An Investigation into the Effect of Water Depth on the Resistance Components of Trimaran Configuration Muhammad,IQBAL 1 and I Ketut Aria Pria, UTAMA 2 1 Department of Naval Architecture Diponegoro University, Semarang 50275, Indonesia 2 Department of Naval Architecture and Shipbuilding Enginering Institut Teknologi SepuluhNopember (ITS), Surabaya 60111, Indonesia Abstract Research, in order to breackdown the resistance components of trimaran hull form, has been carried out worlwide. Almost all of the work is focused on the resistance investigation of trimaran configuration in deep sea condition. None of the research has formulated the estimation of trimaran resistance components into certain equation such as for catamaran. The current work is concentrated on the investigation of the effect of water depth, namely deep, medium and shallow waters, into the total resistance of the trimaran configuration. Experimental investigation using ITS model were carried out at a towing tank at various hull separation (S/L = 0.2, 0.3 and 0.4) and various speeds or Froude Numbers. Special consideration is given to medium and shallow water depth because the Froude Numbers are based on water depth and not based on ship length such as in deep water condition. CFD investigation using a CFD code called Tdyn, is also conducted in order to validate the results of the experimental investigation. The results of the experimental test and CFD analysis are in good agreement and comparative studies with other published data strengthen the findings. Keywords: trimaran, resistance, model test, CFD. 1. Background One of the most popular type of vessels at present is the multihulls where this vessel has several benefits compared to monohull. Trimaran is one type of multihull vessels which has three hulls connected by bridge construction hence the trimaran has wider deck space area compared to monohull of similar displacement. Trimaran has been investigated by many experts and naval architects in order to replace the use of monohull attributed to several advantages [1,2,3,4] explained that there are several benefits of the use of trimaran compared to monohull, namely lower wave resistance at higher speeds, wider deck space area, better transverse stability and better maneuverability hence more comfortable for passengers. Among those advantages, the difference of ship operational condition such as difference of water depth has caused unique hydrodynamics phenomena compared to deep sea condition. A ship moving at shallow water can cause its speed to decrease and consume more fuels. Moreover, the vessel is vulnerable for grounding, which is the situation when the bottom of ship hits the sea bottom. This is also dangerous for the vessel itself, where a ship moving at shallow waters can harm the maritime environment, onshore construction, and other vessels or objects situated nearby [5]. There is significant increase of resistance when a vessel moving at shallow waters. Based on the curve of resistance, there is peak of the curve which indicates the highest resistance among other speeds. This condition occurs at Frh 1,00 where Frh is called depth Froude number [6,7]. When a vessel moving at restricted waters, it may cause interaction between the bottom of ship and the bottom of seawaters. This interaction is caused by the significant pressure changes due to the change of flow speed under the ship [7]. In addition, interference between hulls can also cause the increase of ship s resistance. 2. Research Method 2.1. Main Dimension The experimental model tests were carried out at ITS towing tank at the model scale of 1:8 at the speeds of 1.0371 1.7657 m/s (5.7 9.7 knots of the real vessel speed) or in term of Froude
numbersfr L 0,21 0,41 orfr h 0,88 1,70without rudder and propeller. The ship model can be seen in Figure 1 and the principal particular can be found in Table 1. Side hull MainHull Side hull Figure 1. Ship model Table 1. Principal particular of ship and model Dimensions Main Hull Side hull Full Scale Model Full Scale Model Length between waterline, LWL (m) 14.50 1.8125 12.00 1.50 Breadth, B (m) 2.00 0.25 1.147 0.1434 Draft, T (m) 0.72 0.09 0.52 0.065 Height, H (m) 1.44 0.18 1.239 0.1549 Displacement, Δ (ton) 6.96 0.01359 2.42 0.00473 Block Coeffisient, Cb 0.384 0.384 0.39 0.39 Watted Surface Area, WSA (m 2 ) 26.874 0.4199 14.278 0.2231 Total Displacement Total WSA Full scale = 11.8 ton Full scale = 55.43 m 2 Model = 0.023 ton Model = 0.866 m 2 2.2. Sidehull Position The position of sidehull is notified as S/L ratio where S is distance between main-hull centreline and side-hull centreline and L or LWL is the length of main-hull in m. The values of S/L used for the tests were 0.2, 0.3 and 0.4. Details of the paramaters can be seen in Figure 2 and Table 2. Figure 2. Variation of sidehull position
