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AN EXPERIMENTAL AND COMPUTATIONAL STUDY OF THE EFFECTS OF PROPULSION ON THE FREE-SURFACE FLOW 704 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 ASTERN OF MODEL 5415 An Experimental and Computational Study of the Effects of Propulsion on the Free-Surface Flow Astern of Model 5415 T.Ratcliffe (Naval Surface Warfare Center, Carderock Division, USA) ABSTRACT Experimental measurements of the Kelvin wake, and the near- and far-field wave field, both with and without the model propeller operating, were obtained from a surface ship model representing the preliminary design of the DDG-51 hull form, represented by DTMB Model 5415. Wave height measurements were performed in the Carriage II basin at David Taylor Model Basin (DTMB) using two different techniques. The first technique uses capacitance probes attached to the side of the model basin to obtain longitudinal wave cuts. The second technique uses mechanical probes attached to a traversing system at the stern of the model to measure the surface wave field behind the model. The data from the mechanical probes are used to generate a wave height topography map. The results from both measurement techniques are used as a basis for comparison with computational fluid dynamics (CFD) predictions. Free-surface predictions from Mississippi State University's UNCLE code, with a. propeller body force-model incorporated, are documented and the trends are compared with the experimental data. INTRODUCTION An ONR Free-Surface Flow Initiative for validating and transitioning to industry Reynold's Averaged Navier Stokes and Potential Flow computational codes was begun in 1995. Model 5415 was chosen as a representative naval combatant hull form on which a rigorous set of experimental data would, be obtained. The model has been tested both bare hull and appended. The data base includes bare hull resistance and wave field measurements, nominal wake velocities obtained with pitot tubes as well as velocities astern of the operating propeller measured with Laser Doppler Velocimetry The data base can be accessed from the Model 5415 web site at http://www50.navy.mil/5415. This paper documents the free- surface wave height data obtained on the appended model, both with and without the propellers operating. As part of the ONR Free-Surface Initiative, computations of the free surface flow and sub-surface velocities were obtained on the bare hull model with two RANS prediction codes, UNCLE and University of Iowa's CFDSHIP. In addition to the RANS predictions, potential flow codes including SWAN, LAMP, and UMDELTA, were also used to predict the free surface flow around the model. The results of this effort along with descriptions of the prediction codes are documented in Ratcliffe (1998). MODEL DESCRIPTION Model 5415 was built of wood in 1980 to a linear scale ratio of 24.824 and is representative of a modern naval combatant hull form. Electronic files representing the geometry of the hull form, both bare hull and with appendages can be downloaded from the Model 5415 web site. Figure 1 shows a photograph of the stern of the model, fully outfitted for this experiment with removable appendages (shafts and struts). The model has twin rudders which are set at an angle of zero degrees relative to the model centerline. The model was not fitted with bilge keels. Turbulence stimulator studs 3.2 mm in diameter and 2.5 mm in height were fitted to the model in accordance with Hughes and Allen (1951). Figure 1—Model 5415 with Removable Appendages (shafts and struts) the authoritative version for attribution. During the propelled experiments, the model was fitted with design propellers designated as DTMB

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AN EXPERIMENTAL AND COMPUTATIONAL STUDY OF THE EFFECTS OF PROPULSION ON THE FREE-SURFACE FLOW 705 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 ASTERN OF MODEL 5415 propellers 4876 and 4877. These represent 5.49-meter full-scale diameter propellers. A photograph of the propellers on the model is shown in Figure 2. Figure 3 shows an isometric view of the appended model. Table 1 provides model dimensions and other particulars. Figure 2—DTMB Propellers 4876 and 4877 on Model Figure 3—Isometric View of Model 5415 EXPERIMENTAL PROCEDURES The experiments described herein were obtained both with and without the propellers operating. To obtain the most accurate free-surface measurements, in these experiments the model was mounted in a fixed trim condition corresponding to the running trim of the model at a Froude number of either 0.28 (2.06 m/sec) or 0.41 (3.10 m/sec). When the measurements were obtained with the propellers operating, the propeller RPM was set at the ship self-propulsion point. A table of operating conditions of the propellers during the propelled experiments is presented in Table 2. During these experiments, two techniques were used to measure wave heights generated by the model. The first technique measures longitudinal wave cuts using stationary capacitance probes fixed to the side of the basin. The second technique measures wave heights in a rectangular area aft of the stern using mechanical whisker probes attached to