<p>This paper presents the development and application of TURB-3D, a Galerkin finite element – based computational fluid dynamics (CFD) model for simulating turbulent flows in open channels. The model solves the Reynolds-averaged Navier – Stokes (RANS) equations using a penalty method for incompressibility, a nonlinear algebraic stress closure, and the standard k–ε turbulence formulation. The Galerkin finite element method minimizes the residual in a weighted norm, ensuring that the approximate solution is the most accurate representation within the chosen function space. A key motivation for this work arises from the limitations of widely used hydrodynamic solvers such as Delft3D-FLOW and MIKE3. Although often labeled as three-dimensional, these are in fact hydrostatic layered models: vertical momentum is reduced to a hydrostatic balance, while vertical velocity is reconstructed from continuity rather than solved dynamically. Combined with σ- or z-layer coordinate systems, this reduces their ability to capture vertical accelerations, secondary circulations, and non-hydrostatic pressure gradients. Such models are therefore better described as quasi-3D (2.5D) tools, suitable for large-scale shallow-water applications but inadequate for strongly three-dimensional flows. In contrast, most high-resolution 3D CFD solvers, such as FLOW-3D, OpenFOAM, TELEMAC, and ANSYS-CFX, commonly employ isotropic eddy-viscosity turbulence models (e.g., k–ε or k–ω), which represent turbulence in a manner similar to that in confined duct flows. Consequently, secondary currents, turbulence anisotropy near free surfaces, and wall-shear variations are often inadequately captured unless more advanced closures—such as Reynolds Stress Models or anisotropic Large Eddy Simulation (LES) approaches—are utilized. TURB-3D overcomes these limitations by incorporating an anisotropic turbulent viscosity formulation and free-surface proximity functions, which enable realistic prediction of secondary currents, velocity-dip phenomena, and boundary shear stress distributions. Its finite element discretization and penalty scheme provide a significant gain in computational efficiency, making it more accessible for practical engineering use than conventional CFD solvers that demand millions of elements. Validation against laboratory experiments and benchmark CFD studies shows good agreement in velocity profiles, turbulence quantities, and shear velocities, with relative errors in the predicted average shear velocity of −1.8% for AR = 2 and −4.4% for AR = 1. TURB-3D successfully reproduces key three-dimensional flow features, including the depression of velocity maxima, corner-induced vortex structures, and secondary motion cells. The current implementation is limited to steady, fully developed channel flows, and relies on an empirical turbulence closure. Nevertheless, TURB-3D represents a computationally efficient and physically realistic tool for hydraulic engineering, offering a practical framework for channel design, flood analysis, and flow regulation. By bridging the gap between simplified 2D models and resource-intensive full CFD solvers, TURB-3D contributes a novel and robust methodology for simulating turbulent open channel flows.</p>

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TURB-3D: CFD model for open channels turbulent flow with secondary motion and anisotropic turbulent viscosity

  • Youssef I. Hafez

摘要

This paper presents the development and application of TURB-3D, a Galerkin finite element – based computational fluid dynamics (CFD) model for simulating turbulent flows in open channels. The model solves the Reynolds-averaged Navier – Stokes (RANS) equations using a penalty method for incompressibility, a nonlinear algebraic stress closure, and the standard k–ε turbulence formulation. The Galerkin finite element method minimizes the residual in a weighted norm, ensuring that the approximate solution is the most accurate representation within the chosen function space. A key motivation for this work arises from the limitations of widely used hydrodynamic solvers such as Delft3D-FLOW and MIKE3. Although often labeled as three-dimensional, these are in fact hydrostatic layered models: vertical momentum is reduced to a hydrostatic balance, while vertical velocity is reconstructed from continuity rather than solved dynamically. Combined with σ- or z-layer coordinate systems, this reduces their ability to capture vertical accelerations, secondary circulations, and non-hydrostatic pressure gradients. Such models are therefore better described as quasi-3D (2.5D) tools, suitable for large-scale shallow-water applications but inadequate for strongly three-dimensional flows. In contrast, most high-resolution 3D CFD solvers, such as FLOW-3D, OpenFOAM, TELEMAC, and ANSYS-CFX, commonly employ isotropic eddy-viscosity turbulence models (e.g., k–ε or k–ω), which represent turbulence in a manner similar to that in confined duct flows. Consequently, secondary currents, turbulence anisotropy near free surfaces, and wall-shear variations are often inadequately captured unless more advanced closures—such as Reynolds Stress Models or anisotropic Large Eddy Simulation (LES) approaches—are utilized. TURB-3D overcomes these limitations by incorporating an anisotropic turbulent viscosity formulation and free-surface proximity functions, which enable realistic prediction of secondary currents, velocity-dip phenomena, and boundary shear stress distributions. Its finite element discretization and penalty scheme provide a significant gain in computational efficiency, making it more accessible for practical engineering use than conventional CFD solvers that demand millions of elements. Validation against laboratory experiments and benchmark CFD studies shows good agreement in velocity profiles, turbulence quantities, and shear velocities, with relative errors in the predicted average shear velocity of −1.8% for AR = 2 and −4.4% for AR = 1. TURB-3D successfully reproduces key three-dimensional flow features, including the depression of velocity maxima, corner-induced vortex structures, and secondary motion cells. The current implementation is limited to steady, fully developed channel flows, and relies on an empirical turbulence closure. Nevertheless, TURB-3D represents a computationally efficient and physically realistic tool for hydraulic engineering, offering a practical framework for channel design, flood analysis, and flow regulation. By bridging the gap between simplified 2D models and resource-intensive full CFD solvers, TURB-3D contributes a novel and robust methodology for simulating turbulent open channel flows.