Numerical Prediction of Asymmetric Natural Convection in a Narrow Vertical Annulus Closed at Top and Open at Bottom

ABSTRACT

Natural convection flow in a vertical cylindrical annulus closed at the top and opened at the bottom is numerically investigated. The outer wall of the annulus is cooled and maintained at constant temperature T_w. The inner wall and the top wall are kept adiabatic. Hot fluid enters through the bottom opening and is cooled by transferring heat to the cold outer wall. An in-house code developed using finite volume method solves the unsteady, three dimensional governing equations based on polar co-ordinate system on a structured and staggered grid system. The convection and diffusion terms are approximated by second order accurate central difference scheme, decoupling of pressure and velocity is obtained by a projection method. The numerical results are visualized using an open-source visualization software, ParaView. The flow through the gap is steady and axi-symmetric for larger annular gaps. For smaller annular gaps, the flow becomes asymmetric, consisting of several circumferential rounding loops. Flow maps using stream traces, isothermal surfaces, Nusselt number and circumferential temperature variations for different values of Ra are presented and discussed for 2% gap and unit aspect ratio.

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