the towing carriage aft, of the model. Table 1—Model 5415 Dimensions and Particulars Lambda 24.824 LBP, LWL 5.72 m Displacement 548.8 kg 4.92 m2 Appended Wetted Surface Sinkage at FP (Fn=0.28) −0.0027L Sinkage at AP (Fn=0.28) −0.00086L Sinkage at FP (Fn=0.41) −0.00054L Sinkage at AP (Fn=0.41) −0.0083L Propellers Port 4877 Starboard 4876 Propeller Diameter 22.10 cm Table 2—Propeller Operating Conditions (KT and KQ determined from open water tests; D is propeller diameter, n is revolutions per second) KT=T/(pD4n2) KQ=Q/(ρD5n2) Speed, V (m/sec) RPM J=V/nD 2.06 0.178 0.0461 436 1.28 3.10 0.232 0.0562 722 1.175 The following discussion of experimental procedures is divided by technique used, and then further divided into four sections; theory of operation, experimental setup, calibration, and operating procedures. LONGITUDINAL WAVE CUTS the authoritative version for attribution. Theory of Operation The sensing element of the capacitance probe is a 30-gauge (AWG) silver-plated copper wire with 0.11 mm kynar insulation, 38.1 cm in length. Attached to the sensing element is a weighted 1.21-m length of mylar fishing line, used to provide probe stability in waves. The sensing element is suspended with half its length submerged in the basin. The basin water provides the ground reference for the sensing elements on

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AN EXPERIMENTAL AND COMPUTATIONAL STUDY OF THE EFFECTS OF PROPULSION ON THE FREE-SURFACE FLOW 706 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 ASTERN OF MODEL 5415 the circuit card. With the copper wire completely insulated from the water, the sensing element behaves as a capacitor with one plate being the copper wire, the second plate the water, and the wire insulation acting as the dielectric. As waves in the basin change the submerged height of the sensing element, they change the effective capacitor plate size, which results in a change in capacitance. The change in capacitance is proportional to the wave height. By attaching the wave wire, a varying capacitor, to a timing circuit, a d.c. voltage is generated that is directly proportional to the capacitance of the probe and, therefore, the wave height being measured. Experimental Setup A wave boom (truss section), cantilevered from the basin wall over the water, provides a structure from which the instrumentation is mounted. The wave boom extends 6.83 m from the basin wall. A motorized uni-slide with an attached horizontal bar is mounted vertically on the wave boom. The capacitance probes' electronics are mounted on the horizontal bar of the uni-slide. The uni-slide allows precise placements of the probes' vertical position, probe emergence, used during static calibration of the probes. Figure 4 shows the longitudinal wave cut hardware in place in the basin. Two probes were used for this experiment. The placements of the probes are referenced to centerline of the model, with probe number 1 being inboard and probe number 2, outboard. The probe placements are provided in Table 3. A photo sensor is set to trigger data collection when the forward perpendicular of the model reaches a predefined distance from the wave probes. A 133 MHz Pentium-class computer, using an ADC488 16-bit analog to digital (A/D) converter, collects and stores the data. Table 3—Longitudinal Wave Cut Probe Locations Probe Number Transverse Distance from Model Centerline (y) y/B 1 0.56 m 0.73 2 15.44 m 2.44 Calibration Insitu calibrations are performed after the completion of the test setup. In order to calibrate the probes, the motorized uni-slide is traversed in 2.54-cm increments for a total of ±7.62 cm. Data is collected at each increment for each of the probes. A straight line fit is performed and a slope is calculated and stored for each probe. The insitu calibration permits calibration of the probes, the signal conditioning amplifiers, and the A/D converter as a system. Figure 4—Longitudinal Wave Cut Set Up Operating Procedures Probe zeroes are collected in calm water before each run. The model is then run past the probes at a constant speed. As the model approaches the test section, a strip of reflective tape positioned on the carriage triggers a photosensor placed at the side of the basin which starts data collection. The position of the photosensor and the duration of data collection is adjusted to insure that the maximum amount of data is collected before tank wall reflections occur. Data is filtered at 10 Hz with a 3 pole Bessel filter and collected at a sampling rate of 100 Hz for 20 to 30 seconds depending on model speed and photosensor position. Data analysis is performed on the PC after each run. First, calibrations are applied to the A/D voltages, and then the probe zeroes are subtracted. The data from each probe is then plotted to ensure that the measurements are of good quality. Further analysis on the longitudinal wave cut data is often performed in order to compute free wave spectra and wave pattern resistance. STERN TOPOGRAPHY Theory of operation The whisker probe is a vertically oriented, mechanical probe, that continuously searches for the free surface. The sensing element of the probe is a 0.38 mm diameter, 5.08 cm long stainless steel wire. The wire is mounted in a copper tube that makes up the body of the probe. A geared rack, attached to the probe body, allows the probe to be driven up and the authoritative version for attribution. down, vertically, by a servomotor. Opening and closing a circuit between the probe and the water is sensed by an electronic circuit which drives the servomotor. When the probe is not in contact with the water surface there is an open

