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.
This paper presents the methods developed and key findings of the IWEC project performed by Ocean Harvesting Technologies AB (OHT). It aimed to reduce the levelized cost of energy (LCoE) of OHT’s wave energy converter InfinityWEC, by analysing how different key parameters impact cost and annual output using a model of a 100-MW array installation. Component-level cost functions were developed and mapped to key parameters and constraints of the system. A large number of system configurations were then evaluated with a numerically efficient 3 degree-of-freedom (DoF) nonlinear radiationdiffraction model in WEC-Sim along with OHT’s sea statetuned polynomial reactive control (PRC). The most promising configurations were identified and investigated in more detail. The configuration with the best LCoE were finally identified and analysed further, including estimation of the effect of changing the PRC to model predictive control, which resulted in 17-34% higher annual output and 12-23% lower LCoE. The final LCoE was found to be 93-162 EUR MWh at 100 MW installed capacity. An important finding from the study is that using simplified metrics such as CAPEX/ton was found to be irrelevant. Numerical wave tank testing, high-fidelity computational fluid dynamics (CFD), were used to tune the viscous drag of the 3 DoF WEC-Sim model. Applying verification and validation (V&V) techniques the CFD simulations showed a relatively large numerical uncertainty, but the average power and the motion responses were found to be sufficiently accurate.
For the assessment of experimental measurements of focused wave groups impacting a surface-piecing fixed structure, we present a new Fully Nonlinear Potential Flow (FNPF) model for simulation of unsteady water waves. The FNPF model is discretized in three spatial dimensions (3D) using high-order prismatic - possibly curvilinear - elements using a spectral element method (SEM) that has support for adaptive unstructured meshes. This SEM-FNPF model is based on an Eulerian formulation and deviates from past works in that a direct discretization of the Laplace problem is used making it straightforward to handle accurately floating structural bodies of arbitrary shape. Our objectives are; i) present detail of a new SEM modelling developments and ii) to consider its application to address a wave-body interaction problem for nonlinear design waves and their interaction with a model-scale fixed Floating Production, Storage and Offloading vessel (FPSO). We first reproduce experimental measurements for focused design waves that represent a probably extreme wave event for a sea state represented by a wave spectrum and seek to reproduce these measurements in a numerical wave tank. The validated input signal based on measurements is then generated in a NWT setup that includes the FPSO and differences in the signal caused by nonlinear diffraction is reported.
A 3D fully nonlinear potential flow (FNPF) model based on an Eulerian formulation is presented. The model is discretized using high-order prismatic – possibly curvi-linear – elements using a spectral element method (SEM) that has support for adaptive unstructured meshes. The paper presents details of the FNPF-SEM development and the model is illustrated to exhibit exponential convergence. The model is then applied to the case of focused waves impacting on a surface-piecing fixed FPSO-like structure. Good agreement was found between numerical and experimental wave elevations and pressures.
We present a high-order nodal spectral element method for the two-dimensional simulation of nonlinear water waves. The model is based on the mixed Eulerian–Lagrangian (MEL) method. Wave interaction with fixed truncated structures is handled using unstructured meshes consisting of high-order iso-parametric quadrilateral/triangular elements to represent the body surfaces as well as the free surface elevation. A numerical eigenvalue analysis highlights that using a thin top layer of quadrilateral elements circumvents the general instability problem associated with the use of asymmetric mesh topology.We demonstrate how to obtain a robust MEL scheme for highly nonlinear waves using an efficient combination of (i) global L2 projection without quadrature errors, (ii) mild modal filtering and (iii) a combination of local and global re-meshing techniques. Numerical experiments for strongly nonlinear waves are presented. The experiments demonstrate that the spectral element model provides excellent accuracy in prediction of nonlinear and dispersive wave propagation. The model is also shown to accurately capture the interaction between solitary waves and fixed submerged and surface-piercing bodies. The wave motion and the wave-induced loads compare well to experimental and computational results from the literature.
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.
Monopiles are often the preferred foundation concept for an offshore wind turbine. The interaction between extreme waves and the large diameter monopile will in some cases result in a vertical jet of water uprush on the monopile (i.e., wave run-up) which subsequently may lead to large slamming loads on monopile appurtenances like the external working platform.
