Numerical prediction of hydrodynamic forces on a ship passing through a lock with different configurations*

WANG Hong-zhi (王宏志), ZOU Zao-jian (邹早建)

School of Naval Architecture, Ocean and Civil Engineering and State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China, E-mail: wangbazhi@hotmail.com

Numerical prediction of hydrodynamic forces on a ship passing through a lock with different configurations*

WANG Hong-zhi (王宏志), ZOU Zao-jian (邹早建)

School of Naval Architecture, Ocean and Civil Engineering and State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China, E-mail: wangbazhi@hotmail.com

(Received November 5, 2012, Revised July 3, 2013)

A CFD method is used to numerically predict the hydrodynamic forces and moments acting on a ship passing through a lock with a constant speed. By solving the RANS equations in combination with the RNG kε- turbulence model, the unsteady viscous flow around the ship is simulated and the hydrodynamic forces and moments acting on the ship are calculated. UDF is compiled to define the ship motion. Meanwhile, grid regeneration is dealt with by using the dynamic mesh method and sliding interface technique. Under the assumption of low ship speed, the effects of free surface elevation are neglected in the numerical simulation. A bulk carrier ship model is taken as an example for the numerical study. The numerical results are presented and compared with the available experimental results. By analyzing the numerical results obtained for locks with different configurations, the influences of approach wall configuration, lock configuration symmetry and lock chamber breadth on the hydrodynamic forces and moments are demonstrated. The numerical method applied in this paper can qualitatively predict the ship-lock hydrodynamic interaction and provide certain guidance on lock design.

ship-lock hydrodynamic interaction, numerical prediction, lock configuration, lock design

Introduction

Passing through a lock is a specific ship motion as a ship usually moves at low speed. During the passing process, due to the geometrical restriction of the lock chamber, the shallow water and bank effects on the hydrodynamic forces may be remarkable, and the ship hydrodynamic behaviors are quite different from those in unrestricted waters. However, the hydrodynamic mechanism is not yet fully understood. Vantorre and Richter[1]gave an overview of the hydrodynamic effects acting on a ship approaching a lock by some factors, including approach channel and approach structure layouts, density currents, translation waves, return flow, cushion effects, and retardation. Ship behavior changes drastically due to these hydrodynamic effects. To gain a clear insight into the hydrodynamic behaviors of a ship passing through a lock, it is necessary to investigate the flow field around the ship and the hydrodynamic forces acting on the ship, with the shallow water and bank effects being taking into account.

The most commonly used method to investigate the hydrodynamic behaviors of a ship passing through a lock is the model test method. In the 1990s, a systematic captive model test was carried out in the Towing Tank for Manoeuvres in Shallow Water (cooperation Flanders Hydraulics Research and Ghent University) in Antwerp to study the feasibility for receiving bulk carriers with larger beam in the Pierre Vandamme Lock in Zeebrugge[2]. In 2007-2008, selfpropelled model tests were conducted to investigate the behaviors of vessels transiting the future Panama Canal Third Set of locks[3,4]. The navigation behaviors of three different ship models in the locks were assessed and the influences of approach wall configurations, eccentricities, propeller rates, approach scenarios and under keel clearances were analyzed. Recently, Verwilligen et al.[5]analyzed the entering manoeuvre of full form ships into the West Lock in Terneuzen bymeans of model tests, full-scale trials and real-time simulations. Some numerical methods were also developed to study ship behavior in lock. Chen[6]formulated a one-dimensional unsteady hydraulic narrow-channel model for the flow coupled to the ship motion in surge, heave and pitch and calculated the ship motions during lock entry. Vergote[7]improved a mathematical model to calculate the translation waves generated during the lock entry.

Nowadays, CFD-based numerical methods have been widely used in the hydraulic design of navigation locks. Thorenz[8,9]gave an overview of the state-ofthe-art of CFD in lock designs and used CFD to evaluate filling and emptying systems for the new Panama Canal locks. Stockstill et al.[10,11]investigated the application of computational hydraulics for the evaluation of navigation structures and lock filling system. De Mulder[12]gave an overview about the main features, progress and challenges of CFD modeling for lock design.

