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1
Yeates, Peter Stafford. "Deep mixing in stratified lakes and reservoirs." University of Western Australia. Centre for Water Research, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0046.
Full textAbstract:
The onset of summer stratification in temperate lakes and reservoirs forces a decoupling of the hypolimnion from the epilimnion that is sustained by strong density gradients in the metalimnion. These strong gradients act as a barrier to the vertical transport of mass and scalars leading to bottom anoxia and subsequent nutrient release from the sediments. The stratification is intermittently overcome by turbulent mixing events that redistribute mass, heat, dissolved parameters and particulates in the vertical. The redistribution of ecological parameters then exerts some control over the ecological response of the lake. This dissertation is focused on the physics of deep vertical mixing that occurs beneath the well-mixed surface layer in stratified lakes and reservoirs. The overall aim is to improve the ability of numerical models to reproduce deep vertical mixing, thus providing better tools for water quality prediction and management. In the first part of this research the framework of a one-dimensional mixed-layer hydrodynamic model was used to construct a pseudo two-dimensional model that computes vertical fluxes generated by deep mixing processes. The parameterisations developed for the model were based on the relationship found between lake-wide vertical buoyancy flux and the first-order internal wave response of the lake to surface wind forcing. The ability of the model to reproduce the observed thermal structure in a range of lakes and reservoirs was greatly improved by incorporating an explicit turbulent benthic boundary layer routine. Although laterally-integrated models reproduce the net effect of turbulent mixing in a vertical sense, they fail to resolve the transient distribution of turbulent mixing events triggered by local flow properties defined at far smaller scales. Importantly, the distribution of events may promote tertiary motions and ecological niches. In the second part of the study a large body of microstructure data collected in Lake Kinneret, Israel, was used to show that the nature of turbulent mixing events varied considerably between the epilimnion, metalimnion, hypolimnion and benthic boundary layer, yet the turbulent scales of the events and the buoyancy flux they produced collapsed into functions of the local gradient Richardson number. It was found that the most intense events in the metalimnion were triggered by high-frequency waves generated near the surface that grew and imparted a strain on the metalimnion density field, which led to secondary instabilities with low gradient Richardson numbers. The microstructure observations suggest that the local gradient Richardson number could be used to parameterise vertical mixing in coarse-grid numerical models of lakes and reservoirs. However, any effort to incorporate such parameterisations becomes meaningless without measures to reduce numerical diffusion, which often dominates over parameterised physical mixing. As a third part of the research, an explicit filtering tool was developed to negate numerical diffusion in a threedimensional hydrodynamic model. The adaptive filter ensured that temperature gradients in the metalimnion remained within bounds of the measured values and so the computation preserved the spectrum of internal wave motions that trigger diapycnal mixing events in the deeper reaches of a lake. The results showed that the ratio of physical to numerical diffusion is dictated by the character of the dominant internal wave motions.
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Hnidei, Stephen D. "Selective withdrawal of a linearly stratified fluid in a triangular reservoir." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/28834.
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The water in most reservoirs is density stratified with depth. This stratification leads to the inhibition of vertical movement, consequently, when water is withdrawn from the reservoir it tends to move in a jet-like layer called a withdrawal layer, towards the sink. By placing the sink at a certain depth, one is able to selectively withdrawal water from a limited range of depths and thus obtain water of a desired quality.
Much work has been done in this field by considering a simplified boundary geometry, usually rectangular. However little attention has been given to the effects of accurate boundary geometry. For this thesis, five numerical experiments were conducted for the problem of a two-dimensional, viscous, incompressible, slightly-stratified flow towards a sink in a triangular reservoir.Science, Faculty of
Mathematics, Department of
Graduate
3
Marti, Clelia Luisa. "Exchange processes between littoral and pelagic waters in a stratified lake." University of Western Australia. Centre for Water Research, 2004. http://theses.library.uwa.edu.au/adt-WU2005.0005.
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[Truncated abstract] The lake boundaries are an important source of sediment, nutrients and chemicals. For life inside the lake, the exchange between the lake boundaries (littoral) and lake interior (pelagic) is of central importance to Limnology as the net flux of nutrients into the water column is both the driving force and limiting factor for most algae blooms found during the stratification period. Consequently, the understanding of the relevant processes defining such an exchange is a further step toward a sound basis for future decisions by lake managers in order to ensure high water quality. The objective of this research was to investigate the physical processes responsible for the exchange of water and particles between the lake boundaries and the lake interior. An integrated approach using field experiments and 3D modelling as applied to Lake Kinneret (Israel) is presented. The field data revealed large-scale metalimnion oscillations with amplitudes up to 10 m in response to westerly diurnal winds, the existence of a well-defined suspended particle intrusion into the metalimnion of the lake, characterized by high concentrations of organic matter, and a well-mixed benthic boundary layer (BBL). The changes in the thermal structure explained the observed vertical and horizontal movements of the suspended particle intrusion. The horizontal advective transport via the metalimnion, associated with the velocities induced by the basin-scale mode-two Poincare wave, controlled the exchange between the lake boundaries and lake interior on daily time scales. The observed BBL over the lake slope varied markedly with time and space. Detailed comparison of simulation results with field data revealed that the model captured the lake hydrodynamics for time scales from hours to days. The model could then be used to extract the residual motions in the various regions of the lake. The residual motions below the surface layer were predominantly forced by the basin-scale internal wave motions, but the residual motion in the surface layer was found to be very sensitive to the curl of the wind field. The residual circulation was responsible for redistributing mass throughout the lake basin on time scales from days to weeks. A clear connection of dynamics of the BBL with the large-scale features of the flow was addressed. The time history of the mixing in the BBL and the resulting cross-shore flux was shown to vary with the phase of the basin-scale internal waves.
4
Dunbar, Donald Stanley 1953. "A numerical model of stratified circulation in a shallow-silled inlet." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/25571.
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A numerical model has been developed for the study of stratified tidal circulation in Indian Arm - a representative inlet on the southern coast of British Columbia. Equations for horizontal velocity, salt conservation, continuity, density (calculated as a linear function of salinity), and the hydrostatic approximation govern the dynamics. All equations have been laterally integrated under the assumption of negligible cross-inlet variability. The model is time dependent and includes nonlinear advective terms, horizontal and vertical turbulent diffusion of salt and momentum, and variations in width and depth. Provisions for surface wind stress and a flux of fresh water are also included, although neither was utilized in this study. An explicit finite difference scheme centred in both time and space was used to solve for the horizontal and vertical velocity components, salinity, and surface elevation on a staggered rectangular grid. A backward Euler scheme was used to suppress the computational mode. Tests using a semi-implicit scheme to solve the finite difference
equations over realistic topography led to numerical instabilities at modest values of the time step - in spite of the unconditional stability criteria - suggesting that linear stability analysis may give misleading results for strongly nonlinear systems. Surface elevations
calculated from tidal harmonic analysis and salinity timeseries derived from linearly interpolated CTD casts were prescribed at the open boundary.
