Unsteady confined buoyant plumes

Abstract

Two-dimensional time-dependent buoyancy-induced flows above a horizontal line heat source inside rectangular vessels, with adiabatic sidewalls and top and bottom walls maintained at uniform temperature, are studied numerically. Transitions to unsteady flows are performed by direct simulations for various depths of immersion of the source in the central vertical plane of air-filled vessels. For a square vessel and a line source near the bottom wall, the numerical solutions exhibit a sequence of instabilities, called natural swaying motion of confined plumes, beginning with a periodic regime having a high fundamental frequency followed by a two-frequency locked regime. Then, broadband components appearing in the spectra indicate chaotic behaviour and a weakly turbulent motion arises via an intermittent route to chaos. For rectangular vessels of aspect ratio greater than 2 and depths of immersion greater than the width, the flow undergoes a pitchfork bifurcation. This symmetry breaking is driven by the destabilization of an upper unstable layer of stagnant fluid above the plume. Then a subcritical Hopf bifurcation occurs. On the other hand, if the depth of immersion is lower than the width of the vessel, a stable layer of fluid is at rest below the line source. Then penetrative convection sets the whole air-filled vessel in motion and an oscillatory motion of very low frequency arises through supercritical Hopf bifurcation followed by a two-frequency locked state.

High Dynamic Range Particle Image Velocimetry Applied to Heat Convection Studies

“…These mechanisms depend on the ratio of depth of immersion to vessel width. The oscillation frequency f = 0.0657Ra 0.433 (0.310 6 < Ra < 810 6 ) [28] as per earlier results [27]. For a pair of cylinders, Eckert and Soehngen [29] found that the induced temperature and velocity fields due to the buoyant plume from downstream cylinders have opposing effects.…”

“…A greater body of research is available on swaying plumes from thin horizontal wires, regarded as line heat sources [25,26,27]. Desrayaud and Lauriat [28] investigated buoyancy induced flow from a horizontal wire heat source; for rectangular vessels two destabilizing mechanisms lead to low frequency motion due to instability of the buoyant plume. These mechanisms depend on the ratio of depth of immersion to vessel width.…”

Numerical Simulation of Buoyant Plumes Using a Fixed Point Iterative Method

“…Numerical simulation has been applied to this kind of flows and results with a 2D Direct Numerical Simulation (DNS) have been reported in [5] and [6]. For the validation of our results we are comparing them with those reported in the cited bibliography.…”

Prediction of Unsteady Natural Convection within a Square Cavity Containing an Obstacle at High Rayleigh Number Value

“…The side walls and the upper wall are maintained at a cold temperature T c , while the remaining walls are kept adiabatic. In addition, in order to deepen our knowledge about natural convection, a special attention will be considered to investigate the phenomena of the unsteady state [4,5].…”