Fluid dynamics of a bifurcation

Abstract

The objectives of the present paper are to accurately determine the modifications to a three-dimensional flow field caused by a bifurcation module, to study the downstream evolution of the generated flow field, and to enhance understanding by establishing the individual and combined roles of five factors (viz. curvature of flow path, flow division at the bifurcation ridge, possible change in flow area from mother to daughter branches, complex shape changes in the bifurcation and inertia of the flow) in giving rise to such a flow field in the bifurcation module. The effects of the aforementioned five factors on the loss production in a bifurcation module and on the potential of further loss in downstream units are also studied, and new correlations are developed. The detailed analysis is systematized here by establishing two novel methods of construction of a bifurcation, viz. “co-joining of two bent pipes” and “splitter in a pipe”, and by formally deriving the equivalence condition for the flow in a bifurcation and its constituent elements. Through this systematization an attempt is made to understand comprehensively the complexity of the fluid dynamics occurring in a single bifurcation, which is often masked in the usual studies of flow in large bifurcating networks. Several bifurcation geometries are studied, and about 500 separate three-dimensional computations are performed to achieve a degree of generalization. Use of fine grid (with up to 20 million computational elements in some simulations), double-precision arithmetic and stringent convergence criteria (10−8 for each scaled residual) ensures high accuracy of the computed solutions. Both primary and secondary flow fields are investigated. Flow path curvature is responsible for the development of Dean-type secondary motion while flow division at the bifurcation ridge generates secondary motion opposite to that induced by curvature. An increase of flow area from inlet to outlet results in an increase of asymmetry in cross-sectional velocity distribution. Although the loss across a bifurcation may sometimes be smaller than that across its constituent elements, it is shown here through the introduction of two parameters that a greater potential for incurring losses in a following straight section is generated in the bifurcation.