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Twenty-Fourth Symposium on Naval Hydrodynamics (2003)

Chapter: Bow Waves on a Free-Running, Heaving, and/or Pitching Destroyer

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Suggested Citation:"Bow Waves on a Free-Running, Heaving, and/or Pitching Destroyer." National Research Council. 2003. Twenty-Fourth Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press. doi: 10.17226/10834.
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Suggested Citation:"Bow Waves on a Free-Running, Heaving, and/or Pitching Destroyer." National Research Council. 2003. Twenty-Fourth Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press. doi: 10.17226/10834.
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Suggested Citation:"Bow Waves on a Free-Running, Heaving, and/or Pitching Destroyer." National Research Council. 2003. Twenty-Fourth Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press. doi: 10.17226/10834.
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Suggested Citation:"Bow Waves on a Free-Running, Heaving, and/or Pitching Destroyer." National Research Council. 2003. Twenty-Fourth Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press. doi: 10.17226/10834.
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Suggested Citation:"Bow Waves on a Free-Running, Heaving, and/or Pitching Destroyer." National Research Council. 2003. Twenty-Fourth Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press. doi: 10.17226/10834.
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Suggested Citation:"Bow Waves on a Free-Running, Heaving, and/or Pitching Destroyer." National Research Council. 2003. Twenty-Fourth Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press. doi: 10.17226/10834.
×
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Suggested Citation:"Bow Waves on a Free-Running, Heaving, and/or Pitching Destroyer." National Research Council. 2003. Twenty-Fourth Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press. doi: 10.17226/10834.
×
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Suggested Citation:"Bow Waves on a Free-Running, Heaving, and/or Pitching Destroyer." National Research Council. 2003. Twenty-Fourth Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press. doi: 10.17226/10834.
×
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Suggested Citation:"Bow Waves on a Free-Running, Heaving, and/or Pitching Destroyer." National Research Council. 2003. Twenty-Fourth Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press. doi: 10.17226/10834.
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Suggested Citation:"Bow Waves on a Free-Running, Heaving, and/or Pitching Destroyer." National Research Council. 2003. Twenty-Fourth Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press. doi: 10.17226/10834.
×
Page 220
Suggested Citation:"Bow Waves on a Free-Running, Heaving, and/or Pitching Destroyer." National Research Council. 2003. Twenty-Fourth Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press. doi: 10.17226/10834.
×
Page 221
Suggested Citation:"Bow Waves on a Free-Running, Heaving, and/or Pitching Destroyer." National Research Council. 2003. Twenty-Fourth Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press. doi: 10.17226/10834.
×
Page 222
Suggested Citation:"Bow Waves on a Free-Running, Heaving, and/or Pitching Destroyer." National Research Council. 2003. Twenty-Fourth Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press. doi: 10.17226/10834.
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24th Symposium on Naval Hydrodynamics Fukuoka, JAPAN, 8-13 July 2002 Bow Waves on a Free-Running, Heaving And/or Pitching Destroyer Howard B. Markle and T. Sarpkaya (Naval Postgraduate School, USA) ABSTRACT Measurements of the near-surface evolution of the bow wave were made on a 1/250-scale model of a destroyer and compared with those obtained from the sea tests of the subject destroyer wherever possible. The effects of steady motion, heave, pitch and combinations thereof were subjected to controlled experiments to quantify the base flow in comparison to the prototype. The Froude Number for the majority of the runs was 0.26. Model scale frequencies ranged from 1 to 5 Hz, pitch angles from 0.85 degrees to 3.75 degrees and heave amplitudes from 3 mm to 15 mm. This resulted in a large amount of data. Here only the most relevant and most unexpected ones are discussed in some detail. Emphasis is placed on the bow region where a ship's character is prescribed. The model and the prototype data are shown to be in good agreement and are expected to serve as a step towards the validation of full-scale ship codes and the improvement of the performance of such ships through additional physical and numerical experiments. INTRODUCTION Brief Review The interaction of a ship with the ocean gives rise to numerous complex phenomena, dictated primarily by the shape and motion of the bow. The breaking of bow waves is a significant fraction of the resistance experienced by the ship. It is because of these reasons that warships, in particular, and commercial ships, in general, have been studied for many years. The present investigation concerns itself with a typical destroyer. The ultimate objective of the systematic investigation is to minimize the wave resistance in all circumstances (free-run in waves, in random seas, in heave and pitch) and to reduce the spray formation, air entertainment and deck wetness. The shape of the destroyer bows and the sonar dome distinguish them from other commercial ships. An extensive search of the relevant literature have shown that there have been numerous studies particularly during the past 50 years to predict the bow wave and ship resistance (Miyata and Inui, 1984; Grosenbaugh and Yeung, 1989; Longo et al. 1993; Stern et al, 1996a; Fontaine and Cointe, 1997; Dong et al, 1997; Beddhu et al, 1998; Cusanelli, 1998; Larson et al, 1999; Subramani et al, 1999; Rhee and Stern, 2001). In the earlier years, no special emphasis has been placed on bow sheet separation and subsequent spray. Technological advances have necessitated higher speeds and increased protection from the adverse effects of spray, particularly on the deck. These efforts led to many physical and numerical experiments. The theoretical studies, while benefiting from the advent of the computer, were primarily concerned with 'thin ships' operating in inviscid fluids (see, e.g. Fontaine and Cointe, 1997; Wu et al, 2000; and the references cited therein). There is not, at present, a computer code that could predict the response of a destroyer in a random sea, the ship resistance, the bow waves, bow sheet separation, jet/spray formation, subsequent aeration, and the extent of the white water region in the wake of the ship in a viscous fluid with or without surfactants. However, significant advances have been made (Beddhu et al, 1998) towards the validation of the UNCLE solver with experimental results tthe flow field around Series 60 CB = 0.6 at Froude number of 0.316 (Stern et al, 1996b)] and by Rhee and Stern (2001) for the simulation of the boundary layer and wake and wave field for a surface ship advancing in regular head waves, but restrained from body motions, using an unsteady RAN S method.

