Numerical analysis of span-wise aspect ratio effect on the 2D flow stability in Lid-driven cavity using the energy gradient theory

Mapanga Mbemba Cloud Messie Rodelay, Hua-Shu Dou

Abstract: The two-dimensional flow characteristics in the lid- driven square cavity are simulated using the computational Fluid Dynamic (CFD). The governing equations are Navier-Stokes Equations, they are discretized with Finite Volume Method (FVM) and the software Fluent is used to calculate. A stretched quadrilateral mesh with 75000 cells was used. Various Reynolds numbers (100, 500,1000 and 2000) and aspect ratio H/L (0.5, 1, 2 and 4) in the flow characteristics is studied. Then the calculating results are compared with the numerical results in literature and the results obtained shows a good agreement. After that, the shape of vortex was investigated and the instability of the flow field was analyzed by the energy gradient theory. It has been found that the magnitude of K is proportional to the Reynolds number, the higher Reynolds number is, the bigger the K value becomes which means that the fluid become more unstable. The Kmax is located at the corner region between the circulation vortices and the static walls of the square. According to energy theory the Kmax position will lose the stability earlier than the other position. The Kmax position change and tends to settle to the left wall of square when the Reynolds number increase. The shape of the vortex is controlled by the aspect ratio as well as the Reynolds numbers.