The drainage time of liquid-filled PET bottles can be greatly reduced by pre-rotating the bottle with a certain angular velocity. Depending on the magnitude of the angular velocity, up to four different flow regimes can be distinguished during the emptying of a bottle: bubble regime, transition regime, vortex regime and the swirl regime. At zero or low pre-rotation, the flow is in the so-called bubble regime in which the intermittent downward liquid flow is accompanied by an upward motion of irregularly shaped air bubbles into the bottle. At sufficiently high pre-rotation, the picture is completely different. After initial transient behaviour in which the flow is first in the bubble regime, the flow undergoes transition towards a so-called vortex regime. This is characterized by regular downward motion of liquid along the bottle wall in a free-surface vortex and accompanying upward motion of air through the nozzle core. Finally, close to the end of the drainage process another transition towards a so-called swirl regime takes place, in which the last bit of liquid swirls around in the bottle before being slowed down sufficiently to exit the bottle through the nozzle opening. Dimensional analysis indicates that for a specific bottle geometry the non-dimensional total drainage time td/td,0, where td,0 is a characteristic drainage time scale for stationary low-viscosity fluids in the bubble regime, depends primarily on 3 non-dimensional numbers: (1) the rotation number, Π (2) the Morton number, Mo, and (3) the E¨otvos number, Eo. The former represents the characteristic ratio of centrifugal to hydrostatic forces inside the liquid phase. The objective of this study is to determine the relationship between the non-dimensional drainage time and Π and gain insight in the influence of E¨otvos and Morton onto this. To this purpose, a parametric CFD study of a model PET bottle has been conducted and the results have been compared with previous preliminary experiments performed in our group. The numerical study is divided into three categories, each discussing the influence of one of the dimensionless parameters. The influence of the Π-number was studied by altering the initial rotational velocity of the bottle. It was found that at some critical Π-number, the drainage time was minimal. A further increase beyond the critical Π-number resulted in a longer drainage time, due to the stronger centrifugal force acting on the liquid layer. It was found through an analytical solution and verified with the numerical results that the rate at which the Π-number grows in relation to the dimensionless drainage time is to the power 3 for the laminar case and to the power 3/2 for the turbulent case. Below the critical value, the flow is expected to remain in the so-called bubble regime, also increasing the drainage time. Furthermore, the onset of the vortex regime was expected to occur at a constant value of Π. This was also verified with the numerical results and a strong correlation was found between the onset and the corresponding local Π-number. The influence of the Morton number is also discussed, where an increase in the Morton number was realized with an increase in viscosity. It was found that the drainage time got substantially reduced with an increase in viscosity. The effects of viscous dissipation resulted in a bigger effective area and higher axial downward flow velocity. However, increasing the Morton number excessively would result in the flow regime remaining in the bubble regime. Therefore, the critical Πnumber shifts depending on the different fluid compositions. When varying the E¨otvos number, by both changing the viscosity and the surface tension, it was found that the latter had negligible effect on the generation of the air-core or the drainage time.

The presence of particles in a flow can change the flow behaviour in an unpredictable manner, that leads us to multiphase flow. Multiphase flows are present in nature and in everyday life around us. The most common example of a multiphase flow, that one can think of, is the treatment of drinking water using liquid-solid fluidization in softening processes. Multiphase flows can also have very high relevance in various practical applications ranging from sedimentation of particles for process industries, transport of a dense suspension (slurry) through a pipe and dredging applications for land reclamation. Even though a lot of research has been done on liquid-solid fluidization in inertial and viscous dominated regimes, it remains far from being understood completely. Experimental studies were conducted on the fluidization of monodisperse solid spheres within a rectangular channel. This research saw the development of an experimental setup, to study this phenomenon. The bulk solid volume fraction was studied in three different regimes. At a dilute regime (Φ ≤ 4%), moderate regime (Φ = 8 − 14%), and a dense regime (Φ ≥ 15%). To study the impact of inertia, three distinct Galileo numbers in the inertial regime were examined: 𝐺𝑎 = 147, 196, and 252. At these values, a singular settling/rising sphere presents markedly varied wake and path characteristics. Throughout the study, the particle/fluid mass density ratio remained constant at 0.87. Results indicate that within the range of Φ = 4 − 18%, both the microstructure and dynamics of the suspension are heavily influenced by the bulk solid volume fraction. This aligns qualitatively with previous literature. Enhanced fluidization was noticed in the experiments. This is usually driven by the formation of clusters. Particle clustering within these regimes is driven by various mechanisms: trapping of particles in wakes, a drafting–kissing–tumbling (DKT) instability causing vertically aligned particles to swiftly realign horizontally, and multiparticle interactions with collisions playing a minor role. On the macrostructure level, intrinsic convection was captured in the fluidization column. To further study these characteristics, instantaneous snapshots were illustrated for varying cases. Profiles for both mean velocity and root-mean-square (RMS) velocity were obtained. Wall effects emerged as pronounced, diminishing in importance with increased bulk solid volume fraction and augmented 𝐺𝑎 values. Intrinsic convection is observed in these experiments, and the velocity profiles provided an indication. Probability density functions (pdf) for normalized velocities highlighted evident particle clustering.

