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Macro Wake Measurements for a Range of Ships

M.Hoekstra, A.Aalbers (Marine Research Institute, The Netherlands)

Abstract

An extensive experimental investigation has been carried out to measure the global structure of the wake, including possibly-related free surface elevations, of various ship models. While wake measurements on ships are usually restricted to the propeller disc region, here the wake structure was recorded in several transverse planes, and in each plane over an area of several propeller diameters wide and extending well below the keel plane of the ship. Moreover, several longitudinal and transverse wave cuts were made. No less than 8 ship models were involved in the project, and some of them in more than one operational condition. The measurements comprised:

  • the three components of the velocity vector

  • the six components of the Reynolds stress tensor

  • longitudinal and transverse wave profiles

The measurement equipment, a three-component LDV system and two types of wave probes, is described. An error analysis is included to provide an estimate of the accuracy of the data.

The huge amount of data gathered does not permit a complete presentation of all results. Instead, the paper will address the most relevant and most unexpected results. Emphasis is placed on the differences in the wake structure between propelled and towed hulls, on the remarkable effect of the rudder, and on the influence of the trim/loading condition, the beam-draft ratio and the bulb.

The data sets are available as validation material for computational methods.

1.
Introduction

Synthetic Aperture Radar (SAR) has successfully been operating from a NASA scientific satellite called SEASAT to record images of ships and their wakes. When environmental conditions were not disturbing, most of these images revealed fairly consistent wake features as well as some indicators as to the potential military or commercial use of the images for detection and recognition of ships. Naturally questions arose about the interpretation of the images and whether the wake scar left by a passing ship could be minimised under a given set of environmental conditions. It turned out soon that these questions are more easily posed than answered. Information on how the wake of a ship —or more precisely the manifestation of the wake at the free surface—is affected by operational and hull geometric aspects is scarce, scattered and incomplete. Since factors in hydrodynamic ship design that could influence the wake might also lead to reduced fuel consumption or power required, the exploration of the structure of ship wakes has a wider relevance than just radar image interpretation, and might well yield benefits in other areas than remote sensing.

The above was the incentive to start an extensive model-scale experimental investigation on ship wakes, carried out in the period from 1987 to 1990 at the Maritime Research Institute Netherlands on behalf of the United States Navy. The investigation was the second part of the project on 'Advanced Fluid Dynamic Experimentation and Analysis for Signature Reduction' (AFDEASR). The primary goal of the investigation was to set up a data base



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Twenty-First Symposium on NAVAL HYDRODYNAMICS Macro Wake Measurements for a Range of Ships M.Hoekstra, A.Aalbers (Marine Research Institute, The Netherlands) Abstract An extensive experimental investigation has been carried out to measure the global structure of the wake, including possibly-related free surface elevations, of various ship models. While wake measurements on ships are usually restricted to the propeller disc region, here the wake structure was recorded in several transverse planes, and in each plane over an area of several propeller diameters wide and extending well below the keel plane of the ship. Moreover, several longitudinal and transverse wave cuts were made. No less than 8 ship models were involved in the project, and some of them in more than one operational condition. The measurements comprised: the three components of the velocity vector the six components of the Reynolds stress tensor longitudinal and transverse wave profiles The measurement equipment, a three-component LDV system and two types of wave probes, is described. An error analysis is included to provide an estimate of the accuracy of the data. The huge amount of data gathered does not permit a complete presentation of all results. Instead, the paper will address the most relevant and most unexpected results. Emphasis is placed on the differences in the wake structure between propelled and towed hulls, on the remarkable effect of the rudder, and on the influence of the trim/loading condition, the beam-draft ratio and the bulb. The data sets are available as validation material for computational methods. 1. Introduction Synthetic Aperture Radar (SAR) has successfully been operating from a NASA scientific satellite called SEASAT to record images of ships and their wakes. When environmental conditions were not disturbing, most of these images revealed fairly consistent wake features as well as some indicators as to the potential military or commercial use of the images for detection and recognition of ships. Naturally questions arose about the interpretation of the images and whether the wake scar left by a passing ship could be minimised under a given set of environmental conditions. It turned out soon that these questions are more easily posed than answered. Information on how the wake of a ship —or more precisely the manifestation of the wake at the free surface—is affected by operational and hull geometric aspects is scarce, scattered and incomplete. Since factors in hydrodynamic ship design that could influence the wake might also lead to reduced fuel consumption or power required, the exploration of the structure of ship wakes has a wider relevance than just radar image interpretation, and might well yield benefits in other areas than remote sensing. The above was the incentive to start an extensive model-scale experimental investigation on ship wakes, carried out in the period from 1987 to 1990 at the Maritime Research Institute Netherlands on behalf of the United States Navy. The investigation was the second part of the project on 'Advanced Fluid Dynamic Experimentation and Analysis for Signature Reduction' (AFDEASR). The primary goal of the investigation was to set up a data base

