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Sailing in oblique stern waves causes a ship to make sharp turns and uncontrollable course deviation, which is accompanied by a large heel and sometimes leads to capsizing. Studying the control algorithm in oblique stern waves is imperative because an excellent controller scheme can improve the ship's course-keeping stability. This paper uses the Maneuvering Modelling Group (MMG) method based on hydrodynamic derivatives and the Computational Fluid Dynamics (CFD)-based self-navigation simulation to simulate ship navigation in waves. This study examines the effect of proportion-integral-derivative (PID) controller schemes on the stability of course maintenance based on hydrodynamic derivatives and 3DOF MMG methods. Then, the optimized PID control parameters are used to simulate the ship's 6DOF self-propulsion navigation in oblique waves using the CFD method. The nonlinear phenomena during the process, such as side-hull emergency, slamming, and green water, are considered. This study found that the range of the control bandwidth should be optimized based on the ship's heading and wave parameters. [ABSTRACT FROM AUTHOR]

This paper investigates a calculation method for the heave and pitch motion of a trimaran, which includes direct and indirect calculation methods. In the direct calculation method, Computational Fluid Dynamics (CFD) simulation is applied to calculate trimaran motion. In the indirect calculation method, there exist three steps to achieve motion calculation: first, a standard wave spectrum is chosen to excite the wave force and moment acting on the trimaran; second, particle swarm optimization (PSO) and polynomial fitting methods are adopted to identify the function of wave force and moment; finally, the mathematical model of the trimaran is established. To compare the effectiveness of the direct and indirect methods, the model test of the trimaran is performed in a towing tank. The results of the model test proved that the direct and indirect methods are all effective for calculating the heave and pitch motions of a trimaran. [ABSTRACT FROM AUTHOR]

Wet-deck slamming affects the structural integrity of trimarans sailing under severe sea conditions. In this study, a Cartesian-grid computational fluid dynamics code is adopted to simulate the water-entry process of a trimaran cross-section. The numerical simulation results of the wet-deck slamming pressure and evolution of the free surface agree well with the experimental results. The spatial distribution of the wet-deck slamming pressure and the process by which the slamming pressure increases to its maximum are analyzed via simulation. Simultaneously, the wet-deck slamming characteristics are compared with three different main-hull profiles. We found that the occurred of the flow separation is related to the bilge curvature of the trimaran, which makes the slamming pressure near the main hull smaller than the other positions on wet deck. Moreover, the dimensionless peak slamming pressure on wet deck is less affected by the main-hull profile, while the time required for slamming pressure rise to its maximum is longest for the main-hull profile with smallest bilge curvature. These results can provide a better understanding of the relationship between the main-hull profile and the wet-deck slamming characteristics, which may be considered in future design for the trimaran section. • The non-uniform spatial distribution of the wet-deck slamming are mainly caused by the main-hull water-entry. • The flow separation angle near the main hull increased with the bilge curvature. • The dimensionless peak slamming pressure on wet deck is less affected by the main-hull profile. • The time required for wet-deck slamming pressure rise to its maximum is longest for the smallest bilge curvature. [ABSTRACT FROM AUTHOR]

Using the axe-bow to reduce total ship resistance on monohull ships has been well-known. This advantage has been further applied to a trimaran configuration together with its space-to-length (S/L) ratio differences. The investigation was carried out experimentally using an ITTC standard towing tank and numerically using computational fluid dynamics (CFD) analysis. The base model for the study uses an NPL 4a both for the mainhull and sidehulls of the trimaran, and later the mainhull is modified by attaching a front bulb known as an axe-bow. The resistance analysis of the trimaran was conducted with and without an axe-bow on the mainhull together with S/L ratios of S/L = 0.3 and S/L = 0.4 and at various Froude (Fr) numbers: 0.15, 0.2, 0.25, 0.3, 0.4, and 0.5. The results showed that the monohull with an axe-bow had a smaller drag than that without an axebow of an order up to 11.5%, whereas in the trimaran form, the reduction of drag was up to 8.4%. This indicates a positive influence of using the axe-bow on the total resistance of the trimaran configuration. Both experimental and CFD methods showed positive agreement of the order 2.7% discrepancy for the monohull form and a 3.4% discrepancy for the trimaran configuration. [ABSTRACT FROM AUTHOR]

