Numerical Prediction of Natural Convection in a Vertical Annulus Closed at Top and Opened at Bottom

Abstract

A numerical prediction for natural convection flow in a vertical annulus closed at the top and opened at the bottom is presented. The outer cylindrical surface of the annulus is cooled to a low temperature, and a hot fluid is maintained below the open end temperature. The inner cylinder and the top wall of the annulus are insulated. The numerical technique used is a second-order accurate hybrid finite-element/finite-volume method. A pressure boundary condition at the opening in conjunction with an iterative scheme is employed to predict the regions of inflow and outflow and the velocity distributions. An in-house code developed has been validated by solving the natural convection through an open-ended vertical annulus. The characteristics of flow and heat transfer in the annulus are presented using contour plots of streamlines, isotherms, and isovorticities, and variations of velocity, volume rate of flow, Nusselt number, and temperature of adiabatic wall. Heat transfer through the annulus is subjected to sharp spatial variations due to the typical flow pattern at high values of Rayleigh number and is influenced by upstream conduction at low values of Rayleigh number. Correlations for average Nusselt number and volume rate of flow are obtained as functions of Rayleigh number (in the range of 103 to 105) and percentage gap ratio (from 2 to 20).