Numerical estimation of wall friction ratio near the pseudo-critical point with CFD-models

In this paper, the STAR-CCM+ CFD code is used in the attempt to reproduce the values of friction factor observed in experimental data at supercritical pressures at various operating conditions. A short survey of available data and correlations for smooth pipe friction in circular pipes puts the basis for the discussion, reporting observed trends of friction factor in the liquid-like and the gas-like regions and within the transitional region across the pseudo-critical temperature. For smooth pipes, a general decrease of the friction factor in the transitional region is reported, constituting one of the relevant effects to be predicted by the computational fluid-dynamic models. A limited number of low-Reynolds number models are adopted, making use of refined near-wall discretisation as required by the constraint y+ < 1 at the wall. In particular, the Lien k–ɛ and the SST k–ω models are considered. The values of the wall shear stress calculated by the code are then post-processed on the basis of bulk fluid properties to obtain the Fanning and then the Darcy–Weisbach friction factors, based on their classical definitions. The obtained values are compared with those provided by experimental tests and correlations, finding a reasonable qualitative agreement. Expectedly, the agreement is better in the gas-like and liquid-like regions, where fluid property changes are moderate, than in the transitional region, where the trends provided by available correlations are reproduced only in a qualitative way.