Manganese nodules have been lying on the deep sea soil for centuries before they became known. The first ones to discover the nodules were Murray and Renard, during their scientific cruise between 1872 and 1876 (Murray and Renard, 1876). The Clarion-Clipperton Zone, located between Mexico and Hawaii, appears to have a virtually inexhaustible amount of mineral resources. The manganese nodules consist mainly of man- ganese, but because they also contain metals such as copper and cobalt, the nodules become more and more interesting for our modern society. Another name for the manganese nodules is polymetallic nodules, be- cause of the content of many other metals. By means of a vertical hydraulic transport system the manganese nodules will be transported upwards from the seabed. Given that the nodules are located at a depth of about 5000 meter, it is plausible that they come into contact with the pipe wall during transport. When a nodule interacts with the wall, abrasive wear can occur. Abrasive wear, or sliding wear, causes the nodule to degrade, or decrease in mass, through the sliding contact with the pipe wall. The main research question of this Master Thesis is formed as follows: What is the contribution of abrasive wear to the degradation of polymetallic nodules, in a vertical transport system? The contribution of abrasive wear is tested on the basis of the equation of Archard (1953). In the MTI laboratory in Kinderdijk various manganese nodules are tested in a specially designed experimental setup. The polymetallic nodules available for this Master Thesis originate from the Clarion-Clipperton Zone (CCZ). The first set of experiments is focused on single nodule degradation. The nodules are weighted before and after a test run, hereafter the nodule mass after a test run is divided by the initial nodule mass, resulting in the normalized remaining mass. Each test run consists of a specific sliding length. With the sliding length and normalized remains mass, a prediction can be made of the material specific wear rate factor, noted as k [m2/N]. The experiments resulted into a value of k = 4.16·10−9 [m2/N]. With this k-factor, in the worst case, 97% of the original nodule mass is remaining after 1000 meters of sliding contact. Subsequently, a batch of nodules is tested in the experimental setup, with the expectation that the con- tribution of abrasive wear increases to the total nodule degradation, due to the presence of particle-particle interaction. Recently, Blue Mining has conducted trials in Freiberg, Germany, in an abandoned mine shaft. A vertical pipe of almost 130 meters has been placed inside, and the effect of abrasion on a batch of nodules has been observed. During the batch experiments in Kinderdijk, where the batch of nodules was in a horizontal position, it is seen that the contribution of abrasion is greater, compared to the tests in Freiberg. Using the open-source program OpenFOAM, a vertical turbulent pipe flow is modeled. The pipe has simi- lar dimensions to the pipe of the experimental setup. The simulation was done using a Large Eddy Simulation (LES). By means of a one-way coupling, the data of the flow field is linked to the movement of the simulated particle. Subsequently, point particles were released at various points at the entrance of the pipe. The first series of point particles consists of a diameter of one-third of the pipe diameter, corresponding to the com- mon size of a manganese nodule. The collisions between the point particle and the pipe wall are solved with a Discrete Element Method (DEM), which makes use of a (non-linear) spring-damper system. To test the sensitivity of the model, point particles of one-sixth and one-tenth of the pipe diameter are also released. The number of collisions per total number of simulations are compared with each other. After the sensitivity analysis it turned out that in 15% of the simulations there was contact with the pipe wall, regardless of the diameter of the particle. When this 15% is compared to the experimental results using single nodules, there is a weight loss of around 0.5%. This holds a weight loss of only a single - to a few - gram(s) for the average polymetallic nodule. It can be concluded, according to the experimental trials with polymetallic nodules from the Clarion- Clipperton Zone and by means of a one-way coupled CFD-DEM model, that the contribution of abrasive wear results into a (maximum) remaining mass of 97%. However, it is advised to extend the computer model with a two-way (or multi-way) coupling between the liquid and the solids. It is also recommended to conduct vertical abrasive wear tests with nodules, in order to validate the model and gain more insight in degradation behaviour.

