Newtonian radial entrance flow

Abstract

The laminar flow of a Newtonian fluid is considered through a prototype radial entrance geometry that consists of a circular pipe joined to the bottom plate of a pair of parallel circular plates, a configuration that mimics and idealizes important practical flows. The equations of motion are solved numerically to compute the velocity field as a function of the Reynolds number Re and the geometrical aspect ratio e. This work extends limited previous results on flow development in this entrance geometry. A range of e and Re are considered, and the Re–e parameter space corresponding to flow separation is delineated. The computed results are used to illustrate the role of the aspect ratio in influencing flow development for small e≲1 and are analyzed to quantify the large e asymptotic behavior of various quantities characterizing the developing flow field. The limiting value of aspect ratio beyond which the asymptotic behavior applies is relatively small e≳2. The dependence of these quantities on Re also is analyzed. The results are discussed in light of available experimental measurements and existing analytical results. An important implication of the results in the context of confined laminar impinging jet heat transfer is described. The entrance configuration is contrasted with a companion radial entrance flow (radial source flow); although flow separation occurs in both cases, some basic features are quite distinct. The influence of the elongational character of this radial flow field is highlighted by comparing certain aspects of flow development between this axisymmetric configuration and its 2-D Cartesian analog.