Critical assessment of turbulence prediction in square duct flow

Prandtl's secondary flows of the second kind occur when turbulent fluid flows through straight, non-circular geometries, even with a uniform axial inlet flow. A prominent example of such geometry is the square duct, where one of its applications is the square cold leg. In this work, fully developed turbulent flow in a square duct is simulated and validated with reference Direct Numerical Simulation (DNS) of a simplified pressurized thermal shock (PTS) scenario. Six turbulent models implemented in Simcenter STAR-CCM+ software were evaluated: v2-f k-ε low Re, linear k-ε low Re, linear SST k-ω, Reynolds Stress Model (RSM), and cubic constitutive relation models (Cubic k-ε low Re and Cubic SST k-ω). The results demonstrated that RSM and cubic constitutive relation models effectively capture the characteristic shape of Prandtl's secondary flow of the second kind. Furthermore, the linear standard (Formula presented) with low Re provides the most accurate prediction for u⁺and the mean axial velocity, owing to the relatively weak secondary flow. For predicting the secondary flow velocity field itself, the cubic standard (Formula presented) with low Re model exhibited the best performance.