Steady State Vortex Structure of Lid Driven Flow Inside Shallow Semi-Ellipse Cavity

Abstract

In this paper, the lid driven cavity flow inside a semi-ellipse shallow cavity was simulated using the stream function vorticity approach emphasising the non-uniform grid method. Three aspect ratios of 1:4, 1:3 and 3:8 were simulated using laminar flow conditions (range of Reynolds numbers of 100-2000). Primary and secondary vortexes were monitored extensively through centre vortex location, streamlines pattern and peak stream function values. Secondary vortexes developed at Re 1500 for the aspect ratio of 1:4, whereas secondary vortexes formed at an earlier Reynolds number of 1000 for the aspect ratios of 1:3 and 3:8. The size of secondary vortexes increases as the Reynolds number increases. Similar trends can be observed in the differences between primary vortex separation angle and reattachment angle. For the entire streamline pattern, many primary vortex centre locations were situated at the right side of the cavity.

Four-Sided Lid-Driven Cavity Flow using Time Splitting Method of Adams-Bashforth Scheme

“…The flow inside a square cavity has been widely used to demonstrate fluid flow using simple geometry. The flow structure in a one-sided lid-driven cavity problem has been reported by many researchers (Ghia, Ghia, & Shin, 1982;Idris, Ammar, Tuan Ya, & Amin, 2013;Idris, Irwan, & Ammar, 2012;Musa, Abdullah, Azwadi, & Zulkifli, 2011;Rosdzimin, Zuhairi, & Azwadi, 2010;Sidik & Attarzadeh, 2011). Later, research on different cavity geometries has been reported, such as a deep cavity (Patil, Lakshmisha, & Rogg, 2006), semi-circular cavity (Yang, Shi, Guo, & Sai, 2012), trapezoidal cavity (Zhang, Shi, & Chai, 2010) and triangular cavity (González, Ahmed, Kühnen, Kuhlmann, & Theofilis, 2011).…”

Circle grid fractal plate as a turbulent generator for premixed flame: an overview

“…Reference such as F. C.G.A. Nicolleau [3] used different pattern in their experiment, they found that pressure drop from a lower value to higher value by increasing the distance. The blockage ratio used in their experiment is 33.6%.…”

Transient Semi-Circular Lid-Driven Cavity Flow using Non- Uniform Structured Grid Method with Upwind Scheme

“…First and second order derivatives of the non-uniform grid approximation were used and represented by the following equations (Idris et al, 2012) which were first discovered by (Veldman & Rinzema, 1992):…”

“…A non-uniform grid with the finite difference method has never been tested before, to the authors' knowledge after thorough research. However, while there is already a report based on this method, it is applied to an elliptical shaped lid-driven cavity flow (Idris, Ammar, & M Irwan, 2012). Thus, in this study a nonuniform grid and finite difference method will be applied to a semi-circular cavity to obtain validation, and once this is completed, the transient behavior of the streamline and vorticity contour will be studied until the steady state is achieved.…”