Predicting Local Velocity Gradients in a Rushton Turbine Stirred Tank: Turbulence Closure Strategies and Implications for Flocculation Design

This study compares the predictive capability of four turbulence modelling approaches for local velocity gradients in a Rushton turbine stirred tank representative of coagulation and flocculation applications. Three finite-volume RANS closures – standard k–ɛ, k–ω SST, and the Reynolds Stress Model (RSM) – Implemented in Siemens STAR-CCM+ are evaluated alongside a Lattice-Boltzmann LES solver (M-Star CFD) against a publicly available CFD-grade PIV dataset. Normalized radial velocity profiles are compared at two radial positions and two impeller speeds (650 and 1500 rpm), with model accuracy quantified by the normalized root-mean-square deviation (NRMSD). The standard k–ɛ model achieves the lowest average NRMSD (0.052), followed by M-Star LBM-LES (0.066), RSM (0.110), and k–ω SST (0.125). A key finding is the systematic amplification of velocity errors when converted to local velocity gradients: moderate velocity deviations produce disproportionately large gradient errors that cross the floc breakage threshold (80–200 s⁻¹), with direct implications for flocculation design. Spatial analysis of the predicted velocity fields reveals a qualitative distinction between the two paradigms: RANS solutions produce smooth, diffused fields, whereas LBM-LES retains fine-grained spatial heterogeneity that better represents the local gradient distributions governing floc fate. The results support a two-tier recommendation: k–ɛ for scalar accuracy of mean flow predictions, and LBM-LES where spatially resolved gradient distributions are required.