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Breaking waves generated by a fast displacement ship model A. Olivieri, F. Pistani, A. Di Mascio and R. Penna. INSEAN, (Italian ship model basin), Via di Vallerano 139, 00128 Roma. ABSTRACT Bow and shoulder wave-breaking, generated by a fast displacement ship model (INSEAN model 2340) has been experimentally investigated. Both the mean and the rms point wise values of the wave height have been obtained by means of a finger probe. The intensity of the breaking is highlighted by the highest values of the wave fluctuations nearby the bow wave crest. The velocity field under the free surface was measured 0.2 Lpp downstream the fore perpendicular by means of a 5-hole Pitot probe. These measurements were performed just downstream the maximum of the wave fluctuation. Very detailed database for CFD validation was carried out for the wave height. The measured velocity field completes the database and highlights interesting flow features. Uncertainty assessment of the wave height and velocity results was performed following the AIAA Standards S-071-1995. Preliminary CFD results from a RANSE code (without a breaking model) are shown in comparison with the measured data. INTRODUCTION Although wave-breaking phenomena are frequently present in naval hydrodynamics applications, they are far from being completely understood. From the physical point of view, it is crucial to understand how breaking waves are generated, and how they modify the flow field. Furthermore, from the engineering point of view, it is important to have a physical model in order to take into account the effect of the wave-breaking. Nonetheless, all models need a calibration that can be performed only if experimental data are available. Presently, available models for breaking wave simulations are not able to describe the three-dimensional case, while, they well reproduce 2D classical experimental results [2], (see e. g. t33~. Colagrossi et al. [4] recently proposed a "2D+tmeshless model " in order to simulate breaking waves around a ship, obtaining results that qualitatively represent the breaking scenario. Intensive experimental works have been carried out in order to obtain experimental data on ships breaking waves. Dong et al. provide a very complete and useful database for the case of the DTMB 4817 model, in terms of mean and instantaneous cross-flow by PIV system [51. A critical point in wave breaking experiments being the effect of the surface tension, which can determine formation of capillary waves, it is necessary to obtain experimental results independent of it. In fact, surface tension is a physical characteristic of the water used in the experiments and it changes in different experimental realizations. Furthermore is not easy to measure the surface tension in order to quantify its effect on breaking. The presence of surfactants is not avoidable in large basins, so surface tension can change even during the same experiment. The influence of capillary waves on the wave breaking process is increasingly important for smaller wavelength t6, 73. Thus, it is necessary to perform experiments on large- scale model flows and relatively high Froude number in order to generate long waves. For these motivations, we decided to perform measurements of the breaking wave flow generated by a large model scale (Lpp = 5.72 m) at relatively high Froude number (Fr = 0.35~. The model INSEAN 2340 is an identical geosym of the DTMB 5415 model that has been adopted by the International Towing Tank (ITTC) as a recommended benchmark for CFD validation for resistance and propulsion (ITTC, 1996 [101~. A previous experimental study, regarding far field wave elevation was performed for Froude numbers Fr = 0.28 and Fr = 0.41 [13. In the case of Fr = 0.28, the wave breaking was too gentle and affected by capillary waves formation, while at Fr = 0.41 the breaking was largely developed, plunges and large spray formation was observed. The present Froude number (Fr=0.35) has been selected on the bases of a previous photographic study. We observed that for Froude numbers larger than Fr = 0.325, the bow wave breaks without appearance of capillary waves. On the other hand at Froude number larger than Fr = 0.35, the bow wave breaks producing large spray, which makes the wave height measurement not practicable. Preliminary results from numerical simulation using a RANSE code have been reported. It has been noted the tendency to develop a roll close to the surface even without a model for the breaking waves.