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Twenty-First Symposium on NAVAL HYDRODYNAMICS of 'macro wake' measurements for a wide range of ships, wide enough to cover a large part of the world's ship population. TABLE I Overview of Data Sets Data set no. Cb L/B B/Ta Prop. Bulb Loading Speed m/s Tankers   11 0.84 6.4 2.5 single yes full 1.3 12 0.79 6.4 4.7 single yes ballast 1.3 21 0.78 5.7 4.2 single yes full 1.3 22 0.76 5.7 5.1 single yes ballast 1.3 31 0.82 5.0 4.0 twin, inw. yes full 1.3 32 0.82 5.0 4.0 twin, outw. yes full 1.3 34 0.75 5.0 5.8 twin, outw. yes ballast 1.3 Containerships   41 0.69 7.1 2.8 single yes full 2.0 51 0.61 6.1 3.6 single yes full 2.0 61 0.62 5.4 3.7 twin, inw. yes trimmed 2.0 62 0.62 5.4 3.7 twin, outw. yes trimmed 2.0 64 0.62 5.4 3.7 twin, outw. no trimmed 2.0 Frigates *)   71 0.50 8.0 4.0 twin, inw. no full 2.0 81 0.44 7.3 3.2 single no full 2.0 *) A third frigate data set was obtained at DTRC in the U.S.A. [2] With the term 'macro wake' we follow the terminology of [1] and it is used here with the intention to convey two things: i) that the measurements have not been restricted to the propeller disc area, as is the common practice in ship model testing, and ii) that the emphasis is on the detection of large scale features in the wake. This paper starts with an overview of the scope of the investigation, i.e. the main characteristics of the ship models used, the kind and the extent of the measurements, etc. The description of the measuring devices and an error analysis follows in section 3. Subsequently, a summary is given of the main findings, extracted from a careful examination of the collected experimental data, in section 4. Closing remarks in section 5 complete the paper. 2. Scope of investigation Wake data were acquired for 8 ship models: 3 tankers, 3 container or auxiliary vessels and 2 frigates (complementary data for a third frigate were collected at DTRC [2]). The bodyplans of the hulls are shown in Fig.1. Each data set has an identification number of two digits of which the first refers to the hull geometry and the second to an operating condition. A change of operating condition is either a draft variation or a reversal of the direction of rotation of the propellers; in one case however a local bow form change is involved. Table I gives a summary. It is noted that each data set includes results with and without operating propeller(s). Moreover, additional measurements were carried out under data set 21 for the propelled hull in absence of the rudder. The measurements comprised: the three components of the velocity vector; the six components of the Reynolds stress tensor; longitudinal and transverse wave profiles. The velocity and Reynolds stress measurements were made in several transverse planes. An overview of the number of planes and their position for each data set is given in Appendix I.

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Twenty-First Symposium on NAVAL HYDRODYNAMICS Fig. 1. Bodyplans of models involved in the project Fig. 2. Test setup for flow speed measurement

