Determination of suction forces and moment on parallel manoeuvring vessels for a future control system GIERUSZ Witold 1,a, WASZKIEL Anna 2,b

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1 Solid State Phenomena Online: ISSN: , Vol. 180, pp doi: / Trans Tech Publications, Switzerland Determination of suction forces and moment on parallel manoeuvring vessels for a future control system GIERUSZ Witold 1,a, WASZKIEL Anna 2,b 1,2 Gdynia Maritime University, Morska 81-87, Gdynia, Poland a wgierusz@am.gdynia.pl, b anwas@am.gdynia.pl Keywords: ship to ship interactions, CFD, suction forces and moments Abstract Vessels moving on parallel courses on the border of two mediums interact together. Ship to ship interaction is caused by irregular pressure distribution around the hull. The higher velocity of the fluid between hulls causes decreased pressure amidships. This is the base of the suction forces and moments generation. Analytical computations and computer based CFD simulations were carried out on the basis of 3DOF models of two training ships a VLCC and a Passenger Car Ferry. The results of both methods are comparable. Therefore the analytical semi-empirical equations can be implemented in a future control system, which requires ship to ship interactions estimations to ensure proper working conditions. Introduction In recent years more emphasis has been placed on the safety of Ship-to-ship navigation. Interactions take major role in the safety of the steering process of a pair of vessels moving parallel. As an example of parallel ships motion Underway Replenishment (UNREP) operations, fishing boats trawling in pair, pipe laying operations and some research situations could be mentioned. Suction forces and moments are determined on the basis of analytical calculations or simulations in Fluid Dynamics Computer (CFD) programs. Investigation of the interactions was initiated by Davis W. Taylor [11], who showed in 1909 that suction phenomenon exists when two ships pass close to each other. In 1965 Newman [9] used slender body theorem as a code to solve the interaction problem. Tuck cooperated with Newman to extend the theory to shallow water interactions [12]. Nowadays suction forces and moments acting on ships are implemented in ships simulators. A new generic algorithm was presented by Varyani and others in [13]. Hydrodynamic interactions are very important during replenishment operations, because here two ships operate in a close proximity for a long period of time. Motions of two hulls were examined by McTaggart and others in [8]. The main aim of the research carried out is to assess the magnitude of the impact of suction forces and moments on vessels in parallel in order to allow them to maintain fixed position relative to each other. Modification of the mathematical model of the vessel, taking into account the suction phenomenon, is necessary to build compact navigator decisions support system. This system will be used during parallel motion of the pair of vessels. Research was carried out on the basis of two ships models of Foundation for Safety of Navigation and Environment Protection. They are VLCC (scale 1:24) and Passenger Car Ferry (scale 1:16). The suction phenomenon between vessels Ship moving with constant longitudinal speed in two mediums water and air, causes a rise of dynamic pressure and tangential stress along the whole hull. Dynamic pressure is the result of ship movement on the border of two centers, while tangential stress is caused by water and air circumfluenting the hull. The viscosity of the air is much lower, so the effect caused by air is also lower than that caused by water. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-11/05/16,19:52:46)

2 282 Mechatronic Systems, Mechanics and Materials Fig. 1. Pressure distribution around hull As a result of apparent motion of the mass of water and air around the hull, velocity of fluid streams increases. In fact, this means that two regions of increased pressure (bow and stern) and one region of decreased pressure (amidships) are formed (Fig. 1). This pressure distribution determines ship to ship interactions. These interactions are clearly seen when ships are in a longitudinal distance of +/- 2 ship lengths. However, they are the strongest in a longitudinal distance of +/- 1 ship length. They drop away when the lateral distance reaches 1.5L multiplied by the tangent of the encounter wave angle (Eq. 1) [10]. d = 1. 5L tgγ (1) where: d lateral distance, L ships length overall, gamma tangent of the encounter wave. Considering conditions in which the suction phenomenon occurs, case of two ships (VLCC Blue Lady and Passenger Car Ferry Kołobrzeg) moving on parallel courses is presented. These are shown in Fig. 2. Controlled parallel motion is divided into three phases. First approach of the slave vessel, second parallel motion and third departure of the controlled vessel. Fig. 2 shows the second phase of movement parallel motion, during which velocity and track are controlled. Blue Lady Kołobrzeg Fig. 2. Ships surfaces Ship to ship interactions increase with a growing disproportion of ships dimensions, lateral distance between the ships sides, planes and also an increasing speed of maneuvering vessels. Suction force is described as a function of several variables according to Eq F s = f ( L, T, u, d ) (2) where: F s suction force, L length overall, T draft, u longitudinal velocity, d lateral distance between ships sides. Suction force increase because of an increased speed of fluid between hulls, causing a reduced pressure area in the mentioned space.

