Interaction behavior of triple transitional round fountains in a homogeneous fluid

Abstract

In this study, the PIV and flow visualization techniques and three-dimensional direct numerical simulation are used to investigate the behavior of triple transitional round fountains, which are aligned along a straight line, interacting with each other in a homogeneous fluid over the ranges of 1 ≤ Fr ≤ 10 and 100 ≤ Re ≤ 1000, at a fixed spacing of D/X0=6, where Re and Fr are the Reynolds and Froude numbers, D is the spacing between the two neighbouring fountain sources, and X0 is the radius of orifices at the fountain source, respectively. The results show that the interaction behavior of triple transitional round fountains, over the ranges of Re and Fr studied, is dominated by the bobbing and flapping motions, and is either steady, or unsteady weakly multi-modal, or unsteady strongly multi-modal. In a steady interaction, the bobbing-flapping motions are only present in its initial development stage and the interaction will attain a steady state in the later stage in which the bobbing-flapping motions are no longer present. In contrast, in an unsteady interaction, the interaction remains unsteady all the time and the bobbing-flapping motions are present at all stages. Among all cases considered, a steady interaction occurs at Re ≤ 300 with Fr=1 and at Re=100 with Fr ≤ 5; an unsteady weakly multi-modal interaction occurs at Re=100 with 6 ≤ Fr ≤ 10, at 200 ≤ Re ≤ 300 with 2 ≤ Fr ≤ 10, and at Re=400 with Fr=1; and an unsteady strongly multi-modal interaction occurs at 600 ≤ Re ≤ 1000 with Fr=1 and at 400 ≤ Re ≤ 1000 with 2 ≤ Fr ≤ 10. Such interaction behavior is found to be similar to that of twin transitional round fountains over comparable ranges of Re and Fr, as discovered by us in an earlier study. It is also found that the two interaction regions formed by the three fountains have essentially symmetrical behavior about the middle fountain for all cases considered. Furthermore, the maximum fountain penetration heights and the maximum thicknesses of the interaction regions of the triple transitional round fountains are quantified with the experimental and numerical results and compared to the available scalings for single fountains at comparable Fr and Re values. Several scaling relations are then developed for these parameters over the ranges of Fr and Re considered.