The wash or ship-generated waves from high speed craft has become a common subject in research and development of marine transportation. Since some time now the wake wash of high speed craft has become a problem in particular on inland or confined waterways. This wake wash has an impact on safety and environment such as bank/shoreline erosion, risk to people on shore and small boats in harbors and changes in the local ecology. This paper describes the results of model test of a high speed patrol, together with theoretical prediction of wake wash

Abdul Ghani, Mohamad Pauzi

Abdul Rahim, M. N.

English

Universiti Teknologi Malaysia Institutional Repository

  Jurnal Mekanikal December 2008, No. 26, 129 - 140 129  THE PREDICTION OF WAKE WASH IN THE TOWING TANK  Mohamad Pauzi Abdul Ghani1*, M.N. Abdul Rahim2  1Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 UTM, Skudai,  Johor  2PETRONAS, KLCC, Kuala Lumpur   ABSTRACT   The wash or ship-generated waves from high speed craft has become a common subject in research and development of marine transportation. Since some time now the wake wash of high speed craft has become a problem in particular on inland or confined waterways. This wake wash has an impact on safety and environment such as bank/shoreline erosion, risk to people on shore and small boats in harbors and changes in the local ecology. This paper describes the results of model test of a high speed patrol, together with theoretical prediction of wake wash.    Keywords: Ship-generated waves, wake wash  1.0 INTRODUCTION  Ship moving through the water generates two sets of waves, divergent waves which move out at an angle from the centerline of travel and transverse waves, which move out from the stern perpendicular to the centerline of travel. These are easily noticed when viewed from above in an airplane or from a bridge as a vessel passes beneath [1]. They are illustrated in Figure 1.   The generation of the divergent waves is a function of hull form (prismatic coefficient), angle of entry, speed, and speed-length ratio V/(Ls)0.5 and is significant in the development of the height and energy of the wave train, particularly at low or intermediate speeds. The transverse wave form is usually negligible at low speeds but increases with speed up to a length Froude Number of about 0.6 and at higher speeds the transverse wave disappears in the range of     0.6 ≤ Fn ≤ 1.0 leaving a bow divergent wave and a stern divergent wave [2].  The angle α in salt water develops to be 19.46° initially for all ships but the angle of obliquity β, varies with hull form and speed, being lower at higher speed length ratios (4°-10°) and higher for lower speed length ratios and fuller hull forms (20°-30°).                                                   * Corresponding author: E-mail: pauzi@fkm.utm.my    Jurnal Mekanikal, December 2008 130               Figure 1: Ship-generated waves [2]    The significance of the angle of obliquity (β), is that the direction of the movement of the energy front will be as shown in figure 1 and the wave length (L) and wave period (T) will be affected by the angle of wave generation. In general, the finer the bow entry, the smaller the angle β and thus the smaller the wavelength and period. This smaller wavelength results in a lower energy density for a vessel’s wash [3].  2.0    SHIP WAKE WASH PATTERNS         The best measure of deep water for vessel generated waves is the Depth Froude Number, given by [4]:   ghVFnh =  (1)  where        V  is vessel speed, g  is the gravitational constant, h  is the water depth   For the purpose of wash comparison, vessels may be considered to be free of shallow water effects when h /LwL exceeds 1.  The Depth Froude Number is critical in determining wash characteristics in shallow water, just as the Length Froude Number is in determining wash characteristics in deep water. However, the influence of the critical value of Fnh is much more visible, dramatic and well defined than that of the Length Froude Number. The Length Froude Number is given by [4]:    )(LWLgVFnl =  (2)  The main categories are as follows;   • sub-critical, Fnh < 1 • critical ,  ship speed = maximum wave speed , Fnh = 1  Divergent wave Cusp line Transverse wave V sin β  Jurnal Mekanikal, December 2008  131 • super-critical , ship speed > maximum wave speed , Fnh > 1 • high speed sub-critical similar to sub-critical but recognizes that high speed ships in deep water can produce divergence waves with or without the transverse wave component depending on the length Froude number (the ratio of ship velocity to a function of waterline length), • trans-critical or near-critical depth Froude numbers between 0.85 and 1.1.  