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Due to the complex flow interference by side hulls, load prediction has been one of the obstacles to achieve structural health monitoring and intelligent navigation of trimarans. According to the machine learning theory, a short-term prediction method towards trimaran loads is studied by using an optimized data-driven model. In the research, the monitoring data from a trimaran model test is applied for the training and testing of long short-term memory (LSTM) neural network. The impact analysis on the factors such as input length, neuron number, artificial neural network (ANN) optimizer, and output scope, are taken. To highlight the trimaran high-frequency load fluctuation and improve the prediction accuracy, the LSTM neural network combines with different signal decomposition algorithms, such as Empirical Mode Decomposition (EMD), Ensemble Empirical Mode Decomposition (EEMD), Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), and Variational Mode Decomposition (VMD). Through the comprehensive comparison of statistical indicators at different positions and wave environment, the VMD-LSTM model is selected by considering its highest load prediction ability among these artificial neural network models. The research will improve the load prediction accuracy in the structural health monitoring systems and offer effective technical support for intelligent unmanned trimarans.

Since the slamming load could cause severe damage of wet deck of ship hull girder, the interaction between the structural response and hydrodynamic loading should be considered. A large scaled model of trimaran was designed, which could consider the structural elastic for studying the structural response of trimaran hull girder. The testing model was vertically dropped into still water in the tank to simulate typical hydroelastic slamming load, in which various impact velocities were considered. Each load condition was conducted several times to verify the repeatability and reproducibility of the experimental data. The slamming pressure and strain distributions are presented and discussed. The ranges of maximum slamming pressure and the danger area are identified for design of this type of trimaran. [ABSTRACT FROM AUTHOR]

To predict the wave loads of a flexible trimaran in different wave fields, a one-way interaction numerical simulation method is proposed by integrating the fluid solver (Star-CCM+) and structural solver (Abaqus). Differing from the existing coupled CFD-FEA method for monohull ships in head waves, the presented method equates the mass and stiffness of the whole ship to the hull shell so that any transverse and longitudinal section stress of the hull in oblique waves can be obtained. Firstly, verification study and sensitivity analysis are carried out by comparing the trimaran motions using different mesh sizes and time step schemes. Discussion on the wave elevation of uni- and bi-directional waves is also carried out. Then a comprehensive analysis on the structural responses of the trimaran in different unidirectional regular wave and bi-directional cross sea conditions is carried out, respectively. Finally, the differences in structural response characteristics of trimaran in different wave fields are studied. The results show that the present method can reduce the computational burden of the two-way fluid-structure interaction simulations. [ABSTRACT FROM AUTHOR]

An aquatic robot is proposed that moves due to the motion of an internal flywheel. The body of the robot represents a trimaran that consists of a capsule and three floats rigidly attached to it. The floats are submerged into the water and ensure that the capsule is afloat. The horizontal cross-section of each float has the shape of an airfoil. The body moves in a horizontal plane. The rotation axis of the internal flywheel is vertical. The control system makes the flywheel to oscillate, which results in oscillations of the robot body together with the floats. It is known that, when an airfoil oscillates in pitch in fluid, a thrust force is produced. As a result, the center of mass of the body moves along a serpentine trajectory. The goal of the study is to describe the effect of geometrical parameters of the robot and coefficients of the control law on the average speed of propulsion. A quasi-steady model is used to describe the hydrodynamic forces acting upon the trimaran. In order to take into account non-steady effects, added masses are considered. This approach allows for describing the robot dynamics with the ODE system. Numerical simulation of the system behavior is performed. Attracting periodic solutions are found using the relaxation method. Parametric analysis of such solutions is performed. A laboratory model is manufactured, and a series of experiments is performed. It is shown theoretically and experimentally that the speed of propulsion of the robot depends non-monotonically on the control frequency. [ABSTRACT FROM AUTHOR]

The aerodynamic interaction between a helicopter and a trimaran ship's flight deck can be complex and have an impact on handling quality and performance, especially in turbulent conditions. This article presents research on the flight deck geometry of a trimaran vessel without the presence of a helicopter. Both Particle Image Velocimetry (PIV) and computational fluid dynamics (CFD) were used to analyze the effect of wind velocity on air pressure in the flight deck region. The study proposed and evaluated different geometries of the top structure at several air velocities to minimize pressure differences. The results of the numerical simulation were validated by experimental measurements using PIV, which showed that the effect of the Reynolds number on the non-dimensional pressure near the top structure is negligible except for the biggest Reynolds number (Re = 50e6), while at x/L = 0.5 the significant difference can be seen, however, the same result found for Re = 38e6 and 50e6. At the farthest distance (x/L = 1), the pressure difference for different Reynolds numbers case studies is negligible. Among the various geometries assessed, the maximum non-dimensional pressure differences along the lines show the highest value occurs for the base geometry (A) while geometries C and F show lower values, which have chamfering along the middle and side horizontal edges at a 45-degree angle and chamfering along all vertical and horizontal edges at a 30-degree angle.

