Aerodynamic-driven topology optimization of compliant airfoils
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RESEARCH PAPER
Aerodynamic-driven topology optimization of compliant airfoils Pedro Gomes1 · Rafael Palacios1 Received: 17 December 2019 / Revised: 28 February 2020 / Accepted: 2 April 2020 © The Author(s) 2020
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 hyperelastic 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. Keywords Fluid-structure interaction · Topology optimization · Coupled discrete adjoints
1 Introduction Topology optimization represents a radical departure from conventional sizing methods as it allows an optimum material distribution to be identified. It has been applied to aircraft structures for over two decades (Balabanov and Haftka 1996). In most applications, 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. While sometimes the analysis can be simplified by assuming “frozen” fluid loads (see Zhu et al. 2016), this assumption can lead
Responsible Editor: Axel Schumacher Rafael Palacios
[email protected] Pedro Gomes [email protected] 1
Imperial College, London, SW7 2AZ, UK
to suboptimum results, especially in the design of large components with strong FSI (Maute and Allen 2004). 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). However, doing so will limit the effectiveness of the technique if more performance-oriented objectives, such as drag, are to be considered and lowers the accura
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