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    The interactions of pyroclastic density currents with obstacles : a large-scale experimental study : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Earth Sciences at Massey University, Manawatū, Palmerston North, New Zealand
    (Massey University, 2023) Corna, Lucas
    Pyroclastic Density Currents (PDCs) are hot multiphase flows of volcanic particles and gas that are frequently produced during explosive volcanic eruptions. These fast-moving currents show variable runout distances that range from a few kilometres to more than 100 kilometres from their sources. Through their high velocities, large contents of respirable fine ash, temperatures and dynamic pressures, PDCs constitute extreme suffocation, burn and damage hazards for people living around volcanoes. An important additional source of hazard arises from the ability of PDCs to surmount significant topographic obstacles, such as hills and ridges. Because of their ferocity, to date there are no direct observations and measurements of PDCs interacting with obstacles and current knowledge comes from characterizing PDC deposits and PDC damage features across terrain after eruptions. The interaction of dense granular flows and dilute aqueous and gaseous particle-laden gravity currents with simple topographic barriers has been studied in laboratory experiments. These represent dense, non-turbulent or dilute, fully turbulent end-members of PDC behaviour. How the behaviour of dense and dilute end-member flows interacting with obstacles differs from those of real-world PDCs, which encompass a complete multiphase spectrum from dilute to dense transport regimes, remains unknown. This PhD research aims at bridging this gap in knowledge through synthesizing the behaviour of interaction of PDCs with ridge-shaped obstacles in large-scale experiments. The experiments were designed and conducted at the eruption simulator facility PELE (Pyroclastic flow Eruption Large-scale Experiment) to visualise the processes of PDCs interacting with obstacles, measure the changes in the flow velocity and density structure induced by this interaction, characterise the effects of the interaction on downstream flow behaviour, and study the variations in deposition across obstacles. Three hill-shaped obstacles were designed for these experiments, with the same shape and aspect ratio, but varying sizes compared to the size of the experimental PDC. The experiments reveal strong changes in the vertical velocity and density structures of the currents immediately before and after obstacles and strong losses in flow momentum. This is associated with flow compression and acceleration along the stoss side of the ridge, flow detachment with boundary layer separation behind the ridge crest, and formation of a turbulent wake underneath the detached flow before re-attachment. The amount of flow acceleration, the size of the turbulent wake and the flow re-attachment distance increase with obstacle size. High-speed video footage of the interaction shows evidence for a typical sequence of transient behaviour that could be linked to the time-variant velocity and density structure of the head, proximal body, distal body and a tail regions of the experimental PDCs. Four phases of interactions are noted in all three experiments: (1) during head passage - flow acceleration and compression on the stoss side, followed by detachment after the crest, generation of the wake behind the hills and re-attachment downstream; (2) during passage of the proximal body - the development of an alternatively thickening and collapsing turbulent jet structure along the stoss side that forms the base of the detached flow, and which separates and shields the wake from the detached flow above; (3) during passage of the remaining body - an increase in flow density leads to the blocking of a dense underflow forming thick deposits on the stoss side and to the advection of particles from the lower flow region into the detached flow above the wake; (4) during waning flow and passage of the gravity current tail - the velocity field rotates and the angle of attack of the flow approaches the inclination of the lee side of the obstacle. In this situation, the size of the turbulent wake decreases and eventually flow detachment ceases. The compression and acceleration of material on the stoss side of obstacles allow particles at the base of the flow to be conveyed upward back into the detached flow. The higher the obstacle, the stronger the acceleration and the larger the proportion of the flow that is advected. Ballistic trajectory models, which have been used to predict flow paths of dense and dilute analogues flows across simple obstacles, do not describe well the wake measured in experiments and under-estimate its dimensions. As evidenced by vortex shedding and high detachment angles in a flow with high Reynolds number, PDC-obstacle interactions are instead controlled by boundary layer separation in a turbulent flow. Therefore, they are linked to the drag coefficient of the hill and the drag force exerted by the obstacle onto the flow. A study of the wake dimensions revealed that a lift force assists in maintaining the wake aloft and in countering gravity. The ratio between the drag and lift forces controls the wake dimensions. An empirical scaling relationship between the re-attachment distance of the flow and the height of the obstacle was derived and tested against