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]

In recent years, trimarans have been used in high-speed transport and in warships, but studies of them have made little progress. We designed a trimaran model and used it to perform a water-entry experiment to find a way to reduce the slamming pressure. The process of the model entering the water was divided into several steps, and different theoretical models were designed for each step, together with their force analysis. Relying on our experimental platform, we designed three flexible coating thicknesses and six drop heights as the different working conditions. With an analysis of the results under these experimental conditions, the experiment clearly indicates that the flexible cladding on the model can decrease the impact force when the model slams into water. Furthermore, the theoretical models and their corresponding force analyses are validated by the experimental results. [ABSTRACT FROM AUTHOR]

Due to the complex fluid interference between outrigger and main hull, it is difficult to predict the trimaran load fluctuation accurately in different marine environments. Therefore, a time-domain Rankine method is developed to improve the accuracy of trimaran load prediction. This method successfully adds the nonlinear load components in time-domain load simulation by taking into account the factors such as instantaneous hull wetted surface, steady ship waves, green wave and slamming. Additionally, the nonlinear growth of green wave and slamming is also observed at outrigger and wet deck, with the increasing of speeds and wave heights. Finally, the relatively smaller errors in the Rankine method are confirmed by comparison with the values from a trimaran model test and linear time-domain load prediction method. Furthermore, the weakly nonlinear Rankine method is considered to be more suitable for trimaran load prediction under harsh marine environment.

The trimaran is an advanced ship with high hydrodynamic performance, but the study of its electromagnetic characteristics and Doppler spectrum is insufficient. This study presents a new procedure for evaluating the scattering echo and Doppler spectrum of a trimaran in a time-varying ocean environment. First, based on the Reynolds-averaged Navier–Stokes equations, the interpolation wave-making method is proposed for the prediction of the six degrees of freedom motion of the trimaran. The method takes into account the viscous effect of the flow field and the complexity of wave motion, which applies to the seakeeping prediction of high-speed trimaran under different sea states. Second, an accelerated geometrical optics and physical optics algorithm using the light source function (GO-PO/LSF) is proposed, which uses the light source function to realize the visibility judgment of surfaces and greatly reduces the computation time. Then, the influence of different motion conditions on the backscattering echo of the composite scene is demonstrated by the capillary wave modification facet scattering model and GO-PO/LSF. Finally, the Doppler spectrum characteristics of the trimaran are presented by the standard spectrum estimation method, which provides a reference for radar detection and identification of ships in the microwave band.

With a rapid increase in various number of marine tourism destinations, especially in The Bunaken National Park with the amount of tourists that has increased throughout the year rising by 23% for domestic tourists and 12% for international tourists between 2002 and 2018. Unfortunately, to enjoy the underwater scenery of The Bunaken National Park can access by diving and snorkeling which is not all tourist can do that. Furthermore, in order to support the marine tourism industry in Indonesia, a semi-submersible tourism ship was developed with a glass at the hull's bottom based on the standard spiral design and the safety standard established by the rules so the tourists can easily enjoy the underwater ecosystem. The concept design of bottom-glass ship with trimaran hull type is offered as a problem-solving in this paper. The final design of the main dimensions are length of overall (LOA): 23,1 meters, width (B): 8 meters, Draft (T): 2.22 meters but the maximum submerged up to 2,5 meters, speed of 10 knots, and passenger capacity of 44 persons.

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]

The design principle of the hull structure is to ensure sufficient strength and avoid excessive waste of materials. The equivalent dynamic coefficients (EDC) possess the advantages of both static analysis and dynamic analysis in engineering. However, there is still no clear method for determining the EDC of a trimaran. In this work, the EDC of the cross-decks are chosen as the research objects. The EDC of the plate, longitudinal girders, and transverse frame of the cross-decks are calculated respectively. A method considering material nonlinearity and a method considering transverse bending moment (TBM) are proposed, and the effect of elastic-plastic material and TBM on EDC is presented. Results show that it is feasible to use the EDC to analyze the trimaran under slamming loads. Besides, the EDC of different parts of the trimaran is different, hence it is not recommended to use the fixed value given by the ABS rules. [ABSTRACT FROM AUTHOR]

The development of medium-to large-scale and high-performance unmanned surface vehicles (USVs) is a burgeoning trend in intelligent marine systems. The heading controller is crucial for USVs to execute diverse missions, especially given their inherent underactuation characteristics and constraints. Recent efforts have focused on enhancing the robustness of controllers against external disturbances and employed two main strategies: one converges the control error to a bounded residual set through robust modifications, while the other eliminates the error by modelling disturbances. Notably, these enhancements have primarily catered to small USVs, where disturbances significantly impact their manoeuvrability, necessitating such robust control strategies. This focus has somewhat overshadowed the inherent robustness of closed-loop control systems. Compared with small USVs, medium-to large-scale USVs are less affected by external disturbances, despite undertaking more complex missions. Leveraging the intrinsic robustness of controllers presents an opportunity to simplify controller design, thereby reallocating computational resources towards enhancing mission capabilities. Model Predictive Control (MPC) has attracted significant attention recently, and its receding horizon and optimality theoretically provides a new level of inherent robustness, which remains under-explored in real sea. This paper focuses on the inherent robustness of MPC in managing the heading of a medium-scale unmanned trimaran subjected to the thrust angle and angular velocity constraints. A model predictive controller considering the constraints is designed based on the identified Nomoto model and the asymptotic stability is ensured with a terminal cost. Conducted real-sea experiments and comparative analyses with a Proportional-Integral-Derivative (PID) controller, the most widespread and dominant control algorithm in practical USV engineering, underscore the superiority of MPC in maintaining satisfactory closed-loop performance. Furthermore, the MPC controller is also successfully applied to real-sea path-following missions and demonstrated good tracking performance in various sea conditions ranging from level 3 to 5 and wind speeds spanning from level 6 to 8. This validation opens up new avenues for motion control strategies in the evolving landscape of larger-scale USVs. • The inherent robustness of the MPC to reject external disturbances is validated by real-sea experiments. • An MPC heading controller is designed to directly handle the input constraints of a 20-m medium-scale unmanned trimaran. • The controller is successfully applied to real-sea path-following missions and demonstrated good tracking performance. [ABSTRACT FROM AUTHOR]

