

hull type (c:combatant,t:tanker,cc:container/cargo,S60:Series 60,w:Wigley)

facility(tt:towing tank,wc:waterchannel)

propulsor (w: with, wo: without)

forces and moments

surface-pressure wave-profile wave-elevation mean-velocity MP mean pressure turbulence proprietary? (yes/no) data no data Database entryi 1 HT ,

IF

P

FM SP WP

J

WE MV MP

T

PR Rank

1.

Cooperative Experimental Program 16thi17th,18th ITTC, (1987,1990,1993)

S60,t,w tt,we wo 11 4 4 -no 9 2.

David Taylor Research Center Fry, D.J. and Kim, Y.H., (1988)

S60,c,cc tt wo , -no 11 .

David Taylor Research Center Lindenmuth, W.T. and Fry, D.J., (1995)

c tt w,wo -4 -4 yes 13 4.

Osaka University/IIHR Toda et al., (1988)

S60 tt w,wo I 4 --no 14 5.

Hitachi Shipbuilding Ltd. Hasegawa et al., (1989)

t we . . .. wo -no 10

Osaka Prefecture University Okuno et al., (1989)

t we wo -no 6.

David Taylor Research Center Ratcliffe, T. and Lindenmuth, W.T., (1990)

c tt w,wo -no 11 7.

MARIN Hoekstra, M. and Ligtelijn, (1991)

c,t,cc t t w,wo -4 -yes 13/14 8.

Iowa Institute of Hydraulic Research Tdda et al., (1992)

S60 t t wo no 14 19.

Hamburg Ship Model Basin Bertram.et al., (1994)

c tt w,wo q I -no 10

10. Ishikawajima-Harima Heavy Industries Co., Ltd.

Ogiwara, S., (1994) t t w,wo 4 -no 10

11. Iowa Institute of Hydraulic Research

Longo, J., (1995) S60 tt wo 4 .s./ I I -no 15

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Table 2: Data ranking.

Data Ranking I Points

Physics

Comprehensive Limited 1

CFD Validation: Qualtity

Uncertainty analysis Rigorous Partial 2 None 1 Accuracy Excellent Good

CFD Validation: Quantity

Large mapping and dense Large mapping and coarse Partial mapping and dense

Partial mapping and coarse 1

CFD Validation: Documentation

_ Detailed . Partial . Limited Maximum I 15

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Table 3: Summary of reported accuracies. Database entry-> jJi 2 3 5 6 7 j 8

101 1 1

121

11321143

143 Geometry(mm) np np np up np np c 1.5 c np 1.5 1.5 np 1.5

Carriage speed (Uc)

fly) p np ±.03% up rip ±.25% ±.33% lip np ±.33% ±.36% ±.07%

Forces and moments (4)

tip -.5-5% -5-5% np up .5-5% -1-3.5%

-Surface pressures (CO

np tip -±.01 -fl I -Wave profiles (mm)

video and camera grid/marker

±1.5

±.5

±2.5

±.5

Longitudinal elevations (mm)

capacitance wire laser slope stereo photography

±2 ±1 -1.37 ±.7 ±.5 ±.1 ±.5 . Transverse elevations (mm)

servo-mechanism ultrasonic point gage

±1.5 ±3 -±1.25 ±.5 -±.5

-Mean velocity and pressure U

(pitot) V W . CD np rip np np - - -_ - -[a] 1.5% 1.5% 1.5% ±.05 np np np -- - -- -[a] 1.5% 1.5% 1.5% ±.05 - -np np tip -[a] 1.5% 1.5% 1.5% ±.05 -- - -[b] 2-5% 2-5% 2-5%

-Shear stress (preston tube)

np -Mean velocity U (LDV) V W - - -[c] <.5% <1.5% <1.5% [c] .08% .88% .09% - - -- - -[1:1] .5% .5% .5% - -[a] 2% 2% 2% - - -- - -le] [f] 1.52% 1.90% .30% .94% .44% .72% - -[g] 1.22% .99% 5% Reynolds stress uv (LDV) uw VW - -- - -rip np np - -- - -[h] 5% 5% 5% - -- - -- -- - -[i] 0] 6.12% 7.45% 7.64% 7.92% -- -- - -Normal stress U2 (LDV) v2 2 - -- - -np np up - - -- -- - -[h] 5% 5% 5% - - -- -- -- - -[i] U] 5.92% 5.45% 8.65% 4.87% 7.64% 6.91% - -' --

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-speed ranges: Fr=:08-.27,.1-.35,.1-.35,.12-.27 for studies 4,8,11,13, respectively no data c : confirmed np : not published :

%Uc based on calibration tests and average repeatability

:

%Uc baselion matrix and hydrolanalysis methods; 2% difference between matrix and

hydro analysis methods with consistently lower results for

the former; and hydro:analysis method.consistently 2-3% higher than

LDV data : % (U,V,W) : %Uc 60%,confidence :

% Uc 95%,confidence; low-turbulence region

:

% Uc 95% confidence; high turbulence region

[8]

%U

[h]

:

%Uc2 based on calibration tests and

average repeatability

[1]

:

%Uc2 95% confidence; low-turbulence,region

[j]

:

%Uc2 95% confidence; high-turbulence region

1 : Stern et al., (1994) 2 : Forgach, K.M., (1994) 3 :

(19)

full-plane half-plane pitot data

Table 4: Summary of data uantities.

Measurements, Quantities1 Forces/ moments Surface pressure Wave profiles , _ Wave elevations (longitudinal) Wave elevations (transverse) Mean

, velocity & pressure*

Turbulence Coarse 12 100 hull 15 50 pts/m 130 pts/m2 -t50 pts/st $100 pts/st Dense 35 60 dome 376 stern 41 385 pts/m, 960 pts/mL , 20 pts/cut $1400 pts/st $300 pts/st

(20)

APPENDIX A: LETTER TO ITTC MEMBER ORGANIZATIONS

21 May 1993

ITTC Representative

Dear Colleague:

The Iowa Institute of Hydraulic Research is currently involved in a project entitled "Evaluation Of Surface-Ship Boundary-Layer And Wake And Wave-Field Model-Scale Database", sponsored jointly by the SNAME T & R/ Panel H - 11 and the Office of Naval Research. The objective is to perform an evaluative cataloging of the current available

model-scale data for surface ship boundary layers and wakes and wave fields.

