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Two numerical particle models, the Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi-implicit (MPS) methods, coupled with a sub-particle scale (SPS) turbulence model, are presented to simulate free surface flows. Both SPH and MPS methods have the advantages in that the governing Navier¿Stokes equations are solved by Lagrangian approach and no grid is needed in the computation. Thus the free surface can be easily and accurately tracked by particles without numerical diffusion. In this paper different particle interaction models for SPH and MPS methods are summarized and compared. The robustness of two models is validated through experimental data of a dam-break flow. In addition, a series of numerical runs are carried out to investigate the order of convergence of the models with regard to the time step and particle spacing. Finally the efficiency of the incorporated SPS model is further demonstrated by the computed turbulence patterns from a breaking wave. It is shown that both SPH and MPS models provide a useful tool for simulating free surface flows.

This study aimed to understand the processes that govern free surface behaviour in depth-limited turbulent flows. Experimental data has shown that the turbulence properties at a point near the free surface relate directly to the properties of the free surface pattern. This would suggest a direct linkage between the free surface and the underlying turbulence field, but this cannot be true since the free surface pattern is strongly dynamic while the sub-surface turbulence field is relatively persistent. An oscillatory spatial correlation function was derived which explains the de-linkage, showing that the turbulence-generated surface pattern periodically inverts as it advects downstream. A model was developed, which shows that the observed free surfaces can be considered as an ensemble of overlapping but behaviourally independent oscillons. These are shown to influence a zone of fluid beneath the surface and invert at a frequency which is a function of the root-mean-square roughness height of the free surface. The spatial frequency of free surface oscillation relates strongly to the spatial frequency of turbulent structures, suggesting that the oscillon motion may form the trigger for near-bed bursting events. Given these relationships, it is proposed that measurement of the free surface behaviour may allow remote measurement of flow conditions. An acoustic wave probe was developed, which is able to remotely recover the key features of the water surface pattern. An array of such probes is proposed for the accurate measurement of temporal and spatial properties of turbulent free surfaces and hence the underlying bulk flow conditions.

<p> </p> <p>Interfaces separating two fluids are incredibly complex physical structures and are common throughout science, technology, and nature. Examples from daily life include the air-water interface separating a water drop that is dripping from a leaky faucet from the surrounding air and the interface of a soap bubble (which actually consists of two interfaces) separating the interior of the bubble from its exterior. Other common examples from nature include interfaces between falling rain drops and the surrounding air, and the mist that one encounters at beaches, waterfalls, and fountains where the spray droplets are separated from the surrounding air by an interface. Interfaces and manipulating them are key to technological applications such as thin film coating flows and diverse processes involving drop-by-drop processing such as ink-jet printing, drop-wise manufacturing, spray coating, DNA microarraying, and chemical separations, e.g. extraction. Aside from the coating flows example, the aforementioned situations are all examples of free surface flows that involve abrupt and catastrophic topological changes of interfaces that include physical processes such as breakup (also called pinch-off) as in drop breakup, rupture as in liquid-film or liquid-sheet rupture, and coalescence as in drop or bubble coalescence (similar phenomena also arise in sintering and/or fusion of ceramic, metallic, and polymer particles). These topological changes entail what are referred to as finite-time hydrodynamic singularities. For example, at the location(s) where a drop breaks, the thickness of the drop locally tends to zero while fluid pressure and velocity diverge (hence the reason for the word singularity). In addition to hydrodynamic singularities, the presence of surface-active agents or surfactants at fluid interfaces in free surface flows is another reason scientists have been attracted to the study of such problems.</p> <p>Adsorption onto and lowering of the surface tension of a fluid interface by surfactants are exploited in applications such as enhanced oil recovery, coating flows, lung surfactants, drop/jet breakup, and film/sheet rupture, with the latter two being among the prime motivators for this PhD thesis. However, surfactant concentration can be nonuniform at the interface because surfactant molecules can be transported along it by convection and diffusion and also due to normal dilatation and tangential stretching of the interface. Thus, aside from simply lowering surface tension, nonuniformity in surfactant concentration causes gradients in surface tension and gives rise to tangential interfacial (Marangoni) stresses. The latter brings about rich physics including tears of wine, interfacial turbulence in mass transfer, and droplet bouncing. In addition to lowering surface tension and the Marangoni effect, surfactants may also induce surface rheological or viscous effects as surfactant molecules deform against each other. The primary goal of this thesis is to advance the understanding of surface rheological effects in situations involving the breakup of surfactant-covered liquid threads (which also includes jets and drops) and liquid sheets. The fundamental understanding developed in this thesis is likely to prove indispensable in and/or assist the development of new technologies where surface rheological effects are central to the processes at hand, e.g. in controlling drop size distributions and avoiding undesirable satellite droplets and/or misting. An initially unexpected but highly rewarding outcome of the research has been the development of techniques for the measurement of surface viscosities, a task that has heretofore proven to be a formidable challenge to experimentalists.</p> <p>In this thesis, surface rheological effects in free surface flows are examined through both analytical and numerical solution of the incompressible Navier-Stokes equations subjected to the traction boundary condition augmented by the Boussinesq-Scriven constitutive equation to account for surface viscous effects. Rigorous and robust numerical algorithms based on the Galerkin finite element (GFEM) method are developed for predictions of surfactant transport, surface rheological effects and hydrodynamics in response to the motion of moving boundaries. The accuracy of computational predictions is verified by demonstrating that computed results accord well with scaling theories.</p>