natural data of preserved tree patches behind hills. The experimental measurements also showed that loss in flow momentum due to obstacle drag is associated with complete blocking of the basal granular-fluid underflow and partial blocking of the upper dilute turbulent part of the experimental PDCs. Data from the three experimental runs, in combination with measurements from experiments with no obstacles, allowed extrapolation of the minimum ridge size that leads to complete flow blocking. This relationship agrees well with results from previous laboratory experiments on dilute gas-particle gravity currents and could find application in volcanic hazard estimates. The increasing loss in flow momentum with increasing obstacle size is associated with a strong reduction in the bulk flow density. Thus, experimental PDCs propagating over larger obstacles show a lower density contrast with the ambient air, and therefore a lower driving force, than currents propagating over smaller obstacles. Despite this, the final runout distances are remarkably similar in experiments with different obstacle sizes. This finding is explained by two different processes. First, flow compression and acceleration on the stoss side of obstacles leads to the acceleration of internal gravity waves. The gravity waves move faster than the surrounding flow, intrude and provide momentum into the PDC head. Initially slower currents behind large obstacles thus accelerate periodically and ‘catch up’ with less compressed and less accelerating currents downstream of smaller obstacles. Second, particles that sedimented below the level of the obstacle crest before the obstacle become advected with the detached flow into flow regions above the height of the crest. Larger obstacles, which induce stronger flow acceleration, advect particles higher into the detached flow than smaller obstacles. The duration and downstream length over which the advected particles re-sediment, deposit and eventually become inactive to drive the flow as excess density therefore increases with obstacle size. With increasing obstacle height, this second process generates increasingly hotter flows with slightly coarser and thicker deposits downstream of obstacles. The experimental results and relationships derived in this research add critical complexity to the understanding of PDCs interacting with topographic obstacles and resulting downstream hazards. The reported compressibility effects in the experimental PDCs are currently not captured in PDC flow and hazard models. The local flow acceleration against gravity on the obstacle stoss side warrants caution for the application of kinetic to potential energy conversion models that are used to estimate bulk velocities of PDCs. These findings encourage further experimental and numerical experiments to investigate, for instance, the more complex situations of three-dimensional obstacles, systematic test of different obstacle geometries and series of obstacles in PDC pathways to help development of predictive PDC flow and hazard models.
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    A multi-compartmental mathematical model of the postprandial human stomach : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Anatomy and Physiology at Massey University, Palmerston North, New Zealand
    (Massey University, 2020) Mary Vijay, Nikhila
    Computational fluid dynamics of the human stomach helps to understand the gastric processes such as trituration, mixing, and transit of digesta. Their outcomes give greater insight into the design of food and orally dosed drug delivery system. Current models of gastric contractile activity are primarily limited to the gastric antrum and assume global values for the various physiological characteristics. This thesis developed a unified compartmental gastric model with correctly informed anatomical and physiological data. The gastric geometry incorporated the actions of multiple compartments, such as the gastric fundus, body, antrum, pyloric canal, proximal duodenal cap, and the small intestinal brake. Lattice-Boltzmann Method (LBM) is used to simulate the fluid dynamics within the stomach. This thesis quantified the effects of transgastric pressure gradient (TGPG) between the fundus and the duodenum, the effect of antral propagating contraction (APC) amplitude, and the viscosity of the gastric contents on gastric flow, mixing, and gastric emptying. The results of this work suggest that TGPG influences gastric emptying where as APCs do not play major role in gastric emptying. Flow rate without TGPG obtained in this work agrees with previous work (Pal et al., 2004); however, it is higher in the presence of a TGPG. Results show that APCs promote recirculation, and the amplitude of APC is vital in this regard. The 'pendulating' flow of gastric content observed in this work is reported previously in duplex sonography experiments (Hausken et al., 1992). This work quantified the gastric shear rates (0.6 - 2.0 /s). This work also suggests that the viscosity of the content influences gastric fluid dynamics. This work is a simplified first step towards a 3D gastric model. Hence, these simulation studies were performed under two simplifications: dimensionality and rheology, i.e., we have assumed a Newtonian fluid flow in 2D gastric geometry. A 3D gastric model with more rheologically realistic fluid to explore the pseudoplastic fluid dynamics within the stomach in the future is recommended.