In the present paper, based on the general purpose CFD package Fluent, an unsteady RANS solver in conjunction with the RNGkε- turbulence model is applied to simulate the viscous flow around a ship entering the Pierre Vandamme Lock and to calculate the hydrodynamic forces on the hull. Different approach wall configuration, lock configuration symmetry and lock chamber breadth are considered and the numerical results are compared to investigate the influence of the lock configuration on the ship hydrodynamic behaviors.

1. Numerical formulation

A ship passing through a lock with the constant speedUis considered. The ship speed is assumed to be so low that the wave-making effect on the hydrodynamic forces can be neglected. The flow around the ship is assumed to be a viscous flow of incompressible fluid which is governed by the time-averaged continuity equation and Navier-Stokes equations as follows:

Fig.1 Computational domain and its boundaries

Fig.2 Definition of moving zone

Fig.3 Lock configuration in towing tank tests

Table 1 Ship characteristics, bulk carrier

The RNGkε- model is adopted to make the equation system closed. The transportation equations of turbulence kinetic energykand its rate of dissipationεare

whereGkrepresents the generation of turbulence kinetic energy due to the mean velocity gradients andtμis the turbulence viscosity, which are expressed as

Fig.4 Calculated hydrodynamic forces compared with the model test results

The other terms have the following values and expressions:

Fig.5 Calculated vertical displacements of the fore and aft perpendiculars compared with the model test results

Fig.6 Lock with different approach wall configurations

Fig.7 Effect of the approach wall configuration on the ship hydrodynamic behaviors

2. Numerical solution

2.1Computational domain and boundary conditions

As is shown in Fig.1, the computational domain is bounded by the ship hull, the water bottom, the undisturbed free surface, the approach channel bank and guide wall, the lock wall, the lock gate and a fictitious outflow boundary. On the ship hull, the water bottom, the channel bank and guide wall, the lock wall and the lock gate, the wall boundary condition is imposed. Onthe undisturbed free surface, the symmetry boundary condition is imposed. On the outflow boundary, the pressure outlet condition is imposed.

2.2Grid generation and dynamic mesh method

A combination of mixed tetrahedral mesh with hexahedral mesh grid is adopted. The hexahedral grid is used in mid-ship part and the adaptable tetrahedral grid is used in bow and stern parts, where geometric hull is complex. In the rest of the flow field the hexahedral grid is used. The total number of cells is about 500 000. The density of grid in calculation refers to Wang[13]. Convergent numerical results are obtained when the number of cells is about 500 000.

The dynamic mesh method is used to simulate the relative motion between the ship and the lock. There are three kinds of methods in Fluent: smoothing, layering and remeshing. In this paper, the layering method is chosen to update the mesh. When using this method, boundaries between the moving zone and stationary zone are set as interface. As is shown in Fig.2, the zone containing the ship is set as moving zone which moves at the ship speed, and the dashed line indicates the interface. Boundaries in solid ellipse and dashed ellipse are places where grids split and collapse.

2.3Solution settings

In the computation, the user defined function (UDF) is used to set the speed of the ship, to define the gravity center of the ship and to calculate the force and moment on the ship. The unsteady part in the governing equations is discretized by the first-order implicit scheme. The algorithm SIMPLE is applied to solve the velocity-pressure coupling problem. The momentum, turbulent kinetic energy and turbulent dissipation rate are discretized by the second-order upwind scheme. Time step is set as 0.1 s to make sure that the product of the time step times the ship speed is smaller than the mesh size in moving zone.

3. Numerical results

3.1Study object

To compare with the available model test results[2], a bulk carrier ship model passing through the Pierre Vandamme Lock is chosen as study object. The lock has a length of 500 m, a width of 57 m and a depth of 18.5 m. The scale model of the lock was constructed in the towing tank, with special attention to the asymmetric layout of the approach channel and guide wall, as shown in Fig.3. The model scale ratio is 1/75. The main dimensions of the ship and the model are listed in Table 1. The ratio of water depth to draft(h/T)is 1.2, and the model speed is 0.15m/s (=Fr0.0258, =Re4.55×105).

3.2Numerical results for comparison

The hydrodynamic forces and moments acting on the hull are obtained by the numerical method at each time step (interval 0.1 s). The mean sinkageσand trimτ(positive sinkage downwards and positive trim bow-up) are determined from the calculated sinking forceZand trim momentMby the following formulae at each time step:

whereAwrepresents the waterplane area andIwdenotes the longitudinal moment of inertia of the waterplane area about the center of floatation.

