# Browsing by Subject "Fluid dynamics"

Now showing 1 - 20 of 37

- Results Per Page
1 5 10 20 40 60 80 100

- Sort Options
Ascending Descending

Item Cleanup of internal filter cake during flowback(2005) Suri, Ajay; Sharma, Mukul M.Show more The flow initiation pressure (FIP) is used as an estimate of the differential pressure (between the reservoir and the well) required to initiate production. The standard practice to measure FIP uses a constant flowback rate. This method is shown to be inadequate to measure the FIP. An improved flowback method, which uses a series of constant differential pressures, is used instead to measure the FIP. This method closely represents the constant drawdown experienced between the reservoir and the wellbore. In addition the permeability during flowback is measured at increasing differential pressures, resulting in a spectrum of return permeability values. Two types of drilling fluids (sized calcium carbonate and bentonite) are used for conducting the filtration and flowback experiments for porous media ranging in permeability from 4 to 1500 md. Both single-phase and two-phase experiments are conducted in lab-simulated open-hole and perforated completions to better understand the factors affecting the FIP and the return permeability spectra. vii We observe small values for FIP in all the experiments (considerably smaller than those measured using the constant flowback method). The values of FIP yield pressure gradients that are achievable in vertical wells but may not be easily achieved in horizontal wells. The FIP and the return permeability spectra are controlled by the cleanup of the internal filter cake. A Bingham fluid in a network of pores is used to model the cleanup of the internal filter cake during flowback. The results indicate that very large pressure gradients are required during flowback to cleanup the entire internal filter cake. However, a pressure gradient of 10 psi / inch is found to yield a skin factor < 1 for most open-hole completions. For perforated completions, pressure gradients up to 20 psi / inch and flow rates up to 0.3 bbl/day/perf yield skin factors < 2.Show more Item Coherent structures and two-dimensionalization in rotating turbulent flow(2005) Ruppert-Felsot, Jori Elan; Swinney, H. L., 1939-Show more We study laboratory-produced fluid turbulence under the influence of rapid rotation. Three-dimensional (3D) turbulence is generated by strong pumping through sources and sinks at the bottom of a rotating tank (48.4 cm high, 39.4 cm diameter) filled with water. This flow evolves toward quasi-two-dimensional (quasi-2D) turbulence with increasing height in the tank. Digital Particle Image Velocimetry (DPIV) measurements were taken using tracer particles illuminated by a horizontal laser light-sheet. The quasi-2D flow near the top of the tank contains many long-lived coherent vortices and jets with a wide range of sizes near the top of the tank. The vertical vorticity field exhibits complex dynamics such as vortex birth, merger, scattering, and destruction. Measurements using two synchronized cameras and vertically separated light sheets revealed coherent structures that were columnar and extended vertically throughout the tank. The effect of rotation greatly increased the vertical correlation of the flow, even for small rotation rates. A gradual decay in the correlation of increasingly vertically separated vii planes was observed, rather than a sharp transition. The discrete wavelet packet transform (DWPT) and discrete wavelet transform (DWT) were used to extract and study the dynamics of the localized coherent structures near the top of our tank. We separated the flow into a low-entropy “coherent” and a highentropy “incoherent” component by thresholding the coefficients of the DWPT and DWT of the vorticity field. Similar thresholdings using the Fourier transform and JPEG compression, the Okubo-Weiss criterion and Proper Orthogonal Decomposition (POD) were also tested. We found that the DWPT and DWT yield similar results and are much more efficient at representing the total flow than other methods. Only about 3% of the largeamplitude coefficients of the DWPT and DWT were necessary to represent the coherent component and preserve the vorticity probability density function, transport properties, and spatial and temporal correlations of the measured fields. The remaining small amplitude coefficients represent the incoherent component, which has near Gaussian vorticity PDF, contains no coherent structures, rapidly loses correlation in time, and does not contribute significantly to the transport properties of the flow. This suggests that one can faithfully describe and simulate such turbulent flow using a relatively small number of wavelet or wavelet packet modes.Show more Item A direct numerical simulation of fully developed turbulent channel flow with spanwise wall oscillation(2005) Zhou, Dongmei; Ball, K. S.; Bogard, David G.Show more Low-Reynolds-number, fully developed turbulent channel flow with wall motion has been simulated by direct numerical simulation to examine the