The predictive capabilities of blade-resolved unsteady Reynolds averaged Navier-Stokes (URANS) and detached eddy simulation (DES), the most commonly used hybrid RANS/large eddy simulation (LES) model, are assessed for hydrokinetic turbine performance and mean and turbulent flows in the intermediate-wake region, and results for a range of tip-speed ratio encompassing design and off-design conditions are analyzed to understand the wake recovery mechanism. The performance predictions compared within 5% of the experimental data. Both URANS and DES models performed reasonably well for the near wake predictions, where the errors were < 15%. DES outperformed URANS for both mean wake deficit and turbulence predictions in the intermediate-wake region and both quantities compared within 10% of the experiments. The improved prediction by DES is because of 1) its ability to predict the tip vortex breakdown, which plays a critical role in the wake recovery, especially for higher tip speed ratios; 2) the presence of the free-surface which created an upper bypass region of accelerated flow. The study reveals that the tip vortex breakdown mechanism depends on tip speed ratio. For lower values of tip speed ratio, instabilities generated in the root vortex core are identified to be the cause of breakdown. For higher values, the breakdown occurred because of the instabilities generated during the vortex filament entanglement. The presence of the free-surface led to an early vortex breakdown and the interaction between the wake and free-surface is initiated by the interaction of stanchion with the free-surface. Future work should focus on investigation of other hybrid RANS/LES models to address the limitations of the DES models, and extension of the study to include wave effects.

In this thesis the impact of inverted cones on a liquid surface is studied. It is known that with the right combination of velocity, geometry, and surface treatment, a cavity of air can be formed behind an impacting body and extended for a considerable distance. Other investigators have shown that the time and depth of the cone when this cavity collapses and seals follows a different power law for flat objects such as disks, then it does for slender objects such as cylinders. Intuitively it can be expected that a more slender body will have less drag and that the streamlined shape will not push the fluid out of it's way at impact to the same extent as a more blunt body, therefore forming a smaller cavity behind it. With a smaller initial cavity, the time and depth of it's eventual collapse can be expected to be less than that of a much more blunt object, such as a flat disk. To study this, a numerical model has been developed to simulate cones with the same base radius but different angles impacting on a liquid surface over a range of velocities, showing how the seal depth, time at cavity seal, and drag forces change. In order to ensure the numerical model is accurate, it is compared with experimental data including high speed video and measurements made of the force with time. It is expected that the results will fall inside the power law exponents reported by other authors for very blunt objects such as disks on one end of the spectrum, and long slender cylinders on the other. Furthermore, we expect that the drag force exerted on the cones will become lower as the L/D of the cone is increased. / Master of Science

