Browsing by Author "Thomson, David Lee"
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Item Low Dean number flows in helical ducts of rectangular cross section(1996) Thomson, David Lee; Bayazitoglu, Yildiz; Meade, Andrew J., Jr.The flow in a helical duct is characterized by increased fluid mixing, accomplished by the inducement of a secondary flow in the plane normal to the helix centerline. Two independent phenomena interact to produce this secondary flow. First, the curvature of the duct (i.e. its torroidal nature) causes Dean's type recirculation. Second, the torsion due to the non-planarity of the helix causes additional mixing. The secondary flow alters the axial velocity profile and increases the pressure drop compared to a straight duct. Imposing a rectangular cross section on such a duct complicates the analysis compared to a circular or elliptical cross section. A series solution based on curvature is introduced. The components of the series are determined using appropriate eigenfunction expansions. However, the resulting low order solution is limited to low Dean number flows. The analytical solution is useful for flows where curvature (torroidal ducts) or curvature and torsion (helical ducts) are important.Item Sequential function approximation of the radiative transfer equation(2000) Thomson, David Lee; Meade, Andrew J., Jr.; Bayazitoglu, YildizHeat transfer in a radiatively participating medium involves higher coupling than is typical for pure conduction and/or convection problems. Consequently, standard discretizing techniques such as partitioning regions of a finite volume domain on separate processors are inefficient. Additionally, standard angular decompositions may introduce discontinuities into the solution which are difficult to model accurately. A scalable method for parallelizing the radiative transport equation is presented. A standard discrete ordinates formulation is used to transform the integro-differential equation into a system of partial differential equations. The resulting system of equations is then solved by an optimal grid-independent, sequential-function approach that captures discontinuities accurately without additional user interaction. Results for one- and two-dimensional cases are given.