MODEL GEOMETRY AND EXPERIMENT DESIGN The INSEAN model 2340 is an identical geosym of the DTMB 5415 model, adopted by the International Towing Tank Conference (ITTC) as a recommended benchmark for CFD validation for resistance and propulsion [101. It was conceived as a preliminary design for a surface combatant. The model, whose lines are shown in Fig. 1, presents a transom stern and a bulbous bow of peculiar shape, designed for the sonar lodging. Its length between the fore and aft perpendiculars is Lpp = 5.72 m, which corresponds to a scale ~ = 24.8. The main geometric parameters of the model are given in Tab. 1. All tests have been performed with the bare hull. The model has been made of wood at the INSEAN workshop. In order to stimulate turbulent flow, a row of cylindrical studs of 3 mm height and 3 mm diameter have been fitted on the model 0.05 Lpp downstream the fore perpendicular, with 30 mm spacing. The experiments have been performed at INSEAN basin n. 2, which is 220 m long, 9 m wide and 3.5 m deep. During the tests, the model was held fixed, with trim and sinkage set to the values previously determined in unrestrained conditions t81. The nominal speed has been set to U0 = 2.621 m/s, corresponding to Froude number Fr = 0.35 and Reynolds number Re = l.sx107. The wave height has been measured by a servo-mechanic probe (Kenek SH), mounted on a system of slides fixed to the carriage. The wave field has been obtained measuring point by point along 81 transverse cuts from the bow to about midship. The transverse displacements (2 cm) were actuated automatically, while the longitudinal ones (4 cm) were obtained manually. The acquisition time interval was set to 2.2 s and the sample rate to 1000 Hz. The carriage acceleration was lowered as much as possible in order to reduce the wave fluctuations due to the transient wave components (see for example [23~. Velocity field has been measured on the port side, at a x-station located 0.2 Lpp downstream the fore perpendicular, using a 5-hole Pitot probe. A classical Pitot tube has been used to measure the static pressure in the undisturbed flow region, far enough from the model. Five differential pressure transducers (Valydine DP15) have been connected to the five Pitot holes and to the static pressure hole of the Pitot tube t81. The acquisition system run automatically, guided by software implemented at INSEAN. Two orthogonal slides, actuated by two step-motors, drove the Pitot to the measuring point, starting from a reset position. The two step-motors have a resolution of 200 steps per revolution and the manoeuvring screw has a pitch of 10 mm, so that the spatial resolution of the device is 0.05 mm in vertical and transverse direction. The carriage speed signal was checked by the software before starting the acquisition and during the acquisition itself. When the signal was within a pre-defined range, the acquisition started. At the end of the acquisition, the system moved the Pitot to the next measuring point. A regular grid with square cells, whose side dimensions are ~ xg = ~ yg = 0.0025 Lpp, has been drawn just below the free surface. The adopted sample rate was fs= 100 Hz and the acquisition time interval was set to la = 4.6 S. depending on the distance from the free surface, in according with a previous analysis performed to determine the time needed to have a steady average. The three-velocity components and the pressure coefficient, in the measuring point, were calculated by software through the calibration maps [8], with real time preview. In the following, the Cartesian frame of reference is considered fixed to the hull, with the origin at the intersection between the fore perpendicular and the undisturbed water plane. In particular, x, y and z axes are in the direction of the uniform flow, starboard side of the hull and upward, respectively, and the corresponding velocity components are ~ (axial), v (transverse) and w (vertical). Description Fig. 1: test model INSEAN 2340 Scale factor ~ Length between perpendiculars LPP (m) Draft Displacement Displaced Volume Wetted surface area 142.0 B (m) 18.9 T (m) 6.16 (t) 8636.0 V (m3) 8425.4 Sw (m2) Hull coefficients Lpp /B 7.530 B/T 3.09 1 _ ) 11.0 Ship Model 24.824 5.720 0.76 2949.5 0.248 0.549 0.549 4.786 CB V/( LppBT) 0.506 Cp V/( LppAx) 0.613 Cx AX/BT 0.825 Tab. 1: Geometrical data for INSEAN model 2340 and full-scale ship. 2
