Finite element analyses of flow in a cavity with internal blockages

Abstract

Although studies of flows in cavities without internal blockages are extremely common, those in which blockages arise are correspondingly rare. The present work describes a numerical study of one such flow using two complementary finite element approximations to the governing Navier-Stokes equations. Two formulations are adopted: the first employs a streamfunction-vorticity representation that has proven effective in elucidating fine flow detail in related cavity flows while the second is expressed in terms of primitive variables. The advantages and disadvantages of each formulation in relation to ease of application of boundary conditions and efficiency of numerical solution are compared and contrasted. In both cases, results for the chosen test problem are found to be in excellent agreement and reveal that previously reported data for this problem are in error. Moreover, results are presented that demonstrate the rich variety of flow patterns, recirculation regions and stagnation points that can arise as the cavity geometry and external wall speeds are varied.