Optimization of CFD Simulation Parameters for a NACA 4412 Airfoil

Removing Guesswork from CFD Mesh Setup

CFD accuracy is highly sensitive to mesh configuration, yet mesh parameters are often chosen by trial identify the mesh configuration that best reproduces wind-tunnel data for a NACA 4412 airfoil at Re = 1×10⁶, using only 8 simulations instead of a full factorial campaign. The study was carried out as a 4-person team project.

• Test case: NACA 4412 airfoil, α = 0°, Re = 1×10⁶, V∞ = 42 m/s, c = 0.2 m
• Turbulence model: k-ω SST (RANS)
• Method: Taguchi L8 orthogonal array on 3 mesh parameters
• Validation: comparison against experimental CL and CD reference data

Taguchi Design of Experiments

A composite error function was defined to jointly evaluate lift and drag prediction accuracy, weighting CD by a = CL,exp / CD,exp = 8.75 to balance the two coefficients' relative magnitude. Three mesh parameters, each at two levels, were then studied using a Taguchi L8 orthogonal array, reducing the required simulations from 2³ = 8 full-factorial runs' worth of variables to 8 structured runs while still resolving all main effects and two-factor interactions.

Geometry, Domain & Mesh

The NACA 4412 geometry (4% max camber at 40% chord, 12% max thickness) was built in Design Modeler. The computational domain followed standard CFD best practices: 7.5c upstream, 15c downstream and 7.5c laterally, sized to prevent boundary conditions from artificially influencing the near-field flow and to fully capture wake development.

Effects, Interactions & Optimal Configuration

Each of the 8 runs produced a composite error ranging from 0.79% to 97.46%, confirming that mesh configuration has a first-order effect on CFD accuracy for this case. Factor and interaction effects were then computed by comparing mean error between high and low levels of each variable.

This configuration corresponds to Run 5, which achieved the lowest composite error of the campaign at 0.96%, consistent with the effects model's prediction of 2 to 4% for the optimal factor combination.

Comparison with Experimental Data

The optimal configuration (Run 5) was checked for solution convergence, then its predicted aerodynamic coefficients were compared directly against wind-tunnel reference data.

Pressure and velocity fields are physically consistent with expected airfoil aerodynamics: overpressure on the pressure side and suction on the suction side generating lift, flow acceleration on the suction side per the Venturi effect, a regular boundary layer with no separation at this angle of attack, and a stable, symmetric wake.

Limitations & Recommendations

The study's scope and its practical implications for future CFD work were both examined critically.

• Favor quadrilateral elements when geometry and meshing tools allow it
• Refine the mesh at the wall, leading edge and trailing edge specifically
• Maintain y+ below 1 to properly resolve the viscous sublayer with k-ω SST
• Systematically monitor residuals, aerodynamic coefficients and mass flow for convergence
• Validate new mesh configurations against experimental or analytical data whenever possible

Key Takeaways

The Taguchi method proved to be an efficient framework for CFD parameter optimization, identifying the best-performing mesh configuration from only 8 simulations while quantifying the relative influence of each parameter and their interactions, a structured, reproducible alternative to trial-and-error mesh setup.

• Quantified the relative influence of mesh size, edge size, mesh method and their interactions on CFD accuracy
• Identified an optimal configuration (10 mm mesh, 100 mm edge sizing, quadrilateral elements) reducing error from up to 97.46% to under 1%
• Validated the approach directly against wind-tunnel CL/CD data for the NACA 4412 airfoil
• Established a reproducible DOE methodology directly transferable to other CFD mesh-sensitivity studies