WAVE-HEIGHT FIELD A preliminary photographic study has been carried out in order to set the Froude number. In particular, we observed that, for low Froude numbers (<0.35), the breaking occurs with appearance of capillary waves, due to the relatively small wavelength of the divergent waves. This occurs only for the ship model case, so that the analysis on the wave pattern cannot be extended to the full-scale case. On the other hand, for relatively high Froude numbers the breaking is characterized by the presence of spray, which makes the wave height measurements not practicable. As a satisfactory compromise between the two requisites, the Froude number has been set to Fr = 0.35. Photographs of the ship model bow-wave are shown in figures 2- 8, for seven different Froude of numbers, from Fr = 0.28 to Fr = 0.45. n 's (transient) wave components and electronic noise. Patterns of the mean and rms value of the wave elevation are shown in figures 9 and 10. The highest values of the rms indicate presence of fluctuations of the wave elevation due to wave breaking. The bow wave breaking is quite strong with the maximum of the rms value of about 1/10 of the maximum wave height. A typical trace of the acquired signal in the breaking region is shown in figure 11. Although the shoulder wave crest is under the undisturbed water level, it manifests a gentle spilling wave breaking, as underlined by the grey strip in figure 10. The shoulder wave breaking is probably induced by the bow breaking wave. In fact, in the farther field the shoulder wave crest is positive and does not break [113. Figs 2-4: bow breaking wave generated by the INSEAN 2340 model at Froude numbers smaller than Fr = 0.35; 1) Fr = 0.28, 2) Fr = 0.30, 3) Fr = 0.325. Figs 5-7: bow breaking wave generated by the INSEAN 2340 model at Froude numbers larger than Fr = 0.35; 4) Fr=0.375,5)Fr=0.41,6)Fr=0.45. -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 x Fig 9: wave height contours (mean value) -0.2, -0.~S -0.05 o 0.05 Fig 8: bow breaking wave generated by the INSEAN 2340 model at Froude number Fr = 0.35. The wave height in the bow and shoulder region of the near field wave pattern has been measured. The mean value and the rms value have been carried out after frequency analysis and filtering, which allowed to reduce the error due to the presence of spurious n nnF+nn 7 27F.11d ~17F Be Q Ills F.n~ -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 X Fig 10: wave height contours (rms value) 15 1O ' is Fig 11: breaking and non-breaking wave height signal time traces 3
VELOCITY FIELD INDUCED BY THE BOW BREAKING WAVE The velocity field has been measured on a cross-section just downstream the bow wave front (x = 0.2~. Measurements have been obtained by S-hole Pitot probe. The adopted procedure is the one described in [81. The results are shown in figures 12.15 in terms of axial velocity contours and cross-flow vectors, transverse velocity contours, vertical velocity contours and axial vorticity. n .n n1 on, -0.1 y -0.075 Fig 12: axial velocity contours and cross-flow vectors at section x = 0.2; reference vector (top-right) is equal to the nominal velocity U0 = 2.621 m/s, the mean value of the wave height is shown by solid line + the rms value (dashed lines). -0.02 on', .n no Fig 15: axial vorticity contours at section x = 0.2, the mean value of the wave height is shown by solid line + the rms value (dashed lines). The wake field generated by the bow breaking wave is clearly shown by axial velocity and vorticity contours. Although the maximum of the axial vorticity is inside the wake, it is possible to recognize presence of vertical flow, quite far from the wake. This is more clearly shown in figure 16 where an offset value has been subtracted to the cross flow velocity components. According to this results, the picture in figure 17 displays the presence of vertical flow (rolls), quite far from the hull and very close to the free surface. o.o~ -0.125 -0.1 y -0.075 ADS Fig 13: transverse velocity contours at section x = 0.2; the mean value of the wave height is shown by solid line + the rms value (dashed lines). on' _ .02 _ . ...,... ..,, .. -- ~ I-.... 1 . l l -1 Fig 14: vertical velocity contours at section x = 0.2; the mean value of the wave height is shown by solid line + the rms value (dashed lines). on 25 ~.1 Fig 16: cross-flow associated to the rolls (obtained subtracting an offset value to the transverse and vertical velocity components); reference vector (top-right) is equal to the nominal velocity U0 = 2.621 rn/s Fig 17: vortices induced by wave-breaking 4
