Browsing by Subject "fluid dynamics"
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Item Coastal Microstructure: From Active Overturn to Fossil Turbulence(2012-02-14) Leung, Pak TaoThe Remote Anthropogenic Sensing Program was a five year effort (2001- 2005) to examine subsurface phenomena related to a sewage outfall off the coast of Oahu, Hawaii. This research has implications for basic ocean hydrodynamics, particularly for a greatly improved understanding of the evolution of turbulent patches. It was the first time a microstructure measurement was used to study such a buoyancy-driven turbulence generated by a sea-floor diffuser. In 2004, two stations were selected to represent the near field and ambient conditions. They have nearly identical bathymetrical and hydrographical features and provide an ideal environment for a control experiment. Repeated vertical microstructure measurements were performed at both stations for 20 days. A time series of physical parameters was collected and used for statistical analysis. After comparing the data from both stations, it can be concluded that the turbulent mixing generated by the diffuser contributes to the elevated dissipation rate observed in the pycnocline and bottom boundary layer. To further understand the mixing processes in both regions, data were plotted on a Hydrodynamic Phase Diagram. The overturning stages of the turbulent patches are identified by Hydrodynamic Phase Diagram. This technique provides detailed information on the evolution of the turbulent patches from active overturns to fossilized scalar microstructures in the water column. Results from this study offer new evidence to support the fossil turbulence theory. This study concluded that: 1. Field Data collected near a sea-floor outfall diffuser show that turbulent patches evolve from active (overturning) to fossil (buoyancy-inhibited) stages, consistent with the process of turbulent patch evolution proposed by fossil turbulence theory. 2. The data show that active (overturning) and fossil (buoyancy-inhibited) patches have smaller length scales than the active+fossil (intermediate) stage of patch evolution, consistent with fossil turbulence theory and with laboratory studies. 3. Compared to a far-field reference, elevated dissipation rates near the diffuser were found in the seasonal pycnocline as well as in the bottom boundary layer. 4. More than 90% of the turbulent patches observed in the water column were non-overturning (active+fossil and fossil). Such patches can provide significant mixing in the interior of the ocean, far from surface and bottom boundary layers.Item Fast Algorithms for Biharmonic Problems and Applications to Fluid Dynamics(2013-10-22) Ghosh, AditiMany areas of physics, engineering and applied mathematics require solutions of inhomogeneous biharmonic problems. For example, various problems on Stokes flow and elasticity can be cast into biharmonic boundary value problems. Hence the slow viscous flow problems are generally modeled using biharmonic boundary value problems which have widespread applications in many areas of industrial problems such as flow of molten metals, flow of particulate suspensions in bio-fluid dynamics, just to mention a few. In this dissertation, we derive, implement, validate, and apply fast and high order accurate algorithms to solve Poisson problems and inhomogeneous biharmonic problems in the interior of a unit disc in the complex plane. In particular, we use two methods to solve inhomogeneous biharmonic problems: (i) the double-Poisson method which is based on transforming biharmonic problems into solving a sequence of Poisson problems (sometime also one homogeneous biharmonic problem) and then making use of the fast Poisson solver developed in this dissertation.; (ii) the direct method which uses the fast biharmoninc solver also developed in this dissertation. Both of these methods are analyzed for accuracy, complexity and efficiency. These biharmonic solvers have been compared with each other and have been applied to solve several Stokes flow problems and elasticity problems. The fast Poisson algorithm is derived here from exact analysis of the Green?s function formulation in the complex plane. This algorithm is essentially a recast of the fast Poisson algorithm of Borges and Daripa from the real plane to the complex plane. The fast biharmonic algorithms for several boundary conditions for use in the direct method mentioned above have been derived in this dissertation from exact analysis of the representation of their solutions in terms of problem specific Green?s function in the complex plane. The resulting algorithms primarily use fast Fourier transforms and recursive relations in Fourier space. The algorithms have been analyzed for their accuracy, complexity, efficiency, and subsequently tested for validity against several benchmark test problems. These algorithms have an asymptotic complexity of O(log N ) per degree of freedom with very low constant which is hidden behind the order estimate. The direct and double-Poisson methods have been applied to solving the steady, incompressible slow viscous flow problem in a cir- cular cylinder and some problems from elasticity. The numerical results