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Twenty-First Symposium on NAVAL HYDRODYNAMICS 3. Measurement equipment The measurement equipment comprised the following elements: A DANTEC three-component LDV system for the mean velocity, turbulence intensity and the Reynolds stresses; A laser-based wave profile measuring device for longitudinal wave cuts and wave slope/direction; A needle type wave probe for the measurement of free surface elevation on transverse wave cuts. In addition, standard electronic equipment was used for the measurement of tow speed, ship model position and coordinates of traversing systems for the optical head of the LDV and the needle wave probe. 3.1. Setup Because measurements had to be made as far as two ship lengths behind the stern, a 25 m longitudinal girder was rigidly fixed to the towing carriage. The LDV equipment was installed at the rear end of the carriage, while the ship model was connected to the girder at various positions to obtain the required distances. Fig.2 gives an impression of the test setup. The laser-Doppler velocimeter used is a two-colour backscatter system for the simultaneous measurement of the three velocity components [3]. The laser light source is a 4 Watt argon laser, mounted on the towing carriage. The laser light is transmitted via a mono-mode fiber to the optical head, the assembly of all optical components in a waterproof housing. In the optical head the laser light is split into two blue beams (λ=488.0 nm) and three green beams (λ=514.5 nm). These five beams are directed so as to intersect at a common point in the flow, the measurement location, which is at a distance of 815 mm from the optical head. The probe volume measures 1.3×0.4×0.4 mm. The scattered light is received by the optical head and fed into three burst spectrum analysers (BSA's), which derive the three velocity components [4]. The location of the probe volume is fixed with respect to the optical head. Its location with respect to the ship model is adjusted by traversing the optical head. The traversing system has two degrees of freedom with a reach of 1.15 m in one direction and 0.85 in the other. Fig. 3. Test setup for longitudinal wave cuts The wave profile measurement system, using a 1 Watt argon laser, was mounted at a fixed position in the basin and data recording took place while the model passed by. The setup in the basin is shown in Fig.3. The system uses two types of position-sensitive camera's to measure wave elevation and wave direction and slope respectively. The needle wave probe measurement system was mounted on a traversing system with servo motors for moving the two sub-carriages in x and y direction respectively. The traversing system was mounted on the towing carriage. The measurement grid for the needle probe partly overlapped the longitudinal wave laser cuts, allowing a comparison as shown in Fig.4. It illustrates that the consistency of the wave profile measurements is quite good. 3.2. Accuracy An elaborate accuracy evaluation was carried out. The results are summarised in the following subsections.

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Twenty-First Symposium on NAVAL HYDRODYNAMICS Fig. 4. Comparison of wave height recordings by two different methods 3.2.1. LDV measurements of macro wake The accuracy evaluation concerns two aspects: the LDV measurement of flow speed and the position in the grid with respect to the ship. Typical values for the speed are: LDV flow velocity: 0.002m/s Carriage speed: 0.45% When the LDV measurements are nondimensionalised with tow speed, the inaccuracy of the carriage speed is introduced. This applies to the longitudinal velocity component only. For the grid point location with respect to the ship also two aspects can be distinguished: the location of the grid plane with respect to the ship's aft perpendicular and the location of the grid points in the plane. Typical values are: x-coordinate of grid plane: 0.0035 m y- & z-coord. of grid plane: 0.028 m y- & z-coord. of grid point: 0.0025 m Note that the accuracy of the y and z-coordinate of the grid plane is with respect to the ship centre line and specified draft. The larger error is caused by the 0.1 degree uncertainty in the alignment of the longitudinal girder to which the model was connected. The reference was at the grid plane just aft of the aft perpendicular, so that for that plane the y and z-coordinate accuracy is as good as 0.0035 m. The data rate of the LDV was not always fully under control. Sometimes it was good enough to allow the recording of turbulence frequencies up to about 100 Hz, but at other instances it dropped substantially with a consequent reduction of the accuracy of the Reynolds stresses. 3.2.2. Wave profile measurements The needle type wave probe scans can be analysed as to the wave elevation error and the error in the reference of the traversing system. The following values apply: Wave elevation: 0.0018 m Vertical reference: 0.003 m x-coord. of plane: 0.0035 m y-coord. of plane: 0.028 m The value for the vertical reference can be related to the bias in the comparison of the two wave scanning systems in Fig.4. The errors in the x and y coordinates are similar to those for the LDV grid planes since the same model tow arrangement was used. For the laser type wave cuts the following accuracy limits apply: Wave elevation: 0.0015 m Wave slope: 3% in amplitude 0.1 degr. bias x-coordinate: 0.01 m y-coordinate: 0.004 m 3.2.3. LDV near-free-surface measurements The LDV equipment was also used to measure the flow as close as possible to the free surface. The velocities measured follow the accuracy analysis of the normal LDV signals given in 3.2.1, but for the vertical position the local position of the free surface was used as a reference. The LDV laser beams were used to determine the location of the water surface, whereupon the grid point was defined as 0.002 m below the water surface. The vertical position accuracy was 0.00025 m if the water surface was smooth. For the near-surface

