Three-dimensional fluid mechanics of particulate two-phase flows in U-bend and helical conduits

Abstract

The results of numerous studies performed to date have shown that the performance of various hydraulic systems can be significantly improved by using curved conduit geometries instead of straight tubes. In particular, the formation of Dean vortices, which enhance the development of centrifugal instabilities, has been identified as a factor behind reducing the near-wall concentration buildup in particulate flow devices (e.g., in membrane filtration modules). Still, several issues regarding the effect of conduit curvature on local multidimensional phenomena governing fluid flow still remain open. A related issue is concerned with the impact that conduit geometry makes on the concentration distribution of a dispersed phase in two-phase flows in general, and in particulate flows (solid/liquid or solid/gas suspensions) in particular. It turns out that only very limited efforts have been made in the past to understand the fluid mechanics of such flows via advanced computer simulations. The purpose of this paper is to present the results of full three-dimensional (3D) theoretical and numerical analyses of single- and two-phase dilute particle/liquid flows in U-bend and helical curved conduits. The numerical analysis is based on computational fluid dynamics (CFD) simulations performed using a state-of-the-art multiphase flow computer code, NPHASE. The major issues discussed in the first part of the paper are concerned with the effect of curved/coiled geometry on the evolution of flow field and the associated wall shear. It has been demonstrated that the primary curvature (a common factor for both the U-bend and helix geometries) may cause a substantial asymmetry in the radial distribution of the main flow velocity. This, in turn, leads to a significant, albeit highly nonuniform, increase in the wall shear stress. Specifically, the wall shear around the outer half of tube circumference may become twice the corresponding value for a straight tube, and gradually decrease to the straight tube level when approaching the inner bend location. Another important issue is concerned with the effect of the length of the curved section and of the straight tube just upstream of the bend. Specifically, the discontinuity in curvature at the straight-to-curved transition location results in a localized change in the wall shear distribution around the tube circumference. On the other hand, if the curved tube is sufficiently long, such as in the case of a helix, the asymmetric velocity profile eventually reaches a fully developed pattern. The effect of nondimensional flow parameters, the Reynolds and Dean numbers, on the entry length along the curved helix geometry is also investigated in this paper. It is shown that the predicted developing length agrees well with the existing experimental data. The objective of the second part of the paper is to investigate the mutual interactions between the liquid flow and solid particles in particulate two-phase flows in both the U-bend and helical geometries. It is shown that particle inertia causes an increase in the wall shear. At the same time, two interesting aspects are shown of Dean vortices on particle concentration under the effect of gravity. One of them is the shift in the particle settling zone from the bottom of the horizontal (or nearly horizontal) tube toward the inner bend of the tube. The other, even more important, is a dramatic reduction in peak concentration with increasing Dean number. Both effects are important for equipment design and optimization in biotechnology and process industries.