A simplified mathematical approach for modelling stack ventilation in multi-compartment buildings

A simple mathematical model of stack ventilation flows in multi-compartment buildings is developed with a view to providing an intuitive understanding of the physical processes governing the movement of air and heat through naturally ventilated buildings. Rules of thumb for preliminary design can be ascertained from a qualitative examination of the governing equations of flow, which elucidate the relationships between 'core' variables - flow rates, air temperatures, heat inputs and building geometry. The model is applied to an example three-storey office building with an inlet plenum and atrium. An examination of the governing equations of flow is used to predict the behaviour of steady flows and to provide a number of preliminary design suggestions. It is shown that control of ventilation flows must be shared between all ventilation openings within the building in order to minimise the disparity in flow rates between storeys, and ensure adequate fresh air supply rates for all occupants. © 2013 Elsevier Ltd.

Stack ventilation in multi-storey atrium buildings: A dimensionless design approach

Using a simplified mathematical model, a preliminary design strategy for steady stack ventilation in multi-storey atrium buildings is developed. By non-dimensionalising the governing equations of flow, two key dimensionless parameters are identified - a ventilation performance indicator, λ, and atrium enhancement parameter, E - which quantify the performance of the ventilation system and the effectiveness of the atrium in assisting flows. Analytical expressions are determined to inform the vent sizes needed to provide the desired balance between indoor air temperature, ventilation flow rate and heat inputs for any distribution of occupants within the building, and also to ensure unidirectional flow. Dimensionless charts for determining the required combination of design variables are presented with a view to informing first-order design guidance for naturally ventilated buildings. © 2013 Elsevier Ltd.

Transient ventilation dynamics induced by heat sources of unequal strength

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 B1 and B2 > B1. 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 λj and mean buoyancies δj 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 dδ1/dτ α 1/λ1 and dδ2/dτ α 1/λ2, where τ is a dimensionless time. When S 1, the intermediate layer is shallow (small λ1), whereas the top layer is relatively deep (large λ2) and, in this limit, δ1 and δ2 evolve on two characteristically different time scales. This produces a time lag and gives rise to a 'thermal overshoot', during which δ1 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 < Aoh and are strongly dependent on the time history of the flow. We establish the region of {A, ψ} space where rapid development of δ1 results in δ1 > δ2, 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.