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Twenty-First Symposium on NAVAL HYDRODYNAMICS points right behind the ship the water surface was turbulent and the positioning accuracy dropped to some 0.001 m 3.3. Conclusion The accuracy of the LDV measurements was sufficient to have the flow patterns in the far field reliably measured. The accuracy margins are defined as “standard deviations with respect to the truth in the model basin”. Hence, possible scale effects are ignored. With respect to the inaccuracy in the model reference position of the grid planes and wave cuts, our evaluation of the results suggests that the achieved accuracy for the bulk of the measurements is better than the theoretical values, because for the evaluation conservative values were applied. 4. Presentation and discussion of results Limits on the size of this paper do not permit a presentation of all the data collected in the AFDEASR project. Instead, the most relevant and most unexpected results will be discussed. Emphasis is placed on the differences in the wake structure between propelled and towed hulls, on the effect of the rudder, and on the influence of the trim/loading condition, the beam-draft ratio and the bulb. The description is phenomenological, here and there illustrated with specific examples. For details the data base should be consulted, which is available for that purpose as well as for validation of computational methods. Requests for data release should be directed to DTRC. In the presentation of the data a right hand coordinate system x,y,z is used with the origin at the intersection of the aftperpendicular and the undisturbed free surface. The x-coordinate is positive in the direction from bow to stern; y is positive to starboard and z in upward direction. 4.1. Mean flow and vortex systems 4.1.1. Wake of unpropelled hulls We start with a brief account of the structure of the nominal wakes, i.e. the wakes behind the unpropelled hulls, without rudder (on the twin-screw models skegs, shafts and brackets were present). For most of the hulls the vector plots of the transverse velocity components revealed patterns which indicate the presence of longitudinal vortices. That ship hulls can generate such vortices is well-known from ordinary wake measurements in the propeller plane. In general two pairs of counter-rotating vortices are observed; an example is given in Fig.5. One pair, created close to the stern in the bilge region—and therefore often referred to as the ‘bilge vortex' pair—usually passes through the propeller disc area. These vortices, one on either side of the symmetry plane, are close to each other and the path they follow on being carried downstream is visibly influenced by their mutual induction: they both tend to move slowly downward. Fig. 5. Example of transverse flow at x/L=0.240 The other pair, generated near the waterline and here for convenience called 'side vortex' pair, is often outside the influence region of the propulsion device. These vortices are far apart, whence they show little interaction. It should be noted however that with regard to vortex kinematics the free surface behaves almost as a free-slip symmetry plane. Therefore an imaginary vortex system above the free surface can be added to account for the effect of the free surface on the vortex motion. So each vortex has a nearby imaginary companion and, again by mutual induction, the core position of the side vortices tends to move away from the longitudinal symmetry plane of the ship with increasing distance to the stern. Not all ships produce two clearly identifiable vortex pairs; a dependency on the stern shape is evident. With a (hypothetical) axisymmetric body shape no longitudinal vortices would be generated. It is the need to install a propeller with shafting and machinery and the need to increase the waterline length as much as possible to minimize wave formation which give ship hulls the typical shape that produces longitudinal vortices. Not only the