As a high-performance ship, the trimaran holds significant potential in military and civilian fields. This study proposes a novel numerical method based on the Rankine panel method for predicting the time domain motion and wave loads of trimarans navigating in waves. This approach incorporates a more accurate steady flow model for trimarans and meticulously derives the boundary value problem for the unsteady disturbance potential, while retaining the steady terms related to steady flow throughout the process. This approach ensures a comprehensive consideration of the impacts of speed effect and ship wave. The method was innovatively validated using the trimaran hull form, and its accuracy and reliability were confirmed through comparisons with experimental data. Then, the influence of steady flow on time domain motions and added resistance of trimarans was thoroughly investigated. Comparative analysis of different steady flow models demonstrates that the steady flow model for trimaran proposed provides high precision and advantages in predicting the time domain motions of high-speed trimarans in waves. Furthermore, a systematic investigation into the effects of ship speed and side hull layouts on trimaran's motion and added resistance in waves has been conducted, offering crucial technical support for trimarans' seakeeping optimal solution selection. • A code is developed on VS platform for accurate prediction of motions and added resistance of a trimaran sailing in waves. • Further insights into the impacts of steady flow and speed effect on the motions and wave loads of a trimaran in waves. • A systematic comparative analysis was conducted to assess the impact of side hull layouts on the seakeeping of a trimaran. • The advantages and applicability of the proposed numerical method were thoroughly elucidated. [ABSTRACT FROM AUTHOR]

The tendency to design high-performance ships demonstrates the importance of the trimaran and the cross-deck is of particular interest due to its exclusive structures and wave loads. Limited by the high cost of structural numerical simulation, relevant studies emphasize the effectiveness of a specific design scheme. This paper introduces the polynomial chaos expansion (PCE) and the bias-variance tradeoff to explore the statistical characteristics of the cross-deck's strength. The geometric model of a high-speed trimaran is built and the load case is designed. Samples are obtained using the Latin hypercube sampling technique and the corresponding stress response of the cross-deck is extracted by the finite element method. To overcome the limitation of sample size, the PCE is applied as a surrogate model to compute the statistical indicators of the stresses and the bias-variance tradeoff is introduced to select the hyperparameter of the PCE. The results show that the stresses at the cross-deck's corner are much higher and more sensitive to the plate thickness than those at other locations. Furthermore, the PCE is also compared with the Monte Carlo simulation to demonstrate its advantages, and it is shown that the PCE performs better under the limitation of sample size considering accuracy and convergence. The feasibility and efficiency of the PCE and bias-variance tradeoff in the statistical analysis of trimaran cross-deck structure is proved. The insights and recommendations summarized will be a useful aid for the design and optimization of the trimaran. • The characteristics of a trimaran's cross-deck structure are quantitatively investigated from a statistical perspective. • The PCE is applied as a surrogate model and the bias-variance tradeoff is introduced to select the optimal hyperparameter. • The results are compared with those of MC and the superiority of the PCE in terms of convergence and accuracy is validated. [ABSTRACT FROM AUTHOR]

Efforts to reduce emission of toxic gases into the atmosphere by sea transportation have been consistently carried out by the International Maritime Organisation (IMO) since 2009. IMO has introduced a regime known as energy efficiency design index (EEDI) to monitor and quantify the emission of CO2 because of its global climate impact. A comparison was conducted between trimaran hull forms without and with Axe-Bow on the main-hull with S/L=0.3 and 0.4, as well as a comparison with a monohull of comparable displacement. The CFD method was used to analyse resistance. Overall, the trimaran without the Axe-Bow can decrease resistance by 22.6%, while the trimaran with the axe-bow can reduce resistance by 25.0%. Additionally, this resulted in a 54.8% decrease in EEDI on trimarans without axe-bow and a 55.4% reduction on trimaran equipped with axe-bow when compared to MV Sabuk Nusantara 104. In addition, despite little diff erence between trimaran with and without axe-bow, the introduction of axe-bow has shown apparent benefits to lower EEDI. [ABSTRACT FROM AUTHOR]

Trimaran hull forms have been popular recently in both commercial and military usage due to reduction in resistance at high speeds, better stability, and greater deck area compared to conventional monohull vessels. Determination of the location of the side hulls is most critical to get higher hydrodynamic performance. Therefore, many studies in the literature are related to defining the location of the side hulls for trimaran vessels. Most of the studies have been carried out experimentally or numerically. In this study, an artificial neural network (ANN) model was used to predict the residual resistance coefficient of a trimaran model. The model uses four parameters which are the transverse and longitudinal positions of the side hulls, the longitudinal centre of buoyancy and the Froude number to predict the residual resistance of the trimaran model. The experimental data of the trimaran model were used to train the neural network model in order to develop a more reliable model. Several neural network models were developed and tested to find the one with minimum error. The study showed that the residual resistance coefficients of the trimaran model were predicted with high accuracy levels compared to the model experimental data. It was also shown that an ANN is a useful alternative method to model tests and numerical simulations. The developed model can be used to reduce the number of model tests or numerical simulations as well as to obtain the optimum location of the side hulls in terms of resistance.

