Experimental and Simulation Studies on Fast Delft372 Catamaran Maneuvering and Course Stability in Deep and Shallow Water

11 th International Conference on Fast Sea Transportation FAST 211, Honolulu, Hawaii, USA, September 211 Experimental and Simulation Studies on Fast Delft372 Catamaran Maneuvering and Course Stability in Deep and Shallow Water Evgeni Milanov 1, Valya Chotukova 1, and Frederick Stern 2 1 BSHC- Bulgarian Ship Hydrodynamics Centre, Varna, Bulgaria 2 IIHR-Hydroscience & Engineering, the University of Iowa, USA ABSTRACT The results of a series of 3-DOF model experiments for high speed water jet propelled Delft372 catamaran in deep and shallow water are described. The hydrodynamic derivatives are estimated from captive model test in shallow towing tank condition and used to predict the maneuverability and course stability of the vessel using 3-DOFsystem based simulations. Then the simulation results are validated by free running model tests. The both results are in relatively good compliance, but analysis shows necessity of simulation model refinement. KEY WORDS Catamaran maneuverability, water jet, shallow water. 1. INTRODUCTION The ONR-funded project on high speed Delft372 catamaran design is focused on experimental and numerical investigations of vessel powering characteristics and maneuverability in extreme navigation conditions such as shallow water and waves. To obtain catamaran bare hull hydrodynamics characteristics at high speed in shallow water a large amount of PMM tank tests have been carried out and accomplished with CFD simulations (Zlatev et al., 29 and Milanov et al., 21). An intensive work has been done in catamaran water jet (WJ) propulsion design and optimization Georgiev et al. (21). The present paper addresses WJ Delft372 catamaran maneuvering and course keeping ability when the vessel advances with small under keel clearance at high Froude depth number Fnh. The authors use the PMM captive model tests approach to predict the hydrodynamic derivatives of the mathematical model. The test matrix is designed to study the variations of maneuvering motion kinematical parameters and h/t ratio and to investigate the maneuvering at sub-critical and critical Fnh numbers. The sets of hydrodynamic derivatives are calculated by appropriate regression analysis. Also, the water depth influence on forces acting on the hulls and controllers was investigated and the essential terms are added into the simulation model. Special attention was paid to the vessel s stability in various depth and speed conditions. When speed increases at high values of Fnh, the observations of the flow around the demihulls and analysis of measured forces show the necessity of simulation model modifications as a future work. 2. CAPTIVE MODEL TESTS To obtain hydrodynamic derivatives in maneuvering equations an extensive model test program has been executed by means of BSHC PMM facility. Since the project is concentrated on the catamaran maneuvering behavior in shallow water the experimental investigations with captive model have been carried out in shallow water tank at specific Froude numbers while the free running tests are carried out in BSHC maneuvering tank. 2.1 Model used and test program In PMM tests a 4m model of Delft catamaran 372 design (Veer, 1998) have been used - Table 1. Table 1. Delft372 catamaran model particulars. Main Dimension Symbol Value Length between perpendiculars L PP [m] 3.627 Breadth /demihull/ B [m].29 Draft at midship T [m],2 Displacement volume Δ [m 3 ].25 Block coefficient C B [-].43 During the tests the model was free to pitch and heave. By use of four 2-components strain gauges the horizontal forces have been measured. One of the specific features of the experiments was individual measurement of hydrodynamic load on each demihull as shown on Fig. 1 which provides an opportunity to have better understanding of the role of each hull and to evaluate CFD results in more detail Fig. 1. Set-up for individual demihull forces measurement. 438 211 American Society of Naval Engineers

