A comparative assessment of the second-moment differential and algebraic models in turbulent natural convection

Abstract

Abstract Results of direct numerical simulation (DNS) of turbulent natural convection between two differentially heated infinite vertical plates for Ra=5.4 × 105 (Versteegh and Nieuwstadt 1996, Boudjemadi et al. 1996a) have been used to assess models of various terms in the transport equations for the turbulent heat-flux vector θ u i and the temperature variance θ 2 . The hypotheses used to truncate the differential model into algebraic forms have also been examined. We present some results of the computation of natural convection in the tall cavity, obtained with a fully differential and a four-equation ( k−e− θ 2 −e θθ ) algebraic model. Despite the unsatisfactory reproduction of individual terms in the equations, computations yielded acceptable agreement with available experimental and DNS data. Based on new evidence, possible improvements of the model are briefly discussed, aimed at ensuring a better term-by-term modelling of the transport equations for θu i and θ 2 .