Thesis (Ph. D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 68-02, Section: B, page: 0993. Adviser: Kenneth S. Suslick. Includes bibliographical references. Available on microfilm from Pro Quest Information and Learning.

<p>With a new generation of lepton colliders being conceived, muons have been proposed as an alternative particle to electrons. Muons lose less energy to synchrotron radiation and a Muon Collider can provide luminosity within a smaller energy range than a comparable electron collider. This allows a circular collider to be built. As part of the accelerator, it would also be possible to allow the muons to decay to study neutrinos. </p><p> Because the muon is an unstable particle, a muon beam must be cooled and accelerated within a short amount of time. Muons are generated with a huge phase space, so radio frequency cavities placed in strong magnetic fields are required to bunch, focus, and accelerate the muons. Unfortunately, traditional vacuum RF cavities have been shown to break down in the magnetic fields necessary. </p><p> To successfully operate RF cavities in strong magnetic fields, the cavity can be filled with a high pressure gas in order to mitigate breakdown. The gas has the added benefit of providing cooling for the beam. The electron-ion plasma created in the cavity by the beam absorbs energy and degrades the accelerating electric field of the cavity. As electrons account for the majority of the energy loss in the cavity, their removal in a short time is highly desirable. The addition of an electronegative dopant gas can greatly decrease the lifetime of an electron in the cavity. </p><p> Measurements in pure hydrogen of the energy consumption of electrons in the cavity range in 10^-18 and 10^-16 joules per RF cycle per electron. When hydrogen doped with dry air is used, measurements of the power consumption indicate an energy loss range of 10^-20 to 10^-18 joules per RF cycle per ion, two orders of magnitude improvement over non-doped measurements. The lifetime of electrons in a mixture of hydrogen gas and dry air has been measured from &lt; 1 ns, up to 200 ns. The results extrapolated to the parameters of a Neutrino Factory and Muon Collider indicate that a high pressure gas filled RF cavity will work in a cooling-channel for either machine. </p>

Multiphase flows are frequently encountered in many important physical and industrial applications. These flows are usually characterized by very complicated structure that involves free moving surfaces inside the fluid domain and discontinuous or even singular material properties of the flow. The application range for the multiphase flow phenomena is extremely wide, ranging from processing industry to environmental problems, from biological applications to food industry and so on. Unfortunately, due to the inherent complexity of these problems, their solution proved to be a considerable challenge. Thus, in the many applications, the predictive capability and physical understanding must rely heavily on numerical models. In this thesis we develop and analyze a finite element based method for the solution of multiphase problems. This thesis consists of four papers. In paper 1 we develop our finite element based method for the elliptic interface problems. The interface jump conditions that are present due to the discontinuity of the coefficients and presence of the singular forces are derived. Using these jump conditions, we enrich the finite element spaces in order to account for the irregularities in the flow. The resulting method was applied to the interface Stokes problem, modeling a thin elastic rubber band immersed in the homogeneous fluid. In order to apply the introduced method, the interface Stokes problem was rewritten as a sequence of three Poisson problems, one for the pressure and two for the velocity components. Paper 2 is an extension of the ideas used in paper 1. Namely, third order Hermitian polynomials are used as basis functions, their modification according to the interface jump conditions is presented and analyzed, both theoretically and numerically. The rigorous error analysis of the introduced method for two-dimensional elliptic problems is presented in paper 3. The results imply that our method is second order accurate in the L2 norm. Finally, paper 4 concerns with the extension of our method to a coupled interface Stokes problem, that contains both singular forces and discontinuities in the material properties. An application to the Rayleigh-Taylor instability problem is presented. / QC 20100806

The problem of bluff body flows and the drag associated with them has been the subject of numerous investigations in the literature. In the two-dimensional case, the flow past a circular cylinder has been most widely studied both experimentally and computationally. As a result, a well documented understanding of the gross features of the near-wake around a circular cylinder exists in the literature. In contrast, very little is understood on the general features of three-dimensional bluff body near-wakes, except that the vortex shedding is known to be less intense. Control or management of bluff body flows, both from the point of view of drag reduction as well as suppressing unsteady forces caused by vortex shedding, has been an area of considerable interest in engineering applications. The basic aim in the different control methods involves direct or indirect manipulation (or modification) of the near-wake structure leading to weakening or inhibition of vortex shedding. Many passive and energetic techniques (such as splitter plates, base and trailing edge modifications and base bleed) have been effective in the two-dimensional case in increasing the base pressure, leading to varying amounts of drag reduction; a large body of this work is centered around circular cylinders because of direct relevance in