The data will be evaluated and cataloged with regard to its value in elucidating various physical phenomena (e.g., mean-flow and turbulence properties, vortex systems and vortex/free-surface interactions, wave patterns, wave breaking, wave=induced

separation, near free-surface flow, wave/boundary-layer and wake interactions,

propeller/hull interaction, etc.), in providing insight on the effects of various types of hull forms and appendages or other geometric features, and as test cases for validating

computational methods.

The data to be considered will include known data bases (e.g., [1] - [7]) as well as those discovered through inquiry. Recommendations will be given with regard to appropriate applications of the current database and concerning future data-base needs in

support of technological developments.

This letter is in request of your aid in identifying possible relevant data from your

institution for inclusion in the database. Please provide us with either a copy or appropriate

reference to such data. Also, any comments or suggestions that you may have regarding this project are welcome and inform us as to your interest in receiving a copy of the final report.

Thank you in advance for your help with this matter.

Sincerely,

Fred Stern

Associate Professor

and Research Engineer

cc: Dr. E. Rood, ONR

(21)

Selected References

Toda, Y., Stern, F., an. J., "Mean-Flow Measurements in the

Boundary Layer and Wake and Wave Field of a Series 60 CB= .6 Ship Model - Part 1:

Froude Numbers .16 and .316," J. Ship Research, Vol. 36, No. 4, December 1992, pp. 360-377.

2 Longo, J., Stern, F., and 'Toda, Y., "Mean-Flow Measurements in the Boundary Layer

and Wake and Wave Field of a Series 60 CB= .6 Ship Model - Part 2: Scale Effects on Near-Field Wave Patterns and Comparisons with Inviscid Theory," J. Ship Research, Vol. 37, No. 1, March 1993, pp. 16-24.

3 Toda, Y., Stern, F., Tanaka, I., and Patel, V.C., "Mean-Flow Measurements in the

Boundary Layer and Wake of a Series 60 CB= .6 Model Ship With and Without

Propeller," J. Ship Research, Vol. 34, No. 4, 1990, pp. 225-252.

4 Hoekstra, M. and Ligtelijn, Ir J. Th., "Macro Wake Features of a Range of Ships,"

1VIAMN Report 410461-1-PV, Maritime Research Institute Netherlands, Wagenningen,

The Netherlands, 1991.

5 IT'TC, (1987), "Report of the Resistance and Flow Committee," Proc. 18th hit.

Towing Tank Conf., Kobe, Japan, pp. 47-92.

6 Fry, D.J. and Kim, Y.-H., (1988), "Bow Flow Field of Surface Ships," Proc. 17th

ONR S'ymp. on Naval Hydro., The Hague, pp. 319-346.

7 Lindenmuth, W. and Fry, D., "Viscous Macro-Wake Behind a Twin-Screw High

Speed Surface Ship," Report No. DTRC/SHD-1273-01, David Taylor Research Center, September 1988.

(22)

APPENDIX B: SUMMARY TABLES AND TYPICAL RESULTS

(23)

:

based on a water temperature of 15°C and published values hull type (y: yatch, t: tanker, cc: container/cargo,

m: mathematical)

46 a c.,-,

..

,.. na a e U

Hull type and class

-(1)Wigley Hull (m), (2)Series 60 CB=.6 (cc), (3)Athena

Hull (y), (4)11SVA (t)t

Rank

Special

conditions

global measurements published for all models; local measurements published for models (1)

and (2) 'Measurements) Parameters 1 Wave .Wave Forces/ Surface Wave elevations elevations Mean Turbulence moments pressure profiles (longitudinal) (transverse) 1 velocity Froude No. . .08-.49 (1) .10-.43 (2) .18-1.0 (3) .09-.19 (4) .21-.32 (1) .18-.32 (2) .16-.41 (1), .22-.35 (2) .28-.65 (3) .13-.19 (4)'1 -. ,Re No. (0106)* .97-23.0 (1) .75-20.7 (2) 3.2-7.4 (3) 3.2-6.8 (4) L4-14.8 (1) 1.9-14.7 (2) 3.1-15.0 (1) 2.7-16A (2) 5.0-27.5 (3) 4.7-6.8 :(4) -_ Fixed/free condition fixedlind free

fixed and free

fixed and free

-Instrumentation dynamometer , pressure transducers 35mm camera -, -Physics

wave profiles; attitude effects;

forces and moments; viscous effects

wake surveys;

on hull surface pressure

skin friction;

fields; blockage

scale effects on resistance

effects on global

and wave

and local measurements

profiles; hull I I>

.,

." Meas. uncertainty (CO (CO (C) I o of Meas. accuracy No, of stations

-=5-10 =21 -.t.'. 11 a a CY Location of stations waterlines bow 5 mid 11 stern 5 wake 0

-'No, of data points

..20/study

-100/study

21/study

-'Documentation Total ranking)

Table B 1: Database entry 1.

Lpp

(24)

-.3

-2

12(t

AXIAL SECTIONS OF SERIES 60 ce.6 SHIP MODEL

CTs-._ I/ 2.9u-s- Ls= 121.9Zrn l_rn

4x10----BSH

C 70M Z, HYUNDAI 6.967m ---DINSRDC6.096m CSSRC 6.0m (' ....

_RT Series 60 Fixed Cond.

Rostock 5.0 m Helsinki 5.0" K I MM1364877" K I MM'83

ALM

4.0" S N U 3.387 a° .15 0 0 0 0 Glasgow U 3.0m U T 3 T U MARIC}2.5" 15 Zagrev1.829"-2 0 0 00 Or:" .35 3 _11 II

,

.3 .38 x1C0 .08 4 -4) 01 _ FP. 9

Figure B1 Typical results for database entry 1.

19 2%/62 Series 60 Models Wave Profiles 21<4 7 6 5. a 2 1 AP Pressure on Hulls Cp=

F.

1/2 pl.12 ICp=0.1 Fn= 0.25 e41.1 -375 F

rt*

14--.6251 .125 0 -325 -.8501' 1.00 0 35 _ 2 .25 .3 Fn ...35 , cr.= Acir.41dA :Sinkage Fit. 2 I-13P t 44 IdLp-Adp : Trim 0 A-grotip 8-group 9 9 a oBSH CSSRC o KIMM NSRDC +Rostock MARI C .04 A-grouP(17ITTC)

0-

elt. 08 442 + 04

" 44 B-GrouP(Towing point:CB)

04141$40itt,.

KU2.5mmodel height from keel;

44 L Crgroup ( Towing height series)

itres.,o4.,.4

08t 0 0.856d .536d (CB) 0.140d

.... ...

15 .2 .25 .3_ .35 - Fn-LA/7-n - . a A -.041 0 .0 e 0 ° C-group

011901.

