In this review we explore the recent developments in the use of Magnetic Resonance Imaging (MRI) for studying granular flows. While MRI has been a valuable tool in this field for the past 40 years, recent advances in imaging hardware, reconstruction software and particles synthesis have significantly enhanced its capabilities. This article provides an overview of the current challenges of MRI and progress in the field of granular media, and gives a perspective of the possible future developments in the field.

@en

The study of haemodynamics, or the mechanics of blood flow, has been a topic of significant interest since ancient times, as it provides critical insights into both the normal functioning of the circulatory system and the mechanisms underlying various diseases. A robust scientific understanding of these dynamics facilitates the development of innovative prevention and intervention strategies, such as advanced, less invasive surgical techniques and cost-effective medical devices, which can dramatically improve global health outcomes. Over the centuries, experimental, analytical, and, more recently, computational methods have enhanced our knowledge of cardiovascular and cerebrovascular conditions, leading to improved diagnostic and therapeutic approaches that enhance life quality and expectancy.

Despite these advancements, substantial challenges remain, particularly in diagnosing and understanding haemodynamic complications such as stroke, stenosis, and regurgitation. Modern imaging techniques like MRI and sonography are limited by spatial and temporal resolution, requiring significant hardware improvements to overcome these constraints. Moreover, while analytical models have evolved to address the complex nature of blood flow and vessel behavior, they often struggle to accurately represent in vivo scenarios, especially in areas like the cerebral vasculature that are difficult to image. The presence of anomalies such as medial calcifications - which are responsible behind numerous life altering conditions and diseases such as, diabetes, kidney disease and hypertension - further complicates the accurate modeling of blood flow dynamics by introducing departure from axisymmetry, changes in material properties of the tissue and impacting the physics at localized scale.

To address the impact of medial calcifications, this thesis presents a detailed approach starting with the development of a three-dimensional (3D) model that represents the physiological fluid-structure interaction (FSI) phenomenon of pulsatile blood flow through an Internal Carotid Artery (ICA) with medial calcification. ICA is a critical vessel within the Circle of Willis which itself is one of the most crucial cerebro-vascular networks. Following this, a physics based one-dimensional (1D) Reduced Order Model (ROM) is developed, integrated with which is a data-driven constitutive modelling framework trained on the 3D simulation data, to account for changes in material proeprties introduced by medial calcifications. This ROM aims to provide a computationally efficient yet accurate representation of the physiological changes caused by medial calcifications. The thesis includes a comprehensive theoretical framework, detailed validation and verification processes, and comparisons between the 1D and 3D models to ensure accuracy and clinical relevance. The overarching goal is to create a well-validated ROM that maintains essential physical details while reducing computational costs, with an emphasis on evaluating its performance in clinical scenarios and exploring its potential applications and future research directions.

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.

Magnetic resonance imaging (MRI) experiments have been performed in conjunction with direct numerical simulations (DNS) to study neutrally buoyant particle-laden pipe flows. The flows are characterized by the suspension liquid Reynolds number (Res), based on the bulk liquid velocity and suspension viscosity obtained from Eilers' correlation, the bulk solid volume fraction (φb), and the particle-to-pipe diameter ratio (d/D). Six different cases have been studied, each with a unique combination of Res and φ, while d/D is kept constant at 0.058. The selected cases ensure that the comparison is performed across different flow regimes, each exhibiting characteristic behavior. In general, an excellent agreement is found between experiment and simulation for the average liquid velocity and solid volume fraction profiles. Root-mean-square errors as low as 1.7% and 5.3% are found for the velocity and volume fraction profiles, respectively. This study presents accurate and quantitative velocity and volume fraction profiles of semidilute up to dense suspension flows using both experimental and numerical methods. Three different flow regimes are identified, based on the experimental and numerical solid volume fraction profiles. These profiles explain observations in the drag change. For low bulk solid volume fractions a drag increase (with respect to an equal Res single-phase case) is observed. For moderate volume fraction distributions the drag is found to decrease, due to particle accumulation at the pipe center. For high volume fractions the drag is found to decrease further. For solid volume fractions of 0.4 a drag reduction higher than 25% is found. This drag reduction is linked to the strong viscosity gradient in the radial direction, where the relatively low viscosity near the pipe wall acts as a lubrication layer between the pipe wall and the dense core.

