Mixed convection in horizontal channel with unstable stratification for low-Prandtl-number fluids

Mixed convection with unstable stratification for low-Prandtl-number fluids is an important momentum and energy coupling transport process, which attracts growing interest in engineering practical scenarios. In this study, a series of scale-resolving implicit large-eddy simulations is conducted with high-pass filter technique in high-order spectral element method. The nominal friction Reynolds number is up to Reτ,N=1020 for engineering practical use. The range of the Richardson number is 0≤Ri≤10 and the Prandtl number is fixed at Pr=0.025 to investigate mixed convection for liquid metals under different buoyancy conditions. The quasi-streamwise longitudinal counter-rotating rollers with streamwise meandering fulfill the entire channel width to enhance turbulent heat transfer. The flow pattern similarity is quantitatively discussed through Reynolds stress invariants and Monin–Obukhov (MO) similarity, finding that the flow pattern is mainly controlled by the Richardson number. A new scaling of MO length scale is proposed, and the results show that the buoyant effect is more pronounced for low-Prandtl-number fluids. Furthermore, the power-law Businger–Dyer–Panofsky flux profile relationship is still applicable to MO universal functions for low-Prandtl-number fluids. New empirical correlations and scaling are proposed for friction drag and heat transfer with the average maximum relative deviation no larger than 25%. The premultiplied co-spectra of friction drag and heat transfer indicate that flow similarity also exhibits in statistical wavenumber space with the typical streamwise wavelength λx≈8h of buoyancy-induced large-scale motions. The extension of Fukagata–Iwamoto–Kasagi identity is conducted to study the contributions of shear turbulent motions and buoyancy-induced large-scale motions on friction drag and heat transfer. The results show that buoyancy-induced large-scale motions only cost 20%–25% friction drag loss, but contribute nearly 60% heat transfer, showing good profits on less friction and more heat transfer.