° -aa trim by bow '9 7 3 1.2 WL BTL _ -+Hyundai; o A L M(L)

SHIIIHI

(25)

based on a water temperature of 15°C and published values hull type (c: combatant, t: tanker, cc: container/cargo)

u5 a 0 T. ;co

:

1 u

Hull type and class

(1)5415-1 high-speed`model CB=.506 (c), (2)4287

Series 60 CB=.6 (cc), (3)5326-1 medium-speed model (cc)t

Rank

Special

conditions

high-speed model equipped with bulb below the keel-line, S60 has fine bow

entrance angle, medium speed model

equipped with bulbous bow

'Measurements-3 Parameters i Forces/ moments Surface pressure Wave profiles Wave elevations (longitudinal) Wave elevations (transverse) Mean velocity 1 Turbulence Froude No. _ .41 (1) .28 (1) _ Al (1) .32 (2). ..41 (1) .32 (2) .41 (1) .28 (1) .32 (2) .26 (3) _ Re No. (.106)* _ 17.6 (1) 11.7 (1) ' . 17.6 (1), 15.1 -(2): 17.6 (1) 15.1 (2) 17.6 (1) 11.7 (1) 15.1 (2) 13.4 (3) -Fixed/free condition -fixed -fixed fixed fixed ' Instrumentation -pressure ' transducers -cameras

ultrasonic probes point gauges

3-component

ldv

-Physics

bow flow; wave elevations; free-surface

breaking; mean

effects

velocity and

on the bow-flow

pressure fields; surface field

pressure and shear stress; wave profiles and

... 7.... Meas. uncertainty (Cr) (C) ±2.5mm (0 ±2mm (U,V,W) <.5,1.5,1.5% 3 o Co Meas. accuracy 3 No. of stations --7 -unknown 16 cuts 17 -2 0.1 ... Iiii a a CY Location of stations -bow 60 mid 0' stern o wake

-wave field coverage 6mx15m

bow 16 mid 0 stern 0 wake 0 bow 17 mid 0 stern 0 wake 0

-No. of data points

-60 pts/Fr -unknown 20 pts/cuts 60-200 pts/st -Documentation . 2 Total ranking-4 . I 11

Table B2: Database entry 2.

Lpp

(1)5.72m,(2)6.1m,(3)6.53m

IJ

(26)

CROSSFLOW

, VECTORS

SCAM

.3 U.

BODY PLAN FOR MEDIUMSPEED SHIP

BODY PLAN FOR HIGH-SPEED SHIP

nall11111111111

ALIRIME51.1011,1W/1/111111 intanwiwww.ur11111111M1111111t VLWINLINIWINICS,T 111111WIMME1=11111 M1E1111,11111 ONL.W.11W1M2.IIMIMIVARMOtali : X= 0.009 1.691N.L. BASEL INS 1.00 1I.L CROSSFLOW VECTORS VAIL 1..5. STREAM WISE CONTOURS '43//13Vang ST AT (

/

ANL:6.s

;.-Figure B2 TypiCal results for database entry 2.

SCALE: CROSSFLOW VECTORS ILL 11/. .11..

'Ilvamsvost sTnlit ettuavasc srintr.

Yi.Nsvmsz strritt

21

BODY PLAN FOR SERIES 60. BLOCK 60

/

11

&WW1 I lU 7.

/111

SIIIMMINAIM/1111

INE1111 I I ,/ ;11, 1.1:; X= 0.040 X = 0.504

(27)

:

based on a water temperature of 15°C and published values

t

:

hull type (c: combatant, t: tanker, cc: container/cargo)

Table B3: Database entry 3.

Lpp

5.72m

3.08m/s 2 04m/s

`11 0 o ....

.

6. of o

'Hull type and class

5415-1 high-speed CB=.506 (c)t

Rank

Special

conditions

high-speed ship equipped with bulb below the keel-line; appendages include bilge keels, rudders, shafting and

struts;

propulsion provided by 5-bladed model propellers, No. 4876(RH) and No. 4877(LH)

Measurements) Parameterta Forces/ moments Surface pressure Wave profiles Wave elevations (longitudinal) Wave elevations (transverse) Mean velocity Turbulence Froude No. -.41 .41 .41 and .28 Al and .28 C) Re No. (440 6)* . -17.6 17.6 17.6 and 11.7 17.6 and 11.7 Fixed/free condition -fixed fixed fixed fixed Instrumentation -cameras

ultrasonic probes point gauges

3-component ldv HF-anemometer 3-component ldv Physics .

bow and stern wave elevations flow; wave breaking and their generation

and breaking wave wakes; mean velocity fields; free-surface effects on turbulence;

2 o, ..., Meas. uncertainty (C) ±2.5rnin (C) ±1mm (U,V,W) <.5,1.5,1.5% (uiuj) -3 a Co Meas. accuracy 3 No. of stations -unknown 3:8 1 3 118 o,4., :ill a os o Co Location of stations -.

-wave field coverage 6mx15m

bow 1 0 mid 4 stern 3 wake 21 bow 5 mid 2 stern 3 wake 3 bow 0 mid 0 stern 0 wake 5 3 No of data points -1 unknown unknown -23Opts/st 230pts/st Documentation 2 ...=.1.1. 1 3 Total ranking) 111

(28)

asita/t

111MeAll fillEIVINI

WAVT151111/AVAFA 1.7k 0 O 0 gri 0 VELOCITY SCALE: 2-D VELOCITY VECTORS

FOR TRANSVERSE PLANE X = 16.00

V NM.

1401

X 4

\

V. A -20.0 -15.0 -10.0 -6.0 0.0 5.0 en. A IP 11. A

STREAMWISE STD.DEV. CONTOURS FOR TRANSVERSE PLANE X = 16.00

10.0 15.0 20.0 25.0

23

-25.0 -20.0 -15.0 -10.0 -6.0 0.0 6.0 10.0 15.0 20.0 25.0

TRANSVERSE COORD. (in.)

(29)

based on a water temperature of 15°C and published values hull type (c: combatant, t: tanker, cc: container/cargo)

Table B4: Database entry 4.

Lpp

4.0m

0 0

Hull type and class

Series 60 CB=.6 (cc)t.