Initial and boundary conditions based on observations in Burrard Inlet and Indian Arm during the winter of 1974-75 were used to study the inlet's response to tidal forcing and to simulate the deep-water renewal that occurred during this period. Coefficients for the horizontal
turbulent diffusion of momentum and salt were set equal to 10⁶ cm² s⁻¹. Reducing this value by a factor of two was found to have little impact on the solution. A further reduction to 10³ cm² s⁻¹ led to numerical instabilities under conditions of dense water inflow. The side friction term in the momentum balance was tuned to match calculated and observed dissipation rates in Burrard Inlet; leading to good agreement between the observed and calculated barotropic tide. Contour plots of tidal amplitudes and phases for model currents and salinities revealed a standing wave pattern for the K₁ and M₂ internal tides in Indian Arm; thus allowing for the possibility of resonance. A comparison of model results with vertical amplitude and phase profiles from harmonic analysis of Cyclesonde current meter timeseries at two locations in Indian Arm was consistent with this result. A least-squares fit was made of the vertical modal structure in the model to the complex tidal amplitudes. This led to calculations of the kinetic energy contained in each of the modes along the model inlet for the M₂ and K₁ constituents. Most of the energy was found to be contained in the barotropic and first baroclinic modes, with the latter dominating in the deep basin, and the former dominating near the sill. Second mode energy was significant for the K₁ constituent at some locations in Indian Arm. There are clear indications in the model of barotropic tidal energy being radiated into the inlet basin via the internal tide.
Simulations of the influx of dense water into Indian Arm yielded exchange rates that are consistent with observed values and suggest the possibility of fine-tuning the model coefficients to allow prediction of future overturning events.Science, Faculty of
Earth, Ocean and Atmospheric Sciences, Department of
Graduate
5
Shimizu, Kenji. "Application of modal analysis to strongly stratified lakes." University of Western Australia. Faculty of Engineering, Computing and Mathematics, 2009. http://theses.library.uwa.edu.au/adt-WU2009.0079.
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Modal analysis for strongly stratified lakes was extended to obtain a better understanding of the dynamics of the basin-scale motions. By viewing the basin-scale motions as a superposition of modes, that have distinct periods and three-dimensional structures, the method provides a conceptual understanding for the excitation, evolution, and damping of the basin-scale motions. Once the motion has been decomposed into modes, their evolution and energetics may be extracted from hydrodynamic simulation results and field data. The method was applied to Lake Biwa, Japan, and Lake Kinneret, Israel, and used for a theoretical study. The real lake applications showed that winds excited basin-scale motions that had a surface layer velocity structure similar to the wind stress pattern. Three-dimensional hydrodynamics simulations of Lake Biwa indicated that most of the energy input from winds was partitioned into the internal waves that decayed within a few days. The gyres, on the other hand, received much less energy but dominated the dynamics during calm periods due to their slow damping. Analyses of field data from Lake Kinneret suggested that the internal waves, excited by the strong winds every afternoon, were damped over a few days primarily due to bottom friction. Theoretical investigations of damping mechanisms of internal waves revealed that bottom friction induced a velocity anomaly at the top of the boundary layer that drained energy from the nearly inviscid interior by a combination of internal wave cancelling and spin-down. These results indicate that gyres induce long-term horizontal transport near the surface and internal waves transfer energy from winds to near-bottom mixing. Modal structure of dominant basin-scale internal waves can induce large heterogeneity of nearbottom mass transfer processes. The method presented here provides a tool to determine how basin-scale motions impact on biogeochemical processes in stratified lakes.
6
Zhang, Xizheng. "Mathematical modelling of nonlinear ring waves in a stratified fluid." Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/18587.
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Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this thesis, we study long linear and weakly-nonlinear ring waves in a stratified fluid in the presence of a depth-dependent horizontal shear flow. It is shown that despite the clashing geometries of the waves and the shear flow, there exists a linear modal decomposition, which can be used to describe distortion of the wavefronts of surface and internal waves, and systematically derive a 2+1-dimensional cylindrical Korteweg-de Vries (cKdV)-type equation for the amplitudes of the waves. The general theory is applied to the case of the waves in a two-layer fluid with a piecewise-constant shear flow, with an emphasis on the effect of the shear flow on the geometry of the wavefronts. The distortion of the wavefronts is described by the singular solution (envelope of the general solution) of the nonlinear first order differential equation, constituting generalisation of the dispersion relation in this curvilinear geometry. There exists a striking difference in the shape of the wavefronts: the wavefront of the surface wave is elongated in the shear flow direction while the wavefront of the interfacial wave is squeezed in this direction. We solve the derived 2+1-dimensional cKdV-type equation numerically using a finite-difference scheme. The effects of nonlinearity and dispersion are studied by considering numerical results for surface and interfacial ring waves generated from a localised source with and without shear flow and the 2D dam break problem. In these examples, the linear and nonlinear surface waves are faster than interfacial waves, the wave height decreases faster at the surface, the shear flow leads to the wave height decreasing slower downstream and faster upstream, and the effect becomes more prominent as the shear flow strengthens.
7
Jung, Kyung Tae. "On three-dimensional hydrodynamic numerical modelling of wind induced flows in stably stratified waters : a Galerkin-finite difference approach." Title page, contents and summary only, 1989. http://web4.library.adelaide.edu.au/theses/09PH/09phj95.pdf.
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Eaves, Thomas Scott. "Generalised nonlinear stability of stratified shear flows : adjoint-based optimisation, Koopman modes, and reduced models." Thesis, University of Cambridge, 2016. https://www.repository.cam.ac.uk/handle/1810/260824.
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In this thesis I investigate a number of problems in the nonlinear stability of density stratified plane Couette flow. I begin by describing the history of transient growth phenomena, and in particular the recent application of adjoint based optimisation to find nonlinear optimal perturbations and associated minimal seeds for turbulence, the smallest amplitude perturbations that are able to trigger transition to turbulence. I extend the work of Rabin et al. (2012) in unstratified plane Couette flow to find minimal seeds in both vertically and horizontally sheared stratified plane Couette flow. I find that the coherent states visited by such minimal seed trajectories are significantly altered by the stratification, and so proceed to investigate these states both with generalised Koopman mode analysis and by stratifying the self-sustaining process described by Waleffe (1997). I conclude with an introductory problem I considered that investigates the linear Taylor instability of layered stratified plane Couette flow, and show that the nonlinear evolution of the primary Taylor instability is not coupled to the form of the linearly unstable mode, in contrast to the Kelvin-Helmholtz instability, for example. I also include an appendix in which I describe joint work conducted with Professor Neil Balmforth of UBC during the 2015 WHOI Geophysical Fluid Dynamics summer programme, investigating stochastic homoclinic bifurcations.
