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.