Computational analysis of Newtonian fluid in a 2-D square cavity with kinetic energy, enstrophy, and palinstrophy in the presence of bottom corner obstacle - Dalmalka Praveen Kumar; Yadagiri Rameshwar; Rifaqat Ali; S. Nazari; Mohamed Kallel; Ahmed M. Galal (Results in Physics)
Understanding the impact of obstacles on lid-driven cavity (LDC) flows is critical for advancing flow control and optimization in fluid dynamics. In this study, we numerically investigate steady, two-dimensional Newtonian fluid flow within a square cavity featuring a lid-driven motion at Reynolds number Re = 100 by solving governing equations with the Fractional Step Method on a staggered grid in the Finite Volume framework, providing high-resolution streamline plots and vorticity contours. A rectangular obstacle with a fixed width (W = 0.2L) and varying heights (H = 0.20L,0.25L,0.50L,0.60L,0.80L and 0.95L) is systematically placed in three configurations: 1) bottom left-corner, 2) bottom right-corner and 3) both bottom (left–right) corners. The study investigates the influence of obstacle placement and height on kinetic energy (KE), enstrophy (Z), and palinstrophy (P) as well as obstacles focusing on the modulation of primary (PV) and secondary (SV) vortices, energy metrics, and flow topology in lid-driven cavity (LDC) flows, focusing on configurations with single and double corner. Fluid motion control in constrained environments, such as industrial mixing where vortex dynamics in lid-driven cavities optimize mixing and reduce dead zones by adjusting obstacle configurations and heat transfer, demands a detailed understanding of energy dissipation and rotational dynamics. The physics involved in KE and vortex dynamics is that increasing obstacle height progressively reduces the kinetic energy across all configurations, with the sharpest decline (38 %) observed in dual-corner obstacles due to amplified flow constriction and enhanced boundary layer effects. Single-corner obstacles disrupt the flow asymmetrically, whereas dual-corner setups create balanced but more confined vortex structures, impacting energy distribution and flow control. In rotational energy (Z) and gradient intensities (P), dual-corner obstacles induce the highest rotational energy (192 % increase in Z) and vorticity gradients (127 % increase in P), revealing the interplay of sharp edges, shear layers, and enhanced vortex interactions. These features emphasize the potential for intensified mixing but also highlight the risks of energy dissipation in constrained environments. In flow structure transformations, obstacle-induced changes in streamline topology reveal critical transitions in vortex formation and interaction. In dual-corner configurations, secondary vortices coalesce into a single dominant structure at critical heights say at H = 0.50L, leading to a dramatic 1366.92 % increase in vortex area. However, excessive heights (H = 0.95L) suppress these vortices, creating stable but inefficiently mixed flow regimes. In addition, we discovered a new empirical relation among Pressure potential energy (PE) in three configurations for the steady-state solution and it can be generalised and holds for any positive reals H and W up to almost near 1L and 0.50L respectively. Also, the flow separation, reattachment with their locations of the formation and diminishing of tertiary vortices above the corner obstacles were captured and analysed.