This thesis deals with the problem of the asymptotic behavior of solutions to several nonlinear equations from fluid dynamics on both mesoscopic and macroscopic levels, including Boltzmann equation, compressible Navier-Stokes equations and the system of viscous conservation laws with positive definite viscosity matrix. The main purpose is to study the asymptotic behavior of solutions to those equations towards linear and nonlinear waves, such as shock waves, rarefaction waves and contact discontinuities as either the times goes to infinity, or the viscosity and heat conductivity go to zero for the macroscopic equations or the mean free path goes to zero for the mesoscopic equations. Those limit processes are singular. For the system of viscous conservation laws, we show the large time asymptotic nonlinear stability of a superposition of viscous shock waves and viscous contact waves for the system of viscous conservation laws with small initial perturbations, provided that the strengths of these viscous waves are small and of the same order. The results are obtained by elementary weighted energy estimates based on the underlying wave structure and a new estimate on the heat equation. For the Boltzmann equation, the main purpose is to study the asymptotic equivalence for the hard-sphere collision model to its corresponding Euler equations of compressible gas dynamics in the limit of small mean free path. When the fluid flow is a smooth rarefaction (or centered-rarefaction) wave with finite strength, the corresponding Boltzmann solution exists globally in time, and the solution converges to the rarefaction wave uniformly for all time (or away from t = 0) as the mean free path epsilon → 0. A decomposition of a Boltzmann solution into its macroscopic (fluid) part and microscopic (kinetic) part is adopted to rewrite the Boltzmann equation in a form of compressible Navier-Stokes equations with source terms. As a by-product, the same asymptotic equivalence of the full compressible Navier-Stokes equations to its corresponding Euler equations in the limit of small viscosity and heat-conductivity (depending on the viscosity) is also obtained. / Zeng, Huihui. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 70-09, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 102-110). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Direct real-space multi-point measurements of the velocity and temperature fields were carried out in various places of the convection cell. In the central region of the cell it is found that both velocity and temperature exhibit the same scaling behavior that one would find for the velocity and for a passive scalar in homogeneous and isotropic Navier-Stokes turbulence. Near the cell's sidewall where thermal plumes abound, vertical velocity and temperature exhibit different scalings. A model, taking into account both buoyancy and energy dissipation, is proposed and its predictions agree well with the sidewall experimental results. / This thesis aims to address three key issues in convectioe thermal turbulence: heat transport, statistics of turbulent fluctuations of the velocity and temperature fields, and flow dynamics. / Through measurement of 2D velocity at different cross sections of the cylindrical cell with Gamma = 1, we investigate the 3D flow structures and dynamics of turbulent thermal convection. Our result reveals how thermal plumes synchronize their emissions and organize their motions spatially between the top and bottom plates, leading to an oscillatory motion in the bulk region of the fluid. In Gamma = 0.5 small cell, we successfully identified the relationship between 2D instantaneous velocity map and the time-averaged 3D flow pattern. This experiment also showed that a particular value of Nu can be unambiguously associated with a specific large-scale flow mode in the convection cell. By taking into account the effects of the evolution in the circulation path of the mean wind and of the counterflow, we provide a solution to the riddle about the scaling exponent dispersion of the Reynolds number Re with Ra and show that the scaling exponent has a universal value of 0.5. / To study the confinement effect on heat transport at high levels of turbulence, we conducted high precision measurements of the Nusselt number Nu as a function of the Rayleigh number Ra in a 1 m diameter cylindrical cell filled with water with aspect ratio Gamma = 0.67, l, 2, 5, 10, 20. The measurements were conducted at the Prandtl number Pr ≃ 4 with Ra varying from 1 x 10 7 to 5 x 1012. It is found that Nuinfinity can be described by a combination of two power laws for all aspect ratios, and that the asymptotic large Gamma behavior may have been reached for Gamma ≥ 10. By studying the statistics of temperature fluctuations inside the conducting plates, we found that the product of temperature skewness and the skewness of temperature time derivative may be used to quantify the intensity of plume emissions. / Sun Chao = 熱湍流對流的實驗研究 / 孙超. / "July 2006." / Adviser: Keqing Xia. / Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1697. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (p. 132-140). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / School code: 1307. / Sun Chao = Re tuan liu dui liu de shi yan yan jiu / Sun Chao.

