No / An incompressible smoothed particle hydrodynamics (SPH) method is presented to simulate Newtonian and non-Newtonian flows with free surfaces. The basic equations solved are the incompressible mass conservation and Navier¿Stokes equations. The method uses prediction¿correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting deviation of particle density is then implicitly projected onto a divergence-free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. Various SPH formulations are employed in the discretization of the relevant gradient, divergence and Laplacian terms. Free surfaces are identified by the particles whose density is below a set point. Wall boundaries are represented by particles whose positions are fixed. The SPH formulation is also extended to non-Newtonian flows and demonstrated using the Cross rheological model. The incompressible SPH method is tested by typical 2-D dam-break problems in which both water and fluid mud are considered. The computations are in good agreement with available experimental data. The different flow features between Newtonian and non-Newtonian flows after the dam-break are discussed.

Recent technological advances are based on effectively using complex multiphysics concepts. Therefore, there is an ever increasing need for accurate numerical al-gorithms of reduced complexity for solving multiphysics problems. Traditional mesh-based simulation methods depend on a neighbor connectivity information for formulation of operators like derivatives. In large deformation problems, de-pendence on a mesh could prove a limitation in terms of accuracy and cost of preprocessing. Meshless methods obviate the need to construct meshes thus al-lowing simulations involving severe geometric deformations such as breakup of a contiguous domain into multiple fragments. Smoothed Particle Hydrodynamics (SPH) is a meshless particle based Lagrangian numerical method that has the longest continuous history of development ever since it was introduced in 1977. Commensurate with the significant growth in computational power, SPH has been increasingly applied to solve problems of greater complexity in fluid mechanics, solid mechanics, interfacial flows and astrophysics to name a few. The SPH approximation of the continuity and momentum equations govern-ing fluid flow traditionally involves a stiff equation of state relating pressure and density, when applied to incompressible flow problems. Incompressible Smoothed Particle Hydrodynamics (ISPH) is a variant of SPH that replaces this weak com-pressibility approach with a pressure equation that gives a hydrostatic pressure field which ensures a divergence-free (or density invariant) velocity field. The present study explains the development of an ISPH algorithm and its implementa-tion with focus on application to free surface flows, interaction of fluid with rigid bodies and coupling of incompressible fluids with a compressible second phase. Several improvements to the exiting ISPH algorithm are proposed in this study. A semi-analytic free surface model which is more accurate and robust compared to existing algorithms used in ISPH methods is introduced, validated against experi-ments and grid based CFD results. A surface tension model with specific applica-bility to free surfaces is presented and tested using 2D and 3D simulations. Using theoretical arguments, a volume conservation error in existing particle methods in general is demonstrated. A deformation gradient based approach is used to derive a new pressure equation which reduces these errors. The method is ap-plied to both free surface and internal flow problems and is shown to have better volume conservation and therefore reduced density fluctuations. Also, comments on instabilities arising from particle distributions are made and the role of the smoothing functions in such instabilities is discussed. The challenges in imple-menting the ISPH algorithm in a computer code are discussed and the experience of developing an in-house ISPH code is described. A parametric study on water entry of cylinders of different shapes, angular velocity and density is performed and aspects such as surface profiles, impact pressures and penetration velocities are compared. An analysis on the energy transfer between the solid and the fluid is also performed. Low Froude number water entry of a sphere is studied and the impact pressure is compared with the theoretical estimates. The Incompressible SPH formulation, employing the proposed improvements from the study is then coupled with a compressible SPH formulation to perform two phase flow simulations interacting compressible and incompressible fluids. To gain confidence in its applicability, the simulations are compared against the theoretical predication given by the Rayleigh-Plesset equation for the problem of compressible drop in an incompressible fluid.

This thesis consists of two papers dealing with a stabilization method for free-surface flows. The method was initially developed to stabilize mantle-convection simulations, but is in this work extended to ice-sheet- and glacier modeling. The objective of this thesis is to assess the method when applied glaciological simulations, with regards to stability and accuracy. It is shown that the method works well and increases stable time-step sizes substantially both for ice-sheet- and glacier simulations, without loss of accuracy. The increased stability properties might be useful for performing long-term simulations and increasing sea-level-rise predictions on a centennial time scale. / Denna avhandling består av två artiklar som inom ramen för ismodellering undersöker en stabiliseringsmetod för flöden med en fri yta. Metoden framtogs först för stabilisering av simuleringar av mantelkonvektion, men har i den här avhandlingen anpassats till ismodellering. Avhandlingens mål har varit att utvärdera metoden med avseende på stabiltet och noggrannhet. Från de utförda studierna framkommer det att metoden ökar längden på stabila tidssteg avsevärt, utan att nämnvärt påverka noggrannheten hos islösaren. De ökade stabilitetsegenskaperna hos metoden kan exempelvis innebära ökad nogrannheten i fastställandet av framtida havsnivåhöjning genom möjliggörandet av långtidssimuleringar på en tidsskala av flera hundra år.

