Nonlinear Potential Flow Solver Research Articles

An efficient domain decomposition strategy for wave loads on surface piercing circular cylinders

A fully nonlinear domain decomposed solver is proposed for efficient computations of wave loads on surface piercing structures in the time domain. A fully nonlinear potential flow solver was combined with a fully nonlinear Navier–Stokes/VOF solver via generalized coupling zones of arbitrary shape. Sensitivity tests of the extent of the inner Navier–Stokes/VOF domain were carried out. Numerical computations of wave loads on surface piercing circular cylinders at intermediate water depths are presented. Four different test cases of increasing complexity were considered; 1) weakly nonlinear regular waves on a sloping bed, 2) phase-focused irregular waves on a flat bed, 3) irregular waves on a sloping bed and 4) multidirectional irregular waves on a sloping bed. For all cases, the free surface elevation and the inline force were successfully compared against experimental measurements.

3-D seakeeping analysis with water on deck and slamming. Part 1: Numerical solver

A three-dimensional seakeeping numerical solver is developed to handle occurrence and effects of water-on-deck and bottom slamming. It couples (A) the rigid-ship motions with (B) the water flowing along the deck and (C) bottom slamming events. Problem A is studied with a 3-D weakly nonlinear potential flow solver based on the weak-scatterer hypothesis. Problem B, and so local and global induced green-water loads, are investigated by assuming shallow-water conditions onto the deck. Problem C is examined through a Wagner-type wedge-impact analysis. Within the coupling between A and B: the external seakeeping problem furnishes the initial and boundary conditions to the in-deck solver in terms of water level and velocity along the deck profile; in return the shallow-water problem makes available to the seakeeping solver the green-water loads to be introduced as additional loads into the rigid-motion equations. Within the coupling between A and C: the instantaneous ship configuration and its kinematic and dynamic conditions with respect to the incident waves will fix the parameters for the local impact problem; in return the slamming and water-entry pressures are integrated in the vessel region of interest and introduced as additional loads into the rigid-motion equations. The resulting numerical solver can study efficiently the ship interaction with regular and irregular sea states and the forward motion with limited speed of the vessel. This is crucial to perform reliable and feasible statistical investigations of vessel behavior. Main elements of the solver are described and validated against reference numerical solutions and model tests.

Did the Draupner wave occur in a crossing sea?

The ‘New Year Wave’ was recorded at the Draupner platform in the North Sea and is a rare high-quality measurement of a ‘freak’ or ‘rogue’ wave. The wave has been the subject of much interest and numerous studies. Despite this, the event has still not been satisfactorily explained. One piece of information that was not directly measured at the platform, but which is vital to understanding the nonlinear dynamics is the wave's directional spreading. This paper investigates the directionality of the Draupner wave and concludes it might have resulted from two wave-groups crossing, whose mean wave directions were separated by about 90 ° or more. This result has been deduced from a set-up of the low-frequency second-order difference waves under the giant wave, which can be explained only if two wave systems are propagating at such an angle. To check whether second-order theory is satisfactory for such a highly nonlinear event, we have run numerical simulations using a fully nonlinear potential flow solver, which confirm the conclusion deduced from the second-order theory. This is backed up by a hindcast from European Centre for Medium-Range Weather Forecasts that shows swell waves propagating at approximately 80 ° to the wind sea. Other evidence that supports our conclusion are the measured forces on the structure, the magnitude of the second-order sum waves and some other instances of freak waves occurring in crossing sea states.

Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrödinger equation-based model

This paper sets out an approximate analytical model describing the nonlinear evolution of a Gaussian wave group in deep water. The model is derived using the conserved quantities of the cubic nonlinear Schrödinger equation (NLSE). The key parameter for describing the evolution is the amplitude-to-wavenumber bandwidth ratio, a quantity analogous to the Benjamin–Feir index for random sea-states. For smaller values of this parameter, the group is wholly dispersive, whereas for more nonlinear cases, solitons are formed. Our model predicts the characteristics and the evolution of the groups in both regimes. These predictions are found to be in good agreement with numerical simulations using the NLSE and are in qualitative agreement with numerical results from a fully nonlinear potential flow solver and experimental results.

Surface Ship Total Resistance Prediction Based on a Nonlinear Free Surface Potential Flow Solver and a Reynolds-Averaged Navier-Stokes Viscous Correction

A fast turnaround and an accurate computational fluid dynamics (CFD) approach for ship total resistance prediction is developed. The approach consists of a nonlinear free surface potential flow solver (PShip code) with a wet-or-dry transom stern model, and a Reynolds-averaged Navier-Stokes (RANS) equation solver that solves viscous free surface flow with a prescribed free surface given from the PShip. The prescribed free surface RANS predicts a viscous correction to the pressure resistance (viscous form) and viscous flow field around the hull. The viscous free surface flow solved this way avoids the time-consuming RANS iterations to resolve the free surface profile. The method, however, requires employing a flow characteristic-based nonreflecting boundary condition at the free surface. The approach can predict the components of ship resistance, the associated wave profile around the hull, and the sinkage and trim of the ship. Validation of the approach is presented with Wigley, Series 60 (CB = 0.6), and NSWCCD Model 5415 hulls. An overall accuracy of ±2% for ship total resistance prediction is achieved. The approach is applied to evaluating the effects of a stern flap on a DD 968 model on ship performance. An empirical viscous form resistance formula is also devised for a quick ship total resistance estimate.