3 Solid State Phenomena Vol Calculation of the suction forces and moment Three degrees of freedom (3DOF) model of a ship is considered, because the heave, pitch and roll motions are decoupled from steering dynamics. Their negligibly small values [4] are the reason for this simplification. The outcomes used for a simulation validation were computed using semiempirical equations. Analytical computing method. There are two basic ways of an analytical determination of the suction forces and moment. First of them was proposed by J. N. Newman in 1965 [9] and is based on the slender body theory. It is a set of flow potential equations which consider longitudinal and lateral movements of a slender body in fluid. Inner solution defines problem near the ship hull, and outer solution allows for correct calculations in infinity. Merging these two cases allows the performance of surge and sway force and yaw moment calculations. Second method of suction forces and moment computation is based on semi-empirical equations provided by Brix [1]. This method of estimation of the ship to ship interactions is based on an empirically tested history of forces and moments in accordance to the relative longitudinal setting of two vessels. Maximal values of longitudinal force, transversal force and yawing moment (Eq. 3, Eq. 4, Eq. 5) are multiplied by correction factors, depending on ships relative positions. Geometry of ships and sign conversion for this case is illustrated in Fig. 3. Velocity u 2 >u 1 in this case. The guide ship is moving with constant speed. X Y S max S max N S max ρ 2 = umlmtmc XS max (3) 2 ρ 2 = um LmTmCYS max (4) 2 ρ 2 2 = umlmtmc NS max (5) 2 where: ρ - water density, u m - mean longitudinal speed, L m - mean length overall, T m mean draft. Maximum values of forces and moments are determined by fluid (sea water, fresh water), vessels dimensions and loading conditions and a parameter of the movement speed. Main limitation of this method is the condition of comparable ships dimensions. This is the reason for the usage of mean parameters in Eq More details of this method can be found in [1]. Fig. 3. Forces and moment acting on the hull [1].

4 284 Mechatronic Systems, Mechanics and Materials CFD (Computational Fluid Design) simulation method. Nowadays computer simulations are a popular way of flow prediction and hydrodynamic forces and moments calculations. Computer Fluid Dynamics (CFD) commercial programs are based on solving conservation equations for mass and momentum. Chen, Lin and Hwang in [2] showed that RANS method combination can be successfully used in the ship to ship interactions prediction. Commercial CFD computer programs, such as Ansys Fluent, solve Navier-Stokes equations based on Newton s second law applied to fluid flow. When the problem is a 3D case, computer fluid dynamics solver works by computing the result of mass conservation and Navier-Stokes equations during each iteration, for each tetrahedral element of mesh. More detailed description of the method is in [8]. Modeling ships interactions requires a consideration of turbulent flow around hulls. Basic turbulences model is a k-є model, because of sufficient accuracy and quite high speed of calculation. In this model turbulence kinetic energy (k) and dissipitation rate (є) are computed from transport equations [3]. For simulations of ships models interactions during research, the kinetic turbulence energy was adopted as: turbulent intensity 2% and length scale 0.07L=0.95[m], according to Gucma and others [7]. The third important aspect of flow around hull modeling is to take into account the movement of vessels within the boundary of two medias water and air. This is the aim of usage of Volume of Fluid (VOF) model to describe free surface problem in CFD computer program. During computation one additional continuity equation is solved [3]. This allows interactions between two phases and a mass transfer between them to be taking into account. Computer simulation program Ansys Fluent takes as an input data a grid containing fluid velocity inlet, mass of fluid, walls representing ships hulls and top, bottom and side walls of the virtual simulation tank, and fluid outflow. These surfaces have to be drawn and grid must be performed before the start of the simulation. Grid accuracy and smoothness must be high, in order to avoid calculation errors. As an effect of simulation pressure distribution and velocity distribution on the hull and in the mass of fluid are obtained. Pressure distribution contours and velocity fields can be observed on any planes in post processing stage. In addition, forces and moments acting on the walls (and also on the hull) are calculated and displayed. Case study Description of vessels models. Research was carried out on the basis of dynamic models of two ships used by Foundation for Safety of Navigation and Environment Protection. These are VLCC Blue Lady and Passenger Car Ferry Kołobrzeg. Main characteristics and silhouettes of the two vessels models used during research computations are presented in Table 1 and Fig. 4. a. b. Fig. 4. Ships models silhouettes a. VLCC Blue Lady, b. Passenger Car Ferry Kołobrzeg [5,6] Table 1. Main dimensions of ships models VLCC Blue Lady Passenger Car Ferry Kołobrzeg Length overall L[m] Breadth B[m] Draft T[m] Displacement D[T] Max. speed [kn]