9
Ben, Cheikh Samir. "Etude numerique comparative des solutions exactes et approchees de la convection naturelle instationnaire en milieu confine stratifie." Poitiers, 1987. http://www.theses.fr/1987POIT2257.
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Darbyshire, Oliver Richard. "Modelling of turbulent stratified flames." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/247473.
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Due to concerns about pollutant emission combustion systems are increasingly being designed to operate in a lean premixed mode. However, the reduction in emissions offered by lean premixed combustion can be offset by its susceptibility to instabilities and ignition and extinction problems. These instabilities, caused by the coupling of unsteady heat release and pressure fluctuations can cause significant damage to combustion devices. One method of avoiding these problems whilst still operating a globally lean system is to employ a stratified premixed mode where areas of richer mixture are used to enhance the stability of the flame. In this thesis a computational modelling methodology for the simulation of stratified premixed flames is developed. Firstly, several sub-models for the dissipation rate of a reacting scalar are evaluated by the simulation of two laboratory scale flames, a turbulent stratified V-flame and a dump combustor fed by two streams of different mixture strength. This work highlights the importance of this quantity and its influence on the simulation results. Any model for stratified combustion requires at least two variables to describe the thermochemical state of the gas: one to represent the mixing field and another to capture the progress of reaction. In turbulent stratified flames the joint probability density function (pdf) of these variables can be used to recover the mean reaction rates. A new formulation for this pdf based on copula methods is presented and evaluated alongside two alternative forms. The new method gives improved results in the simulation of the two test cases above. As it is likely that practical stratified combustion devices will have some unsteadiness to the flow the final part of this work applies the modelling methodology to an unsteady test case. The influence of the unsteady velocity forcing on the pollutant emissions is investigated. Finally the methodology is used to simulate a developmental, liquid fuelled, lean burn aero-engine combustor. Here the model gives reasonable predictions of the measured pollutant emissions for a relatively small computational cost. As such it is hoped that the modelling methodology presented can be useful in the iterative industrial design process of stratified combustion systems.
11
Williams, Paul David. "Nonlinear interactions of fast and slow modes in rotating, stratified fluid flows." Thesis, University of Oxford, 2003. http://ora.ox.ac.uk/objects/uuid:5365c658-ab60-41e9-b07b-0f635909835e.
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This thesis describes a combined model and laboratory investigation of the generation and mutual interactions of fluid waves whose characteristic scales differ by an order of magnitude or more. The principal aims are to study how waves on one scale can generate waves on another, much shorter scale, and to examine the subsequent nonlinear feedback of the short waves on the long waves. The underlying motive is to better understand such interactions in rotating, stratified, planetary fluids such as atmospheres and oceans. The first part of the thesis describes a laboratory investigation using a rotating, two-layer annulus, forced by imposing a shear across the interface between the layers. A method is developed for making measurements of the two-dimensional interface height field which are very highly-resolved both in space and time. The system's linear normal modes fall into two distinct classes: 'slow' waves which are relatively long in wavelength and intrinsic period, and 'fast' waves which are much shorter and more quickly-evolving. Experiments are performed to categorize the flow at a wide range of points in the system's parameter space. At very small background rotation rates, the interface is completely devoid of waves of both types. At higher rates, fast modes only are generated, and are shown to be consistent with the Kelvin-Helmholtz instability mechanism based on a critical Richardson number. At rotation rates which are higher still, baroclinic instability gives rise to the onset of slow modes, with subsequent localized generation of fast modes superimposed in the troughs of the slow waves. In order to examine the generation mechanism of these coexisting fast modes, and to assess the extent of their impact upon the evolution of the slow modes, a quasi-geostrophic numerical model of the laboratory annulus is developed in the second part of the thesis. Fast modes are filtered out of the model by construction, as the phase space trajectory is confined to the slow manifold, but the slow wave dynamics is accurately captured. Model velocity fields are used to diagnose a number of fast wave radiation indicators. In contrast to the case of isolated fast waves, the Richardson number is a poor indicator of the generation of the coexisting fast waves that are observed in the laboratory, and so it is inferred that these are not Kelvin-Helmholtz waves. The best indicator is one associated with the spontaneous emission of inertia-gravity waves, a generalization of geostrophic adjustment radiation. A comparison is carried out between the equilibrated wavenumbers, phase speeds and amplitudes of slow waves in the laboratory (which coexist with fast modes), and slow waves in the model (which exist alone). There are significant differences between these wave properties, but it is shown that these discrepancies can be attributed to uncertainties in fluid properties, and to model approximations apart from the neglect of fast modes. The impact of the fast modes on the slow modes is therefore sufficiently small to evade illumination by this method of inquiry. As a stronger test of the interaction, a stochastic parameterization of the inertia-gravity waves is included in the model. Consistent with the laboratory/model intercomparison, the parameterized fast waves generally have only a small impact upon the slow waves. However, sufficiently close to a transition curve between two different slow modes in the system's parameter space, it is shown that the fast modes can exert a dominant influence. In particular, the fast modes can force spontaneous transitions from one slow mode to another, due to the phenomenon of stochastic resonance. This finding should be of interest to the meteorological and climate modelling communities, because of its potential to affect model reliability.
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Wells, Judith R. (Judith Roberta). "A laboratory study of localized boundary mixing in a rotating stratified fluid." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/58062.
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Thesis (Ph. D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, and the Woods Hole Oceanographic Institution), 2003.Includes bibliographical references (p. 145-148).
Oceanic observations indicate that abyssal mixing is localized in regions of rough topography. How locally mixed fluid interacts with the ambient fluid is an open question. Laboratory experiments explore the interaction of mechanically induced boundary mixing and an interior body of linearly stratified rotating fluid. Turbulence is generated by a vertically oscillating horizontal bar, located at middepth along the tank wall. The turbulence forms a region of mixed fluid which quickly reaches a steady state height and collapses into the interior. The mixed layer thickness ... is independent of the Coriolis frequency f. N is the buoyancy frequency, co is the bar frequency, and the constant, Y=1 cm, is empirically determined by bar mechanics. In initial experiments, the bar is exposed on three sides. Mixed fluid intrudes directly into the interior as a radial front of uniform height, rather than as a boundary current. Mixed fluid volume grows linearly with time ... The circulation patterns suggest a model of unmixed fluid being laterally entrained with velocity, e Nhm, into the sides of a turbulent zone with height hm and width Lf ... where Lf is an equilibrium scale associated with rotational control of bar-generated turbulence. In accord with the model, outflux is constant, independent of stratification and restricted by rotation ... Later experiments investigate the role of lateral entrainment by confining the sides of the mixing bar between two walls, forming a channel open to the basin at one end. A small percentage of exported fluid enters a boundary current, but the bulk forms a cyclonic circulation in front of the bar. As the recirculation region expands to fill the channel, it restricts horizontal entrainment into the turbulent zone. The flux of mixed fluid decays with time.