Ocean waves are a renewable energy source with abundant reserves in Indonesia. With the vast waters of Indonesia, the development of a sea wave power plant needs to be developed. This research focuses on the development of easy-operated and maintained ocean wave converter–pendulum system (OWC – PS). The numerical simulation and experimental analysis were conducted to obtain the relation between the motion response of the pontoon array and its pendulum. The pontoon used is the trimaran type, which consists of a cylindrical pontoon as the main hull and two outriggers on its side. This study analyses the most stable array arrangement that produces maximum pitching motion and pendulum deviation. The simulation results show that the largest pitching value is in array 1, i.e., 27.91° for pontoon 1 and 38.92° for pontoon 2, which results in a maximum pendulum deviation of 100 ° for pendulums 1 and 56.2 ° for pendulum 2 over a wave period of 9 seconds. The backward motion of the pendulum in both array configurations tends to have a greater deviation than that of the forward motion. The pendulums of array 1 have different motion characteristics, represented by different deviation values in both pendulums. This phenomenon does not occur in array 2, since both pendulums in array 2 have the same deviation (with only a small discrepancy).

Research on the development of multihull vessels has investigated the breakdown of trimaran side hulls and produced a new type of vessel popularly known as a pentamaran. This study into the resistance characteristics of pentamarans was carried out using a towing tank belonging to the Institute Technology at Sepuluh Nopember in Surabaya, Indonesia. A test of trimaran resistance was included for comparison. The investigation focused on total resistance estimation and interference analysis for the two types of multihull vessels at separation–length ratios (S/Ls) of 0.2, 0.3, and 0.4. The dominant resistance value for the pentamaran was higher than that for the trimaran, with an average of 5.2%, due to the more complex interference between hulls. The average total resistance interference was 9.5% for the trimaran and 12.5% for the pentamaran.

In recent years, trimarans have been used in high-speed transport and in warships, but studies of them have made little progress. We designed a trimaran model and used it to perform a water-entry experiment to find a way to reduce the slamming pressure. The process of the model entering the water was divided into several steps, and different theoretical models were designed for each step, together with their force analysis. Relying on our experimental platform, we designed three flexible coating thicknesses and six drop heights as the different working conditions. With an analysis of the results under these experimental conditions, the experiment clearly indicates that the flexible cladding on the model can decrease the impact force when the model slams into water. Furthermore, the theoretical models and their corresponding force analyses are validated by the experimental results.

In this article, the nonlinear motion response of a Trimaran with SWATH-type center hull vessel (TriSWACH) is investigated and compared with the linear response using a hybrid method combining a regression analysis of the viscous damping generated by the hulls with a nonlinear potential flow simulation of rigid body motions. The TriSWACH is a hybrid trimaran hull form, developed using the SWATH (small waterplane area twin hull) technology, from which a single small waterplane area center hull is retained. It is designed to keep the magnitude of its motion response below its equivalent monohull counterpart while also benefiting from large intact transverse stability provided by its side hulls. Since a significant portion of the total damping generated by the submerged hull girder is viscous in nature, an accurate prediction of the steady-state motion response near natural frequency is highly dependent upon the correct modeling of the boundary layer flow. The total damping coefficients obtained experimentally from motion response transfer functions are used to augment the potential flow solution and improve the numerical prediction method at large angles of inclination, characteristic of operation in rough weather near the peak frequency of the motion response. [ABSTRACT FROM AUTHOR]

The selection of the outrigger layout plays a significant role in trimaran design as it will has effect on various hydrodynamic performance of the trimaran. In this paper, the high-speed slender body theory (2.5D method) is applied to the problem of trimaran swaying motion and added resistance prediction. Furthermore, in order to optimise the resistance and swaying motion of the trimaran, this paper propose a trimaran outrigger layout optimisation method with resistance and swaying motion are considered comprehensively based on NSGA-II. By analysing the convergence of the results, the optimisation method proposed in this paper is verified. In addition, this paper gives a suggested outrigger layout for a trimaran sailing in oblique waves with wavelength to ship length ratio equals 1.0 and F n = 0.4. The optimisation result is also compared with the other six layouts in the experiment to verify the outrigger layout optimisation method proposed in this paper. [ABSTRACT FROM AUTHOR]

ObjectivesThe hull plate of a trimaran cross-deck bottom is often subjected to slamming loads under high-level sea conditions, potentially causing severe structural damage. The objective of this study is to analyze the influence of the air cushion effect on the impact load of a trimaran cross-deck plate and propose a new type of hull plate for the cross-deck bottom in order to reduce the slamming load.MethodsThe two-phase flow problem of a trimaran ship section is simulated using the computational fluid dynamics (CFD) method. First, the accuracy of the numerical model is verified by comparing the predicted results with the experimental measurements. The influence of the air cushion on the slamming load of the trimaran cross-deck structure is then obtained by analyzing the evolution of the flow field. Finally, the influence of the air cushion is analyzed and the effects of different shapes and sizes of the proposed hull plate are evaluated.ResultsThe numerical results show two slamming peaks that appear during the process of a trimaran entering the water. The rectangular shaped plate reduces the slamming load by around 20% compared with the flat plate bottom.ConclusionsThe air cushion has a significant effect on the slamming load. A rectangular shaped hull plate can be used to cover the trimaran cross-deck bottom.

