Contamination of ground water by non-aqueous phase liquids (NAPLs) has received increasing attention. The most common approach to numerical modeling of NAPL movement through the unsaturated zone is the use of the finite difference or finite element methods to solve a set of partial differential equations derived from Darcy's law and the continuity equations (Abriola and Pinder, 1985; Kaluarachchi and Parker, 1989). These methods work well in many settings, but have given little insights as to why certain non-ideal flow phenomena will occur. The network modeling method, which considers flow at the pore-scale, was used in this study to better understand macroscopic flow phenomena in porous media. Pore-scale network models approximate porous medium as a connected network of pores and channels. Two and three-dimensional pore-scale network models were constructed in this study. A uniform statistical distribution was assumed to represent the random arrangement of pore and tube sizes. Both hysteristic scanning curves and intermediate fluid distribution are studied. The simulation results suggested that network models may be used to predict the characteristic curves of three-phase systems. The results also suggested that three-dimensional models are necessary to study the three-phase problems. Two-dimensional models do not provide realistic results as evidenced by their inability to provide scale-invariant representation of flow processes. The network sizes used in this study ranged from 10 x 5 (50) to 156 x 78 (12168) pores for two-dimensional and from 10 x 5 x 5 (250) to 100 x 50 x 5 (25000) pores for three-dimensional domains. The domain size of 100 x 50 x 5 pores was large enough to provide descriptions independent of the domain scale. The one important limitation of network models is the considerable computational requirements. The use of very high speed computers is essential. Except for this limitation, the network model provides an invaluable technique to study fluid transport mechanisms in the vadose zone. / Graduation date: 1996

The response of slotted plate, Venturi meter and standard orifice to the presence of two phase, three phase and low differential flows was investigated. Two mixtures (air-water and air-oil) were used in the two-phase analysis while a mixture of air, water and oil was employed in the three-phase case. Due to the high gas void fraction (α>0.9), the mixture was considered wet gas. A slotted plate was utilized in the low differential pressure analysis and the discharge coefficient behavior was analyzed. Assuming homogeneous flow, an equation with two unknowns was obtained for the multi-phase flow analysis. An empirical relation and the differential response of the meters were used to estimate the variables involved in the equation. Good performance in the gas mass flow rate estimation was exhibited by the slotted and standard plates for the air-water flow, while poor results were obtained for the air-oil and air-water oil flows. The performance of all the flow meter tested in the analysis improved for differential pressures greater than 24.9 kPa (100 in_H2O). Due to the tendency to a zero value for the liquid flow, the error of the estimation reached values of more than 500% at high qualities and low differential pressures. Air-oil and air-water-oil flows show that liquid viscosity influences the response of the differential pressure meters. The best results for high liquid viscosity were obtained in the Venturi meter using the recovery pressure for the gas flow estimation at differential pressures greater than 24.9 kPa (100 in_H2O). A constant coefficient Cd was used for the low differential pressure analysis and results did show that for differential pressure less than 1.24 kPa (5 inH2O) density changes are less than 1% making possible the incompressible flow assumption. The average of the computed coefficients is the value of Cd.

This thesis deals with the heat evolution duringsolidification and its relation to the formation of porosity.It intends to improve the current understanding of theformation of porosity in cast materials with special interestin nodular cast iron and the spray forming process. Twodifferent systems, a Fe-based alloy, Cast iron, and a Ni-basedalloy, Inconel 625, are examined. The effect on the heatevolution of the morphology and the processing parameters inspray forming are treated. An evaluation of the microstructural features, segregationbehavior and physical properties such as latent heat of fusionis performed byusing thermal analysis under cooling ratesranging from 0.1 to 104 K/s. In order to achieve this amodified differential thermal analysis (DTA) equipment, amirror furnace and levitation casting are used. Results arepresented in terms of the fraction of solidified, the coolingrate and the microstructure observed. The measured latent heatof fusion is not constant throughout the solidificationprocess. Variations in morphology and cooling rate affect therelease of the latent heat. A thermodynamic model is used to describe the experimentalobservations and to explain the formation of pores in nodularcast iron by taking into consideration the formation of latticedefects during the liquid/solid transformation. In this casethe formation of porosity is regarded as a consequence ofchanges in the volume fraction ratio graphite/ during thesolidification process. A numerical model of the spray forming process is developedby means of CFD modelling and compared with experimentalmeasurements performed in an industrial facility. Stagnationpressure measurements provided information about the gas flowvelocity and an analysis of the overspray powder providedinformation about the particle thermal history. Evaluation ofthe deposit was also performed. It is observed that the processconditions in spray forming promote non-equilibriumsolidification even though solidification at the deposit occursat a lower rate. In this case the porosity formed near theinterface substrate/deposit depends largely on the substratetemperature. The presence of certain reactive elements, such astitanium, affects the porosity levels in the rest of thedeposit. <b>Keywords:</b>Thermal Analysis, Nodular Cast Iron, Inconel625, CFD, Flow Assesment, Multiphase Flow, Spray Deposition,Microporosity, Superalloys

