# Airfoils

In the ease of wing design we will need to include 2D airfoil shapes as wing sections, with data usually resulting from previous development. Having gone through CFD design and analysis, sometimes also through experimental investigations, these given data should be dense sets of coordinates without the need to smooth them or otherwise make geometric changes which are not accompanied by flow analysis. Airfoil research has its main applications in high aspect ratio wing applications in the subsonic and transonic flight regime. Supersonic applications with low – aspect ratio also need airfoils but their implementation to wing shaping requires mainly investi – gating the whole 3D problem. This leads to the option in the present geometry generator to provide again airfoil input data, but with only few coordinates: These can be used for spline interpolation in a suitably blown-up scale (Figure 56). For such few supports each point may take the role of an independent design parameter, wavy spline interpolation may be avoided if dislocations are small compared to distances to fixed points. Along one airfoil contour to be modified, portions of fixed contour with dense data distribution may be given while other portions may be controlled by only one or two isolated supports. This option was used in an early version of this geometry tool to optimize wing shapes in transonic flow (118].

Figure 56 Spline fit obtained for airfoil in blown-up scale with few support points |

Analytical sections and input for inverse design

Spline fits arc well suited for redistribution of qualitatively acceptable dense data The possible occurrence of contour wiggles has restricted their use in the geometry tool discussed here to the abovcmcntioned option accepting external data, which is realistic for airfoils to be implemented in wing design. For a more independent approach we may ask for a more elegant analytical representation of wing sections, especially if these shapes still should be optimized. An important question arising is how many free parameters arc needed for representation of arbitrary, typical wing sections, with the shape close enough to duplicate CFD or experimental results of aerodynamic performance with reasonable accuracy Our successive refinement of airfoil generator subroutines using variously segmented curves as depicted in Figure 54 has shown that an amount of 10 to 25 parameters (numbers as listed in the table in Figure 54) may suffice for quite satisfactory representation of a given airfoil. The upper limit applies to transonic and laminar flow control airfoils with delicate curvature distribution as illustrated for a shock-free transonic airfoil. Figure 60 in chapter 7. where the influence of local curvature variations on the drag polar can be seen The lower limit seems to apply for simpler yet practical subsonic airfoils and for most supersonic sections.

With a library of functions applied to provide parametric definition of airfoils, another application of this technique seems attractive: new inverse airf oil and wing design methods need input target pressure distributions for specified operation conditions and numerical results arc found for airfoil and w ing shapes. The status of these methods is reviewed in the next book chapter Given the designer’s experience in aerodynamics for selecting suitable pressure distributions. choice of a few basic functions and parameters may provide a dense set of data cp(x/c) just like geometry coordinates arc prescribed, the amount of needed parameters for typical attractive pressure distributions about the same as for the direct airfoil modelling.

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