The longitudinal motion characteristics of a slender trimaran equipped with and without a T-foil near the bow are investigated by experimental and numerical methods. Computational fluid dynamics (CFD) method is used in this study. The seakeeping characteristics such as heave, pitch and vertical acceleration in head regular waves are analyzed in various wave conditions. Numerical simulations have been validated by comparisons with experimental tests. The influence of large wave amplitudes and size of T-foil on the longitudinal motion of trimaran are analyzed. The present systematic study demonstrates that the numerical results are in a reasonable agreement with the experimental data. The research implied that the longitudinal motion response values are greatly reduced with the use of T-foil. [ABSTRACT FROM AUTHOR]

Highlights • A shiphull modification method has been developed and applied to the optimization of a trimaran. • Verified CFD has been carried out to assess the total resistance of the ship. • MIGA (multi-island genetic algorithm) combined with RS (response surface) has been used to optimize the drag. • Both side hull arrangement and main hull modification are taken into account as the design variables. Abstract A ship hull modification method called self-blending, combined with CFD (Computational fluid dynamics) and MIGA (Multi-island genetic algorithm), has been developed and applied to the optimization of a trimaran. The modification of ship hull has been carried out through merging the given cross sections picked from the original ship hull. Six parameters are used to perform the hull form modification, three of which are self-blending parameters of the main hull. For the other three, two being the parameters of controlling the relative location of side hull, the rest one being length ratio of new side hull to original side hull. Verified CFD method is used to evaluate the objective function (C T , coefficient of total resistance of the vessel). A RS (response surface) has been built to reduce the computation expense of optimization. The coefficient of total resistance of the optimized vessel decreases about 21.34% in comparison with the original hull which proves that the methods are valid for optimization of the trimaran. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate the hydrodynamic characteristics of high speed catamaran and trimaran ships at different speeds and finite depths using Computational Fluid Dynamics (CFD) techniques. Three dimensional Rankine Source Panel Method with non-linear free-surface boundary condition is used to capture free-surface potential flow around ship hull. Wave pattern, wave resistance, sinkage and trim for varying lateral and longitudinal separation of hull with varying water depths are determined and compared with each other to investigate spacing and depth effects on multihull ship. Computed results show a significant increase in total resistance for water of finite depth compared to deep water. A significant increase in sinkage and trim has also been found in the case of shallow water for both vessels. [ABSTRACT FROM AUTHOR]

A trimaran has excellent characteristics of transverse stability and less resistance because of its unconventional multiple slender hull form. However, the multi-hull configuration potentially triggers parametric roll due to the periodical fluctuation of metacentric height. In this study, an efficient numerical model was established to investigate the effects of the outriggers on trimaran stability in longitudinal waves, based on Froude-Krylov assumption and hydrostatic assumption. Then, the relationship between the metacentric height of the trimaran and the outrigger position was discussed, and the influence of heave/pitch motion responses on the wave stability of the trimaran was evaluated. Furthermore, a method of predicting the stability zone was proposed and checked by numerical simulation based on computational fluid dynamics. The relationship between the outrigger position and the potential risk of the parametric roll was analyzed by the obtained stability zones. It was found that the decrease in the outrigger displacement ratio and the increase in the clearance can significantly raise the risk of parametric roll of a trimaran. • An efficient numerical model was established to investigate the effects of outriggers configuration on trimaran stability. • A method of predicting the stability zone of a trimaran was presented and validated by numerical simulation. • The decrease in the outrigger displacement ratio can significantly raise the risk of the parametric roll. [ABSTRACT FROM AUTHOR]

The clam water resistance as well as the resistance components of a trimaran test model with and without appendage is calculated by CFD method in the different conditions, taking viscous effect and the free surface into account, in order to investigate the effect of trimming and sinkage on the resistance calculation. The viscous flow field around the trimaran without appendage restrained and free in 6 degrees of freedom is simulated at different velocities, the numerical results of the free model are compared with the test data and show good agreement. The total resistance and the resistance of the main hull, as well as the outriggers are calculated and the details of the flow field are discussed. Then, the numerical results of the free model and the captive model are compared in order to analyse the effect of trimming and sinkage. The analysis of the comparison suggests that some of the resistance components are susceptible to the gesture. After that, the viscous flow field of the trimaran with T-foil is simulated and the total resistance, resistance components as well as the gesture are calculated. The comparison of the numerical results of the free model with T-foil and the experimental data also shows good agreement, and the details of viscous flow field as well as the resistance components are analyzed. [ABSTRACT FROM AUTHOR]

