International Journal of Mechanical and Industrial Technology ISSN 2348-7593 (Online) Vol. 9, Issue 1, pp: (19-33), Month: April 2021 - September 2021, Available at: www.researchpublish.com Page | 19 Research Publish Journals 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* Faculty of Mechanical Engineering and Automation, Zhejiang Sci -Tech University Xiasha Higher Education Area, Hangzhou, Zhejiang 310018, PR China, 3287399585@qq.com , cloudmessie@yahoo.co.uk 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   is located at the corner region between the circulation vortices and the static walls of the square. According to energy theory the   position will lose the stability earlier than the other position. The   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. Keywords: Numerical simulation, laminar flow, lid driven cavity, energy gradient theory. Nomenclatures L [m] length of the cavity in x direction H [m] height of cavity normal direction H/L [-] aspect ratio P [N/  2 ] Pressure Re [-] Reynolds numbers U [m/s] x- component velocity V [m/s] y- component velocity K [-] Energy gradient Greek Symbols µ [Pa. s] fluid dynamic viscosity ρ [kg/ 3 ] fluid density  Energy dissipation function 1. INTRODUCTION The lid driven cavity flow is the motion of the fluid inside a rectangular cavity created by constant translational velocity of one side while the other sides remain statics. Lid driven cavity flow are important in many industrial processing applications such as short dwell and flexible blade coasters. They also provide a model understanding more complex flows with closed re-circulation regions, like flow over a slit, contraction flow and roll coating flows. Cavity flows contain a full range of flow types from pure rotation near a center of re-circulation region to strong extension near edges of the lid. Fluid flow behaviors inside lid driven cavities have been the subject of extensive computational and experimental studies over the past years.