Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1912. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, Department of Physics, December 2003. / CD-ROM contains PDF files of the entire dissertation. Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 72-74). Available also in a digital version from Dissertation Abstracts.

Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, March 2002. / Thesis advisor(s): Fotis A. Papoulias. Includes bibliographical references (p. 15). Also available online.

Thesis (Ph. D.)--University of Hong Kong, 1980.

Thesis (Ph. D.)--West Virginia University, 2003. / Title from document title page. Document formatted into pages; contains ix, 110 p. : ill. (some col.). Vita. Includes abstract. Includes bibliographical references (p. 90-94).

Theoretical studies are presented in this thesis on the hydrodynamic dispersion due to electro-osmotic flow (EOF) through a parallel-plate or circular channel under the combined effects of wall heterogeneities, including surface topography, hydrodynamic slip, and zeta potential. These wall properties, which are periodically varied along the channel, are called wall patterns in general. The electric potential field and the velocity field of the EOF are determined by solving the linearized Poisson-Boltzmann (P-B) equation and the Stokes equation, respectively, subject to the spatially varying electrohydrodynamic boundary conditions caused by the wall patterns. In particular, for wall patterns with discrete step changes (in contrast with slowly varying and continuous ones), the solutions are expressed by Fourier series that satisfy the mixed-type boundary conditions. The effective expression for the dispersion is derived using the theory of homogenization by introducing multiple-scale variables and expansions. The effective dispersion coefficient is determined either by purely analytical analysis or numerical methods combined with analytical deduction, depending on the complexity of the problem formulation. This thesis consists of two parts. In the first part, the aggregate effect on the flow due to non-uniformly distributed wall properties is studied in two problems. The first problem considers the combined effects of wall corrugations and slippage modulation on pressure-driven cross (transverse) flow through a thin parallel-plate channel in terms of the hydrodynamic effective slip length and flow enhancement. The second problem considers the combined effects of charge distribution and slippage modulation on both longitudinal and transverse EOF through a channel with the same geometry in terms of the electroosmosis (EO) mobility and flow morphology. It is shown that the interaction between different wall patterns due to surface heterogeneity can play a significant role in determining the flow velocity as well as the local convection pattern, both quantitatively and qualitatively. In the second part, hydrodynamic dispersion due to EOF under the aggregate effect of surface heterogeneities in wall potential and hydrodynamic slippage is studied also in two problems. The first problem considers a limiting case where certain geometric and dynamic requirements are satisfied so that the theory of lubrication approximation can be applied to simplify the analysis, for which analytical solutions are obtained for the flow as well as the dispersion. The second problem is for a similar but more general case without using the lubrication approximation, in which the velocity of the flow, the dispersion coefficient and the plate height for the mass transfer are numerically determined after the mathematical formulation of the problem. It is remarkable that the introduction of hydrodynamic slippage can dramatically change the dispersion arising from EOF in various aspects, especially when both the slippage and electric potential are non-uniformly distributed on the channel wall. / published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