@en

Particle-laden pipe flows are ubiquitous in industrial applications. Examples are industries like dredging, slurry transport, and the transport of reactants and products in chemical industries. One of the most important factors in these transport processes is the friction coefficient which relates directly to the pumping power which is a significant parameter for industries when viewed from an economic standpoint. The migration of particles in dense suspensions can significantly impact the friction coefficient in pipe flow. The clustering of particles in the core can lead to a reduction in the friction factor compared to a well-mixed particle suspension. This reduction is attributed to the decreased effective viscosity near the pipe wall. While the development lengths of single-phase flows are well known, limited knowledge exists regarding the development of velocity and concentration profiles in suspension flows.

The goal of this thesis is to study the development of neutrally buoyant suspension pipe flows. The experimental setup was validated using pressure drop measurements and the entrance length for single-phase pipe flow was obtained. The experiments for suspension flows involved varying the suspension Reynolds number and volume fractions keeping the particle size constant. Ultrasound imaging technique is used to circumvent the opacity of the suspension to study the development of suspension pipe flow. The inlet conditions for concentration were characterized, obtaining a uniform distribution at the inlet. Measurements are conducted at various locations downstream of the pipe and the velocity of the dispersed phase is obtained using ultrasound imaging velocimetry. Additionally, insights into the development of the concentration profile are obtained by checking the convergence towards a fully developed intensity profile, despite the fact that the image intensity doesn’t directly correlate to concentration profiles. The velocity profiles and intensity profiles were analyzed to understand the effect of radial migration on both concentration and velocity profiles. The entrance lengths for concentration and velocity were obtained for volume fractions ranging from 0.17 to 0.25 and suspension Reynolds numbers ranging from 500-2000. The results obtained revealed that the entrance length for concentration was greater than the entrance length for velocity. Scaling of the concentration entrance length with suspension Reynolds number and volume fractions were determined, and suspension Reynolds number scaled with an exponent of -1.62 and volume fraction scaled with an exponent of -2.1. This implies that the entrance length decreases with an increase in suspension Reynolds number and volume fraction. However, no definite trend was observed for the velocity entrance length.

Abstract: Ultrasound imaging velocimetry (UIV) refers to the technique wherein ultrasound images are analysed with 2D cross-correlation techniques developed originally in the framework of particle image velocimetry. Applying UIV to opaque, particle-laden multiphase flows have long been considered to be an attractive prospect. In this study, we demonstrate how fundamental differences in acoustical imaging, as compared to optical imaging, manifest themselves in the 2D cross-correlation analysis. A chief point of departure from conventional particle image velocimetry is the strong variation in the intensity profile of the acoustic wavefield, primarily caused by the attenuation of ultrasonic waves in particle-laden flows. Attenuation necessitates using a larger ensemble of correlation planes to obtain satisfactory time-averaged velocity profiles. For a given combination of imaging and flow conditions, attenuation sets upper limits on volume fraction, penetration depth, as well as temporal resolutions that may be accessed confidently. This behaviour is demonstrated in two experimental datasets and is also supported by a modified cross-correlation theory. The modification is brought about by incorporating a lumped model of ultrasonic backscattering in suspensions into existing spatial cross-correlation analysis. The two experimental datasets correspond to two distinct particle-laden pipe flows: (1) a neutrally buoyant non-Brownian suspension in a laboratory-scale flow facility, wherein particle sizes are comparable to the ultrasonic wavelength and (2) a non-Newtonian slurry in an industrial-scale flow facility, wherein particle sizes are much smaller than the ultrasonic wavelength. We illustrate how and to what extent correlation averaging can counteract the adversity caused by attenuation. The work herein offers a template for one to evaluate the performance of UIV in particle-laden flows. Graphical abstract: [Figure not available: see fulltext.].