Below the critical value of Fnh = 1.0 the wash pattern for a vessel with a Fnl less than about 0.9 appears as shown in Figure 2.    Figure 2: Sub-critical wash pattern for displacement vessels [4]  If a vessel is transiting from deep water to shallow water at constant speed, at Fnl values less than about 0.9, and we cross this critical depth in relation to that speed, the direction of wave propagation will be seen to change from that shown in Figure 2 to the pattern shown in Figure 3.     Figure 3: Critical wash pattern for displacement vessels [4]  For vessels with a value of Fnl approaching and exceeding 1.0, the wash pattern will be the standard pattern depicted in Figure 4, and will not produce the critical wave shown in Figure 3. Wave Propagation Direction  Fnh < 1.0  Fnl < 0.65 Fnh = 1.0  Transverse Wave  V sin βα βDivergent Wave Cusp line   Jurnal Mekanikal, December 2008 132   Figure 4: Wash pattern for supercritical operation                        and vessels at speeds above Fnl = 0.9 [4]  For vessels that are somewhere below Fnl ≈ 0.9 but not in the region below the hump (Fnl < ~0.65), the wash pattern will be somewhere between the two conditions of Figure 4 and Figure 2. All of this can be quite important in predicting the character of the wash and where it will reach a given beach.  3.0 EFFECT OF WATER DEPTH  In shallow water, the pressure gradient on the hull, and therefore the wave pattern generated by the vessel is influenced by the waves reflecting from the sea bottom. When a wave is propagating in water having a depth of less than approximately half the length of the wave, the wave induced water particle motion reaches the bottom and the water depth affects wave characteristics. In shallow water the wave speed (celerity) of a gravity wave is given by[5],  gdTLC ==  (3)   The ratio of the vessel speed to the maximum wave celerity in shallow water is often used to classify the wash produced by a vessel. This ratio, called the Depth Froude Number is defined as follows [5];   ghVFnh =  (4)   At Fnh = 1, the wave speed increased to its physical maximum of gd  . Normally the transverse wave will travel at the same speed as the vessel, however Supercritical speed all vessels Fnh > 1.0             Fnl > 0.9 Subcritical speed and critical speed for vessel with Fnl > 0.9 β2 β1   Jurnal Mekanikal, December 2008  133 since it physically cannot go any faster, the wave gets much larger, and the ship resistance increases dramatically. In deep water the vessel length Froude number,   )(LWLgVFnl =  (5)  is used to classify wash. At a critical value of Fnl ~ 0.4 to 0.55 the wavelength of the transverse waves equals the ship length giving a condition similar to the critical condition in shallow water.   For most displacement vessels, in normal speed ranges, there is no strong wave bottom interaction if the water depth to draft ratio, d/T, is greater than 3 to 5. The d /T ratio will most often be less than 3 for the displacement vessels being studied, thus Fnh has been used in analysis.   Vessel generated wake wash in shallow water is usually classed in three categories. Those produced by vessels that travel at sub critical Froude numbers, those produced at the critical Froude number of 1, and those produced by vessels that operate at supercritical Froude numbers such as planning craft and multi hulls. Normally the cruise ship operates at sub critical Froude numbers whereas the patrol vessel generally operates at supercritical speeds and is treated separately [6].  4.0  EXPERIMENTAL STUDY  4.1 Model Testing Experiment to investigate wake wash from patrol craft were conducted in calm water over a wide range of speeds corresponding to a range of depth Froude numbers Fnh 0.6 to 1.4 in towing tank 120 m x 4 m x 2.5 m of Marine Technology Laboratory UTM. During the model tests to measure the wash, resistance, heave and trim were also recorded by D.A.A.S at towing carriage. The wash or wave cuts was measured by 4 wave probes and recorded by LabView software which integrates with wave probes, signal conditioning unit and computer as shown in Figure 5.   For this experimental study a model of Harbor Patrol Boat (MTL 0029) with 8.75 scale ratio as shown in Figure 8 was used for wake wash investigations. The principal particulars of the model and ship are shown in Table 1.   