It is with the full realization of the strengths and shortcomings of the existing contributions that a major investigation has been undertaken to delineate the characteristics of the bow wave on a typical destroyer tshown in Figure (1~] under a series of imposed motions (free running, heave, pitch as well as combinations of heave and pitch). The preliminary studies led to certain facts which have not been previously realized. These will now be described in some detail. An. Ace_ ~ ~~ - ~: - .... :~ t. ~ ~ ~ ~ , ~ . ... ! .. ... as_ ~e. ~ ~ ~ ~ 'a,—_ _~" - ~_ Figure 1: Bow wave and spray generation on a typical Destroyer (Fr= 0.264. Bow Wave, Sheet Separation, and Spray When a ship is in free run in a calm ocean, it has an imposed Froude number (Frs) given by equation (1) where Vs is the velocity of the ship, g is the gravitational acceleration and Ls is the length of the ship. V Frs = 3W (1) The resistance is also influenced by the effect of viscosity and surface tension. They are expressed as the Reynolds number (Res) and Weber number (Wes) in equations (2) and (3), respectively, where p is the density, v is the viscosity and ~ is the coefficient of surface tension. Re = pVSLs s ~ We = pV~ Ls (2) (3) Figure 1 shows that the bow sheet for the ship under consideration separates from the hull and gives rise to spray. In general, the ship Froude number, the shape of the ship (particularly the bow geometry), the sea state, and the type of motion of the ship determine the characteristics of the bow waves and spray generation and, hence, most of the wave resistance. However, all separated sheets do not give rise to spray. The local Froude, Weber, and Reynolds numbers, the hull curvature, and the surface roughness at or near the point of separation must exceed certain critical values. Obviously, the Froude number of the separated sheet is not an independent parameter and is uniquely determined by Frs and the other parameters cited above. The same is true for the local Weber and Reynolds numbers as shown by Sarpkaya and Merrill (2001~. The fact of the matter is that the Froude number of the ship is subcritical (Frs < 1) but the Froude number of the breaking sheet is supercritical. This leads to a well-known dilemma regarding the use of models. Since the physical properties of the fluid (p, c,, A) and g must be kept constant, the specification of the ship speed and length defines the Froude number. Thus, for identical model and ship Froude numbers (and physical properties), the Weber and the Reynolds numbers for the model are smaller by (Lm/Ls)2 and (Lm/Ls)3/2' respectively. Even for a model of 1/25 scale, the Weber and Reynolds numbers of the model are 625 and 125 times smaller, respectively, than those of the ship. Likewise, the specification of a supercritical Froude number and sheet thickness for the separated-sheet embodies all the effects of gravity, surface tension and viscosity. Thus, one realizes the existence of two Froude numbers that govern two distinctly different phenomena in two different regions of the ship. This mandates two 2

