Improving transonic performance with adjoint-based NACA 0012 airfoil design optimization

• The study investigates the discrete adjoint method for high-fidelity aerodynamic shape optimization, focusing on efficiently computing derivatives of a target function for various design variables. It is applied to a NACA0012 airfoil at transonic speeds, evaluated under Mach 0.7 and Reynolds number 15.96 million. • Utilizing the Spalart-Allmaras turbulence model for improved computational efficiency, the study demonstrates the effectiveness of the Discrete Adjoint method with OpenFOAM. Results show a significant drag coefficient (Cd) reduction to 0.00871, a 62.2 % decrease from previous studies. • The research validates the discrete adjoint method's capability to generate optimal aerodynamic configurations, showcasing its novelty and efficiency through substantial improvements in optimized performance metrics. • While not addressing the post-processing of sensitivity calculations, the study lays the groundwork for future research. It aims to meet the educational and training needs of researchers, engineers, and graduate students. It comprehensively introduces discrete adjoint aerodynamic design optimization and presents a novel methodology for future advancements. This study delves into the discrete adjoint method, a powerful tool in high-fidelity aerodynamic shape optimization that efficiently computes derivatives of a target function for different design variables. It offers a theoretical exploration of its implementation as an innovative tool for calculating partial derivatives (sensitivities) related to objective functions and design variables. It is implemented to a NACA0012 airfoil at a transonic speed. This designated test case is qualitatively evaluated, considering specified Mach number and Reynolds number values of 0.7 and 15.96 million, respectively. The standard Spalart-Allmaras turbulence model is adapted to improve computational cost efficiency. The results validate the efficiency of Discrete Adjoint with OpenFOAM, showcasing its capability to generate optimal configurations. The achieved optimized performance is evidenced by minimizing the drag coefficient value (Cd) to an impressive value of 0.00871, 62.2 % lower than the previous studies, thus securing a novelty. While this research does not consider the post-processing of sensitivity calculations, it enables the potential for future research. The primary target of this paper is to assess the educational and training needs of researchers, engineers, and graduate students, offering a comprehensive introduction to discrete adjoint aerodynamic design optimization, presenting a novel methodology, and contributing to future advancements in the design optimization field.