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Twenty-First Symposium on NAVAL HYDRODYNAMICS presence, but also the strength of a vortex—and hence its identifiability—depends on the hull lines. Sometimes only a single vortex pair is observed, either the bilge or the side vortex pair. The pattern of the iso-lines of the mean longitudinal velocity in the nominal wake of a ship looks usually like an upside-down rimmed hat (see Fig.6 for an example). One can observe a central lobe at or below the keel level and two side lobes close to the free surface. To some extent the pattern reflects the frame shape of the afterbody, but it is also clearly correlated with the structure of the transverse flow field: often the longitudinal velocity component exhibits a local minimum near the core of a longitudinal vortex. Fig. 6. Example contourplot of longitudinal velocity at x/L=0.594 The smallest axial velocity is usually found in the symmetry plane of the wake near the free surface. But there are exceptions. When strong side vortices are produced, the minima occur near their cores, again at or directly below the free surface. Outside the main-wake region there may be small momentum-deficit areas near the free surface which are attributed to wave breaking. 4.1.2. Wake of propelled hulls The wake of a ship with running propeller(s) is quite different from the wake of a towed hull (nominal wake). The differences are not only related to the diminished momentum deficit— because all wake measurements on propelled hulls were carried out under the condition of the so-called self-propulsion-point-of-ship a small deficit remains —but also to the interaction between the propeller-induced flow and the hull wake. A propeller in a uniform onset flow tends to accelerate the flow ahead as well as in the jet behind, and to weakly decelerate the flow outside these regions. Moreover, the propeller jet aft of the propeller disc rotates in the same sense as the propeller itself. Ahead of the propeller and outside the jet there is no propeller-induced rotation. For a qualitative analysis of the interaction of the propeller-induced flow and the nominal wake, let us first recall that vorticity, once generated, is carried with the flow and is spread by diffusion like heat, on the understanding that at a high Reynolds number the convection dominates the diffusion. Now imagine a stream tube, encompassing all the flow going through the propeller disc. Due to the acceleration of the flow by the propeller, this streamtube is contracting. When a hull-generated vortex happens to be inside the streamtube—which is usually the case for the bilge vortices—the vortex is subjected to this contraction as well; as a result, the vorticity is concentrated. This process is often referred to as vortex stretching. The streamlines in the aforementioned stream tube start to swirl around the centreline of the propeller jet as soon as they have passed the propeller disc. This must hold for an embedded longitudinal vortex as well. In the case of a single-screw ship, both the port and the starboard bilge vortex are captured in the screw race and start swirling. Moreover, due to the strong mixing in the propeller jet, the bilge vortices soon loose their identity, i.e. they are not recognizable as vortices in a graphical representation of the transverse velocity field. Only the rotation in the propeller jet remains. A swirling vortex pair does not generate the downwash effect found in nominal wakes. But usually a rudder is fitted behind the propeller which causes that the downwash is maintained, albeit in an oblique direction, as we shall see later. In the case of a twin-screw vessel each propeller jet will capture one bilge vortex, if present. Usually the bilge vortex and the propeller jet are nearly coaxial. If, in addition, they are co-rotating an accumulation effect will occur. On the other hand, for outward rotating propellers the jet rotation is opposite to the bilge vortex rotation; the amount of swirl found in the wake will therefore be smaller than for inward rotating propellers. Hence a better propulsive efficiency is to be expected under such circumstances for outward rotating propellers (a fact

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Twenty-First Symposium on NAVAL HYDRODYNAMICS Fig. 7. Development of maximum flow speed in the propeller jet as a function of x/L that has found ample corroboration in model tank propulsion tests). The presence of a propulsion unit has a strong influence on the axial velocity distribution also. Of course the propeller jet appears as a dominant feature, but there are strong additional effects caused by the interaction between the propeller-induced flow and the longitudinal hull-vortices. It would be wrong to suppose that the wake of a propelled hull can be obtained by a simple superposition of the nominal wake and the propeller-induced flow. Where in most towed-hull wakes the smallest axial velocity occurs in the symmetry plane, this is seldom the case in the propelled-hull wake; two minima away from the symmetry plane but at or near the free surface are commonly observed. The implication is a more-than-average acceleration of the flow in the symmetry plane near the free surface. While this flow is clearly outside the propeller jet which is at a much lower position, we suppose that this is accomplished primarily by the bilge vortices which are very effective in transporting momentum from the propeller jet or the outer flow to that location. In ideal-flow propeller models (actuator disk, lifting line or lifting surface models) the axial velocity in the propeller jet is greater far downstream than at the location of the propeller. In the present experimental data, however, the maximum axial velocity decreases steadily, at least from a position x/Lpp=0.25 on (see Fig.7). Apparently the viscous diffusion effects are so strong as to more than neutralize the acceleration effect. This may not be true, though, for the region between the propeller and x/Lpp=0.25. 4.1.3. Effect of rudder The presence of a rudder can have an appreciable influence on the structure of the macro wake. If a rudder is fitted directly behind the propeller so as to cut the propeller jet in two halves as it were, it effectively eliminates the jet rotation. It does not Fig. 8. Oblique downwash with rudder behind propeller necessarily take all the axial vorticity out of the propeller jet but what remains is not identifiable as a single-vortex flow structure. The bilge vortices can pass the rudder without encountering significant obstruction and are not much affected. The same holds of course for the propeller jet if the rudder is not placed in it, such as in the case of a twin-screw ship with a single central rudder. The elimination of the propeller jet rotation by the rudder has important consequences for the behaviour of the bilge vortices of single-screw ships

