Numerical solutions of 2D Navier-Stokes equations based on generalized harmonic polynomial cell method with non-uniform grid

It is essential for a Navier-Stokes equations solver based on a projection method to be able to solve the resulting Poisson equation accurately and efficiently. In this paper, we present numerical solutions of the 2D Navier-Stokes equations using the fourth-order generalized harmonic polynomial cell (GHPC) method as the Poisson equation solver. Particular focus is on the local and global accuracy of the GHPC method on non-uniform grids. Our study reveals that the GHPC method enables use of more stretched grids than the original HPC method. Compared with a second-order central finite difference method (FDM), global accuracy analysis also demonstrates the advantage of applying the GHPC method on stretched non-uniform grids. An immersed boundary method is used to deal with general geometries involving the fluid-structure-interaction problems. The Taylor-Green vortex and flow around a smooth circular cylinder and square are studied for the purpose of verification and validation. Good agreement with reference results in the literature confirms the accuracy and efficiency of the new 2D Navier-Stokes equation solver based on the present immersed-boundary GHPC method utilizing non-uniform grids. The present Navier-Stokes equations solver uses second-order FDM for the discretization of the diffusion and advection terms, which may be replaced by other higher-order schemes to further improve the accuracy.

Jump bifurcation phenomenon during varying wind speeds in floating offshore wind turbines

Floating Offshore Wind Turbines (FOWTs) are susceptible to an instability which has come to be called negative damping. Conventional land based wind turbine controllers when used with FOWTs may cause large amplitude platform pitch oscillations. Most controllers have since been improved to reduce motions due to this phenomenon. In this paper, the motions induced using one of the original controllers is studied. The current study is performed using the coupled time domain program FAST-SIMDYN that was developed in Marine Dynamics Laboratory (MDL) at Texas A&M University. It is capable of studying large amplitude motions of Floating Offshore Wind Turbines. FOWTs use various controller algorithms of operation based on the available wind speed depending on various power output objectives i.e., to either maximize or level out power absorption. It is observed that the transition region for controllers is often chaotic. So most studies focus on operations away from the transition region below and above the transition wind speeds. Here we study the transition region using the theoretical insight of non-linear motion response of structures. This study reveals the presence of a very interesting and potentially hazardous nonlinear phenomenon, bifurcation. This finding could help explain the chaotic motion response that is observed in the transition region of controllers. Understanding the nature and cause of bifurcation could prove very useful for future design of FOWT controllers.

Numerical simulations of a freely falling rigid sphere in bounded and unbounded water domains

Numerical studies were conducted on the hydrodynamics of a freely falling rigid sphere in bounded and unbounded water domains to investigate the drag coefficient, normalized velocity, pressure coefficient, and skin friction coefficient as a function of dimensionless time. The bounded domain was simulated by bringing the cylindrical water container's wall closer to the impacting rigid sphere and linking it to the blockage ratio (BR), defined as the ratio of the projection area of a freely falling sphere to that of the cross-section area of the cylindrical water container. Six cases of bounded domains (BR= 1%, 25%, 45%, 55%, 65%, and 75%) were studied. However, the unbounded domain was considered with a BR of 0.01%. In addition, the k–ω shear stress transport (SST) turbulence model was employed, and the computed results of the bounded domain were compared with those of other studies on unbounded domains. In the case of the bounded domain, which has a higher value of BR, a substantial reduction in normalized velocity and an increase in the drag coefficient were found. Moreover, the bounded domain yielded a significant increase in the pressure coefficient when the sphere was half-submerged; however, an insignificant effect was found on the skin friction coefficient. In the case of the unbounded domain, a significant reduction in the normalized velocity occurred with a decrease in the Reynold number (Re) whereas the drag coefficient increases with a decrease in Reynolds number.

Head Wave Simulation of a KCS Model Using OpenFOAM for the Assessment of Sea-Margin

The paper presents calm water and head wave simulation results for a KRISO Container Ship (KCS) model. All simulations have been performed using the open source CFD toolkit, OpenFOAM. Initially, a systematic verification study is presented using the ITTC guideline to assess the simulation associated uncertainties. After that, a validation study is performed to assess the accuracy of the results. Next, calm water simulations are performed with sinkage and trim free condition at varying speeds. Later, head wave simulations are performed with heave and pitch free motion. Simulations are repeated for varying wave lengths to assess the encountered added resistance by the ship in design speed. The results are validated against available experimental data. Finally, power predictions are made for both calm water and head wave cases to assess the required propulsion power. The paper tries to assess the validity of using 25% addition as sea margin over calm water prediction to consider wave encounters

Three-dimensional numerical simulation of a flat plate perpendicularly submitted to current with a blockage ratio of 0.214: URANS and DES

The uniform flow over a nominally two-dimensional normal thin flat plate with blockage ratio 0.214 was numerically investigated in three dimensions by three methods: unsteady Reynolds-averaged Navier–Stokes (URANS) based on the realizable k-epsilon (RKE) turbulence model, URANS based on the k–omega shear stress transport (SST) turbulence model and detached eddy simulation (DES). The Reynolds number based on the inlet flow velocity and the chord width of the plate was 117000. A comprehensive comparison against earlier experimental results showed that URANS-SST method only could give a correct Strouhal number but overestimated the mean base pressure distribution and mean drag coefficient, while URANS-RKE and DES methods succeeded in giving accurate prediction of all. Moreover, by comparing the instantaneous vorticity contours and 3D turbulent flow structures, it is found that DES is better suited for the present case because it can capture irregular small-scale structures and reproduce the three-dimensionality and low-frequency unsteadiness of the vortex shedding. Finally, through the volume-of-fluid (VOF) based simulation of the free surface, it is demonstrated that the free surface has no significant effect on mean drag coefficient and Strouhal number.

