Direct simulation of fountains with intermediate Froude and Reynolds numbers

Abstract

Fountains with intermediate Froude and Reynolds numbers are of fundamental interest, especially for understanding the mechanism of turbulence and entrainment in turbulent fountains. However there has been little work done to investigate the behavior of these transitional fountains. In this work, the transient behavior of axisymmetric fountains with 1 ≤ Fr ≤ 8 and 200 ≤ Re ≤ 800 is studied by direct numerical simulation. It is found that when Re ≤ 200, there is little mixing between the downflow of the fountain and the ambient, even for Fr as high as 8; However, when Re ≥ 400, the mixing between C67 the fountain downflow and the ambient becomes stronger, indicating that the entrainment and the turbulence are mainly due to Re and the contribution from Fr is much smaller; The maximum fountain penetration height z m fluctuates, even when the flow reaches the quasi-steady state, due to the interaction between the downflow and the bottom boundary and/or the entrainment between the downflow and the ambient; The averaged z m scales with FrRe

The rise and fall of turbulent fountains: a new model for improved quantitative predictions

“…Evolution of the steady-state height of a fountain as a function of the Froude number The steady-state height reached by a turbulent fountain is usually calculated by using the prediction of the initial maximum height corrected with the factor z m /z ss assumed constant at 1.43. For low-and very low-Froude-number fountains, numerical solutions of Lin & Armfield (2004) show that the ratio z m /z ss is close to 1. Turner (1966) presented experiments that consisted in injecting dense jets of salty water upwards in a tank of fresh water.…”

“…In most of the experiments investigated, the Reynolds number of the flow is high and the general behaviour of the fountain is controlled by the source Froude number. The experiments of Zhang & Baddour (1998) implied that p = 1.3, whereas the numerical simulations of Lin & Armfield (2004 showed a dependence on the source Reynolds number Re 0 1/4 , with p = 1 (Lin & Armfield 2004) and p = 3/2 . Based on theoretical analysis and laboratory experiments Kaye & Hunt (2006) suggest that p = 2/3 for low-Froude-number fountains (Fr 0 < 1) and p = 2 for intermediate Froude number (1 < Fr 0 < 10).…”

Impinging plane fountains in a homogeneous fluid

“…Laminar/transition Lin and Armfield [9] zm $ Fr 2=3 Re À2=3 0:0025 6 Fr 6 0:2; 5 6 Re 6 800 Lin and Armfield [10] zm $ Fr 0:2 6 Fr 6 1:0; Re ¼ 200 Lin and Armfield [11] zm $ FrRe À1=2 0:2 6 Fr 6 1:0; 5 6 Re 6 200 Lin and Armfield [18] zm $ FrRe 1=4 1:0 6 Fr 6 8:0; 100 6 Re 6 800 Philippe et al [19] zm $ FrRe 1=2 1 K Fr K 200; 0 < Re K 80 Williamson et al [24] conducted a series of experiments on round fountains and observed some different interesting flow behaviours. They broadly classified fountains as laminar for Re < 120 and transitional/turbulent for higher Re, independent of Fr.…”

Numerical simulations of negatively buoyant jets in an immiscible fluid using the Particle Finite Element Method

“…Sketch of a strong (a) and a weak (b) fountain. Currently, only limited numerical simulations of the dynamics of negatively buoyant jets have been presented [17][18][19][20][21][22][23][24] because they still pose a major research challenge from both theoretical and computational point of view. significant progress has been made in understanding the dynamics of negatively buoyant jets arriving at a general description of their flow behavior, summarized in the next section.…”

“…significant progress has been made in understanding the dynamics of negatively buoyant jets arriving at a general description of their flow behavior, summarized in the next section. Currently, only limited numerical simulations of the dynamics of negatively buoyant jets have been presented [17][18][19][20][21][22][23][24] because they still pose a major research challenge from both theoretical and computational point of view. These studies performed direct numerical simulations of thermal axisymmetric and plane fountains using the finite volume method; being the cause of the density gradient between both fluids is the difference in temperature.…”