(related but separate) investigations in two separate facilities to examine the bow waves of a ship and the separation of the bow sheet with all of its attendant consequences. The result of utilizing a supercritical jet facility is seen in Figure 2. The sheet separates from the hull and breaks up into filaments and droplets. There are no other alternatives unless one wishes to conduct the experiments with very large models or with the actual ship itself under the influence of difficult-to-control environmental conditions. 1 _1115 Figure 2: Representative supercritical flow and spray generation about a bow model. As to the effect of the more complex motions, it is shown that one can extract the basic bow wave from all other time dependent motions (heave, pitch, yaw, etc.) experienced by the ship. Consequently, the delineation of the excursions of a given bow-wave above or below the maximum or minimum of the basic bow wave may be very important in assessing the operational resistance and total hydrodynamic performance of a ship and the spray generation as a function of the bow and sonar geometry. This fact has been effectively used by Cusanelli (1998) in improving the performance of near-surface bow bulbs in irregular waves. EXPERIMENTAL FACILITIES Experiments have been carried out in two distinctly different facilities. The first was for the purpose of understanding the breakup of a bow sheet and the formation of filaments and droplets, with or without the effect of surfactants (both soluble and insoluble in seawater). The second facility was for the purpose of characterizing the bow wave. A typical destroyer model was manufactured at the David Taylor Model Basin to 1/250 scale out of resin material utilizing a stereo-lithograph laser cutting system. These are described in some detail below. Supercritical Flow Facility A rectangular supercritical wall jet discharging into air from a carefully constructed nozzle was used to study the transition, surface deformation and filaments formation on the free surface with or without surfactants. The nozzle was supplied by a large water tunnel. Additional details about the facility are described in Sarpkaya and Merrill (2001~. The jet Froude numbers ranged from approximately 2 to 30 by varying the thickness and velocity of the jet over smooth and rough surfaces. The filaments and drop formations were photographed with several high- speed imagers, including a digital camera and an infrared laser. The data (filament geometry and drop size) were deduced through the use of suitable software in terms of the prevailing Froude, Reynolds, Weber, and roughness numbers for the jet. Bow Wave Facility The ship models were mounted at the test section of a recirculating water tunnel. A rendering of the tunnel is shown in Figure 3. __ _ 1 1 __ 1 ~ ~ __ 1 __ 1 ~ Figure 3: The recirculating water tunnel. At the top and to one side of the test section, two motors of appropriate characteristics were mounted and connected to the model to achieve heave and pitch motions that were independent or phase- coupled with one another. The base on which the 3

motors were mounted was pivoted to induce desired angles of yaw to the models. The speeds with which the tunnel operated corresponded to Froude numbers of 0.26 and 0.65. The majority of the data were taken at Frs = 0.26. The primary reason for this selection was the availability of video footage of the prototype destroyer in free-run tests in essentially calm seas with Froude numbers in the range of 0.26. This was of extreme importance for the comparison of the model and sea experiments for the verification of the quality of the model experiments and for the establishment of the shape of the bow wave at the speed chosen. The fluid motion, particularly in the bow region, was recorded on video and analyzed through the use of an analog to digital convertor. Fluorescein dye was used during the videoing of the bow wave to sharpen the ship/wave interface as shown in Figure (4~. Figure 4: Model of a typical destroyer (scale: 1/250) Each test run was evaluated at different times to minimize the errors in the measurement of tunnel speed, wave height, stem height and the unsteady oscillations of the wave surface on the ship bow. The edge ofthe wave climbs up the hull, wets the surface at some frequency, and gives rise to a string of 'pearls' crowning the top of the bow wave. Their small curvature reflects the light differently from the bow wave itself. The heave and pitch motions were conducted independently as well as in combination (with appropriate phase angle differences) in the range of heave and pitch amplitudes deemed to be most desirable. The establishment of the individual values will be discussed later. The data were evaluated at every frame (1/30-second intervals) for any given cycle of oscillation. This was done partly to assess the overall accuracy of the data and partly to account for the aforementioned, relatively small, free-surface oscillations. RESULTS AND DISCUSSION The results will be described in the following order: the basic bow wave; the independent as well as combined effects of heave and pitch on the model; the surge phenomena (i.e., the differences between the basic bow wave and mean heave as well as mean pitch at Frs = 0.26~; the case of a higher Froude number (only in the free running case); and the elect of surfactants on the characteristics of free-surface structures in simulated separated sheets at supercritical Froude numbers. Basic Bow Wave Figure (Sa) shows plots of representative data for the model at rest in uniform flow at Frs = 0.26. The x-axis is the horizontal distance normalized by the ship length. The y-axis shows the vertical position Y of the free surface normalized by the mean of the water elevations H(O)m~bar' at the stem. It is rather remarkable that there is relatively little scatter. The bow wave reaches its maximum at a value of X/L between 0.02 and 0.025. The initial rate of rise between the stem and X/L = 0.025 is the strongest. After the wave reaches its maximum elevation, it loses its height gradually and at a value of X/L between 0.09 and 0.1, it drops to the mean water level. Figure 5a Y/H(O)m~bary versus X/L: bow-wave shape on the model in steady flow (Frs= 0.26~. Figure 5b shows the average of the data shown in Figure 5a. It is interesting that the slope of the wave elevation for X L > 0.05 is nearly linear. 4

