Blending of Liquids Starting From a Stably Stratified State

Blending of liquids starting from a stably stratified state

We have conducted direct numerical simulations of blending of two miscible liquids with different density and equal kinematic viscosity in a baffled mixing tank equipped with an axial impeller (a 45-degrees pitched-blade turbine). As the starting point of each simulation the denser liquid occupies the lower half of the tank volume, the lighter liquid the upper half, and the flow velocity in the tank is zero everywhere. At time equals zero we switch on the impeller and monitor the development of the flow and mixture fraction field in the tank. In addition to the geometrical layout of the tank and impeller, the flow system is governed by two dimensionless numbers: a Reynolds number (Re) and a Richardson number (Ri). Reynolds numbers are in the range 3,000 to 12,000 so that we cover transitional and mildly turbulent flow regimes and are able to fully resolve the flow (direct simulations). In the base-case the impeller is down pumping and placed with an off-bottom clearance of one-third of the tank height. In this situation mixing patterns and associated mixing times show interesting trends with respect to the Richardson number. At low values of Ri mixing patterns are akin to what is observed for Ri=0 (left figure): the interface between light and heavy liquid is sucked into the impeller swept volume and macro-mixing occurs relatively quickly with somewhat longer mixing times (compared to the situation with Ri=0). If Ri ³ 0.5 the impeller is no longer able to draw down the interface. In these situations mixing is largely due to erosion of the interface between light and heavy liquid (the right figure) which results in dramatically longer mixing times. Operating the impeller in an up-pumping mode in most cases reduces mixing times, as also does placing the impeller higher up (halfway) in the tank.