The model was appended with water jet drive and designed and tested at BSHC (Georgiev, 21). The jet stream is deflected by steering the outlet nozzles in horizontal plane and by reverse ducts in vertical plane as shown in Fig. 2. This would provide the full control of catamaran maneuvering. Fig. 2. Water jet drive and flow control ducts. The steering angle of jet nozzles in horizontal plane was varied in the operation range <-2; +2> degrees while the reversing duct could be deflected at 25, 5 and 1% of full closed position. The PMM test program consisted of static and dynamic tests listed in Table 2. Some specific tests have been performed with variation of the reverse duct position for the set of water jet propellers advance ratio. Table 2. PMM test program. Test type Static tests Dynamic tests Motion parameter Value Value J Propulsion ratio J.2-1.3 1. Drift angle (deg) -4;-2;;2;4; 6;8;1;12 ; 4; 8 Nozzles steering angle ;3;5;1;15; (deg) 2 Reverse duct lowered (%) ;25;5;1 Sway acceleration vdot (-).2;.4;.6 Yaw rate r (-).2;.4;.6 Yaw acceleration rdot (-).18;.36.53 Surge acceleration udot (-).2;.4;.6;.8;.1 In order to investigate the effects of speed and water depth on catamaran maneuvering characteristics, the experiment was executed for different conditions as given in Table 3. Table 3. Test conditions. Water depth condition h/t (-) Fnh (-) Deep water 7.4.74 Shallow water 1 2..6; 1.; 1.272 Shallow water 2 1.5.6;.8; 1. 2.2 PMM test results The total hydrodynamic and inertial forces are measured on the individual demihulls, i.e. without estimation of hullpropulsors-controls interaction. The stationary and dynamic data are processed and nondimensionalyzed in accordance with the standard PMM procedure (Goodman, 1976). In the text and on figures the longitudinal force X, lateral force Y and yaw moment N are represented by non-dimensional coefficients related with corresponding kinematical parameters. Due to the large amount of experimental data recorded and processed the following analysis is focused on main task objectives, namely on shallow water, Fnh values effects and catamaran course stability. 2.2.1 Effects of Water Depth As known, with decreasing of under keel clearance the ship resistance increases. The model tests have been carried out at sub-critical and trans-critical Fnh values. In this section, the influence of water depth on catamaran performances at Fnh=1. are analyzed when peak of the resistance is observed. As shown in Fig. 3 according to this change the self-propulsion point in shallow water shifts to higher propulsion ratio values. X' [-].4.3.2.1 -.1.5 1 1.5 2 2.5 -.2 eta=j/j [-] -.3 -.4 deep water -.5 h/t=2. Fnh=1. -.6 h/t=1.5 Fnh=1. Fig. 3. Tow force versus propulsion ratio coefficient. Mean steady sinkage values at bow and stern measured during straight ahead towing test with working water jets are given in Fig. 4. The sinkage of catamaran afterbody part in shallow water is twice as in deep water when the bow vertical position remains almost unchanged. 211 American Society of Naval Engineers 439

sinkage [mm] deep water h/t=2. Fnh=1. bow 8 h/t=1.5 Fnh=1. 6 4 2 eta=j/j [-] -2.5 1 1.5-4 -6-8 stern As mentioned earlier, the catamaran model is equipped with two water jet drives with flow control in horizontal and vertical planes. The first basic operation mode gives possibility for generation of lateral control forces by deflecting WJ nozzles while the second one reverses the jet flow by appropriate bucket to terminate the maneuvering test. The effect of WJ nozzles deflection is plotted in Fig. 7. The propulsion characteristics of the vessel change up to 1degrees drift. deep water h/t=2. h/t=1.5 Fig. 4. Sinkage during straight-line motion. As shown in Fig. 5 the side hull force is affected by under keel clearance very strongly. Similar tendency is observed for the corresponding yaw moment due to drift. It should be pointed out that slopes of Y ( ) curves in the vicinity of zero drift angle increases with decreasing h/t which should result in course stability improvement. Y' [-].3.25.2.15.1 ht=7.4 Fnh=.74 ht=2. Fnh=1. ht=1.5 Fnh=1..5 -.5 5 1 15 Fig. 5. Lateral force versus static drift angle. In oblique flow, when catamaran advances with drift angle, the dependency of vertical dynamic position of bow and stern on drift angle is shown in Fig. 6. In comparison with straight motion case the stern sinkage diminishes while bow slightly emerges out of the water at relatively large drift angles (1-12deg). sinkage [mm] 8. 