Table 2. Distance between mainhull and sidehull positions (m) S/L Full Scale Model 0.2 2.90 0.363 0.3 4.35 0.544 0.4 5.80 0.725 2.3. Depth of Water The depth of water of the tests was divided into three: deep, medium and shallow waters and notified as h/t where h is the depth of water (m) and T is ship s draught (m). The depth of water was categorized based on h/t values: 1.2 1.5 for shallow water, 1.5 19.3 for medium water and > 19.3 for deep water [8] and tabulated in Table 3. Table 3. Water depth (m) h/t Full Scale Model 1.22 (shallow water) 0.88 0.11 1.56 (medium water) 1.12 0.14 20 (deep water) 14.40 1.80 3. Results and Discussion 3.1 Experimental and CFD The results of resistance tests can be seen in Figure 3. Both experiment and CFD results demonstrated similar trends where at shallow waters the curve of total resistance decreases from Fr L 0,24 to 0,41. At medium waters, the curve of resistance increases from Fr L 0,24 to 0,28 and later decreases until Fr L 0,41. Meanwhile, at deep waters the curve of resistance does not change significantly. Figure 3. Comparison of CFD and Experiment
Coefficient of Total Resistance (CT) The 9 th International Conference on Marine Technology 3.2. Category of Vessel Speed at Shallow Waters The determination of speed when a ship is operated at shallow waters is very important. Its resistance in deep waters, at the same speed, can increase drastically in shallow waters. This depends highly on the speed category and in order to describe this category, the curve of resistance is figured out in term offr h. If the speed of ship is the same of the speed of wave at shallow waters (c), notified as c = gh, hence the speed is called critical speed (Fr h = 1,00). Whilst, if the speed v < c, it is called subcritical (Fr h < 1,00) and ifv > c it is called supercritical (Fr h > 1,00). This category is popularly knows as Froude Number Based on Depth(Fr h ). The three categories provides differennt effects on ship resistance. 0.030 0.020 0.010 0.000 0.80 1.00 1.20 1.40 1.60 1.80 Froude Number Based on Depth (Frh) Shallow S/L 0.2 Shallow S/L 0.3 Shallow S/L 0.4 Medium S/L 0.2 Medium S/L 0.3 Medium S/L 0.4 Figure 4. Category of the speed of ship It can be seen in Figure 4 that with the same Fr L, the value of Fr h can be different because of different water depth condition. At shallow waters, the wave resistance coefficient lies from Fr h 1,00 and at medium waters fromfr h 0,88. Figure 5. Medium water depth Fr L 0,244 critical speed Fr h 0,890 Figure 6. Medium water depth Fr L 0,284 critical speed Fr h 1,035
Figure 7. Medium water depth Fr L 0,410 supercritical speed Fr h 1,495 Figure 8. Wave contour elevation at medium water depth Figures 5 to 7 show the difference among subcritical, critical and supercritical speeds based on experimental model tests, whereas Figure 8 demonstrates the difference from CFD analysis. Those show similar trend. Both experiment and CFD results show that wave at the bow part at critical speed is higher than that of subcritical speed. Meanwhile, the wave angle of entrance at critical speed is close to 90 o and this is in agreement with statement from [7]. At the critical speed the submerge transom part appears, but it does not appear at subcritical speed. At supercritical speed, the created wave is dominated by divergent wave, whilst the transverse wave disappears. According to [7], it is attributed to gravity waves, which does not occur at c > gh. 3.3. Variation of Pressure and Speed of Flow Figure 9 shows the measurement positions of pressure and speed of flow. Measurement if pressure is carried out in order to seek the interaction between the bottom of ship and see bed which affects pressure and fluid flow. The position of measurement lies at 0.01 m beneath ship model or it is 0.1 m below water surface if assumed that the coordinate from x = 0 showing that the after perpendicular (AP) until x = 1.8125 m showing the fore perpendicular (FP).
Velocity (m/s) Pressure (Pa) The 9 th International Conference on Marine Technology Figure 9. Position of pressure and flow speed measurement at the bottom of model 400 200 0-200 0.00 0.50 1.00 1.50 2.00-400 Figure 10. Pressure at the bottom of ship atfr L 0,244, S/L 0,3 1.30 1.20 1.10 1.00 0.90 0.80 0.70 X Coordinate (m) 0.00 0.50 1.00 1.50 2.00 X Coordinate (m) Figure 11. Speed of flow at the bottom of ship at Fr L 0,244, S/L 0,3 Figure 10 shows the measurement of pressure at Fr L 0,244, S/L 0,3 where the shallower the water depth, the pressure at ship bow increase drastically whilst at stern it drops drastically. Conversely, Figure 11 shows that the shallower the water depth, the speed of flow at bow decreases and it increases drastically at stern. According to [7], the increase and decrease of pressure and flow of speed has attracted the squat effect where the ship hull is likely to be pulled to the bottom hence caused the change of trim and snkage significantly. The stronger the pulling force to the bottom, the quicker the bottom of ship touching the bottom and this is called grounding, and this is certainly dangerous for the safety of ship. Furthermore, [9] described that the creation of wave resistance is caused by pressure of fluid works normal or perpendicular to ship hull. This explains that the existence of significant pressure changes on the hull surface due to the changes of fluid pressure has caused the wave resistance to increase. 