Abstract
The accuracy of airfoil polar predictions is limited by the usage of imperfect turbulence models. Can machine-learning improve this situation? Will airfoil polars teach the effect of turbulence on skin-friction? We try to answer these questions by refining turbulence treatment in the Rfoil code: boundary layer closure relations are learned from airfoil polar data. Two turbulent closure relations, for skin friction and energy shape factor, are parametrized with a class-shape transformation. An experimental database is then used to define code inaccuracy measures that are minimized with an interior point gradient algorithm. Results show that airfoil polars contain exploitable information about turbulent phenomena. Inferred closures agree with direct numerical simulation results of skin friction and the new code predicts drag more accurately. Maximum lift remains under-predicted but Rfoil maintains its robustness and suitability for optimization of wind energy airfoils.
Highlights
Wind turbine airfoils operate in high Reynolds flows with intricate eddies that cannot be resolved in practical simulations
Flow solvers model the effect of unresolved turbulent phenomena by combining mechanistic insight with closure relations
While the boundary-layer partial-differential-equations (BL-PDE) (1) are closed, system (2) comprises two ordinary differential equations (ODEs) that depend on five variables
Summary
Wind turbine airfoils operate in high Reynolds flows with intricate eddies that cannot be resolved in practical simulations. Flow solvers model the effect of unresolved turbulent phenomena by combining mechanistic insight with closure relations. Closures inject empirical knowledge into simulations and dominate errors in airfoil predictions [1,2,3] – be it for Viscous-Inviscid (VII) [4,5], Reynolds Averaged Navier-Stokes (RANS) [6], Large-Eddy (LES) [7] or Lattice-Boltzman [8] environments. That is why we use experimental airfoil polars to learn new turbulent closure relations for the. Results comprise a tailored Rfoil code and closure relations for turbulent skin friction (Cf ) and energy shape factor (H∗). The boundary-layer (BL) flow is solved with an integral method based on the Von Karman equations [41, 43]:
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