Figure 5b: Y/H(O)m~bar' versus X/L: average model data for the runs shown in Figure Sa. Figure 6a shows, as before, Y/H(O)m~bar' versus X/L for the data extracted from the videotapes of the destroyer. It is not surprising that it exhibits larger scatter due to the randomness of the sea state, the changes in speed of the ship, the difficulties of deducing precisely the scales from the photos, and the variations in the ship direction. All measurements of the model and ship have shown that the actual value of H(O)m~ba~' at a Froude number of 0.26 is 2.2 feet. Figure 6b shows the average of the data shown in Figure 6a. 2.3' _ ~ 2 -- o 1.5 o.s Do -os ~ _ . . it_ ~ . X/L Figure 6a: Y/H(O)m~bar' versus X/L: bow wave data for the ship (Frs= 0.26~. 2S' . H 15 Figure 6b: Y/H(o~m~bar' versus X/L: averaged bow wave data for the ship (Frs = 0.26~. is Top line: Model Bottom: Ship M90~ To X/L Figure 7: Y/H(O)m(bar) versus X/L: comparison of the basic bow wave shapes of the ship and the model (Fr = 0.26 for both). Figure 7 shows the average of Figure 6a (basic bow wave shape) and its comparison with the averaged model data (Figure Sb), at a Froude number of 0.26. There is a remarkable similarity between the two sets of data. The key parameters such as the position of the maximum elevation on the ship and the point at which the sea level is reached are either in perfect agreement or very close to each other. The ship data begin to deviate from those of the model at approximately X/L = 0.04 and, as expected, is slightly lower. The extensive observations of the video of the ship show that the bow sheet begins to separate from the ship and eventually break into spray at approximately the same point as the deviation between the ship and model data. However, the most important feature of Figure 7 is that it points out the establishment of the basic bow wave shape in the subcritical Froude number regime and the point of inception of the supercritical regime (X/L > 0.04~. Heave Motions Figure 8a is the average heave profile (the mean of the maximum and minimum of the elevations) plotted over the steady state obtained from data of Figure 5b. One of the interesting features of Figure 8a is that the surge due to the heave, for the amplitude and frequency shown, is confined to the bow region very near the stem, primarily reflecting the effect of the sonar dome. Further away from the bow region, the average heave is nearly the same as the steady bow wave shape. It is of importance to note that this, as well as the following two figures, is plotted in terms of dimensional variables to give some idea of the size of the bow wave on the model and to simplify the presentation without distorting the

figures. Figures 8b and 8c show similar data at the same frequency but at increasing amplitudes of heave. Figure 8a: Y(cm) versus X(cm): comparison of the average heave with the basic bow wave (for Frs = 0.26, fm = 1.5 Hz, hm = 0.32 cm). Figure 8b: Y(cm) versus X(cm): comparison of the average heave with the basic bow wave (for Frs = 0.26, fm = 1.5 Hz, hm = 0.96 cm). 0.75 E 05 0.2s o -0.2s The previous three figures compared the steady flow bow data with the mean of the heave at one frequency and three different heave amplitudes. In Figures 9a through 9c, the heave data are presented in terms of Y/Hmax versus X/L for one frequency and one amplitude, where Hmax is the maximum wave amplitude. Figure 9a begins at time 't-1' when the model is at its maximum downward excursion. Clearly, the bow wave at this time is not at its highest position. As the model begins to go up, the wave rises to its maximum height at time 't-3' and beyond this point continues to decrease as shown from times 't-4' through 't-8'. The time of the maximum wave height lags the maximum downward excursion of the model by 2/45 seconds. In other words, if the model reaches its maximum excursion at time 't-1', then the maximum wave height occurs at time 't-3', as noted earlier. Clearly, the rate of fall of the bow wave is not uniform everywhere in the bow region. The smallest changes in the amplitude are very near the stem as noted by the labeled times of 't-9' through 't-17'. The subsequent figures show heave at additional times. The lowest position of the bow wave is arrived at rather uniformly as evidenced by a cursory examination of figures at times 't-11' through 't-15'. Thereafter, the bow wave continues to rise as shown in Figure 9c and the new cycle of the wave motion begins at time 't-23' at which time the model is at its maximum downward excursion at time 't-25'. Figure 9b, in particular, shows that the heave motion does not induce uniform rise and fall of the bow wave along the model. When the bow wave reaches a minimum position along the model (time 't-14'), the water from the remainder of the ship rushes toward the lowest point and gives rise to a wave breaking that is not related to the breaking of the bow sheet. The wave- break point is often below the design water line. 0.9 0.75 0.6 0.4s ~_ o0;3 ~~.z ~a 2 ~ o o~ = ~6 o.5 -o.~s _~ _ ~ fm= 1.5 Hz hm= 1.28 cm ~_ . . ~, t-2 t~3 t4 t~S ~ _t~ . ~ t-7: t-X: x (cm) Figure 8c: Y(cm) versus X(cm): Comparison of the average heave with the basic bow wave (for Frs = 0.26, fm = 1.5 Hz, hm = 1.28 cm). Figure 9a: Y/Hmax versus X/L: single cycle heave history of the bow wave (Frs = 0.26, fm = 1.5 Hz, hm = 1.28 cm) 6

