Turbulent plumes with internal generation of buoyancy by chemical reaction

Abstract

Turbulent plumes, which are seen in a wide number of industrial and natural flows, have been extensively studied; however, very little attention has been paid to plumes which have an internal mechanism for changing buoyancy. Such plumes arise in e.g. industrial chimneys, where species can react and change the density of the plume material. These plumes with chemical reaction are the focus of this study. An integral model describing the behaviour of a plume undergoing a second-order chemical reaction between a component in the plume (A) and a component in the surrounding fluid (B), which alters the buoyancy flux, is considered. The behaviour of a reactive plume is shown to depend on four dimensionless groups: the volume and momentum fluxes at the source, the parameter ε which indicates the additional buoyancy flux generated by the reaction, and γ which is a dimensionless rate of depletion of species B. Additionally, approximate analytical solutions are sought for a reactive plume rising from a point source of buoyancy when species B is in great excess.These analytical results show excellent agreement with numerical simulations. It is also shown that the behaviour of a reactive plume in the far field is equivalent to an inert plume issuing from a virtual source downstream of the real source and the dependence of the location of the virtual source on ε and γ is discussed. The effects of varying the volume flux at the source and the Morton source parameter Γ 0 are further investigated by solving the full governing equations numerically. These solutions indicate that ε is important in determining the buoyancy generated by the reaction, and the length scale over which this reaction occurs depends on γ when γ > 1. It is also shown that when the dimensionless buoyancy 1 − < ε , the reaction can cause the plume to collapse.3

Straight-sided solutions to classical and modified plume flux equations

“…This problem has been addressed in the context of buoyancy generated by phase changes (Bhat & Narasimha 1996;Basu & Narasimha 1999) and buoyancy generated by chemical reactions (Conroy et al 2005;Diez & Dahm 2007;Conroy & Llewellyn Smith 2008;Campbell & Cardoso 2010). Buoyancy generated by latent heat release in clouds was analysed experimentally by Bhat & Narasimha (1996) who ran experiments in which the buoyancy flux of a plume was increased linearly with height.…”

“…More recently, modified versions of the MTT equations have been used to model chemically reacting plumes, in which there is a change in buoyancy flux due to the heat of reaction (Diez & Dahm 2007;Conroy, Smith & Caulfield 2005;Conroy & Llewellyn Smith 2008;Campbell & Cardoso 2010), and plumes with unsteady source conditions (Scase, Caulfield & Dalziel 2006a;Scase et al 2006b). …”

“…In the next section, we review the modelling approach of Hunt & Kaye (2005) and re-state their results for jets and plumes. We then apply this modelling approach to the work of Caulfield & Woods (1998), on plume propagation through non-uniformly stratified environments, and Diez & Dahm (2007), Conroy et al (2005), Conroy & Llewellyn Smith (2008) and Campbell & Cardoso (2010) on chemically reacting plumes. Finally we examine certain properties of the straight-sided solutions of the unsteady plume equations of Scase et al (2006a,b).…”

Turbulent acidic jets and plumes injected into an alkaline environment

“…Conroy & Llewellyn-Smith (2008) analysed second-order irreversible exothermic and endothermic reactions between a point source plume and a second species in the ambient. Campbell & Cardoso (2010) and Cardoso & McHugh (2010) examined the influence of internal buoyancy generation through irreversible reactions resulting in phase change on the development of plumes in stratified and unstratified environments. Cardoso & McHugh (2010) experimentally analysed a plume containing calcium carbonate particles descending in an acidic aqueous solution where the generation of carbon dioxide bubbles on the surface of the particles modified the buoyancy flux of the plume.…”

Turbulent two-phase plumes with bubble-size reduction owing to dissolution or chemical reaction

“…While inert plumes have been studied for seven decades, as recently reviewed by Woods (2010) and Hunt & van den Bremer (2011), few studies have been undertaken on reactive plumes. Most of these built upon the work of Morton, Taylor & Turner (1956), such as the studies of Conroy & Smith (2008) and Campbell & Cardoso (2010) for single-phase plumes involving a reaction with a second-order rate law. In both of these works, the variation of the plume's buoyancy flux with the ascent distance differs from that of an inert plume by an extra term which depends on the chemical reaction and on the fluxes of chemical species.…”