Stricter regulations imposed on emissions are motivating the scientific community to consider studying alternative fuels to achieve low emission, high efficient dual-fuel (DF) marine engines. In this context, three dimensional computational fluid dynamic (CFD) simulations are performed to study the combustion and emission formation under two-stroke, dual-fuel marine engine-like conditions. The DF engine configuration consists of a pilot diesel fuel and a high-pressure, direct injection (HPDI) of natural gas (NG). The simulation results are validated under both high load (high charge density) and low load (low charge density) operating conditions. Detailed analysis of the flame development and emission formation are performed. The interaction between the pilot diesel jets and the methane flame jets is studied. Based on the results, the further methane jets penetration in the low load case leads to better air–fuel mixing and a higher combustion intensity than that in the high load. Effects of the pilot fuel injection timing on combustion and emission formation and the governing mechanisms are also investigated in detail. Results indicate that the intense combustion of the accumulated methane expands the methane flame towards the piston when the pilot injection timing is retarded. The NO formation is lower in the high load case with higher charge density due to the lower combustion intensity. Also, retarding the pilot injection timing decreases the NO formation.
The depth-integrated shallow water equations are frequently used for simulating geophysical flows, such as storm-surges, tsunamis and river flooding. In this paper a parallel shallow water solver using an unstructured high-order discontinuous Galerkin method is presented. The spatial discretization of the model is based on the Nektar++ spectral/hp library and the model is numerically shown to exhibit the expected exponential convergence. The parallelism of the model has been achieved within the Cactus Framework. The model has so far been executed successfully on up to 128 cores and it is shown that both weak and strong scaling are largely independent of the spatial order of the scheme. Results are also presented for the wave flume interaction with five upright cylinders.
Offshore pipelines and structures require regular marine growth removal and inspection to ensure structural integrity. These operations are typically carried out by Remotely Operated Vehicles (ROVs) and demand reliable and accurate feedback signals for operating the ROVs efficiently under harsh offshore conditions. This study investigates and quantifies how sensor delays impact the expected control performance without the need for defining the control parameters. Input-output (IO) controllability analysis of the open-loop system is applied to find the lower bound of the H-infinity peaks of the unspecified optimal closed-loop systems. The performance analyses have shown that near-structure operations, such as pipeline inspection or cleaning, in which small error tolerances are required, have a small threshold for the time delays. The IO controllability analysis indicates that off-structure navigation allow substantial larger time delays. Especially heading is vulnerable to time delay; however, fast-responding sensors usually measure this motion. Lastly, a sensor comparison is presented where available sensors are evaluated for each ROV motion’s respective sensor-induced time delays. It is concluded that even though off-structure navigation have larger time delay tolerance the corresponding sensors also introduce substantially larger time delays.
We present a depth-integrated Boussinesq model for the efficient simulation of nonlinear wave–body interaction. The model exploits a ‘unified’ Boussinesq framework, i.e. the fluid under the body is also treated with the depth-integrated approach. The unified Boussinesq approach was initially proposed by Jiang (2001) and recently analyzed by Lannes (2017). The choice of Boussinesq-type equations removes the vertical dimension of the problem, resulting in a wave–body model with adequate precision for weakly nonlinear and dispersive waves expressed in horizontal dimensions only. The framework involves the coupling of two different domains with different flow characteristics. Inside each domain, the continuous spectral/hp element method is used to solve the appropriate flow model since it allows to achieve high-order, possibly exponential, convergence for non-breaking waves. Flux-based conditions for the domain coupling are used, following the recipes provided by the discontinuous Galerkin framework. The main contribution of this work is the inclusion of floating surface-piercing bodies in the conventional depth-integrated Boussinesq framework and the use of a spectral/hp element method for high-order accurate numerical discretization in space. The model is verified using manufactured solutions and validated against published results for wave–body interaction. The model is shown to have excellent accuracy and is relevant for applications of waves interacting with wave energy devices.
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998)[5], although the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively removes any aliasing driven instabilities while retaining the high-order accuracy of the numerical scheme. The additional computational cost of the over-integration is found insignificant compared to the cost of solving the Laplace problem. The model is applied to several benchmark cases in two dimensions. The results confirm the high order accuracy of the model (exponential convergence), and demonstrate the potential for accuracy and speedup. The results of numerical experiments are in excellent agreement with both analytical and experimental results for strongly nonlinear and irregular dispersive wave propagation. The benefit of using a high-order – possibly adapted – spatial discretisation for accurate water wave propagation over long times and distances is particularly attractive for marine hydrodynamics applications.
