Mixing in three-dimensional cavity by moving cavity walls
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O R I G I NA L A RT I C L E
Alex Povitsky
Mixing in three-dimensional cavity by moving cavity walls
Received: 11 February 2020 / Accepted: 27 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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 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. Keywords Flow in enclosure · Mixing rate · Laminar · Three-dimensional · Numerical 1 Introduction Because of the variety of natural, industrial and biomedical prototype applications, steady-state 2D cavity flows have been widely studied by both experimental and numerical investigations, see reviews [1,2]. Studies of 3D cavity flows started after the pioneering experimental work [3]. However, very few studies have been conducted on the transient flow establishment and mixing phase [4,5]. Ref. [6] quantifies the mixing characteristics of a two-dimensional, lid-driven blinking Stokes flow (Re < 1) to evaluate fluidic components that are critical parts of micro- and nano-scale systems. The latter can be used for detecting both chemical and biological agents and explosives, monitoring the environment for hazardous chemicals or toxins, and diagnosing and treating medical problems. These fluidic components can be used for transporting and mixing small amounts of materials that are subsequently analyzed or delivered to predetermined sites. The above-listed applications include fluid dynamics in small channels that have etched or engraved geometric features, such as grooves [6]. Most results to date of chaotic advection (generation of small-scale structures by the stretching and folding in flui
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