Recent developments in estimation of the survivability of a U.S. Navy transport barge in random seas are extended to improve accuracy. The single Degree-of-Freedom (DOF) model of a extreme roll response of a barge used in previous research is replaced by a 3-DOF roll-heave-sway model to include linear and nonlinear static and kinematic coupling between roll, sway and heave. The predominant nonlinearity in the model arises in an improved approximation of the roll righting moment and heave buoyant restoring force by coupling roll with heave. Kinematic coupling is introduced by allowing extreme displacements and rotations in the barge response. System coefficients in the 3-DOF roll-heave-sway model and a simpler 2-DOF roll-heave model are identified by comparing time domain simulations with measured physical model tests of barge motions. Predictions of the 3-DOF and 2-DOF models are compared to measured test data for the case of random waves. Monte Carlo simulations of the equations of motions are performed to predict the reliability of the barge in an operational sea state for a specified mission duration. Use of parallel computer processing is found to make this a viable option for stability estimations as we move into the next century. The stochastic nature of the ocean waves are modeled via filtered white noise. Estimations of the joint probability of the barge responses are presented after application of density estimation kernels. Both the 3-DOF roll-heave-sway model and 2-DOF roll-heave model are tested and compared. Last, examples are provided of some observed nonlinear behavior of the barge motions for variation in damping or ocean wave amplitude. Transient and intermittent chaotic responses are observed for deterministic input waves and quasiperiodic cases are illustrated. / Graduation date: 1996

The diseases of cardiovascular system and the respiratory system have been the second and third killers causing deaths in Hong Kong. In this stressful civilized world, the prevalence and incidence of these diseases increased prominently which arouse our concern on the theories behind the pathological conditions. This report will focus on the biofluid mechanics in the large artery and in the upper airway. Thoracic aortic dissection, characterized by the tearing in the middle layer of vessel wall, is a catastrophic vascular disorder. The wall of the newly formed channel, the false lumen, is weakened and prone to aortic events. Endovascular repair is a minimally invasive technique for treating dissection patients. The biomechanical factors and the length of endograft were studied by computational fluid dynamics. Two geometrical factors showed a significant impact on the backflow in the false lumen. A larger false lumen and a larger distal tear size greatly affected the extent of thrombosis in the false lumen. It made the false lumen under a higher risk of vessel rupture. The computational prediction also demonstrated a more stable hemodynamic condition in the model with a longer endograft. These results provide important information for the clinicians to propose the surgical procedures and to improve the design of endografts. Airway obstruction is a common breathing disorder but it is always underdiagnosed. Obstructive sleep apnea (OSA) and different dentofacial deformities are two pathological conditions in which the patients have the abnormal sizes of airways. Computational fluid dynamic was employed in both conditions with patient–specific models. In the part of OSA, pre– and post–operative models were studied. The dimensions and flow resistance of the upper airway showed a significant improvement after mandibular distraction. The percentage of stenosis and the flow resistance was reduced by 27.3% and 40.7% respectively. For the patients in three facial skeletal deformity groups, the cross–sectional area and the flow resistance were compared. The patients with Class II deformity had the smallest retroglossal and retroplatal dimensions as well as the greatest flow resistance. The results confirmed the effectiveness of mandibular distraction and also provide valuable implications for the clinicians on the treatment planning, particularly for the Class II subjects. / published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

Not available / text

Not available / text

Not available / text

This dissertation considers the effect of measuring randomly varying local hydraulic conductivity K(x) on one's ability to predict transient flow within bounded domains, driven by random sources, initial head distribution, and boundary functions. The first part of this work extends the steady state nonlocal formalism by Neuman and Orr [1992] in order to obtain the prediction of local hydraulic head h(x, t) and Darcy flux q(x, t) by means of their ensemble moments <h(x, t)> (c) and <q(x, t)>(c)conditioned on measurements of K(x). These predictors satisfy a deterministic flow equation which contains a nonlocal in space and time term called a "residual flux". As a result, <q(x, t)>(c) is nonlocal and non-Darcian so that an effective hydraulic conductivity K(c) does not generally exist. It is shown analytically that, with the exception of several specific cases, the well known requirement of "slow time-space variation" in uniform mean hydraulic gradient is essential for the existence of K(c). In a subsequent chapter, under this assumption, we develop analytical expressions for the effective hydraulic conductivity for flow in a three dimensional, mildly heterogeneous, statistically anisotropic porous medium of both infinite extent and in the presence of randomly prescribed Dirichlet and Neumann boundaries. Of a particular interest is the transient behavior of K(c) and its sensitivity to degree of statistical anisotropy and domain size. In a bounded domain, K(c) (t) decreases rapidly from the arithmetic mean K(A) at t = 0 toward the effective hydraulic conductivity corresponding to steady state flow, K(sr), K(c), exhibits similar behavior as a function of the dimensionless separation distance ρ between boundaries. At ρ = 0, K(c) = K(A) and rapidly decreases towards an asymptotic value obtained earlier for an infinite domain by G. Dagan. Our transient nonlocal formalism in the Laplace space allows us to analyze the impact of other than slow time-variations on the prediction of <q(x, t)>(c),. Analyzing several functional dependencies of mean hydraulic gradient, we find that this assumption is heavily dependent on the (relaxation) time-scale of the particular problem. Finally, we formally extend our results to strongly heterogeneous porous media by invoking the Landau-Lifshitz conjecture.

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.

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.