Verification of a Numerical Simulation Technique for Natural Convection

Among the fundamental heat transfer processes in buildings, convection is the least understood. In contrast to conduction and radiation, the equations governing convective heat and mass transfer in fluids, that is, the continuity, momentum, and energy equations, do not have closed solutions even under steady-state conditions. During recent years, considerable attention has been given to both experimental and numerical investigations of natural convection in enclosures. A number of review papers [1, 2] have been published, although a majority of the reported studies cover a range of Rayleigh numbers (Ra < 10⁸) and aspect ratios (H/L > 1), which are not typical of buildings. Most recently, de Vahl Davis [3, 4] has performed a comparison study between a large number of numerical methods for laminar natural convection in a square cavity.

To develop an improved understanding of convection in buildings, a coordinated analytic and experimental effort has been undertaken at Lawrence Berkeley Laboratory. A computer program (CONVEC2) has been developed that numerically simulates two-dimensional natural convection in rectangular enclosures at Rayleigh numbers on the order of 10¹⁰. Small-scale experiments have been carried out [5, 6] to provide for (a) verification of the numerical analysis, and (b) development of empirical heat transfer correlations for a few enclosure configurations. Once it has been carefully verified against experiments, CONVEC2 can be used to simulate convection processes occurring in a broad range of enclosures for a variety of boundary conditions. From this numerically generated heat transfer "data base," engineering correlations can be developed [7].

The present paper describes a verification of CONVEC2 for single-zone geometries by comparison with the results of two natural convection experiments [6, 8] performed in small-scale rectangular enclosures. These experiments were selected because of the high Rayleigh numbers obtained (2.6x10⁸ ≤ Ra ≤ 1.3x10¹⁰) and the small heat loss (<5 percent) through the insulated surfaces. Comparisons are presented for (i) heat transfer rates, (ii) fluid temperature profiles, and (iii) surface heat flux distributions.