Masters Degrees (Applied Mathematics)
Permanent URI for this collection
Browse
Browsing Masters Degrees (Applied Mathematics) by browse.metadata.advisor "Du Plessis, J. P."
Now showing 1 - 2 of 2
Results Per Page
Sort Options
- ItemHydrodynamic permeability of staggered and non-staggered regular arrays of squares(Stellenbosch : Stellenbosch University, 2003-12) Lloyd, Cindy; Du Plessis, J. P.; Stellenbosch University. Faculty of Science. Department of Mathematical Sciences.ENGLISH ABSTRACT: This work entails an analysis of two-dimensional Newtonian flow through a prismatic array of squares. Both in-line and staggered configurations are investigated, as well as the very low velocity Darcy regime, where Stokes' flow predominates, and the Forchheimer regime, where interstitial inertial effects such as recirculation are present. As point of departure two recently developed pore-scale models are discussed and their results compared to Stokes' flow computational analysis for flow through regular arrays of rectangles. The commercial CFX code is also used to analyse the problem and to determine the accuracy of the assumptions used for the development of the pore-scale models. Finally an improvement is suggested to the RRUC model towards more accurate prediction of permeabilities, especially for porosities below 75%, and whereby its quantitative predictive capability is thus enhanced considerably.
- ItemPore-scale modelling for fluid transport in 2D porous media(Stellenbosch : University of Stellenbosch, 2006-12) Cloete, Maret; Du Plessis, J. P.; University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics.In the present study, a model to predict the hydrodynamic permeability of viscous flow through an array of solid phase rectangles of any aspect ratio is derived. This also involves different channel widths in the streamwise and the transverse flow directions which may be chosen irrespectively to the rectangular shape itself. It is shown how, with the necessary care taken during description of the interstitial geometry, a volume averaged approach can be used to obtain results identical to a direct method. Insight into the physical situation is gained during the modelling of the two-dimensional interstitial flow processes and resulting pressure distributions and this may prove valuable when the volume averaging method is applied to more complex three-dimensional cases. The analytical results show close correspondence to numerical calculations, except in the higher porosity range for which a more realistic model is needed. Tortuosity is studied together with its inverse. Correspondences and differences regarding the definitions for the average straightness of pathlines, expressed in literature, are examined. A new definition, allowing different channel widths in the streamwise and the transverse flow directions, for the tortuosity is derived from first principles. A general relation between newly derived permeability and tortuosity expressions was obtained. This equation incorporates many possible geometrical features for a two-dimensional unit cell for granules. Three possible staggering configurations of the solid phase along the streamwise direction are also included in this relation.