Line fountain behavior at low-Reynolds number

Abstract

In this paper, we present the line fountain behavior at low-Reynolds numbers obtained by experiments. The experiments are conducted over the range of Reynolds number 2.1<=Re<=127 and Froude number 0.4<=Fr<=42. It is observed that the fountain behavior can be categorized broadly into four regimes: the steady; flapping; laminar mixing; and jet-type mixing behavior, at full development. The critical Froude number for transition from a steady to unsteady flow varies with the Reynolds number. For Re>=60, the transition is independent of Re and is well described by the Fr~1.0 line. Over the range 10<Re<=50, the transition can be approximated by a constant FrRe^(2/3) line. For Re<=10, there is a higher dependency on the Reynolds number with a very sharp increase in the critical Froude number and it is hypothesized that the demarcation line follows Fr~Re^(-n), where n~2-4. The fountain exhibits flapping behavior in the range 13Re^(-2/3)<=Fr<=37Re^(-2/3). These observed fountain behaviors are mapped on to a Re-Fr plot. In addition, the observed, non-dimensionalized fountain height zm is found to be in a reasonable agreement with previous results on laminar line fountains. In particular, the experiment results confirm the scaling zm~FrRe^(-1/2) in the steady regime which was obtained previously by scaling analysis.