6. 4. 2.. -2. 5 1 15-4. -6. -8. deep water h/t=2. Fnh=1. h/t=1.5 Fnh=1. bow stern.1.8.6.4.2 X' [-]. -3-2 -1 -.2 1 2 3 steering angle [deg] Fig. 7. Tow force versus WJ steering angle. As a result of jet flow deflection, the control side force and yaw moment are generated as shown in Fig. 8. While the dependency of the force & moment on nozzles steering angle is fairly linear, the influence of shallow water is very strong and nonlinear. N.3.2.1. -3-2 -1 1 2 3 Y deep water h/t=2. h/t=1.5 -.1 -.2 -.3 Y', N' [-] steering angle [deg] Fig. 8. Side control force & moment versus WJ steering angle. In maneuvering motion with drift angle the effective inflow velocity into WJ intake chamber is altered but the influence on WJ flow is negligible as is evident from the Fig. 9. The characteristics of control force Y are shifted equidistantly by the values of corresponding drift forces. Due to this reason drift-steering angle cross-coupling terms in simulation model the can be discarded. Fig. 6. Sinkage in oblique motion. 44 211 American Society of Naval Engineers

deep water.2.1.1. -.1 Y' [-] Drif t angle= deg Drif t angle=6 deg Drif t angle=12 deg -25-2 -15-1 5 1 15 2 25 Steering angle [deg] Fig. 9. Side control force in oblique flow. Added mass in sway direction - related with in-phase component of measured forces - changes slightly with water depth change as indicated in Fig. 1. The sway damping characteristics are estimated by performance of static drift test shown in Fig. 5 in which the data are more reliable than those obtained in dynamic test mode. deep water Fnh=.74 ht=2. Fnh=1. ht=1.5 Fnh=1..15.1.5 -.1 -.8 -.6 -.4 -.2 v'_dot [-] Y'in [-] Fig. 1. Added mass in sway motion. The yaw acceleration terms in pure yaw motion are measured and shown in Fig. 11. In very shallow water the added mass due to yaw is significantly affected by under keel clearance. r'_dot [-] -.12 -.8 -.4 The yaw damping force is influenced slightly by water depth as shown in Fig. 12. The same tendency was observed for the moment in pure yaw as well. deep water Fnh=.74 h/t=2. Fnh=1. h/t=1.5 Fnh=1. drift angle =.6.4.2 -.12 -.8 -.4 r' [-] Fig. 12. Damping force in pure yaw motion. 2.2.2 Effects of Speed Y'out [-] The vessel speed and under keel clearance are intimately linked. In the Fig. 13 resulting tow force at self propulsion point for sub-critical and trans-critical catamaran speed is given..4.3.2.1 -.1 -.2 -.3 -.4 X' [-] Fnh=.6 Fnh=1. Fnh=1.272.5 1 1.5 2 eta=j/j [-] h/t=2. Fig. 13. Towing force at set of speed regimes. In oblique motion in shallow water the moment due to the drift is affected strongly by the speed as indicated in Fig. 14. Fnh=.6 Fnh=1. Fnh=1.27 -.2 N' [-].5.4 h/t=2. -.4.3 deep water Fnh=.74 -.6 h/t=2. Fnh=1. h/t=1.5 Fnh=1. Fig. 11. Added moment in pure yaw motion. Y'in [-].2.1 -.1 5 1 15 -.2 Fig. 14. Drift moment in oblique motion. 211 American Society of Naval Engineers 441

According to the increase of forward speed, the control yaw moment N due to deflection of steering nozzles changes non-monotonically as illustrated by Fig. 15. Similar nonmonotonic tendency in yaw damping change as a function of Fnh value is observed in Fig. 16. h/t=2. X'port h/t=1.5 X'port.1 X' [-].5 h/t=2. X'sb h/t=1.5 X'sb Fnh=.6 Fnh=1. Fnh=1.27.1.8.6 h/t=2..4.2. -3. -2. -1.-.2. 1. 2. 3. -.4 -.6 -.8 -.1 steering angle [deg] N' [-] Fig. 15. Yaw moment due steering with WJ nozzles. At critical speed in pronounced shallow water (h/t=1.5) the reduction of yaw damping is more then 5% compared with deep water case. r' [-] Fnh=.6 Fnh=.8 Fnh=1. h/t=1.5.8.6.4.2 -.1 -.8 -.6 -.4 -.2 Fig. 16. Yaw damping in very shallow water. 