Aerodynamic design optimization of a NACA 0012 airfoil: An introductory adjoint discrete tool for educational purposes.

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Title: Aerodynamic design optimization of a NACA 0012 airfoil: An introductory adjoint discrete tool for educational purposes.
Authors: Ntantis, Efstratios L.1 (AUTHOR) entantis@amityuniversity.ae, Xezonakis, Vasileios2 (AUTHOR)
Source: International Journal of Mechanical Engineering Education. Jul2025, Vol. 53 Issue 3, p611-630. 20p.
Subjects: Mach number, Reynolds number, Derivatives (Mathematics), Structural optimization, Educational objectives
Abstract: The adjoint method is a powerful tool in high-fidelity aerodynamic shape optimization, providing an efficient means to compute derivatives of a target function with respect to various design variables. This paper delves into the discrete adjoint method. It offers a theoretical exploration of its implementation as an innovative tool for calculating partial derivatives (sensitivities) related to objective functions and design variables, specifically applied to a subsonic NACA0012 airfoil. The study conducts a qualitative evaluation using a designated test case, considering specified Mach number and Reynolds number values of 0.297 and 6,667 million, respectively. The Spalart-Allmaras turbulence model is employed to enhance computational cost efficiency. The results affirm the efficacy of the introduced tool, DAFoam, showcasing its ability to generate optimal geometries. The achieved performance optimization is evidenced by minimizing the drag coefficient value (CD) to an impressive 0.0131. While this research does not delve into the post-processing of sensitivity calculations, it acknowledges the potential for future investigations. The primary objective and novelty of this study is to provide the elementary background of the state of the art test case (NACA0012) within the subsonic regime, introducing the pioneer discrete adjoint aerodynamic optimization methodology (DAFoam) with the potential to explore its higher order capabilities in other aerodynamic related studies. Furthermore, it caters the educational needs of both graduate students and engineers in this exciting field. By presenting this cutting-edge methodology, it contributes to future advancements for the aerodynamicists in terms of optimal solutions. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Mechanical Engineering Education is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Aerodynamic design optimization of a NACA 0012 airfoil: An introductory adjoint discrete tool for educational purposes.
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Mechanical+Engineering+Education%22">International Journal of Mechanical Engineering Education</searchLink>. Jul2025, Vol. 53 Issue 3, p611-630. 20p.
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  Data: <searchLink fieldCode="DE" term="%22Mach+number%22">Mach number</searchLink><br /><searchLink fieldCode="DE" term="%22Reynolds+number%22">Reynolds number</searchLink><br /><searchLink fieldCode="DE" term="%22Derivatives+%28Mathematics%29%22">Derivatives (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+optimization%22">Structural optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Educational+objectives%22">Educational objectives</searchLink>
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  Group: Ab
  Data: The adjoint method is a powerful tool in high-fidelity aerodynamic shape optimization, providing an efficient means to compute derivatives of a target function with respect to various design variables. This paper delves into the discrete adjoint method. It offers a theoretical exploration of its implementation as an innovative tool for calculating partial derivatives (sensitivities) related to objective functions and design variables, specifically applied to a subsonic NACA0012 airfoil. The study conducts a qualitative evaluation using a designated test case, considering specified Mach number and Reynolds number values of 0.297 and 6,667 million, respectively. The Spalart-Allmaras turbulence model is employed to enhance computational cost efficiency. The results affirm the efficacy of the introduced tool, DAFoam, showcasing its ability to generate optimal geometries. The achieved performance optimization is evidenced by minimizing the drag coefficient value (CD) to an impressive 0.0131. While this research does not delve into the post-processing of sensitivity calculations, it acknowledges the potential for future investigations. The primary objective and novelty of this study is to provide the elementary background of the state of the art test case (NACA0012) within the subsonic regime, introducing the pioneer discrete adjoint aerodynamic optimization methodology (DAFoam) with the potential to explore its higher order capabilities in other aerodynamic related studies. Furthermore, it caters the educational needs of both graduate students and engineers in this exciting field. By presenting this cutting-edge methodology, it contributes to future advancements for the aerodynamicists in terms of optimal solutions. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Mechanical Engineering Education is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1177/03064190241254020
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      – Code: eng
        Text: English
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        PageCount: 20
        StartPage: 611
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      – SubjectFull: Mach number
        Type: general
      – SubjectFull: Reynolds number
        Type: general
      – SubjectFull: Derivatives (Mathematics)
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      – SubjectFull: Structural optimization
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      – SubjectFull: Educational objectives
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      – TitleFull: Aerodynamic design optimization of a NACA 0012 airfoil: An introductory adjoint discrete tool for educational purposes.
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            – D: 01
              M: 07
              Text: Jul2025
              Type: published
              Y: 2025
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