Dong, Liqiang, Lin, Wenxian, Armfield, Steven W., Kirkpatrick, Michael P., Williamson, Nicholas, and Khatamifar, Mehdi (2023) Direct numerical simulation of “fountain filling box” flow with a confined weak laminar plane fountain. Heat Transfer, 52 (1). pp. 193-215.

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Abstract

A “fountain filling box” flow produced by discharging a weak laminar plane fountain in a confined open channel is studied numerically. Two-dimensional direct numerical simulations were performed for weak plane fountains. The development of the fountain flow experiences five stages; the initial upflow and the subsequent downflow after the fountain penetrates to the maximum height, followed by the outward movement of the intrusion of the fallen fountain fluid on the channel bottom, and then the wall fountain formed by the impingement of the intrusion on the vertical sidewall, which results in the reversed flow, and finally the gradual stratification of the fluid. The behavior of the intrusion can be approximately described with the plane gravity current theory. The period for the intrusion to reach the bounded side wall increases with increasing Re or decreasing Fr. Three regimes are found for the wall fountain behavior; “no-falling,” “slumping down,” and “rolling down” behavior. Convection, mixing, conduction, and filling all contribute to the formation and development of stratification, but their effects vary at different stages. For the initial stages, convection and mixing play a key role, resulting in an increasing bulk entrainment rate, while conduction and filling are dominant after quasi-steady stratification is created, presenting a decreasing bulk entrainment rate.

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