# Aerodynamic Validation of a Parametric Airfoil Description

I. Introduction A fundamental part of aircraft design involves wing airfoil design and optimization, establishing an outer shape of the wing, which has good aerodynamic performance for the design mission, good internal volume distribution for fuel and systems and which also serves as an efficient structural member supporting the load of the weight of the aircraft. There are different methods for airfoil modelling used, depending on where in the design loop the work is done. In the conceptual phase a flat plate might suffice as wing profile model, while in later stages the airfoil might be selected from a database or being modifications of database airfoils. One key aspect of the data making up the airfoil is how it is stored. Several approaches to parameterization of wing profiles can be found in the literature: Airfoils can be described by point clouds as done in most airfoil libraries [1] or they could be described as mathematical functions as is the case with the NACA 4 digit libraries [2] [3] and as the Joukowsky airfoils [4]. A more modern representation method is the class function/shape function transformation CST method[5]. The wing profile representation method used for this paper, the Beziér interpolation is described in [6].The airfoil's top and bottom curves are both modelled by two cubic Beziér curves in parametric form, being C1 continuous at the defined top and bottom points. At the leading edge, the profile will also be guaranteed C1 continuous, whereas the trailing edge is allowed to be discontinuous to allow for a trailing edge gap.Generally a four part cubic Beziér curve requires 13 control points are needed to define the curve, giving 26 variables when both x and y coordinates are taken into account. However when some symmetries and simplifications are taken into account the number of independent parameters is reduced to 14. In order to ascertain that the parametric model indeed is accurately modelling the aerodynamic properties of the original point cloud airfoil, a comparative study was made. The Aerodynamic properties of a large set of airfoils were analysed using the CFD software Fluent. The computation was performed used automated grid generation with C-grids and grid convergence analysis for both the point cloud airfoils and the parameterized airfoils. The turbulence was handled with Menter’s SST k-? model, developed to accurately predict separation in adverse pressure gradient flow. Skin friction and pressure coefficient distributions at flight Reynolds and Mach number were collected together with stall angle of attack and post stall behaviour. Figure 1 shows the skin friction coefficient of a Withcomb profile modelled with the point cloud representation and the parameterized curves. Figure 2 show the Nearfield Mach number distribution of a parameterized Whitcomb profile set at zero degrees angle of attack at the critical Mach number. The difference in critical Mach number is less than 1% between the original point cloud and the para meterized profile. By collecting comparative data for a large set of profiles, a statistical analysis of the entire cohort was possible. The preliminary results show a good agreement between the aerodynamic properties of the point cloud representation and the parameterized. In conclusion, the two methods can be said to be equivalent.