2D VISCOUS SHAPE DESIGN OPTIMIZATION AND MESH ADAPTATION USING THE ADJOINT METHOD

Document Type : Original Article

Authors

1 Postdoc researcher, Department of Mechanical Engineering, Vrije Universiteit Brussel, Pleinlaan 2 -1050 Brussels- Belgium.+

2 Assistant Professor, Helwan University, Faculty of Engineering - Mattaria, Department of Mechanical Power Engineering, Masaken El-Helmia, 11718 Cairo, Egypt.

3 PhD student, Department of Mechanical Engineering, Vrije Universiteit Brussel, Pleinlaan 2 -1050 Brussels- Belgium.

4 Professor, Department of Mechanical Engineering, Vrije Universiteit Brussel, Pleinlaan 2 -1050 Brussels- Belgium.

Abstract

ABSTRACT
The majority of the adjoint methods applications focus on research in aerodynamic shape design optimization such as flow in airfoil cascade. This paper presents the application of the adjoint method technique in simple test cases of engineering relevance. The goal of this work is to extend the adjoint method into more engineering applications for viscous and incompressible flow, and to further improve the performance. Two test cases of engineering relevance have been selected. (1) Mesh adaptation for 2-D lid-driven cavity. (2) Drag reduction using an optimized upstream rod. The adjoint method has been used to efficiently adapt the 2-D lid-driven cavity mesh to minimize the discretization errors in calculating the swirl number. Based on the adaptation for the sensitivity magnitude, a uniform mesh of 1600 cells has been refined until a total 6586 cells, with finer mesh at the locations of highest sensitivities. The application of the adjoint method for the passive drag reduction problem results in a modified shape and position for the upstream cylinder. This change reduces the drag force on the main cylinder by 46%.

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