Numerical and experimental analyses of hydrodynamic performance of a channel type planing trimaran*

SU Yu-min (苏玉民)

State Key Laboratory of Autonomous Underwater Vehicle, Harbin Engineering University, Harbin 150001, China, E-mail: suyumin@hrbeu.edu.cn

WANG Shuo (王硕)

Dalian Shipbuilding Industry Engineering and Research Institute Co. Ltd, Dalian 116011, China

SHEN Hai-long (沈海龙), DU Xin (杜欣)

State Key Laboratory of Autonomous Underwater Vehicle, Harbin Engineering University, Harbin 150001, China

Numerical and experimental analyses of hydrodynamic performance of a channel type planing trimaran*

SU Yu-min (苏玉民)

State Key Laboratory of Autonomous Underwater Vehicle, Harbin Engineering University, Harbin 150001, China, E-mail: suyumin@hrbeu.edu.cn

WANG Shuo (王硕)

Dalian Shipbuilding Industry Engineering and Research Institute Co. Ltd, Dalian 116011, China

SHEN Hai-long (沈海龙), DU Xin (杜欣)

State Key Laboratory of Autonomous Underwater Vehicle, Harbin Engineering University, Harbin 150001, China

(Received May 5, 2013, Revised July 28, 2013)

This paper studies the hydrodynamic performance of a channel type planing trimaran. A numerical simulation is carried out based on a RANS-VOF solver to analyze the hydrodynamic performance of the channel type planing trimaran. A series of hydrodynamic experiments in towing tank were carried out, in which both the running attitude and the resistance performance of the trimaran model were recorded. Some hydrodynamic characteristics of the channel type planning trimaran are shown by the results. Firstly, the resistance declines significantly, with the forward speed across the high-speed resistance peak due to the combined effects of the aerodynamic and hydrodynamic lifts. Secondly, the resistance performance is influenced markedly by the longitudinal positions of centre of the gravity and the displacements. Besides, the pressure distribution on the hull and the two-phase flow in the channel are discussed in the numerical simulations.

hydrodynamic performance, channel type planing trimaran, numerical simulations, RANS-VOF solver, towing tank tests

Introduction

The channel type planing trimaran is a vessel with combined characters of the planing craft, the channel type planing craft and the high-speed multi-hull, and with three interrelated parts–the central planing hull, the planing tunnels and the rigid skirts. It has a special M-shaped geometry and enjoys an improved hydrodynamic performance.

The three parts of the ship and the water surface constitute a ring closed channel with a large inlet at the bow and a small outlet at the stern of the ship. The air and the bow waves are compressed by entering the ring closed channel from the large inlet and exiting at the small outlet when the trimaran sails on the ocean. The compressed two-phase mixture in the channel provides additional uplift forces and improves the dynamic stability of the ship. The uplift of the hull caused by the combined effects of aerodynamics and hydrodynamics in the channel reduces the draft and the resistance. The stern wake also sees a significant reduction. By capturing the forth bow wave, the vapor/ fluid flow field passively dampens the visible and acoustic signature of the ship. The stern wake energy that moves away from the vessel is inhibited by the presence of millions of captured air bubbles under and trailing the ship. In the same way, the noise from the vessel passage and its machinery is reduced.

The studies and the applications of the channel type planing trimaran have reached a mature stage in abroad in recent years. But very few published data can be found about this kind of ships because of its superior operational performance in military applications. In China, there are no related papers published on the channel type planing trimaran at present, except those about the channel type craft and the planing multi-hull. Liu et al.[1]carried out a series of experimentsto study the hydrodynamic performance and the design parameters of the wave-absorbing planing trimaran. Sun et al.[2-4]conducted towing tank tests to study the planing trimaran and the stepped planing trimaran. Wang[5]presented both numerical and experimental studies of a planing trimaran. The resistance and the stability of the planing trimaran were also discussed.

In this work, the hydrodynamic performance of the channel type planing trimaran is analyzed in the following two steps. First, we use the commercial CFD code STAR CCM+ to simulate the channel type planing trimaran sailing in a calm water. The numerical simulation is based on a RANS-VOF solver and a 6 degrees of freedom body-motion module[6,7]. The running attitude and the resistance performance are calculated in the numerical simulations[8,9]. The pressure distribution on the hull and the two-phase flow in the channel are also analyzed, focusing on the hydrodynamic performance of the channel type planing trimaran. Secondly, a series of towing tank tests are performed to validate the numerical results. At different towing speeds, the running attitudes (the heave motions and the pitch angles) and the resistance are measured[10]. The numerical and experimental results are compared and analyzed. The influence of the longitudinal centre of gravity (LCG) and the displacements on the resistance performance is discussed[11].

