Flow in Cavities With Curved Boundaries

Fluid dynamics for a Newtonian fluid in the absence of body forces in a two-dimensional cavity with top and bottom curved walls was studied numerically. The vertical walls are fixed and the curved walls are in motion. The Navier-Stokes equations were solved using the finite element method combined with the operator splitting scheme. We analyzed the behaviour of the velocity fields, the vorticity fields and the velocity profiles of the fluid inside the cavity. The analysis was carried out for two different Reynolds numbers of 50 and 500 with two ratios (R = 1, −1) of the top to the bottom curved lid speed. For these values of parameters the flow is characterized by vortex formation inside the cavity. The spatial symmetry on the flow patterns are also investigated. We found that when the velocities of the top and bottom walls have opposite direction only one cell is formed in the central part of the cavity; however when the velocities of the top and bottom walls have the same direction the vortex formation inside the cavity is more complex.