rat ,( 015 =~== -0.3 -0.45 X/L Figure 9b: Y/Hmax versus X/L: the continuation of Figure 9a for heave motion (Frs = 0.26, fm = 1.5 Hz, hm= 1.28 cm). ,.05 1 fm= 1.5 Hz _ 0 is ~ ~7 hm = 1 .28 —1 he 0.45 j ~= =031 1 ~_ . ~ ~ . O ' ' ~ ' ' . o.oq 0.08 0.12 - _ 0.2 -0.15 -0.3 . .45 X/L _~-17: _~-18: t-l9: a: ~~ ~ t-20: ~-21: ~_-22: ~-23: .-24: Figure 9c: Y/Hma'` versus X/L: the continuation of Figure 9b for heave motion (Frs = 0.26, fm = 1.5 Hz, Em= 1.28 cm). Pitch Motions Figures lea through lOc show the comparison of the average pitch motion with steady runs for a given frequency and three different amplitudes (measured in degrees). As before, the pitch affects the near stem region of the bow and exhibits similar characteristics as those shown in Figures 9a through 9c for the heave motion. The differences are primarily due to the rotational motion about the longitudinal center of buoyancy. Figures 1 1 a through 1 1 c show the variation of the instantaneous position of the bow wave during one cycle. As before, the bow-wave maximum lags the model's maximum excursion by 2/45 seconds. .. . . ~ . .. E o 0.2s . r o- -Q25 ~ ~ Eve P itch I | E teddy | l 1 2 3 Figure lea: Y(cm) versus X(cm): comparison of the average pitch and steady motions (Frs= 0.26, fm= 1.5 Hz, pitch= 0.85 degrees 0.7s E 05 >0.2s -Q25 vgPitd~ I tesiv I me. ~ ~ ~ 1~ I 1 2 3 4 X(cm) 7 Figure lab: Y(cm) versus X(cm): comparison of the average pitch and steady motions (Frs= 0.26, fm = 1.5 Hz, pitch = 2.5 degrees) 07 _ 0.5- __ 0.25 o- ~25 Of _ f ~ 1 3 Figure lOc: Y(cm) versus X(cm): comparison of the average pitch and steady motions (Frs = 0.26, fm = 1.5 Hz, pitch= 3.35 degrees. 7