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AN EXPERIMENTAL AND COMPUTATIONAL STUDY OF THE EFFECTS OF PROPULSION ON THE FREE-SURFACE FLOW 707 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 ASTERN OF MODEL 5415 circuit and the servomotor drives the probe down towards the surface of the water. Once contact is made between the probe and the surface of the water, a closed circuit is sensed and the probe is driven up, out of the water. This process is repeated continuously, causing the probe to oscillate around the free surface at approximately 20 Hz. The probe is connected to a potentiometer that tracks its position along the z-axis (wave height). Probe position is recorded by a sample and hold circuit during the instant the probe makes initial contact with the water surface. This manner of sampling probe position alleviates position error from meniscus effects, due to surface tension. Experimental Setup To create a topography of the free surface at the stern of the model, four probes are mounted together on a bracket attached to a uni-slide. The probes are oriented in the longitudinal direction, parallel to the centerline of the model, with a 5.08 cm spacing between probes. The probes operating behind Model 5415 can be seen in Figure 5. The array of probes are attached to an XY-traverse that is mounted to the carriage at the stern of the model. Two string pots attached to the traverse are used to track the longitudinal (X) and transverse (Y) positions of the probes. A 133 MHz 486 computer, using an ADC488 16-bit A/D converter, collects and stores the data. The data collection computer is networked with a 350 MHz Pentium II laptop computer that is used for data analysis and plotting. Data are filtered at 10 Hz with a 3-pole Bessel filter and collected at a sampling rate of 100 Hz. Figure 5—Whisker probes operating behind Model 5415 Calibration Static calibrations are performed on the whisker probes in the lab, prior to the experiment. The probes are positioned over a container of water, and allowed to track the calm free surface as the uni-slide is traversed in 2.54-cm increments for a total of ±7.62 cm. Data is collected at each increment for each of the probes. A straight line fit is performed and a slope is calculated and stored for each probe. Operating Procedures The forward most probe is aligned longitudinally (X) and transversely (Y) with the aft perpendicular and centerline of the model respectively. The longitudinal and transverse string pots are zeroed at this location, and all future measurements are referenced to this position. In order to collect the data needed to generate a complete topography of the stern area, the area is divided into a number of transverse cuts. One transverse cut collects an area of 15.24 cm by 1.32 m. Starting as close to the stern of the model as possible (1.27 cm), successive transverse cuts are made with an advancement of 20.32 cm along the x-axis between cuts. For this experiment the completed mapped area measured 1.32 m by 2.38 m. The possible number of transverse cuts per run is dependent on model speed. Once the number of traverse cuts per run is determined, a command file is generated which controls the positioning of the probes during the run. Prior to each run a zero collection is performed. A zero run consists of performing an identical collection run of transverse cuts, but with the model stationary. This procedure eliminates bias errors due to misalignment or sagging of the traverse's XY- plane relative to the surface of the water, which should be parallel to one another. After the zero run is performed, the model is brought up to a constant speed and a collection of transverse cuts are started. This process is repeated at successive transverse locations until the desired area behind the model has been completely mapped. Analysis of the stern topography data is done by applying the calibration factor to the A/D voltages from the at-speed data and the zero-speed data, and then subtracting out the zero-speed data to produce a set of zero-compensated data. Next, filter coefficients are calculated for a Butterworth filter with an optional number of poles, chosen by the user (in this case, 3 poles were specified.) The zero compensated probe data is then filtered in both directions to eliminate data phase shifts. The next step before plotting, is to extract data from the data, set. A grid pattern is established with an x-value at every longitudinal probe position and a y-value which starts at the beginning of each transverse probe position and extends to the ending probe position, in increments of 0.5 cm. Probe data closest to the desired grid locations are extracted from the data set and saved. These data are then placed into a format for the authoritative version for attribution.