5 Solid State Phenomena Vol In order to carry out the research on a control system for the two ships operating in parallel, a modification of mathematical models is needed. Model of the guiding ship is not going to be modified in the first phase of the research. Existing three degrees of freedom models, proposed by Gierusz in [5,6], were used. VLCC model depends on propeller[x prop, Y prop, N prop ], rudder[x rud, Y rud, N rud ], stern and bow thrusters[x sstd, Y sstd, N sstd, X sstr, Y sstr, N sstr ], and wind[x w, Y w, N w,] forces and moments. Modification necessary for parallel guidance of ships comprises an addition of forces and moments due to suction[x s, Y s, N s,]. Modified ships dynamics equations (Eq.6, Eq.7, Eq.8) are expressed in the following form: m( u rv) = X + X + X + X + X + X X [ N] (6) h prop rud sstd sstr w + m( u ru) = Y + Y + Y + Y + Y + Y Y [ N] (7) h prop rud sstd sstr w + I r = N + N + N + N + N + N N [Nm] (8) z h prop rud sstd sstr w + where: u longitudinal velocity [m/s]; v transversal velocity [m/s]; r angular velocity; m ships mass [kg]; I z mass moment of inertia [kgm 2 ]. Results of calculations. As an example data, longitudinal velocity of 1.5[m/s] and transversal distance of 1.5[m] between ships were considered. Fig. 5 presents results of analytical calculations based on semi-empirical equations [1]. s s s Suction forces and moments forces and moment value[n, Nm] Ys[N] Ns[Nm] -1,1-0,6-0,1 0,4 0,9 longitudinal relative stagger [mean ships length] Fig. 5. Suction forces and moments due to ship to ship interaction Suction forces and moments are sinusoidal curves shifted relatively to each other and of different magnitude. The highest transversal suction force is computed when the ships are in relative distance of 0.25 of mean ships length. When this relative position has been reached the control system should be most sensitive to changes in the distance between the ships. Ship to ship transversal suction forces become negligible when relative distance reaches 1.0 of mean ships length. Suction yaw moment is the biggest when the relative distance is +/-0.5 of mean ships length. This is important information for the control system. In this position it should be most sensitive to the rate of turn. There is no yaw moment when relative distance is about 0.1 of mean ships length. Some simulations of free surface flow around the two ships moving parallel in close proximity were run. Contours of the total pressure and of the dynamic pressure versus relative ships positions are presented in Fig. 6.

