Application of compressible Reynolds-averaged governing equations to turbulent mixed convection in supercritical fluids in heated vertical tubes

Accurate estimation of thermal-hydraulic characteristics of supercritical flows has long been an attractive but elusive subject to many researchers in spite of tremendous effort devoted to the development of suitable turbulence models. One of the key reasons for the difficulty is a lack of measured turbulence data, which might have been used to formulate adequate turbulence models suitable for highly buoyant fluids. Turbulence models are typically based on the log-law, while the velocity profile in buoyant fluids substantially deviates from the log-law because of significant density variation in a turbulent boundary layer. In this paper, axisymmetric compressible Reynolds-Averaged governing equations were employed together with the property-dependent turbulent Prandtl number to reproduce experimental data representing heat transfer deterioration and consequential sudden temperature increase. The additional turbulence terms associated with turbulent mass flux appeared in the governing equations were modeled using the simple gradient diffusion hypothesis (SGDH). The proposed model successfully reproduced the experimental data. The various turbulence properties are presented and discussed.