Scale-induced numerical uncertainty on the hydrodynamic characteristics of circular cylinders near the free surface

This study investigates scale-induced numerical uncertainty in the hydrodynamic forces and vortex-shedding characteristics of a two-dimensional (2D) circular cylinder near a free surface at high Reynolds numbers (Re). OpenFOAM simulations are conducted over a range of gap ratios (GR), Froude numbers (Fr), Re, and geometric scales. An uncertainty estimation framework based on four data sets is implemented following International Towing Tank Conference (ITTC) verification procedures and a correction-factor-based approach. The results show that the free-surface effects on hydrodynamic coefficients and vortex-shedding threshold are sensitive to geometric scale. The largest absolute uncertainty occurs near GR = 0.5, where the corrected uncertainty in lift coefficient amplitude CLRMS reaches approximately 38%, whereas that in the Strouhal number (St) is only about 0.09%. After normalization by the corresponding GR = 3 value, the additional free-surface-induced uncertainty is mainly reflected in St and the time-averaged lift coefficient CL, while drag coefficient CD and CLRMS show weaker sensitivity. The metastable vortex-shedding threshold varies around GR = 0.25, with uncertainty below 5%. An absolute-grid-size strategy is also examined and reduces the corrected normalized scale-induced uncertainty by up to approximately 39%, but increases the cell number and computational time. These results highlight the need to balance similarity preservation, uncertainty reduction, and computational cost in scale-transfer computational fluid dynamics simulations of near-free-surface bluff-body flows.