This thesis presents the results from the computational fluid dynamics simulations of surface effect ship model tests. The model tests being simulated are of a generic T-Craft model running in calm seas through a range of Froude numbers and in two head seas cases with regular waves. Simulations were created using CD-adapco's STAR-CCM+ and feature incompressible water, compressible air, pitch and heave degrees of freedom, and the volume of fluid interface-capturing scheme. The seals are represented with rigid approximations and the air cushion fans are modeled using constant momentum sources. Drag data, cushion pressure data, and free surface elevation contours are presented for the calm seas cases while drag, pressure, heave, and roll data are presented for the head seas cases. The calm seas cases are modeled both with no viscosity and with viscosity and turbulence. All simulations returned rather accurate estimations of the free surface response, ship motions, and body forces. The largest source of error is believed to be due to the rigid seal approximations. While the wake's amplitude is smaller when viscosity is neglected, both viscous and inviscid simulations' estimations of the free surface qualitatively match video footage from the model tests. It was found that shear drag accounts for about a quarter of the total drag in the model test simulations with viscosity, which is a large source of error in inviscid simulations. Adding the shear drag calculated using the ITTC-1957 friction coefficient line to the total drag from the inviscid simulation gives the total drag from the viscous simulations within a 6% difference. / Master of Science

In this dissertation, an approach for determining parameters for a nonlinear Lagrangian mechanical system model of a submerged vessel maneuvering near waves is presented. The nonlinear model with determined parameters is capable of capturing nonlinear effects neglected by other linear models, and therefore can be applied to improve maneuvering performance and expand the operating envelope for submerged vessels operating in elevated sea states. To begin, a first principles Lagrangian nonlinear maneuvering (LNM) model for a surface-affected submerged vessel derived by using Lagrangian mechanics cite{BattistaPhD2018} is reformulated to allow the application of data from a medium fidelity potential flow code. In the reformulation process, the order of integration and differentiation in the integro-differential parameters are switched and partial derivatives of the Lagrangian function are computed with readily available data from the panel code solution. As a result, all model parameters can be computed individually using the panel code, wherein the need for additional numerical discretization is circumvented in the computation process through use of solutions already performed by the basic panel code, enabling higher accuracy and lower computational cost. Furthermore, incident wave effects are incorporated into the reformulated LNM model to yield a Lagrangian nonlinear maneuvering and seakeeping (LNMS) model. The LNMS model is numerically validated by confirming the proposed methods and by comparing steady and unsteady hydrodynamic force calculations from the LNMS model against panel code computations for various vessel motions in calm water and in plane progressive waves. Finally, methods for computing physically intuitive components of the model parameters, as well as methods for making approximations of the terms accounting for memory effects are presented, leading to a model formulation amenable to control design. By applying the methods proposed in this dissertation, each and every parameter of the Lagrangian mechanical system model of a submerged vessel maneuvering in waves can be obtained accurately and with computational efficiency by using a potential flow panel code. The resulting nonlinear motion model provides higher model fidelity than existing unified maneuvering and seakeeping models, especially in applications such as nonlinear control design and simulation. / Doctor of Philosophy / A unified maneuvering and seakeeping model for a submerged vessel maneuvering near waves describes mathematically the relationship between input values to the dynamical system, such as thrust from the propulsors, and output values from the system, such as the position and orientation of the vessel. This unified model has a wide range of applications, ranging from vessel hull form optimization in the early design phase to motion controller tuning after the vessel has been constructed. In order for a unified model to make accurate predictions, for instance, for a submerged vessel making a rapid turn near large waves, nonlinear effects have to be included in the model formulation. To that end, a nonlinear motion model for a marine craft affected by a free surface has been developed using Lagrangian mechanics. This dissertation describes an approach for determining the parameters of the nonlinear motion model using a potential flow panel code, which is originally designed to determine flow velocity of the fluid and pressure distribution over marine vessels. The nonlinear motion model is reformulated and the software implementation is modified to support parameter computations. In addition, the methods are numerically validated by comparing computations using the model against solutions output by the panel code. Compared to traditional parameter estimation approaches, the proposed methods allow for a more accurate and efficient determination of parameters of the nonlinear potential flow model for a submerged vessel operating near waves. The resulting Lagrangian nonlinear maneuvering and seakeeping (LNMS) model with determined parameters is able to capture critical nonlinear effects and has applications such as nonlinear control design, rapid design optimization and training simulator development.