(cont.) ... The production of mixed fluid depends on the size of the mixing zone as well as on the balance between turbulence, rotation and stratification. As horizontal entrainment is shut down, longterm production of mixed fluid may be determined through much weaker vertical entrainment. Ultimately, the export of mixed fluid from the channel is restricted to the weak boundary current.
by Judith R. Wells.
Ph.D.
13
Lai, Wing-chiu Derek, and 黎永釗. "The propagation of nonlinear waves in layered and stratified fluids." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B29750441.
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Guvenen, Haldun. "Aerodynamics of bodies in shear flow." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184917.
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This dissertation investigates spanwise periodic shear flow past two-dimensional bodies. The flow is assumed to be inviscid and incompressible. Using singular perturbation techniques, the solution is developed for ε = L/ℓ ≪ 1, where L represents body cross-sectional size, and ℓ the period of the oncoming flow U(z). The singular perturbation analysis involves three regions: the inner, wake and outer regions. The leading order solutions are developed in all regions, and in the inner region higher order terms are obtained. In the inner region near the body, the primary flow (U₀, V₀, P₀) corresponds to potential flow past the body with a local free stream value of U(z). The spanwise variation in U(z) produces a weak O(ε) secondary flow W₁ in the spanwise direction. As the vortex lines of the upstream flow are convected downstream, they wrap around the body, producing significant streamwise vorticity in a wake region of thickness O(L) directly behind the body. This streamwise vorticity induces a net volume flux into the wake. In the outer region far from the body, a nonlifting body appears as a distribution of three-dimensional dipoles, and the wake appears as a sheet of mass sinks. Both singularity structures must be included in describing the leading outer flow. For lifting bodies, the body appears as a lifting line, and the wake appears as a sheet of shed vorticity. The trailing vorticity is found to be equal to the spanwise derivative of the product of the circulation and the oncoming flow. For lifting bodies the first higher order correction to the inner flow is the response of the body to the downwash produced by the trailing vorticity. At large distances from the body, the flow takes on remarkably simple form.
15
Blue, Julie Elena. "Predicting tracer and contaminant transport with the stratified aquifer approach." Diss., The University of Arizona, 1999. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu_e9791_1999_426_sip1_w.pdf&type=application/pdf.
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Wong, Ka-chung Colin, and 黃家聰. "Hydraulics of bottom rack chamber for supercritical flow diversion." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B42664469.
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Henry, Eric James. "Contaminant induced flow effects in variably-saturated porous media." Diss., The University of Arizona, 2001. http://hdl.handle.net/10150/191256.
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Dissolved organic contaminants that decrease the surface tension of water (surfactants) can have an effect on unsaturated flow through porous media due to the dependence of capillary pressure on surface tension. One and two-dimensional (1D, 2D) laboratory experiments and numerical simulations were conducted to study surfactant-induced unsaturated flow. The 1D experiments investigated differences in surfactant-induced flow as a function of contaminant mobility. The flow in a system contaminated with a high solubility, mobile surfactant, butanol, was much different than in a system contaminated with a sparingly soluble, relatively immobile surfactant, myristyl alcohol (MA). Because surface tension depression caused by MA was confined to the original source zone, the MA system was modeled using a standard unsaturated flow model (HYDRUS-1D) by assigning separate sets of hydraulic functions to the initially clean and source zones. To simulate the butanol system, HYDRUS-1D was modified to incorporate surfactant concentration-dependent changes to the moisture content-pressure head and unsaturated hydraulic conductivity functions. Following the 1D study, a two-dimensional flow cell (2.4 x 1.5 x 0.1 m) was used to investigate the infiltration of a surfactant contaminant plume from a point source on the soil surface, through the vadose zone, and toward a shallow aquifer. Above the top of the capillary fringe the advance of the surfactant solution caused a drainage front that radiated from the point source. Upon reaching the capillary fringe, the drainage front caused a localized depression of the capillary fringe and eventually a new capillary fringe height was established. Horizontal transport of surfactant in the depressed capillary fringe caused the propagation of a wedge-shaped drainage front in the downgradient direction. The numerical model HYDRUS-2D was modified to account for surfactant concentration-dependent effects on the unsaturated hydraulic functions and was successfully used to simulate the surfactant infiltration experiment. The extensive propagation of the drying front and the effect of vadose zone drainage on contaminant breakthrough time demonstrate the potential importance of considering surface tension effects on unsaturated flow and transport in systems containing surface-active organic contaminants or in systems where surfactants are used for remediation of the vadose zone or unconfined aquifers.
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Zeidan, Dia Hussein Abdulhameed. "Mathematical and numerical study of two-phase flow models." Thesis, Manchester Metropolitan University, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.396533.
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Wang, Ying, and 王瑩. "A study of mutual fund flow and market return volatility." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B26843572.
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BASEGHI, BEHDAD. "THREE-DIMENSIONAL SEEPAGE THROUGH POROUS MEDIA WITH THE RESIDUAL FLOW PROCEDURE." Diss., The University of Arizona, 1987. http://hdl.handle.net/10150/184107.
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The purpose of this study is to present the development and application of residual flow procedure for analysis of three-dimensional (3-D) steady-state and transient seepage. The finite element equations are derived using a pseudo-variational principle which leads to a transient residual flow (load) vector that, in turn, is used to correct the position of the free surface iteratively. The procedure involves a fixed mesh which requires no mesh regeneration during transient analysis and during iterations. The procedure is also capable of handling material nonhomogeneities and anisotropy with relative ease. Several applications are made including verification with respect to closed-form solutions, and with results from a laboratory glass bead model simulating three-dimensional situations. For these glass beads, the coefficients of permeability and specific storage are also evaluated experimentally.
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Chan, Johnson Lap-Kay. "Numerical procedure for potential flow problems with a free surface." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/28637.
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A numerical procedure based upon a boundary integral method for gravity wave making problems is studied in the time domain. The free-surface boundary conditions are combined and expressed in a Lagrangian notation to follow the free-surface particle's motion in time. The corresponding material derivative term is approximated by a finite difference expression, and the velocity terms are extrapolated in time for the completion of the formulations. The fluid-body intersection position at the free surface is predicted by an interpolation function that requires information from both the free surface and the submerged surface conditions. Solutions corresponding to a linear free-surface condition and to a non-linear free-surface condition are obtained at small time increment values. Numerical modelling of surface wave problems is studied in two dimensions and in three dimensions. Comparisons are made to linear analytical solutions as well as to published experimental results. Good agreement between the numerical solutions and measured values is found. For the modelling of a three dimensional wave diffraction problem, results at high wave amplitude are restricted because of the use of quadrilateral elements. The near cylinder region of the free surface is not considered to be well represented because of the coarse element size. Wave forces calculated on the vertical cylinder are found to be affected by the modelled tank length. When the simulated wave length is comparable to the wave tank's dimension, numerical results are found to be less than the experimental measurements. However, when the wave length is shorter than the tank's length, solutions are obtained with very good precision.Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate
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Liu, Peng, and 刘鹏. "Flow mechanisms in horizontal sediment-laden jets." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B49799496.