Properties of polymers in thin films are distinct from those in the bulk due to the significant effects of free or substrate surfaces. The presence of a free surface allows an increased mobility of polymer chains in the near surface region, therefore, a lower glass transition temperature (T_g). With this lower surface T_g, a surface-specific crystallization phenomenon occurring at temperatures much lower than the bulk crystallization temperature (T_c) in polymers including PET, PEN and PVOH has previously been observed. However, whether or not this surface-specific crystallization is a phenomenon observable in all crystallizable polymers is still a question. Similarly, due to this greater mobility, phase separation may also be able to take place in the near-surface region of a polymer blend at a temperature much lower than the bulk phase separation temperature. Yet, no such investigation on polymer blends has been carried out. In addition, it is interesting to study the thin-film behaviours of a block copolymer that undergoes both phase separation and crystallization and compare these with corresponding bulk behaviour. In this thesis, the thin-film crystallization behaviour of polyamide 12 (PA12) in spin-cast films is presented together with some investigation of crystallization of polyamide 6 (PA6) and polystyrene. Polystyrene and poly(methyl methacrylate) (PS/PMMA) systems are used to illustrate the phase behaviours specific to the near-surface region. Finally, the microstructural evolution in high hard block content thermoplastic polyurethane (TPU) thin films on annealing has also been investigated. These TPUs have hard segments (HS) extended by 2 methyl 1,3 propanediol (2M13PD) or 1,5 pentanediol (15PD). With its flexible chains, PA12 crystallizes during spin coating forming as-spin-cast crystals with morphology that varies with solvent evaporation rate and film thickness. Despite the as spin-cast crystals, the free surface allows secondary surface crystallization of PA12 at an annealing temperature (T_a) roughly 20°C below the bulk T_c. The secondary surface crystals were indicated to exist in the most stable crystalline phase of PA12. Similar secondary surface crystallization has also been observed in the PA6 films but at a higher T_a due to the higher T_g of PA6. In addition, surface-specific crystals have been observed in PS (semicrystalline, likely due to some stereoregularity of composition), a polymer with bulky side groups. The PS surface crystals are, however, flat-on oriented showing the important effect of side groups on the morphology or growth shape of surface crystals. The discovery of these surface crystals supports the universality of surface specific crystallization. Using fast solvent quenching, it is possible to "freeze in" a structure containing both PS and PMMA in the near surface region. On annealing, surface-specific phase behaviours (observable as pits, undulations and aggregations) confined to the near-surface region take place first at temperatures around or just below the bulk polymer T_g, while bulk vertical phase separation and dewetting of PS to PMMA, forming holes, network structures and islands, occur at temperatures well above T_g. This surface specific phenomenon, being a result of the free surface, should be applicable to other phase separation systems with a free surface as well. An increase in the crystallinity of PS was found to promote the phase separation process, but the free surface effect is independent of the interplay between the crystallization and phase separation. Rather than having a two-phase morphology, as was previously observed in melt-quenched bulk samples, 2M13PD extended TPU spin-cast films showed a single-phase morphology as-spin-cast. However, the HS ordering, the formation of mesophase, the melting of HS ordered regions, and microphase mixing observed in thin films are consistent with the bulk results but with slightly different transition temperatures due to spatial confinement. With a more flexible chain extender, e.g. 15PD, the hard and soft phase separation is more limited. The thin film investigations have allowed a better understanding of the microstructural evolution in these high hard block content TPUs on annealing by imaging the morphology directly. A thin-film specific phenomenon: formation of large multilayer flat-on crystals, was also observed in these TPU thin films. These crystals are initially developed from preformed aggregations and are believed to be induced by the significant substrate effect in thin films and the free surface effect.

