NUMERICAL ANALYSIS OF TURBULENT FLOW IN A SQUARE DUCT USING THE REYNOLDS-AVERAGED NAVIER-STOKES EQUATIONS WITH K-Ω SST MODEL

Abstract

In computational fluid dynamics (CFD), accurately predicting turbulent flow in non-circular ducts remains a major challenge with significant implications for internal piping networks, heat exchangers, and HVAC systems. This study provides a numerical analysis of fully developed, incompressible turbulent flow in a square duct using the Shear Stress Transport (SST) k-ω turbulence model in addition to the Reynolds-Averaged Navier-Stokes (RANS) equations. The primary objective was to evaluate how well the model captured secondary flow phenomena, specifically Prandtl's secondary flow of the second kind and the associated anisotropic Reynolds stress distribution caused by turbulence. A hydraulic diameter (Dh) of 0.1 m was used to create a three-dimensional computational. The finite volume method in ANSYS Fluent was used for simulations at a Reynolds number (Re) of 20,000, with enhanced wall treatment for better near-wall resolution. The axial velocity profile results showed a good agreement with known experimental data. More significantly, the unique eight-vortex secondary flow pattern inside the duct cross-section which is impacted by the anisotropy of normal Reynolds stresses was correctly predicted by the simulation. However, when compared to Direct Numerical Simulation (DNS) benchmarks, quantitative variations in the magnitude of these secondary velocities were observed. This work highlights the usefulness of RANS-based approaches for engineering evaluations of internal flows and highlights the persistent difficulties in solving complex turbulence-driven secondary motions due to isotropic eddy-viscosity assumptions.

Keywords: RANS, Computational Fluid Dynamics, Square Duct Flow, Secondary Flow, Turbulence Modeling, Navier-Stokes Equations, and k-ω SST