The Computation of Buoyant Flows in Differentially Heated Vertical and Inclined Cavities

This study explores the potential of a recently developed wall-function strategy, based on the analytical solution of simplified, boundary-layer, forms of the momentum and enthalpy transport equations, for the economical and reliable prediction of natural convection flows. Comparisons are also drawn with results from the conventional wall-function strategy, based on the log-law. These near-wall modelling strategies have been combined with different high-Reynolds-number turbulence models, including the k-, a basic form of 2nd-moment closure, and a more elaborate version, which satisfies certain physical realizability constraints. In the 2nd-moment computations, in addition to the generalized gradient diffusion hypothesis, more complex algebraic forms have also been employed for modelling the turbulent heat fluxes, involving the solution of transport equations for the temperature variance and its dissipation rate. Four test cases have been computed: a square cavity with differentially heated vertical walls, and a tall cavity with similar heating arrangements at three different angles of inclination; vertical, 60o and 5o to the horizontal. The resulting comparisons show that the more elaborate wall function shows distinct predictive advantages, and in some cases even returns superior predictions to a low-Re model. The k- model, when used with the new near-wall approach, is satisfactory in most cases. Of the second-moment closures, the realizable version, used with the more complex thermal field models, yields the most satisfactory flow and thermal predictions.