Rank

iSpecial

conditions

All measurements were for the full-load condition; propulsion provided by

a 5-bladed, constant-6° pitch, zero skew,

model propeller with MAU n=25 sections

Measurements, 'Parameters.!. Forces/ moments Surface pressure Wave profiles Wave elevations (longitudinal) Wave ,elevations (transverse) Mean 'velocity & pressure Turbulence, Froude No. .08-.27 .16 .3,.25;.16 .16 Re No. (.106)* 1.6-5.4 3.08 6.0,5.0,3.2 3.2. Fixed/free condition free fixed fixed fixed Instrumentation dynamometer pressure transducers camera video camera 5-hole pitot probes Physic's

forces and mo propeller-hull ments; wave pro interaction

files and elevatio ns; surface pressure and shear stress; mean velocity and pressure fields;

2 a. CY ,Meas. uncertainty (Ct) .5,5% (Cr) ±.01 (U,V,W,Cp) 1.5,1.5,1.5% ,±.05 2 Meas. accuracy 3 es 00 No. of stations 25 13 4 Location of stations bow 0 mid 0 stern 9 wake bow 8 mid 9 stern 8 wake bow 0 mid 3 stern 110 wake 0

No. of data points

22

376 pts/Fr

=25 pts/Fr

400-700 pts/st

Documentation Total. ranking>

(30)

r toner 200

0.8

AXIAL SECTIONS OF SERIES 60 Ce.6 SNIP MODEL

...

.

...

...

...

.. .

...

.

...

...

...

...

.

...

. ...

... ... 300 211.0 1.1 V00010 0f00.0af 0.0 1.0 -0.02 0.9 I ,

I*

i t I 1.... s, ,.' 0 0.02 004 ... . -, -2CC ,00,. 200 0 Cp>0(Step 0.02) Cp=0 - Cp<O(Step 0.02) with propeller

Figure B4 Typical results for database entry 4.

...

...

...

...

. . .

...

r _ ... , , ,// / -. ,...11 /(414,...;4r

I,

.

"

300 nem propeller plane 1.0 300 Z(mm) 25 -200 rah pr00010. 0.0 I.0 1.05 8 4M SERIES 60 Co. 0.6

GROUND SPEED RESISTANCE TEST FREE CONDITION

-7 STUD BLOCKAGE

HEIGHT (cm) A./AT

... 0 PRESENT 8.7n(1.6 °C)* 1.5 0.0033

ITTC 87 ALM 8.7 °C 2.0 0.0013

;.- 6

TEMPERATURE CORRECTION APPLIED FOR Cm

c to r. A. 5 (XrTc, Iasi) 00 Ll 4 ITTC 1957 3 2 t 0.10 0.15 0.20 0.25 0.30 0.35 0.05

(31)

based On a water temperature of 15°C and published values hull type (c: combatant, t: tanker, cc: container/cargo)

Table B5: Database entry 5a.

Lpp Ue 2.0m .80m/s ' CY Special conditions

Froude No. Re No. (*10 )4 Fixed/free

condition

Instrumentation Physics Meas. uncertainty Meas. accuracy No, of stations Location of stations No, of data points

IDocumentation ITotal ranking)

II

trim=0,.5%L; heel=0,5°; a=0,10°; fully loaded without propulsor

Mean V elocity .181 1.60 fixed Turbulence, Rank 3-hole pitot probe

bow flow; boundary-layer development; yaw effects; vortex evolution and tracking in the flow field

(U) 2 bow 2 mid 2 stern 0 wake 0 3 pts/st 1 10 Measurements) ril .0 Parameterssi, Forces/ moments Surface .pressure Wave ,profiles Wave elevations (longitudinal) Wave elevations (transverse)

high-speed hull with fine bow form and transom stem, CB=.525 (cc)t

(32)

:

-ULLA' WS.

:

t

(rem) isce,

Flow pattern (0° ahead)

caloratm.wect; Wax

OZSP,41strew iff*

Flow pattern (10° oblique)

rns. gl.use 7 *mow, Mem SU flat "et@ Velocity profiles at Sq. St. 7 1/2 z 5 ice '.ie Botta+ v ies 2Arayle.

Figure B5 Typical results for database entry 5a.

Velocity profiles at keel center and bottom flat

27

Distribution of cross flow velocity

(33)

based on a water temperature of 15°C and published values hull type (c: combatant, t: tanker, cc: container/cargo)

,

2 a ix e.)

Hull type and class

-high-speed hull with fine bow form and transom stern, CB=.525 (cc)t

Rank

Special

conditions

trim=0,.5%L; heel=0,5°; a=0,10°; fully loaded' without propulsor

Measurements-) Parameters1 Forces/ moments Surface pressure Wave profiles Wave elevations (longitudinal) Wave elevations (transverse) Mean

velocity & pressure

Turbulence Froude No -.181 -Re No (4406)* -1.60 Fixed/free _condition , fixed Instrumentation I 5-hole pitot robes Physics .!..^ .- 11,1 o co Meas. uncertainty Meas. accuracy

-No, of stations

.'

74 as o co Location of stations

No. of data points Documentation

1

Total ranking-)

10

Table B6: Database entry 5b.

Lpp

2.0m

(34)

",

... A .P. ... Sire view :D.P.Of MO NM PLOD MILACI ... 5.5.1 r, ' ... ; : .. ; .01110101.0.... S.S.4 : .-;;:., .. .. 5.5.8 5.5.9 5.5.6 ....I,

Crossplane-flow velocity vectors ( v w)

Bottom vies

...WIT GP val.:m...1f

Figure B6 Typical results for database entry 5b.

Vorticity distribution in A. P. section

Wake distribution in A.P. section

29

Waterplaneflow velocity vectors (u, v)

(35)

based on a water temperature of 15°C and published values hull type (c: combatant, t: tanker, cc: container/cargo)

Table B7: Database entry 6.

Lpp (1)9.6m,(2)7.09m,(3)5.95m,(4)6.51m,(5)5.72m = (1)2 43 (2)2 08 (3) (4) (5) la al

a

7.1. go a U

Hull type and class

(11)5063 CB=.623 (c,aircraft

carrier), (2)5201 CB=.511 (c,cruiser), (3)4645 C=.531 (c,destroyer), (4)5359 CB=.503

(c,destroyer), (5)5415 CB=.506 (c,prototype destroyer)t. Rank Special conditions '

All models tested in without-propeller condition except model 5201

where both with and without conditions were

tested; trim by bow and stern condition for model 5201; all models

were run through a range of Fr with Fr= 25 common

to all Measurements> ' P a r a m e t e r s 1 Forces/ moments Surface pressure Wave profiles VVave elevations (longitudinal) Wave elevations (transverse) ' Mean velocity , Turbulence Froude No. -.25 -Re No. (*106) t -23.1 (1) 1L3 (2) 14.7 (3)1 12.9 (4) 10.6 (5); -, . , Fixed/free condition -fixed -Instrumentation -70mm cameras -Physics

hull-form effects effects on wave

on wave elevations

patterns; Fr effects

and wave

on wave patterns

generation; propulsion effects on stern-wave systems(3); hull-attitude

o , .., Irs Meas. uncertainty (0 1.37mm -2 0 01 Meas. accuracy 3 No, of stations -unknown -..t. a o 01 Location of stations _ _

wave field coverage

6.1mx10.66m

.

