Impact of surface roughness on CFD performance prediction of francis turbines: Grid convergence analysis and experimental validation across variable operating conditions

This study presents a comprehensive numerical investigation of a medium-head Francis turbine performance using computational fluid dynamics with emphasis on grid sensitivity analysis and wall roughness effects. Four progressively refined meshes ranging from 3.28 to 8.77 million cells were evaluated using the Grid Convergence Index (GCI) methodology to quantify numerical uncertainty. The finest mesh achieved GCI values of 0.42% for power output with dimensionless wall distance (y⁺) below 3 on critical surfaces, while hydraulic efficiency demonstrated grid independence with maximum variation of ±0.06%. Steady-state Reynolds-Averaged Navier-Stokes simulations employing the SST k-ω turbulence model were conducted using the Multiple Reference Frame approach. The incorporation of realistic surface roughness ( k s = 0.045 – 0.18 mm) proved critical for accurate performance prediction, with simulations achieving agreement within 1-2% of experimental measurements across rotational speeds from 400 to 1000 rpm. The turbine demonstrated distinct operational characteristics: flat efficiency profile (49-51%) at 400 rpm indicating viscous-dominated flow, peaked efficiency (75.5%) at 700 rpm showing transition behavior, and broad high-efficiency operation (>80%) at 1000 rpm confirming design optimization. Detailed flow field analysis revealed progressive evolution of blade loading patterns, with pressure differentials increasing from 90 kPa to 220 kPa across the speed range. Draft tube flow exhibited progression from stable columnar vortices at low speed to precessing vortex rope structures at high speed, with corresponding pressure recovery efficiency varying from 65% to 75%. Three-dimensional visualization of pressure distributions and near-wall streamlines confirmed the correlation between flow organization and performance metrics. The study demonstrates that wall roughness modeling is essential for accurate turbomachinery CFD predictions, particularly at off-design conditions where boundary layer effects significantly influence overall performance. The validated numerical framework provides reliable performance prediction capabilities for Francis turbine design optimization and operational analysis.