1. The physical model

The channel type planing trimaran is designed by using the reverse reconstruction technique. The body plans and the three-dimensional physical model are shown in Fig.1. The channel type planing trimaran is constituted with three parts-the planing hull, the tunnel and the rigid skirts. The general splash and bow waves of the planing hull are absorbed by the large inlet of the channel. At a high forward speed the splash will slam on the tunnel and the air enters into the channel with the bow waves. The air and the water are compressed due to the reduction of the space in the channel, and the pressure is increasing in the channel that makes a contribution to the uplift of the ship. The stern wake is also reduced by the small outlet of the channel.

The principal features of the model are shown in Table 1. The resistance performance of the channel type planing trimaran is shown by different displacements and LCGs in the towing tank tests. The towing positions of the model tests are set in the same positions as the gravity centre.

2. The numerical method

Merchant CFD software STAR CCM+ is used to simulate the hydrodynamics of the channel type planning trimaran.

2.1 RANS equation

The flow field is assumed to be viscous and incompressible. Therefore, the continuity and momentum equations can be described as:

whereρis the density of the fluid,νis the kinematic viscous coefficient,uiis the transient velocity component,u′is the fluctuating velocity component, uiis the mean velocity component and Siis the source item. Thek-ωsst two-equation model is appliedfor the effect of the turbulence. In the volume of fluid (VOF) method, a volume fraction field F(0＜F＜1) is introduced, and for each element in the computational grid there is a fraction of that element volume that is occupied by a specific fluid.

The trimmed mesh module also has the ability to automatically refine the cells anywhere defined by the user in the flow field. The trimmed surface and volume mesh is shown in Fig.2. The regions near the ship, especially, the tunnel and the free surface of two phases are refined. There are about 800 000 CVs (control volume) in the whole flow field[14].

The layer meshes are required in the simulation of the turbulence, especially, in cases of high Reynolds number. A prism layer mesh model is used to generate the layer mesh. The prism layer mesh is composed of orthogonal prismatic cells that reside next to the wall boundaries in the volume mesh. Typically, for the wall function based model, one to four layers are used. Figure 3 shows a four layer mesh and the trimmed mesh of the section of the planing craft. The thickness of the prism layer mesh is 0.0005 m with a stretching factor of 1.5[15].

2.3 Body-motion module

Two orthogonal Cartesian reference systems are used: one is fixed on the earth (dynamic fastening), the other is fixed on the ship (moving fastening), with the origin of the moving coordinate at the ship’s centre of gravity.G,Gx,GyandGz , respectively, stand for the intersecting lines passing the waterline plane, the cross profile and the longitudinal section. Assume that the mass of the water glider ism , the speed of the centre of gravityG is V(u,v,w), the angular velocity isΩ(p,q,r), the force is F(x,y,z), the torque of that force with respect to the centre of gravity isM(L,M,N).

According to the theorem of motion about the centre of mass and the theorem of moment of momentum about the centre of mass

where B is the momentum,Kis the momentum torque relative to the mass centerG. For the dynamic fastening, Eq.(3) takes the form

Rewritten Eq.(3) into the projection formula for the dynamic fastening:

Equation (5) concerns the ship’s 6 DOF of motions. In this paper, the channel type planing trimaran is simulated sailing in a calm water with 2 degrees of freedom (heave and pitch motions). As a result Eq.(5) issimplified from 6 formulas to two.

In this work, a general approach is implemented, extending a Navier-Stokes code to couple the fluid with the body motions induced by the flow and by external forces. This allows not only to compute the dynamic sinkage and trim but also to simulate the unsteady craft motions in 6 DOFs. The robustness of this methodology is mainly due to the simplicity of tracking the ship’s motion without deforming the numerical mesh or using complicated multi-mesh strategies. In the single-grid strategy used in these simulations, the computational domain moves as a whole relative to the waterplane. The boundary conditions (the mean flow velocity, the orbital velocity, the turbulence parameters and so on) have to be very carefully imposed at each instant relative to the undisturbed waterplane.

For example, in a 2 DOF (pitching and heaving) numerical simulation of the channel type planing trimaran the convergence curves of the heave motions and the pitch angles are shown in Fig.4. When the impulses of heaving and pitching disappear, the roll moment could be recorded as a result. The liquid surface of the flow field is shown in Fig.5. The VOF method in conjunction with a moving, rigid mesh is shown to be effective. The free surface of the two phases (air and water) is captured accurately and distinctly.