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    Inside pyroclastic surges - a characterisation of the flow behaviour, hazard impact mechanisms and sedimentation processes through large-scale experiments : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Earth Science at Massey University, Palmerston North, New Zealand
    (Massey University, 2020) Brosch, Ermanno
    Dilute pyroclastic density currents (or pyroclastic surges) are frequently occurring and highly dangerous volcanic flows generated during explosive volcanic eruptions. These fast and ground-hugging flows of hot volcanic particles and gas swiftly sweep across landscapes to cause significant risk to life and infrastructure at many volcanoes globally. Understanding the flow dynamics of pyroclastic surges, and developing a quantitative understanding of the mechanisms behind their hazard impacts, are thus important requisites for the development and testing of robust hazard mitigation strategies. Despite strong progress through field, theoretical, laboratory and numerical approaches during the past 50 years, the understanding of the flow and hazard behaviour of pyroclastic surges is still highly fragmentary. An important reason behind current gaps in knowledge stems from the hostile nature of these currents, which, to date, has prevented any direct observations and internal measurements. This leaves many theories behind flow and hazard models untested and un-validated. Over the past ten years, large-scale experiments have provided a novel approach to generate the missing ‘view’ inside pyroclastic density currents. While recent experiments have improved the understanding of the internal flow behaviour of dense pyroclastic density currents, comparable large-scale experimental studies for pyroclastic surges remain outstanding. This thesis describes the first systematic series of large-scale experiments that aimed to obtaining detailed measurements of the dangerous interior conditions of pyroclastic surges. Conducted at the international eruption simulator facility PELE (the Pyroclastic flow Eruption Large-scale Experiment), this study aimed to provide answers to the following three research questions: What are the flow-internal processes that cause the extreme destruction potential of pyroclastic surges? What is the detailed internal structure of pyroclastic surges? What are the particle-transport and sedimentation processes occurring in the basal region of dilute PDCs? Through the development of new measurement techniques and the refinement of existing set-up approaches, a systematic series of experiments were completed, which provided comprehensive datasets of dilute PDC analogues. The main results and implications of this research are as follows. Direct measurements of the internal velocity and density structure inside experimental flows show that turbulence is an important driver of the destructiveness of pyroclastic density currents. The effects of turbulence manifest themselves through three cumulative mechanisms. First, most of the flow energy becomes focussed into large eddies whose turbulent excursions generate destruction-causing dynamic pressures that exceed traditionally estimated mean values manifold. Second, self-developed pulsing inside flows, associated with the propagation of large coherent turbulence structures, leads to high dynamic pressures, propagating and perpetuating downstream. Third, the characteristic frequencies associated with large eddy motion are able to excite resonance in large buildings. The characterisation of gas-particle interactions inside the dynamically and kinematically scaled experimental pyroclastic surges revealed that commonly assumed near-homogeneous coupling between particles and gas is the exception, while strong to intermediate feedback loops between gas and solid phases are omnipresent throughout most of the evolving flow. This leads to interesting mesoscale turbulence effects, which are here shown to modify and control the evolving vertical flow stratification, the spatiotemporally varying deposition mechanisms, and the generation of turbulence in addition to the typically assumed shear and buoyancy processes. The spatially variable velocity of the leading front of the experimental surges is here demonstrated to behave differently to aqueous particle-laden gravity currents. The propagation of flow-internal pulses inside the highly turbulent gravity currents is a key mechanism in determining the flow runout and consequent hazard characteristics. The deposits of the experimental pyroclastic surges are here shown to have strong similarities to real-world deposits. Simultaneous measurements of the evolving structure of the lower flow boundary and the accreting deposit add complexity to our current qualitative view of the sediment transport and deposition mechanisms inside pyroclastic surges. The occurrence of mesoscale turbulence modifies particle supply into the lower flow boundary and, through the rapid passage of large-eddy passages in this region, gives rise to dynamic changes between a range of bedload transport processes and deposition rates. A correlation of the contribution of the different regions of the experimental surge to the spatially and temporally evolving deposit provides new insights in to how real-world deposits originate and how best to sample them to characterise the behaviour of past PDC-forming eruptions. Parts of the experimental datasets obtained during this research form the first international benchmark case to test, validate and compare the current range of numerical dilute PDC flow and hazard models.