A dynamic simulation of the response of an inflatable dam subjected to a flood was carried out to determine the survivability envelope of the dam where it can operate without rupture, or overflow. A fully nonlinear free-surface flow was applied in two dimensions using a mixed Eulerian-Lagrangian formulation. An ABAQUS finite element model was used to determine the dynamic structural response of the dam. The problem was solved in the time domain which allows the prediction of a number of transient phenomena such as the generation of upstream advancing waves, and dynamic structural collapse. Stresses in the dam material were monitored to determine when rupture occurs. An iterative study was performed to find the service envelope of the dam in terms of the internal pressure and the flood Froude number for two flood depths. It was found that the driving parameter governing failure of the dam was the internal pressure. If this pressure is too low, the dam overflows; if this pressure is too high, the dam ruptures. The fully nonlinear free-surface flow over a semi-circular bottom obstruction was studied numerically in two dimensions using a similar solution formulation as that used in the previous study. A parametric study was performed for a range of values of the depth-based Froude number up to 2.5 and non-dimensional obstacle heights up to 0.9. When wave breaking does not occur, three distinct flow regimes were identified: subcritical, transcritical and supercritical. When breaking occurs it may be of any type: spilling, plunging or surging. In addition, for values of the Froude number close to 1, the upstream solitary waves break. A systematic study was undertaken, to define the boundaries of each type of breaking and non-breaking pattern, and to determine the drag and lift coefficients, free surface profile characteristics and transient behavior. / Master of Science

Model-H is used to describe structures found in the phase separation in films of binary liquid mixture that have a surface that is free to deform and also may energetically prefer one of the components. The film rests on a solid smooth substrate that has no preference for any component. On the one hand the study focuses on static aspects by investigating steady states that are characterised by their concentration and film height profiles. A large variety of such states are systematically analysed by numerically constructing bifurcation diagrams in dependence of a number of control parameters. The numerical method used is based on minimising the free energy functional at given constraints within a finite element method for a variable domain shape. The structure of the bifurcation diagrams is related to the symmetry properties of the individual solutions on the various branches. On the other hand the full time dependent model-H is linearised about selected steady states, in particular, the laterally invariant, i.e.\ layered states. The resulting dispersion relations are discussed and related to the corresponding bifurcation points of the steady states. In general, the results do well agree and confirm each other. The described analysis is performed for a number of important cases whose comparison allows us to gain an advanced understanding of the system behaviour: We distinguish the critical and off-critical case that correspond to zero and non-zero mean concentration, respectively. In the critical case the investigation focuses on (i) flat films without surface bias, (ii) flat films with surface bias, (iii) height-modulated films without surface bias, and (iv) height-modulated films with surface bias. Each case is analysed for several mean film heights and (if applicable) energetic bias at the free surface using the lateral domain size as main control parameter. Linear stability analyses of layered films and symmetry considerations are used to understand the structures of the determined bifurcation diagrams. For off-critical mixtures our study is more restricted. There we consider height-modulated films without and with surface bias for several mean film heights and (if applicable) energetic bias employing the mean concentration as main control parameter.