We consider the Tramp Ship Routing and Scheduling Problem (TSRSP) in which we plan routes for a fleet of tramp shipping vessels operating on a combined contract and spot market. Earlier research has been fragmented due to variations in the side constraints studied. Hence we present the first unified model that can handle speed optimization, chartering costs, bunker planning, and hull cleaning. The model is solved by column generation, where the columns represent the possible routes of a vessel, while the master problem keeps track of the binding constraints. The pricing problem is solved efficiently using a time–space graph and several dominance rules. Real-life instances with up to 40 vessels, 35 geographic regions, and four months planning horizon can be solved to optimality in less than half an hour. The optimized routes increase earnings by 7% compared to historical schedules. Furthermore, policy-makers can use the model as a simulation of a rational agent behavior.
Accurate prediction of wave transformation is key in the design of coastal and nearshore structures which typically depends on numerical models. Turbulent and rotational effects call for the use of Computational Fluid Dynamics (CFD) solvers of which a large range of formulations including free surface treatments exists. Physical wave flume tests of wave propagation over a submerged bar with various levels of nonlinearity, regularity, and wave-breaking, dedicated to numerical model benchmarking or validation, were carried out in the Ocean and Coastal Engineering Laboratory of Aalborg University. Three fundamentally different CFD models each widespread within their category are benchmarked against the experimental data. The CFD models are based on (i) the Volume of Fluid (VoF) based interFoam solver of OpenFOAM, (ii) the sigma-transformation solver of MIKE 3 Waves Model FM, and (iii) the weakly compressible delta-SPH solver of DualSPHysics. Accuracy of the numerical models is assessed from surface elevation time series, evaluation metrics (averaged errors on surface elevations, amplitudes, phases, and wave set-up), and spectral analyzes to calculate the amplitude and phase contents of primary and higher-order components along the wave flume. Applicability is assessed from computational costs and ease-of-use factors such as the effort to configure the numerical models and achieve convergence. In general, the numerical models have high correlation to the physical tests and are as such suitable to model complex wave transformation with an accuracy sufficient for most coastal engineering applications. The VoF model performs more accurately under the turbulent conditions of breaking waves, increasing its relative accuracy in the prediction of downwave surface elevation. The sigma transformation model has simulation times one to two orders of magnitude lower than those of the VoF and SPH models.
Our recent experimental investigations of flexible side-by-side blades under both steady and unsteady flows have observed flutter in both scenarios. Flutter significantly impacts blade kinematics and the hydrodynamic drag experienced by the blades. Our numerical approach [1], utilizing the reactive force model, successfully reproduces flutter phenomena. In contrast, the traditional Morison’s equation fails to trigger flutter. In the static regime where flutter does not occur, the bulk drag coefficients calibrated from experiments in steady and unsteady flows can be unified through an effective Cauchy number, allowing for the use of analytical models developed for steady flows in unsteady flows. In the flutter regime, using the bulk drag coefficient from steady flows underestimates the drag load in oscillatory flow.
In this article, we develop a deep neural network model to estimate the wave added resistance. The required data to train the model is generated using strip theory calculations over a wide range of hull geometries and operational conditions. The model is efficient as it only requires the ship’s main particulars: length, beam, draft, block coefficient, and slenderness ratio. In addition, we present an application of this model in a vessel performance framework. This will be used for predicting propulsion power and analyzing the degree of biofouling on ships from the company Ultrabulk2. The study shows that the developed deep neural network model produces reliable results in predicting the added wave resistance coefficient in comparison to strip theory calculations. Also, the developed ship propulsion and biofouling analysis display satisfactory output for monitoring hull performance under actual ship operational conditions.
The present study investigates three-dimensional gap resonance between two fixed side-by-side barges under combined wave and uniform current excitation using a fully nonlinear numerical wave tank based on the Navier–Stokes equations. It examines how currents aligned with regular waves affect the gap response under head and beam seas. In beam seas, the free surface in the gap primarily exhibits a modal-type response in the form of a standing wave. The maximum gap response, consistently occurring at the midpoint of the gap, increases gradually with the current speed. Conversely, in head seas, the maximum response decreases slightly with increasing current speed, and the occurring location shifts downstream. Moreover, resonant free-surface responses along the gap in head seas manifest as propagating waves rather than modal-type standing waves, consisting of a wider spectrum of wave components around the resonant ones and traveling faster than the incident waves regardless of current speed. The wavelengths of those resonant waves tend to increase with increasing current speed. Additionally, the presence of current significantly enlarges the transverse first-harmonic and mean-drift wave forces on the barges under beam-sea conditions. The study highlights the necessity of considering current effects on three-dimensional gap resonances in marine operations at coastal and offshore locations.