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Particle-laden jets are an important type of multiphase flow which can be found in various natural and technical processes. This study focuses on the flow mechanisms in a horizontally discharging sediment-laden jet that is of particular interest in environmental science and engineering.
Experimental techniques and mathematical models are developed to investigate horizontal sediment-laden jets, both for the buoyant and non-buoyant jet discharge cases. In the laboratory, the separation of images of the fluid and the particulate phases is achieved by harnessing light signals of visualization at different wavelengths. Whole field measurements of velocities of the two phases are made by the adoption of particle image velocimetry (PIV) algorithms. Numerical models are developed in two approaches with regard to the treatment of the particulate phase. In the Lagrangian approach, individual sediment particles are tracked while the flow field of the fluid phase is computed with large-eddy simulation (LES). This simulation successfully captures the transient nature of the particle-laden flow. In the Eulerian approach, a two-phase model is used to obtain steady flow simulations in a much shorter computation time.
The experimental and numerical results for the horizontal momentum jets show that, at low initial particle concentrations, the sediment particles generally follow the jet flow but with some levels of deficit velocities. In the upper layer of the jet the particles do not follow the fluid flow as well as in its lower layer. More particles are observed in the lower layer than in the upper one. For the momentum-dominated zone of a horizontal buoyant jet, the flow exhibits similar behaviors as the horizontal particle-laden momentum jet, except that there are some slight modifications from the effects of buoyancy. In the bending zone of the buoyant jet, the effects of buoyancy become significant. Notably, the locations of maximum velocity magnitude and those of maximum turbulence intensity are well separated in this zone. A strong correlation of particle abundance and high turbulence intensity is observed in the lower outer jet layer in this bending zone.
Significant modifications to the global behaviors of horizontal sediment jets are observed as the particle concentration increases to relatively high levels. The jet trajectories are brought downwards by the particle loads and the jet widths are also increased. For the flow regime being investigated, turbulence intensity in the fluid flow is found to be increased by the presence of sediment particles.
The results suggest that turbulence helps suspend sediment particles in horizontally discharging jets. A Stokes number is proposed to represent the ability of particles to follow the fluid flow. It is defined as St=W_s/U_j , where ws is the particle settling velocity in still fluid and Uj is the jet exit velocity, which indirectly governs the turbulence characteristics of the jet flow.
The advecting large eddies in a turbulent jet are found to play the role of organizing particles in patches. Interaction and coalescence between particle-concentrated eddies may result in the sudden drop of a group of particles, which contributes to sediments falling from a horizontal jet in the form of particle-rich “fingers”.published_or_final_version
Civil Engineering
Doctoral
Doctor of Philosophy
23
Zoebelein, Till. "Development of an LU-scheme for the solution of hypersonic non-equilibrium flow." Thesis, Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/12509.
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Wong, Ching-chi, and 黃精治. "Flow and pollutant dispersion over idealized urban street canyons using large-eddy simulation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/206698.
Full textAbstract:
Flows and pollutant dispersion over flat rural terrain have been investigated for decades. However, our understanding of their behaviours over urban areas is rather limited. Most cases have either focused on street level or in the roughness sub-layer (RSL) of urban boundary layer (UBL). Whereas, only a handful of studies have looked into the coupling between street-level and UBL-core dynamics, and their effects on pollutant dispersion.
In this thesis, computational fluid dynamics (CFD) is employed to examine the flows and pollutant transport in and over urban roughness. Idealised two-dimensional (2D) street canyons are used as the basic units fabricating hypothetical urban surfaces. A ground-level passive and chemically inert pollutant source is applied to simulate the flows and pollutant dispersion over rough surfaces in isothermal condition. Large-eddy simulation (LES) with the one-equation subgrid-scale model is used to solve explicitly the broad range of scales in turbulent flows. Arrays of idealized street canyons of both uniform and non-uniform building height are used to formulate a unified theory for the flows and pollutant dispersion over urban areas of different morphology. The geometry of roughness elements is controlled by the building-height-to-street-width (aspect) ratio (0.083 ≤ AR ≤ 2) and/or the building height variability (BHV = 0.2, 0.4 and 0.6), in which the characteristic regimes of skimming flow, wake-interference and isolated roughness are covered.
A detailed analysis on the roof-level turbulence structure reveals parcels of low-speed air masses in the streamwise flows and narrow high-speed down-drafts in the urban canopy layer, signifying the momentum entrainment into the street canyons. The decelerating streamwise flows in turn initiate up-drafts carrying pollutants away from the street canyons, illustrating the basic pollutant removal mechanism in 2D street canyons. Turbulent transport processes, in the form of ejection and sweep, are the key events governing the exchanges of air and pollutant of street canyon. Air exchange rate (ACH) along the roof level is dominated by turbulent transport, in particular over narrow street canyons.
The LES results show that both the turbulence level and ACH increase with increasing aerodynamic resistance defined in term of the Fanning friction factor. At the same AR, BHV greatly increases the friction factor and the ACH in dense built areas (AR ≤ 0.25). The turbulence intensity is peaked on the windward side of street canyons that does not overlap with the maximum velocity gradient near the leeward building corners, suggesting the importance of background turbulence in street-level ventilation. Over the building roughness, pollutant plume dispersion after the ground-level area source in cross flows resumes the self-similar Gaussian shape in the vertical direction in which the vertical plume coverage is proportional to the square root of downwind distance in the streamwise direction. Moreover, the vertical dispersion coefficient is proportional to the one-fourth power of friction factor over idealised street canyons. Conclusively, friction factor can be used to parametrise ventilation and pollutant dispersion over urban areas.published_or_final_version
Mechanical Engineering
Doctoral
Doctor of Philosophy
25
Grm, Aleksander. "Mathematical analysis of macroscopic models for slow dense granular flow." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=98408214X.
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Peng, Jixian, and 彭继娴. "Macroscopic characteristics of dense road networks." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/195994.
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In the continuum modeling of traffic networks, a macroscopic cost-flow function (MCF) and macroscopic fundamental diagram (MFD) can be used to represent the fundamental relationships between traffic quantities such as speed, flow, and density. The MCF governs the steady-state cost-flow relationship, whereas the MFD represents the instantaneous inter-relationship between speed, flow, and density of traffic streams. This thesis explores the influence of network topologies on the MCF and MFD.
