On the transition from finite-volume negatively buoyant releases to continuous fountains

Abstract

AbstractAn experimental investigation to identify the source conditions that distinguish finite-volume negatively buoyant fluid projectile behaviour from fountain behaviour in quiescent environments of uniform density is described. Finite-volume releases are governed by their source Froude number ${\mathit{Fr}}_{D} $ and the aspect ratio $L/ D$ of the release, where $L$ denotes the length of the column of fluid dispensed vertically from the nozzle of diameter $D$. We establish the influence of $L/ D$ on the peak rise heights of a release formed by dispensing saline solution into fresh water for $0\lesssim {\mathit{Fr}}_{D} \lesssim 6$ and $0\lesssim L/ D\lesssim 34$. Within these ranges, we determine the source conditions for which a flow may be regarded, in terms of the initial rise height attained, as either finite-volume or continuous flux. The critical aspect ratio $ \mathop{ (L/ D)} \nolimits _{f} $, for a given ${\mathit{Fr}}_{D} $, which when exceeded no longer influenced release behaviour, led to the determination of $\{ {\mathit{Fr}}_{D} , \mathop{ (L/ D)} \nolimits _{f} \} $ paired source conditions that give rise to solely Froude-number-dependent, i.e. fountain-like, behaviour. As such, we make the link between finite-volume releases and continuous fountains. The $\{ {\mathit{Fr}}_{D} , \mathop{ (L/ D)} \nolimits _{f} \} $ pairs led us directly to the classification of a $\{ {\mathit{Fr}}_{D} , L/ D\} $ space from which source conditions giving rise to either negatively buoyant projectiles or fountains may be readily identified. The variation of $ \mathop{ (L/ D)} \nolimits _{f} $ with ${\mathit{Fr}}_{D} $ corresponds closely to established fountain regimes of very weak, weak and forced fountains. Moreover, our results indicate that the formation or otherwise of a primary vortex, as fluid is ejected, has a profound influence on the length of the dispensed fluid column that is necessary to achieve rise heights equal to fountain rise heights.