@en

Abstract: We discuss empirical techniques to extract quantitative particle volume fraction profiles in particle-laden flows using an ultrasound transducer. A key step involves probing several uniform suspensions with varying bulk volume fractions from which two key volume fraction dependent calibration parameters are identified: the peak backscatter amplitude (acoustic energy backscattered by the initial layer of the suspension) and the amplitude attenuation rate (rate at which the acoustic energy decays with depth owing to scattering losses). These properties can then be used to reconstruct spatially varying particle volume fraction profiles. Such an empirical approach allows circumventing detailed theoretical models which characterize the interaction between ultrasound and suspensions, which are not universally applicable. We assess the reconstruction techniques via synthetic volume fraction profiles and a known particle-laden suspension immobilized in a gel. While qualitative trends can be easily picked up, the following factors compromise the quantitative accuracy: (1) initial reconstruction errors made in the near-wall regions can propagate and grow along the reconstruction direction, (2) multiple scattering can create artefacts which may affect the reconstruction, and (3) the accuracy of the reconstruction is very sensitive to the goodness of the calibration. Despite these issues, application of the technique to particle-laden pipe flows shows the presence of a core with reduced particle volume fractions in laminar flows, whose prominence reduces as the flow becomes turbulent. This observation is associated with inertia-induced radial migration of particles away from the pipe axis and is observed in flows with bulk volume fractions as high as 0.08. Even transitional flows with low levels of intermittency are not devoid of this depleted core. In conclusion, ultrasonic particle volume fraction profiling can play a key complementary role to ultrasound-based velocimetry in studying the internal features of particle-laden flows. Graphic abstract: [Figure not available: see fulltext.]

@en

This study focuses on the measurement accuracy of Magnetic Resonance Velocimetry (MRV) in high-speed turbulent flows. One of the most prominent errors in MRV is the displacement error, which describes the misregistration of spatial coordinates and velocity components in moving fluids. Displacement errors are particularly critical for experiments with high flow velocity and high spatial resolution. The degree of displacement error also depends on the sequence structure of the MRV technique. In this study, two MRV sequence types are examined regarding their measurement capabilities in high-speed turbulent flows: a conventional MRV sequence based on the popular “4D FLOW” technique, and a newly developed sequence, named “SYNC SPI”. Compared to conventional MRV, SYNC SPI is designed for high measurement accuracy, and not for imaging speed, which limits its application to statistically stationary flows. Both sequence types are evaluated in a flow experiment with a converging–diverging nozzle. Time-averaged results are presented for velocities up to 12 m/s at the throat. Supported by Particle Imaging Velocimetry, it is shown that SYNC SPI is capable of acquiring accurate velocity data in these highly turbulent flows. In contrast, the data from the conventional MRV sequence exhibits substantial displacement errors with a maximum displacement of 21 mm. The long acquisition time is the main disadvantage of the SYNC SPI sequence. Therefore, it is examined if undersampling and non-linear reconstruction, known as Compressed Sensing, can be utilized to make data acquisition more efficient. In the presented measurements, Compressed Sensing is successfully applied to shorten the acquisition time by up to 70% with almost no reduction in measurement accuracy.@en

The phenomenon of lateral migration of neutrally buoyant rigid spheres is studied experimentally for Poiseuille Flow. The study relied on the particle migration technique to capture the distribution of particles radial position at different flow parameters. In this thesis, the varying experimental parameters are flow Reynolds number and particle concentration. These two parameters have been reported to have an opposing effect on the migration. Reynolds number is varying at Re=200-1200 and the particle concentration at φ = 0.05-0.5% . The results reveal that an increase in Reynolds number and particle concentration causes the migration to develop at a longer distance from the inlet. The migration is said to be developed when the particles have migrated to the region between the tube-axis and tube-wall. An increase in particle concentration shows a similar effect with the Reynolds number on the migration which the migration develop at a longer distance. An interesting result occurred at high particle concentration, at which the significance of the Reynolds number in altering the migration is decreasing. The study is also conducted to the secondary phenomena following the migration, the generation of inner annulus and the formation of trains of particles. It is shown that the variation of Reynolds number and particle concentration are significantly affected these secondary phenomena.

The main goal of this master thesis is to reproduce by CFD computations the characteristic cavitation dynamics in a venturi which were experimentally discovered at TU Delft by Jahangir and al. The different cavitation regimes were obtained by modifying the global static pressure and flow velocity in the flow loop. Based on this, three different cloud cavitation shedding regimes were identified. One of the mechanisms appears at high cavitation number and can be attributed to the presence of a re-entrant liquid jet. Another dominant shedding mechanism was found at lower cavitation number, with the presence of propagating bubbly shock waves. A transition regime was also observed where both mechanisms seem to coexist. A two phases flow model is implemented in the open-source software OpenFOAM. The transition regime from the bubbly shock to the re-entrant jet dominated regime will be identified and compared to experimental findings. The three cavitation shedding regimes will be investigated by using different cavitation numbers. The simulations will mostly be conducted using an inviscid and incompressible solver.