Numerical simulation of upward flowing supercritical fluids using buoyancy-influence-reflected turbulence model

The mechanism behind heat transfer deterioration, occurring in fluids at supercritical pressures under particular conditions accompanying strong property variations, is not fully understood. The numerical simulations employing RANS type turbulence modelings have never succeeded in reproducing the thermal field of fluids under such conditions, although some success in particular cases has been reported, since the widely-used turbulence models do not account for the property variations and consequential boundary layer deformation. The authors recently reported that an introduction of varying dimensionless damping length (A(+)) as a function of the shear stress ratio between the wall and boundary layer edge into a turbulence model greatly improved the RANS type numerical simulation of highly buoyant flows. In this paper, the authors attempted to directly integrate the momentum equation under appropriate assumptions and approximations, and to establish a functional relation between A(+) and shear stress in the buffer layer (tau(delta t)). The introduction of A(+) as a function of tau(delta t) in the eddy viscosity formula in addition to the property-dependent turbulent Prandtl number, which was proposed earlier by the first author, resulted in numerical simulations of supercritical fluid with strong buoyancy agreeing excellently with the experimental data.