This study demonstrates the application of the discrete adjoint method for aerodynamic shape optimization of the NACA2412 airfoil used                  in Cessna 172R at moderate Reynolds numbers (Re = 2.2 ´ 10⁶) and low Mach numbers (M = 0.13). The open-source CFD solver OpenFOAM is coupled with DAFoam-discrete adjoint with OpenFOAM to efficiently compute the sensitivities of the drag coefficient concerning shape design variables. The SST (Shear Stress Transport) k-ω turbulence model is employed for its superior performance in predicting flow separation over airfoils. The airfoil geometry is parameterized using B-spline curves with control points  as design variables. A discrete adjoint method for a multidisciplinary optimization algorithm minimizes the drag coefficient subject to lift constraints by automatically adjusting the control point positions. The optimized airfoil exhibits significantly reduced drag compared to the baseline NACA2412. Optimizing the airfoil shape reduced drag coefficient by 4.89%, increased lift coefficients, and increased lift-to-drag ratios at different angles of attack over the original design.

OpenFOAM, DAFoam, drag coefficient, discrete adjoint method, geometric optimization

Received: March 31, 2025; Revised: April 28, 2025; Accepted: May 13, 2025; Published: June 9, 2025

How to cite this article: Thi-Hong-Nhi Vuong, Gia-Hung Long, Thi-Hong-Hieu Le and Thanh-Long Le, Improvement in aerodynamic performance of airfoils using aerodynamic shape optimization, JP Journal of Heat and Mass Transfer 38(3) (2025), 427-445. https://doi.org/10.17654/0973576325021

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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