The Hong Kong road system is divided into unit-sized road networks with various physical characteristics for which the network structure and signal timings are reserved. By universally scaling the origin-destination (OD) matrices of the morning peak, traffic conditions ranging from free-flow to congestion are created for microscopic simulation. From the simulation results, an MCF that relates the average journey time and the number of vehicles traveling through the network in one hour and an MFD that relates space to the mean speed and average density aggregated across 300s intervals are derived. The MCF and MFD are calibrated with mathematical models for each network.
The density of roads, junctions, and signal junctions all influence the value of the macroscopic parameters in the MCF and MFD, and predictive equations are constructed that relate the macroscopic parameters to the network topological characteristics. Based on the fitting performance of the mathematical models, recommendations are made for selecting MCF and MFD models for continuum modeling.published_or_final_version
Civil Engineering
Master
Master of Philosophy
27
Yan, Li, and 顏理. "On the traffic flow control system." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B39431174.
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Poon, Hao-chi Cynthia, and 潘顥之. "Numerical simulation of turbulent flow and microclimate within and above vegetation canopy." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B45589677.
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Rinaldi, Stephanie. "Experiments on the dynamics of cantilevered pipes subjected to internal andor external axial flow." Thesis, McGill University, 2009. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=111615.
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The main objective of this thesis is to study and investigate the dynamics and stability of cantilevered structures subjected to internal, external, or simultaneous internal and external axial flows. This was accomplished, in some cases, by deriving the linear equations of motion using a Newtonian approach and, in other cases, by making the necessary modifications to existing theoretical models. The continuous cantilevered systems were then discretized using the Galerkin method in order to determine their complex eigenfrequencies. Moreover, numerous experiments were performed to compare and validate, or otherwise, the theoretical models proposed. More specifically, the four cantilevered systems studied were the following: (i) a pipe conveying fluid that is fitted with a stabilizing end-piece, which suppresses flutter by blocking the straight-through exit of flow at the downstream end; (ii) a pipe aspirating fluid, which flutters at low flow velocities in its first mode; (iii) a free-clamped cylinder (i.e. with the upstream end free and the downstream end clamped) in confined axial flow, which also flutters at low flow velocities in its first mode and eventually develops a buckling instability; and (iv) a pipe subjected to internal flow, which after exiting the pipe is transformed to a confined counter-current annular flow, that becomes unstable by flutter too.
30
Yue, Yang, and 樂陽. "Spatial-temporal dependency of traffic flow and its implications for short-term traffic forecasting." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B35507366.
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Wong, Chung-yin Philip, and 黃仲賢. "The development of pedestrian flow model." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B48194025.
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This dissertation reported on the findings of the characteristics of the pedestrian
flows in Chinese New Year Eve Fair in Hong Kong and, the recommendations to its
crowd control measures. Since most of the pedestrian flow models were developed
for general purposes under normal condition, special models developed specifically
for major events such as bazaars, fairs and festivals in Hong Kong were required to
understand their pedestrian flow patterns. In this dissertation, pedestrian flows in the
Fair were videotaped and data was extracted for calibrating several pedestrian flow
models. These included the conventional models developed by Greenshields,
Greenberg, Pipes-Munjal, Underwood, Drake, Wong et al. and four modifications of
these models for simulating isotropic and bi-directional pedestrian flow scenarios.
The free flow speed of the pedestrians in the Chinese New Year Eve Fair was found
to be around 0.69-0.84 m/s, slower than those identified in other researches. Besides,
the results of these models showed the relationships between walking speed, density
and flow of the pedestrians in the Fair. Also, the effects of bi-directional flow to
pedestrian flows were assessed and quantified. These findings obtained from models
were then used as a basis for formulating crowd control strategy of major events in
Hong Kong.published_or_final_version
Transport Policy and Planning
Master
Master of Arts in Transport Policy and Planning
32
Richard, Paul François. "A computer analysis of the flow of water and nutrients in agricultural soils as affected by subsurface drainage." Thesis, University of British Columbia, 1988. http://hdl.handle.net/2429/29171.
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A computer model was developed in order to determine the effects of drainage practices on nutrient losses from level agricultural soils.
The model performs a daily simulation of the vertical flow of water, nitrogen, phosphorus, and heat, and of the growth of crops. A water flow submodel calculates the depth of the water table based on daily predictions of evaporation, transpiration, flow to drains and ditches, and deep percolation. An original saturated-unsaturated flow algorithm is used to determine moisture infiltration, redistribution, and upward flow in the soil matrix, as well as bypassing flow in the soil macropores and horizontal flux between the soil matrix and the macropores, and surface runoff. Nutrient movement occurs by mass flow. Heat flow, nutrient biochemical transformations, and crop growth are determined by using well established relations.
Field tests were carried out for a period of two years on an experimental site in the Lower Fraser Valley of British Columbia. The water table depth was measured on a continuous basis. Grab samples of drainwater and observation wells were obtained periodically and analyzed for nitrogen (N0₃-N, NH₄-N, and TKN) and phosphorus (P0₄-P and TP). The field results show a decrease in the concentration of all nutrients over the sampling period, and provide evidence that denitrification and bypassing flow are important mechanisms affecting the nutrient balance of this soil.
These results were used to calibrate the model. An excellent fit of the observed water table profile and an adequate fit of the observed drain concentration of nitrate were obtained. The simulation revealed that bypassing flow is a very important transfer mechanism in this soil and must be included in order to obtain a satisfactory fit of the experimental data.
A sensitivity analysis of the model showed that the patterns of moisture flow have a predominant influence on the rate of nutrient leaching. In particular, it was found that the nutrient concentration in drain water is a strong function of the hydraulic conductivity of the soil matrix and of the horizontal distance between the soil macropores, which control the ratio of moisture flow in the soil matrix to the macropore flow and the lateral diffusion of nutrients between the soil matrix and the macropores.
The effects of four different drainage designs on nutrient losses were simulated over a period of two years for three different soils and two different nutrient distributions in the soil. It was found that there is a large difference between the amount of nutrients leached from drainage systems using different drainage coefficients. There was also a large difference in the response of two drainage designs based on the same drainage coefficient but using different depth and spacing of drains. Transient effects, as determined by the initial vertical distribution of the nutrients, were seen to remain dominant over the two year duration of the simulation.
The model was found to be useful in explaining the apparent contradictions found in the literature assessing the effects of subsurface drainage on nutrient losses. The results from the model show these effects to be strongly site and condition specific. Furthermore, the model shows that soils and drainage designs that produce similar volumes of drain flow may exhibit very different leaching responses, and that drainage designs equivalent from a hydraulic standpoint can be very dissimilar in their potential for leaching nutrients. The model provides a tool which can be used to determine the appropriateness of different drainage designs in soils where minimizing nutrient losses is critical.Science, Faculty of
Resources, Environment and Sustainability (IRES), Institute for
Graduate
33
Brihi, Sarra. "Mathematical analysis and numerical approximation of flow models in porous media." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMC263/document.
