A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a formulation of a fully nonlinear and dispersive potential flow water wave model with random inputs for the probabilistic description of the evolution of waves. The model is analyzed using random sampling techniques and nonintrusive methods based on generalized polynomial chaos (PC). These methods allow us to accurately and efficiently estimate the probability distribution of the solution and require only the computation of the solution at different points in the parameter space, allowing for the reuse of existing simulation software. The choice of the applied methods is driven by the number of uncertain input parameters and by the fact that finding the solution of the considered model is computationally intensive. We revisit experimental benchmarks often used for validation of deterministic water wave models. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in comparison with experimental measurements could be partially explained by the variability in the model input. Finally, we present a synthetic experiment studying the variance-based sensitivity of the wave load on an offshore structure to a number of input uncertainties. In the numerical examples presented the PC methods exhibit fast convergence, suggesting that the problem is amenable to analysis using such methods.
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.
Floating wave energy converters (WECs) operating in the resonance region are strongly affected by non-linearities arising from the interaction between the waves, the WEC motion and the mooring restraints. To compute the restrained WEC motion thus requires a method which readily accounts for these effects. This paper presents a method for coupled mooring analysis using a two-phase Navier-Stokes (VOF-RANS) model and a high-order finite element model of mooring cables. The method is validated against experimental measurements of a cylindrical buoy in regular waves, slack-moored with three catenary mooring cables. There is overall a good agreement between experimental and computational results with respect to buoy motions and mooring forces. Most importantly, the coupled numerical model accurately recreates the strong wave height dependence of the response amplitude operators seen in the experiments.
Efficient control schemes of Autonomous underwater vehicle (AUV) are challenging due to uncertainties and highly nonlinearities. In this paper, improved fractional order PID controller is proposed for the control of AUV motion with six degrees of freedom (DOF). Genetic algorithm and Particle Swarm Optimization (PSO) are employed to find suboptimal coefficients of FOPID controller to improve performance of the AUV motion. These optimal adjusted coefficients of FOPID controllers minimize the step response characteristics such as maximum deviation and settling time. Simulation results are presented to verify the advantages of the FOPID with respect to the previous works specially proportional-integral-derivative controller (PID).
The goal of this paper is to introduce and design a cost-effective Oil-in-Water (OiW) measuring instrument, which will be investigated for its value in increasing the efficiency of a deoiling hydrocyclone. The technique investigated is based on Electrical Resistivity Tomography (ERT), whose basic principle is to measure the resistivity of substances from multiple electrodes and from these measurements create a 2-D image of the oil and gas component in the water. This technique requires the measured components to have different electrical resistances, such as seawater which has a lower electrical resistance than hydrocarbon oil and gas. This work involves construction of a pilot plant, for testing the feasibility of ERT for OiW measurements, and further exploring if this measured signal can be applied as a reliable feedback signal in optimization of the hydrocyclone's efficiency. Different algorithms for creating 2-D images and the feasibility of estimating OiW concentrations are studied and evaluated. From both steady state and continuous laminate flow perspectives, with respect to the objective which is to use this measurement for feedback control purposes.
The current offshore oil & gas multi-phase production and transportation installations have big challenges related to the slugging flow: An unstable multi-phase flow regime where the flow rates, pressures and temperatures oscillate in the considered processes. Slug can be caused by different operating conditions and installation structures. The most severe slugs are often induced in long vertical risers or production wells, where liquid blocks gas at the riser/well base and correspondingly it causes the pressure to accumulate and hence originates the oscillating performance. There are many severe consequences to the production processes because of the slugging flow. This paper reviews some observed latest status and key challenges about slug detection, dynamical modeling and elimination of slugging flows. Mathematical modeling of slug has been used to investigate the slug mechanism and anti-slug control. Most of available models are based on mass-balance formulations, which often require sufficient data for reliable parameter tuning/identification. Slug elimination and control have been investigated for many years and there exist many solutions to eliminate the slug, but some of these methods can simultaneously reduce the oil & gas production, which is a very big concern as the production rate is the key evaluation parameter for offshore production. We conclude that the slugging flow is a well-defined phenomenon, even though this subject has been extensively investigated in the past decades, the cost-effective and optimal slug modeling and control are still open topics with many related challenges.
Slugging flow in offshore oil & gas multi-phase transportation pipelines cause big challenges as the flow regime induces flow and pressure oscillations in the multi-phase pipelines. The negative impacts of the most severe slugs are significant and thus the elimination of slugging flow in the pipelines is a highly investigated topic. To eliminate the slug in an online manner real-time slug detection methods are often required. Traditionally topside pressure transmitters upstream of a 3-phase separator have been used as the controlled variable. In this paper Electrical Resistivity Tomography (ERT) has been examined as an alternative to the traditional pressure transmitters. A lab-scaled testing facility has been constructed in order to obtain test data from an ERT transmitter with 12 probes. Different flow regimes have been generated by a pump and a compressor where 2-phase flow can be tested. Based on the results, the study concludes that the ERT is able to detect the slug very well when the oil and water are well mixed. Furthermore, the traditional pressure transmitters have the limitation that pressure variations can be caused by other operating conditions than slug, such as change in the back pressure from control valves. The biggest limitation using ERT is the lack of ability to distinguish between gas and oil, and thus the ERT can only be used as an effective slug detect measurement when the oil-to-water ratio is low.
We present computations of cavitating flow over a NACA0015 hydrofoil. The simulations are performed by a finite volume compressible Euler model with dynamic mesh adaptation. The adaptive mesh refinement (AMR) is driven by a generic, simple and efficient error estimator based on the jump in value between cell faces for a given variable. It is shown that AMR based on vapour fraction provide unsatisfactory results both for (quasi-) steady and unsteady cavitation, as the major flow features are not captured. Instead, adaptivity driven by the Q-value proved successful even for resolving the cavity interface.
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.
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.