High velocity channels are typically designed to discharge surplus water during severe flood events, and these types of flow are distinguished by high velocity, usually supercritical. A major challenge in high velocity channel design is to predict the free surface flow. Being able to predict the free surface flow profile beforehand can assist in selecting the best design for the channel as a whole. When the flow encounters a bridge pier, the streamline of the flow is separated and pressure may drop to a minimum; in contrast, velocity rises to its maximum value. As a result, cavitation damage may occur. The present study has used the computational fluid dynamics code ANSYS-CFX to investigate a full scale, three-dimensional engineering flow simulation of high velocity channels with different cross sections. The simulations were carried out on a high performance computing HPC cluster with 32 nodes. The code is based on the finite volume method and the Volume of Fluid (VOF) method was used to predict the position of the free surface profile. The impact of variation of the following parameters was investigated in terms of the free surface flow profile, both along the centreline and the wall of the channel: the minimum cavity index, and maximum shear stress on both bed and wall of the channel and on bridge pier; aspect ratio (channel bed width/flow depth), bed and side slopes of the channel, different discharges, which are represented by Froude numbers; the length and thickness of the bridge pier. First, the code sensitivity tools for convergence were examined. For this purpose, cases with different mesh sizes were examined and the best size chosen, depending on computation expense and convergence. Then, different turbulence models, such as the standard k-ε, RNG k-ε, and SST turbulence models were tested. The results show that the standard k-ε gives satisfactory results. Next, efforts were made to establish whether the flow achieved steady state conditions. This involved simulating two cases, one with steady state and the other with a transient state. Comparison of the two results shows that the flow properties do not change after three seconds and stay stable thereafter, so the flow can be considered as attaining a steady state. Finally, symmetry within the model geometry was tested, as this would allow a reduction in computation time, with only one side of the symmetrical model needing to be simulated. Two cases were investigated: firstly a simulation of only half of the channel geometry, and secondly a full geometry simulation. A comparison of the results of each case showed that the flow can be considered symmetrical along the centreline of the channel. Next, the code was validated against both numerical and experimental published results. For the free surface flow profile and velocity distribution the published experimental and numerical work of Stockstill (1996) was used; the ANSYS-CFX code results agree more closely with Stockstill’s experimental data than Stockstill’s numerical data. To test for shear stress distribution on the wall, uniform flow within a trapezoidal cross section channel was investigated and the results compared with those presented in the literature. The comparison shows good agreement between the ANSYS-CFX and published experimental works, for the predicted shear stress distributions on the walls and the bed of the channel. In total, sixty cases were simulated in order to investigate the impact of variations in the aforementioned parameters on maximum flow depth (both along the centreline and the wall of the channel) minimum cavity index, and maximum shear stress on both bed and wall of the channel and on bridge pier. Finally, non-dimensional curves are provided in addition to formulae derived from the data regression, which are intended to provide useful guidelines for designers.

Kinetic energy extraction devices for ocean and river flows are often located in the vicinity of the fluid free surface. This differs from wind turbines where the atmosphere may be considered to extend to infinity for the purposes of numerical modelling. As most kinetic energy extraction devices are based on lifting surfaces, a numerical model is sought which can model both lifting and free surface flows. One such model is the boundary element method which has been successfully applied to free surface problems and to lifting flows as well as the combined problem. This study seeks to develop a high order boundary element method that is capable of modelling unsteady lifting and free surface flows in three dimensions. Although high order formulations of boundary element methods are common for free surface problems, providing improved accuracy and computational time, their usage for lifting flows is less frequent. This may be due to the hypersingular boundary integral equation (HBIE) which must be solved in order to find the velocity of the vortex wakes behind lifting surfaces. In previous lifting flow studies using high order boundary element methods the wake velocities have been determined at the element centres and then interpolated to the collocation points. Not until the paper of Gray et al. (2004b) has a method been available for the direct solution of the HBIEs at the edges of three dimensional high order elements with C0 continuous interfaces. The solution employs a technique known as the Galerkin boundary element method. This study shows, for the first time, that the Galerkin boundary element method is applicable to the solution of the HBIE on the vortex wake of a lifting body. The application of the technique is then demonstrated as part of the numerical model developed herein. The model is based on the high order boundary element method developed by Xu (1992) for non-linear free surface flows. This formulation is extended to include steady uniform flow throughout the computational domain as well as the presence of lifting and non-lifting bodies. Several verification cases are implemented to test the accuracy of the model.

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.

The development of a three dimensional B-Spline based method, which is suitable for the steady-state potential flow analysis of free surface piercing bodies in hydrodynamics, is presented. The method requires the B-Spline or Non Uniform Rational B-Spline (NURBS) representation of the body as an input. In order to solve for the unknown potential, the source surface, both for the body as well as the free surface, is represented by NURBS surfaces. The method does not require the body surface to be discritized into flat panels. Therefore, instead of a mere panel approximation, the exact body geometry is utilized for the computation. The technique does not use a free surface Green's function, which already satisfies the linear free surface boundary conditions, but uses a separate source patch for the free surface. By eliminating the use of a free surface Green's function, the method can be extended to considering non-linear free surface conditions, thus providing the possibility for wave resistance calculations. The method is first applied to the double body flow problem around a sphere and a Wigley hull. Some comparisons are made with exact solutions to validate the accuracy of the method. Results of linear free surface conditions are then presented.