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AN EXPERIMENTAL AND COMPUTATIONAL STUDY OF THE EFFECTS OF PROPULSION ON THE FREE-SURFACE FLOW 708 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 ASTERN OF MODEL 5415 plotting the stern topography contour maps, using TECPLOT software. It is important to note that these contour maps represent the average of a time-varying data set with an RMS variation about the mean contour level. PRESENTATION OF RESULTS The coordinate system for the measurements is difined with the x-axis being parallel to the model centerline, the y- axis athwartships and the z-axis perpendicular to the calm water surface. All data and axes have been non- dimensionalized using the model length. The forward perpendicular is denoted at x/L=0, and the aft pependicular as x/ L=1.0. Longitudinal Wave Cut Measurements Longitudinal wave cuts for Model 5415 with and without propellers operating, at Froude numbers of 0.28 and 0.41, are shown in Figures 6 and 7. A longitudinal wave cut can be characterized by four waves or wave systems. The first wave is the “bow wave,” generated by the bow and shoulder. The bow wave is followed by the waves generated along the mid-body, followed by a “stern wave,” generated by the stern. Lastly a set of transverse waves decaying behind the model are observed. At a Froude number of 0.28, at the inner probe location of y/B of 0.73, the effect of propulsion is dominant in the transverse wave system aft of the model. With the propellers operating at 436 RPM, there is a 10 percent increase in the transverse wave heights over the unpropelled case. The effect of the operating propeller is particularly noticeable in the amplitude of the stern wave, which is augmented by 20 percent. At the outer probe location (y/B is 2.44) the effect of propulsion on the stern wave is less; only accounting for an increase of 10 percent. There is also a noticeable phase shift in the transverse wave system between the unpropelled and propelled condition. The transverse wave system of the propelled model is shifted aft by 12 percent of the transverse wave length (2πV2/g). This phase shift is more evident at large values of x/L. At a Froude number of 0.41, where the propellers operate at 722 RPM, propulsion has a minimal effect on the wave system, accounting for only a 6 percent increase in the stern wave amplitude and 2 percent increase in the amplitude of the transverse wave system at the inner probe location. At the outer probe location, propulsion accounts for a 9 percent increase in the stern wave amplitude and a negligible increase in the amplitudes of the transverse wave system. At this speed, the large stern wake is dominated by the flow around the transom stern, so the effect of the operating propellers is less evident than at a Froude number of 0.28. The effect of propulsion on the longitudinal wave cuts generated by a model representing another combatant hull form has been shown to be larger than seen here for Model 5415. This data set is presented in Lindenmuth and Ratciffe (1989). Stern Topography A comparison of the propelled and unpropelled near-field wave systems at a Froude number of 0.28, measured with the whisker probe, is shown in Figure 8. The difference between, the two conditions has been quantified in Figure 9. Propulsion increases the wave amplitudes along the stern wave crest line on the order of 35 percent. In the region behind the stern, between an x/L of 1.05 and 1.15, propulsion effects account for local increases in wave heights of 25 to 35 percent. At this Froude number the flow is still attached to the transom. At a Froude number of 0.41, the transom is completely clear (dry) and the flow converges in a highly turbulent region covering an area of 0.15 ship lengths, longitudinally by 0.05 ship lengths, transversely. Figure 10 shows the differences due to propulsion in the wave field behind the transom at a Froude number of 0.41. Figure 11 serves to quantity those differences. The differences due to propulsion at this the authoritative version for attribution. Figure 6—The Effect of Propulsion on the Far-field Wave System as Measured with Stationary Capacitance Probes, at a Froude number of 0.28

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AN EXPERIMENTAL AND COMPUTATIONAL STUDY OF THE EFFECTS OF PROPULSION ON THE FREE-SURFACE FLOW 709 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 ASTERN OF MODEL 5415 higher Froude number are more scattered over the complete stern area than was the case for the Froude number of 0.28. The effect of propulsion accounts for differences on the order of 20 percent in two regions; along the stern wave crest and, aft of the transom. The area aft of the transom, located at an x/L of 1.2 is farther downstream than the affected area at a Froude number of 0.28. At this higher Froude number, the propellers have a smaller effect on the stern wave system than they do at a Froude number of 0.28. Figure 8—The Effect of Propulsion on the Near-field Wave System of Model 5415 as Measured with Whisker Probes, at a Froude Number of 0.28. Figure 7—The Effect of Propulsion on the Far-field Wave System as Measured, with Stationary Capacitance Probes, at a Froude number of 0.41 Figure 9—Stern Topography Differences (Propelled- Unpropelled) in the Near-field Wave System of Model 5415 at a Froude number of 0.28 Figure 11—Stern Topography Differences (Propelled- Figure 10—The Effect of Propulsion on the Near-field Unpropelled) in the Near-field Wave System of Model Wave System of Model 5415 as Measured with Whisker 5415 at a Froude Number of 0.41. Probes, at Froude Number of 0.41. the authoritative version for attribution.

