Direct simulation of weak axisymmetric fountains in a homogeneous fluid

Abstract

The weak axisymmetric fountain that results from the injection of a dense fluid upwards into a large container of homogeneous fluid of lower density is studied numerically. Using a time-accurate finite volume code, the behaviour of fountains with both a uniform and a parabolic profile of the discharge velocity at the source has been investigated. The evolution of the transient fountain flow has been analysed and two distinct stages have been identified. The time series of the passage of the fountain front has been presented and the initial, temporary and final characteristic fountain heights have been determined and scaled with the Froude number at the source. At steady state, the final fountain height and the fountain width are found to be the height and horizontal length scales which provide the full parameterization of the flow in the fountain core. The vertical velocity and temperature on the symmetry axis have been scaled with the height scale and an explicit correlation is also obtained for the former. The radial distributions of both the vertical and horizontal velocities in the zone of self-similarity in the fountain core at steady state have been scaled with the two length scales and empirical correlations have been obtained.

Direct simulation of fountains with intermediate Froude and Reynolds numbers

“…A nonuniform mesh of 298 × 297 grids has been used in this study to enable the regions of rapid solution variation to be accurately resolved while limiting the total number of nodes. Detailed descriptions of these schemes were given in [6,7] and the code has been successfully used for the simulation of a range of buoyancy dominated flows. τ=50 τ=100 τ=150 τ=200 τ=250 τ=350 τ=750 τ=500 …”

“…Such fountains have no distinguishable upward and downward flows, instead the streamlines curve and spread from the source. Our recent analytical and numerical studies showed that these weak fountains demonstrate different behavior patterns to those of turbulent fountains [6,7,8,9,10]. It was found that Z m has the following scaling relation with Fr and Re,…”

Interaction between a Vertical Turbulent Jet and a Thermocline

“…4. Figure 4a shows the decay of the axial vertical velocity of the jet in the thermocline versus that of the weak fountain in a homogeneous fluid (Lin and Armfield 2000). Figure 4b shows several LES profiles of the vertical velocity in the thermocline (each normalized by its centerline value U c , while R 0 corresponds to the distance, where U avg 5 0) and compares them to the experimental data by Ezhova and Troitskaya (2012).…”

“…Validation of our LES model (Fr 5 13, thick thermocline) against the data on weak fountains in a homogeneous fluid by Lin and Armfield (2000) and experiments on turbulent jets in a stratified fluid by Ezhova and Troitskaya (2012) is shown in Fig. 4.…”

Warm discharges in cold fresh water: 2. Numerical simulation of laminar line plumes

“…Previous authors have done much analysis of both turbulent and laminar fountains in the more usual situation of linear dependence of density on temperature, with a negatively buoyant fluid being injected upwards into a less dense ambient. Lin and Armfield [6,7] used computational models for axisymmetric and two-dimensional laminar . Here x 0 is the half-width of a line source or the radius of an axisymmetric source, V 0 and g 0 are respectively the mean velocity and reduced gravity at the source, and the numerical coefficients a 0 and a 1 depend on the source geometry (axisymmetric or line source) and velocity profile.…”