2.2.3 Demihulls interaction Y'out [-] Asymmetric cross flow around demihulls during catamaran motion with drift angle has been investigated by Couser et al. (1998). In the present study, the visual observations of wave pattern between catamaran demihulls when moving with drift angle as well as forces measurements on individual demihull show a very asymmetric hydrodynamic load. The drag distribution on port and starboard hull for two h/t ratios is illustrated in Fig. 17. 5 1 15 -.5 Drift angle [deg] -.1 -.15 -.2 Fnh=1. Fig. 17. Drag on demihulls at incidence. The same tendency was found for lateral force shown in Fig. 18. The difference in side force for port and starboard demihulls increases with decreasing water depth almost twice in comparison with data at h/t=2...25.2.15.1.5 h/t=2. Y'port h/t=1.5 Y'port Y' [-] Fnh=1. h/t=2. Y'sb h/t=1.5 Y'sb 5 1 15 -.5 Fig. 18. Side force on demihulls at incidence. To obtain information about side force acting point position at each individual demihull a ratio of yaw moment and side force coefficients has been calculated. It should be pointed out that at small drift angles the force acting points along the hull for both hulls are different while at larger than 6 degrees drift angles they converge to about ¼ from bow as shown in Fig. 19. 1.5 1.5-4 4 8 12 -.5-1 -1.5 Port demihull xp=n/y [-] SB demihull h/t=1.5 Fnh=1. -2 Fig. 19. Side force application point on demihulls. 442 211 American Society of Naval Engineers

3. SYSTEM BASED SIMULATIONS The experimental data used to obtain the hydrodynamic derivatives in maneuvering equations in calm water. At the moment of paper preparation the seven sets of coefficients for different h/t and Fnh values have been calculated and simulation of standard maneuvers for corresponding test cases was performed. Basically the Chislett (1974) third order model was used with cross-coupling terms such as X vr, Y rv, Y rrrv, N rv, N rrrv. 3.1 Turning maneuver Figure 2 shows the comparison between result of simulation and free running model test data for hard starboard maneuver at h/t=2.. It can be judged that the both type of results agree well for steady turning diameter but not for advance and tactical diameter. steering angle 2 deg yaw rate [deg/s] 2 15 1 5 steering angle 2 deg exp sim 1 2 3 4 5 time [s] Fig. 21. Yaw rate in turning. The speed drop in turning motion is given by Fig. 22. The discrepancy between the both type of the results is rather big. steering angle 2 deg 16 xg[m] 14 12 1 8 6 exp sim speed [m/s] 1.6 1.4 1.2 1.8.6.4.2 exp sim 1 2 3 4 5 time [s] 4 2-4 1 6 11 16 yg [m] Fig. 2. Turning trajectory. The time history of measured and simulated yaw rate during above turning maneuver differ in both the slope in transient period and the gain in steady motion phase as shown in Fig. 21. Fig. 22. Speed reduction in turning. Similar degree of correlation between simulated and experimentally obtained data has been recognized for the rest of test cases. Careful re-analysis of PMM data and regression models used show necessity of inclusion the higher order terms in the simulation model. 3.2 Spiral maneuver and course stability In the frame of previous project investigations (Milanov et al., 21) for the bare hull PMM tests it was found that catamaran is inherently unstable on course in deep and shallow water. Such tendency has been reported by Ishiguro (1993) and Salvesen (25). This fact was proved by free running catamaran model tests. To keep straight course, the amplitude of 4 degrees corrections in jet nozzles steering angle is necessary at rather high frequency as shown in Fig. 23. Therefore, a new autopilot was designed for the tests (with build-in PID controller) where the appropriate gain coefficients are adjusted and tested for high speed catamaran model case. 211 American Society of Naval Engineers 443

