On the entrainment coefficient in negatively buoyant jets

Abstract

Integral models proposed to simulate positively buoyant jets are used to model jets with negative or reversing buoyancy issuing into a calm, homogeneous or density-stratified environment. On the basis of the self-similarity assumption, ‘top hat’ and Gaussian cross-sectional distributions are employed for concentration and velocity. The entrainment coefficient is considered to vary with the local Richardson number, between the asymptotic values for simple jets and plumes, estimated from earlier experiments in positively buoyant jets. Top-hat and Gaussian distribution models are employed in a wide range of experimental data on negatively buoyant jets, issuing vertically or at an angle into a calm homogeneous ambient, and on jets with reversing buoyancy, discharging into a calm, density-stratified fluid. It is found that geometrical characteristics such as the terminal (steady state) height of rise, the spreading elevation in stratified ambient and the distance to the point of impingement are considerably underestimated, resulting in lower dilution rates at the point of impingement, especially when the Gaussian formulation is applied. Reduction of the entrainment coefficient in the jet-like flow regime improves model predictions, indicating that the negative buoyancy reduces the entrainment in momentum-driven, negatively buoyant jets.