Detrainment from a turbulent plume produced by a vertical line source of buoyancy in a confined, ventilated space

Abstract

AbstractNew experiments are presented which explore the dynamics of a turbulent buoyant plume produced by a vertically distributed linear source of buoyancy of strength $f$ per unit height. In a uniform environment, the plume volume flux increases with height from the base of the source, $z$, as $q(z) = {2^{-1/3}} {\pi }^{2/3} \alpha ^{4/3} f^{1/3} z^2$ where the entrainment coefficient, $\alpha = 0.09\pm 0.01$. In an enclosed space, with a net upward vertical ventilation flow $Q_V$, the buoyant plume generates a steady ambient stratification. The lowest part of the space, $z<h_i$, where $q(h_i)=Q_V$, is filled with fluid supplied by the ventilation flow and there is a net upflow in the ambient. Above this, $z>h_i$, the ambient fluid is linearly stratified with a reduced gravity gradient $f/Q_V$, and has no net vertical motion. Instead, for $z>h_i$, the time-averaged volume flux in the plume equals the ventilation flow. The intermittent entrainment of ambient fluid into the plume is now matched by intermittent detrainment from the plume, and the mean buoyancy in the plume relative to the ambient remains constant. The supply of fresh ventilation fluid to the ambient in the linearly stratified zone only occurs through the local detrainment and consequent horizontal intrusion of fluid from the plume. This has key implications for design of ventilation systems, in which there may be vertically distributed sources of buoyancy.