This research concentrates on damage ship stability and means for assessing dynamic ship performance in this state. A consolidation of many approaches for tackling damage ship dynamics has been undertaken, culminating in the development of a numerical tool for simulating ship behaviour while accounting for progressive flooding and the ensuing effects of floodwater motion. General features that have been accounted for in a new purposely developed numerical program PROTEUS3 include the following: Linear concepts regarding intact ship hydrodynamics based on strip theory and Rankine source method (RSM). These are further utilised by convolution and spectral transformations in deriving relevant time domain force realisations. Non-linear excitation/restoring forces calculated from pressure integration up to the instantaneous undisturbed wave profile. Non-linearities in hydrodynamic properties arising from variation of mean underwater geometry due to occurrence of non-stationary asymm etries in mass distribution are taken into account by a database approach. Forward speed in arbitrary heading. Progressive flooding through a ship with any internal subdivision and floodwater motion simulations based on free-mass-on-potential-surface (FMPS) model. Non-linear treatment of the effects of cargo shift or floodwater motions on the overall ship dynamic behaviour. The underlying modelling has been explained by rigorous derivation of all the relevant equations from first principles. Validity of the model has been tested comprehensively through comparison with available physical model tests data. A thorough investigation on the new effects of modelling advancements concerning the accuracy of the developed model has been undertaken and the results are presented and discussed. Despite the introduction of simplifying assumptions concerning floodwater behaviour, the predictions show consistency with physical experimental data. It is believed that this pragmatic approach constitutes a very efficient tool for predictions of vessel performance in extremely adverse conditions. This effectiveness has been demonstrated by undertaking forensic analysis of two of the most controversial accidents of the last two decades, namely the loss of MV Derbyshire and the NW Estonia disaster.

Three interrelated topics in ship hydrodynamics - resistance, wave-making and wave decay - are investigated in an attempt to improve the accuracy of some simple methods used in the preliminary design of thin ships. Several published sets of data from classical and recent boundary layer experiments on flat plates are used to estimate boundary layer quantities such as thicknesses and eddy viscosities. These quantities are subsequently used to modify the hull shape and the free-surface boundary condition as a means of including viscous effects on wave-making and ship-wave decay. A recent technique is used to analyse 161 experimental flat-plate turbulent boundary layer velocity profiles, and a new skin-friction line is derived. Some practical methods are proposed for the numerical quadrature of integrals arising in thin-ship hydrodynamics. We demonstrate that for some integrals, rapid oscillation, rather than being a hindrance to accurate quadrature, can actually be beneficial if appropriate techniques are employed. We find that boundary layer displacement thickness effects on wave resistance are very small and can be safely ignored for full-size vessels. On the other hand, the idea of a detachment layer, an indication of where the boundary layer begins to thicken rapidly, is shown to have a significant effect on wave resistance. A modification to the Kelvin free-surface boundary condition is used as a means of including viscous effects on wave-making. Detailed comparisons of total resistance predictions and experiments are made for three model-size Wigley hulls. It is shown that inclusion of viscous effects smooths out the well-known humps and hollows in the wave resistance curves calculated using Michell's (inviscid) integral. Predictions of the total resistance of a model Wigley hull using Michell's integral and a simple skin-friction line are shown to be as good as those of a modern CFD computer code. Furthermore, the simple method does so in a very small time on an inexpensive computer. The effect of employing a form factor on the skin-friction is shown to improve correlations between resistance predictions and experiments. It has recently been proposed that a form factor should also be applied to the wave resistance. We show that good predictions are indeed possible, but that the use of a modified form of Michell's integral and an “appropriate" value of the eddy viscosity leads to even better agreement. Two existing wave-decay models are examined and a new formulation is suggested that combines the theoretical – 1/2 decay rate of transverse waves with the -1/3 decay rate of diverging waves. The effects of viscosity on ship-wave decay are considered. It is found that large values of the viscosity, of the order required to have a significant effect on wave resistance, lead to an over-damping of far-field waves at low Froude numbers. We show that it may be possible to get a rough estimate of the (ambient) eddy viscosity from an analysis of the decay of ship-waves with transverse distance from the sailing line, without resorting to computationally expensive Fourier transform methods. Three wave decay models are used to estimate the eddy viscosity from the behaviour of the wave decay. The model that uses the theoretical decay rates of transverse and of diverging waves is found to be slightly better at recapturing the original eddy viscosity than the other two models. / Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2009