3. Hydrodynamic experiments

All experiments were conducted in the Highspeed Hydrodynamic Laboratory of Special Aircraft Research Institute of China (No. 605 Institute). The parameters of the tank are as follows:

Length: 510 m,

Breadth: 6.5 m,

Depth: 6.8 m,

Water depth: 5.0 m,

Carriage speed: 0.1 m/s-22m/s.

The tank has a manned carriage with a dynamometer installed for measuring the model total resistance together with a computer and various instrumentation facilities for automated data acquisition.

The experiments are to verify the running attitude and the resistance performance of the channel type planning trimaran at high forward speeds. Schematic views of the experimental setup are shown in Fig.6 (in a side view). The ship model free in heaving and pitching is attached to a high speed towing carriage through a load cell and it is towed horizontally at a constant forward speed as shown in Fig.7.

Figure 8 and Fig.9 show the model towed at a high forward speed of 11 m/s (Fr=2.60). The channel type planing trimaran enjoys a good dynamic stability at the high speed. The wake at the rear of the model is composed of water and bubbles.

4. Results and discussions

Numerical and experimental methods are applied to study the hydrodynamic performance of the channel type planing trimaran. The hydrodynamic characteristics of the ship are studied firstly by two validated methods. The general two parameters for a planing type ship–the LCG and the displacement are discussed. The effects of the two parameters on the hydrodynamic performance of the ship are analyzed by experimental results. The two-phase flow, the pressure distribution at the bottom and the stern wake are discussed through the numerical simulation.

4.1 The hydrodynamic characteristics of the channel type planing trimaran

The running attitude and the resistance obtained from the numerical simulation and the experiments are compared and discussed in this section. Figures 10-12 show the heave motions, the pitch angles and the drags of the channel type planing trimaran model by experiments and calculations.

The discrepancy of the running attitude (heave and pitch) between computational and experimental results is less than 5%. The body-motion model is efficient and accurate in the 2 DOF simulation. The discrepancy of the drag between computational and experimental results increases with the sailing speed. The calculating drag at a high speed is less than the experimental results, and the average discrepancy is about 10%. The discrepancy at a high speed is probably caused by the limits of the grid size. With the increase of the forward speed, the spray component of the resistance increases. In the VOF strategy, the small size spray is ignored in a large size mesh. Hence, the spray resistance component is underestimated in the numerical simulations.

The comparison indicates that both numerical simulations and experiments can reflect the hydrodynamic characteristics of the channel type planing trimaran at a high forward speed. The numerical simulation and the hydrodynamic experiments are all validated for the analyses of the hydrodynamic performance.

The trends of the heave motions and the pitch angles against the speeds of the channel type planing trimaran are similar to those of a planing craft. The heave motion increases rapidly when the planing trimaran enters the planing attitude, and it then rises slo-wly with the increase of the speed. The pitch angle has a peak at the half-planing condition, and decreases with the increase of the speed. The drag curve of the channel type planing trimaran has two peaks. The high-speed peak of the drag curve is distinctive as compared with the case of ordinary planing crafts. With the increase of the speed across the high-speed drag peak, the drag force decreases to a valley at the towing speed of 12.0 m/s. Comparing Fig.10 with Fig.12 at 12.0 m/s, the heave motion has a distinct increase. The running attitude and the drag force indicate that the uplift at a high-speed is caused by the aerodynamic and hydrodynamic effects in the tunnels which are responsible for the unique resistance performance of the channel type planing trimaran.

4.2 The influence of LCG on hydrodynamic performance

The LCG is a significant parameter in the design of a planing type vessel. By adjusting the LCG, the running attitude (the trim angle) is set to the design value. The influence of the LCG on the hydrodynamic performance of the channel type planing trimaran is firstly studied by the experimental method.

Figure 13 and Fig.14 show the draft of the centre of gravity (CG) measured in experiments with different longitudinal positions. The trend of the draft is the same as the increase of Fr∇as the planing trimaran is uplifted gradually while the draft decreases. When XCGdecreases (the centre of gravity moves to the stern of the ship), the draft of CG declines.

Figure 15 and Fig.16 show the influence of Fr∇on the trim angle of the channel type planing trimaran at two different displacements. The trim angles increase significantly at all speeds when XCGdecreases (the centre of gravity moves to the stern of the ship) especially at the half-planing condition (Fr∇=1.0-2.0).

