Bifurcation of antiparallel motion of the flow in a two-sided lid-driven cavity

In this paper, the multiplicity of flow solutions in a two-sided lid-driven cavity of antiparallel wall motion has been analyzed numerically. The finite volume method combined with a coupled algorithm is used to simulate the Navier–Stokes and mass conservation equations. The Reynolds number (100 ≤ Re ≤ 10 000) is used as a continuation parameter for the cases of an aspect ratios within (0.1 ≤Γ ≤ 0.9), while the Reynolds number (0 ≤ Re ≤ 7000) is used for aspect ratio within (1 ≤ Γ ≤ 3). Two-dimensional conventional multiple stable solutions exist in the aspect ratio range (1 ≤ Γ ≤ 3) and are presented by the well-known two-vortex flow, cat's eye flow, and asymmetrical flow. Two additional flows were found to exist besides the conventional flows’ solutions. The first one is point symmetric about the cavity center named additional symmetrical flow and exists for Γ = 1, 1.1, and 1.2. The second one is asymmetric named additional asymmetrical flow and exists for a larger aspect ratio range, 1.3 ≤ Γ ≤ 2. Critical Reynolds numbers of the existence range of multiple flow states are identified. Three steady point-symmetry solutions are presented and four steady asymmetric solutions exist as pair two with their counterpart, where only two are presented in this work. The streamline contours are displayed to illustrate the flow structure that exists in each specified tracked path. Flow unicity distinct solution is obtained for the aspect ratio ranges within (0.1 ≤ Γ 1). These results can provide valuable insights into the dynamics of cavity-driven flows with moving boundaries, with relevance to diverse engineering and industrial applications such as lubrication systems, short-dwell coating, polymer processing, microfluidic mixing, drying technologies, material shaping, and thermal management in electronic cooling.