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AN EXPERIMENTAL AND COMPUTATIONAL STUDY OF THE EFFECTS OF PROPULSION ON THE FREE-SURFACE FLOW 710 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 ASTERN OF MODEL 5415 MEASUREMENT UNCERTAINTY Measurement uncertainty has been determined for both the longitudinal wave cut and whisker probe data, at each of the two speeds where data were obtained. The analysis is in accordance with standard uncertainty analysis practices of the “Guide to the Expression of Uncertainty in Measurement” as documented in 1993 by the International Organization for Standardization (ISO), and explained further in ANSI/ASME (1998) and the AIAA Standard (1998). Detailed explanations and examples of the uncertainty analysis are given Coleman and Steele (1998). For each speed and condition at which wave cuts were conducted, a mean wave was calculated from the repeat passes that were collected. The mean wave from these repeat passes was calculated by averaging Z/L (the wave heights), at each X/L, (the longitudinal distance from the aft perpendicular). Seven repeat passes were collected at a Froude number of 0.28 for the propelled and unpropelled condition, and eight repeat passes were collected at a Froude number of 0.41. For the whisker probe data, transverse cuts were used to calculate the mean waves in the transverse direction (Y/L). Six repeat runs were obtained at a Froude number of 0.28 and nine at a Froude number of 0.41. The precision limits are based on the standard deviations of the wave. The standard deviation at each X/L or Y/L location is calculated when the mean wave is averaged from the repeat passes. The standard deviations across the whole wave are multiplied by the proper student-t value scalar from the 95% certainty curve to produce the precision limits. These precision limits, vary with the position in the wave, usually greater at the crests and troughs of the wave than at the zero-crossings. The bias limit is determined by calibrations done insitu and are a scalar applied across the entire mean wave. The uncertainty is computed by the root-sum-square of the bias and precision limits (also commonly referred to as the systematic and random errors). The combined uncertainty for the propelled and unpropelled condtions are presented in Table 4. COMPUTATIONS Computations were performed with the UNCLE code from Mississippi State University. This time-accurate, steady incompressible RANS code has been used extensively to compute the free-surface flow field around surface ship models. (Beddhu, 1998). A propeller body force model was introduced in the code to compute the free-surface elevations with an operating propeller. This body force-model was run for the Froude number of 0.28 condition. The body force propulsor module in UNCLE is based on the model of Yang, Hartwich and Sundram (Yang, 1990). The prescribed body forces are based on the thrust and torque coefficients as well as an assumed circulation distribution. An adequate number of grid points must be present in the propeller plane to ensure good results. The results are shown in Figure 12. In the region aft of Table 4—Summary of Measurement Uncertainty for Longitudinal Wave Cuts and Stern Topography at Two Froude Numbers Bias Error (% of total Precision (Random) Error (% Total Uncertainty (% of largest uncertainty) of total uncertainty) value) Fn=0.28 86.0 14.0 2.73 Longitudinal Wave cuts 64.8 35.2 4.60 Stern Topography Fn=0.41 66.4 33.6 3.54 Longitudinal Wave cuts 32.4 67.6 9.20 Stern Topography the authoritative version for attribution. Figure 12—UNCLE Free-surface Computations at Fn=0.28 Without (Top) and With (Bottom) Propeller Body Force

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AN EXPERIMENTAL AND COMPUTATIONAL STUDY OF THE EFFECTS OF PROPULSION ON THE FREE-SURFACE FLOW 711 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 ASTERN OF MODEL 5415 the stern there is an increase in the amplitude of the waves, although not over as great an extent as is seen in the experimental data. The body force-model also predicts an increase in the amplitude of the stern wave crest. The magnitude of this increase is consistent with that seen in the measurements obtained at a similar Froude number. CONCLUSIONS This data provides a comprehensive documentation of the effect of propulsion on the wave system around a naval combatant hull form. The use of both near- and far-field