Extreme wave run-up interaction with an external working platform is often an area of concern during the design phase of an offshore wind project as an overly conservative assessment of the run-up loads may lead to unneeded costs in material and an increased project carbon footprint. An insufficient assessment of the run-up loads may lead to structural failure of the appurtenances and subsequent costly maintenance and repair works, further exacerbated by possibly difficult access to the damaged platform.
The practical process in the assessment of wave run-up on monopiles and associated loads on appurtenances can be a challenge to the designer due to lack of guidance on this topic in governing standards. The designer may then have to rely on several sources of available literature and must assess and include the effect of associated uncertainties like: Adjustment to site specific environmental conditions, unclear or unconcise terminology in the literature, lack of model test results representing the actual geometry and limited knowledge of spatial and temporal run-up load distribution on the appurtenances.
The aim of the present paper is to describe a complete methodology for assessment of wave run-up on monopiles and associated loads on appurtenances. The methodology, which will serve as a practical guide, is based on a collection of existing methods with new analysis to consider the pressure distribution on modern asymmetric grated platforms. This was based on experiences gained and challenges encountered during a detail design project of a monopile foundation for an offshore wind turbine in extreme environmental conditions. The sensitivity of the run-up assessment related to the design input (water depth, wave height and period, associated water level and current conditions) is discussed by considering a matrix with various environmental input combinations representing extreme environmental conditions.
This thesis presents the numerical study of combustion under marine engine like condi- tions. The thesis is divided into two main parts. In the first part, combustion is studied in a large two-stroke marine engine with conventional diesel fuel. In the second part, two different dual-fuel combustion modes of diesel-methane i.e. non-premixed combus- tion and premixed combustion are studied. All numerical models are validated with the experimental data.
First, in a simplified geometry of the marine engine, conjugate heat transfer (CHT) calculations are applied to simultaneously solve the in-cylinder gas phase dynamics and the temperature field within the liner of the engine. The effects of different initial tem- peratures across the liner and the effects of the amount of water vapor in the air on the sulfuric acid formation and condensation in a large two-stroke marine engine are studied. An initial temperature is calculated based on heat transfer modeling and it is observed that the sulfuric acid vapor formation is more sensitive to the variation of the water vapor amount than the sulfuric acid condensation. In the next step, the effects of the turbulence modelling on the simulation of the full cycle of the engine including scavenging process, combustion, and emission formation is studied in a real geometry of a large two-stroke marine research engine. The Unsteady Reynolds Averaged Navier- Stokes (URANS) and Large Eddy Simulation (LES) turbulence models are utilized for modeling of in-cylinder turbulent flow. The accuracy of the tangential velocity and swirl flow in the top of the cylinder where the fuel is injected is crucial to predict the air-fuel mixing correctly. It is found that URANS predicts a solid body rotation for the tangential velocity in this region. However, LES predicts a tangential velocity that is uniformly distributed in the radial direction that is consistent with experimental results. Furthermore, during the scavenging process, LES is able to predict the Burgers vortex upstream of the cylinder near the scavenging ports. Also, LES predicts a higher angu- lar momentum inside the cylinder in comparison with URANS. During the combustion process, the LES model shows a moderately better performance in capturing the experi- mental pressure and heat release rate profiles than URANS. However, the predicted gas temperature at the liner wall is approximately 45 % higher for URANS than LES during the expansion stroke, which is attributed to a higher predicted turbulent viscosity in the URANS case. A higher temperature of gas beside the liner wall may decrease the sulfuric acid formation and increase the heat transfer. The higher predicted swirl by LES than that in URANS leads to an earlier and stronger interaction between the flame and the spray, decreasing the oxidation of the emissions. The second cycle LES simula- tion shows that the solutions after the scavenging process are in-sensitive to the initial conditions and the main governing parameters are boundary conditions and injection characteristics.
Next, two different dual-fuel combustion modes of non-premixed combustion and premixed combustion are studied. The non-premixed combustion is simulated and val- idated with the experimental data of a large two-stroke marine research engine under low and high engine loads. Based on the results, 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 diesel 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 due to the lower combustion intensity. Also, retarding the pilot injection timing decreases the NO formation. Furthermore, the effect of the direction of pilot diesel injection is investigated which shows a significant effect on the methane start of combustion and intensity as well as flame propagation direction which leads to different heat transfer trends from the combustion chamber walls.
