Double-diffusive natural convection in an asymmetric trapezoidal enclosure: unsteady behavior in the laminar and the turbulent-flow regime

Abstract

In the present work the natural convective heat and mass transfer in an asymmetric, trapezoidal enclosure is studied numerically. Such a configuration is encountered in greenhouse-type solar stills, where natural convection in the enclosed humid air due to vertical temperature and concentration gradients between the saline water and the transparent cover, plays a decisive role. In this double-diffusion problem, the relative magnitude of the thermal and the concentration (or solutal) Rayleigh numbers, expressed by their ratio N is a key parameter. The two-dimensional flow equations, expressed here in a stream function-vorticity ( Ψ − Ω) formulation, along with the energy and concentration equations are solved. Due to the large values of the Rayleigh numbers encountered under realistic conditions (10 7 ⩽ Ra ⩽ 10 10), mostly turbulent flow conditions prevail. A two-equation, low-Reynolds number turbulence model has thus been selected and a curvilinear coordinate system is employed, allowing for better matching of the computational grid to the enclosure geometry. The numerical solutions yield a multi-cellular flow field, with the number of cells depending on the Rayleigh number for a fixed Lewis number and geometry. For a positive value of N ( N = 1) the solution is qualitatively similar to the case with only thermal buoyancy present ( N = 0). However, for negative values ( N = −1), more complex unsteady phenomena arise, having a different nature in the laminar and the turbulent flow regime, which are both investigated. Correlations for the mean convective heat and mass transfer coefficients are obtained for a wide range of Rayleigh numbers, and comparisons are made for the different values of N, showing lower values and different rate of increase with Ra for N = −1.