Flow of Newtonian fluids through axisymmetric converging-diverging channels



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A new cone flow based lubrication theory which gives a "higher order" approximation than the classical Poiseuille flow based lubrication theory has been developed. The theory has the advantage over the classical theory in that it allows the analysis of inertia-free flow in "large angle" convergingdiverging flows. The method was used to analyze flow in two geometries, namely: (a) flow in a sinusoidal tube, and (b) flow in a "Venturi-Section" and good agreement was obtained between the theoretical predictions and the "exact" results obtained from numerical and other solutions. Under the appropriate conditions, the method represents an attractive alternative to classical lubrication theory and to straight numerical methods for the analysis of flow in complex geometries. An experimental system, involving flow in a sinusoidal tube, has been built and a friction factor versus Refolds number curve for the entire flow region has been experimentally determined. In the "creeping flow" region, good agreement was obtained between the theory and the experiment, thus providing validation of the theory and the experimental techniques. Flow visualization studies were carried out and the differences in the flow patterns corresponding to the different regimes were identified. An evaluation of an existing approach to predict the laminar-turbulent transition Reynolds numbers for flow of Newtonian fluids in tubes with axially varying diameter indicated that the postulate that transition occurs when the distribution of momentum between the rotational and the frictional modes reaches a certain critical ratio, is not valid for such geometries. Finally, the theoretical predictions of the corresponding "creeping" flow behavior were coupled with an existing porous media model to analyze the effect of the unit cell shape on the inherent flow resistance prevalent in flow in porous media. The analysis indicated that the permeability predictions are relatively insensitive to the unit cell shape.