Bubbly flows around ships have been studied for years, mostly in relation with ship acoustic signatures. Bubbles are generated at the bow and shoulder breaking waves, at the hull/free surface contact line, the propeller and the highly turbulent stern flow. These bubbles are further transported downstream by the flow forming a two-phase mixture in the wake that can be kilometers long. The presence of bubbles in the wake of a ship significantly affects the acoustic response of the medium and can be detected by measuring acoustic attenuation and backscattering making a ship vulnerable to detection. Additionally, the bubbly wake shows at the surface as a characteristic signature of white water, and given the length of the bubbly wake, it makes a ship visible from satellites. Therefore, the bubbly wake can be used to detect and identify surface ships. Bubbly flows do not scale to model scale experiments, and experiments on full scale ships are scarce mostly due to difficult access areas and the high speeds involved. It is therefore of interest to simulate the bubbly flow around ships to provide information difficult, if not impossible, to obtain with experiments. This work presents the development of a code for the simulation of polydispersed bubbly flows with a focus on ship hydrodynamics. The mathematical model implemented is based on a two-fluid formulation coupled with a Boltzmann-like transport equation describing the bubbly phase. The tool developed attempts to include most of the relevant physics of the problem to represent better the conditions of real scenarios. The resulting code allows the simulation of polydispersed bubbly flows in situations including free surface and air entrainment, high void fraction levels and moving control surfaces and propulsors. The code is two-way coupled, with a strong coupling between the two phases and between the bubble sizes. The complexity of the problems tackled in this research required the development of novel numerical methods solving issues never identified before or simply neglected. These methods play an essential role in the accuracy, robustness and efficiency of the code and include: a two-phase projection method that not only couples pressure and velocity but also implicitly couples void fraction, a time splitting marching scheme to solve separately coupling in space and in bubble sizes, and a stable numerical method to integrate the strong coupling introduced by collision forces. The implemented code is applied to the simulation of the bubbly flow around a full scale ship using the latest available models and computational techniques. A study is performed on the influence of several mechanisms on the predicted bubbly wake and comparisons with available experimental data are presented. The influence of breakup in the boundary layer is analyzed in detail as well. In addition, this work identifies several modeling and implementations issues and attempts to provide a path for future studies. To illustrate the flexibility and robustness of the code, a final demonstration case is presented that includes rotating propellers. The computation is performed at full scale, with the fully appended geometry of the vessel and includes incoming waves, oceanic background and rectified diffusion models. Many of these features are unique to this computation and make it the first of its kind.