effectiveness and the near-wall mechanics using spanwise wall oscillation to reduce friction drag. The three-dimensional unsteady Navier-Stokes (and energy) equations are solved using Fourier-Chebyshev-Tau spectral methods combined with a second-order semi-implicit time-advancement scheme. The effects of spatial resolution and computational box size on the computed turbulence and the drag reduction percentage were investigated. Finer spanwise resolution has a greater effect on achieving a better solution and the turbulent flow is well resolved for a spanwise grid spacing of Δ 3 <10 + x . It was also confirmed that the dynamics of turbulence in a natural full channel could be reproduced by a minimal channel. Parameter studies have been performed to examine the variation of drag reduction value with wall oscillation frequency, velocity amplitude, peak-to-peak amplitude, and oscillation orientation, and drag reduction data were discovered to correlate better with peak-to-peak amplitude for frequencies 01 > 0. + f in contrast to the previous finding of its correlation with peak-wall-speed. At the optimal wall oscillation conditions, net power savings of about 5% are obtained after the power input to move the wall is accounted for, even though more than 40% friction drag reduction has been achieved in the turbulence flow. Significant drag reduction is accompanied by the suppression of the turbulent bursting process and production of turbulence, and by a reduction in the intensity of streaks and streamwise vortices. A thickened viscous sublayer is indicated through the observed outward shift of statistical quantities such as velocity fluctuations and Reynolds shear stress in the moving-wall channel flow. Drag reduction by spanwise wall oscillation is mainly due to the suppression of ejection-sweep motions and the disruption in the cycle of the turbulence selfsustaining process, starting with the wall streaks that are distorted and reduced in number and extent. The intensity and the number of vortical structures are also reduced by the wall motion. The suppression of the regeneration of new streamwise vortices above the wall in turn further suppresses the ejection-sweep motions, thus leading to the reduced skin-friction levels at the wall.Show more Item A discontinuous Petrov-Galerkin methodology for incompressible flow problems(2013-08) Roberts, Nathan Vanderkooy; Demkowicz, Leszek; Moser, Robert deLanceyShow more Incompressible flows -- flows in which variations in the density of a fluid are negligible -- arise in a wide variety of applications, from hydraulics to aerodynamics. The incompressible Navier-Stokes equations which govern such flows are also of fundamental physical and mathematical interest. They are believed to hold the key to understanding turbulent phenomena; precise conditions for the existence and uniqueness of solutions remain unknown -- and establishing such conditions is the subject of one of the Clay Mathematics Institute's Millennium Prize Problems. Typical solutions of incompressible flow problems involve both fine- and large-scale phenomena, so that a uniform finite element mesh of sufficient granularity will at best be wasteful of computational resources, and at worst be infeasible because of resource limitations. Thus adaptive mesh refinements are required. In industry, the adaptivity schemes used are ad hoc, requiring a domain expert to predict features of the solution. A badly chosen mesh may cause the code to take considerably longer to converge, or fail to converge altogether. Typically, the Navier-Stokes solve will be just one component in an optimization loop, which means that any failure requiring human intervention is costly. Therefore, I pursue technological foundations for a solver of the incompressible Navier-Stokes equations that provides robust adaptivity starting with a coarse mesh. By robust, I mean both that the solver always converges to a solution in predictable time, and that the adaptive scheme is independent of the problem -- no special expertise is required for adaptivity. The cornerstone of my approach is the discontinuous Petrov-Galerkin (DPG) finite element methodology developed by Leszek Demkowicz and Jay Gopalakrishnan. For a large class of problems, DPG can be shown to converge at optimal rates. DPG also provides an accurate mechanism for measuring the error, and this can be used to drive adaptive mesh refinements. Several approximations to Navier-Stokes are of interest, and I study each of these in turn, culminating in the study of the steady 2D incompressible Navier-Stokes equations. The Stokes equations can be obtained by neglecting the convective term; these are accurate for "creeping" viscous flows. The Oseen equations replace the convective term, which is nonlinear, with a linear approximation. The steady-state incompressible Navier-Stokes equations approximate the transient equations by neglecting time variations. Crucial to this work is Camellia, a toolbox I developed for solving DPG problems which uses the Trilinos numerical libraries. Camellia supports 2D meshes of triangles and quads