No description available.

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The problem studied is the laminar flow over inclined, finite flat plates for moderately high Reynolds numbers in two and three dimensions. There are only few prior analyses, mainly for two dimensional flow, for this problem, and thus it was decided that it was worthwhile to study it now in great detail. The full Navier-Stokes equations were solved using a weak Galerkin formulation for the Finite Element Method with the pressure determined by a penalty approach. The influence of grid resolution, boundary conditions and size of the domain was studied. The true nature of the flow for different Reynolds numbers was also examined through steady and unsteady simulations of the two dimensional cases for 6600 â ¤ ReL â ¤18000. Results for the three dimensional flow over square plates at two angles of attack, a = 3.0 and 8.0 degrees for ReL = 100 are presented. The results are given in terms of skin friction and pressure coefficient variations along with flowfield visualization. Comparison between the two dimensional and three dimensional flow indicates the influence of the third coordinate to the flow. The analysis indicated that the two dimensional flow over a finite thick plate at 3.0 degrees angle of attack is steady up to Re = 12000. The solution for the upper surface is strongly influenced by the presence of a recirculation bubble at the leading edge. The slope of the lift curve for the 2D viscous flow is less than 2Ï , the result predicted by the thin wing theory. The solution for the three dimensional flow is strongly influenced by the the existence of the tip vortices. The slope of the lift curve for the 3D viscous flow is less than the one corresponding to the 2D flow. In addition, the effect of the aspect ratio on the lift does not agree with the inviscid lifting line theory prediction. / Master of Science

Bibliography: leaves 184-190 / viii, 190 leaves : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1987

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This thesis describes a simple efficient and robust numerical technique for solving two-dimensional incompressible laminar steady flows at moderate-to-high Reynolds numbers. The method uses an incremental multigrid method and an extrapolation procedure based on minimum residual concepts to accelerate the convergence rate of a robust block-line-Gauss-Seidel solver for the vorticity-stream function equations. Results are presented for the driven cavity flow problem using uniform and nonuniform grids and for the flow past a backward facing step in a channel. / M.S.

The two-dimensional, confined, laminar flow over a downstream facing step was studied using a finite element, Navier-Stokes equation solver. The weak form of the stationary, incompressible Navier-Stokes equations in primitive variable form was obtained using the conventional Galerkin technique for mixed problems. Biquadratic Lagrange interpolating polynomials were used to construct the basis functions that generated the finite-dimensional subspace containing the approximate solutions to the velocity field, while the pressure field was represented by a discontinuous, piecewise-linear approximation. This particular combination of solution subspaces was previously shown in a mathematically rigorous fashion to yield stable, consistent solutions to the Navier-Stokes equations. The results of the computations were benchmarked against the experimental data of Denham and Patrick, and also compared to earlier calculations by Ecer and Thomas, both of whom utilized alternative, unconventional formulations. These comparisons indicate that with the proper choice of basis functions, a conventional Galerkin scheme can yield results that are in as good and in many cases better agreement with the available experimental data than those of unconventional schemes that rely upon an infusion of artificial dissipation to enhance their numerical stability. The computational algorithm was also used to ascertain the cause of the noticeable lack of development and skewness that characterized the experimental data of Denham and Patrick both at and upstream of the step. The results of this study indicated that as suspected by Denham and Patrick, the skewness as well as the lack of development of the velocity profiles near the step were caused by the geometry of the test apparatus upstream of the step rather than by the presence of the step itself. The numerical experiments conducted here have been carefully documented so as to facilitate future comparisons intended to assess the relative efficiency of the present method of computation. / Doctor of Philosophy

Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006. / An analytical modelling procedure for predicting the streamwise pressure gradient for steady laminar incompressible flow of a Newtonian fluid through homogeneous isotropic granular porous media is introduced. The modelling strategy involves the spatial volume averaging of a statistical representative portion of the porous domain to obtain measurable macroscopic quantities from which macroscopic transport equations can be derived. A simple pore-scale model is introduced to approximate the actual complex granular porous microstructure through rectangular cubic geometry. The sound physical principles on which the modelling procedure is based avoid the need for redundant empirical coefficients. The model is generalized to predict the rheological flow behaviour of non-Newtonian purely viscous power law fluids by introducing the dependence of the apparent viscosity on the shear rate through the wall shear stress. The field of application of the Newtonian model is extended to predict the flow behaviour in fluidized beds by adjusting the Darcy velocity to incorporate the relative velocity of the solid phase. The Newtonian model is furthermore adjusted to predict fluid flow through Fontainebleau sandstone by taking into account the effect of blocked throats at very low porosities. The analytical model as well as the model generalizations for extended applicability is verified through comparison with other analytical and semi-empirical models and a wide range of experimental data from the literature. The accuracy of the predictive analytical model reveals to be highly acceptable for most engineering designs.