For design validation of offshore structures and conceptualisation of wave energy converters, physical model testing performed in wave basin laboratories is often applied. In such cases, knowledge about the wave conditions is of great significance. For validation of the wave condition in such tests, different methods for estimation of the directional wave spectra may be applied. However, different assumptions are imposed in the methods and deviations here from providing uncertainties in the results. The following paper quantifies the influence of nonlinear effects on the accuracy of the estimated directional wave spectra. This is done by analysis of idealised, synthetically generated waves based on second order wave theory and secondly with simplified amplitude dispersion included. The present analyzes show that the uncertainties of the directional wave spectra are proportional to the level of nonlinearity present in the wave field.
The main objective of this research is to present an improved and more accurate formula to estimate the reflection coefficient (K R ) for rubble mound breakwaters. Physical model tests were performed for this purpose and existing data was also considered. The evaluation of existing prediction formulas for K R based on the Iribarren number (ξ) shows that the scatter in the experimental results increases with increasing ξ. This is caused by the wavelength having greater influence on the reflection than the wave height and thus the use of the wave steepness is inappropriate. The influence of potentially dimensionless parameters on the wave reflection from literature was analyzed. The major dimensionless parameters were found to be the relative water depth (h/L) and the structure front slope angle (α). Hence, a formula to estimate wave reflection for rubble mound breakwaters based on these two parameters is proposed.
In the hydroelastic analysis of large floating structures, the structural and hydrodynamic analyses are coupled, and the structural stiffness plays an important role in the accurate prediction of the response. However, there is usually a large difference between the longitudinal and the cross-sectional scales of modern ships, and the sectional configurations are generally complex, making it difficult to obtain the exact structural stiffness. Using a full finite element model to calculate the structural stiffness is inevitably time-consuming. Since modern ship structures are usually nearly periodic in the longitudinal direction, we treat the hull as a periodic Euler–Bernoulli beam and use a novel implementation of asymptotic homogenization (NIAH) to calculate the effective stiffness. This can greatly improve the computational efficiency compared with a full finite element model. Based on a combination of finite element and finite difference methods, we develop an efficient analysis technique to solve the hydroelastic problem for nearly-periodic floating structures. The finite element method is used to efficiently calculate the structural stiffness, and the finite difference method is used to solve the hydrodynamic problem. This proposed technique is validated through several test cases with both solid and thin-walled sections. A range of representative mid-ship sections for a container ship are then considered to investigate the influence of both transverse and longitudinal stiffeners on the structural deformations. A simple method for including non-periodic end effects is also suggested.
This paper models the large periodic plate structure as Kirchhoff-Love plates and introduces a novel implementation of asymptotic homogenization (NIAH) to enable an efficient calculation of the structural stiffness. Compared to full finite element models, applying NIAH to a unit-cell model greatly reduces computational costs. This paper systematically presents the derivation and finite element formulation of asymptotic homogenization (AH), and the development of NIAH. Benchmark cases, including solid, thin-walled, multi-material plates, and a plate with octagonal holes, are used to validate the NIAH implementation. A series of representative fish cage designs are analyzed to investigate the influence of pontoon components, structural layouts, and material distribution on structural stiffness. To ensure the reliability of the calculations, the choice of unit-cell model and the sensitivity of the results to mesh density and unit-cell size are also discussed.
An adaptive spectral/hp discontinuous Galerkin method for the two-dimensional shallow water equations is presented. The model uses an orthogonal modal basis of arbitrary polynomial order p defined on unstructured, possibly non-conforming, triangular elements for the spatial discretization. Based on a simple error indicator constructed by the solutions of approximation order p and p-1, we allow both for the mesh size, h, and polynomial approximation order to dynamically change during the simulation. For the h-type refinement, the parent element is subdivided into four similar sibling elements. The time-stepping is performed using a third-order Runge-Kutta scheme. The performance of the hp-adaptivity is illustrated for several test cases. It is found that for the case of smooth flows, p-adaptivity is more efficient than h-adaptivity with respect to degrees of freedom and computational time.