-No. of data points

-14Opts/m2 -Documentation ITotal ranking, 1 ' 11

(36)

PO'

A.

liddl7//

!.inPreaci asome---0 GE 0 -a3 50 100 150 200 CI) 250 X. INCHES CONTOUR INTERVAL = 0.02 Tiko

Contour plot of Kelvin wake generated by Model 5415 at =0.28.

300

Figure B7 Typical results for database entry 6.

350 400

31

(37)

co

Hull type and class

'(1)4041 CB=.84 (t), (2)4041 CB=.79

(Of

Special

conditions

model 4041 equipped with a bow bulb; model(1) tested at full-load and model(2) tested

at ballast condition; both

configurations tested with and without a 4-bladed, fixed pitch, right-hand turning, model propulsor; appendages include rudder and propeller-boss for with-propeller configuration

Measurements) Parametersi Froude No. Re No. (*106)4 Fixed/free

condition

Instrumentation Physics Meas.

uncertainty

Meas. accuracy No. of stations Location

of stations

No, of data points Documentation Total ranking)

Forces/ moments Surface pressure Wave profiles Wave elevations (longitudinal) Wave, elevations (transverse) Mean velocity Turbulence ,Rank :

based on a water temperature of 15°C and published values

:

hull type (c: combatant, t: tanker, cc: container/cargo)

Table B8: Database entry 7a.

Lpp 6.258m 1.1c = 1.3m/s .166 (1) .166 (2) .166 (1) .166 (2) .166, (1) .166 (2) .166 (1) .166 (2) 8.08 (1) 8.08 (2) fixed 8.08 (1) 8.08 (2) fixed 8.08 (1) 8.08 (2) fixed 8.08 (1) 8.08 (2) fixed

argon-ion laser PSD camera CCD camera

servo-type probe 3-component ldv 3-component ldv propeller-hull .mean-velocity

interaction; turbulence; and turbulence fields;

mean-velocity

hull-attitude

fields; wave

effects; near-frees

elevations; propuls urface flows

or-effects on w ake elevations;

2 ±.7mm ±1.25mm (U,V,W) (tqui) 5% 3 3 2 38 13 (1) '13 (2)' 13 (1) 13 (2) 4 y/B=0,1.97 bow', mid 9 stern 4 Wake. 19 bow mid 0 stern .20 wake 6 bow 0 mid 0 stern . 20 wake 6 385 pts/m unknown -300 pts/st ..300 pts/st 2 14

(38)

A P

TRANSVERSE COMPO4ENT v/111.1

TRANSVERSE COMPONENT -.LvL/111:1

VERTICAL COMPONENT -o-ix/10:1

. LongiludLnoL-pocircknote X/Lpp 0.879

TONING SPEED 11./N/gLpp. - 0.166

sHnrT C.L. AT T/8 - omo AND 2/To - -0.738 10.1 .91. 7 . y I ..,---,... ...,-- 3 -4 __,... ... _-.9.. __,.., .,__,. 0. r-a. VY S. ,Y W W . It A V V E we A A R .kt F F A A q V V E . A A 40.

Av.%

< w at p A -0.2 0.0 0.2 0.4 0.6 0.8 1.0 _LoogiLinlinOL coordLnOLe X/pp 0.879

TONING SPEED 11./VOLpp. - 0.166

swirT C.L. AT T/B - 0.000 AND 2/To -0738

_,.

0.0005

..;

Z CE

4/

\ \

X

2.,

.0/.//4 .4, v 41

-4

.', \

0 D E-lk 14 44

v ,

v ii .I.. w<-- .r.- v r-->v

r_,'.

---,..-CC 8->

.

. 4 1,1 ---:a,,---).__:-3

0

- Aei/ '4 4-.' i° / <-:

. vy

to -0.6 -OA -0.2 kO.

i.\i\l

\\\

-0.2 .0.4 0.6. 0.8 1.0

TRANSVERSE CO-ORDINATE (MI

-Figure B8 Typical results for *database entry-7a.

33 ' EQ ...rl . yEnTicni COMPONENT w/10.1 ..e...- .1 Li , 44 4E-.4- ..E-...eE- E-v .7 N... CC . A A .,fi v A ' C.) -J CC A 7 If W % 4 .1-4 4 4 4 . V

(39)

:

based on a water temperature of 15°C and published values

f

:

hull type (c: combatant, t: tanker, cc: container/cargo)

ir a

,

o .;;

Hull type and class

., (1)6703B CB=.79 (t), (2)6703B CB=.76 (Of Rank Special conditions

model 6703B equipped with a bow bulb; model(1) tested at fidl-load and model(2) tested

at ballast condition; both

configurations tested with and without a 6-bladed, fixed pitch, right-hand turning, model

propulsor; appendages

include rudder and propeller-boss for with-propeller configuration;

one plane of data taken for with and without rudder

condition and with rudder set at 0° and 3.5°

Measurements-4 Parameters 1 Forces/ moments Surface pressure Wave Profiles Wave elevations (longitudinal) Wave elevations (transverse) . Mean velocity Turbulence 8.11 mi a o U Froude No. -.167 (1) .167 (2) .167 (1) , .167 (2) .167 (1) .167 (2) .167 (1) .167 (2) ,Re No. (*106) t -7.94 (I) 7.94 (2) 7.94 (1) 7.94 (2) 7.94 (1) 7.94 (2) 7.94 (1) 7.94 (2) Fixed/free condition -. -fixed fixed fixed fixed Instrumentation

-argon-ion laser PSD camera CCD camera

servo-type probe 3-component ldv 3-component Idv Ph ysits propeller-hull mean-velocity

interaction; turbulence; and turbulence fields;

mean-velocity

hull-attitude

fields; wave

effects; effects of lifting

elevations; propulsor-effects

and no-lift rudder;

on wake near-free-surface elevations; flows . o-.

.