of variable polynomial order, allows simple specification of variational forms, supports h- and p-refinements, and distributes the computation of the stiffness matrix, among other features. The central contribution of this dissertation is design and development of mathematical techniques and software, based on the DPG method, for solving the 2D incompressible Navier-Stokes equations in the laminar regime (Reynolds numbers up to about 1000). Along the way, I investigate approximations to these equations -- the Stokes equations and the Oseen equations -- followed by the steady-state Navier-Stokes equations.Show more Item Discrete Lagrange equations for reacting thermofluid systems(2009-05) Hean, Charles Robert, 1960-; Fahrenthold, Eric P.Show more The application of Lagrange's equations to non-equilibrium reacting compressible thermofluid systems yields a modeling methodology for thermofluid dynamics compatible with the discrete energy methods used extensively in other energy domains; examples include mechanical systems simulations and molecular dynamics modeling. The introduction of internal energies as generalized coordinates leads to a thermomechanical model with a simple but general form. A finite element interpolation is used to formulate the ODE model in an ALE reference frame, without reference to any partial differential equations. The formulation is applied to highly nonlinear problems without the use of any time-splitting or shock-tracking methods. The method is verified via the solution of a set of example problems which incorporate a variety of reference frames, both open and closed control volumes, and moving boundaries. The example simulations include transient detonations with complex chemistry, piston-initiated detonations, canonical unstable overdriven detonations, high-resolution induction-zone species evolution within a pulsating hydrogen-air detonation, and the detonation of a solid explosive due to high-velocity impact.Show more Item The effective granular temperature based on the fluctuation-dissipation theorem(2007-08) Buck, Alexander, 1983-; Swinney, H.L., 1939-Show more Dissipative granular systems that are driven continuously by an external forcing, like vertical shaking or fluid flow pulses, exhibit fluid like properties. Different definitions of granular temperature have been proposed for these systems, in analogy to regular fluids of microscopic particles. On the road to creating a setup for measuring both the temperature based on the fluctuation-dissipation theorem TFD and the kinetic temperature Tkin, experiments to measure TFD of a water-fluidized bed of glass beads (d = 250 μm) were performed with a torsion oscillator. For low flow rates around the onset of fluidization, (flow rate Q ∼ 0.30 ml/s) the temperature was on the order of kBTFD ∼ 10−16 J and showed a linear increase with the flow rate. A sharp increase of the damping of the torsion oscillator was found for decreasing flow rates around the onset of fluidization, which can be interpreted as the approach to a glassy regime of the fluidized bed.Show more Item End-effects regime study in full-scale and laboratory scale setups(2015-12) Rojo, Raymondo Mendivil, III; Goldstein, David Benjamin, doctor of aeronautics; Tinney, Charles Edmund, 1975-; Ruf, JosephShow more Full-scale launch data from a cluster of three rocket engines employing a Thrust Optimized Parabolic contour nozzle and hot gas was compared with a laboratory-scale representation. The laboratory setups comprised of both three-nozzle and four-nozzle cluster aerodynamically scaled for use with cold gas. The evolving free-shock separated and restricted separated shock flow states seen in the full-scale was reproduced in the laboratory as well as an end-effects regime prior to flowing full. Acoustic pressure waveforms recorded on the base of both vehicles and behind the rocket clusters are analyzed using various statistical metrics as well as time-frequency analysis, along with the influence staggered starts have on these waveforms. Wall pressure data captured near the lip of these nozzles were compared with the acoustics and analyzed for evidence of nozzle interaction. During the end-effects regime, the nozzles produced high intensity loads and steepened waveforms given by raises the overall sound pressure level, and in both the skewness and kurtosis values of the acoustic pressure time derivative. The finding reveals a 3 dB reduction in end-effect regime loads when a stagger was introduce. However, the effects of stagger had neglible influence on the skewness and kurtosis of the acoustic pressure time derivative as they rose to the same levels, thereby demonstrating the intermittence and impulsiveness of the acoustic waveforms that form during rocket engine startup.Show more Item A field study to assess the value of 3D post-stack seismic data in forecasting fluid production from a deepwater Gulf-of-Mexico reservoir(2005) Gambús Ordaz, Maika Karen; Torres-Verdín, CarlosShow more This dissertation describes a study undertaken to appraise the reliability of spatially complex hydrocarbon reservoir