Direct simulations and modelling of basic three-dimensional bifurcating tube flows

Abstract

Three-dimensional bifurcating internal flow is studied for a single mother tube branching into two equal but diverging daughter tubes. The mother tube is straight and of circular cross-section, containing a fully developed incident motion, while the diverging daughters are straight and of semi-circular cross-section. This basic configuration is treated first by direct numerical simulation and secondly by slenderflow modelling, for a variety of Reynolds numbers and angles of divergence. The direct simulations and modelling highlight different forms of three-dimensional separation or flow reversal as well as enhanced upstream and downstream influence and pressure loss induced by the bifurcations especially at increased divergence angles. Comparisons between the results from the simulations and those from the slender-flow modelling show relatively close agreement at medium values of Reynolds number. In particular, as the angle of divergence increases for a given Reynolds number, there is generally first an increase in flow attachment on to the inner divider wall(s) and then, at higher angles, an increasing trend to flow reversal at the corners formed by the junctions of the outer wall with the divider; longitudinal vortex motion is also enhanced then. The agreement persists over a surprisingly wide range of divergence angles.

Multi-branching three-dimensional flow with substantial changes in vessel shapes

“…The present investigation includes these relevant, largely unstudied, non-symmetrical three-dimensional effects of three-dimensional wall shaping, presuming them to act over a relatively long axial length scale. Such an assumption seems reasonably valid in many parts of the cerebrovascular system, owing simply to the slender physical shapes of the vessels involved, while concerning other shapes the results of Tadjfar & Smith (2004) indicate the possible validity of the approximations made subsequently in this paper for significantly non-slender shapes such as with a right-angled bend, suggesting a very wide range of applicability in practice. As a result, the geometry and hence the flow adjusts a great deal before the ridge separating neighbouring daughter vessels, from here onwards knows as the carina, is reached.…”

Multi-branching flows from one mother tube to many daughters or to a network

“…Moreover, it is useful to discover the range of Reynolds numbers over which the approximations in Smith & Jones (2003) apply satisfactorily. Simulations and theoretical work by Tadjfar & Smith (2004) for three-dimensional motion show fair agreement, even at relatively low Reynolds numbers and high divergence angle. The response at a branching, especially of type I, can be a vital component in a cranial or cardiovascular network (see references cited above), and this emphasizes the need to assess the accuracy of local branching analysis.…”

Fluid flow through various branching tubes

“…The work is partly review but partly new, specifically in terms of the new comparisons, the common features found, the new direct simulations on multi-branching flow and the new three-dimensional flow study. Overall, the approximations of high throughput are found to work well at Reynolds numbers above about 100 or even lower in practice [9,[27][28][29][30][31].…”