Flap optimization

Two dimensional flap shape and position optimization

The middle section of the outer flap element of a swept wing has been optimized (figure 1). The two–dimensional geometry and the freestream flow conditions were defined according to the “principle of cosine?” [1]. A 2D numerical optimization procedure, based on a parametric CAD model, a mesh generator and a CFD code, has been developed and applied for the design of the flap shape and the relative position optimization.

Flap section position on the wing planform

Fig. 1. Flap section position on the wing planform

The flap is assumed to be extended along 30% of the wing chord. Its geometry is limited by the spoiler installation and the shroud whose position is imposed at 90% of the chord (figure 2).

Flap installation

Fig. 2. Flap installation

Setup of the optimization procedure

The flap geometry is modeled by a parametric CAD software. The lower side of the flap element, which must correspont to the exposed airfoil geometry, is maintained unchanged. The leading edge and the upper geometry is modeled by an arc, a conic and a spline curve connected maintaining continuity on the second derivative. The parameters governing the flap shape are the leading edge radius, the conic shape parameter and the horizontal position of the maximum camber (figure 3).

Leading edge radius  Conic parameter
Max camper position

Fig. 3. Flap shape parameterization

The computational domain consists in a multiblock structured grid composed by 90000 cells (figure 4). The farfield is located 50 chords away from the model and the cells are clustered on the wall at a Y+ distance lower than 1 (the boundary layer is solved up to the wall) with a growing rate of 1.2. The mesh is automatically generated by a batch procedure that loads the updated geometry into the mesh generation software, loads the predefined blocking file, regenerates the mesh and exports it in the CFD code format. A fully turbulent CFD computation is performed using the k–ω SST turbulence model.

Computational domain

Fig. 4. Computational domain

Two additional parameters, named Gap and Overlap, governing the position of the flap relatively to the shroud, are added to the three geometric parameters to represent the variables of the optimization problems. The Nelder–Mead simplex algorithm has been applied in order to optimize the flap in take–off configuration (20 deg.). The objective was the maximization of the lift coefficient. An almost complete convergence was obtained after 100 iterations (figure 5).

Convergence history

Fig. 5. Convergence history


A numerical optimization procedure, coupling a parametric CAD model, a mesh generator and a CFD code, was setup and applied to the optimization of the 2D flap section of a swept wing. The starting geometry was designed by a direct aerodynamic design and its position defined according to literature [2]. The performance improvement was then contained but the procedure was very robust and efficient showing its potentialities as tool for aerodynamic design.


[1] Losito, V., “Fondamenti di Aeronautica Generale”, Accademia Aeronautica, 1991.

[2] Abbott, I. H. and Von Doenhoff, A. E., “Theory of Wing Sections”, Dover, Mineola, NY, 1959.