models constructed with the use of 3D post-stack seismic amplitude data and well logs. Developments center about the interpretation of data acquired in an active hydrocarbon field in the deepwater Gulf of Mexico. The availability of measured time records of fluid production and pressure depletion provides an independent way to quantify the accuracy and reliability of several methods commonly employed to construct static reservoir models. We make use of geostatistical inversion to construct spatial distributions of porosity and permeability that simultaneously honor well logs and 3D poststack seismic amplitude data. The constructed reservoir models are compared against models constructed with standard geostatistical procedures that do not make use of seismic amplitude data or else that use a simple statistical correlation between reservoir properties and seismic - inverted acoustic impedances. We perform multi-phase fluid-flow simulations to assess the consistency of the constructed reservoir models against the measured time record of flow rates of gas/water and shut-in well pressures. For the hydrocarbon field under consideration, the joint stochastic inversion of well logs and 3D post-stack seismic amplitude data consistently yields the closest match to dynamic measurements of fluid production and pressure depletion. Our study also compares the influence of petrophysical and rock-fluid parameters on the reliability and accuracy of the predicted fluid production against the influence of spatial variability of porosity and permeability.Show more Item Finite element methods in linear poroelasticity: theoretical and computational results(2005) Phillips, Phillip Joseph; Wheeler, Mary F. (Mary Fanett)Show more Linear Poroelasticity refers to fluid flow within a deformable porous medium under the assumption of relatively small deformations. Some of the areas that are being modeled with the equations of linear poroelasticity include reservoir engineering, soil mechanics and, more recently, biomedical engineering. The purpose of this dissertation is to present original results for the development, analysis and application of numerical finite element algorithms in the field of linear poroelasticity. A fully coupled finite element method involving continuous elements for displacements and a mixed space for flow is developed (CG/Mixed). Existence, uniqueness and optimality results are provided. The norm measuring the pressure error, however, depends on the value of the constrained specific storage coefficient. For degenerate values, this leads to a slightly weaker optimality result. For the not untypical case of a null constrained specific storage coef- ficient, the solution produced by the CG/Mixed scheme sometimes produces non-physical pressure oscillations, a phenomenon referred to as locking. One potential remedy is to eliminate the continuity requirement for the elements approximating displacements. Therefore, a family of schemes which couples discontinuous elements for displacements and a mixed space for flow is introduced (DG/Mixed). Existence and uniqueness are established, optimal a priori error estimates are provided, and some success in the removal of locking is shown. Direct verification of several benchmark analytical solutions shows that solutions in linear poroelasticity can lack regularity. This sometimes manifests in pressure boundary layers which might degrade the rate of convergence of numerical solutions. The situation can often be ameliorated with the development of adaptive grid refinement strategies. This motivates a posteriori estimates in terms of computable residual quantities. Interestingly, it is also shown that the CG/Mixed method can be combined with adaptive grid refinement as an alternative means to eliminate locking. The produced algorithms are then applied to some interesting application areas. In one instance, they are used to analyze the deformation and pressure dynamics in a cantilever bracket. Additionally, a variety of miscellaneous problems ranging from subsidence and well placement to scuba suit design highlight intriguing applications.Show more Item Fluid dynamics of thin films in semiconductor manufacturing processes(2021-08-03) Ban, Yang Hun; Bonnecaze, R. T. (Roger T.); Ekerdt, John G; Ganesan, Venkat; Sepehrnoori, KamyShow more Nanostructures and nanomaterials are means to dramatically improve the performance of LEDs, solar cells, hard disk drives, laser diodes, and displays. This improvement comes from fabricating nanostructures inside or on the surface of a substrate. Fabrication of these nanostructures often involves the coating and imprinting of thin films onto a substrate. However, defects produced during the manufacturing process destroy the functionality of nanostructures. Thus, the fluid dynamics of thin fluid films involved in the manufacturing process is an interesting scientific and engineering problem. The first system studied in this dissertation is the UVNIL. It is a promising high-resolution nanopatterning process and a key technique for the commercialization of nanostructure