A high fidelity computational fluid dynamics approach to perform direct simulations of ship maneuvers is presented in this thesis. The approach uses dynamic overset grids with a hierarchy of bodies to enable arbitrary motions between objects, and overcome the difficulties in simulation of the moving rudder and rotating propeller. To better resolve propeller/rudder interaction a Delayed Detached Eddy Simulation turbulence model based on Menter’s SST is used. The methodology was implemented in the general purpose RANS/DES/DDES research code REX, and is applied to the KRISO Container Ship (KCS) with moving rudder and rotating propeller in deep and shallow water. For the first time, a grid study is conducted for the self-propulsion condition for the propeller RPM, thrust, torque and lateral force, and for the roll and pitch motions, using grids of 8.7 (coarse), 24.6 (medium) and 71.3 (fine) million points. A grid study is also performed for the zigzag maneuver evaluating the maximum and minimum values of propeller thrust, torque and lateral force roll, pitch, yaw, roll rate, yaw rate and drift throughout the maneuver. An extensive comparison between predicted motions and forces of the direct simulations and the experimental data collected by Schiffbau-Versuchsanstalt Potsdam GmbH (SVA) and Flanders Hydraulics Research (FHR) are presented. While the results and comparisons with experimental data show that using direct CFD to compute modified and standard maneuvers with moving rudder and rotating discretized propeller is feasible, computational cost remains an impediment for many practical applications. Coupling a dynamic overset CFD solver with a potential propeller code can dramatically reduce the computational time to perform maneuvering simulations by using one order of magnitude larger time step than direct simulation. This thesis investigates the ability of a coupled CFD/potential propeller code approach to simulate maneuvers in ships, where the rudder is located downstream of the propeller. While the approach has been successfully applied to submarine maneuvers, in which the propeller wake is free of interference, the concept had not been evaluated before for cases where an object (the rudder) is immersed in the wake. The study is performed using the CFD code REX and the propeller code PUF-14. Performance of the coupled REX/PUF-14 approach is first tested studying propeller/rudder interaction, evaluating influence of the propeller/rudder gap size and rudder deflection on propeller performance curves and rudder forces, comparing against DDES simulations with a discretized rotating propeller. A grid study was performed for advance coefficient J=0.6 and a rudder angle δ=20 degrees for a propeller rudder gap of 0.2 times the rudder radius, with the resulting grid uncertainties for propeller thrust and torque coefficients suggesting that the effects of the grid changes are small for the present range of grid sizes. A 15/1 zigzag maneuver for the KCS container ship, in which case the rudder is very close downstream of the propeller, is then analyzed, and compared against discretized propeller simulations and experimental data. Self-propulsion coupled REX/PUF-14 results agree very well with experiments and discretized propeller simulations. Prediction of motions, forces and moments, and mean flow field with the coupled REX/PUF-14 approach are comparable to results obtained with discretized propeller simulations and agree with experiments well, though as implemented the coupled approach is unable to resolve tip vortices and other flow structures that interact with the rudder, potentially affecting prediction of flow separation. It can be concluded that coupled CFD/potential flow propeller approaches are an effective and economical way to perform direct simulation of surface ship maneuvers with CFD.

High-fidelity CFD-MBD FSI (Computational Fluid Dynamics - Multi Body Dynamics Fluid-Structure Interaction) code development and validation by full-scale experiments is presented, for a novel hull form, WAM-V (Wave Adaptive Modular Vessel). FSI validation experiments include cylinder drop with suspended mass and 33 ft WAM-V sea-trials. Calm water and single-wave sea-trails were with the original suspension, while the rough-water testing was with a second generation suspension. CFDShip-Iowa is used as CFD solver, and is coupled to Matlab Simulink MBD models for cylinder drop and second generation WAM-V suspension. For 1DOF cylinder drop, CFD verification and validation (V&V) studies are carried out including grid and time-step convergence. CFD-MBD results for 2DOF cylinder drop show that 2-way coupling is required to capture coupled physics. Overall, 2-way results are validated with an overall average error value of E=5.6%DR for 2DOF cylinder drop. For WAM-V in calm water, CFD-MBD 2-way results for relative pod angle are validated with E=14.2%DR. For single-wave, CFD-MBD results show that 2-way coupling significantly improves the prediction of the peak amplitude in pontoon motions, while the trough amplitudes in suspension motions are under-predicted. The current CFD-MBD 2-way results for single-wave are validated with E=17%DR. For rough-water, simulations are carried out in regular head waves representative of the irregular seas. CFD-MBD 2-way results are validation with E=23%D for statistical values and the Fourier analysis results, which is reasonable given the differences between simulation waves and experiments.