measurement systems results in a thorough mapping of the wave field around this hull form. The data presented here shows that there is a greater effect of propulsion on the wave system near the model at Froude number of 0.28 than at a Froude number of 0.41. It is likely that this is due to the different nature of the hydrodynamic flow at each of these Froude numbers. At a Froude number of 0.28, the flow is still attached to the transom and the effect of the operating propellers is to change the character of the local wave system. This change is manifested as an increase in the maximum wave heights along the stern wave crest line and an increase in the wave heights behind the model. At a Froude number of 0.41, where the transom is dry, the flow field is dominated by the flow at the edges of the transom converging astern, and the effects of the operating propulsor are smaller than were observed at a Froude number of 0.28. UNCLE computations with propeller body force show similar trends of the effect of propulsion on the wave system as the experimental data. There is a visible increase in the amplitude of the stern wave crest and an increase in the amplitudes of the waves in the region astern of the model. It is hoped that this data will continue to provide an insight into the effect of propulsion on the hydrodynamic flow around transom stern models, and will be used to evaluate the way in which computational fluid dynamics prediction codes model propulsors in the computations. ACKNOWLEDGEMENTS The author wishes to thank Jim Rice and Ian Mutnick for their support during the collection of these data sets. Scott Percival and Steve Fisher helped prepare the figures for this paper. Much appreciation goes to William Boston and Peter Congedo documented the hull form and the hydrodynamic flow, photographically. Finally, I would like to thank Edwin Rood at the Office of Naval Research for his vision which recognized the contributions that CFD predictions could make to ship design and his commitment to obtaining the best possible experimental data for validation of these prediction codes. REFERENCES AIAA (1998), AIAA Standard S-071–1005, Assessment of Wind Tunnel Data Uncertainty. ANSI/ASME (1998) Standard PTC 19, Test Uncertainty. Beddhu, M., Y.Jiang,, D.L.Whitfield, L.K.Taylor, and A.Arabshahi (1998) “CFD Validation of the Free-surface Flow Around DTMB Model 5415 Using Reynolds Averaged Navier-Stokes Equations,” Third Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Design, Osaka, Japan. Coleman, H. C, and W.G.Steele, (1998) Experimentation and Uncertainty Analysis for Engineers, 2nd Ed. Hughes, C. and J.F.Allen (1951) “Turbulence Stimulation on Ship Models,” SNAME Transactions, Vol. 59. Lindenmuth, W., and T.J.Ratcliffe (1989) “Kelvin Wake Measurements Performed on Five Surface Ship Models,” DTRC-89/038. Ratcliffe, T. (1998) “Validation of Free-Surface Reynold's Averaged Navier Stokes (RANS) and Potential Flow Codes,” 21st Symposium on Naval Hydrodynamics, Washington, D.C., 1998. Yang, C-I, P.M.Hartwich, and P.Sundram (1990) “A Navier-Stokes Solution for Hull-Ring Wing-Thruster Interaction,” Eighteenth Naval Hydrodynamics Symposium, University of Michigan, Ann Arbor, MI. the authoritative version for attribution.

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AN EXPERIMENTAL AND COMPUTATIONAL STUDY OF THE EFFECTS OF PROPULSION ON THE FREE-SURFACE FLOW 712 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 ASTERN OF MODEL 5415 DISCUSSION H.Chun Pusan National University, Korea. When you measured the wave profiles, were the models free or fixed? If the models were free, were the sinkages and trims of the two model conditions with and without the propellers the same as each other? If they are the same, how did you adjust them? AUTHOR'S REPLY Thank you for your important questions regarding the sinkage and trim of Model 5415. For both the longitudinal wave cut experiments and the stern topography experiments, the model was fixed at a sinkage and trim corresponding to the trim the model would achieve at a given Froude number. The fixed trim was chosen to be that assumed by the unpropelled model.. The model was then fixed at this same trim when the propellers were operating. Obtaining data around the model at the same trim condition, with and without propellers operating provided a self-consistent set of data for CFD validation. the authoritative version for attribution.