Table 1: Ship and model particulars Item Ship Model Length Overall LOA, m 15.0 1.71 Length Between Perpendicular, m 12.6 1.44 Breath B, m 4.2 0.48 Trim, m 0.063 0.0072 Draught Forward Tf , m 1.038 0.119 Draught Aft Ta, m 0.911 0.104 Volume Displacement ∇, m3 19.60 0.0293 VCG or KG, m 1.948 0.223 LCG from AP 5.385 0.615 Block Coefficient, CB 0.392 0.392 Midship Coefficient, Cp 0.709 0.709   Jurnal Mekanikal, December 2008 134    Figure 5: Wash measurement apparatus [6], [7]    Figure 6: Wave probe arrangement [7]    Figure 7: Model ready for testing [7]  Signal conditioning unit Wave probe Wave probe holder   Jurnal Mekanikal, December 2008  135 5.0 THEORETICAL APPROXIMATION  The values of ship generated wave heights were predicted using a recently published regression model produced by Kriebel, Seelig, and Judge [8]. The equations are developed from regression analyses of data collected by the authors with adjustments to satisfy some theoretical considerations. The model also is based upon a regression analysis of ship generated wave data from model tests of a wide variety of vessels include patrol craft.  The formulas they provide are mostly a modification and combination of those produced by Sorensen and Weggel, [9] and Gates and Herbich [10]. The vessels in the data set were only tested at Fnh up to 0.8, with most of the data points in the 0.3 to 0.8 range. So formulas are only relevant for Fnh up to 0.8, and those predictions below Fnh of 0.3 will be less accurate.  Table 2: The formulas proposed by Kriebel et. al [8]   where  H Maximum ship generated wave height, m C  Celerity, m/s (wave speed) FL  Length based Froude number Fd  Depth based Froude number F*  Modified depth based Froude number LBP Ship length between perpendiculars, m d Water depth, m R  Ship draft, m Cb  Ship block coefficient Le  Bow entrance length, m Vs  Ship Speed, m/s α  Coefficient related to hull form – used in wave height regression analysis β  Coefficient related to bow shape – used in wave height regression analysis y Distance from sailing line, m Lw  Wavelength, m θ  Angle between sailing line and line perpendicular to direction of diverging waves    Jurnal Mekanikal, December 2008 136 6.0 RESULTS AND DISCUSSION  There are several methods which can be used to analyze the measured data. The first approach utilizes the wave energy method, i.e the calculation of the energy of the wave system at the measuring position. The second approach is based on the maximum and minimum amplitude of the generated wave (or to find the highest wave in the measured data). This study only covers the second approach and the results are tabulated in Table 3. This table shows the maximum wave height for the model as function of Fnh at 4 different probe locations. It is obvious from this table that the largest waves are produced at depth Froude number is near the so-called critical Froude number, Fnh ≈ 0.9. The result was validating with theoretical approach equation in Table 2 suggested by Kriebel, Seelig and Judge [8]. However, these formulas are only relevant for Fnh up to 0.8, and the predictions below Fnh of 0.3 will be less accurate. Table 4 shows the theoretical results of maximum wash height by using formula as suggested by Kriebel et. al.   Figure 8 shows the total model resistance plotted against depth Froude number and model. It can be seen that model resistance rising rapidly as the shallow water critical speed was approach. In this figure also, it can be seen that there was an increase in resistance in shallow water at sub-critical speeds, rising to a peak just below the depth Froude number, Fnh = 1.1 , but at super critical speeds a reduction in resistance was obtained when compared with the value in deep water at the same speed.  Figures 9 and 10 show the heave and pitch in shallow and deep water respectively. From these figures, it can be concluded that when ship achieve critical speed it try to plan as a planning craft characteristic and this condition will influence the length to beam ratio (LWL/B) simultaneously wash height because wash height are inversely proportional to length to beam ratio. Figure 11 shows the relationship between the divergence of the leading wave crest and the depth Froude number. The correlation with the experimental is quite good.  Table 3: Experimental maximum wash height  probe 1 probe 2 probe 3 probe 4  y/L = 0.53 y/L = 0.66 y/L = 0.79 y/L = 0.93 Fnh Hmax (mm) Hmax (mm) Hmax (mm) Hmax (mm) 0.6 9.86 9.18 7.65 6.19 0.7 18.78 17.26 15.21 13.32 0.8 31.49 29.62 27.25 23.34 0.9 44.72 42.43 39.23 35.14 1.0 35.27 33.13 30.88 26.75 1.1 33.15 31.02 27.53 23.97 1.2 35.86 32.84 29.97 25.83 1.3 36.83 33.58 30.34 26.36 1.4 36.97 35.84 34.86 32.92       Jurnal Mekanikal, December 2008  137 Table 4: Theoretical maximum wash height  probe 1 probe 2 probe 3 probe 4  y/L = 0.53 y/L = 0.66 y/L = 0.79 y/L = 0.93 Fnh Hmax (mm) Hmax (mm) Hmax (mm) Hmax (mm) 0.6 12.94 12.03 11.33 10.73 0.7 25.91 24.09 22.68 21.48 0.8 46.77 43.47 40.94 38.77  Table 5: Experimental divergent angle Fnh Divergent Angle, θ 0.6 32.13 0.7 31.73 0.8 30.75 0.9 25.37 1.0 12.86 1.1 24.38 1.2 32.48 1.3 35.82 1.4 41.37  Table 6: Theoretical divergent angle Fnh Divergent Angle, θ 0.6 34.98 0.7 34.30 0.8 32.07 0.9 24.64 1.0 0.00 1.1 24.62 1.2 33.56 1.3 39.72 1.4 44.42    Jurnal Mekanikal, December 2008 138 Fx vs Fnh0.05.010.015.020.025.030.00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6FnhFx (N)shallow waterdeep water    Figure 8: Total model resistance against depth froude number  Heave vs Fnh-20.00-15.00-10.00-5.000.005.0010.0015.000.