Supercomputer technology has revolutionized our studies of the most energetic astrophysical phenomena. Here, I present my simulations of energetic outbursts of gamma rays and the explosions of massive stars, and my efforts to further the computational astrophysics frontier with the development of a radiation hydrodynamics code. First, I present axisymmetric hydrodynamical simulations of the long-term accretion of a rotating gamma-ray burst (GRB) progenitor star, a "collapsar," onto the central compact object, which we assume is a black hole. The simulations were carried out with the adaptive mesh refinement code FLASH in two spatial dimensions and with an explicit shear viscosity. The evolution of the central accretion rate exhibits phases reminiscent of the long GRB [gamma]-ray and X-ray light curve, which lends support to the proposal by Kumar et al. (2008a,b) that the luminosity is modulated by the central accretion rate. In the first "prompt" phase, the black hole acquires most of its final mass through supersonic quasiradial accretion occurring at a steady rate of ~ 0.2 [solar mass] s⁻¹. After a few tens of seconds, an accretion shock sweeps outward through the star. The formation and outward expansion of the accretion shock is accompanied by a sudden and rapid power-law decline in the central accretion rate [mathematical formula], which resembles the L [subscript x] [is proportional to] t⁻³ decline observed in the X-ray light curves. The collapsed, shock-heated stellar envelope settles into a thick, low-mass equatorial disk embedded within a massive, pressure-supported atmosphere. After a few hundred seconds, the inflow of low-angular-momentum material in the axial funnel reverses into an outflow from the thick disk. Meanwhile, the rapid decline of the accretion rate slows, which is potentially suggestive of the "plateau"' phase in the X-ray light curve. We complement our adiabatic simulations with an analytical model that takes into account the cooling by neutrino emission and estimate that the duration of the prompt phase will be ~ 20 s. The model suggests that the steep decline in GRB X-ray light curves is triggered by the circularization of the infalling stellar envelope at radii where the virial temperature is below 10¹⁰ K, such that neutrino cooling is inefficient and an outward expansion of the accretion shock becomes imminent; GRBs with longer prompt [gamma]-ray emission should have more slowly rotating envelopes. Observational evidence suggests a link between long GRBs and Type Ic supernovae. I propose a potential mechanism for Type Ic supernovae in LGRB progenitors powered solely by accretion energy. I present spherically-symmetric hydrodynamic simulations of the long-term accretion of a rotating gamma-ray burst progenitor star, a "collapsar," onto the central compact object, which we take to be a black hole. The simulations were carried out with the adaptive mesh refinement code FLASH in one spatial dimension and with rotation, explicit shear viscosity, and convection in the mixing length theory approximation. Once the accretion flow becomes rotationally supported outside of the black hole, an accretion shock forms and traverses the stellar envelope. Energy is carried from the central geometrically thick accretion disk to the stellar envelope by convection. Energy losses through neutrino emission and nuclear photodisintegration are calculated but do not seem important following the rapid early drop of the accretion rate following circularization. We find that the shock velocity, energy, and unbound mass are sensitive to convective efficiency, effective viscosity, and initial stellar angular momentum. Our simulations show that given the appropriate combinations of stellar and physical parameters, explosions with energies ~ 5 x 10⁵⁰ ergs, velocities ~ 3000 km s⁻¹, and unbound material masses > 5 [solar mass] are possible in a rapidly rotating 16 [solar mass] main sequence progenitor star. Further work is needed to constrain the values of these parameters, to identify the likely outcomes in more plausible and massive LRGB progenitors, and to explore nucleosynthetic implications. In many high-energy astrophysical phenomena, the force of radiation pressure will have a direct effect on the hydrodynamics. Observing radiation is also the primary way we investigate our universe. With this in mind, I present my expansion of the FLASH hydrodynamics code, where I have implemented a gray, flux-limited diffusion (FLD) radiation hydrodynamics (RHD) solver. My solver utilizes the FLASH's diffusion packages that are powered by HYPRE. I have written a new, efficient radiation-matter coupling solver, which exactly integrates the equations for radiation-matter coupling and operates without any time step restrictions. I have also rewritten the unsplit hydrodynamics solver in FLASH to incorporate the changes in PPM characteristic tracing and the Riemann solver required to properly capture the radiation pressure force in regions that are not entirely optically thick. This has required the addition of a new Riemann solver to FLASH, similar to the Riemann solver in the CASTRO RHD code. I then present my validation tests of the code. This code will be made publicly available. / text

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Mixing efficiency in stirred tanks is an important consideration in the design of many industrial processes. Computational fluid dynamics (CFD) techniques have been employed in the present work to study the hydrodynamics in a tank stirred by a Rushton turbine. The effect of the impeller clearance on the velocity field and mixing has been investigated. It has been shown that at a low impeller clearance, the Rushton turbine generates a flow field that evolves from the typical two loops to a single loop flow pattern similar to that of an axial impeller. This single loop flow pattern resulted in an increase in axial flow and a decrease in mixing time at a constant power number. It has been found that a draft tube can be used with a single Rushton turbine, at a low clearance to aid axial flow and mixing, and this resulted in 50% reduction in mixing time. There was a good comparison between laser Doppler velocimetry (LDV) experimental and CFD simulation flow fields, both of which showed that the draft tube improved mixing in the tank by suppressing secondary circulation loops.