Evolution of a chemically reacting plume in a ventilated room

Abstract

The dynamics of a second-order chemical reaction in an enclosed space driven by the mixing produced by a turbulent buoyant plume are studied theoretically, numerically and experimentally. An isolated turbulent buoyant plume source is located in an enclosure with a single external opening. Both the source and the opening are located at the bottom of the enclosure. The enclosure is filled with a fluid of a given density with a fixed initial concentration of a chemical. The source supplies a constant volume flux of fluid of different density containing a different chemical of known and constant concentration. These two chemicals undergo a second-order non-reversible reaction, leading to the creation of a third product chemical. For simplicity, we restrict attention to the situation where the reaction process does not affect the density of the fluids involved. Because of the natural constraint of volume conservation, fluid from the enclosure is continually vented. We study the evolution of the various chemical species as they are advected by the developing ventilated filling box process within the room that is driven by the plume dynamics. In particular, we study both the mean and vertical distributions of the chemical species as a function of time within the room. We compare the results of analogue laboratory experiments with theoretical predictions derived from reduced numerical models, and find excellent agreement. Important parameters for the behaviour of the system are associated with the source volume flux and specific momentum flux relative to the source specific buoyancy flux, the ratio of the initial concentrations of the reacting chemical input in the plume and the reacting chemical in the enclosed space, the reaction rate of the chemicals and the aspect ratio of the room. Although the behaviour of the system depends on all these parameters in a non-trivial way, in general the concentration within the room of the chemical input at the isolated source passes through three distinct phases. Initially, as the source fluid flows into the room, the mean concentration of the input chemical increases due to the inflow, with some loss due to the reaction with the chemical initially within the room. After a finite time, the layer of fluid contaminated by the inflow reaches the opening to the exterior at the base of the room. During an ensuing intermediate phase, the rate of increase in the concentration of the input chemical then drops non-trivially, due to the extra sink for the input chemical of the outflow through the opening. During this intermediate stage, the concentration of the input chemical continues to rise, but at a rate that is reduced due to the reaction with the fluid in the room. Ultimately, all the fluid (and hence the chemical) that was originally within the room is lost, both through reaction and outflow through the opening, and the room approaches its final steady state, being filled completely with source fluid.