Direct numerical simulation of natural convection in a vertical channel

This study presents direct numerical simulations of natural convection for air (Pr = 0.709) in a vertical channel driven by differentially heated walls at Rayleigh numbers (Ra) up to 2.0 × 107. The present data is validated with that from Versteegh and Nieuwstadt [9] for Ra = 5.0 × 106. Using the present data for higher Ra, we appraise and compare the various proposed scaling laws for the mean temperature defect, Th−T , and the streamwise velocity, u, by Versteegh and Nieuwstadt [9], Hölling and Herwig [2] and Shiri and George [6] (cf. George and Capp [1]). For the mean temperature profile, the present data supports the inner temperature scaling, Ti = [| fw|/(gβα)], proposed by all the three studies, where fw is the heat flux at the wall, g is the gravitational acceleration, β is the thermal expansion coefficient and α is the heat diffusion coefficient. Using compensated temperature gradients, constants are found for the wall function for mean temperature, which takes the form of a power-law: Th −T Ti =−3.6 (