1.05 o.s. 0.75 . E , a=== 1 0''5i 004~1 -0.3 -0.45 X/L 1 am., _= -2: . t-3: . .... ~~ ...~-4: ~-5: _~-6: _~-7: t-8: 1 Figure lla: Y/Hmax versus X/L: single cycle Ditch history of the bow wave (Frs = 0.26, pitch = 3.35 degrees). . fm = 1.5 Hz, .05 or 0.75 A ~ Y ~~ C~ ~ 0.45 ; 0.3 0.15 .15 -0.3 -0.45 XIL ~==~ ~ *~'2 ~ tar ~ . I o.o~ my,_ ~ o.os #` ?:~' Oslo ~ '-— 1 ~: ''he - _t- 10: t- I 1: t- 1_: . ~< ~ A, 1 3: t- 14: t- 15: mat- 16: t- 17: —t-18: t-19: t-20: Figure Fib: Y/Hmax versus X/L: the continuation of Figure 1 la for heave (Frs = 0.26, fm = 1.5 Hz, pitch = 3.35 degrees). .05 0.9 0.75 r ^ 06 0.15' ~` ~ =tt~,6 o _~ _< ~t-~7: .15 0.04 o.og o.l~ —.,~ -0.3 -0.45 X/L Figure tic: Y/Hmax versus X/L: the continuation of Figure 1 lb for heave (Frs = 0.26, fm = 1.5 Hz, pitch = 3.35 degrees). Combined Heave and Pitch Motions The data obtained for a heave-pitch combination using a frequency of 1.5 Hz, a heave amplitude of 0.32 cm, a pitch amplitude of 2.5 degrees, and a phase angle of 120 degrees (between the pitch and heave) are shown in Figures 12a through 12c. These figures are not intended to convey the impression that an attempt was made to optimize the combinations of the controlling parameters (frequency, heave amplitude, pitch amplitude and phase angle), but rather to show that the combination of the two motions produced the largest maximums as well as the lowest minimums which were below the design water line during some part of the cycle. It should be emphasized that the frequency of 1.5 Hz does not represent the natural frequency of the prototype. The optimization of the various key parameters is left to a future study. 1.05 0.9 0.75 0.6 0.4s 0.3 As o -o.tS - -0.3 . -0.4s X/L . 1 e? ~ ~_ rtt23 I . 1~- ~ t-4 - _t-s: I —~ \~ _ 1 1 `~ - ~ l~t-6: V ma,= - , -— tt-7: 1 ~ of,—~ Off _- I A: I 0.04 o.o~r ~40 0.16 0.2 As_ 1 ~ _ ~ 1 t-9 1 _y~~~ I t-10' 1 Figure 12a: Y/Hmax' versus X/L: single cycle time history of the bow wave for Frs = 0.26, fm = 1.5 Hz, hm = 0.32 cm, pitch =2.5°, phase = 120°, (t-1 - t-10). ~ 0.45 — 0.3- 0.~5- o -0.15 - -0.3 - -0.45- 1 X/L 1 Figure 12b: Y/Hmax versus X/L: continuation of Figure 12a, (Frs= 0.26, fm = 1.5 Hz, hm = 0.32 cm, pitch = 2.5°, phase = 120°), (t- 1 1 - t-20). 8

Laos 0.9 . . 0.75 0.6 # 0.4s E e: 0-3 i 0.15 o -0.15 .0.3 t\ AC . ~ ' . . ~.2.' : , Figure 12c: Y/Hmax versus X/L: continuation of Figure 12b, (Frs = 0.26, fm = 1.5 Hz, hm = 0.32 cm, pitch = 2.5°, phase = 120°), (t-21 - t-294. Figure 13 shows a single cycle time history of the bow wave (times t-1, t-3, through t-13, and t-14) for Frs = 0.26, fm = 1.5 Hz, hm = 0.32 cm, pitch = 2.5°, phase= 120°. The black line on the hull represents the design water line along the ship. The times at which the bow wave is below the mean water level are seen clearly in the last three frames. Ship at Higher Frs with Yaw As previously stated, the existence of two distinct flows and Froude numbers along the ship near the bow necessitates two distinct experiments in two separate facilities. Figure 2 was obtained in the supercritical jet facility and shows that one must utilize the supercritical values of the controlling parameters (Froude, Reynolds and Weber numbers) to accurately model sheet separation and subsequent spray on any model smaller than the ship. Figure 14 shows representative pictures of a larger model of scale 1/150 at a Froude number of 0.65 with a yaw angle of 15 degrees. The separation of the sheet is precipitated by the yaw of the model as well as by the speed of the flow as evidenced by the breaking of the bow wave. The point to be made here is that the bow-sheet separation and the resulting jet breakup and spray formation can be investigated either on very large models or at very large Froude numbers (using a separate supercritical jet facility). Figure 13. A single cycle history of the bow wave. 9

Figure 14. Photographs showing the breaking of the bow wave on the model at rest in uniform flow with Frs= 0.65, yaw = 15 degrees. Surfactants and Supercritical Flow It is a well-known fact that clean surfaces are relatively rare in nature and the presence of non- dissolvable and/or adsorbable solutes provide a ready means for the establishment of variations in surface or interracial tension along the fluid phase boundary. The surfactants render the free-surface more rigid, reduce surface deformation, smoothen the free surface, and enhance the generation of secondary vorticity (Sarpkaya, 1996~. Thus, the shear-free free- surface condition and the no-slip condition are incompatible. The consequences of surface tension reduction may manifest themselves in various ways under a variety of circumstances in both supercritical and subcritical flows. These have been discussed by Sarpkaya (1996, and references therein), and more recently by Reed and Milgram (2002) in the context of ship wakes. In spite of some favorable predictions of the image features of ship wakes, the effect of surfactants on the attenuation of the short sea waves and surface structures by ship-generated currents and turbulence remain in the realm of limited measurements, empirical equations, and descriptive knowledge. It is because of these reasons that a comprehensive effort was undertaken to delineate the effects of both soluble and insoluble surfactants on both the supercritical and subcritical free surface flows. Previously, Sarpkaya and Merrill (2001) have shown, through the use of DPIV (See Fig. 15), that the ejection of the filaments from the surface of a supercritical flow is necessarily controlled by the dynamics of the turbulent flow field. Figure 15. DPIV measurements and the regions of focussed areas with large upward velocities. 10

