Resolving the stratification discrepancy of turbulent natural convection in differentially heated air-filled cavities – Part I: Reference solutions using Chebyshev spectral methods

The problem of the long established thermal stratification discrepancy between numerical and experimental results is investigated in three companion articles. The Part I article establishes reference solutions by means of three-dimensional (3D) spectral direct numerical simulations of a buoyancy-driven flow (RaH = 1.5 × 109). Two configurations of differentially heated air-filled cavity are considered: an idealized cavity (perfectly adiabatic cavity, PAC) and an Intermediate Realistic Cavity (IRC) making use of experimentally measured temperature distributions (Salat, 2004) on its top and bottom walls. The IRC flow structure as well as its associated rms fluctuations correspond to the experimentally observed flow dynamics. However both configurations keep resulting in a core thermal stratification value equal to 1.0 whereas experiments lead to a stratification of about 0.5. It is proved that this stratification paradox is neither related to three-dimensional effects nor to the experimental thermal distributions applied on the horizontal walls. Resolving this stratification discrepancy is the subject of the parts II and III articles ( Sergent et al., 2013 and Xin et al., 2012).

► Spectral 3D DNS results are presented for turbulent differentially heated cavity.
► Adiabatic or measured temperature distributions applied at the top and bottom walls.
► Experimental thermal stratification is incorrectly predicted with the set BC.
► Part 2 LES show that experimental temperature distributions at each wall are required.
► Resolving the stratification discrepancy needs a full thermal coupling at walls (Part 3).