Turbulent thermals with chemical reaction

Abstract

This study investigates the behaviour of a turbulent thermal undergoing a second-order chemical reaction with the fluid entrained from the environment. Environments with uniform and stratified density are considered. We show that the dynamics of such a reactive thermal is fully determined by three dimensionless groups, $N/E$, $G/R$ and $R/E$, where $N$ is the buoyancy frequency of the environment, $G$ measures the ability of the reaction to change buoyancy, $R$ reflects the rate of consumption of the chemical species and $E$ is the rate of entrainment of reactive species from the environment. Exact analytical solutions are found for the limiting cases of slow and instantaneous chemical reaction. The effect of each governing group on the time for neutral buoyancy and depletion of the source chemical is assessed numerically. Our theoretical predictions compare well with new experimental results for the limits of a moderately slow chemical reaction and an instantaneous reaction. It is shown that fast reactions, with $R/E\gg 1$, occur only in a fraction of the total volume of the thermal due to incomplete mixing. Finally, our model is applied to study the dynamics of a radioactive cloud formed after a nuclear accident.