There has recently been a surge in demand for multi-hull vessels for military and commercial purposes. The need for multi-hull ships increase from the necessity to balance speed and cargo requirements. Among others, the trimaran is one such hull type. The current study performs a CFD resistance analysis for trimaran as a parameter range of feasible hull forms based on the NPL systematic series. The resistance of trimaran hull shapes are calculated using CFXTM, a commercial CFD code that belongs to ANSYS. The trimaran model was tested at one fixed transverse separation (S/L=0.2) together with 3 longitudinal separations, R/L=0, 0.25, and 0.5, at different Froude numbers (based on length) from 0.2 to 0.6. Testing on the individual hull is also carried out to quantify the effect of resistance interference on the trimaran configuration. The CFD simulation results indicate that the trimaran model with side hulls parallel to the stern (R/L=0) has the least resistance. The interference effect of resistance on Trimaran with R/L=0, 0.25, 0.5 are 2.8%, 4.6%, 6.8% as opposed to non-interference trimaran model, respectively. These findings provide an approach for appropriately selecting the trimaran model with longitudinal side hull configurations.

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 axe-bow 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.

Trimaran as a high-performance vessel, possesses excellent characteristics such as high speed, low wave-making resistance, and good seakeeping performance. Different from conventional monohull ship, the design of a trimaran requires additional consideration of the outrigger layout, as the position of two outriggers can affect its hydrodynamic performance. In this study, high-speed slender body potential flow theory (also named the 2D+t theory or the 2.5D method) was employed to calculate the heave and pitch motion in order to evaluate the seakeeping performance of trimarans with different outrigger layouts at varying speeds. Model experiments were subsequently conducted to validate the effectiveness of the 2.5D method in simulating the motion of trimarans under different outrigger layouts. Three multi-objective evolutionary algorithms, including Non-dominated sorting genetic algorithm II (NSGA-II), Non-dominated sorting genetic algorithm III (NSGA-III), and Multi-objective evolutionary algorithm based on decomposition (MOEA/D), as well as their applications in the optimization of trimaran outrigger layouts were introduced. Utilizing the 2.5D method based computational program as the solver, the efficiency and performance of these multi-objective evolutionary algorithms were compared. Discuss the advantages and disadvantages of three multi-objective evolutionary algorithms in solving trimaran outrigger layout optimization problem by comparing the optimization results from two aspects: optimization efficiency, and optimal solution performance. The results indicate that for optimization efficiency, the weighted sum approach based MOEA/D exhibits best optimization efficiency. NSGA-II and NSGA-III show a good advantage in terms of optimal solution performance, and compared to NSGA-II, NSGA-III can obtain more Pareto solutions. • The 2.5D method in motion prediction of a trimaran has been validated. • Three multi-objective algorithms are introduced in outrigger layout optimization. • The performance of three optimization methods are compared and discussed in details. [ABSTRACT FROM AUTHOR]

• The significant negative pressure occurred at the front of the wet deck. • The wet-deck slamming is more severe under the short-wave condition. • The slamming behaviour is more severe at the front part of the wet deck. • The water-entry of the main hull causes the wet-deck slamming pressure near the outrigger larger than that of the main hull. Wet deck may suffer from strong slamming effects when sailing under severe sea conditions, which could damage it locally and compromise the structural integrity of trimarans. The wet-deck slamming characteristic for trimaran sailing in head waves is studied in this work using both experimental and numerical simulation methods. We found that the negative pressure occurred at the front of the wet deck, which is caused by the wet deck exit from the wave crest. Regarding the spatial distribution in longitudinal, the slamming behaviour is more severe at the front part of the wet deck, as the relative vertical impact velocity decreased from the front to the back part of it. Simultaneously, the wet-deck slamming is more severe under the short-wave condition. Regarding the spatial distribution in lateral, we found that the water-entry of the main hull could cause the wet-deck slamming pressure near the outrigger larger than that of the main hull. Moreover, the wet deck has been divided into three regions according to their different lateral distribution characteristics of the wet-deck slamming. These results can provide a better understanding of the wet-deck slamming characteristics when trimaran sailing in waves, which can be considered in future designs for the trimaran. [ABSTRACT FROM AUTHOR]

Ocean waves are a renewable energy source with abundant reserves in Indonesia. With the vast waters of Indonesia, the development of a sea wave power plant needs to be developed. This research focuses on the development of easy-operated and maintained ocean wave converter-pendulum system (OWC - PS). The numerical simulation and experimental analysis were conducted to obtain the relation between the motion response of the pontoon array and its pendulum. The pontoon used is the trimaran type, which consists of a cylindrical pontoon as the main hull and two outriggers on its side. This study analyses the most stable array arrangement that produces maximum pitching motion and pendulum deviation. The simulation results show that the largest pitching value is in array 1, i.e., 27.91° for pontoon 1 and 38.92° for pontoon 2, which results in a maximum pendulum deviation of 100 ° for pendulums 1 and 56.2 ° for pendulum 2 over a wave period of 9 seconds. The backward motion of the pendulum in both array configurations tends to have a greater deviation than that of the forward motion. The pendulums of array 1 have different motion characteristics, represented by different deviation values in both pendulums. This phenomenon does not occur in array 2, since both pendulums in array 2 have the same deviation (with only a small discrepancy). [ABSTRACT FROM AUTHOR]

