47 research outputs found
A Simple Analytical Model for Estimating the Dissolution-Driven Instability in a Porous Medium
No full textThis article deals with the stability problem that arises in the modeling of the geological sequestration of carbon dioxide. It provides a more detailed description of the alternative approach to tackling the stability problem put forth by Vo and Hadji (Physics of Fluids, 2017, 29, 127101) and Wanstall and Hadji (Journal of Engineering Mathematics, 2018, 108, 53–71), and it extends two-dimensional analysis to the three-dimensional case. This new approach, which is based on a step-function base profile, is contrasted with the usual time-evolving base state. While both provide only estimates for the instability threshold values, the step-function base profile approach has one great advantage in the sense that the problem at hand can be viewed as a stationary Rayleigh–Bénard problem, the model of which is physically sound and the stability of which is not only well-defined but can be analyzed by a variety of existing analytical methods using only paper and pencil
Analytical investigations of convective effects on a solid-liquid interface
No full textA thin layer of a single-component Boussinesq fluid, contained between two rigid horizontal plates of low thermal conductivity, is cooled from above and heated from below. In the steady-static state, a heat flux traverses the system so that the temperature attained at the upper boundary of the layer is in the solid phase. An interface is planar in the conductive state, and corrugated in the convective regime. A small amplitude expansion study reveals that the critical Rayleigh number and the critical wavenumber for the onset of the interface deformation increase with the solid layer thickness. A weakly nonlinear stability analysis reveals that there is subcritical instability irrespective of the interface shape. The stable forms of the solidified front are then found. In the case of hexagonal pattern, the fluid motion is shown to be upward at the cells centers. Hexagons are also found to exhibit a higher heat flux than either rolls or squares. The non-planar interface is shown to have a cellular structure identical to the convection patterns which arise in this situation.A long wavelength approximation is used to derive a non-linear evolution equation for the leading order interface pertubation. This evolution equation is found to be ill-posed when the dimensionless thickness of the solid layer A exceeds 0.256. The equation is then solved numerically for A between 0 and 0.256. The curve shifts to the right as A approaches the value 0.256.The linear stability analysis for the binary alloy case is performed. This part complements the work done by Caroli et al. (1985). The critical value for the pulling velocity V at which both the morphological and convective instabilities are excited at the same concentration level is determined numerically.Made available in DSpace on 2011-05-07T14:13:41Z (GMT). No. of bitstreams: 2
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Previous issue date: 1989Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding ([email protected]) on 2011-05-07T15:04:23Z
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Long Wavelength Analysis of a Model for the Geographic Spread of a Disease
No full textWe investigate the temporal and spatial evolution of the spread of an infectious disease by performing a long-wavelength analysis of a classical model for the geographic spread of a rabies epidemic in a population of foxes subject to idealized boundary conditions. We consider twodimensional and three-dimensional landscapes consisting of an infinite horizontal strip bounded by two walls a finite distance apart and a horizontal region bounded above and below by horizontal walls, respectively. A nonlinear partial differential evolution Equation for the leading order of infectives is derived. The Equation captures the space and time variations of the spread of the disease in the weakly super critical region
The influence of cylindrical inclusions on the stability of a directionally solidified interface
No full text
INSTABILITIES DUE TO SORET DIFFUSION COUPLED TO THE MORPHOLOGY OF A SOLID-LIQUID INTERFACE
No full textRigidity Effects of Mako Shark Scales As a Passive Control Mechanism in Turbulent Flow
No full textElectronic Thesis or DissertationBio-inspired engineering research has allowed researchers to gain insight from animals that have had time to evolve highly efficient flow control mechanisms. The morphology of birds, bats, insects, fish, and swimming mammals has been studied for their incredible ability to maneuver through air and water swiftly. Several studies have been conducted on butterflies, bats, dolphins, and sharks to determine the specific aspects that allow them to control the flow of the fluids they navigate. Of particular interest for this study is the Shortfin Mako shark, whose scales bristle when met with reversing flow; this unique aspect of the scale geometry may be linked to a passive flow-actuated separation control mechanism. An experimental study of how the bristling angle of these shark scales can affect the separation control mechanism was conducted to understand the limitations and improve the design of bio-inspired surfaces for separation control. An adverse pressure gradient was induced using a rotating cylinder, creating a separated region over several bio-inspired models resembling fixed shark scales at different angles. In this experiment, the boundary layer grows to sizes large enough that the scale of the flow is increased, making it more measurable to digital particle image velocimetry (DPIV).Additionally, the large boundary layer allows models to be sized to fit within the bottom 5-10% of the boundary layer. Plates with model shark scales fixed at 0, 24.5, and 49 degrees were investigated at a Re in the range of 5 x 105. This data was compared to a smooth flat plate and obtained for a model with passively bristling scales, free to move within the flow to verify how the rigidity of the scales affects the reversing flow region
Weakly nonlinear convection induced by the sequestration of CO<sub>2</sub>in a perfectly impervious geological formation
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