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 k − ε 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 k − ε with low Re model exhibited the best performance.