Aerodynamic-driven topology optimization of compliant airfoils

Pedro Gomes,Rafael Palacios

doi:10.1007/s00158-020-02600-9

Pedro Gomes, Rafael Palacios

Open Access

https://doi.org/10.1007/s00158-020-02600-9

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Abstract

A strategy for density-based topology optimization of fluid-structure interaction problems is proposed that deals with some shortcomings associated to non stiffness-based design. The goal is to improve the passive aerodynamic shape adaptation of highly compliant airfoils at multiple operating points. A two-step solution process is proposed that decouples global aeroelastic performance goals from the search of a solid-void topology on the structure. In the first step, a reference fully coupled fluid-structure problem is solved without explicitly penalizing non-discreteness in the resulting topology. A regularization step is then performed that solves an inverse design problem, akin to those in compliant mechanism design, which produces a discrete-topology structure with the same response to the fluid loads. Simulations are carried out with the multi-physics suite SU2, which includes Reynolds-averaged Navier-Stokes modeling of the fluid and hyper-elastic material behavior of the geometrically nonlinear structure. Gradient-based optimization is used with the exterior penalty method and a large-scale quasi-Newton unconstrained optimizer. Coupled aerostructural sensitivities are obtained via an algorithmic differentiation based coupled discrete adjoint solver. Numerical examples on a compliant aerofoil with performance objectives at two Mach numbers are presented.

Highlights

Topology optimization represents a radical departure from conventional sizing methods as it allows an optimum material distribution to be identified
While it would be possible to perform the inverse design step simulating only the structure, we found that doing so can result in an unstable structure that buckles under the small variation of fluid-structure interaction (FSI) loads caused by the small discrepancy between the target response and the response of the discrete-topology structure
We have demonstrated how density-based topology optimization can be used to design the internal structure of a compliant airfoil with the objective of improving load alleviation

Summary

Introduction

Topology optimization represents a radical departure from conventional sizing methods as it allows an optimum material distribution to be identified. The technique is applied locally, e.g., to single ribs (Krog et al 2004), so that the resulting structure can still be manufactured by traditional methods. Another important practical challenge of topology optimization, especially in a fluid-structure interaction (FSI) context, is the computational cost. When coupled FSI is simulated, using medium fidelity methods can be sufficient on the fluid side for stiffnessbased design dominated by pressure loads (e.g., James et al 2014; Dunning et al 2015, Stanford and Ifju 2009). Doing so will limit the effectiveness of the technique if more performance-oriented objectives, such as drag, are to be considered and lowers the accuracy with which buffet constraints (critical for airworthiness, Kenway and Martins 2017) can be imposed

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Discussion

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