The trimaran vessel rolls strongly at low forward speed and may capsize in high sea conditions due to chaos and loss of stability, which is not usually considered in conventional limit-based criteria. In order to perfect the method of measuring roll performance of trimaran, a set of nonlinear roll motion stability analysis method based on Lyapunov and Melnikov theory was established. The nonlinear roll motion equation was constructed by CFD and high-order polynomial fitting method. The wave force threshold of rolling chaos in regular waves is calculated by Gauss-Legendre numerical integration method. The limited significant wave height of rolling chaos in random sea conditions is deduced by the phase space transfer rate, and the complex effect of wind load is superposed in the calculation. The influence of trimaran configuration on the roll system is analyzed through the state differentiation of homoclinic and heteroclinic orbit in phase portrait. The calculation of the maximum Lyapunov exponent further verified the applicability of Melnikov method, and the topological structure change of gradual failure of the rolling system is analyzed by the erosion of safe basin. The complex changes of the nonlinear damping coefficient and the nonlinear restoring moment coefficient caused by the change of the transverse lay-outs between the main hull and side hull have a significant influence on chaos and stability, and the existence of wind load has a certain weakening effect on the stability and symmetry of the system. The conclusion also further indicates the importance of the lay-outs to the dynamic stability of the trimaran vessel, which is significant for its seakeeping design.

Trimaran hydrodynamics have been an important research topic in recent years. Trimarans have even been chosen for naval surface combatants. In this case, investigation of a trimaran with different outrigger positions is important and necessary for better hydrodynamic performance. This paper focuses on the numerical investigation of trimaran hydrodynamics. The trimaran model used in this study is a 1/80 scale high-speed displacement frigate-type concept developed by the Center for Innovation in Ship Design (CISD) at Naval Surface Warfare Center, Carderock Division (NSWCCD). The numerical simulations were conducted for different outrigger positions at low and moderate Froude numbers by using commercial CFD software solving URANS equations. A verification and validation study was carried out for the numerical method in one configuration and one ship velocity. The existing experimental results for the trimaran resistance in the literature were used for validation. Five different outrigger positions were analyzed and the form factor of each configuration was calculated by the Prohaska method. The total resistance was decomposed to its components using the form factor. The interference factor was calculated for each configuration in terms of total resistance, residual resistance and wave resistance. Also, wave profiles using the longitudinal wave cuts in different locations were obtained both numerically and experimentally. It was concluded that the outrigger position had different effects on the interference, total resistance and wave profile at different Froude numbers. It was also shown that the CFD results were in good agreement with the experimental data in all configurations. In conclusion, this study presents the results of interference effects for different trimaran configurations in terms of wave resistance in addition to the total resistance and residual resistance. The numerical method was validated not only with the total resistance test data but also the longitudinal wave profiles along the hull. [ABSTRACT FROM AUTHOR]

The coupled motion of roll and pitch is noticeable when trimaran sails in oblique head waves, which will lead to negative influence on the safety and comfort of navigation. In this paper, the numerical simulation of the trimaran's motion in oblique waves was carried out by open source CFD tool OpenFOAM, and the computed motion response was analyzed to study the characteristics of the torsional rolling. The OpenFOAM-based hybrid method used in this paper was briefly introduced first, and the numerical method was validated and verified by both the grid convergence test and the comparison with experimental result. Both the amplitude and the time history of the computed motion are used for analysis, and the influence of wave steepness, wave heading and forward speed of trimaran on the characteristics of torsional rolling was investigated. The result shows that the large wave steepness and the low forward speed will lead to dangerous torsional rolling motion of trimaran in oblique waves, and the dangerous condition is mainly caused by nonlinear rolling motion; the motion state is more sensitive and changing obviously with other factors at large wave steepness wave conditions. [ABSTRACT FROM AUTHOR]

A CFD-based adjoint solver tool is presented to modify the hullform of a trimaran ship. Cost function of optimization process is considered total for resistance of trimaran at cruise speed. Mesh sensitivity gives sensitivity of the cost function associated with mesh deformation. Mesh morphing tool is implemented to alter the geometry without the need to revisit the CAD environment. The position of mesh morphing's control points are the design variables used in the optimization process. The aim of this optimization is to demonstrate the limitations and capabilities of the mesh morphing adjoint-based method for hydrodynamic complex geometries. Based on the numerical findings, a 6.67% reduction in total resistance of the trimaran is observed in a limited number of iterations. Meanwhile, major modification is observed on the side hull. Development of a CFD-based optimization platform with less computational time and effort (five optimization loops) is the result of the present study. [ABSTRACT FROM AUTHOR]

Objectives The motion attitude (sinkage and trim) of a semi-planing ship (at Froude numberFr > 0.4) have significant effects on its resistance performance during voyage. The sinkage and trim effects on the resistance components (frictional resistance and pressure resistance) is discussed.Methods A CFD study is carried out on the resistance performance of trimaran in calm water, and the k-ε turbulent model and overlapping grid are adopted. The free model and constrained model are computed. The computed results are compared to analyze the effects of sinkage and trim on the resistance components.Results The results show that the change of total resistance caused by sinkage and trim is more than 20% in semi-planing conditions. The sinkage and trim have a significant effect on the pressure resistance, up to nearly 50%; and a relatively small effect on frictional resistance, less than 8.5%. More than 90% of the resistance increase caused by motion attitude comes from the change of pressure resistance.Conclusions Predicting the motion attitudes and resulting pressure resistance changes accurately is extremely important for semi-planing trimaran.

