STUDY ON TURBULENT TRANSPORT IN MIXED CONVECTION WITH UNSTABLE STRATIFICATION FOR LIQUID METALS

The strong thermal diffusivity of low Prandtl number liquid metals makes traditional Reynolds analogy invalidity, and the models concluded from regular fluids are not directly applicable to turbulent transport of liquid metals. The buoyant effect induced by density difference and gravity makes more complex behaviors and mechanisms of turbulent momentum and energy transfer for liquid metals. In this study we conduct the implicit large-eddy simulation of mixed convection with unstable stratification in a horizontal channel for liquid metals based on high-order spectral element method. The Prandtl number is fixed at Pr = 0.025. The nominal friction Reynolds number is up to Re_\tau ,N = 1020 for engineering practical use, and the range of Richardson number is Ri = 0\sim 10 to cover the forced convection and mixed convection with strong buoyancy. The results indicate that buoyancy induced large-scale quasi-streamwise rollers play the dominant role on turbulent momentum and energy transports in mixed convection for liquid metals, and the large-scale structures make the instantaneous flow fields in near wall region show obvious coalescence and intermittency. The one-dimensional streamwise co-spectra show that under mixed convection condition, the turbulent momentum and energy transfer in low wavenumber range are observed with - 1 \mathord\left/ \vphantom - 1 5 \right. 5 and - 1 \mathord\left/ \vphantom - 1 2 \right. 2 power-law scaling at wall vicinity, respectively. The turbulent energy transfer at channel center is observed with - 7 \mathord\left/ \vphantom - 7 3 \right. 3 power-law scaling in mixed convection. Compare to forced convection, buoyancy enhances turbulence anisotropy at wall vicinity and accelerates the turbulent energy transfer rates between different turbulence scales at channel center. The transport equations of Reynolds shear stress and wall-normal turbulent heat flux show that under strong buoyancy conditions, the pressure-related terms dominate the gain and loss of turbulent momentum in near wall region, while the turbulence transport and temperature-pressure gradient terms are remarkably enhanced by buoyancy in turbulence outer region. The turbulent Prandtl number in turbulence outer region and global average turbulent Prandtl number are mainly controlled by Richardson number in mixed convection with unstable stratification. New phenomenological models for turbulent Prandtl number are proposed and the empirical constants are calibrated. The spectral analysis of each term in turbulent Prandtl number shows that the typical wavelength of buoyancy induced large-scale quasi-streamwise rollers for turbulent momentum and energy is 8h, where h is channel half-height. The negative peak at streamwise wavelength 8h in premultiplied spectra of numerator term means that the decrease of turbulent Prandtl number in outer region not only caused by enhancement of turbulent heat transfer, but also worked by the modulation of turbulent momentum transport by buoyancy induced large-scale structures.