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Twenty-First Symposium on NAVAL HYDRODYNAMICS (Fig.8A). Recall that these vortices, except for diffusion effects, follow the streamlines. Therefore, as soon as these vortices have passed the propeller disk, they start to swirl around the propeller axis: behind a right-hand propeller the starboard bilge vortex core moves downward, the port vortex core upward. Upon reaching the rudder, the swirling motion is interrupted and the bilge vortices maintain the orientation they have at that stage (Fig.8B). That orientation obviously depends on the nondimensional advance ratio formed by the axial flow speed, divided by the rotation rate of the propeller and the distance between propeller and rudder. The path followed by the bilge vortices after they have passed the rudder is again influenced by the self-induced downwash. The downwash is not in the vertical direction, however, but in an oblique direction perpendicular to the line connecting the two vortex cores (Fig.8C). In the far wake therefore we see a strong asymmetry: the jet of the propeller, flanked by the two hull vortices, is found on Fig. 9. Migration of propeller jet to port by oblique downwash (top: x/L=0.24; middle: x/L=0.56; bottom: x/L=0.88) port side (right-hand propeller; see Fig.9 for an example) or on starboard (left-hand propeller). The downwash is stronger than in the nominal wake because the vortices have been stretched by propeller induction. The enhancement of the vortex strength by stretching effects is also responsible for the acceleration of the flow in the central region near the free surface, to which has been alluded in section 4.2. As bilge vortices in a nominal wake are effective in reducing the wake peak in the top sector of the propeller disk, the stronger vortices in the propelled-hull wake have a proportional effect on the flow in the central region near the free surface. 4.2. Wave pattern In the wave profile measurements several features of the well-known Kelvin pattern due to a point disturbance, with its characteristic combination of transverse and diverging wave crests, were confirmed. In the longitudinal wave cuts in the symmetry plane of the ship the fundamental wave length λ=2πVs2/g clearly appeared. Recording of this wave length is one of the means to determine the speed of a ship. The longitudinal wave cuts away from the symmetry plane revealed the change in the direction of propagation of the waves. For the initial part of the wave record consists of contributions of the diverging wave components, the end of the record of transverse waves. In closer proximity of the hull the complexity of the wave system is greater but it is of minor importance for the macro wake as long as wave breaking does not occur. When a wave crest breaks—be it a wave generated at the bow, a shoulder or the stern—, wave energy is converted into turbulence kinetic energy, and a clearly identifiable trace is left behind in the wake. The associated peak vlaue of the turbulence kinetic energy decreases with increasing distance to the hull. At the same time the location of the peak moves gradually away from the longitudinal symmetry plane. The turbulence activity is accompanied with a slight but noticeable reduction of the longitudinal velocity component. The occurrence and the intensity of wave breaking depend not only on the hull shape but also on the speed of the vessel. Unlike many other aspects of the wake, the traces of wave breaking will therefore

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Twenty-First Symposium on NAVAL HYDRODYNAMICS even after proper nondimensionalisation change with the Froude number. This makes it impossible to give typical values for the turbulence intensity as a result of wave breaking. Some influence of the propeller on the wave profiles could be detected if the propeller is close to the free surface (e.g. tankers in ballast condition). Even then the effect is usually weak, however. Our measurements have confirmed that the propeller has no noticeable influence on wave breaking. 4.3. Near-free-surface flow With a view to the possibilities of remote wake sensing, free surface phenomena are of greater interest than the flow behaviour at large depths. It is important, therefore, to consider which flow features are visible or detectable at the free surface. The formation of gravity waves, possibly breaking, as discussed in the previous section 4.2, is of course such a feature. But the sub-surface LDV measurements have intentionally been extended to very near the free surface to detect disturbances which might be connected with satellite-observable phenomena. This section is devoted to this “near-free-surface flow”. The near-free-surface velocities measured abreast of the ship models clearly revealed the orbital motion in the waves. If the advance speed of the ship model was subtracted, the velocity vectors in a wave crest and a wave trough respectively were pointing in opposite direction. Although not in all cases flow information has been obtained on port as well as on starboard, the available data seem to indicate that the wake of unpropelled ships is practically symmetric in the near-free-surface flow. But once the propeller is operating, considerable asymmetries can occur, which is exemplified by Fig.10, showing velocity vectors in an earth-fixed reference frame. The occurrence of such asymmetries is directly related to the flow behaviour at greater depth. It has been outlined in section 4.1.3 how the combination of bilge vortices, propeller and rudder can produce strong asymmetry. The typical result for a right-hand single propeller is that the bilge vortex pair migrates to port, causing the apparent symmetry line for the near-free-surface flow to be displaced to starboard. Fig. 10. Asymmetry in near-free-surface flow behind a propelled hull Not all propeller-hull wakes are asymmetric near the free surface, however. For example in our data configuration 11 has the propeller so deeply submerged that the asymmetry does not extend to the free surface. Also twin-screw ships have a symmetric wake. In section 4.1.2 it was pointed out that the distribution of the primary velocity component u in the wake of a propelled hull usually exhibits two minima, one on either side of the vertical symmetry plane. These minima are found very close to the air-water interface and are still identifiable at two ship lengths behind the stern. Fig.11 shows that the local minimum velocity is there about 5 per cent below the undisturbed flow speed; or, in an earth-fixed reference frame, that there is a fluid motion in the advance direction of the ship with a speed of 0.05 Vs at x/Lpp=2.0. The figure also shows the rate of change. Fig. 11. Development of local minimum longitudinal velocity in propelled-hull wakes

