Endothermic and exothermic chemically reacting plumes

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Abstract
We develop a model for a turbulent plume in an unbounded ambient that takes into account a general exothermic or endothermic chemical reaction. These reactions can have an important effect on the plume dynamics since the entrainment rate, which scales with the vertical velocity, will be a function of the heat release or absorption. Specifically, we examine a second-order non-reversible reaction, where one species is present in the plume from a pure source and the other is in the environment. For uniform ambient density and species fields the reaction has an important effect on the deviation from pure plume behaviour as defined by the source parameter Γ. In the case of an exothermic reaction the density difference between the plume and the reference density increases and the plume is ‘lazy’, whereas for an endothermic reaction this difference decreases and the plume is more jet-like. Furthermore, for chemical and density-stratified environments, the reaction will have an important effect on the buoyancy flux because the entrainment rate will not necessarily decrease with distance from the source, as in traditional models. As a result, the maximum rise height of the plume for exothermic reactions may actually decrease with reaction rate if this occurs in a region of high ambient density. In addition, we investigate non-Boussinesq effects, which are important when the heat of reaction is large enough.

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