.4 Ts Meas. uncertainty

()

±.7nain

()

±1.25mm (U,V,W) .5,.5,.5% (ujuj) 5% a 0 Meas. accuracy 3 No. of stations -3 38 13 (1); 13 (2) 13 (1) 13 (2) p... 11 lii a a Co Location of stations -y/B=0,1.79,1.87 bow . 6 mid 10 stern 4 wake 18 bow 0 mid 0 stern 20 wake 6 bow o mid o stern 20 wake 6

No. of data points

-385 pts/m unknown =300 pts/st =300 pts/st Documentation 2 llTotal ranking, 14

Table B9: Database entry 7b.

Lpp

(40)

AP.0

Longitudinal coordinate /Loo 7 0.891

CONTOUR VALUES -vor,../I.up

Longitudinal. coot-di:note X/1..pp. 0.891

- TONING SPEED LI/VgLpp. - 0.167

SHAFT C.L. AT r/B - 0.000

AP

TOWING SPEED 1.1./../gLoo. - 0.167 0.0009;

SHAFT C.L. AT Yi8 - 0.000 AND 2/Ta - -0.183 MOOS 0.000+ 0.0001 0.0007 _ 0.0003 0.00010 0.0007 0.0001 o.00di) 0000 :0001 .000G -0.0002 -0.00025 -0:0003 ,0.000; 0.0004 0.00045 0.0005 35 1.10 AND 2/To -0.483 1.08 1.06 1.04 1.02 1,00 0,98 n 0.96 0.94 s 092 0.90 x 0.88 0.86 0.84 0.82 0.80 0.78 0.76 0.74 0.72 0.70 _ -0.2 0-0 0.2 0.4 0.6 0.8 TRANSVERSE CO-ORDINATE (H) Figure B9 Typical results for database entry 7h.

0.6

-0.6 0.0 0.2 0.4

(41)

:

based on a water temperature of 15°C and published values

t

:

hull type (c: combatant, t: tanker,-cc: container/cargo)

.

0 .0

v

a 0 r..)

Hull type and class

-W3969 C8=.82 (t), (2)3969 CB=.75 OA* Rank Special conditions

model 3969 equipped with a bow bulb; model()) tested at full-load and model(2) tested

at 'ballast condition; both

configurations tested with and without twin 5-bladed, fixed pitch, right- and left-hand turning (inward and

outward),

model propulsors; appendages include rudder, propeller-boss, shafting and

struts for with-propeller configurations

= Measurements) Parameters 1 Forces/ moments Surface pressure Wave .profiles Wave elevations (longitudinal) Wave elevations (transverse) veMloeca1nty Turbulence Froude No. -.172 (1) .172 (2) .172 (1) .172 (2) .172 (1) .172 (2) .172 (1) .172 (2) Re No. (4406)* -. 7.54 (1) 7.54 (2) 7.54 ' (1) 7.54 (2 7.54 (1) 7.54 2) 7.54 (1) 7.54 2 Fixed/free condition Instrumentation Physics

,

propeller-hull interaction; turbulence; mean-velocity fields; wave elevations; propulsor-effects

on wake elevations;

mean-velocity and turbulence fields; hull-attitude effects; effects of lifting and no-lift rudder; near-free-surface flows

it' Ts a Cy Meas. uncertainty .

()

±.7mm

()

±1.25mm (U,V,W) .5,.5,.5% (uini) 5% Meas. accuracy I>, = es 0 Cs .No, of stations -_ 2 39 19 (1) 7 (2) 19 (1) 7 (2) ,Location of stations ' -y/B=0 , 1.64 bow 7 mid 9 stern 4 wake 19 bow 0 mid 0 stern 20 wake 6 bow 0 mid 0 stern 20 , wake 6

No, of data points

-385 pts/m unknown ..200 pts/st 200 pts/st

Documentation Total ranking-4

13

Table B10: Database entry 7c.

1,pp

5.842m

Up

(42)

AP. 0 -0.1 coorcEnele ycpp 1.969 rp.20 0.1 0.3 0.5 0.7 0.9 1.1 _ TRANSVERSE CO-ORDINATE t M

Figure B10 Typica1 results for database entry 7c.

37

TOWING SPEED Ue

/4110, - 0.172 10,5

SWIFT CA:. AT l/8 - 0.128 AND Z/To -0.578 10.0

9.5 9.0 8.5 8.0 7.5 7.0 6:5 6.0 5.5 5,0 4.5 4.0 3,5 Q 2.5 A1.5 . 1.0 ow 065 1

(43)

Table B 1 1 :

Database entry 7d.

a

,

a, ;14

Hull type and class Special

conditions

Measurements*

a

Parameter4 Froude No.

,

.es a 01,

Re No. (.106)* Fixed/free

condition

Instrumentation Physics Meas.

uncertainty

Meas. accuracy No. of stations ,Location

of stations

No. of data points Documentation

(06732 CB=.69 (cc), (2)6732 CB=.64

(cc)t

model 6732 equipped with a bow bulb; model(1) tested at full-load and model(2) tested

at trim condition; both

configurations tested with and without a 4-bladed, fixed pitch, right-hand turning, model propulsor;.

appendages

include rudder and propeller-boss for with-propeller configuration

Forces/ moments Surface pressure Wave profiles Wave elevations (longitudinal) Wave elevations (transverse) Mean veloci'ty Turbulence .263 (1) .263 (1) . .263 (2) .263

(2)263

(1) .263 (1) 11.71 (1) 11.71 (1) 1 11.71 (2) 11.71

(2)1.71

(1) 11.71 (1) fixed fixed fixed fixed

argon-ion laser PSD camera

servo-type 3-component 3-component CCD camera probe ldv ldv Total ranking-3 13

based on-a water temperatureof 15°C and published values

:

hull type (c:. combatant,

tanker, cc: container/cargo)

Lpp Uc

(44)

Ps0 tO 0 , _ -0.6 -0.4 La2690.udLnet_600dLnate. 1-.7611 TR0045vERSC COmP0NENT

vERTIc0L COmP0NENT -u1.L00:1

rs, Longitudinal coo-di-note X/Lpp - 1.761' 0.2 P 26

---10.0005 y. .6 y .a. A A A ' stl,

.