applications. However, the UVNIL suffers from low throughput. The bottleneck is the resist filling step, so the fluid flow in UVNIL has been studied extensively to find the minimum time required for completing filling of features can be found by studying the flow behavior of resist. The second system is a thin film resist used in the lithography industry. Thin liquid coatings, which have thicknesses of tens of nanometers, are frequently used in lithography. However, generating ultra-thin films is challenging because thinner films are more susceptible to defects and disturbances. Efforts to model the evolution of film profile have been made and flow and leveling dynamics of thin-film were modelled successfully.Show more Item Fluid management in immersion and imprint microlithography(2010-12) Bassett, Derek William; Bonnecaze, R. T. (Roger T.); Ekerdt, John G.; Schunk, Randy; Sreenivasan, S. V.; Willson, GrantShow more The important roles of fluid dynamics in immersion lithography (IL) and step-and-flash imprint lithography (S FIL) are analyzed experimentally and theoretically. In IL there are many challenges with managing a fluid droplet between the lens and the wafer, including preventing separation of the fluid droplet from the lens and deposition of small droplets behind the lens. Fluid management is also critical in S FIL because the imprint fluid creates capillary and lubrication forces, both of which are primarily responsible for the dynamics of the template and fluid motion. The fluid flow and shape of the wafer determine how uniform the gap height between the wafer and the template is, and they affect the resistance during the alignment phase. IL was investigated as a methodology to improve laser lithography for making photomasks. The fluid flow in IL was investigated by building a test apparatus to simulate the motion of the fluid droplet during microlithographic production, and using this apparatus to conduct experiments on various immersion fluids and wafer topcoats to determine what instabilities would occur. A theoretical model was used to predict the fluid separation instabilities. Finite element simulations were also used to model the fluid droplet, and these simulations accurately predict the fluid instabilities and quantitatively agreed with the model and experiments. It is shown that the process is viable: capillary forces are sufficient to keep the fluid droplet stable, heating effects due to the laser are negligible, and other concerns such as evaporation and dissolution are manageable. Euler beam theory and the lubrication equation were used to model the bending of an S FIL template and the flow of the fluid between the template and a non-flat wafer. The template filling time, conformance of the template to the wafer, and the alignment phase are investigated with an analytical model and finite element simulations. Analysis and simulations show that uniformity of the residual film thickness and ease of proper alignment depend greatly on the planarity of the wafer, the properties of the template, and the surface tension of the fluid.Show more Item Geochemical effects in two-phase flow(2005) Zuluaga, Elizabeth; Lake, Larry W.Show more Commercial reservoir simulators usually neglect the effect of the permeable media on phase equilibrium, and the thermodynamic interaction between the aqueous phase and the other phases present in the reservoir. These assumptions are not satisfied when gas is injected or produced, because water will be vaporized from the reservoir. This dissertation derives analytical and semianalytical solutions to predict water vaporization and mineral precipitation for gas injection and production in hydrocarbon reservoirs. It also develops and incorporates into the models phase equilibrium relationships that include the effect of capillary pressure and salinity in the predictions. A new equilibrium constant for mineral precipitation has been derived that takes into account capillary pressure and interfacial forces. For gas injection, a traveling wave solution has been adopted with a correction proposed to honor the material balance. The traveling wave solutions were tested against results from the compositional simulator Generalized Equation of State Model (GEM) and against experimental data. The results from the traveling wave solution matched the experimental data closely while GEM failed to make good predictions. A semi-analytical model has been developed for gas production. This semi-analytical model was also tested against results from GEM. The results closely matched the GEM solutions in the absence of capillary pressure, interfacial forces and salinity effects. The results of this research show that the reservoir could be completely depleted from water near the wellbore when gas is produced or under-saturated gas is injected. Therefore, the existence of a residual water saturation value has to be re-evaluated in reservoir modeling. It is also shown that the wetting phase is mobile even at extremely low values of wetting phase saturation: the paradigm of an immobile residual phase is mostly imposed by the