Multi-phase flows are ubiquitous in nature and in everyday life surrounding us, impacting us in almost all possible ways. The presence of particles in a flow can change the flow behaviour in an unpredictable manner. The simplest example of a particle-laden flow, that one can think of, is the settling of a single sphere under gravity in a quiescent fluid. This seemingly simple problem has very high relevance in various practical applications ranging from sedimentation of particles for water treatment, process industries, transport of a dense suspension(slurry) through a pipe and even in land reclamation. The settling/ascension of a single sphere, even after having been subject to extensive study for more than a century, remains far from being understood completely. The path and the wake of a falling/rising sphere in a quiescent fluid may be subject to various instabilities depending upon two dimensionless quantities which are sufficient to characterize the motion. One being the Galileo number (Ga), which is the ratio of the net gravity force to the viscous force and the second one being the mass density ratio, which is the ratio of the density of the solid to the density of the fluid. Depending upon Ga and mass density ratio, the sphere can take up various regimes of motion such as vertical, oblique, zigzagging, helical to name a few. This is mainly due to wake instabilities that trigger such path instabilities. Based on Ga and mass density ratio, various regime maps have been proposed in literature. There have been several disagreements regarding the characterization of such paths taken by the sphere. This is due to the strong solid-fluid coupling and the inherent complexity due to triggering of the instabilities in such cases, which is far from being trivial to model numerically and also to test experimentally. The disagreements between different numerical works and different experimental works make the problem hard pressing and tempting to study. Moreover, the settling behaviour of a single sphere can also aid in understanding the collective effects displayed in the settling of dilute suspensions. The goal of the present study is to shed light on the confusion/disagreements in literature until now and characterize various path instabilities. A detailed experimental investigation is conducted to cover the parameter space (regime map) by employment of over 250 different combinations of Ga and mass density ratio to cover as many regimes of motions as possible within the given time framework. The motion of a sphere is tracked in time using high-speed cameras and corresponding path/regime of motion, higher-order statistics like velocity and physical characteristics such as the Strouhal number/ drag coefficient has been computed. The results validate well for some simple regimes of motion for which results from the previous studies perfectly agree with each other. With the confidence obtained after the validation, the current work attempts to draw points of consensus and disagreements with these earlier works for other more controversial regimes. Some regimes, which had only been observed using numerical simulations, have been observed experimentally for the first time. Also, intriguing bi-stable regimes (coexistence of two regimes) have been observed. Moreover, attempt is also made to characterize the suppression of the high-frequency oscillations with increase in the sphere inertia. An update of the regime maps is proposed with the results obtained from the experiments conducted. The results obtained will also serve as an excellent tool for validation of new numerical models, using which the Ga-mass density ratio parameter space can be covered in great detail. Recommendations for future work are given.

Dense suspension flows, both in the natural environment and industrial settings, are complex phenomena with significant implications. From rivers shaping landscapes to industrial processes involving slurry transport, these flows hold a prominent position in numerous sectors. This thesis delves into a specific facet of these intricate flows: slurry transport within horizontal pipes. Slurry, a mixture of solid particles and a viscous fluid, presents a challenging arena due to its dynamic nature, encompassing multiple flowregimes and diverse phenomena that govern its behavior. This research seeks to unravel the complexities of slurry transport, presenting a comprehensive analysis using interface-resolved Direct Numerical Simulation (DNS). In the context of slurry transport (also referred to as sediment transport), a horizontal pipe is a conduit where particles suspended in a viscous fluid are transported. The dynamics of this transport are governed by several dimensionless numbers, each highlighting distinct aspects of the flow. Prominently, in this work we explore the role of the Reynolds number (Re) which encapsulates the balance between inertial and viscous forces, the Galileo number (Ga) which characterizes the competition between inertial and viscous effects in particle settling under gravity, and concentration of particles which has an influence on particle-particle and particle-fluid interactions. Key flow dynamics that determine the behaviour of the flow include turbulent mixing, gravitational settling of particles, and shear-induced particle migration due to particle-stress gradients. Practical applications of slurry transport are numerous, spanning industries such as mining, agriculture, and chemical processing. Slurry transport is of particular relevance to the dredging industry in the Netherlands to maintain its inland waterways and for land reclamation projects. However, pipeline operators grapple with issues ranging from pressure drop and the prevention of bed formation to the control of excessive pipe abrasion, silting risks, and production instability. These challenges stem from the intricate interplay of particle behavior, fluid dynamics, and pipeline geometry....@en

A significant part of the fuel used for transportation results from the drag in turbulent flows. Techniques for turbulent drag reduction yield associated reductions of the fuel consumption and greenhouse gas emissions, which is desirable from both economic and environmental perspectives (cf. chapter 1). This thesis investigates two passive techniques that could be exploited for the reduction of frictional drag in turbulent flows, namely textured and compliant surfaces. Correspondingly, the aim of the thesis is twofold, namely to explore the drag-reducing potential of riblet-textured surfaces, and to characterize the interaction between time-dependent (possibly turbulent) flows and a compliant wall. The work presented in this thesis was performed as part of the European project SEAFRONT, which aimed at the development of environmentally benign antifouling and dragreducing technologies for the maritime sector… @en

