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Inverse design using adjoint approach

Lee, Jen-Der and Abu-Zurayk, Mohammed and Brezillon, Joel (2009) Inverse design using adjoint approach. In: STAB Mitteilungen. 14. STAB-Workshop, Göttingen.

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Abstract

With the increasing of computational power, the CFD has become a routine tool used for aerodynamic analysis and provides reasonably accurate results. However, the ultimate goal in the design process is to find the optimum shape that maximizes the aerodynamic performance index, which might be the drag coefficient at a fixed lift, the lift-to-drag ratio, or matching the target pressure distribution, with reasonable accuracy and amount of time. The objective of current project is focused on the application of optimization technique based on control theory for airfoil inverse design that was performed using the unstructured Euler and RANS solver developed by DLR (DLR-Tau code). The final goal is to provide an optimization toolbox that is suitable for aerodynamic inverse design, especially for natural laminar flow wing design, for industrial applications. In optimum shape design problems, the true design space is a free surface which has infinite number of design variables and will require N+ 1 flow evaluations for N design variables to calculate the required gradients necessary for gradient-based optimization techniques. To minimize the expensive time required for each flow simulation, we apply the adj oint approach first proposed by Jameson and find the Frechet derivative of the cost function respect to the shape by solving an adjoint equation problem. The total cost, which is independent of number of design parameters, is one flow plus one adjoint solution and this makes this technique very attractive for optimum shape design. The flow solver used in this study is the DLR-Tau code, which solves the Euler and RANS equations on unstructured meshes with multistep time stepping scheme. Rapid convergence to a steady state is achieved via local time stepping, residual averaging, and multi-grid scheme. In contrast to the continuous adjoint approach, the discrete adjoint formulation approach was used to calculate the gradient information of the design variables. In this study, the cost function is defined as the least square of the difference to a given target pressure and this corresponds to an inverse design problem. The shape of airfoil, which is represented by the Class-Shape function Transformation (CST) parameterization, is then modified to match the desired target pressure, Pd. To evaluate the effectiveness of different gradient-based optimization algorithms, three optimization techniques, Steepest descent, Conjugate gradient, and BFGS were tested and the results were presented.

Item URL in elib:https://elib.dlr.de/69261/
Document Type:Conference or Workshop Item (Speech)
Title:Inverse design using adjoint approach
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Lee, Jen-DerUNSPECIFIEDUNSPECIFIED
Abu-Zurayk, MohammedMohammed.Abu-Zurayk (at) dlr.deUNSPECIFIED
Brezillon, JoelJoel.Brezillon (at) dlr.deUNSPECIFIED
Date:November 2009
Journal or Publication Title:STAB Mitteilungen
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Keywords:Inverse design, adjoint approach, unstructured mesh, optimisation
Event Title:14. STAB-Workshop
Event Location:Göttingen
Event Type:Workshop
HGF - Research field:Aeronautics, Space and Transport (old)
HGF - Program:Aeronautics
HGF - Program Themes:Aircraft Research (old)
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Flexible Aircraft (old)
Location: Braunschweig
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > CASE
Deposited By: Brezillon, Joel
Deposited On:17 Mar 2011 08:26
Last Modified:17 Mar 2011 08:26

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