Power Enhancement of WEC Array via Wave Runup in Channel

When waves pass through a channel, wave elevation is observed to increase, a phenomenon known as wave runup. Attempts are made to utilize the wave runup along a channel supported on a floating platform to enhance the energy generation from the array of point absorber WECs. Such floating platforms could be integrated into the floating breakwater, floating pier or other floating platforms utilized as floating cities for efficient ocean space utilization. The channel is created by modelling two vertical walls supported on a floating platform with WECs deployed in the channel. The performance of the wave farm in terms of energy generation and interaction factor are assessed. The paper investigates the effect of channel widths and depths on the power absorption of the arrays. A three-stepped floating platform with varying depths along the channel is then studied to obtain optimal depths along the channel where the highest energy is harvested. Thereafter, three arrays of WECs deployed in a larger three-stepped channel floating platform are considered and the effectiveness of such configuration in harvesting energy is assessed. The wave elevation surrounding the wave farm is presented to show the effect the wave runup has on energy generation. The results show that the energy generation of wave energy converters when the arrays are placed in a three-stepped channel floating platform could be increased significantly. A q-factor above 1.0 could be achieved for wave periods greater than 6s and the array can generate greater energy for omnidirectional waves.

Numerical simulation of wave interaction with a pair of fixed large tandem cylinders subjected to regular non-breaking waves

This paper presents the application of a two-phase Computational Fluid Dynamics (CFD) model to carry out a detailed investigation of nonlinear wave field surrounding a pair of columns placed in the tandem arrangement in the direction of wave propagation and corresponding harmonics. The numerical analysis is conducted using the Unsteady Reynolds-Averaged Navier-Stokes/VOF model based on the OpenFOAM framework combined with the olaFlow toolbox for wave generation and absorption. For the simulations, the truncated cylinders are assumed vertical and surface piercing with a circular cross-section subjected to regular, non-breaking fifth-order Stokes waves propagating with moderate steepness in deep water. Primarily, the numerical model is validated with experimental data for a single cylinder. Future, the given simulations are conducted for different centre-to-centre distances between the tandem large cylinders. The results show the evolution of a strong wave diffraction pattern and consequently, high wave amplification harmonics around cylinders are apparent.

Assessment of Stress Concentration Factors of Dented Rigid Risers under Fatigue Loadings

In the development of oil and gas fields, subsea pipes are used in various applications, like pipelines and risers. During operation, risers can be subjected to accidents, such as collisions with other risers, anchors, rocks, or any heavy equipment or objects, which may lead to mechanical damages. These mechanical damages are commonly characterized as dents. The objective of this work is to study the effect of the introduction of plain dents on the fatigue life of rigid risers under fully reversed bending with the conduction of resonant bending tests. A three-dimensional finite element model was developed to estimate the stress concentration on dented risers under bending. Numerical simulations and experimental tests were carried out to evaluate the resulting stress concentration factors (SCFs). These SCFs can be used in the prediction of the remaining fatigue life of dented rigid risers.

Micro-Testing While Drilling for Rate of Penetration Optimization: Experiments and Simulations

The Rate of Penetration (ROP) is one of the key parameters related to the efficiency of the drilling process. Within the confines of operational limits, the drilling parameters affecting the ROP should be optimized to drill more efficiently and safely, to reduce the overall cost of constructing the well. In this study, a data-driven optimization method called Extremum Seeking (ES) is employed to automatically find and maintain the optimal Weight on Bit (WOB) which maximizes the ROP. The ES algorithm is a model-free method which gathers information about the current downhole conditions by automatically performing small tests with the WOB and executing optimization actions based on the test results. In this paper, this optimization method is augmented with a combination of a predictive and a reactive constraint handling technique to adhere to operational limitations. These methods of constraint handling within ES application to drilling are demonstrated for a maximal limit imposed on the surface torque, but the methods are generic and can be applied on various drilling parameters. The proposed optimization scheme has been tested with experiments on a downscaled drilling rig and simulations on a high-fidelity drilling simulator of a full-scale drilling operation. The experiments and simulations show the method's ability to steer the system to the optimum and to handle constraints and noisy data, resulting in safe and efficient drilling at high ROP.

Focused Plunging Breaking Waves Impact on Pile Group in Finite Water Depth

Accuracy estimation of wave loading on cylinders in a pile group under different impact scenarios is essential for both the structural safety and cost of coastal and offshore structures. Differing from the interaction of waves with a single cylinder, less attention has been paid to pile groups under different arrangements. Numerical simulations of interactions between plunging breaking waves and pile group in finite water depth are performed using the two-phase flow model in REEF3D, an open-source computational fluid dynamics program to investigate the wave loads and flow kinematics characteristics. The Reynolds-averaged Navier-Stokes equation with the two equation k − ω turbulence model is adopted to resolve the numerical wave tank. The model is validated by comparing the numerical wave forces and free surface elevation with measurements from experiments. The computational results show fairly good agreement with experimental data. Four cases are simulated with different relative distances, numbers of cylinders and arrangements. Results show that the wave forces on cylinders in the pile group are effected by the relative distance between cylinders. The staggered arrangement has a significant influence on the wave forces on the first and second cylinder. The interaction inside a pile group mostly happens between the neighboring cylinders.