G. R. Hunt

Virtual origin correction for lazy turbulent plumes

The location of the asymptotic virtual origin of positively buoyant turbulent plumes with a deficit of initial momentum flux when compared with equivalent pure plumes is investigated. These lazy plumes are generated by continuous steady releases of momentum, buoyancy and volume into a quiescent uniform environment from horizontal sources (at z = 0) of finite area, and are shown to be equivalent to the far-field flow above point source pure plumes, of buoyancy only, rising from the asymptotic virtual source located below the actual source at z = − z avs . An analytical expression for the location of the asymptotic virtual source relative to the actual source of the lazy plume is developed. The plume conservation equations are solved for the volume flow rate, and the position of the asymptotic virtual origin is deduced from the scaling for the volume flow rate at large distances from the source. The displacement z avs of the asymptotic virtual origin from the actual origin scales on the source diameter and is a function of the source parameter Γ ∝ Qˆ 2 0 Fˆ 0 / Mˆ 5/2 0 which is a measure of the relative importance of the initial fluxes of buoyancy Fˆ 0 , momentum Mˆ 0 , and volume Qˆ 0 in the plume. The virtual origin correction developed is valid for Γ > 1/2 and is therefore applicable to lazy plumes for which Γ > 1, pure plumes for which Γ = 1, and forced plumes in the range 1/2 z * avs decreases as Γ increases, and for Γ [Gt ] 1, z * avs → 0.853Γ −1/5 . Comparisons made between the predicted location of the asymptotic virtual origin and the location inferred from measurements of lazy saline plumes in the laboratory show close agreement.

The fluid mechanics of natural ventilation-displacement ventilation by buoyancy-driven flows assisted by wind

This paper describes the fluid mechanics of natural ventilation by the combined effects of buoyancy and wind. Attention is restricted to transient draining flows in a space containing buoyant fluid, when the wind and buoyancy forces reinforce one another. The flows have been studied theoretically and the results compared with small-scale laboratory experiments. Connections between the enclosure and the surrounding fluid are with high-level and low-level openings on both windward and leeward faces. Dense fluid enters through windward openings at low levels and displaces the lighter fluid within the enclosure through high-level, leeward openings. A strong, stable stratification develops in this case and a displacement flow is maintained for a range of Froude numbers. The rate at which the enclosure drains increases as the wind-induced pressure drop between the inlet and outlet is increased and as the density difference between the exterior and interior environment is increased. A major result of this work is the identification of the form of the nonlinear relationship between the buoyancy and wind effects. It is shown that there is a Pythagorean relationship between the combined buoyancy and wind-driven velocity and the velocities which are produced by buoyancy and wind forces acting in isolation. This study has particular relevance to understanding and predicting the air flow in a building which is night cooled by natural ventilation, and to the flushing of gas from a building after a leak. c~ 1999 Elsevier Science Ltd. All rights reserved.

Steady-state flows in an enclosure ventilated by buoyancy forces assisted by wind

We examine ventilation driven by a point source of buoyancy on the floor of an enclosure in the presence of wind. Ventilation openings connecting the internal and external environment are at high level on the leeward facade and at low level on the windward facade, so that the wind-driven flow in the enclosure is in the same sense as the buoyancy-driven flow. We describe laboratory experiments that determine the parameters controlling the ventilation under these conditions and compare the results with predictions of a theoretical model. Previous work has shown that when ventilation is driven solely by a single localized source of buoyancy flux B , a stable, two-layer stratification and displacement flow forms. The steady height of the interface, between the buoyant upper layer and the lower layer at ambient density ρ, is independent of B and depends only on the ‘effective’ area A * of the openings, the height H of the enclosure and entrainment into the plume. For wind-assisted flows, the ventilation is increased owing to the wind pressure drop δ between the windward and leeward openings. The two-layer stratification and displacement flow are maintained over a range of wind speeds, even when the wind-induced flow far exceeds the flow induced by the buoyancy force. The steady height of the interface depends upon the Froude number Fr = (Δ/ρ) 1/2 ( H / B ) 1/3 and the dimensionless area of the openings A */ H 2 . Increasing the wind speed raises the position of the interface and decreases the temperature of the upper layer (as does increasing A */ H 2 ), while increasing B lowers the level of the interface and increases the temperature of the upper layer. For significantly larger Fr , the displacement flow breaks down and we investigate some aspects of this breakdown. The implications of these flows to passive cooling of a building by natural ventilation are discussed.

Time-dependent flows in an emptying filling box

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 (

Fundamental atrium design for natural ventilation

T_f

CFD Modelling of Natural Ventilation: Combined Wind and Buoyancy Forces

), proportional to the time taken for fluid from a plume to fill a closed box; and the draining box time (

Displacement and mixing ventilation driven by opposing wind and buoyancy

T_d

Analytical solutions for turbulent non-Boussinesq plumes

), 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

Emptying boxes - classifying transient natural ventilation flows

H

Overturning in a filling box

and cross-sectional area