1 steering angle [deg] course angle [deg] yaw rate [deg/s] xg [m] steering angle change 2/ deg 14 12 5-1 5 1 15 2 time [s] Fig. 23. Course keeping by autopilot. As known, the best criterion for ship course keeping ability is the shape and size of spiral curve. Experimental and simulated catamaran model spiral curves are given by Fig. 24. yaw rate [deg/s] exp sim 2 15 h/t=2. 1 5-2 -15-1 5 1 15 2-1 steering angle [deg] -15-2 Fig. 24. Spiral curve. Despite the both experimental and simulated results- are different regarding the amplitude values, the shapes yaw rate-steering angle dependency are typical for directionally unstable vessel. Based on Fig. 23, the expected spiral loop width can be <; +5> degrees. For estimation of residual yaw rate (with steering controls in neutral position) the pullout maneuver has been performed shown in Fig. 25. From the trajectory of motion it is clear that the model continues to move with high angular velocity after putting the jet flow control nozzles in zero position. Considering this high degree of vessel course instability it should be mentioned that the catamaran is designed for research purposes and in the case of its practical realization most probably a stabilizing fins (skegs) in afterbody part will be fitted similar to number of catamaran designs. yaw rate [deg/s] 1 8 6 4 2-4 h/t=2. -1-2 5 1 15 15 1 5 yg [m] 2 4 6 8 time [s] Fig. 25. Pull-out maneuver results. 4. CONCLUSIONS 1. Total resistance, drift and control forces are increasing with under keel clearance reduction. 2. In oblique flow stern sinkage is decreasing. 3. The WJ steering capabilities are not influenced by the drift. Contrary to the conventional rudder devices, generated side control force & moment are linear in the whole steering angles range. 4. The depth Froude number dependency of the hydrodynamic forces and moment is strong. Unfortunately in some cases this change is not monotonic and needs more attention. 5. In drift motion the side force and induced drag are quite asymmetric for individual demihulls. 6. Standard maneuvers simulation model needs improvement in direction inclusion of higher order terms accounting for depth Froude number effects. 7. Catamaran course stability is very poor therefore technical means for its improvement should be taken. It would be efficient to take some technical measures for its improvement, for instance lifting surfaces mounted in vessel stern part. 444 211 American Society of Naval Engineers

REFERENCES Couser, P.R., Wellicome, J.F.,Molland, A.F., (1998). Experimental Measurement of Sideforce and Induced Drag on Catamaran Demihulls, International Shipbuilding Progress 45 (443) Dand, I.W., Dinham-Peren, T.A.,(1999). Hydrodynamic Aspects of a Fast Catamaran Operating in Shallow Water, Proceedings of the Conference on Hydrodynamics of High Speed Crafts, London, UK Faltinsen, O.M., (25). Hydrodynamics of High-Speed Marine Vehicles, Cambridge University Press, New York Georgiev, S., Milanov, E., (21). Model Tests of Waterjet Propelled Delft372 Catamaran, BSHC Rep. KP926/1, Varna, Bulgaria Goodman, A. Gertler, M.,Kohl R., (1976). Experimental Techniques and Methods of Analysis Used at Hydronautics for Surface-Ship Maneuvering Predictions Proceeding of the 11 th ONR Symposium on Naval Hydrodynamics, London, UK Ishiguro, T., Uchida, K.,Manbe, T., Michida, R.(1993). A Study on the Maneuverability of the Super Slender Twin Hull, Proceedings of the Second International Conference on Fast Sea Transportation FAST 93, Tokyo, Japan Milanov, E., Zlatev, Z., Chotukova, V., Stern, F. (21). Numerical and Experimental Prediction oh the Inherent Course Stability of High Speed Catamaran in Deep and Shallow Water, Proceeding of the 28 th ONR Symposium on Naval Hydrodynamics, Pasadena, USA Van t Veer, R., (1998). Experimental Results of Motions, Hydrodynamic Coefficients and Wave Loads on the 372 Catamaran Model, TU Delft Rep. 1129, Delft, Netherlands Wagner Smitt, L., Chislett, M.S.,(1974). Large Amplitude PMM Tests and Manoeuvring Predictions for a Mariner Class Vessel Proceeding of the 1 th ONR Symposium on Naval Hydrodynamics, Cambridge, USA Zlatev, Z., Milanov, E., Chotukova, V., Sakamoto, N., Stern, F. (29). Combined Model-Scale EFD-CFD Investigation of the Maneuvering Characteristics of a High Speed Catamaran, Proceedings of the 1th International Conference on Fast Sea Transportation, FAST 29, Athens, Greece. ACKNOWLEDGEMENTS This work was performed under the project, financed by ONR grant N14-7-143. The authors wish to acknowledge project supervisor Dr. P. Purtell for his contiguous support of this research. 211 American Society of Naval Engineers 445