The influence of the LCG on the resistance performance is shown in Fig.17 and Fig.18. The resista-nce performance of the channel type planing trimaran is measured by R/Δ. By moving the centre of gravity back to the transom, the resistance declines sharply.

The influence of the LCG on the hydrodynamic performance is similar to the case of the general planning crafts. The tunnel and the rigid skirts make the channel type planing trimaran to have a unique resistance performance at a high forward speed (as described in 5.1), while the ship keeps most of the characteristics of a planing craft due to the component of the planing hull.

4.3 The influence of displacement on resistance performance

The increased payload fraction is one of the advantages of the channel type planing trimaran. The influence of the displacement on the resistance performance is also revealed in hydrodynamic experiments.

Figure 19 and Fig.20 show the resistance curves of different displacements measured by experiments. The trends of R/Δdo not change with displacements. With the increase of the displacements,R/Δdecreases sharply at a high towing speed. By the support of an enough engine power, the channel type planing trimaran shows a superior resistance performance with a large displacement.

4.4 The two-phase (air and water) flow in the tunnel

The tunnel of the channel type planing trimaran is designed to absorb the bow wave and make a contribution to the uplift of the ship. The air and the water spray in the tunnel are mixed and complex. At present, the two-phase flow in the tunnel is not directly observable in the experiments.

The VOF model is effective to capture the surface of the two-phase flow with refined control volumes in the numerical simulation. For example, with Fr∇= 5.53 the two-phase distribution is shown in Fig.21 (The distances from the stern of Sections 1-4 are 1.0 m, 0.7 m, 0.4 m and 0.1 m). The two phase flow around the ship is clarified in the scaled figures. At the bow of the ship (Section 1 and Section 2) the spray of the planing surface is shown. In Section 3 and Section4 the bow wave and the spray are slamming on the top of the tunnel, and the air is compressed to sides. At the bottom of the planing hull, there is also the air phase which may cause a negative pressure.

4.5 The pressure distribution on the bottom of the channel type planing trimaran

The pressure distribution on the bottom obtained by the numerical simulation is shown in Fig.22. High pressure areas are seen at the bow and in the middle of the tunnel. The high pressure areas at the bow are caused by the piercing wave and the slamming water. The high pressure areas in the tunnel are caused by the absorbing bow wave and the compressing of the twophase flow in the tunnel. The positive and negative pressure distributions of the main planing hull are also shown distinctly.

4.6 The comparison of the wake of a planing monohull and the channel type planing trimaran

The reduction of the stern wake is one of the hydrodynamic features of the channel type planing trimaran. The wake can not be measured in the towing tank. The CFD analysis of the stern wake is applied to compare the wake with a planing craft.

Figure 23 shows the body plan and the three-dimensional model of the planing craft. The vessel is a general prismatic planing craft, which is scaled to the same length with the channel type planing trimaran model. The wake of this two vessels are compared under the same Fr =2.36.

The heights of the two-phase surface captured by the VOF model are obtained in the RANS solution. The comparisons of the two ship’s wakes are shown in Fig.24. The wake’s absolute height of the channel type planing trimaran is much smaller than the planing craft. The wake’s shape of the trimaran is also narrower than the planing craft. The reduction of the stern wake is significant.

5. Conclusions

In this paper, both numerical simulations and hydrodynamic experiments are carried out to analyze the hydrodynamic performance of the channel type planning trimaran. The results indicate that the channel type planing trimaran has superior hydrodynamic characteristics.

(1) The resistance curve of the channel type planning trimaran has two peaks (Low speed peak and high speed peak, respectively). The resistance decreases significantly across the high-speed peak.

(2) The trim angle grows and the resistance goes down as the LCG is moved to the stern. The relationship between the hydrodynamics and the CG can be found in the general planning craft as well.

(3) The channel type planing trimaran is superior in terms of the payload. The payload R/Δdrops with the increase of displacements, with more advantages.

(4) The numerical method is validated by the experiments and is applied to analyze the flow field. It can be shown that the numerical simulation is effective and necessary for revealing the hydrodynamic characteristics of the high-speed marine vehicles.

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10.1016/S1001-6058(14)60062-7

* Project supported by the National Nature Science Foundation of China (Grant No. 50879014), the Doctoral Program of Higher Education of China (Grant No. 200802170010).

Biography: SU Yu-min (1960-), Male, Ph. D., Professor