applications. The present work is an attempt to understand some of the major aspects of the near-wake structure of a sphere and to control the same for drag reduction employing a passive technique. Many of the passive control techniques found useful in two-dimensional flows are not appropriate in the context of a sphere. In this thesis, the effects of natural ventilation on the wake and drag of a sphere at low speeds have been studied experimentally in some detail. Natural bleed into the base is created when the stagnation and base regions of a sphere are connected through an internal duct. Although natural ventilation has features broadly similar to the well known base-bleed technique (both involve addition of mass, momentum and energy into the near-wake), there are many significant differences between the two methods; for example, in base bleed, the mass flow injected can be controlled independent of the outer flow, whereas in natural ventilation, it is determined by an interaction between the internal and the external flow around the body. Experiments have been conducted in both wind and water tunnels, which covered a wide range of Reynolds number (ReDj based on the diameter of the sphere) from of 1.7 x 103 to 8.5 x 105 with natural boundary layer transition. The ratio of the frontal vent area to the maximum cross sectional area of the sphere was varied from 1% to 2.25% and the effect of the internal duct geometry, including a convergent and a divergent duct was examined as well. After preliminary force measurements involving different duct geometries and vent areas, it was decided to make detailed measurements with a straight (parallel) duct with a vent area ratio of 2.25%. Extensive flow visualization studies involving dye-flow, hydrogen bubble, surface oil-flow and laser-light-sheet techniques were employed to gain insight into many aspects of the near-wake structure and the flow on the surface of the sphere. Measurements made included model static pressures, drag force using a strain gauge balance and velocity profiles in the near-wake and internal flow through the vent. In addition, wake vortex shedding frequency was measured using a hotwire. In the subcritical range of Reynolds numbers (ReD< 2 x 105), the near-wake of the sphere (without ventilation) was found to be vortex shedding, with laminar separation occurring around a value of0s = 80° (where 0s is the angle between the stagnation point and separation location). In contrast, there was little evidence of vortex shedding in the supercritical range (ReD> 4 x 105), consistent with many earlier observations in the literature; however, flow visualization studies in the near-wake clearly showed the existence of a three-dimensional vortex-like structure exhibiting random rotations about the streamwise axis. In this range of Reynolds numbers, surface flow visualization studies indicated the existence of a laminar separation bubble which was followed by a transitional/turbulent reattachment and an ultimate separation around 0S = 145°. All the above observations are broadly consistent with the results available in the literature. With ventilation at subcritical Reynolds numbers, the pressure distributions on the sphere including in the base region was only weakly altered, resulting in a marginal reduction in the total drag; because of the higher pressure difference between the stagnation and base regions, the mean velocity in the vent-flow was about 0.9 times the free-stream velocity. As may be expected, there was little change in the location of laminar separation on the sphere and the vortex shedding frequency was virtually unaltered due to ventilation. The relatively small effects on pressure distribution and drag suggest weak interaction between the vent-flow and the separated shear layer in the subcritical regime. The time-averaged near-wake flow revealed a stagnation point occurring between the vent-flow and the reverse flow in the near-wake, along with the formation of a torroidal vortex between the stagnation point and the near-wake closure; these features bear some resemblance to those observed with base bleed from a blunt base. With ventilation in the supercritical range of Reynolds numbers (ReD > 4 x 105), significant reduction in the total drag, of as much as 65%, was observed from force measurements. Pressure distributions showed higher pressures in the separated flow zone (consistent with reduced drag) as a result of which the internal mass and the mean velocity of the vent-flow were lower (0.69 times the free-stream velocity) compared to the value in the subcritical flow regime. Flow visualization studies clearly showed that the three-dimensional rotating structure (associated with the wake of the unvented sphere) was significantly modified by ventilation, leading to more symmetric and steady near-wake features. The larger effects on pressure distribution and drag suggest strong interaction between the vent-flow and the separated shear layer, promoted by their close proximity. The comparison of power spectral density of u1 signals in the near-wake showed significant reduction in the amplitude at all frequencies, consistent with observations from flow visualization studies. The time-averaged near-wake flow features a pair of counterrotating ring vortices which are trapped between the outer separated shear layer and the vent-flow shear layer; such a mean flow pattern is qualitatively similar to that behind an axisymmetric base with a central jet with unequal freestream velocities in the jet and outer flow. This study strongly suggests that natural ventilation can provide significant total drag reduction provided the vent-flow is in close proximity of the separated shear layer promoting a strong interaction between them. Drag reduction is associated with more symmetric and relatively steady near-wake features in contrast with the unvented sphere.

