A new formulation of variable turbulent Prandtl number for heat transfer to supercritical fluids

• A new formulation of variable turbulent Prandtl number is proposed.
• Numerical simulations were successful with the proposed variable Prt.
• Assessment of the influence of turbulent boundary layer on Prt.

When a fluid at supercritical pressure approaches the pseudo-critical temperature it experiences a strong variation in physical properties putting applicability of various turbulent flow modelings in question. Earlier numerical calculations showed, without exception, unrealistic over-predictions, as soon as the fluid temperature approached the pseudo-critical temperature. The over-predictions might have been resulted either from an inapplicability of widely used turbulence models or from an unrealistic treatment of the turbulent Prandtl number (Prt) as a constant. Recent research, both numerical and experimental, indicates that Prt is very likely a function of fluid–thermal variables as well as physical properties, when the gradients of physical properties of a fluid are significant. This paper describes the procedure for a new formulation of Prt which varies with physical properties and fluid–thermal variables. The application of the variable Prt was surprisingly successful in reproducing the fluid temperature in supercritical fluids flowing in small-diameter vertical tubes ranging from 4.57 to 20 mm.