Premixed combustion is analysed in a constant volume combustion chamber (CVCC) and validated with experimental data. Results show that by simulation of methane-air mixing, the numerical model is able to capture the ignition delay time (IDT) within a maximum relative difference of 7 % to the measurements. A higher relative difference of 38% is obtained when methane gas injection is omitted and the methane-air and temperature are assumed homogeneous. Therefore, it is concluded that the simulation of methane-air mixing process is crucial in this type of combustion due to the presence of inhomogeneities in both methane fuel and temperature distribution after mixing. Creating the idealized inhomogeneities for separately investigation of methane and tem- perature inhomogeneities shows that the inhomogeneity in the temperature has a more profound influence on the IDT than the inhomogeneity in the methane distribution. Furthermore, the effects of the number of pilot fuel nozzle holes on the auto-ignition are studied. The auto-ignition process in two cases with 4 nozzle holes is investigated and compared with the base case with 8 nozzle holes. Considering the same amount of pilot fuel, the injection rate is assumed to be double in one of the cases, while in the other case, the injection duration is doubled. Results show that a reduction of the nozzle hole numbers can improve the pilot diesel ignition in the case with 4 nozzle holes and double injection duration compared to the base case with 8 nozzle holes. However, combustion in the case with 4 nozzle holes and a double injection rate is incomplete due to flame impingement on the walls.
In a premixed dual-fuel (DF) methane-diesel engine, the ignition of the lean premixed methane/air mixture starts with the assistance of a pilot diesel injection. Auto-ignition of pilot fuel is important as it triggers the subsequent combustion processes. A delay in the auto-ignition process may lead to misfiring, incomplete combustion, and thus higher greenhouse emissions due to methane slip. Hence, a better understanding of the auto-ignition process for the pilot fuel can help to improve the overall engine performance, combustion efficiency, and to lower exhaust emission levels. In the present study, large eddy simulation (LES) is used to investigate the auto-ignition process of micro-pilot diesel in premixed DF combustion in a constant volume combustion chamber (CVCC). The entire DF combustion processes including methane gas injection, methane/air mixing, pilot diesel injection, and ignition are simulated. The numerical model is validated against experimental data. The present numerical model is able to capture the ignition delay time (IDT) within a maximum relative difference of 7% to the measurements. A higher relative difference of 38% is obtained when methane gas injection and mixing are omitted in the simulation and the methane/air is assumed homogeneous. This demonstrates the importance of inhomogeneity pockets. To study the effects of temperature and methane inhomogeneities separately, different idealized inhomogeneities in temperature and methane distribution are considered inside the CVCC. The inhomogeneity in the temperature is observed to have a more profound influence on the IDT than the methane inhomogeneity. The inhomogeneity pockets of temperature advance the first-stage ignition and, subsequently, the second-stage ignition. A sensitivity analysis on the effect of inhomogeneity wavelength reveals that the larger wavelengths enhance the combustion due to the presence of pilot diesel jets in the desirable regions for a longer time duration.
In this paper, the main aim is to examine the performance of turbulence models to shed light on the effect of turbulence modeling in capturing different in-cylinder phenomena under large two-stroke marine engine-like conditions. The Unsteady Reynolds Averaged Navier–Stokes (URANS) and Large Eddy Simulation (LES) turbulence models are utilized. The LES and URANS results are compared with experimental data, in which LES and URANS models show similar accuracy in capturing the pressure and heat release with a moderately better accuracy in the LES case. The predicted gas temperature at the liner wall is approximately 45% higher for URANS than LES during the expansion stroke, which may lead to different sulfuric acid formation and heat transfer prediction. The LES model predicts a 34% higher average swirl than that in the URANS case which leads to an earlier and a stronger interaction between the flame and the spray, decreasing the oxidation of the emissions. Due to the higher predicted in-cylinder temperature in the LES case, the NO emission amount at exhaust valve opening time (EVO) is 7% higher in the LES case. At EVO, the emission in the LES case is predicted to be 3-fold higher than that in the URANS case due to less oxidation of in the post oxidation stage in the LES case. The second cycle LES simulation shows that the solutions after the scavenging process are in-sensitive to the initial conditions.