V / 4 T A 44 A *

i

r . 44 I p i, 4 1 4 v TWIN 5PCt0 - 0.263

SHAFT C.L. AT T/B - 0.000 AND Z/TO '-0.573

0.6 , 0.0

CONTOUR VALUES ,.1.L/1U:1 TONING SPEED11/./gLpp. - 0..263

5HArT C.L. AT x/p 0.000 040057 AND Z/Ta - -0.5730.0005 0.000* 0,0004 0.00031 0.0003 0 0.000a 0.0002 .0.000k 0.0001 *.0.0000 -0.0000: 1,0001 -!0,0010r 70.0002 -0,000z -0.0003 0,0007 0.0001 60.0004,. -0.0005 , -0.4 -0.2 0.0 0.2 OA 0.6 TRANSVERSE CO-ORDINATE ( mI

Figure B11 Typical results for database entry 7d.

1.0 39 E Li . CC

0

I IQ c) C.) CC

i

.

.. 4 .4 11

1-'

A 0.

.

.

4

i

. 4

.

(45)

:

basecLon a water temperature of 15°C and published values

:

hull type (c: combatant, t: tanker, cc: container/cargo)

Table 1312: Database entry 7e.

Lpp Uc

5.25m 2.0m/s

Hull type and class Special

conditions

model 6732 equipped with a bow bulb; model(1) tested at full-load and model(2) tested at trim condition; both configurations tested with and without a 6-bladed, fixed pitch, right-hand turning, model propulsor; appendages include rudder and propeller-boss for with-propeller configuration

V/ PO Measurements, 'Pararneters.i. Forces/ moments Surface pressure Wave profiles Wave elevations (longitudinal) Wave elevations (transverse) Mean velocity Turbulence! Froude No. .279 (1) .279 (2) .279 (1) .279 (2) .279 (I) .279 (1) Re No. (*406)* 10.42 (I) 1042 (2) 10.42 (1) 10.42 (2)' 10.42 (I) 10.42 (1) Fixed/free condition fixed fixed fixed fixed Instrumentation

argon-ion laser PSD camera CCD camera servo-type probe 3-component ldv 3-component ldv Physics

,propeller-hull interaction; turbulence; mean-velocity fields; wave elevations; propulsor-effects on wake elevations; mean-velocity and turbulence fields; hull-attitude effects

2 a es A .LT4 CY Meas. uncertainty ±.7mm ±1.25mm (13,V,W) (tqui) 5% 3

Meas. accuracy No. of stations

36 12 (1) 12 (1) Location of stations y/B=0,2 bow 6 mid 7 stern 4 wake 19

bow mid stern

9 wake 3 bow mid 0 stern 9 Wake 3 3

No. of data points

250 pts/in

unknown

-180 pts/st

.,180 pts/st

Documentation Total ranking*

13

(1)6772 C11=.61 (cc), (2)6772 CB=.55

(cc)f

(46)

-APE°

no

a Longitudinal coordinate %/Lop 0.667

7:)

F.P 20

TralmsvER5E COKPONCHT u/18.1TOWNS SPEED 11././gLap. - 0.279

VERTICAL COMMENT ./03.) [ SHAFT C.L. AT T/8 ... 0.000 10.1 .4.--.v ' R

't

11t, vie 4, 0' $ 1 . . I 71;"77 . -30 ' 0 : . r . . .

ir I

4 4 .. .. . 4 ..e...e-. ..e...e-. . .

viii

..

.

. . 4,7 3. ,.., 11 1 _ 1 ' -0.6 -0.1 -0.2 0.0 0.2 OA

TRANSVERSE CO-ORDINATE IM)

Figure B12 Typical results for database entry 7e. 0.6 AP 41 -0...I-- : 'a y

i

r 1. 11 if

.

4 A 4 44 4 4 1

.

. 0.8 1.0 AND TiTa -0.564

(47)

0 0

based on a water temperature of 15°C and published values hull type (c: combatant, t: tanker, cc: container/cargo)

w, 0 o ... ./.4 V a 0 C..)

Hull type and class

.. (I)6499 CB=.62 (cc), (2)6499 CB=.61 (cc)t Rank Special conditions

model(1) equipped with

a bow bulb; model(2) not equipped with a bow bulb; model(I) and(2) tested at trim condition;

both configurations tested with and without twin 4-bladed, fixed pitch,

right- and left-hand turning (inward and

outward), model propulsors; appendages include rudder, propeller-boss, shafting and

struts for with-propeller.

configurations Measurements) Parameters1 Forces/ moments Surface pressure Wave profiles Wave elevations (longitudinal) Wave elevations (transverse) Mean Turbulence Froude No. -.278 (1) .278 (2) .278 (I) .278 (2) .278 (1) .278 (2) .278 (1) .278 (2) Re No. (*406)* -10.47 (1) 10.47 (2) 10.47 (1) 10.47 (2) 10.47 (1) 10.47 (2) 10.47 (1) 10.47 (2) Fixed/free condition -fixed fixed fixed fixed Instrumentation

-argon-ion laser PSD carnera CCD camera

servo-type probe 3-component ldv 3-component ldv Physics

bow flow and fields; wave elevations; effects; effects bow-geometry of propeller-rotation

propulsor-effects

effects on the macro

on

direction on

flow field; propeller-hull

wake elevations; wave elevations and

interaction;

mean-velocity and

macro flow field

turbulence; turbulence fields; mean-velocity hull-attitude 2 a. .41.11 ' Ts a Co uncertainty (0 ±.7mm

()

±1.25mm ,(U,V,W) .5,.5,.5% (tquj) 5%

Meas. accuracy No. of stations

-_ 3 36 12 (1)1 9 (2) 12 (1) 9 (2) 3 , o.. :t. ro' a 0 CY Location of stations -y/B=0,1.96,2 bow 7 mid 5 stern 4 wake 20 bow 0, mid 0 stern 15 wake 6 bow 0 mid 0 stern 5 1 wake 6

No. of data points

-250 pts/m unknown -150 pts/st =150 pts/st Documentation 2 1 Total ranking) ll ' 13

Table B13: Database entry 7f.

Lpp

(48)

AP 0 niLcng.tud.noL cooedtriole X/Lpp - 1:991 ID 0 -0.1 _LbrO.Ludinoi. coordiricite X/Lpp 1.961 TRANSVERSE COMPONENT ./1141 VERTICAL COMPONENT ./1111 1 TONING 5PODO13/4/VgLpp. - 0.270 WW1 C.L. AT T/8 - 0.167 AND Z/To - -0.461 FP:20

CONTOUR VALUES ./U. l'OING WOO 14/./gLpp. = 0.278

SHAFT ST T/8 = 0.167 1.10 AND Z/To = -0.461 1.09 1.08 1.07 1.66 1.05 1.04 1.03 1..02 0 1.01 A 1.00 *0.99 0.98 0.97 0.96 0.95 0.94 093 0.92 0.91 0.90 43 Li F. CC CC: ry-10.1 * 0 A A 0 A E a E 4 .