3.4. The Effect of Water Depth on the Interference Between Hulls When a trimaran ship mowing at certain speed, each hull will create separate wave patterns. Each of those wave patterns will interfere among others and hence cause the increase of wave resistance. The orbital of wave particles at shallow waters does not create circle form like in deep waters but forming elliptical form. This causes the longer wave length to be produced compared to deep waters [5,10]. Moreover, the created wave length can be along the ship s length. This then describes how the wave resistance interference increase at shallow water as compared to that in deep sea. In order to understand the wave intrference, the superposition of each resistance components of each demihull can be obtained by using Equation (1) [11,12]. This is conducted in order to compare the combination of total demihull resistance coefficient against the total resistance coefficient of trimaran in relation with its S/L ratios. However, the experimental investigation on each hull was not
interference factor interference factor interference factor The 9 th International Conference on Marine Technology carried out. Therefore, the CFD results on the total resistance cannot be compared with the experimental work. It can be found from that comparison that the difference of total resistance for each S/L ratios to each sidehull is called interference factor (η). The calculation of interference factor is formulated in Equation (2). Negative values indicated that the interference is an advantage [12]. Ct tri NI = Ct m S m + 2Ct s S s S tri (1) η = Ct tri Ct tri NI 1,0 (2) The interference of trimaran in the current paper was presented in the same position of sidehull (S/L) but at different water depths. The results are shown in Figures 12 to 14. This shows that with the same S/L, the interference between hulls can be different for each water depths. In general, interference at shallow waters can be smaller compared to that of medium and deep waters and this is attributed to the speed of vessel and position of sidehull. 0.80 0.60 0.40 0.20 0.00-0.20 0.20 0.25 0.30 0.35 0.40 0.45 Froude Number Based on Length (FrL) Figure 12. Interference factor at S/L 0.2 at various water depth 0.80 0.60 0.40 0.20 0.00-0.20 0.20 0.25 0.30 0.35 0.40 0.45-0.40 Froude Number Based on Length (FrL) Figure 13.Interference factor at S/L 0.3 at various water depth 0.80 0.60 0.40 0.20 0.00-0.20 0.20 0.25 0.30 0.35 0.40 0.45-0.40 Froude Number Based on Length (FrL) Figure 14. Interference factor at S/L 0.4at various water depths.
4. Conclusions Based on the experimental and CFD analysis, it can be found that (at the same speed) the total ship resistance in deep waters can increase almost double at medium waters and about two and a half times at shallow waters. The difference between experiment and CFD analysis is quite small, under 10%. The increase of ship resistance is believed to be due to the significant pressure changes caused by significant change of flow speed. Moreover, the effect of water depth onto the interference between hulls is also obvious. In general, the interference at shallow waters is smaller than that of medium and deep waters and it depends highly on the speed of vessels and position of side-hulls. 5. References [1] Fang, M., Chen, T. (2008). A Parametric Study of Wave Loads on trimaran Ships Travelling in Waves, Ocean Engineering, Vol. 35, hal. 749-762. [2] Mynard, T., Sahoo, P.K., Mikkelsen, J., McGreer, D. (2008), Numerical and Experimental Study of Wave Resistance for Trimaran Hull Forms, Australian Maritime College, hal 117-132. [3] Utama, I.K.A.P., Murdijanto., Sulisetyono, A., Jamaludin, A. (2009). Development of Multihull Ship Modes for Safe, Comfort and Efficient River and Ferry Transportations (in Indonesian), Final Report of Applied Intensive Research Scheme (RIT), ITS Research Centre (LPPM-ITS), Surabaya, Indonesia. [4] Min, X., Shi-lian, Z. (2011), A Numerical Study on Side Hull Optimization for trimaran, Journal of Hydrodynamics, Vol. 23, No. 2, hal. 265-272. [5] Lyakhovitsky, Anatoly. (2007), Shallow Water and Supercritical Ships, Backbone Publishing Company, Fair Lawn, NJ-USA. [6] Hofman, M., (2006). Prediction of Wave Making Resistance of Fast Ships in Shallow Water And Computer Program ShallowRess, Report BR001/2006 Technical Solution, Dept. Of Naval Architecture Faculty of Mechanical Engineering University of Belgrade, Serbia. [7] Molland, A.F., Turnock, S.R, Hudson, D.D, (2011), Ship Resistance and Propulsion, Cambridge University Press, Cambridge. [8] Koh, K.K., Yasukawa, H. (2012). Comparison study of a pusher barge system in shallow water, medium shallow water and deep water conditions, Ocean Engineering, Vol. 46, hal. 9-17. [9] Jamaluddin, A. (2012). Experimental and Numerical Analysis of Wave and Viscous Resistance Interference of Catamaran at Various Configurations (in Indonesian), PhD Thesis, Faculty of Marine Technology, ITS, Surabaya, Indonesia. [10] Djatmiko, E. B., (2012). Behaviour and Operability of Floating Bodies in Random Waves (in Indonesian), ITS Press, Surabaya. [11] Pei-young, L., Young-ming, Q., Min-tong, G. (2002), Study of Trimaran Wavemaking Resistance With Numerical Calculation and Experiment, Journal of Hydrodynamics, Vol. 2, hal 99-105. [12] Hafez, K.A., El-Kot, A.A. (2012). Comparative Investigation of The Stagger Variation Influence on The Hydrodynamic Interference of High Speed Trimaran, Alexandria Engineering Journal, Vol. 51, hal. 265-272.