A magnetorheological fluid is a type of smart fluid that can change its rheological properties when a magnetic field is applied to the fluid. The fluid is a suspension of magnetizable particles in a non-magnetic carrier fluid. When a magnetic field is applied to the fluid, the particles will form structures along the magnetic field lines. These structures resist flow, thereby increasing the viscosity of the fluid. In a non-uniform magnetic field that is generated by a permanent magnet, the particles separate from the fluid and aggregate on the surface of the magnet. This phenomenon is of use in hydrodynamic bearings, where textures are used to increase the load capacity of the bearing. Replacing the fluid in the bearing by a magnetorheological fluid and placing permanent magnets at the desired texture locations, results in particles separating from the fluid, aggregating on the permanent magnets and forming textures. These textures are of a self-healing nature, because any particle that is sheared off, returns into the fluid and is replaced by another particle. Currently, not much is known about the formation of these textures and the influence of their formation on the rheological behavior of the magnetorheological fluid. Therefore, several discrete element models are constructed, that can simulate a magnetorheological fluid in non-uniform field. These models use basic physical laws to determine the dynamics of the particles. A single core model is constructed to simulate the behavior of the magnetorheological fluid in small domains using two different methods for the magnetic interaction forces between the particles. A parallel model is made to simulate the magnetorheological fluid in larger domains. Finally, a model that is used to simulate particulate flows, is modified to research whether two-way coupling is required to determine the steady state behavior of the magnetorheological fluid. The models show that the particles do not separate from the fluid due to the attractive force of the magnet by itself, but rather by a combination of the attractive force and the deformation of the structures when a flow is applied. Furthermore, the rheological behavior of the fluid can still be approximated using the standard viscoplastic models. Finally, the modified particulate flow model showed that two-way coupling is not required to determine the steady state behavior of the magnetorheological fluid.

To meet energy demand towards a low-carbon future, the global market demand is growing for metals such as cobalt and nickel which are major elements in batteries. Polymetallic nodules, which are formed on abyssal plains at depths ranging from 4 to 6 kilometres and are distributed in high abundance on the top of the seabed, contains several times more cobalt and nickel than the entire global terrestrial reserves. This has raised the interest to exploit these resources from the deep ocean. The seafloor mining tool (SMT) can move along the soft sea bottom and can collect polymetallic nodules. While doing so, it will also entrain sediments and water. The excess of water and sediment entrained is discharged at the back of the SMT, forming a sediment plume. The sediment plume dispersion has strong adverse impacts on deep-sea environment.Thus, it is essential to study the sediment plume behavior in order to limit plume dispersion and thus to reduce its environmental impact. Experimental research is a powerful technique to study the plume behaviour. However, experiments sometimes take a long time due to complex set-up. In comparision, numerical analysis can save time and costs when solving complex problems. Furthermore, numerical modelling can provide deeper understanding and flexibility for boundary conditions and sediment types, which is applicable on both model and prototype scale. Previous numerical studies have noted the significant role of flocculation in limiting plume dispersion, but flocculation process has not been modelled explicitly. This study aims to establish a numerical model to study flocculation process and its effect on sediment transport. Previous flocculation-fluid dynamics modelling has applied a Euler-Euler method with additional population balance equations. The disadvantage is that many equations need to be solved. To avoid excessive computational costs, the sediment transport is described by a multiphase drift-flux model in this study. The flocculation process is modelled by a discretized form of population balance equations. The author has found that, by multiplying the particle volume, the population balance can be efficiently incorporated in the phase continuity equations in the drift-flux model. The population dynamics of particle aggregation and breakup can thus be characterized by the phase transition terms in the phase continuity equations. Hence, no additional equation needs to be introduced and solved. Verification is carried out to check conservation relationships and iterative convergence of numerical results. Then, an initial numerical investigation has shown the results can qualitatively show the three settling stages (i.e., flocculent settling, hindered settling and compression settling) found in the experimental studies. Afterwards, the collision efficiency is calibrated using the settling column tests conducted by Enthoven (2021). The results of calibration show a good fit to the experimental data. Another advantage is that numerical simulations can provide the particle size distribution over time, which is not measured in the experiments. The major novelty of this study is the coupling of the drift-flux model and the population balance equations, which inherits both the characteristics of population balance and the merits of drift-flux model in reducing computational costs. The flocculation modeling technique as proposed in this study can be incorporated as a module into an extended drift-flux model to predict the dispersion of deep-sea mining plumes.