High Rayleigh number(Ra) turbulent free convection has many unresolved issues related to the phenomenology behind the flux scaling, the presence of a mean wind and its effects, exponential probability distribution functions, the Prandtl number dependence and the nature of near wall structures. Few studies have been conducted in the high Prandtl number regime and the understanding of near wall coherent structures is inadequate for $Ra > 10^9$. The present thesis deals with the results of investigations conducted on high Rayleigh number turbulent free convection in the high Schmidt number(Sc) regime, focusing on the role of near wall coherent structures. We use a new method of driving the convection using concentration difference of NaCl across a horizontal membrane between two tanks to achieve high Ra utilising the low molecular diffusivity of NaCl. The near wall structures are visualised by planar laser induced fluorescence. Flux is estimated from transient measurement of concentration in the top tank by a conductivity probe. Experiments are conducted in tanks of $15\times15\times 23$cm (aspect ratio,AR = 0.65) and $10\times10\times 23$cm (AR = 0.435). Two membranes of 0.45$\mu$ and 35$\mu$ mean pore size were used. For the fine membrane (and for the coarse membrane at low driving potentials), the transport across the partition becomes diffusion dominated, while the transport above and below the partition becomes similar to unsteady non penetrative turbulent free convection above flat horizontal surfaces (Figure~\ref{fig:schem}(A)). In this type of convection, the flux scaled as $q\sim \Delta C_w ^{4/3}$,where $\Delta C_w$ is the near wall concentration difference, similar to that in Rayleigh - B\'nard convection . Hence, we are able to study turbulent free convection over horizontal surfaces in the Rayleigh Number range of $\sim 10^- 10 ^$ at Schmidt number of 602, focusing on the nature and role of near wall coherent structures. To our knowledge, this is the first study showing clear images of near wall structures in high Rayleigh Number - high Schmidt number turbulent free convection. We observe a weak flow across the membrane in the case of the coarser membrane at higher driving potentials (Figure \ref(B)). The effect of this through flow on the flux and the near wall structures is also investigated. In both the types of convection the near wall structure shows patterns formed by sheet plumes, the common properties of these patterns are also investigated. The major outcomes in the above three areas of the thesis can be summarised as follows \subsection* \label \subsubsection* \label The non-dimensional flux was similar to that reported by Goldstein\cite at Sc of 2750. Visualisations show that the near wall coherent structures are line plumes. Depending on the Rayleigh number and the Aspect ratio, different types of large scale flow cells which are driven by plume columns are observed. Multiple large scale flow cells are observed for AR = 0.65 and a single large scale flow for AR= 0.435. The large scale flow create a near wall mean shear, which is seen to vary across the cross section. The orientation of the large scale flow is seen to change at a time scale much larger than the time scale of one large scale circulation The near wall structures show interaction of the large scale flow with the line plumes. The plumes are initiated as points and then gets elongated along the mean shear direction in areas of larger mean shear. In areas of low mean shear, the plumes are initiated as points but gets elongated in directions decided by the flow induced by the adjacent plumes. The effect of near wall mean shear is to align the plumes and reduce their lateral movement and merging. The time scale for the merger of the near wall line plumes is an order smaller than the time scale of the one large scale circulation. With increase in Rayleigh number, plumes become more closely and regularly spaced. We propose that the near wall boundary layers in high Rayleigh number turbulent free convection are laminar natural convection boundary layers. The above proposition is verified by a near wall model, similar to the one proposed by \cite{tjfm}, based on the similarity solutions of laminar natural convection boundary layer equations as Pr$\rightarrow\infty$. The model prediction of the non dimensional mean plume spacing $Ra_\lambda^~=~\lambda /Z_w~=~91.7$ - where $Ra_\lambda$ is the Rayleigh number based on the plume spacing $\lambda$, and $Z_w$ is a near wall length scale for turbulent free convection - matches the experimental measurements. Therefore, higher driving potentials, resulting in higher flux, give rise to lower mean plume spacing so that $\lambda \Delta C_w^$ or $\lambda q^$ is a constant for a given fluid. We also show that the laminar boundary layer assumption is consistent with the flux scaling obtained from integral relations. Integral equations for the Nusselt number(Nu) from the scalar