Oscillatory three-dimensional convection in rectangular cavities and enclosures

Abstract

Numerical experiments of natural convection of a zero Prandtl (Pr) number fluid in 4×1×2 (length to height to width) and 4×1×1 rectangular cavities (with a free top surface) and enclosures (having a solid top surface) are performed. The cavities are referred to as R-F (rigid-free) while enclosures are referred to as R–R (rigid–rigid). The objective of this study is to establish the pattern of three-dimensional convection and to determine the value of the critical Grashof number, Grcrit, at which the flow becomes time dependent. A three-dimensional laminar flow model of a constant property fluid is used. The model equations are solved numerically by a finite volume method. The flow field is steady at relatively low Grashof number (Gr), and is represented by one cell, unlike the multicellular flow predicted by two-dimensional studies. When Gr reaches Grcrit, the flow becomes oscillatory. Transition to time dependence is a function of the geometry and the type of top surface (rigid or free). The R–R flow is more stable than that of the R-F case, for both widths considered (one and two). The width of cavity and/or enclosure has an important effect on transition to oscillatory convection, for it is found that reducing the width from two to one, leads to a much higher Grcrit, making the results of two-dimensional numerical simulations completely inadequate.