Time-dependent flows in an emptying filling box

Abstract

We examine the transient buoyancy-driven flow in a ventilated filling box that is subject to a continuous supply of buoyancy. A rectangular box is considered and the buoyancy input is represented as a turbulent plume, or as multiple non-interacting plumes, rising from the floor. Openings in the base and top of the box link the interior environment with a quiescent exterior environment of constant and uniform density. A theoretical model is developed to predict, as functions of time, the density stratification and the volume flow rate through the openings leading to the steady state. Comparisons are made with the results of small-scale analogue laboratory experiments in which saline solutions and fresh water are used to create density differences. Two characteristic timescales are identified: the filling box time ($T_f$), proportional to the time taken for fluid from a plume to fill a closed box; and the draining box time ($T_d$), proportional to the time taken for a ventilated box to drain of buoyant fluid. The timescale for the flow to reach the steady state depends on these two timescales, which are functions of the box height $H$ and cross-sectional area $S$, the ‘effective’ opening area $A^*$, and the strength, number and distribution of the buoyancy inputs. The steady-state flow is shown to be characterized by the ratio of these timescales ($\mu\,{=}\,T_d/T_f$) which is equivalent to the dimensionless vent area $A^*/H^2$. A feature of these flows is that for $\mu\,{>}\,\mu_c$ the depth of the buoyant upper layer may exceed, or ‘overshoot’, the steady layer depth during the initial transient. The value of $\mu_c$ is determined for both line and point-source plumes, and the sensitivity of the developing flow to the distribution of buoyancy input assessed.

The role of diffusion on the interface thickness in a ventilated filling box

“…Estimates of the interface thickness for the salt bath experiments of Kaye & Hunt (2004) predict an interface thickness in the range of 0.5-0.75 mm. While accurate measurement of this thickness was not possible during those experiments, laboratory images show the steady-state interface to be extremely sharp as can be observed, most especially, from figure 13 of Kaye and Hunt's paper.…”

“…The transient model for a single enclosure was presented by Kaye & Hunt (2004). They demonstrated that the time evolution is controlled by the magnitude of the emptying time…”

Gas build-up in a domestic property following releases of methane/hydrogen mixtures

“…The objective of the analysis was to determine both the variation in the volume of the upper layer, 1 V , (i.e. the change in position of the interface, h ), and the build-up of gas in the upper layer, c , during the transient part of the release and also their steady state values.…”

“…Following Kaye and Hunt [1] the rate of change of the volume of the upper layer can be expressed as:…”

On the thermal buffering of naturally ventilated buildings through internal thermal mass

“…Choosing the amplitude of environmental temperature variations T , the typical ventilation rate is q 0 = A * √ αgH T , giving the time for ventilation to affect the interior temperature as t 4 = V i /q 0 . This time scale is the analogue of the flushing time scale defined by Holford & Hunt (2000) (for a well-mixed space, with the temperature difference scale set by the initial conditions) or Kaye & Hunt (2004) (for a two-layer stratification, with the temperature difference scale set by plume dynamics). In both these earlier studies, the competition between a flushing time scale and a heating (Holford & Hunt 2000) or filling (Kaye & Hunt 2004) time scale was used to understand the dynamics of natural ventilation in an insulated space.…”