In this thesis a set of boundary conditions for multiphase flow is suggested. Characteristic-based boundary conditions are reviewed for single-phase flow. The problem of open-boundary conditions is investigated, and to avoid drifting values, the use of control functions is proposed. The use of control functions is also verified with a new test which assesses the quality of the boundary conditions. Particularly, P- and PI-control functions are examined. PI-controllers have the ability to specify a given variable exactly at the outlet as well as at the inlet, without causing spurious reflections which are amplified. Averaged multiphase flow equations are reviewed, and a simplified model is established. This model is used for the boundary analysis and the computations. Due to the averaging procedure, signal speeds are reduced to the order of the flow speed. This leads to numerical challenges. For a horizontal channel flow, a splitting of the interface pressure model is suggested. This bypasses the numerical problems associated with separation by gravity, and a physical realistic model is used. In this case, the inviscid model is shown to possess complex eigenvalues, and still the characteristic boundary conditions give reasonable results. The governing equations are solved with a Runge-Kutta scheme for the time integration. For the spatial discretisation, a finite-volume and a finite-difference method are used. Both implementations give equivalent results. In single-phase flow, the results improve significantly when a numerical filter is applied. For two-dimensional two-phase flow, the computations are unstable without a numerical filter.

This work presents a number of the practical aspects of developing reduced- order models (ROMs) based on proper orthogonal decomposition (POD). ROMS are derived and implemented for multiphase flow, quasi-2D nozzle flow and 2D inviscid channel flow. Results are presented verifying the ROMs against existing full-order models (FOM). POD is a method for separating snapshots of a flow field that varies in both time and space into spatial basis functions and time coefficients. The partial differential equations that govern fluid flow can then be pro jected onto these basis functions, generating a system of ordinary differential equations where the unknowns are the time coefficients. This results in the reduction of the number of equations to be solved from hundreds of thousands or more to hundreds or less. A ROM is implemented for three-dimensional and non-isothermal multiphase flows. The derivation of the ROM is presented. Results are compared against the FOM and show that the ROM agrees with the FOM. While implementing the ROM for multiphase flow, moving discontinuities were found to be a ma jor challenge when they appeared in the void fraction around gas bubbles. A point-mode POD approach is proposed and shown to have promise. A simple test case for moving discontinuities, the first order wave equation, is used to test an augmentation method for capturing the discontinuity exactly. This approach is shown to remove the unphysical oscillations that appear around the discontinuityin traditional approaches. A ROM for quasi-2D inviscid nozzle flow is constructed and the results are com- pared to a FOM. This ROM is used to test two approaches, POD-Analytical and POD-Discretized. The stability of each approach is assessed and the results are used in the implementation of a ROM for the Navier-Stokes equations. A ROM for a Navier-Stokes solver is derived and implemented using the results of the nozzle flow case. Results are compared to the FOM for channel flow with a bump. The computational speed-up of the ROM is discussed. Two studies are presented with practical aspects of the implementation of POD- based ROMs. The first shows the effect of the snapshot sampling on the accuracy of the POD basis functions. The second shows that for multiphase flow, the cross- coupling between field variables should not be included when computing the POD basis functions.

Flow mechanisms affect transport processes during condensation. Most studies on two-phase flow regimes are qualitative in nature, typically providing only information to guide the identification of the respective regimes and the transitions between them. These studies have, however, not yielded quantitative information to assist the development of pressure drop and heat transfer models. Such qualitative studies have also yielded results with considerable variability between investigators. A comprehensive investigation of flow mechanisms, void fraction, pressure drop and heat transfer during condensation of R404A in microchannels was conducted. In contrast to all prior investigations, high-speed video recordings and image analyses were used to directly measure void fraction, slug frequencies, vapor bubble velocity, vapor bubble dimensions and liquid film thicknesses in tube diameters ranging from 0.508 to 3.00 mm. Experiments were conducted at reduced pressures and mass fluxes ranging from 0.38 to 0.77 and 200 to 800 kg m-2 s-1, respectively, to document their influences on the condensation process at local vapor qualities ranging from 0 to 1. This information was used to develop a model for the void fraction in condensing flows. A complementing set of heat transfer and pressure drop measurements were conducted on the same geometries at similar conditions, and the void fraction model was used in conjunction with these measurements to develop improved heat transfer and pressure drop models. This comprehensive set of experiments and analyses yields a self-consistent and accurate treatment of high-pressure condensation in small hydraulic diameter geometries. Furthermore, the heat transfer model was found to agree well with condensing ammonia and carbon dioxide data that were obtained at significantly different conditions in different tube diameters. The added physical understanding of the condensation process and the models developed will serve as important building blocks for the design of microscale condensers and thermal systems.