limitations of measuring devices in the laboratory and by the length of time of the experiments used to measure relative permeability. A new method to obtain relative permeability at very low wetting phase saturation has been derived, based on fitting the relative permeability exponent to vaporization data in the falling rate period. This research has also quantified the reductions in porosity and absolute permeability caused by mineral precipitation.Show more Item Hydraulic characterization of structured packing via x-ray computed tomography(2006) Green, Christian Wayne; Eldridge, R. Bruce; Allen, David T.Show more Unit operations such as distillation, absorption, and stripping rely on the contacting of vapor and liquid phases to achieve a desired chemical separation. Existing models used to predict the performance of packed columns are primarily empirical. Such models were developed using measurements of column bulk properties, such as overall liquid holdup, pressure drop, and inlet and outlet stream compositions. Variations in column behavior on a local scale are not captured by existing models, and constitute an area in which model improvement has a potentially large impact. Development of improved models will require non-traditional data for validation. X-ray computed tomography (CT) has been evaluated as one possible technique for measuring local flow behavior in packed columns. X-ray CT was used in this work to obtain images of an operating air-water contactor containing Mellapak 250Y stainless-steel structured packing. The image quality of two different X-ray scanner geometries, each with distinct temporal and spatial resolutions, was investigated. The void fraction and liquid holdup was calculated from CT images for a variety of liquid and vapor flow rates below the flood point. In general, average liquid holdup calculated from CT images was within 10 to 15% of holdup measured using traditional techniques. The axial variation in liquid holdup, particularly near packing element joints, was explored. Holdup was shown to vary throughout the column, and was greatest near the joint of adjacent packing elements. The region 0.25 to 0.4 inches above the interface exhibited holdup two to five times higher than the holdup measured in the packing element bulk. Three-dimensional images of the packed bed were acquired for static and dynamic conditions. The packing surface area, interfacial area between vapor and liquid, and the effective fractional area of a packed bed were calculated using three-dimensional reconstruction of two-dimensional CT images. Packing surface area was in good agreement with vendor-supplied values. Interfacial area measurements were compared with experimental data for vapor-liquid reactive area. Finally, both time variation of liquid flow and measurement noise during the course of data acquisition were quantified by analyzing the variation of X-ray transmission data.Show more Item Iteratively coupled reservoir simulation for multiphase flow in porous media(2008-05) Lu, Bo, 1979-; Wheeler, Mary F. (Mary Fanett)Show more Fully implicit and IMPES are two primary reservoir simulation schemes that are currently used widely. However, neither of them is sufficiently accurate or ef- ficient, given the increasing size and degree of complexity of highly heterogeneous reservoirs. In this dissertation, an iterative coupling approach is proposed and developed to solve multiphase flow problems targeting the efficient, robust and accurate simulation of the hydrocarbon recovery process. In the iterative coupling approach, the pressure equation is solved implicitly, followed by the saturation equation, which is solved semi-implicitly. These two stages are iteratively coupled at the end of each time step by evaluating material balance, both locally and globally, to check the convergence of each iteration. Additional iterations are conducted, if necessary; otherwise the simulation proceeds to the next time step. Several numerical techniques are incorporated to speed up the program convergence and cut down the number of iterations per time step, thus greatly improving iterative model performance. The iterative air-water model, the oil-water model, and the black oil model are all developed in this work. Several numerical examples have been tested using the iterative approach, the fully implicit method, and the IMPES method. Results show that with the iterative method, about 20%-40% of simulation time is saved when compared to the fully implicit method with similar accuracy. As compared to the IMPES method, the iterative method shows better stability, allowing larger time steps in simulation. The iterative method also produces better mass balance than IMPES over the same time. The iterative method is developed for parallel implementation, and several test cases have been run on parallel clusters with large numbers of processors. Good parallel scalability enables the iterative method to solve large problems with millions of elements and highly heterogeneous reservoir properties. Linear solvers take the greatest portion of CPU time in