Experimental Investigation of Impinging Axisymmetric Turbulent Fountains

The behaviour of a turbulent, axisymmetric, Boussinesq, vertical fountain that impinges on a horizontal plate a distance H from the fountain source is investigated. Images from Light Induced Fluorescence visualisation of the flow provide a clear picture of the internal structure of the impinging flow. The interaction between the impinging fountain and the plate results in a buoyant radial wall jet that spreads horizontally before separating from the surface at a radius Rsp. The transient development of the flow and behaviour of Rsp with time is described. The steady-state flow is modelled theoretically and a correlation of the nondimensional spread of the impinging fountain is presented that successfully relates Rsp/H to the source-plate separation and the source characteristics of the fountain. Background The characteristics of turbulent plumes are of interest in many industrial and geophysical fluid flows. Frequently a prediction of the distribution of fluid density, velocity and concentration of contaminants, or other products, in the flow is needed for engineering design purposes. Plumes that develop from sources of buoyancy and momentum that act in opposite directions are known as fountains. Turner [1] reported experiments and presented an analytical model of a fountain developing in a uniform and quiescent environment. Baines, Turner and Campbell [2] extended this work to fountains within enclosures and determined the manner in which a fountain and a “filling box” interact. Bloomfield and Kerr [3] have more recently reported on the behaviour of axisymmetric and line fountains in an environment that is initially stratified. The basic flow configuration for a positively-buoyant fountain developing in a homogeneous environment is shown in figure 1a. The outer, upward flowing, stream entrains fluid from both the surrounding ambient and from the downward moving buoyant jet. The focus of the present study is the situation where a fountain impinges on a horizontal plate as shown schematically in figure 1b. This situation is of interest both as a fundamental issue in fluid mechanics and also as the flow is central to a number of practical applications. The latter include the heating of large building spaces by warm jets of air directed downward from the ceiling (e.g. warm air curtains); flow from the jets of vertical takeoff aircraft; modelling of the dispersion of welding fume, as in gas metal arc welding (GMAW) where the plume of welding fume is initially directed downwards and outwards by shielding gas ejected from the GMAW nozzle towards the welding workpiece. In the case of the impinging fountain, the buoyant fluid is forced radially outwards before rising as it impacts on the horizontal plate and thus the flow is wider than the free fountain (figure 1). The major objective the present work is to determine the way in which the presence of the solid plate changes the nature of the fountain and to investigate the flow both in the near field, close to the plate, and in the far field plume that rises above. Researchers who have looked at this problem and similar situations in the past include Lawrence and MacLatchy [4] who investigated the radial spread of a positively-buoyant plume release beneath the surface of a body of water. However, in this situation the stratification setup by the impinging plume is intrinsically stable, unlike the present case where the radial out-flowing jet (shown in figure 1b) is positively buoyant. More recently, Holstein and Lemckert [5] reported a set of experiments on impinging saline fountains. Their work focussed on how the radius of spread, Rsp, of the impinging fountain was related to the source conditions of the fountain, the source radius, R0, and source-plate separation, H. Theoretical Framework The two length scales that determine the behaviour of a free fountain, are the “jet length” (lM = M0/B0) and the “acceleration length” (lQ = Q0/M0 = πR0), where B0, Q0 and M0 are the source buoyancy, volume and specific momentum fluxes, respectively. The fountain source Froude number is then Fr0 = (lM/lQ). Turner [1] determined by experiment that the steady rise height, zm, of a free fountain from a source with Fr0 >>1 is given by zm = 1.85lM. In the present situation the distance of the source from the plate, H, represents the third length scale. The behaviour of the impinging fountain might therefore be expected to be determined by these three length scales and the source Reynolds number, Re0 = D0V0/ν, (D0 = 2R0). After impinging on the plate one might expect the fountain to transform into a radial wall jet as discussed by many authors, e.g. Rajaratnam [6]. However, in the present case the radial outflow is positively buoyant and will separate from the plate when the Coanda effect has diminished sufficiently. In a 2D geometry, the separation distance between the source of a positively-buoyant wall jet flowing over a horizontal surface and the point where the jet detaches from the surface has been briefly reported by Sandberg et al. [7] who found the non-dimensional separation distance Rsp/H to be a function of the source Archimedes number, Ar0 = (Fr0). B0, M0, Q0 B0, M0, Q0