VI..

I co-CD

/ 0

k . L3 : _J CC C.) + 41 A. 4 w A 1.0c;- 4( 0.1 0.3 0.5- 0.7 0.9 1.5 TRANSVERSE CO-ORDINATE (m)

Figure B13 Typical results for database entry 7f.

(49)

based on a water temperature of I5°C and published values hull type (c: combatant, t: tanker, cc: container/cargo)

Table B14: Database entry 7g.

Lpp

4.9059m

.5 a o

°

'Hull type and class

5762 CB=.51 (01'

Rank

'Special

conditions

model 5762 equipped with a transom stern and no sonar dome; tested

at full-load condition; tested with and without

twin 6-bladed, fixed pitch, right- and left-hand turning (inward and outward), model

propulsors; appendages include

rudder, propeller-boss, shafting and struts for with-propeller configurations

Measurements) Parametersi Forces/ moments Surface pressure Wave profiles Wave elevations (longitudinal) Wave elevations (transverse) Mean velocity Turbulence, Froude No. -.288 .288 .288 .288 Re No. (.1.106)* -9.74 9.74 9.74 9.74 Fixed/free condition -fixed fixed fixed fixed Instrumentation

-argon-ion laser PSD camera CCD camera

servo-type probe 3-component Idv 3-component Idv , 'Physics propeller-hull mean-velocity

interaction; turbulence; and turbulence fields;

mean-velocity effects of fields; wave propeller-rotation direction elevations; propulsor-effects on wave elevations on wake elevations; r.. 4..- 111 Meas. uncertainty (0 ±.7mm (0 ±1.25mm (U,V,W) .5,.5,.5% (up.° 5% 3 is CY Meas. accuracy 3 No. of stations -2 33 12 12 3' .,... co Location of stations -y/B=0,2 ,bow 7 mid 7 stern 4 wake 15 bow 0 mid 0 stern 9 wake 3 bow 0 mid 0 stern 9 wake 3

No. of data points

-250 pts/m unknown ..100 pts/st 100 pts/st Documentation . 2 Total ranking > I 13

(50)

ID

LongiLudtnol. mord-note X/Lpp - 0.102

CONTOUR VALUES all. TONING SPEEDA/../oLpp. - 0.283

SHAFT C.L. AT 1/8 - 0.250 45 1.20 AND Z/To - -1.199 1.18 1.16 1..14 1.12 1.10 1.08 1.06 1.04 a 1.02 1.00 0.98 A 0.96 0.94 0.92 46 0.90 0.88 0.86 0.84 0.82 0.80

CONTOUR WILMS IONto:.,:*.:1"/(u TONING SPEED 11././oLpp. - 0.288 20.5

SHAFT C.L. AT 1/8 - 0.250 AND Z/To - -1.199 19.5 18.5 17.5 +16.5 15.5 14.5 13.5 o 12.5 11.6 10.5 9.5 a 8.5 7.5 6.5 5.5 A 4.5 3.5 2.5 1.5 0.5 0.3 1:1.5 0.7 0.9 1.1 1.3 1.5 TRANSVERSE CO-ORDINATE ( M )

Pigure B14 Typical results for database entry 7g. Q.1

AP 0 " FP.20

-0.1 0.1 0.3 0.5 1.1 1.3 1,5

(51)

based on a water temperature of 15°C and published values hull type (c: combatant, t: tanker, cc: container/cargo)

Table B15: Database entry 7h.

Lpp 5.4029m = 2:0m/s , cal

:

..

1

o

0

Hull type and class

5452 CB=.47 (c)t

- ;Rank

Special

conditions

model 5452 equipped with a transom stern and a sonar dome only for wave profile measurements; tested at full-load condition; tested with and without a 4-bladed, fixed pitch, right-hand turning, model propulsor; appendages include rudder, propeller-boss, shafting and strut for with-propeller configuration

Measurements-+ Parameters 1 Forces/ moments Surface pressure Wave profiles Wave elevations (longitudinal) Wave elevations (transverse) Mean velocity Turbulence Froude No. -. -.275 .275 .275 .275 Re No. (*106)* -10.73 10.73 10.73 10.73 Fixed/free condition -fixed fixed fixed fixed Instrumentation

-argon-ion laser PSD camera CCD camera

servo-type probe 3-component ldv 3-component ldv Physics

bow, flow and bow-geometry effects on wave elevations; propeller-hull interaction; turbulence; mean-velocity fields; wave elevations; propulsor-effects on wake elevations, mean-velocity and turbulence fields

2 ' it,'

..

To 01 00 Meas. uncertainty

()

±.7mm (0 ±1.25mm (U,V,W) .5,.5,.5% (tqui) 5% 3 Meas. accuracy 3 No. of stations -2 33 13 13 st'

..

4.4 02 o 0' Location of stations -y/B=0 1.99 , bow 7 mid 8 Stern 4 wake 16 bow 0 mid 0 stern 9 wake 4 bow. 0 mid 0 stern 9 wake 4

No. of data points

-250 pts/m unknown 200 pts/st ..200 pts/st IDocumentation 2 Total ranking-> 13

(52)

,AP 0 ta 1 1 '0.6 Longi.Lud.naL coordLnote X/Lpp 7 1.203 TRANSVERSE COMPONENT v/11.111 VERTICAL COMPONENT ./111.1 10.1 111 4t 4 4

I

'VI 1 r P A A &

,

il 4( ..., . .6 E. 0,4 je. a 1 . . . .1..onti.LudOaL coordialate X/Lpp - 1,203 A 4 -0.4 -0.2 0.0 0.2 OA TRANSVERSE CO-OROINATE (M)

Figure B15 Typical results for database entry 7h. PP 20

Towpm sPpcp U/V9Lpp. - 0.275

SHAFT C.L. AT 1/13 - 0.000;

11

TRANSVERSE COMPONENT -uL,L/Im:1

VERTICAL COMPONENT o0/41:1 TONING SPEED U./VgLpp. -SHAFT C.L. RT 1/8 0.0000.275 AND Z/To - -0:884

0.6 AND Z/To -0484 47 0 LI CC

1

* * 76. )4 10.0005 4 is. al A )4 )4 )4 'IL V )4 4, CC 0 1144e/T4e' 7 .

0

---" de I O-W

W 1. 4

A A W 0.8 1.0 -0.6 0.0 0.2 0.6 0.8 1.0

Cytaty

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