A Physical-Based Damping Model of Gap and Moonpool Resonance in WAMIT

An engineering model to estimate and incorporate quadratic damping of the piston-mode moonpool responses in the proximity of the piston mode period is proposed. The model provides a physical-based equivalent linearized damping coefficient. The method is not limited to forced motion, but applicable to freely floating moonpool vessels. Further, it is not limited to moonopools, but can be generalized to gap resonance problems, such as side-by-side operations. The soundness of the proposed physical-based method is demonstrated using the panel code WAMIT with a linear damping term in the free-surface boundary condition inside the moonpool using two existing moonpool experiments as case studies; (1) a two-dimensional rectangular box with a moonpool subject to forced heave, and (2) a freely floating offshore vessel in incident waves. The WAMIT computations using the proposed method reconstructs the experimentally obtained piston-mode and vessel responses well. We suggest that the proposed method can be used with fair degree of confidence in an early design or operational analysis phase, in the (often) case that the quadratic damping is not known from either experiments or CFD. To our knowledge, this is the first general, physical-based piston-mode damping model that does not require any tuning from experiments.acceptedVersio

Experimental study of floating bridge global response when subjected to waves and current

The present paper investigates the wave- and current-induced responses of the Bjørnafjord phase 5 K12 floating bridge concept based on small-scale model tests. Due to the extensive length of the bridge concept combined with relatively small wave heights governing the design, the experimental model represents a truncated section of the original bridge concept. This truncated section includes a stay-cable tower and ten floating pontoons supporting a horizontally curved bridge girder at varying altitude. The bridge girder truncation points coincide with the tower column and the location just above the first moored pontoon. The girder boundary conditions are simplified as fixed for all degrees of freedom (DOF) on either side of the model while allowing for free rotation around the longitudinal and vertical axes at the location above the otherwise moored pontoon. The instrumentation of the experimental model includes three DOF translational motions captured at 13 locations along the bridge and six DOF motion of each pontoon. Force transducers are used to capture axial forces in all ten tower stay-cables and at the two ends of the bridge girder, while strain gauges capture shear forces and bending- and torsional moments measured at 12 locations along the bridge girder. The dynamic properties of the model are investigated by subjecting the model to both regular waves and broad-banded, long-crested waves, propagating at two different wave directions corresponding to waves travelling in and out of the fjord. These tests are performed with and without collinear current to investigate the effect of current on the bridge responses. Subsequently, the effect of current is investigated for two important long-crested wave conditions, i.e. the 100-year wind wave condition and the 10000-year swell wave condition. For both wave conditions the model tests are performed without current and with 1-year and 10-year current velocities, respectively. Finally, the short-term response from the long-crested wind and swell wave conditions without current are compared to those of short-crested waves without current. Results show that both current and the directional distribution of the waves have a significant influence on the structural responses. It is recommended that both effects are properly accounted for in any future design.publishedVersio

Model test of a hydroelastic truncated floating bridge with a stay-cable tower

Experimental studies of long offshore and coastal structures such as very long floating bridges are challenged by the combination of coastal wave environments with relatively small design waves and excessive structural dimensions. It is often not possible to fit the entire model into the limited available space while at the same time being able to properly model the incoming waves. The sensible choice when deciding between such opposing model scale requirements, is to allow for a proper physical representation of the wave environment while finding alternatives to circumvent the space limitations. One way to do this is by truncating the original model design at carefully selected locations along the bridge and inserting passive or active boundary conditions so as to maintain similar static and dynamic properties as the prototype. The present study gives an in-depth description of the as-build experimental model of a truncated section of the Bjørnafjord phase 5 K12 concept, with simplified passive boundary conditions. The truncated section includes a complex double-curved geometry of the bridge girder connecting a cable-stayed tower at the southern end with ten floating pontoons at the northern end. The truncation points coincide with the tower column and the first moored pontoon of the full bridge. The boundary conditions in the bridge girder at the truncation points are simplified as fixed while allowing for free rotation around the vertical and longitudinal axes at the end with the otherwise moored pontoon. The truncated model is extensively instrumented in order to capture three degrees of freedom (DOF) motions at 13 locations along the bridge girder as well as six DOF motions of each pontoon. Force transducers capture the bridge girder and stay-cable axial forces, while strain gauges measure shear forces, bending moments and torque at 12 locations along the bridge girder and at each pontoon column. The present study aims at documenting fundamental properties of the as-build model in order to act as a base for future verification and calibration of design tools used for similar floating bridge concepts. This encompasses a detailed description of the complex geometry, mass and stiffness properties of the structural parts and important responses from static documentation tests. Natural periods and corresponding modal response of the first two structural modes are captured from a horizontal decay test and finally the responses from pure current tests are discussed. The present study is focused on documenting the as-build experimental model while a separate paper is to be published later on focusing on results from tests with combinations of waves and current.publishedVersio