Marangoni flows are free-surface flows driven by gradients of surface tension. Because surface tension depends on chemical composition, Marangoni flows may be generated by the uneven distribution of surface-active species at an interface. The primary goal of this thesis is to develop a rigorous computational framework for the simulation of the fluid dynamical and interfacial phenomena underlying the physics of Marangoni flows. The focus is on characterizing the different dynamical regimes generated by the presence of surface-active species (surfactants) at an interface. The computational framework was developed using direct numerical simulation, that is, by simultaneously solving the full system of partial differential equations governing the free-surface flow and the surfactant transport on a continually deforming interface. Results from the simulations enabled detailed examination of the interfacial mechanisms of surfactant transport and provided a comprehensive picture of the free-surface flow. Analysis of the results established limits of applicability of scaling solutions previously proposed in the literature, calculated the necessary corrections, and also lead to the discovery of previously unobserved scaling laws in viscous Marangoni flows. New findings from this research not only enhance the fundamental understanding of the physics of Marangoni flows, but also the ability to accurately predict the behaviour of Marangoni flows and the associated transport of surface-active species, which is critical to the understanding of important natural and biomedical processes, ranging from the surfactant-driven propulsion of insects and microorganisms to the spreading of drugs and natural surfactants (proteins) in the eye and lungs. Controlled Marangoni transport of chemical species is also relevant to a wide range of environmental and technological processes, with applications ranging from cleaning of oil spills to coating of microfluidic devices.

Nous étudions la stabilité de l'écoulement de fluide rhéofluidifiant (pseudoplastique) sur plan incliné. La connaissance des conditions d'apparition des instabilités intéresse ici particulièrement le secteur industriel faisant appel à des méthodes de couchage (papeterie, photographie), ou le secteur environnemental dans la compréhension de certaines situations exceptionnelles (coulées de boues, laves torrentielles, écoulements de glaciers). Nous modélisons la viscosité des fluides utilisés par la loi de Carreau. Afin de caractériser nos fluides, nous utilisons l'électrocapillarité comme technique optique consistant à étudier la propagation et l'atténuation d'ondes capillaires. Les résultats de mesures permettent en particulier de déterminer la viscosité à valeur de cisaillement aussi faibles que 10−3s−1. Notre objectif est d'étudier expérimentalement la stabilité de films rhéofluidifiants sur plan incliné. Pour des valeurs fixées de l'angle d'inclinaison, nous avons déterminé le seuil critique expérimental et tracé la courbe marginale de stabilité sur les plans (Re, k) et (Re, c) pour nos différents fluides. Nous trouvons que nos résultats expérimentaux sont en bon accord avec les résultats numériques, et confirment l'effet rhéofluidifiant déstabilisant relativement au cas Newtonien. Nous discutons enfin la validité du théorème de Squire en écrivant l'équation d'Orr-Sommerfeld généralisée aux ondes 3D et aux fluides de Carreau. Analytiquement, les relations de Squire ne sont pas vérifiées, et les résultats numériques montrent que les relations de Squire ne s'écrivent que dans le cas Newtonien / We study the stability of shear-thinning (pseudoplastic) fluid films flow down an inclined plane. This problem is of interest in many industrial applications such as coating, and may explain the manifestation of a specific kind of surface waves, appearing in some spectacular environmental flow configurations such as debris flows or surge waves. We focus on fluids obeying the Carreau law. An optical technique called electrocapillarity has been implemented in order to determine the surface tension and viscosity, at values of the shear rate as small as 10−3s−1, by studying the damping of propagating capillary waves. The main objective of this work is to experimentally study the linear stability of shear-thinning fluid films flow. For a fixed inclination angle, the experimental study essentially consists in measuring the cutoff frequency and wavelength of primary waves, and then determining the critical Reynolds number. The experimental results presented in the (Re, k) and (Re, c) planes are in good agreement with the numerical results, and confirm the destabilizing effect of the shear-thinning properties in comparison with the Newtonian case (the critical Reynolds number is smaller, and the ratio between the marginal waves celerity and the flow velocity at the free surface is larger). Finally, we discuss the validity of the Squire’s theorem in the case of generalized Newtonian fluids film flow down an inclined plane. Analytically, the Orr-Sommerfeld problem with respect to 3D disturbances is not equivalent to a 2D problem, and the numerical results show that the Squire’s transformations can only be used in the Newtonian case