Numerical investigation of instability patterns and nonlinear buoyant exchange flow between enclosures by variable density approach

Abstract

The buoyancy driven flow characteristics through horizontal passage between two enclosures are numerically investigated. The two-dimensional physical model consists of upper and lower enclosures filled with cold and hot fluids connected through ceiling vent. Non-Boussinesq variable density approach is used to model the density variations by primitive variable method. The governing equations are solved by Simplified Marker and Cell (SMAC) algorithm on non-staggered grid using high accuracy compact finite difference schemes. The Grashof number is varied from Gr=106 to 5×107. The nonlinear exchange of lighter and heavier fluids through vent are investigated by varying vent aspect ratio. The net mass flow rate through horizontal passage are oscillatory and bidirectional. The critical Grashof number is identified, and beyond this instabilities intensifies leading to complex flow behavior inside enclosures. The vent widths D=0.05H and 0.2H reduces flow perturbations and enhances stable flow behavior across the vent. Chaotic flow originates for critical vent widths 0.1H⩽D⩽0.15H, and nonlinear oscillations evolves till the system reaches quasi-steady state. Reduced vent thickness results in higher oscillation frequencies and better mixing rates between enclosures. The present mathematical model and numerical method showed good agreement with the existing results available in literature.