Numerical and Experimental Studies of Resonant Flow in Moonpools in Operational Conditions

The present work is relevant for ships with moonpools. A moonpool is a vertical opening through the ship hull, typically used to descend objects into the sea. Model tests and numerical simulations are carried out to investigate the hydrodynamic interaction between ship and moonpool responses. The studies are performed in forced motion and in freely floating conditions. We investigate ships with small, moderate, and large moonpools. Four sets of model tests are carried out. In the first round, moonpools with recess are investigated in forced heave in a two-dimensional setting. The same set-up is investigated in freely floating conditions with incident waves in the second round. In the third round, moonpools without recess are investigated in both forced heave and freely floating conditions. The first three rounds of model tests are carried out in a wave flume at NTNU. These tests serve as a basis for the final and fourth round of experiments, which are carried out in the Ocean Basin at Sintef Ocean. The model tests in the Ocean Basin are the main part of the present work, where we investigate the hydrodynamic interaction between ship and moonpool responses in a three-dimensional setting. The experiments in the Ocean Basin are carried out with a ship model that resembles a real ship, with three different moonpool sizes. By that, we investigate the importance of the moonpool-to-ship-volumeratio on the hydrodynamic interaction between ship and moonpool responses, both in regular and irregular waves. Two numerical solvers are implemented in the present thesis work; a two-dimensional time-domain boundary element method (BEM) code solving the linearized potential flow problem and a two-dimensional hybrid solver combining Navier–Stokes and potential flow solvers. These solvers are used to estimate the moonpool and ship responses, and the numerical simulations are compared against the model tests that are carried out in an idealized two-dimensional setting. WAMIT and an existing hybrid Navier–Stokes solver (PVC3D) are used to perform numerical simulations in 3D. Based on the model tests and numerical simulations, we see that the moonpool and ship responses are strongly coupled for ships with moderate and large moonpools. For small moonpools, the hydrodynamic interaction between ship and moonpool responses is almost negligible. The importance of damping due to flow separation at the moonpool entrance is discussed, both at the piston and sloshing modes. Several nonlinear free-surface effects are discussed, such as Duffing-type moonpool responses, swirling and secondary resonance, where most of them occur in a relevant wave period range with respect to ocean waves in the North Sea

Coupled vessel and moonpool responses in regular and irregular waves

Hydrodynamic coupling between the ship and moonpool responses is investigated. Dedicated experiments are carried out in the Ocean Basin at Sintef Ocean. Three different moonpool sizes are studied, where the moonpool length is 1/20, 1/10 and 1/2 of the ship length. The two former are square moonpools, while the latter is a rectangular moonpool with a width 1/2 of the ship’s beam. Numerical simulations are carried out using WAMIT. The coupling between the ship and moonpool is seen to be highly dependent on the volume of the moonpool relative to the submerged ship volume. WAMIT greatly over-predicts the moonpool responses in the proximity of resonance, which indicates that wave radiation damping is small, and that damping due to flow separation at sharp edges at the moonpool entrance is dominant. Two main nonlinear effects are observed; Swirling-type sloshing and secondary resonance. These nonlinear effects are excited in a range of wave periods where it is expected that a realistic sea environment will contain significant wave energy. This is most prominent in the largest moonpool. The piston mode shape in freely floating conditions is signficantly different relative to the one in forced heave.publishedVersio

A two-dimensional numerical and experimental study of piston and sloshing resonance in moonpools with recess

International audienceThe piston and first sloshing modes of two-dimensional moonpools with recess are investigated. Dedicated forced heave experiments are carried out. Different recess lengths are tested from 1/4 to 1/2 of the length of the moonpool at the mean waterline. A theoretical model to calculate the natural frequencies is developed based on linearized potential flow theory and eigenfunction expansion. Two numerical methods are implemented: a boundary element method (BEM) and a Navier-Stokes solver (CFD). Both the BEM and CFD have linearized free-surface and body-boundary conditions. As expected, the BEM over-predicts the moonpool response significantly, in particular at the first sloshing mode. The CFD is in general able to predict the maximum moonpool response adequately, both at the piston and first sloshing modes. Both numerical methods fail to predict the Duffing-type behaviour at the first sloshing mode, due to the linearized free-surface conditions. The Duffing behaviour is more pronounced for the largest recess. The main source of damping in the proximity of the first sloshing mode is discussed