Fouling release coatings (FRCs) can become damaged and diminished over exposure. Quantifying adverse effect of scratches on FRCs is crucial for damage control. This study investigated the effect of four pre-defined scratches on the re-fouling of a silicone-based FRC (SiFR) undergoing underwater cleaning utilizing a novel automated underwater cleaning system (AUCS). Moreover, barnacle adhesion and coating detachment formation of scratched SiFR were evaluated. Field testing at the CoaST Maritime Test Centre (CMTC) demonstrated that the scratches varying in depths and widths can significantly affect the biofouling behavior and cleaning efficiency of SiFR surface. For wide scratches (i.e. 3-mm-wide), hard fouling (e.g. barnacles, mussels) was more prone to accumulate, and underwater cleaning was effective in preventing hard fouling but not soft fouling on SiFR surface. Additionally, the re-fouling and cleaning difficulty of hard fouling increased with the depth of wide scratches. For narrow scratches (i.e. <50-μm-wide), SiFR was primarily attached by soft fouling (e.g. biofilm, algae), and underwater cleaning performed positive fouling resistance of algae but not biofilm on SiFR surface. Besides, algae became difficult to remove with the depth of narrow scratches. Notably, biweekly cleaning proved to be highly effective in biofouling control of SiFR with narrow and shallow scratches.
Physical model tests are often conducted during the design process of coastal structures. The wave climate in such tests often includes short-crested nonlinear waves. The structural response is related to the incident waves measured in front of the structure. Existing methods for separation of incident and reflected short-crested waves are based on linear wave theory. For analysis of nonlinear waves, the existing methods are limited to separation of nonlinear long-crested waves. For short-crested waves, the only options so far have been to use estimates without the structure in place. The present paper thus presents a novel method for directional analysis of nonlinear short-crested waves: Non-Linear Single-summation Oblique Reflection Separation (NL-SORS). The method is validated on numerical model data, as for such data, the target is well defined as simulations may be performed with fully absorbing boundaries. Second- and third-order wave theory is used to demonstrate that small errors on the celerity of nonlinear components in the mathematical model of the surface elevation can be obtained if a double narrow-banded directional spectrum is assumed, ie the primary frequency and the directional spreading function must be narrow banded. As the increasing nonlinearity of the waves often arise from waves shoaling on a sloping foreshore, the directional spreading of the waves will decrease due to refraction, and a broad directional spreading function will thus not be experienced in highly nonlinear conditions. The new NL-SORS method is shown to successfully decompose nonlinear short-crested wave fields and estimate the directional spectrum thereof.
In this paper, the nonlinear interaction of regular water waves propagating over a fixed and submerged circular cylinder is numerically studied. At the structure’s lee side, the free surface profile experiences strong nonlinear deformation where the superharmonic free wave generated can be significant and is superposed on the transmitted wave. The wave profile then becomes asymmetric and skewed and may eventually reach the point of physical wave breaking. The governing equation and boundary conditions of this wave–structure interaction problem are formulated using both the fully nonlinear and the weak-scatterer theory. The corresponding boundary value problem is numerically solved by the immersed-boundary adaptive harmonic polynomial cell solver. In this study, a pragmatic wave-breaking suppression model is incorporated into the original solver. Both the harmonic free wave amplitudes at the structure’s lee side and the harmonic vertical forces on the cylinder are studied. The simulated harmonic wave amplitudes are compared to other published experiments and theoretical data. In general, good agreement is achieved. The effects of the incorporated wave-breaking suppression model on the simulated results are discussed. In our study, the incorporation of the pragmatic wave-breaking suppression model successfully extends the capabilities of the original fully nonlinear immersed-boundary adaptive harmonic polynomial cell solver.
Design waves have been used in the past for the probabilistic assessment of wave-induced loads and responses of offshore structures. Various response-conditioning techniques have been employed to determine suitable wave episodes, typically based on linear response transfer functions. Nevertheless, extreme events are not always driven by linear phenomena but can be triggered by near-resonant effects, as in the case of the slow-drift motions of moored floating bodies. Limited research has been devoted to addressing this class of responses using response-conditioned waves (RCW). This paper presents a new approach for deriving RCWs that accounts for combined wave- and low-frequency responses. Both the response amplitude operator (RAO) and the quadratic transfer function (QTF) are employed in an iterative response-conditioning procedure. That permits the identification of appropriate short-duration wave episodes that excite resonant slow-drift motions. These wave episodes are then used in a two-step multi-fidelity design wave methodology for the probabilistic evaluation of the fully nonlinear extreme responses. The proposed approach is validated experimentally for predicting the surge excursions of a moored container ship, and good agreement is found against Monte Carlo results in irregular waves.
Due to limited access to domain knowledge and domain-relevant benchmark data, the Container Stowage Planning Problem (CSPP) is notably under-researched. In particular, previous models of the CSPP have lacked two key aspects of the problem: lashing forces and paired block stowage. The former may reduce vessel capacity by up to 10%, and the latter is NP-hard. The Representative CSPP (RCSPP), which captures all critical aspects of the problem is formulated. The presented RCSPP incorporates overlooked constraints such as paired block stowage and lashing, along with an innovative method for estimating lashing forces, all while maintaining simplicity. A heuristic method, STOW, has been developed to identify solutions for the RCSPP using a specially designed benchmark suite based on real-world scenarios. STOW algorithm is an advanced search heuristic employing a diverse range of solution modification strategies, each tailored to address specific aspects of stowage optimization. Feasible solutions were successfully identified for all instances within the benchmark suite. Our initial findings emphasize the importance of accurately modeling lashing forces and employing paired block stowage. Results show that removing the lashing constraint can increase the number of containers stowed by over 7% on average, while disabling paired block stowage can result in nearly a 5% increase.