The circled regions in Fig. 15 show "focussed" areas with upward velocities as large as large v'/UO ~ 0.2. In view of this finding, the tip velocities of all filaments, which eventually gave rise to one or more drops, were evaluated from the Lagrangian measurements, using only the images taken after the initial acceleration period of 5 ms to 10 ms. A typical plot is reproduced in Fig. 16 for the flow without surfactants. Some of the experiments described above and in Sarpkaya and Merrill (2001) have been repeated using 10 micron FluoSpheres (Molecular Probes, Inc.) as surfactant. They do not dissolve in water and contaminate only the free surface. The surface tension for the concentrations used was about 55 dynes/cm. The evaluation of the data along the jet at various sections downstream has shown that the length of the filaments (Figure 17) as well as their ejection velocities decrease rapidly, showing the strong damping effect of the contaminant on the free-surface structures. The resulting data are shown in Fig. 18. It is clear from a comparison of the two sets of data shown in Figure 18 that the contaminant drastically reduces the filament ejection velocities and the focussing effect. The massive data is currently being analyzed for the purpose of assessing the decay of the kinetic energy of the grid-generated turbulence in subcritical channel flows (Fr = 0.26) with non- dissolving as well dissolving contaminants. Figure 17. Ejection of filaments from the free-surface of a supercritical flow with surface contaminants (10 micron FluoSpheres). 0.19 0.18 0.17 o - > 0.14 0.15 0.12 0.11 0.09 0.0 0.1 0.2 0.3 0.4 Frequency Figure 16. Representative frequency distribution of the vertical component of the normalized tip velocity of the filaments in a supercritical wall jet. 0.19 0.18 0.17 ~ 0.15 _ ~ 0.14 r r _ 0.12 0.11 0.09 0.0 0.1 0.2 0.3 0.4 Frequency Figure 18. Comparison of the frequency distribution of the vertical component of the normalized tip velocity of the filaments in a supercritical wall jet with (in red) and without (in black) contaminants. 11

