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Natural laminar flow wing optimization using a discrete adjoint approach

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Abstract

Natural laminar flow is one of the most promising ways to reduce the drag of future aircraft configurations. However, there is a lack of efficient tools for performing shape optimization considering laminar-to-turbulent transition. This is in part because including crossflow instabilities in the optimization is challenging. This paper addresses this need by developing a discrete, adjoint-based optimization framework where transition is modeled considering both Tollmien and Schlichting waves and crossflow instabilities. The framework is based on a Reynolds-averaged Navier–Stokes computational fluid dynamics solver coupled with a transition simulation module externally by incorporating into the Spalart–Allmaras turbulence model through a smooth intermittency function. The transition simulation module consists of a laminar boundary-layer equations solver and a simplified stability analysis method based on the Drela–Giles method and the C1 criterion. A Jacobian-free coupled-adjoint method is used to compute the gradients of the transition prediction. Lift-constrained drag minimization of a transonic infinite span wing with 25∘ of sweep is performed. The optimizer successfully reduces the drag coefficient by 43.34%, owing to an extended laminar region on the wing surface, and finds a pressure distribution that strikes a balance between the Tollmien–Schlichting wave and crossflow instability transition mechanisms.

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Notes

  1. https://github.com/mdolab/idwarp

  2. https://github.com/mdolab/pygeo

  3. https://github.com/mdolab/MACH-Aero, accessed April 20, 2020

  4. https://github.com/mdolab/pyoptsparse

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  1. Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USA

    Yayun Shi, Charles A. Mader & Joaquim R. R. A. Martins

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Responsible Editor: Gregoire Allaire

Replication of results

The numerical results preseted to support the conlusiosn outlined can be obtained using existing approaches described in the literature. To replicate the resulte of Fig. 4, Fig.5, Fig.12, Fig.13, the linear stability theory with method (Cebeci 1977, Drela 1987, Grabe 2018) should to be used. In the Fig.5, the geometry and experimental details are described in Yayun 2020. To replicate the results of the gradient-based verification and optimization results (Fig.6, Fig.7, Fig.8, Fig.9, Fig.10, Fig.11), the derivarives of analytical expressions are described in Kenway 2019 and the corresponding open access code can be found by Mader 2020.

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Shi, Y., Mader, C.A. & Martins, J.R.R.A. Natural laminar flow wing optimization using a discrete adjoint approach. Struct Multidisc Optim 64, 541–562 (2021). https://doi.org/10.1007/s00158-021-02936-w

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