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    Conservative permutation models of two-dimensional fluid flow : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University
    (Massey University, 1997) Turner, Paul Geoffrey
    At a meeting of Massey University Mathematics Department staff and students on 20 March 1997, a project to model fluid flow by constructing successive permutations of lattice cells was discussed. Several assumptions about the fluid being modelled were necessary to make the problem manageable, the chief ones being that the fluid would be two dimensional, ideal and in-compressible. Two square lattice models were developed, one Eulerian and the other more Lagrangian, in which the lattice cells were each initially assigned a value of a vorticity function. The time evolution of these models consisted of finding a permutation of the cells that was "close" to the fluid flow, then permuting the fixed initial vorticity values according to this lattice map. Justification of this method followed from consequences of the assumptions, including advection of vorticities, and the invertibility and area-preserving nature of the fluid flow map. Reliance was placed on two previously published papers: one containing a result guaranteeing that such permutations are possible in certain circumstances, and the other providing the key to their practical construction. An essential algorithm in the latter paper relies on a theorem concerning the selection of a set of distinct elements from several sets. Also as a result of the assumptions, the enstrophy, total vorticity and kinetic energy of such hypothetical fluid flow is conserved, although tests neither conclusively confirmed nor denied all conserving properties of the models.
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    A CFD modelling system for air flow and heat transfer in ventilated packing systems during forced-air cooling of fresh produce : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Food Engineering at Massey University
    (Massey University, 2002) Zou, Qian
    Forced-air cooling is the common method for precooling horticultural produce. Ventilated packaging systems are often used to facilitate cooling efficiency. A computational fluid dynamics (CFD) modelling system was developed to simulate airflow and heat transfer processes in the layered and bulk packaging systems during the forced-air cooling of fresh produce. Airflow and heat transfer models were developed using a porous media approach. The areas inside the packaging systems were categorised as solid, plain air, and produce-air regions. The produce-air regions inside the bulk packages or between trays in the layered packages were treated as porous media, in which the volume-average transport equations were employed. This approach avoids dealing with the situation-specific and complex geometries inside the packaging systems, and therefore enables the development of a general modelling system suitable for a wide range of packaging designs and produce. The calculation domains were discretised with a block-structured mesh system that was referenced by global and local grid systems. The global grid system specifies the positions of individual packages in a stack, and the local grid system describes the structural details inside individual package. The solution methods for airflow and heat transfer models were based on SIMPLER (Semi-Implicit Method for Pressure-Linked equations Revised) method schemes, and the systems of linear algebraic equations were solved with GMRES (Generalised Minimum Residual) method. A prototype software package CoolSimu was developed to implement the solution methods. The software package hid the core components (airflow and heat solvers) from user, so that the users without any knowledge of CFD and heat transfer can utilise the software to study cooling operations and package designs. The user interaction components in CoolSimu enable users to specify packaging systems and cooling conditions, control the simulation processes, and visualise the predicted airflow patterns and temperature profiles. When the predicted and measured product centre temperatures were compared during the forced-air cooling of fresh fruit in several layered and bulk packaging systems, good agreements between the model predictions and experimental data were obtained. Overall, the developed CFD modelling system predicted airflow patterns and temperature profiles with satisfactory accuracy.