To improve the stability performance of the trimaran, appendages were usually installed. Installing a larger-area appendage will increase the ship's resistance, and a smaller-area appendage has a limited stabilizing effect. Therefore, the design of appendages was a problem to be solved. Meanwhile, the installation position of the designed appendages was also worth studying. This study designed the appendages and investigated the installation position of stability appendages for a trimaran using computational fluid dynamics (CFD) simulation. The results of model tests and CFD simulations were compared, which verify the accuracy and feasibility of CFD simulation. T-foil and flap were selected as the trimaran vertical stability appendages. According to the appendage design basis and constraints, the shape and dimension are given through the design process. The flap was installed on the stern of the trimaran. Six longitudinal and four vertical installation positions were selected while the best installation position for the T-foil was obtained. Finally, simulation and experimental results verify that the installation position of appendages is reasonable and effective for improving the trimaran stability performance. • Appendages include T-foil and flap were designed for improving the stability performance of a trimaran. • The installation position of the flap has matched the streamline of the trimaran stern. • Six longitudinal positions and four vertical positions were selected for T-foil installation. • The optimal process of appendages was conducted through CFD simulations and model tests. • CFD simulations and model tests were conducted for verifying the designed and installed appendages. [ABSTRACT FROM AUTHOR]

In this paper, the characteristics of the impact pressure and force of a trimaran section was studied by Computational Fluid Dynamics (CFD). The time domain features of the slamming pressure or force showed a strong correlation with the penetration depth regardless of the specific ways of water entry. The effects of velocity and acceleration on the impact pressure and force were analyzed. It was found that the initial impact of the main hull and the wet-deck slamming were predominantly affected by the entry velocities, whilst the acceleration had almost no effect for initial impact. The impact velocity presented a quadratic relation with slamming pressure/forces, and the relation between acceleration and wet-deck slamming pressure/force was linear. These were consistent with the patterns implied by analytical models such as the Wagner or MLM (Modified Logvinovich model) theories. [ABSTRACT FROM AUTHOR]

In this paper, the slamming pressure and load characteristics of a trimaran cross-section under various conditions were investigated by CFD (Computational Fluid Dynamics) simulations. The computation model was first validated against experimental results. After that, the simulation of different types of motion, i.e. free fall with different mass and entry velocity, entry with constant velocity and harmonic motion with different entry velocities were analysed. It was found that the characteristics of the dynamics during slamming strongly correlates to penetration depth, regardless of the types of entry. Distinguishing features during the wet-deck slam were observed for free fall motion under different conditions, including pressure drop under the main hull during wet-deck slam. The maximum acceleration would start to decrease after the mass has reached a certain value, and the second acceleration peak (corresponding to the wet-deck slam) would be smaller than the first one if the falling height is large enough. [ABSTRACT FROM AUTHOR]

In the present paper, the multi-objective optimization of a waterjet-propelled trimaran was carried out based on computational fluid dynamics (CFD) considering the interactions between the waterjet and the hull. Numerical results were validated with experimental data for one waterjet propulsor and the original hull. The simulation-based design (SBD) optimization was performed for the waterjet and the hull. Furthermore, the parametric reconstruction of the duct was executed based on its shape characteristics. The Lackenby method and the free-form deformation method were applied to transform the hull shape. The optimal Latin hypercube design (Opt LHD) method was used to generate samples, and the surrogate model was developed based on the support vector regression (SVR) method. The non-dominated sorting genetic algorithm II (NSGA-II) was employed to optimize design objectives at the design speed of Fr = 0.628. In comparison to the original shape, the total resistance, the thrust, the torque, and the power consumption of the optimized trimaran at self-propulsion, respectively, decreased by 3.85%, increased by 6.38%, increased by 1.73%, and decreased by 10.39%. Therefore, it can be inferred that the SBD technique is effective to solve multi-objective optimization problems of ship hydrodynamics. • The multi-objective optimization problem of a waterjet-propelled trimaran was divided into three processes: the optimization of the waterjet system, the optimization of the global hull shape, and the optimization of the local hull shape and the arrangement of the waterjet. • At the design speed, the optimal hull indicated a 3.85% reduction in resistance, a 6.38% increase in thrust, and a 1.73% increase in torque. • When the aft-body varied from U-type to more U-type, thus resulting in a decrease in resistance and torque, and a increase in thrust. • The reduction in the distance between two waterjet systems effectively improved the thrust and reduced the torque. [ABSTRACT FROM AUTHOR]