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Aerodynamic Shape Optimization of Airfoils Using Adjoint Equations

Darvishzadeh, Tohid | 2009

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 39920 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Mazaheri, Karim
  7. Abstract:
  8. Adjoint-based aerodynamic optimization has drawn much attention, recently. It is based on gradient optimization procedures and requires the sensitivities of the design variables to find the optimized shape. The advantage of this method is that it estimates the sensitivities by solving an “adjoint equation”, instead of calculating them directly. In this thesis, the method is used to design airfoil shapes both in inviscid and viscous flows. In this regard, a flow solver and an adjoint solver have been developed. First, the validity of the flow solver is tested according to credited data form papers and softwares. Then, the optimizing program is tested using some inverse design problems. Moreover, aerodynamic force optimization is considered. This includes minimization of drag and maximization of lift with various constraints. Using the algorithm, we were able to reduce drag coefficient and increase lift coefficient of a NACA0012 airfoil by 13% and 25%, respectively. Furthermore, three innovative ideas are presented, which include Simultaneous Convergence, Gradient Extrapolation, and Adaptive convergence. Simultaneous Convergence solves flow and adjoint equations along with the optimization process. Gradient Extrapolation finds the valus of sensitivities by extrapolating the values obtained in the previous design cycles. Adaptive Convergence reduces number of flow and adjoint solution iterations. Application of these schemes to the adjoint based aerodynamic shape optimization has proven to reduce the computational cost up to many times. However, one must be careful in choosing the appropriate parameters for best performance of the three schemes.

  9. Keywords:
  10. Optimization ; Gradient Based Method ; Airfoil Optimization ; Aerodynamics ; Adjoint Equations ; Simultaneous Convergence

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