reservoir simulations. This dissertation investigates advanced linear solvers for high performance computers (HPC) for reservoir simulation. Their performance is compared and discussed.Show more Item Measurement of the pressure drop of a liquid metal flowing through a packed bed of uniform conducting spheres with transverse magnetic field(1995-05) McWhirter, Jon David; Not availableShow more Item Measuring void fraction in bubbly air-water mixtures with ultrasonic extinctions(1995-08) Maher, Thomas Francis, 1957-; Not availableShow more Item A mixed spectral and finite volume method for compressible viscous flows(1993) Minyard, Tommy Keith, 1968-; Kallinderis, Y. (Yannis)Show more The thesis presents a mixed spectral/finite volume method for compressible viscous flows. The method is evaluated for accuracy and robustness via test cases for various Mach numbers. The domain is divided into a viscous region and an inviscid region. The viscous region uses the full Navier-Stokes equations, while the inviscid region employs the Euler equations. A high order Chebyshev collocation spectral method is developed for the viscous region to resolve boundary layers. This method avoids the dense grids needed by finite-volume methods to resolve the viscous areas. A finite-volume method based on a Lax-Wendroff type scheme is employed for the inviscid region. A special interface formulation is developed for coupling the spectral with the finite-volume method. Comparisons with analytic results as well as convergence histories are presentedShow more Item Models for internal waves in two-fluid systems(2001-05) Kalisch, Henrik W.; Bona, J. L.Show more Item Models of fluid dynamics in biological tissues for medical imaging and drug delivery(2020-07-22) Woodall, Ryan Thomas; Yankeelov, Thomas E.; Stachowiak, Jeanne C; Rylander, Christopher G; Brenner, Andrew J; Biros, GeorgeShow more Fluid dynamics are essential to accurately describe the transport of any solute or particle delivered to a tumor, whether it is blood, nutrients, oxygen, systemic therapies, or a contrast agent. The purpose of this dissertation is to utilize quantitative medical imaging to inform computational fluid dynamics models of transport in biological tissues for applications in medical imaging and drug delivery, thereby improving our understanding of the imaging modalities, and providing accurate models of contrast agent and drug delivery for clinical use to maximize benefit to the individual patient. This objective is addressed in two distinct parts. First, we develop a high resolution, tissue-based model of contrast agent delivery in the mouse BT474 xenograft model of breast cancer, and simulate the acquisition of dynamic contrast enhanced magnetic resonance imaging data in this domain to test the accuracy of the standard methodology typically used to analyze such data. The results indicate that this widely used methodology for analyzing DCE-MRI data has inherent inaccuracies, as it does not account for passive delivery and distribution of the contrast agent due to diffusion within each voxel. Second, we develop, calibrate, and validate a mathematical model of convection-enhanced delivery of Rhenium-186 nanoliposomes to glioblastoma multiforme. The model is used to identify the optimal placement of the catheter within the tumor, so as to simultaneously minimize radiation exposure to healthy tissue and maximize tumor coverage. While models of convection enhanced delivery of molecular agents are currently on the market, no such models exist which are designed specifically for nanoparticle delivery, and which are calibrated and validated using clinical medical image data. Our results offer a useful model which accurately recapitulates the distribution of these liposomes, and is capable of identifying an optimal catheter placement for the delivery of these nanoparticles which avoids leakage into non-tumor regions.Show more Item Near-field flow structures and transient growth due to subcritical surface roughness(2010-05) Doolittle, Charles Jae, 1985-; Goldstein, David Benjamin, doctor of aeronautics; Tinney, CharlesShow more An immersed boundary spectral method is used to simulate laminar boundary layer flow over a periodic array of cylindrical surface roughness elements. Direct comparisons are made with experiments by using a roughness-based Reynolds number Re[subscript k] of 216 and a diameter to spanwise spacing ratio d/[lamda] of 1/3. Near-field differences between three similar studies are presented and addressed. The shear layer developed over the roughness element produces the downstream velocity deficit region while splitting of the vortex sheet shed the trailing edge forms its lateral modes. Additional geometrical configurations are simulated for comparisons with experimental results and future analysis by linear stability theory. Total disturbance energy E[subscript rms] is fairly consistent with experimental results while spanwise energy components vary significantly. Physical relaxation of the disturbance wake is found to remain a prominent issue for this simulation technique.Show more