This thesis presents two important contributions to the modeling of entrainment of air bubbles in water, with focus on ship hydrodynamics applications. The first contribution consists of a general framework for modeling turbulent air entrainment. The framework attempts to describe the evolution of bubbles from their formation at the free surface, size distribution changes due to breakup and coalescence, and rise due to buoyancy. This proposed framework describes the complex entrainment process as a series of simpler mechanisms which can be modeled independently. For each mechanism a simple but mechanistic model is developed to provide closure while leaving the door open for future improvements. These unique characteristics enable the entrainment model to be used in general problems while still producing results at least as good as the few other available models. The massive entrainment of air that takes place around a ship leads to very high void fractions and accumulation of bubbles against the hull, particularly underneath the flat regions of the hull and in low pressure regions near appendages. These processes also pose challenges for two phase solvers. As a second contribution in this thesis, numerical algorithms for two phase flows are developed to eliminate the numerical instabilities normally occurring at high void fractions or large void fraction gradients. A hybrid method to improve pressure-velocity coupling for collocated grids is introduced, which keeps advantages typical of staggered grids in mass conservation and face flux computations. A new two phase coupling strategy is developed to guarantee stability at high void fraction. The balanced force method is extended to general curvilinear grids to suppress spurious velocities. The overall methodology provides strong coupling among pressure, velocity and void fraction, while avoiding numerical instability, and works for free-surface flows on dynamic overset grids. The proposed numerical schemes are tested for 1D and 2D cases. It is shown that the two phase solver is stable and efficient, even under extreme cases. Good mass conservation properties for multigroup simulations are also demonstrated. The air entrainment model is tested for a 2D wave breaking case and compared with extensive experimental data. The results show good predictions for entrainment location and two-phase properties. Full scale simulations for Athena R/V are performed using the same modeling constants obtained for the 2D wave breaking case. A grid study is also carried out to evaluate grid convergence properties of the model. While the model can predict well experimental data at full scale for the ship, it also shows dramatic improvements respect to previous entrainment models by converging in grid and not needing to re-evaluate the model constants for each new application. The high-speed Kann boat is also simulated at full scale, showing encouraging results for a preliminary entrainment model for aeration due to impact. The proposed numerical schemes are proved stable and robust in high Reynolds number flows with complex relevant geometries. In addition, these full scale simulations also identify modeling and numerical issues for future improvements.

A computational fluid dynamics (CFD) methodology is presented to predict density stratified flows in the near-field of ships and submarines. The density is solved using a higher-order transport equation coupled with mass and momentum conservation. Turbulence is implemented with a k-ε/k-ω based Delayed Detached Eddy Simulation (DDES) approach, enabling explicit solution of larger energy-containing vortices in the wake. Validation tests are performed for a two-dimensional square cavity and the three-dimensional stratified flow past a sphere, showing good agreement with available data. The near-field flow of the self-propelled Research Vessel Athena advancing in a stably stratified fluid is studied, as well as the operation in stratified flow of the notional submarine Joubert BB2 also in self-propelled condition. The resulting density, velocity, pressure and turbulent quantities at the exit plane of the near-field computation contain a description of the relevant scales of the flow and can be used to compute the far-field stratified flow, including internal waves. The generation of internal waves is shown in the case of the submarine for two different conditions, one with the pycnocline located at the propeller centerline, and the second with the pycnocline located slightly below the submarine, concluding that distance to the pycnocline strongly affects the internal wave generation due to the presence of the vessel. It is also shown that, as in the case of surface waves, the generation of internal waves requires energy that results in an increase in resistance. For the case of the surface ship the near field wakes are mostly affected by the separation at the wet transom and propeller mixing. However, in the case of the underwater vessel, the disturbance of the background density profile by the presence of the submarine affects the near-field wakes. Finally, the dead-water phenomenon, which occurs at very low Froude numbers, is studied for R/V Athena. Though the dead water problem has been studied in the literature using potential flow methods, this thesis presents the first attempt at using computational fluid dynamics (CFD) to analyze the flow. Results show that, while CFD can reproduce trends observed in potential flow studies, viscous effects are significant in the wake and the friction coefficient.