6 286 Mechatronic Systems, Mechanics and Materials a) dynamic pressure κ=0l m b) static pressure κ=0l m d) dynamic pressure κ=0.5l m e) static pressure κ=0.5l m f) dynamic pressure κ=-0.5l m g) static pressure κ=-0.5l m Fig. 6. Pressure distribution around hulls in waterline plane according to relative longitudinal distance (κ) between ships. By considering the pressure distribution around the hulls suction forces and moment were computed. They are compared with analytical results in Fig. 7. The longitudinal force (X s ) is not taken into account as it is negligibly small in comparison with the propulsion force. Suction forces and moments forces and moment value[n, Nm] Ys[N] Ns[Nm] Ys sim[n] Ns sim[nm] -1,1-0,6-0,1 0,4 0,9 longitudinal relative stagger [mean ships length] Fig. 7. Suction forces and moments due to ship to ship interaction comparison of analytical and simulation data Summary Some differences in the curves representing analytically computed and simulated data can be noted. Future control system will operate on the basis of the simulated data, which is more accurate than the analytical data. The differences observed reach a few percent. Better accuracy is in the simulation data, because the ships disproportions are taken into account. For such an application as

7 Solid State Phenomena Vol a control system, estimation of ship to ship interaction is needed to ensure proper working conditions. This data is only approximate. it depend on many varying conditions, e.g. wind, waves, water depth, proximity of other vessels and hydraulic engineering constructions. Therefore their effects on the hull that cause ship movements should be validated by other means, for example by measurement of the distance between hulls by laser rangefinders. In this connection the analytical data which is easier to implement and gives faster computation algorithm can be used as a basis for parallel motion control system. Future work includes suction force and moments verification on real objects Blue Lady and Kołobrzeg in Foundation for Safety of Navigation and Environment Protection in Iława. References [1] J. Brix: Manoeuvering Technical Manual, Seehafen Verlag, Hamburg (1993). [2] H.C. Chen, W.M. Lin, W.Y. Hwang: Application of Chimera RANS Method for Multiple-Ship Interactions in a Navigation Channel, Proc. of The Twelfth International Offshore and Polar Engineering Conference Kitakyushu, Japan, May (2002). [3] FLUENT Tutorial Guide, Fluent Inc., (2001) [4] T.I. Fossen: Guidance And Control Of Ocean Vehicles, John Willey & Sons Ltd., Norway (2003). [5] W. Gierusz: Simulation model of the shiphandling training boat "Blue Lady" Int.Conf. Control Application in Marine Systems, Glasgow, Scotland, " July (2001). [6] W. Gierusz: Simulation model of training ship (in polish), Zeszyty Naukowe Wyższej Szkoły Morskiej w Gdyni, 37(1999), p [7] L. Gucma, M. Schoeneich, J. Jachowski: CFD ship squat determination method validation by GPS RTK measurements, Proc. of International Conference on Maritime Traffic Engineering, Poland (2007). [8] K. McTaggart, D. Cumming, C. Hsiung, L. Li: Hydodynamic Interactions Between Ships During Underway Replenishment, Proc. of 6 th Canadian Marine Hydrodynamics Structures Conference, Vancouver, May (2001) [9] J.N. Newman: The Force and Moment on a slender body of revolution moving near a wall, David Taylor Basin, Washington D.C, Report No 2127 (1965) [10] K.J. Rawson, E.C. Tupper: Basic Ship Theory, Buttrworth, Oxford (2001). [11] D.W. Taylor: Some model experiments on suction of vessels, Transaction of the Society of Naval Architects and Marine Engineers, Vol. 17(1909), pp [12] E.O. Tuck, and J.N. Newman: Hydrodynamic interations between ships, Proc. of the 10th Symposium on Naval Hydrodynamics, Cambridge, Mass, Office of Naval Research, Washington, (1974), p [13] K.S. Varyani, A. Thavalingam, P. Krishnankutty: New generic mathematical model to predict hydrodynamic interaction effects for overtaking maneuvers in simulators, Journal of Marine Science and Technology, 9(2004), p.24-31

8 Mechatronic Systems, Mechanics and Materials / Determination of Suction Forces and Moment on Parallel Manoeuvring Vessels for a Future Control System /

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