Mixing in three-dimensional cavity by moving cavity walls

The mixing in three-dimensional enclosures is investigated numerically using flow in cubical cavity as a geometrically simple model of various natural and engineering flows. The mixing rate is evaluated for up to the value of Reynolds number $$\hbox {Re}=2000$$ for several representative scenarios of moving cavity walls: perpendicular motion of the parallel cavity walls, motion of a wall in its plane along its diagonal, motion of two perpendicular walls outward the common edge, and the parallel cavity walls in motion either in parallel directions or in opposite directions. The mixing rates are compared to the well-known benchmark case in which one cavity wall moves along its edge. The intensity of mixing for the considered cases was evaluated for (i) mixing in developing cavity flow initially at rest, which is started by the impulsive motion of cavity wall(s), and (ii) mixing in the developed cavity flow. For both cases, the initial interface of the two mixing fluids is a horizontal plane located at the middle of the cavity. The mixing rates are ranked from fastest to slowest for twenty time units of flow mixing. The pure convection mixing is modeled as a limit case to reveal convective mechanism of mixing. Mixing of fluids with different densities is modeled to show the advantage in terms of mixing rate of genuinely 3D cases. Grid convergence study and comparison with published numerical solutions for 3D and 2D cavity flows are presented. The effects of three-dimensionality of cavity flow on the mixing rate are discussed.