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Cette thèse est consacrée à l'étude des équations du Darcy Brinkman Forchheimer (DBF) avec des conditions aux limites non standards. Nous montrons d'abord l'existence de différents type de solutions (faible, forte) correspondant au problème DBF stationnaire dans un domaine simplement connexe avec des conditions portants sur la composante normale du champ de vitesse et la composante tangentielle du tourbillon. Ensuite, nous considérons le système Brinkman Forchheimer (BF) avec des conditions sur la pression dans un domaine non simplement connexe. Nous prouvons que ce problème est bien posé ainsi que l'existence de la solution forte. Nous établissons la régularité de la solution dans les espaces L^p pour p >= 2.L'étude et l'approximation du problème DBF non stationnaire est basée sur une approche pseudo-compressibilité. Une estimation d'erreur d'ordre deux est établie dans le cas o\`u les conditions aux limites sont de types Dirichlet ou Navier.Enfin, une méthode d'éléments finis Galerkin Discontinue est proposée et la convergence établie concernant le problème DBF linéarisé et le système DBF non linéaire avec des conditions aux limites non standardThis thesis is devoted to Darcy Brinkman Forchheimer (DBF) equations with a non standard boundary conditions. We prove first the existence of different type of solutions (weak, strong) of the stationary DBF problem in a simply connected domain with boundary conditions on the normal component of the velocity field and the tangential component of the vorticity. Next, we consider Brinkman Forchheimer (BF) system with boundary conditions on the pressure in a non simply connected domain. We prove the well-posedness and the existence of a strong solution of this problem. We establish the regularity of the solution in the L^p spaces, for p >= 2.The approximation of the non stationary DBF problem is based on the pseudo-compressibility approach. The second order's error estimate is established in the case where the boundary conditions are of type Dirichlet or Navier. Finally, the finite elements Galerkin Discontinuous method is proposed and the convergence is settled concerning the linearized DBF problem and the non linear DBF system with a non standard boundary conditions
34
Khatibi, Rahman Haghi. "Mathematical open channel flow models and identification of their friction parameters." Thesis, University of London, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263145.
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This thesis l concerned with the mathematical modelling of open channel flows governed by the Saint-Venant equations, which are used as a prediction or identification tools. A survey of the literature in these fields identified the problems in need of Immediate research. Numerical test runs were then devised which led to projecting a clear picture as follows. The performance of twn widely used Implicit finite difference schemes, the 4-point box and 6-point staggered schemes were compared In a wide range of circumstances. it is concluded that both schemes produce 'very close results, but the staggered scheme is prone to convergence problems In some extreme cases. It was also noted that a sharp change in geometric configuration of compound channels produced discontinuous features on the aim ulated depth and discharge hydrographs. The inability of the staggered scheme In handling a head-discharge relationship as a downstream boundary condition was tackled by proposing and implementing a scheme of second order accuracy. As model data are generally corrupted withh errors and noise, their effects together with that of other factors on the Identified friction parameters we Investigated. The results demonstte the paramount Importance of the effect of a choice of objective function on the Identified parameters. While the individual values of the identified M2nning n may vary from one flood event to another, their mean is shown both numerically and rigorously to be dependent upon the choice of objective function. It is shown that an objective function formulated by using absolute errors performs ideally and produces reliable results even in the presence of autocorrelated Gaucian noise samples. The mean of the Identified parameters is also found to be adversely affected if the observation station is affected by localized disturbances. Sensitivity of objective functions to the variation In the value of the friction parameter Is also found to be an Important factor, as Insensitivity leads to ill-conditioning.
35
Lierkamp, Darren. "Simulating the effects of following distance on a high-flow freeway." Full text available online (restricted access), 2003. http://images.lib.monash.edu.au/ts/theses/Lierkamp.pdf.
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"CP830 Research Project and Thesis 2". Includes bibliographical references (p. 80-93) Electronic reproduction.[S.l. :s.n.],2003.Electronic data.Mode of access: World Wide Web.System requirements: Adobe Acrobat reader software for PDF files.Access restricted to institutions with a subscription.
36
Kim, Inchul. "Numerical study of the onset of instability in the flow past a sphere." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184809.
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Experiment shows that the steady axisymmetric flow past a sphere becomes unstable in the range 120 < Re < 300. The resulting time-dependent nonaxisymmetric flow gives rise to nonaxisymmetric vortex shedding at higher Reynolds numbers. The present work reports a computational investigation of the linear stability of the axisymmetric base flow. When the sphere is towed, fixed, or otherwise constrained, stability is determined solely by the Reynolds number. On the other hand, when the sphere falls due to gravity, the present work shows that a additional parameter, the ratio of fluid density to sphere density (β = ρ(f)/ρ(s)) is involved. We use a spectral technique to compute the steady axisymmetric flow, which is in closer agreement with experiment than previous calculations. We then perform a linear stability analysis of the base flow with respect to axisymmetric and nonaxisymmetric disturbances. A spectral technique similar to that employed in the base flow calculation is used to solve the linear disturbance equations in streamfunction form for axisymmetric disturbances, and in a modified primitive variable form for nonaxisymmetric disturbances. For the density ratio β = 0, which corresponds to a fixed sphere, the analysis shows that the axisymmetric base flow undergoes a Hopf bifurcation at Re = 175.1, with the critical disturbance having azimuthal wavenumber m = 1. The results are favorably compared to previous experimental work.
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El, Didy Sherif Mohamed Ahmed 1951. "Two-dimensional finite element programs for water flow and water quality in multi-aquifer systems." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/191110.
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Multiple aquifer systems similar to those that exist at coal gasification sites are complicated groundwater situations. In these types of systems, the aquifers are separated by aquitards through which interaction between aquifers can occur. The movement of the products of combustion into the coal seam and adjacent aquifers is a serious problem of interest. This dissertation presents two-dimensional finite element models for water flow and water quality in multiple aquifer systems. These models can be applied for general problems as well as the problems associated with the burned cavities in coal gasification sites. The Galerkin weightedresidual method is used in both models. Eight-noded isoparametric elements are used. Spatial numerical integration is performed using Gaussian quadrature. A weighted finite difference scheme is used, in both of them, for time integration. The two models are written in FORTRAN V for the CDC CYBER 175. They are applicable to one- or two-dimensional problems involving steady-state or transient flow. Each aquifer can have different initial conditions and boundary conditions. Boundary conditions, pumping rates, and the recharge can be specified as a function of time. The output of the flow program-nodal heads and velocity components is used as an input to the quality program. The numerical models were validated for simple problems that have available analytical solutions.
38
Pincombe, Brandon. "A study of non-Newtonian behaviour of blood flow through stenosed arteries /." Title page, contents and summary only, 1999. http://web4.library.adelaide.edu.au/theses/09PH/09php6469.pdf.
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Khosravi-Dehkordi, Iman. "Load flow feasibility under extreme contingencies." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=100252.
