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

Abstract

We examine the role of diffusivity, whether molecular or turbulent, on the steady-state stratification in a ventilated filling box. The buoyancy-driven displacement ventilation model of Linden et al. (J. Fluid Mech., vol. 212, 1990, p. 309) predicts the formation of a two-layer stratification when a single plume is introduced into an enclosure with vents at the top and bottom. The model assumes that diffusion plays no role in the development of the ambient buoyancy stratification: diffusion is a slow process and the entrainment of ambient fluid into the plume from the diffuse interface will act to thin the interface resulting in a near discontinuity of density between the upper and lower layers. This prediction has been corroborated by small-scale salt bath experiments; however, full-scale measurements in ventilated rooms and complementary numerical simulations suggest an interface that is not sharp but rather smeared out over a finite thickness. For a given plume buoyancy flux, as the cross-sectional area of the enclosure increases the volume of fluid that must be entrained by the plume to maintain a sharp interface also increases. Therefore the balance between the diffusive thickening of the interface and plume-driven thinning favours a thicker interface. Conversely, the interface thickness decreases with increasing source buoyancy flux, although the dependence is relatively weak. Our analysis presents two models for predicting the interface thickness as a function of the enclosure height, base area, composite vent area, plume buoyancy flux and buoyancy diffusivity. Model results are compared with interface thickness measurements based on previously reported data. Positive qualitative and quantitative agreement is observed.

An experimental study of air flow and temperature distribution in a room with displacement ventilation and a chilled ceiling

“…Magnier et al [14] have studied inlet conditions and those near the floor in some detail and verified the similarity to gravity current conditions. Theoretical studies of natural ventilation have been concerned with plume growth and the development of the upper warm layer dividing the room at the horizontal stationary front in both steady state [23,24] and transient conditions [25]. Although such studies, and related physical modelling studies, consider the development of the upper warm layer adjacent the ceiling they do not consider ceiling heat transfer conditions.…”

Validity of thermally-driven small-scale ventilated filling box models

“…at the interface between the upper and lower layers. Kaye et al (2010) examined this effect by proposing a balance between diffusion, acting to smear the interface, and entrainment in the plume, which acts to sharpen the interface. Considering a simple one-dimensional model of a diffusive layer between an initial jump in density, i.e.…”

Buoyancy-driven exchange flow between two adjacent building zones connected with top and bottom vents

“…The ratio of ratio of the diffusion and filling time scales, as suggested by Kaye et al [6], for small-scale experiments is very large. Hence diffusion plays only a minor role and thereby a relatively thin interface is anticipated.…”