UNCERTAINTY ASSESSMENT OF THE EXPERIMENTAL RESULTS Uncertainty assessment of the results has been carried out following the AIAA Standards S-071-1995, for both wave elevation and velocity. Test measurement points and related uncertainties are reported in table 2 and table 3. x _ 0.07s 0.100 0.125 0.150 y -0.09 -0.09 -0.09 -0.09 _ <h> 3.0010 3.91 10 s.20 10 9.07 10- _ <h'7ns> s.so 10- 5.81 10- 7.96 10- 8.53 104 _ Unc. (<h>) 1.45 10 s 7.33 10 8.39 10 4 1.6110 Unc. (ham) 9.5010 .12 10 .40 10 .9910 Tab. 2: Uncertainty assessment results for the wave height | Unc. (m/s) | Unc. /U* _ <u> <v> -0.3258 2.4551 0.9367 1.80 10-2 0.687 % -0. 1243 _ 8.9910-3 1.47 % _ <w> 0.0595 0.0227 9.67 10-3 1.58% Tab. 3: Uncertainty assessment results for the velocity (y = - 0.1015, z = - 0.005); U* = Uo for the axial velocity component, while, for transverse and vertical components U* corresponds to their range of variation in the measured field. NUMERICAL RESULTS The numerical simulation were performed by means of a RANSE code for the simulation of free surface flows, developed at INSEAN. Details of the algorithm and computational examples can be found in (Di Mascio et al., 2001 [123~. The one equation Spalart-Allmaras model t13] was used to compute the eddy viscosity. The flow was computed for the same condition as the towing tank tests. The Froude number was set equal to 0.35 and the Reynolds number to 1.57x107. The solution was computed with a grid made of 13 blocks, for a total of about 1.6x106 cells. The computed wave pattern is reported in figs.18 and 19, close to the bow and the stern, respectively. The global wave pattern is compared with the measured data in fig.20. As it can be noticed, the computed wave height at the bow is higher than the measurements. This is to be ascribed to the lack of any model to simulate the rather strong breaking wave observed in the experiments. The velocity field is reported in fig.21, in terms of axial velocity and cross flow vectors, in the cross sections x= 0.05, 0.10, 0.15 and 0.20. The wave profile in the yz plane can also be observed. Again, the predicted profile is poorly predicted in the breaking region, an probably also the vertical flow caused by the overturning wave is not well represented. Nonetheless, the predicted flow shows the tendency to overturn close to the wave crest as in the experimental data (figs 12, 16 and 20 x = 0.2~. CONCLUDING REMARKS The measurements were intended as a database for CFD validation. In fact, the ship flow predictions obtained by numerical codes in presence of 3D wave breaking is quite difficult and needs many effort in order to predict and follows the breaking waves. Nonetheless, present experimental results give important indication on the physics of the flow generated by ship (model) breaking waves. Measurements on two more cross sections, respectively located at x = 0.15 (:just upstream the section investigated in present work) and x = 0.4, have been planned in order to better understand the rolls generation at the bow breaking wave and the flow resulting from the shoulder breaking wave. Moreover, an extension of the investigated wave field has been planned along the shoulder wave crest [111. The numerical results, even if without any breaking model, show the tendency of the flow to form quasi-streamwise rolls, downstream the bow breaking wave. The modeling of the breaking wave and the production of turbulence and vorticity beneath the breaking region is the subject of further research. 0.4 0.3 _ 0.2 0.1 n n 1~ 0.1 . D.08 0.06 0.04 0.02 s . . :. i,,'~ ~ ' .'....1 ... ;...1...1 J~ 1 i f~ 1 1 ~ -0.7 -0.6 -0.5 -0.4 -0.3 X -0.2 -0.1 _ _ . ,j,. ,- _ , . ,,...' _ ,,. // ~ ~ ~3 ~ ~ ~ ~ X Figs 18,19: numerical wave field
0.02 On -o.od fain! Pond in n 0.02 0.01 1 nnA -o os .n of .n no 0.03 0.02 0.01 o -0.01 -0.02 -0.03 r.O,04 -0.05 -0.06 -0.07 -0.08 -0.0 Yn 1 0.025 0.05 0075 0 1 y 0.02 t nn1 o -0.01 -0.02 ~4 -0.03 Ant .n no -0.06 in n7 0.6 0.5 0.4 0.3 -0.1 -0.2 -0.3 -0.4 W... . DTMB 5415 . Fr=0.35 Re = 1.575e+7 .. NU M ERICAL _...................................................... . . . . . . . . . . . . ..... . .... . ..~-.~ '2".--:''T,~' 6''"~ ', ~'"'~ " ;'' ' i -0.4 -0.2 0 0.2 0.4 0.6 x Fig 20: numerical vs experimental wave field - x=o.oe x=O.1 0 . , 1,. ....... ........... 0 0.025 0.05 0.075 0.1 y Fig. 21: velocity field contours of the axial velocity component and cross flow vectors. 6