from these computations agree well with existing results on these problems.Item Hypersonic Measurements of Roughness-Induced Transient Growth(2014-04-17) Sharp, Nicole SusanneThe effects of surface roughness on boundary-layer disturbance growth and laminar-to-turbulent transition are not well understood, especially in hypersonic boundary layers. The transient growth mechanism that produces algebraic growth of stream wise streaks may play a key role in roughness-induced transition but has not previously been deliberately observed in hypersonic flow. To make such measurements, the present work studies the boundary layer of a 5? half-angle smooth cone paired with a slightly blunted nose tip and a ring of 18 periodically-spaced cube-like discrete roughness elements 1-mm tall by 1.78-mm wide by 1.78-mm long. The roughness element height is approximately equal to the boundary-layer thickness. Measurements are made in the low-disturbance Texas A&M Mach 6 Quiet Tunnel. No transition to turbulence is observed for freestream unit Reynolds numbers between 7.5 ? 10^(6) m^(-1) and 9.8 ? 10^(6) m^(-1). Pitot measurements reveal azimuthally-alternating high- and low-speed streaks growing downstream of the roughness. Large unsteadiness is measured in the roughness wake but decays downstream. The stream wise evolution of the steady and unsteady disturbance energy is consistent with low-speed observations of transient growth in the mid-wake region behind periodically-spaced cylindrical roughness elements. This experiment contains the first quantitative measurements of roughness-induced transient growth in a high-speed boundary layer.Item Interactive simulation of fire, burn and decomposition(2009-05-15) Melek, ZekiThis work presents an approach to effectively integrate into one unified modular fire simulation framework the major processes related to fire, namely: a burning process, chemical combustion, heat distribution, decomposition and deformation of burning solids, and rigid body simulation of the residue. Simulators for every stage are described, and the modular structure enables switching to different simulators if more accuracy or more interactivity is desired. A ?Stable Fluids? based three gas system is used to model the combustion process, and the heat generated during the combustion is used to drive the flow of the hot air. Objects, if exposed to enough heat, ignite and start burning. The decomposition of the burning object is modeled as a level set method, driven by the pyrolysis process, where the burning object releases combustible gases. Secondary deformation effects, such as bending burning matches and crumpling burning paper, are modeled as a proxy based deformation. Physically based simulation, done at interactive rates, enables the user to ef- ficiently test different setups, as well as interact and change the conditions during the simulation. The graphics card is used to generate additional frames for real-time visualization. This work further proposes a method for controlling and directing high resolution simulations. An interactive coarse resolution simulation is provided to the user as a ?preview? to control and achieve the desired simulation behavior. A higher resolution ?final? simulation that creates all the fine scale behavior is matched to the preview simulation such that the preview and final simulations behave in a similar manner. In this dissertation, we highlighted a gap within the CG community for the simulation of fire. There has not previously been a physically based yet interactive simulation for fire. This dissertation describes a unified simulation framework for physically based simulation of fire and burning. Our results show that our implementation can model fire, objects catching fire, burning objects, decomposition of burning objects, and additional secondary deformations. The results are plausible even at interactive frame rates, and controllable.Item Practical Aspects of the Implementation of Reduced-Order Models Based on Proper Orthogonal Decomposition(2012-07-16) Brenner, Thomas AndrewThis 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 ?ow, quasi-2D nozzle ?ow and 2D inviscid channel ?ow. Results are presented verifying the ROMs against existing full-order models (FOM). POD is a method for separating snapshots of a ?ow ?eld that varies in both time and space into spatial basis functions and time coe?cients. The partial di?erential equations that govern ?uid ?ow can then be pro jected onto these basis functions, generating a system of ordinary di?erential equations where the unknowns are the time coe?cients. 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 ?ows. 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 ?ow, 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 ?rst 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 ?ow 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 ?ow case. Results are compared to the FOM for channel ?ow 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 ?rst shows the e?ect of the snapshot sampling on the accuracy of the POD basis functions. The second shows that for multiphase ?ow, the cross- coupling between ?eld variables should not be included when computing the POD basis functions.