Non-Oberbeck–Boussinesq effects on a water-filled differentially heated vertical cavity

Abstract

In this study, we examined non-Oberbeck–Boussinesq (NOB) effects on a water-filled differentially heated vertical cavity through two-dimensional direct numerical simulations. The simulations encompassed a Rayleigh number (Ra) span of 107–1010, temperature difference (Δθ̃) up to 60 K, and a Prandtl number (Pr) fixed at 4.4. The center temperature (θcen) was found to be independent of Ra and to increase linearly with Δθ̃, as presented by θcen≈1.18×10−3 K−1Δθ̃. The thermal boundary layer (BL) thicknesses near the hot and cold walls (λ¯hθ and λ¯cθ, respectively) are found to scale as λ¯h,cθ∼Raγ λ¯h,c, where the scaling exponent γ λ¯h,c ranges from −0.264 to −0.262. For more detail, the scaling exponent γ λ¯h displays an increasing trend, while γ λ¯c demonstrates a decreasing trend. However, the sum of the hot and cold thermal BL thicknesses was found to be constant at a fixed Ra in the presence of NOB effects. Our detailed investigation of the Nusselt number (Nu) and Reynolds number (Re) revealed that Nu∼Ra0.258 and Re∼Ra0.364, showing insensitivity to NOB effects. These exponents were smaller than those for Rayleigh–Bénard convection. The NOB modifications on Nu and Re were less than 1.2% and 2.5%, respectively, even at Δθ̃=60 K. Our results also revealed that key parameters such as θcen and normalized ratios [(λ¯NOBθ/λ¯OBθ)h,c, NuNOB/NuOB, and ReNOB/ReOB] exhibit universal correlations with Δθ̃. Remarkably, these relationships are consistent across varying Ra values. This observation underscored the influence of NOB effects on these parameters could be confidently forecasted using just the temperature difference (Δθ̃) for Ra∈[107,1010].