variance equations for unsteady non penetrative convection are derived. Estimating the boundary layer dissipation using laminar natural convection boundary layers and using the mean plume spacing relation, we obtain $Nu\sim Ra^$ when the boundary layer scalar dissipation is only considered. The contribution of bulk dissipation is found to be a small perturbation on the dominant 1/3 scaling, the effect of which is to reduce the effective scaling exponent. In the appendix to the thesis, continuing the above line of reasoning, we conduct an exploratory re-analysis (for $Pr\sim 1$) of the Grossman and Lohse's\cite scaling theory for turbulent Rayleigh - B\'enard convection. We replace the Blasius boundary layer assumption of the theory with a pair of externally forced laminar natural convection boundary layers per plume. Integral equations of the externally forced laminar natural convection boundary layer show that the mixed convection boundary layer thickness is decided by a $5^{th}$ order algebraic equation, which asymptotes to the laminar natural convection boundary layer for zero mean wind and to Blasius boundary layer at large mean winds. \subsubsection*{Effect of wall normal flow on flux and near wall structures} \label{sec:effect-wall-normal} For experiments with the coarser($35\mu$) membrane, we observe three regimes viz. the strong through flow regime (Figure~\ref{fig:schem}(b)), the diffusion regime (Figure \ref{fig:schem}(a)), and a transition regime between the above two regimes that we term as the weak through flow regime. At higher driving potentials, only half the area above the coarser membrane is covered by plumes, with the other half having plumes below the membrane. A wall normal through flow driven by impingement of the large scale flow is inferred to be the cause of this (Figure \ref{fig:schem}(b)). In this strong through flow regime, only a single large scale flow circulation cell oriented along the diagonal or parallel to the walls is detected. The plume structure is more dendritic than the no through flow case. The flux scales as $\Delta C_w^n$, with $7/3\leq n\leq 3$ and is about four times that observed with the fine membrane. The phenomenology of a flow across the membrane driven by the impingement of the large scale flow of strength $W_*$, the Deardorff velocity scale, explains the cubic scaling. We find the surprising result that the non-dimensional flux is smaller than that in the no through flow case for similar parameters. The mean plume spacings in the strong through flow regime are larger and show a different Rayleigh number dependence vis-a-vis the no through flow case. Using integral analysis, an expression for the boundary layer thickness is derived for high Schmidt number laminar natural convection boundary layer with a normal velocity at the wall. (Also, solutions to the integral equations are obtained for the $Sc\sim 1$ case, which are given as an Appendix.) Assuming the gravitational stability condition to hold true, we show that the plume spacing in the high Schmidt number strong through flow regime is proportional to $\sqrt{Z_w\,Z{_{v_i}}}$, where $Z{_{v_i}}$ is a length scale from the through flow velocity. This inference is fairly supported by the plume spacing measurements At lower driving potentials corresponding to the transition regime, the whole membrane surface is seen to be covered by plumes and the flux scaled as $\Delta C_w^{4/3}$. The non-dimensional flux is about the same as in turbulent free convection over flat surfaces if $\frac{1}{2}\Delta C $ is assumed to occur on one side of the membrane. This is expected to occur in the area averaged sense with different parts of the membrane having predominance of diffusion or through flow dominant transport. At very low driving potentials corresponding to the diffusion regime, the diffusion corrected non dimensional flux match the turbulent free convection values, implying a similar phenomena as in the fine membrane. \subsubsection*{Universal probability distribution of near wall structures} \label{sec:univ-prob-distr} We discover that the probability distribution function of the plume spacings show a standard log normal distribution, invariant of the presence or the absence of wall normal through flow and at all the Rayleigh numbers and aspect ratios investigated. These plume structures showed the same underlying multifractal spectrum of singularities in all these cases. As the multifractal curve indirectly represents the processes by which these structures are formed, we conclude that the plume structures are created by a common generating mechanism involving nucleation at points, growth along lines and then merging, influenced by the external mean shear. Inferring from the thermodynamic analogy of multifractal analysis, we hypothesise that the near wall plume structure in turbulent free convection might be formed so that the entropy of the structure is maximised within the given constraints.