Comprehensive Numerical Analysis of Fluid Flow Characteristics in a Lid-Driven Cavity with a Central Obstacle: Flow Physics

Abstract

Boundary layer flows and vortex dynamics are critical in understanding fluid motion in confined geometries. The lid-driven cavity (LDC) flow is a classical benchmark for analysing fluid behaviour under varying conditions, especially when obstacles are introduced. While past studies have explored primary and secondary vortex structures, the modulation of enstrophy and palinstrophy caused by obstacles has been underexplored. This study aims to bridge that gap by systematically investigating the effect of Reynolds numbers and obstacle aspect ratios on flow properties in a 2D LDC. To analyse the influence of Reynolds number (Re) and obstacle Aspect ratio (AR) on enstrophy (Z) and palinstrophy (P). To evaluate the enhancement in vortex dynamics and flow topology caused by introducing square obstacles at various aspect ratios within the cavity. To identify optimal configurations for improving fluid transport and mixing efficiency. An unsteady, laminar, incompressible flow of Newtonian fluid was simulated by the Finite volume-based Fractional Step Method. Square obstacles with aspect ratios AR=0L,0.4L, 0.5L, and 0.6L were placed at the centre of the cavity with numerical study for a range of Re=10,100,400, and 1000. The interaction between AR and Re dictates vortex dynamics in LDC flows. Higher AR disrupts flow symmetry through sharp-edge interactions, while increased Re elevates inertial effects, causing vortex splitting, secondary vortex formation, and improved fluid mixing. Obstacles boost Z and P by up to 53.08% and 50.85%, with the most significant increases for AR = 0.6L at Re = 1000 compared to a cavity without an obstacle. This suggests stronger vorticity gradients and enhanced mixing due to AR = 0.6L, as the obstacle occupies more of the cavity, restricting flow and creating stronger shear zones near the walls and the obstacle. At high Re, inertial forces dominate, leading to stronger vortex shedding, and more pronounced vorticity changes near sharp edges. Increasing Re from 10 to 1000 for AR = 0.6L raises Z and P by approximately 36.34% and 43.55%, illustrating a shift from viscous-dominated laminar to inertia-dominated flow, enhancing vortex strength, sharpening vorticity gradients, and improving mixing efficiency. The interplay between AR and Re dictates vortex dynamics, with higher AR disrupting symmetry and higher Re amplifying inertial effects, leading to vortex splitting, enhanced secondary vortices, and improved mixing. The increasing obstacle height amplifies Z and P, leading to improved fluid mixing and vortex dynamics, serving as effective tools for flow control and mixing enhancement in industrial and engineering applications.