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Shape optimization of corrugated airfoils. (English) Zbl 1336.74056

Summary: The effect of corrugations on the aerodynamic performance of a Mueller C4 airfoil, placed at a \(5^{\circ}\) angle of attack and \(Re=10,000\), is investigated. A stabilized finite element method is employed to solve the incompressible flow equations in two dimensions. A novel parameterization scheme is proposed that enables representation of corrugations on the surface of the airfoil, and their spontaneous appearance in the shape optimization loop, if indeed they improve aerodynamic performance. Computations are carried out for different location and number of corrugations, while holding their height fixed. The first corrugation causes an increase in lift and drag. Each of the later corrugations leads to a reduction in drag. Shape optimization of the Mueller C4 airfoil is carried out using various objective functions and optimization strategies, based on controlling airfoil thickness and camber. One of the optimal shapes leads to 50% increase in lift coefficient and 23% increase in aerodynamic efficiency compared to the Mueller C4 airfoil.

MSC:

74P20 Geometrical methods for optimization problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76M10 Finite element methods applied to problems in fluid mechanics
76G25 General aerodynamics and subsonic flows

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References:

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