On the Streamwise Development of Density Jumps

The analysis of density jumps in two-layer channel flows of miscible fluids controlled by a downstream obstruction, in which one of the layers is infinitely deep and at rest, is extended to consider the dependence of its features on its streamwise dimension. The momentum conservation equation in the entrainment and roller regions, and the energy conservation equation after the jump are corrected to account for friction. The streamwise coordinate is related to the increase in the density layer height through a linear expression derived from CFD calculations. Three regimes are distinguished: (1) for short distances from the origin to the obstruction, only an entrainment region exists; (2) for medium distances, two regions can be distinguished, i.e., the entrainment region, and the roller region, in which no entrainment is assumed; and (3) for long distances, three regions can be distinguished—the entrainment, the roller, and the postjump regions, characterized by approximate energy conservation. It is shown that initially the dimensionless total entrainment ratio increases as the distance to the obstruction increases, until a roller region appears. A further increase in distance to the obstruction does not have a significant effect on the total entrainment, until the appearance of a postjump region, resulting in a gradual decrease in the total entrainment. These results are supported by numerical calculations using the FLUENT CFD software package, which are in good agreement with experimental results.