Verification and experimental validation of a numerical simulation of natural convection in a slender cylinder

Steady and time dependent natural convection of water confined in a vertical cylindrical container heated from below is studied experimentally and numerically. The container has a circular cross-section and an aspect ratio (height/diameter) of 1.25. Convective motions are analyzed for a constant Prandtl number of 6.7 and a range of Rayleigh numbers from 3.0 × 105 to 2.0 × 106. These conditions include steady and time-dependent flows and in all cases, flow patterns present complex three-dimensional structures. Experimental observations were made with a composed PIV system capable of simultaneously obtaining velocity distributions in two mutually perpendicular planes. The numerical model comprises the solution of the three-dimensional time-dependent Boussinesq equations in cylindrical coordinates. Experimental observations are compared with the numerical model and a satisfactory agreement is obtained for steady flow and averaged values in unsteady flow. The general structure of the present study follows the procedure required for the verification of the numerical model and its validation with experimental observations.