Effect of aspect ratio on entrance length in rectangular minichannels with plenum

Abstract

In the case of a long, straight rectangular channel, hydrodynamic development of flows is influenced by the growth of the boundary layer along the walls of the channel. Though such a geometry is well-studied in the literature, in reality, the flow often happens in channels with plenums on each end and is not studied extensively. This work addresses this gap. There is a sudden contraction from the plenum to the channel which causes the flow to separate at the entrance of the channel. Hence, the flow development is influenced not only by the boundary layer growth but also by recirculation and the presence of a continuous wall along one direction in the case of planar geometries. This causes the centerline velocity in the entrance region to overshoot the value at the fully developed region, which makes the conventional usage of 99% of the fully developed value difficult. Hence, an alternate method of defining entrance length, based on the slowest development across the channel cross section, is proposed. Based on this approach, the entrance length value shows a non-monotonic variation with the aspect ratio (AR)—its value reduces between 0.6 and 1.66; beyond 1.66, it increases up to 20 before becoming flat. The entrance length also shows a weak dependence on the Reynolds number for AR between 2 and 20. A new set of correlations of entrance and recirculation lengths are proposed.