(617f) 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.