Objectives Reducing the weight of the cross-deck is an important method for reducing the weight and center of gravity of a trimaran. Structural strength analysis is used as the premise for judging whether a weight reduction method is feasible.Methods Based on the loading characteristics of a trimaran, a new dispersed cross-deck structure is proposed in which most of the unnecessary panels are removed. The finite element (FE) direct calculation method is adopted to analyze the structural strength of the dispersed cross-deck, and its strength is then compared with that of the traditional integral cross-deck.Results The results show that using the dispersed cross-deck can reduce the structural weight and center of gravity of a trimaran by 6.75% and 5.54% respectively on the premise of meeting the structural strength requirements.Conclusions Using the dispersed cross-deck can greatly reduce the structural weight and vertical location of the center of gravity, which provides new approaches for the structural design of trimarans.

[Objectives] As a high-tech ship, the trimaran is particularly prominent in structural strength. Traditional numerical methods are analysed by deterministic methods. However,such variables as the loads acting on the hull,the uncertainty of the calculating model and the performance of the material are random. Therefore,reliability measures are taken to account for the influence of these factors on hull strength.[Methods] The three-dimensional potential flow theory and direct calculation of strength for the hull structure are used in this paper to obtain the short-term time-period distribution of the von Mises stress of special structural elements,then the distributions of long-term von Mises stress and sequence statistics of extreme value are obtained. The limit state equation is listed in combination with the structural capacity and load requirements of the units to obtain the reliability indexes. The failure probability and safety factor of typical structures are calculated,and certain random components are analysed on impact.[Results] The research shows that the structural strength of a trimaran is concentrated at the connecting bridge,the safety factor is 0.86 and the deck safety factor is 2.4. Due to the high neutral axis,the material uncertainty has a greater influence on the reliability indexes.[Conclusions] The method of yield strength reliability research for trimaran proposed in the study can provide good data-support for the optimization of trimarans.

Trimaran hull forms have been popular recently in both commercial and military usage due to reduction in resistance at high speeds, better stability, and greater deck area compared to conventional monohull vessels. Determination of the location of the side hulls is most critical to get higher hydrodynamic performance. Therefore, many studies in the literature are related to defining the location of the side hulls for trimaran vessels. Most of the studies have been carried out experimentally or numerically. In this study, an artificial neural network (ANN) model was used to predict the residual resistance coefficient of a trimaran model. The model uses four parameters which are the transverse and longitudinal positions of the side hulls, the longitudinal centre of buoyancy and the Froude number to predict the residual resistance of the trimaran model. The experimental data of the trimaran model were used to train the neural network model in order to develop a more reliable model. Several neural network models were developed and tested to find the one with minimum error. The study showed that the residual resistance coefficients of the trimaran model were predicted with high accuracy levels compared to the model experimental data. It was also shown that an ANN is a useful alternative method to model tests and numerical simulations. The developed model can be used to reduce the number of model tests or numerical simulations as well as to obtain the optimum location of the side hulls in terms of resistance. [ABSTRACT FROM AUTHOR]

Research on the development of multihull vessels has investigated the breakdown of trimaran side hulls and produced a new type of vessel popularly known as a pentamaran. This study into the resistance characteristics of pentamarans was carried out using a towing tank belonging to the Institute Technology at Sepuluh Nopember in Surabaya, Indonesia. A test of trimaran resistance was included for comparison. The investigation focused on total resistance estimation and interference analysis for the two types of multihull vessels at separation--length ratios (S/Ls) of 0.2, 0.3, and 0.4. The dominant resistance value for the pentamaran was higher than that for the trimaran, with an average of 5.2%, due to the more complex interference between hulls. The average total resistance interference was 9.5% for the trimaran and 12.5% for the pentamaran. [ABSTRACT FROM AUTHOR]

One of the approaches for numerical prediction of the ship maneuvering in still water is based on the lifting theory. In this paper, a numerical method for the fast prediction of the maneuvering motion of the trimaran in still water is developed based on the Source and Quasi Continuous Vortex Lattice Method (SQCM). By the SQCM, the captive model test of the trimaran could be simulated, and the corresponding hydrodynamic coefficients could be obtained. Combined with the MMG maneuvering motion model, the rapid forecasting of the maneuvering motion characteristics of the trimaran is realized. The numerical method is validated by comparison with the tank test, and the turn and zigzag maneuvers of trimaran of different side-hull arrangements at various speeds are predicted. • The captive model test of the trimaran are simulated to obtain the force, moment, and hydrodynamic derivatives by the SQCM method. • The turn and zigzag maneuvers of the trimaran are predicted by the MMG model and the hydrodynamic derivatives. [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]

To obtain a reasonable evaluation of the performance of waterjet propulsion at the design stage, a semi-theoretical and semi-empirical method is used to calculate the fundamental parameters of waterjet propulsion performance using an iterative approach. To calculate the ship’s resistance, a boundary element method based on three-dimensional potential flow theory is used to solve the wave-making resistance, and an empirical approach is used to evaluate the viscous resistance. Finally, the velocity and pressure of the capture area of the waterjet propulsion control volume are solved based on turbulent boundary layer theory. The iteration equation is established based on the waterjet-hull force-balance equation, and the change in the ship’s attitude and the local loss of the intake duct are considered. The performance parameters of waterjet propulsion, such as resistance, waterjet thrust, thrust deduction, and the physical quantity of the control volume, are solved by iteration. In addition, a PID-controlled free-running ship model is simulated using the RANS CFD method as a comparison. We apply the proposed approach and the RANS CFD method to a waterjet-propelled trimaran model, and the simulation process and the results are presented and discussed. Although there are some differences between the two methods in terms of the local pressure distribution and thrust deduction, the relative error in the evaluation results for the waterjet propulsion performance is generally reasonable and acceptable. This indicates that the present method can be used at the early stages of ship design without partial information about the waterjet propulsion system, and especially in the absence of a physical model of the pump.