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Twenty-First Symposium on NAVAL HYDRODYNAMICS 4.4. Turbulence The results of the Reynolds stress measurements reveal the shear-layer character of the flow. By the composition of the shear stresses and the resulting vectors appear to be roughly perpendicular to the iso-lines of the axial velocity field, to point in the direction of decreasing u, and to attain their greatest length in regions of high gradients in the u-field. These characteristics are typical for thin shear layers. Turbulence activity near the free surface is important for wake signature because it shows up as “white water” behind ocean vessels. The turbulence kinetic energy is a good and convenient measure of turbulence activity. This scalar quantity typically exhibits peaks in the three lobes of the axial velocity field. A breaking bow wave may cause an additional pair of trails of high turbulence kinetic energy. Being isolated from the main wake region, these trails retain their identity well into the far wake. The level of turbulence kinetic energy is remarkably insensitive to the type of ship. For the root-mean-square value of the velocity fluctuations as a fraction of the ship speed (which equals the square root of twice the turbulence kinetic energy) we find in the towed-hull wakes maxima of: 0.106±0.02 at x/Lpp=0.25 0.067±0.01 at x/Lpp=0.60 0.047±0.01 at x/Lpp=1.00 without a clear differentiation with respect to ship types. For the propelled-hull wakes a similar conclusion can be drawn. The decay of the maximum value of the turbulence kinetic energy in the propeller jet is plotted in Fig.12 for several hull/propeller combinations. All data stay within a narrow band. Fig. 12. Decay of maximum value of turbulence kinetic energy in propeller jet We did consider to fit the decay rate into a simple power law, but this turned out to be unjustified. The measurements do not extend far enough to have a region of sufficient length where self-similarity of the flow has been established. A least-squares approximation would certainly yield a misleading figure for the exponent in the power law. 4.5. Effects of ship features 4.5.1. Propulsion configuration The data base allows us to study the differences between the wakes of single and twin-screw propeller configurations. In addition, for twin-screw propeller units the influence of the direction of rotation of the propellers can be examined. Since all hull forms of the data base have port-starboard symmetry, the only source of asymmetry in the time-averaged velocity field behind single-screw ships is the propeller (assuming ideal test conditions). Serious port-starboard asymmetries are therefore basically introduced by the propeller, although bilge vortices and rudder can considerably enhance them (cf. section 4.1.3). Twin-screw configurations, on the other hand, maintain the port-starboard symmetry. The direction of rotation of twin-screw propellers proves to be relevant for the secondary flow pattern found behind the hull. Particularly, when the hull in front of the propellers generates bilge vortices roughly co-axial with the propeller axes, either a cancelling or an amplification effect of the secondary motion occurs, depending on the sense of rotation of the propellers. 4.5.2. Beam-draft ratio There seems to be a strong correlation between the beam-draft ratio and the significance of the side vortices: for low B/T pronounced side vortices are found, while they are virtually absent for high B/T. As a consequence of the presence of strong side vortices with their rapid outboard motion due to the induction effects of the virtual image vortex system, the initial rate of spreading near the free surface is comparatively high for ships with low B/T.

