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Transient ventilation dynamics induced by heat sources of unequal strength

Shrinivas, AB and Hunt, GR (2014) Transient ventilation dynamics induced by heat sources of unequal strength. Journal of Fluid Mechanics, 738. pp. 34-64. ISSN 0022-1120

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We examine theoretically the transient displacement flow and density stratification that develops within a ventilated box after two localized floor-level heat sources of unequal strengths are activated. The heat input is represented by two non-interacting turbulent axisymmetric plumes of constant buoyancy fluxes B 1 and B 2 > B 1 . The box connects to an unbounded quiescent external environment of uniform density via openings at the top and base. A theoretical model is developed to predict the time evolution of the dimensionless depths λ j and mean buoyancies δ j of the 'intermediate' (j = 1) and 'top' (j = 2) layers leading to steady state. The flow behaviour is classified in terms of a stratification parameter S, a dimensionless measure of the relative forcing strengths of the two buoyant layers that drive the flow. We find that dδ 1 /dτ α 1/λ 1 and dδ 2 /dτ α 1/λ 2 , where τ is a dimensionless time. When S 1, the intermediate layer is shallow (small λ 1 ), whereas the top layer is relatively deep (large λ 2 ) and, in this limit, δ 1 and δ 2 evolve on two characteristically different time scales. This produces a time lag and gives rise to a 'thermal overshoot', during which δ 1 exceeds its steady value and attains a maximum during the transients; a flow feature we refer to, in the context of a ventilated room, as 'localized overheating'. For a given source strength ratio ψ = B1/B2, we show that thermal overshoots are realized for dimensionless opening areas A < A oh and are strongly dependent on the time history of the flow. We establish the region of {A, ψ} space where rapid development of δ 1 results in δ 1 > δ 2 , giving rise to a bulk overturning of the buoyant layers. Finally, some implications of these results, specifically to the ventilation of a room, are discussed. © Cambridge University Press 2013.

Item Type: Article
Divisions: Div A > Fluid Mechanics
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:12
Last Modified: 27 Jul 2017 05:23