Numerical simulation of supercritical pressure fluids with property-dependent turbulent Prandtl number and variable damping function

When fluids at supercritical pressure enter into a region close to the pseudo-critical temperature, their numerical simulations with constant turbulent Prandtl number, Prt, and conventional damping function in turbulence modeling are never successful in reproducing the fluid-thermal behaviors, since fluids experience strong physical property variations across the turbulent boundary layer, and their influence has not been properly incorporated into a turbulence model. Several experimental data and numerical studies have indicated that Prt can be very smaller or larger than unity in a region of strong property variation. Recent research, both numerical and experimental, has also indicated that Prt is very likely a function of fluid-thermal variables, when the gradients of the physical properties of the fluid are significant. In this regard, the property-dependent turbulent Prt as a function of physical properties, which has recently been published by the first author, was introduced. Another point deserving attention is that turbulent boundary layer (TBL) deforms so severely, and so does the effective viscous sublayer thickness, A+, such that A+ is no longer a constant, but a function of the degree of TBL deformation due to buoyancy. A+ is expressed as a function of buoyancy and acceleration parameters when using already-known information. With this introduction of the functional form for A+ it is believed that the velocity overshoot and consequential TBL deformation are taken into account. The numerical simulations with property-dependent Prt and buoyancy-dependent A+ of flows under strong buoyancy agreed very well with the experimental data.