0.02 t 0.01 ~ Inns -O.OZ ~4 -0.03 -0.04 nest -0.06 -0.07, 0.03 0.02 0.01 o -0.01 -0.02 -0.03 ~0.04 -0.05 -0.06 -0.07 -0.08 -0.09 -0.1 x=0.1 5 ~- _ ~ _ i,,,.' ~ ~ - I < a. _ - I,,,,,,,,,,,,,,,, I, , J 0.025 0.05 0.075 0.1 0.125 0.15 ~ y 0.02 O01 n .nn1 -0 02 .n~` Ann -0.05 .n no .n no x=0.20 0.03 0.02 0.01 o -0.01 -0.02 4.03 ~0.04 -0.05 -0.06 -0.07 -0.08 -0.09 0.1 0.07' 0.1 Fig. 21 (cont.~: velocity field contours of the axial velocity component and cross flow vectors. ACKNOWLEDGEMENTS This work was sponsored by the Italian "Ministero delle Infrastrutture e dei Trasporti" through the INSEAN Research Program 2000-2002, and by the Office of Naval Research contract N00014-00-1-0344 under the administration of Dr. Patrick Purtell. Special thanks to M. Palini, G. Bartoccioni, M. Sellini, L. Benedetti and F. La Gala for their aid in the preparation of the experimental set-ups and in collecting data. REFERENCES: t1] A. OLIVIERI, F. PISTANI AND R. PENNA. 2000. "Detailed measurements of wave-pattern and nominal wake of a fast displacement ship model". Advances in Fluid Mechanics III. [8] t2] J.H. DUNCAN. 1981. "An experimental investigation of breaking waves produced by a towed hydrofoil". Proc. R. Soc. Lon. A 377, 33 1 -348. t3] A. DI MASCIO, R. MUSCARI "A model for the simulation of spilling breaking waves" submitted to J. Ship Res [4] A. COLAGROSSI, M. LANDRINI, M.P. TULIN, "Numerical Studies of Wave Breaking Compared to Experimental Observations". 4th 7 Numerical Towing Tank Symposium (NuTTS), Hamburg 2001. R.R. DONG, J. KATZ, T.T. HUANG. "On the structure of Bow Waves on a Ship Model" 1997. J. Fluid Mech. 346: 77-1 15 A. IAFRATI, E.F. CAMPANA. "Direct numerical simulation of free surface tension dominated and non-dominated breaking waves" submitted to 24th Symposium on Naval Hydrodynamics, ONR, 2002. [7] A. IAFRATI, A. OLIVIERI, F. PISTANI and E.F. CAMPANA. "Numerical and experimental study of the wave breaking generated by a submerged hydrofoil " 23r~ Symposium on Naval Hydrodynamics, Val de Reuil 2000. A. OLIVIERI, F. PISTANI, G. AVANZINI, F. STERN and R. PENNA "Towing Tank Experiments of Resistance, Sinkage and Trim, Boundary Layer, Wake and Free Surface Flow around a naval combatant INSEAN 2340 Model" IIHR Report N°421, September 2001. [91 H.W. COLEMAN, W.G. STEELE. 1 995. "Engineering Application of Experimental Uncertainty Analysis". AIAA J., Vol.33, N.10, pp. 1888-1895.
[10] ITTC 1996 Report of the resistance and flow committee. 21St International Towing Tank Conference, Trohdheim. [11] A. Olivieri, F. Pistani, R. Penna. 2002. INSEAN Technical Report (in preparation). [12] A. Di Mascio, R. Broglia and B. Favini 2001 "A second order goudunov-type scheme for naval hydrodynamics", Godunov Methods, Theory and Application, edited by E.F. Toro, Kluwer Academic/Plenum Publishers, [13] P. R. Spalart, S.R. Allmaras 1994 "One- equation turbulence model for aerodynamic flows", La Recherce Aerospatiale, Vol. 1, p. 5. 8
DISCUSSION Luis Perez-Rojas Polytechnical University of Madrid, Spain The author presents some values for the uncertainty analysis on the wave elevation measurements. I would like to point out that in these kind of measurements, each point has a value for its uncertainty and in my opinion is not correct to give a mean value for uncertainty analysis 0 refer the error to highest value of wave election. I would appreciate the opinion of the author in this matter. o -0.05 -0.1 A AUTHORS' REPLY We agree with the opinion of the discusser. In fact, we do not give a mean value of the uncertainty in the wave field, but the uncertainty on four pointwise measurements camed out respectively in the non-breaking (1,2), intermediate (3) and breaking (4) regions (fig. Rib. We show the uncertainty on the time-averaged (indicated by "mean" in the paper) and rms value of the wave elevation in these points. Finally, we refer the uncertainty values of the time-averaged wave elevation to its maximum modulus because it is a non-zero representative value of the measured wave field. ~ W~. ~ ''I - , , , ~ , , , , . , , , , , , , , , , , , , , , , 1 0 0.1 0.2 0.3 x Fig R.1: analyzed points for wave elevation uncertainty assessment; iso-levels of h r m s are shown to underlying the wave breaking intensity.