CONCLUSIONS Measurements of the near-surface evolution of the bow wave were made on a 1/250-scale model of a destroyer and compared with those obtained from the sea tests of the subject destroyer wherever possible. The effects of steady motion, heave, pitch and combinations thereof were subjected to controlled experiments to quantify the base flow in comparison to the prototype. The Froude Number for the majority of the runs was 0.26. Model scale frequencies ranged from 1 to 5 Hz, pitch angles from 0.85 degrees to 3.75 degrees and heave amplitudes from 3 mm to 15 mm. It has been shown that there exists two separate Froude numbers that govern two distinctly different phenomena in two different regions of the ship. The subcritical flow dominates the region of unseparated bow wave (X/L smaller than about 0.04~. The supercritical regime corresponds to the region of separated jet and spray formation (X/L larger than about 0.04~. Remarkable similarity was found between the corresponding bow-wave motions of the model and the ship in free-run in heave, pitch, and in combined heave and pitch motions. The bow wave manifests its existence in all other motions (heave, pitch and forced oscillations) imposed on the ship and on a model. Conseouentlv. the determination of the excursions of a given bow wave geometry above or below the maximum or minimum of the basic bow wave (say the vertical surge) is an important measure of the resistance, spray generation, and the overall performance of the ship. All the motions examined produced a minimum wave position below the DWL (design water line) during some part of the cycle. The surge due to heave and pitch motions is confined to the bow region very near the stem with differences between the two due to the rotational pitch motion about the LCB (the longitudinal center of buoyancy).. The rate of rise and fall of the bow wave is not uniform throughout the cycle. The smallest changes in the wave amplitude are very near the bow stem. In both heave and pitch motions, the maximum wave height lagged the maximum downward excursion of the ship by 2/45 seconds for a value of Frs = 0.26. The foregoing has shown once that the character of a ship is, to a large extent, ordained by the shape of its bow. A better understanding of the bow hydrodynamics and numerical methods may come from numerical simulations which reveal details that are impossible to measure. Experiments with non-dissolving surfactants have shown dramatic decreases in the size and ejection velocity of the filaments from supercritical jets. Detailed processing of data from experiments with grid generated turbulence in subcritical channel flows, with and without dissolving and non-dissolving surfactants, will shed considerable light on the decay of the turbulent kinetic energy of the wake and thereby on the decay of short waves. ACKNOWLEDGMENTS This investigation has been supported by the Office of Naval Research. We are particularly indebted to Dr. L. Patrick Purtell, the Program Director, for his continuous guidance and encouragement. A note of special thanks is extended to Dr. Art Reed of DTMB for providing a copy of the videotape of the ocean experiments and for his careful reading of the manuscript. REFERENCES Beddhu, M., Nichols, S., Jiang, M-Y., Sheng, C., Whitfield, D.L., and Taylor, L.K., "Comparison of EFD and CFD Results of the Free Surface Flow Field About the Series 60 CB=0.6 Ship," Proceedings. of the 25th American Towing Tank Conference, 1998, pp. 1-1-11. Cusanelli, D., "Performance of Near-Surface Bow Bulbs in Irregular Waves," Proceedings of the Twentv- Fifth American Towing Tank Conference, 1998, pp. 3-25-34. Dong, R.R., Katz, J., and Huang, T.T., "On the Structure of Bow Waves on a Ship Model," Journal of Fluid Mechanics, Vol. 346, 1997, pp. 77-1 15. Fontaine, E. and Cointe, R., "A Slender Body Approach to Nonlinear Bow Waves,". Philosophical Transaction of the Roval Society, London (A), vol. 355, 1997, pp. 565-574. Grosenbaugh, M.A., and Yeung, R.W., "Flow Structure Near the Bow of a Two-Dimentional Body~" Journal of Ship Research, Vol. 33, No. 4 Dec. 1989, pp. 269-283. Larson, L., Regnstrom, B., Broberg, L., Li, D-Q., and Janson, C.-E., "Failures, Fantasies, and Feats in the Theoretical/Numerical Prediction of Ship Performance," 22nd SYmposium on Naval HvdrodYnamics, 1999, pp. 1 1-32. 12

Longo, J., Stern, F., and Toda, Y., "Mean Flow Measurements in the Boundary Layer and Wake and Wave Field of a Series 60 CB=06 Ship Model—Part 2: Scale Effects on the Near Field Wave Patterns and Comparisons with Inviscid Theory," Journal of Ship Research, Vol. 37,No. 1., 1993, pp. 16-24. Miyata, H., Inui, T., "Nonlinear Ship Waves," Advances in Applied Mechanics, Vol. 24, 1984, pp. 215-288. Reed, A.M, and Milgram, J.H. 2002 "Ship Wakes and Their Radar Images," Annual Review of Fluid Mechanics, Vol. 34, 2002, pp. 469-502. Rhee, S.H., and Stern, F., "Unsteady RANS Method for Surface Ship Boundary Layer and Wake and Wake Field," International Journal for Numerical Methods in Fluids, Vol. 37, 2001, pp. 445-478. Sa~pkaya, T., "Interaction of Vorticity, Free surface, and Surfactants," Annual Review of Fluid Mechanics Vol. 28, 1996, pp. 83-128. Sarpkaya, T. and Merrill, C. F., "Spray Generation from turbulent Plane Water Wall Jets Discharging into Quiescent Air, " American Institute of Aeronautics and Astronautics Journal, Vol. 39, No. 7, 2001, pp. 1217- 1229. Stern, F., Longo, J., Zhang, Z.J., and Subramani, A.K., "Detailed Bow Flow Data and CFD for a Series 60 CB=0.6 Ship Model for Froude Number 0.316," Journal of Ship Research, Vol. 40, No. 3, 1996, pp. 193-199. Stern, F., Paterson, E.G., Tahara, Y., "CFDSHIP- IOWA: Computational Fluid Dynamics Method for Surface-Ship Boundary Layers, Wakes, and Wave Fields," 1996, IIHR, University of Iowa, Report No. 381. Subramani, A., Beck, R., and Scorpio, S., "Fully Nonlinear Free-Surface Computations for Arbitrary and Complex Hull Forms," 22nd Symposium on Naval Hydrodynamics, 1999, pp. 390-402, National Academy Press, Washington D.C. Wu, M., Tulin, M.P., and Fountaine, E., "On the Simulation of Amplified Bow Waves Induced by Motion in Head Seas," Journal of Ship Research,, Vol. 44, No. 4, Dec. 2000, pp. 290-299. 13

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