Numerical simulation of the 3D behavior of thermal buoyant airflows in pentahedral spaces

A numerical study of three-dimensional natural convection in an attic space with heated horizontal base and cooled upper walls is presented. Every previous study pertinent to this subject as of today has assumed that the flow in attics is two-dimensional and restricted to triangular cavities. This problem is examined for fixed aspect ratios holding width to height of 2 and depth to height of 3.33 and Rayleigh numbers ranging from 104 to 8 × 105. The coupled system of conservation equations, subject to the proper boundary conditions, along with the equation of state assuming the air behaves as a perfect gas are solved with the finite volume method. In the conservation equations, the second-order-accurate QUICK scheme was used for the discretization of the convective terms and the SIMPLE scheme for the pressure-velocity coupling. It is categorically found that the flow in the attic is 3D. From the physics of the problem, two steady-state solutions are possible. The symmetrical solution prevails for relatively low Rayleigh numbers. However, as the Ra is gradually increased, a transition occurs at a critical value RaC. Above this value of RaC, an asymmetrical solution exhibiting a pitchfork bifurcation arises and eventually becomes steady. Results are presented detailing the occurrence of the pitchfork bifurcation and the resulting flow patterns are described.