Although the capability of computational fluid dynamics (CFD) in modeling ship hydrodynamics is well explored in many studies, they still have two main limitations. First, those studies ignore the effect of non-uniform shear current which exists in realistic situation. Second, the focus of most studies was laid more on the seakeeping/maneuvering performance and less attention was paid to survivability of ships due to extreme ship response events in waves, which are considered rare events but influential. In this thesis, we explore the capability of CFD in those two areas. In the first part of the thesis, the hydrodynamic performance of KCS in the presence of a non-uniform shear current is investigated for the first time using high-fidelity CFD simulations. Various shear current conditions with different directions were considered and results were compared with the ones with no shear current. The second part of the thesis focuses on study of rare events of ship responses by development of extreme response conditioning techniques to design the wave trail. Two conditioned techniques based on Gaussian and non-Gaussian processes are considered.

The effects of winds and/or waves on ship motions, forces, moments, maneuverability and controllability are investigated with URANS computations. The air/water flow computations employ a semi-coupled approach in which water is not affected by air, but air is computed assuming the free surface as a moving immersed boundary. The exact potential solution of waves/wind problem is modified introducing a logarithmic blending in air, and imposed as boundary and initial conditions. The turbulent air flows over 2D water waves are studied to investigate the effects of waves on incoming wind flow. Ship airwake computations are performed with different wind speeds and directions for static drift and dynamic PMM in calm water, pitch and heave in regular waves, and 6DOF motions in irregular waves simulating hurricane CAMILLE. Ship airwake analyses show that the vortical structures evolve due to ship motions and affect the ship dynamics significantly. Strong hurricane head and following winds affect up to 28% the resistance and 7% the motions. Beam winds have most significant effects causing considerable roll motion and drift forces, affecting the controllability of the ship. A harmonic wave group single run seakeeping procedure is developed, validated and compared with regular wave and transient wave group procedures. The regular wave procedure requires multiple runs, whereas single run procedures obtain the RAOs for a range of frequencies at a fixed speed, assuming linear ship response. The transient wave group procedure provides continuous RAOs, while the harmonic wave group procedure obtains discrete transfer functions, but without focusing. Verification and validation studies are performed for transient wave group procedure. Validation is achieved at the average interval of 9.54 (%D). Comparisons of the procedures show that harmonic wave group is the most efficient, saving 75.8% on the computational cost compared to regular wave procedure. Error values from all procedures are similar at 4 (%D). Harmonic wave group procedure is validated for a wide range of Froude numbers, with satisfactory results. Deterministic wave groups are used for three sisters rogue waves modeling. A 6DOF ship simulation is demonstrated which shows total loss of controllability with extreme ship motions, accelerations and structural loads.

When traditional linearised theory is used to study free-surface flows past a surface-piercing object or over an obstruction in a stream, the geometry of the object is usually lost, having been assumed small in one or several of its dimensions. In order to preserve the nonlinear nature of the geometry, asymptotic expansions in the low-Froude or low-Bond limits can be derived, but here, the solution invariably predicts a waveless free-surface at every order. This is because the waves are in fact, exponentially small, and thus beyond-all-orders of regular asymptotics; their formation is a consequence of the divergence of the asymptotic series and the associated Stokes Phenomenon. In this thesis, we will apply exponential asymptotics to the study of two new problems involving nonlinear geometries. In the first, we examine the case of free-surface flow over a step including the effects of both gravity and surface tension. Here, we shall see that the availability of multiple singularities in the geometry, coupled with the interplay of gravitational and cohesive effects, leads to the discovery of a remarkable new set of solutions. In the second problem, we study the waves produced by bluff-bodied ships in low-Froude flows. We will derive the analytical form of the exponentially small waves for a wide range of hull geometries, including single-cornered and multi-cornered ships, and then provide comparisons with numerical computations. A particularly significant result is our confirmation of the thirty-year old conjecture by Vanden-Broeck & Tuck (1977) regarding the impossibility of waveless single-cornered ships.