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Twenty-First Symposium on NAVAL HYDRODYNAMICS 4.5.3. Trim/Loading condition Tankers operate usually at two distinct drafts, associated with the fully loaded and the ballast condition respectively. The two loading conditions imply different beam-draft ratio's, the effects of which have been reviewed above. Another aspect, however, is the trim. When a tanker operates in ballast condition, it is usually trimmed by the stern. It means that the keel plane is slightly inclined with respect to the direction of the onset flow. Consequently some extra lift production is expected, which is revealed by the increased strength of the bilge vortices. This argument is confirmed by the results of two tankers in the data base. The results for one of them are shown in Fig.13. Unfortunately, the third (31) seems to indicate an opposite effect so that there is no full corroboration. Fig. 13. Comparison of secondary flow behind tanker in full load (top) and ballast (bottom) condition (x/L=0.559) 5. Closing remarks The main aim of the present investigation was the establishment of a data base of macro wake measurements for a broad range of ships. Data have been collected for eight hull forms, a supplementing ninth data set being already available. Although macro wake measurements are not new, the scope of the AFDEASR project went beyond that of all previous ones. A rich source of information has therefore been established. An analysis has been made of the data and the main results have been collected in thid paper. Plausible explanations have been found for some initially puzzling results. In this regard the wide scope of the investigation proved to be helpful: conjectures about the explanation of one data set could be corroborated by another. The results have also provided clues for the deliberate modification of a wake structure. Hull shaping, rudder positioning, propeller turning direction, to name a few, have proved to be means which can affect the global structure of a wake considerably. The analyses presented in this paper are not exhaustive. The data can be used for further analyses and for correlations with either satellite observations or numerical simulations. References 1. Reed, A.M., Beck, R.F., Griffin, O.M. & Peltzer, R.D.: “Hydrodynamics of Remotely Sensed Surface Ship Wakes”, SNAME Transactions, Vol. 98, 1990, pp. 319–363. 2. Lindenmuth, W.T. & Frye, D.: “Viscous Macro-wake Behind a Twin-screw High Speed Surface Ship”, DTRC/SHD-1273–01 ( 1987). 3. Buchhave, P.: “Three-Component LDA Measurements”, DISA Information, No. 29 ( 1984). 4. Tropea, C., Dimaczek, G., Kristensen, J., Caspersen, Chr.: “Evaluation of the Burst Spectrum Analyser LDA Signal Processor”, Fourth International Symposium on Applications of Laser Anemometry to Fluid Mechanics”, Lisbon ( 1988).

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Twenty-First Symposium on NAVAL HYDRODYNAMICS APPENDIX I: Lengthwise position of measurement planes Plane positions are indicated per data set as a fraction of the ship 's length, the positive direction being from bow to stern with the origin at the aft perpendicular. nom.=wake of unpropelled hull prop.=wake of propelled hull 11 12 21 22 31 32 34 nom. prop. nom. prop. nom. prop. nom. prop. nom. prop. nom. prop. nom. prop. –.719   –.719   –.732   –.732   –.770   –.770   –.479   –.479   –.488   –.488   –.514   –.514   –.160   –.160   –.163   –.163   –.171   –.171   .000 .080 .000 .080 .000 .081 .000 .081 .000 .086   .086 .000 .086 .240 .240 .240 .240 .244 .244 .244 .244 .257 .257   .257 .257 .257 .559 .559 .559 .559 .569 .569 .569 .569 .599 .599   .599 .599 .599 .879 .879 .879 .879 .894 .894 .894 .894 .941 .941   .941 .941 .941   1.358   1.358   1.382   1.382   1.455   1.455   1.455   1.838   1.838   1.870   1.870   1.969   1.969   1.969 41 51 61 62 64 71 81 nom. prop. nom. prop. nom. prop. nom. prop. nom. prop. nom. prop. nom. prop. –.678   –.667   –.664   –.664   –.713   –.648   –.509   –.381   –.379   –.379   –.408   –.370   –.170   –.190   –.190   –.190   –.204   –.278   .000 .085 .000 .095 .000 .095   .095 .000 .095 .000 .102 –.185   .254 .254 .286 .286 .284 .284   .284 .284 .284 .306 .306 .000 .093 .594 .594 .667 .667 .664 .664   .664 .664 .664 .713 .713 .278 .278 .933 .933 1.238 1.238 1.233 1.233   1.233   1.325 1.325 .648 .648   1.441   2.000   1.991   1.991   2.140 1.203 1.203   1.781   1.943