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6FnhHeave (mm)shallow waterdeep water   Figure 9: Experimental maximum heave against depth froude number  Pitch vs Fnh0.000.501.001.502.002.503.003.504.004.500.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6FnhPitch (deg)shallow waterdeep water  Figure 10: Experimental maximum pitch against depth froude number   Rtm DeepShallowFnhFnhDeepShallowHeave DeepShalloitch Vs Fnh Fnh Pitch   Jurnal Mekanikal, December 2008  139 Divergent Wave Angle vs Fnh051015202530354045500.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5FnhAngle (Deg)theoryexperimental approach  Figure 11: Angle of divergent against depth froude number 7.0 CONCLUSION  It should be noted that, all results mentioned are based on preliminary investigation of wake wash done in the Marine Technology Laboratory UTM. The wash measurement was done by using in-house developed wave probe and Labview Software. The pattern of the wash wave system has been measured for different depth and length Froude numbers and compared with theoretical predictions. It can be concluded that;  i) The agreement between the theoretical and experimental curve pattern is reasonably good. ii) Wake wash characteristic generated by traveling vessel is largely dependent on the depth Froude number. iii) The hump speed was achieve at depth Froude number, Fnh ≈ 0.9   This study has quantified and analyzed the characteristics of the wake wash generated by the Harbor Patrol Craft but there are still room left for improvements. The following recommendations are made for further study and for better improvement:  i) As the towing tank facility in the Marine Technology Laboratory is limited by several aspects such as shallow water platform too short, so that when vessel transiting from deep water to shallow water wash disturbance occurs during measurement especially at higher depth Froude number. This will contributes to measure exact wake wash. ii) Using computer program such as ship flow to validate all the result collected from experiment. iii) Improve the instrumentation developed to reduce noise as low as possible.    Fnh Exp Theory   Jurnal Mekanikal, December 2008 140 ACKNOWLEDGEMENTS  The authors would like to thank the Marine Technology Laboratory technicians for their assistance in conducting the model tests.   REFERENCES  1. Stumbo, S., Fox, K., Dvorak, F. and Elliot, L, 1999. The Prediction, Measurement, and Analysis of Wake Wash from Marine Vessels, Marine Technology, Vol. 36, No. 4. 2. Whittaker Trevor, J.T., 2001.  An Experimental Investigation of the Physical Characteristics of Fast Ferry Wash, 2nd International Euro-Conference on High-Performance Marine Vehicles HIPER’01, Coastal Engineering; Queen’s University of Belfast. 3. Stumbo, S., Fox, K. and Elliott, L., 2000. An Assessment of Wake Wash Reduction of Fast Ferries at Supercritical Froude Numbers and at Optimized Trim, Marine Technology, Vol. 40, No. 5. 4. Stumbo, S., Fox, K. and Elliot, L., 1999. Hull Form Considerations in the Design of Low Wake Wash Catamarans, International FAST  Conference, Seattle, WA, USA 5. Final Report of MCA Research Project 457, 2001. A Physical Study of Fast Ferry Wash Characteristics in Shallow Water. 6. Abdul Ghani, M.P., 2003. Design Aspects of Catamaran Operating at High Speed in Shallow Water, PhD Thesis, University of Southampton, UK. 7. Final Report of FRGS Research Project Vot 75190, Investigation of wake wash in towing tank 8. Jiang, T., Henn, R. & Sharma, S.D., 2002. Wash Waves Generated by Ship Moving on Fairways of Varying Topography, 24th Symposium on Naval Hydrodynamics, Fukuoka, Japan. 9. Whittaker, T.J.T. et. al, 2000.  A study of leading long period waves in fast ferry wash, Proc. Hydrodynamics of High Speed Craft-wake wash and motions control, RINA, London.. 10. Gates, E.T. and Herbich, J.B, 1977. The squat phenomenon and related effects of chemical geometry, 25th Annual Hydraulics Division Conference, ASCE, Texas. . . .          

The prediction of wake wash in the towing tank

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The prediction of wake wash in the towing tank

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