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This thesis examines the problem of load flow feasibility, in other words, the conditions under which a power network characterized by the load flow equations has a steady-state solution. In this thesis, we are particularly interested in load flow feasibility in the presence of extreme contingencies such as the outage of several transmission lines.Denoting the load flow equations by z = f(x) where z is the vector of specified injections (the real and reactive bus demands, the specified real power bus generations and the specified bus voltage levels), the question addressed is whether there exists a real solution x to z = f( x) where x is the vector of unknown bus voltage magnitudes at load buses and unknown bus voltage phase angles at all buses but the reference bus. Attacking this problem via conventional load flow algorithms has a major drawback, principally the fact that such algorithms do not converge when the load flow injections z define or are close to defining an infeasible load flow. In such cases, lack of convergence may be due to load flow infeasibility or simply to the ill-conditioning of the load flow Jacobian matrix.
This thesis therefore makes use of the method of supporting hyperplanes to characterize the load flow feasibility region, defined as the set the injections z for which there exists a real solution x to the load flow equations. Supporting hyperplanes allow us to calculate the so-called load flow feasibility margin, which determines whether a given injection is feasible or not as well as measuring how close the injection is to the feasibility boundary. This requires solving a generalized eigenvalue problem and a corresponding optimization for the closest feasible boundary point to the given injection.
The effect of extreme network contingencies on the feasibility of a given injection is examined for two main cases: those contingencies that affect the feasibility region such as line outages and those that change the given injection itself such as an increase in VAR demand or the loss of a generator. The results show that the hyperplane method is a powerful tool for analyzing the effect of extreme contingencies on the feasibility of a power network.
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Li, Xianxiang, and 李顯祥. "Large-eddy simulation of wind flow and air pollutant transport inside urban street canyons of different aspect ratios." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40687326.
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Marshall, David D. "Extending the functionalities of Cartesian grid solvers : viscous effects modeling and MPI parallelization." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/11999.
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Sheng, Jopan. "Multiphase immiscible flow through porous media." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/53630.
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A finite element model is developed for multiphase flow through soil involving three immiscible fluids: namely air, water, and an organic fluid. A variational method is employed for the finite element formulation corresponding to the coupled differential equations governing the flow of the three fluid phase porous medium system with constant air phase pressure. Constitutive relationships for fluid conductivities and saturations as functions of fluid pressures which may be calibrated from two-phase laboratory measurements, are employed in the finite element program. The solution procedure uses iteration by a modified Picard method to handle the nonlinear properties and the backward method for a stable time integration. Laboratory experiments involving soil columns initially saturated with water and displaced by p-cymene (benzene-derivative hydrocarbon) under constant pressure were simulated by the finite element model to validate the numerical model and formulation for constitutive properties. Transient water outflow predicted using independently measured capillary head-saturation data agreed well with observed outflow data. Two-dimensional simulations are presented for eleven hypothetical field cases involving introduction of an organic fluid near the soil surface due to leakage from an underground storage tank. The subsequent transport of the organic fluid in the variably saturated vadose and ground water zones is analysed.Ph. D.
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Morland, Lawrence Christopher. "Mathematical models for a fluid flow arising in turbine blade cooling passages." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.330029.
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Woudberg, Sonia. "Laminar flow through isotropic granular porous media." Thesis, Link to the online version, 2006. http://hdl.handle.net/10019/1320.
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Ho, Wai-man, and 何慧敏. "A numerical study on turbulent oscillatory plane Couette flow." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B2977083X.
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Amikiya, Emmanuel Adoliwine. "Flow and reactive transport processes in porous media." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85838.
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Thesis (MSc)--Stellenbosch University, 2013.ENGLISH ABSTRACT: Flow and reactive transport of chemical species is a very common phenomenon that occurs in natural and artificial systems. However in this study, the topic is related to acid mine drainage in the South African mining environment. Due to the hazards associated with acid mine drainage, prevention or treatment of mine effluent water before discharging to receiving waters and other environments is a necessity. A new time-dependent mathematical model is developed for a passive treatment method, based on multi-scale modelling of the coupled physico-chemical processes such as diffusion, convection, reactions and filtration, that are involved in the treatment process. The time-dependent model is simulated on a two-dimensional domain using finite volume discretization to obtain chemical species distributions.
AFRIKAANSE OPSOMMING: Vloei en reagerende transport van chemiese spesies is ’n baie algemene verskynsel wat in natuurlike en kunsmatige stelsels plaasvind. In hierdie studie is die onderwerp egter verwant aan suurmyndreinering in die Suid-Afrikaanse mynbou-omgewing. As gevolg van die gevare wat verband hou met suurmyndreinering, is die voorkoming of die behandeling van die afval-mynwater voor dit in opvangswaters en ander omgewings beland ’n noodsaaklikheid. ’n Nuwe tydafhanklike wiskundige model vir ’n passiewe behandelingsmetode is ontwikkel. Dit is gebaseer op die multi-skaal modulering van gekoppelde fisies-chemiese prosesse soos diffusie, konveksie, reaksies en filtrasie, wat by die behandelingsproses betrokke is. Die tydafhanklike model word gesimuleer op ’n twee-dimensionele domein met behulp van eindige volume diskretisasie om die verspreiding van chemiese spesies te bepaal.
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Atamtürk, Alper. "Conflict graphs and flow models for mixed-integer linear optimization problems." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/26002.
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溫建勇 and Kin-yung Wan. "Biham-middleton-levine traffic model in different spatial dimensions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B3122183X.
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Wong, Chun-kuen, and 黃春權. "Dynamic macroscopic modeling of highway traffic flows." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B31243757.
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Freedland, Graham. "Investigation of Jet Dynamics in Cross-Flow: Quantifying Volcanic Plume Behavior." PDXScholar, 2016. http://pdxscholar.library.pdx.edu/open_access_etds/3314.
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Volcanic eruption columns inject high concentrations of ash into the atmosphere. Some of this ash is carried downwind forming ash clouds in the atmosphere that are hazardous for private and commercial aviation. Current models rely on inputs such as plume height, duration, eruption rate, and meteorological wind fields. Eruption rate is estimated from plume height using relations that depend on the rate of air entrainment into the plume, which is not well quantified. A wind tunnel experiment has been designed to investigate these models by injecting a vertical air jet into a cross-flow. The ratio of the cross-flow and jet velocities is varied to simulate a weak plume, and flow response is measured using particle image velocimetry. The plumes are characterized and flow data relative to the centerline is examined to measure the growth of weak plumes and the entrainment velocity along its trajectory. It was found that cross-flow recirculates behind the jet and entrainment occurs both up and downstream of the jet. Analysis of the generation of turbulence enhanced results by identifying the transition point to bending plume and the growth of the shear layer in a bending plume. This provides information that can be used to improve models of volcanic ash concentration changes in the atmosphere.