The purpose of this work was twofold: first, to develop correlations for the entrainment of small fuel droplets into water in a stratified fuel/water shear flow; second, to implement the correlations in a CFD code and validate it with experimental effluent fuel concentration data. It is assumed that the droplets act as passive scalars and are advected far from their generation regions where they may cause fuel contamination problems far down-stream. This work relied upon extensive experimental data obtained from a stably stratified shear flow: droplet number, droplet PDF, fluid fraction and velocity field data. The droplet data was expressed as a nondimensional entrainment velocity (E) for the volume flux of fuel due to small droplets. The fluid fraction and velocity fields at the interface were expressed in terms of Richardson numbers (Ri). It was found that E = CeRi−n where n = 1 and Ce is a constant, gives a good fit for the two experimental velocity cases. The best correlation was implemented in a computational simulation of the stably stratified shear flow, and the results show that the simulation can predict the entrainment quite well. A second simulation was performed for a flow with energetic vertical buoyant jets (“buoyant flow events”) and stably stratified shear flows with very large Richardson numbers. In this case, the simulations underpredicted effluent fuel concentrations by two orders of magnitude. Ad hoc corrections to the entrainment correlations show marked improvements.
A Theoretical Study of Turbulent Energy Spectra in Stably Stratified Shear Flow.