Fig.8 Locks with symmetric configuration

The vertical displacement of the fore and aft perpendicularszFPandzAPat each time step can be obtained as

Figure 4 shows the time history of the calculated hydrodynamic forces compared with the model test results. Figure 5 shows the corresponding vertical displacements of the fore and aft perpendiculars. All results are plotted as a function of the longitudinal position of the mid-ship section of the model. It can beseen that the lateral forceYand the yawing momentNacting on the ship are evaluated with good accuracy in comparison with the experimental data. However, for the ship entering the lock, the longitudinal forceXis underestimated compared with the experimental results because of the increasing blockage in navigation lock under test conditions. As we can see from Fig.5, the numerical method overestimates thesinkageσand trimτ. The reason is that in the numerical simulation the ship is fixed and the sinkage and trim are determined from the calculated sinking force and trim moment, hence the retardation effect of the restoring force and moment induced by the sinkage and trim cannot be taken into account, while in the model test the retardation effect of the restoring force and moment induced by the sinkage and trim in facthas an effect in mitigating the sinkage and trim, which makes the sinkage and trim smaller than those obtained by the numerical calculation.

Fig.9 Effect of lock configuration symmetry on the ship hydrodynamic behaviors

Fig.10 Effect of lock chamber breadth on the ship behaviors

3.3Effect of approach wall configuration

An approach wall offers a structure where the ship can be moored before the opening of the gates or helps the pilots to align the ship with the longitudinal axis of the lock. The drawback is that its asymmetry may induce unfavorable lateral forces on the ship.

Figure 6 shows two types of approach walls (Fig.3 shows the lock configuration without wall). Figure 7 shows the calculated hydrodynamic behaviors of the ship changing with the different types of approach wall. The rolling momentKis also calculated. From Fig.7 we can see that the left closed wall increases the hydrodynamic forces, while the right one reduces the magnitude of the hydrodynamic forces.

3.4Effect of lock configuration symmetry

The original lock configuration is asymmetrical (see Fig.3). In fact, the lock could be designed as leftsymmetrical or right-symmetrical, as shown in Fig.8, and the hydrodynamic forces acting on a ship passing through the two types of lock can be calculated to investigate the influence of lock configuration symmetry. In Fig.9, the numerical results are depictured. It can be seen that the symmetry largely reduce the lateral force, rolling moment and yawing moment. The right-symmetrical lock configuration increases the longitudinal force and trim moment, while the leftsymmetrical one decreases them.

3.5Effect of lock chamber breadth

Figure 10 shows the calculated hydrodynamic quantities changing with the lock chamber breadth. It can be seen that the lock chamber breadth has a major effect on the hydrodynamic quantities. As the lock chamber breadth decreases, the magnitudes of the hydrodynamic forces and the vertical displacements of the fore and aft perpendiculars increase.

4. Conclusion

Taking a bulk carrier ship as study object, the hydrodynamic behaviors of the ship passing through the Pierre Vandamme Lock have been studied numerically. The unsteady viscous flow around the ship model passing through the lock model is simulated by solving the unsteady RANS equations. The numerical results are presented and compared with the available experimental results. In general, the present numerical results are in good agreement with the experimental data. The effects of approach wall configuration, lock configuration symmetry and lock chamber breadth on the hydrodynamic forces are investigated. The left closed wall increases the hydrodynamic forces, while the right closed wall reduces the hydrodynamic forces. The lock configuration symmetry can reduce lateral force, rolling moment and yawing moment to a larger extent. The lock chamber breadth has a major effect on the hydrodynamic quantities. The reasonable lock configuration can reduce the hydrodynamic forces and make a ship passing through the lock safely. Therefore, it is important to design an appropriate lock configuration. The present numerical study is helpful to understand the influence of lock configuration and may provide certain guidance to the lock design.

Acknowledgment

The authors would like to express their sincere thanks to the Knowledge Centre Manoeuvring in Shallow and Confined Water (Flanders Hydraulics Research and Ghent University) for providing the model test data.

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10.1016/S1001-6058(14)60001-9

* Project supported by the National Natural Science Foundation of China (Grant Nos. 51061130548, 51179019).

Biography: WANG Hong-zhi (1990-), Male, Ph. D. Candidate

ZOU Zao-jian,

E-mail: zjzou@sjtu.edu.cn