Driven flow motion by a dually moving lid of a square cavity

Abstract

One of the important prototype problems of fluid mechanics, the lid-driven cavity flow is revisited such that the single lid is separated into two joint active/passive walls representing potential stirrers during a chemical mixing process. The right part of the wall is released freely to move right with a uniform velocity, while the left part attached to the adjacent wall at a point of dislocation is considered stationary or movable freely with a constant speed. The novel cavity wall mechanism introduced in this manner has the capability of driving the pressure of the fluid and resulting in formation of the primary/secondary vortex structures. This sort of cavity setup might be useful if mixing process of a fluid is demanded to be in different sections of the cavity or if a mixture is desired to be purified in different sections of the cavity. Special attention should be drawn here that this kind of wall action is dissimilar to the familiar lid-driven cavity flow problem due to moving one, two or more parallel/crossing sides of the cavity studied earlier in the literature. Having conveniently made the usual equations of motion non dimensional, three dimensionless parameters are arisen governing the physical phenomenon, namely the point linking the lid parts, the velocity of left part of the lid and the Reynolds number associated with the right part. A finite element approach is adopted to simulate the resulting pressure and flow fields affected by variation of these parameters. From the simulations, the mixing properties of flow as a result of the triggered pressure are elucidated at three distinct parts of the lid; (a) when the lid is separated close to the left portion of the wall, (b) when the lid separation is set at the middle of the wall and (c) when the parts of the lid are connected next to the right portion of the lid. Depending on the above scenarios, a quite rich phenomenon of pressure distribution and the resultant recirculating primary/secondary vortex flow in the form of streamline patterns is observed. Assisting and opposing influences of the dually moving lid and its control over the small and high Reynolds number driven flow regimes are explored through graphical illustrations as well as tabular forms.