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.

[Objectives]To study the influence of side-hull layout of trimaran on its motion performance,[Methods]A new method which is based on Monte Carlo method and potential flow theory is presented to help side-hull layout of trimaran optimize its motion and multi-objective optimization models and calculation techniques are provided. Firstly,we use Monte Carlo method to select the solutions and use AQWA software(potential flow theory) to calculate the motion responses of these solutions. Then by comparing the rolling,pitching and heaving motion responses of these solutions,we select the optimization solution in which these three indicators are all smaller than those of the original ship.[Results] The results show that in the regular wave,the motion responses of the trimaran are reduced when side-hull is located before the mid-ship of the main-hull. In irregular wave,the roll motion of the trimaran is decreased when side-hull is located before the mid-ship of the main-hull;Also in the regular wave,the roll motion and pitch motion are decreased when we increase the lateral distance between the side-hull and the main-hull.[Conclusions]To study the influence of side-hull layout on the motion of trimaranon, using Monte Carlo method and potential flow theory can increase calculation efficiency and guarantee high calculation accuracy.

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]

This paper focuses on the knowledge of propulsive and hydrodynamic characteristics in a Trimaran vessel with respect to an equivalent monohull platform in an optimum sizing range for oceanic escort ships. This research project has been carried out in the Channel of Hydrodynamic experiences of El Pardo (CEHIPAR), the project includes the dimensioning of the ship’s live part construction, design of main hull shapes and design alternatives for side hulls. The hydrodynamic quality of the hull alternatives was evaluated by using nonlinear potential CFD Computational Fluid Dynamics calculations, and the trimaran platform was analysed by difficult numerical calculation, showing that the trimaran bottom is satisfactory, with stability characteristics for the displacement.

The hydrodynamic performance of trimaran hulls has been previously investigated for optimum performance in calm water, but there is still a limited understanding of its motion response; therefore, a CFD-based numerical approach was developed and applied on a trimaran hull in the presence of regular and irregular waves. To validate the CFD method, a comparison was conducted using both experimental and 3D panel method data. In this study, two different turbulence models were surveyed, and the SST Menter k-Omega (k-ω) turbulence model was shown to be a more accurate model than the realizable k-Epsilon (k-ε) model. The different features of the proposed numerical model include the implementation of an overset mesh method, unique mesh plan refinement, and wave-damping region. The discrepancy between the experimental data and the results of other seakeeping calculation methods have always been problematic, especially for low-speed strip theory and 3D panel methods, but good consistency was observed between the proposed CFD model and experimental data. Unlike potential-based or conformal mapping seakeeping analysis methods, the effect of nonlinear waves, hull shape above the waterline, and other ship dynamic phenomena were considered in this CFD application. The proposed CFD method reduces the simulation time and computational efforts for ship motion calculations. [ABSTRACT FROM AUTHOR]

In recent years, the trimaran as a novel ship has been greatly developed. The subsequent large vertical motion needs to be studied and resolved. In this article, an experimental study for a trimaran vertical stabilization control is carried out. Three modes including the bare trimaran (the trimaran without appendages, the trimaran with fixed appendages, and the trimaran with controlled appendages) are performed through model tests in a towing tank. The model tests are performed in regular waves. The range of wave period is 2.0–4.0 s, and the speed of the carriage is 2.93 and 6.51 m/s. The results of the three modes show the fixed appendages and the actively controlled appendages are all effective for the vertical motion reduction of the trimaran. Moreover, the controlled appendages are more effective for the vertical stability performance of the trimaran. [ABSTRACT FROM AUTHOR]

Based on CFD method, the numerical method for the manoeuvre simulation of trimaran and asymmetric twin hull by OpenFOAM was applied in this paper. The grid independency test was carried out, and the computed result of turn and zigzag manoeuvres was compared with the result of self-propulsion experiment to validate the numerical method. Then, the numerical method was applied to simulate the turn and zigzag manoeuvres of both an actual trimaran and an actual asymmetric twin hull. By the manoeuvre simulation in calm water with hull attitude fixed and free, the effect of hull attitude on the manoeuvre of trimaran and asymmetric twin hull with different layouts and Froude number was discussed, and the importance of hull attitude for the numerical simulation of turn and zigzag manoeuvres was illustrated. The result shows that, the numerical method in this paper is valid for the manoeuvre simulation of trimaran and asymmetric twin hull, and it makes sense to take the hull attitude into account for the manoeuvre simulation of trimaran and asymmetric twin hull. [ABSTRACT FROM AUTHOR]

This article investigates a model predictive control (MPC) with disturbance observer (DOB) for a trimaran longitudinal motion control. Firstly, to design the trimaran longitudinal motion stability controller, the mathematical model of the trimaran requires to be obtained. The hydrodynamic coefficients in the mathematical model are obtained by the computational fluid dynamics simulation. Secondly, a T-foil with the fixed attack angle is selected as an antipitching appendage. It is verified that the T-foil is effective in restraining the longitudinal motion of the trimaran through numerical simulation. Lastly, to enhance the ability of the T-foil for restraining the severe longitudinal motion, a controller based on the MPC method with DOB is designed to control the attack angle. The effect of the proposed algorithm is verified by theoretical analysis and simulation. [ABSTRACT FROM AUTHOR]