This thesis presents an axisymmetric numerical model to simulate interfacial flows near a sharp corner, where contact line pinning occurs. The method has been used to analyze drop imbibition into a capillary. To evaluate the performance of the numerical method, for a liquid drop initially placed partially within a capillary, a thermodynamic model has also been developed, to predict equilibrium states. The first part of this thesis presents an axisymmetric VoF algorithm to simulate interfacial flows near a sharp corner. (1) A new method to exactly calculate the normals and curvatures of any circle with a radius as small as the grid size is presented. This method is a hybrid least squares height function technique which fits a discretized osculating circle to a curve, from which interface normals and curvature can be evaluated. (2) A novel technique for applying the contact angle boundary condition has been devised, based on the definition of an osculating circle near a solid phase. (3) A new flux volume construction technique is presented, which can be applied to any split advection scheme. Unlike the traditional approach where the flux volumes are assumed rectangular, the new flux volumes can be either trapezoidal or triangular. The new technique improves the accuracy and consistency of the advection scheme. (4) Explicit PLIC reconstruction expressions for axisymmetric coordinates have been derived. (5) Finally, a numerical treatment of VoF for contact line motion near a sharp corner is presented, base on the idea of contact line pinning and an edge contact angle. The second part of the thesis is on the imbibition of a drop into an open capillary. A thermodynamic analysis based on minimization of an interfacial surface energy function is presented to predict equilibrium configurations of drops. Based on the drop size compared to the hole size, the equilibrium contact angle, and the geometry of the capillary, the drop can be totally imbibed by the capillary, or may not wet the capillary at all. The thesis concludes with application of the numerical scheme to the same problem, to examine the dynamics of wetting or dewetting of a capillary. All of the simulations yield results that correspond to the equilibrium states predicted by the thermodynamic analysis, but offer additional insight on contact line motion and interface deformation near the capillary edge.

The primary focus of this thesis is to present a simple and practical implementation of an optimal-time response controller for multiphase interleaved dc-dc SMPS. This novel solution enables equal current sharing between phases not only in steady-state, but also during load transients, as well as bump-less transition between those two states. A digital voltage loop and multiple analog peak current programmed mode current loops are combined to implement a capacitor charge balance control algorithm with fairly simple hardware. This algorithm provides recovery from a disturbance in a single on-off switching action, which is performed in virtually the fastest possible time. The hybrid interface between the loops is provided through a structure combining a sample-and-hold circuit and a relatively slow successive-approximation DAC that provides control signals for all the loops in the system. Furthermore, for operation under light load conditions, the controller automatically switches into simply implemented pulse-frequency mode of operation.

This thesis presents an axisymmetric numerical model to simulate interfacial flows near a sharp corner, where contact line pinning occurs. The method has been used to analyze drop imbibition into a capillary. To evaluate the performance of the numerical method, for a liquid drop initially placed partially within a capillary, a thermodynamic model has also been developed, to predict equilibrium states. The first part of this thesis presents an axisymmetric VoF algorithm to simulate interfacial flows near a sharp corner. (1) A new method to exactly calculate the normals and curvatures of any circle with a radius as small as the grid size is presented. This method is a hybrid least squares height function technique which fits a discretized osculating circle to a curve, from which interface normals and curvature can be evaluated. (2) A novel technique for applying the contact angle boundary condition has been devised, based on the definition of an osculating circle near a solid phase. (3) A new flux volume construction technique is presented, which can be applied to any split advection scheme. Unlike the traditional approach where the flux volumes are assumed rectangular, the new flux volumes can be either trapezoidal or triangular. The new technique improves the accuracy and consistency of the advection scheme. (4) Explicit PLIC reconstruction expressions for axisymmetric coordinates have been derived. (5) Finally, a numerical treatment of VoF for contact line motion near a sharp corner is presented, base on the idea of contact line pinning and an edge contact angle. The second part of the thesis is on the imbibition of a drop into an open capillary. A thermodynamic analysis based on minimization of an interfacial surface energy function is presented to predict equilibrium configurations of drops. Based on the drop size compared to the hole size, the equilibrium contact angle, and the geometry of the capillary, the drop can be totally imbibed by the capillary, or may not wet the capillary at all. The thesis concludes with application of the numerical scheme to the same problem, to examine the dynamics of wetting or dewetting of a capillary. All of the simulations yield results that correspond to the equilibrium states predicted by the thermodynamic analysis, but offer additional insight on contact line motion and interface deformation near the capillary edge.

The primary focus of this thesis is to present a simple and practical implementation of an optimal-time response controller for multiphase interleaved dc-dc SMPS. This novel solution enables equal current sharing between phases not only in steady-state, but also during load transients, as well as bump-less transition between those two states. A digital voltage loop and multiple analog peak current programmed mode current loops are combined to implement a capacitor charge balance control algorithm with fairly simple hardware. This algorithm provides recovery from a disturbance in a single on-off switching action, which is performed in virtually the fastest possible time. The hybrid interface between the loops is provided through a structure combining a sample-and-hold circuit and a relatively slow successive-approximation DAC that provides control signals for all the loops in the system. Furthermore, for operation under light load conditions, the controller automatically switches into simply implemented pulse-frequency mode of operation.