Presentation of Modern Non Linear Lifting Line Methods

A review of Non-linear Lifting Line Theory (NLLT) algorithm allowing the predic- tion of aerodynamic coefficients is presented. Inspired by recent works, a modern algorithm able to efficiently predict the aerodynamic... [ view full abstract ]

A review of Non-linear Lifting Line Theory (NLLT) algorithm allowing the predic-
tion of aerodynamic coefficients is presented. Inspired by recent works, a modern
algorithm able to efficiently predict the aerodynamic coefficients in the complete lift-
curve, including in the post stall region is developed. The effect of strongly coupled
methodology is analyzed and artificial viscosity is used to properly capture the post
stall characteristics at high angle of attack. The algorithm is tested on elliptical wing,
which allow a comparison with analytic solutions. The validated algorithm is then ap-
plied to complex configurations, including high lift systems, and show good agreements
with wind tunnel and/or high-fidelity numerical data for the prediction of the maxi-
mum lift coefficient and the post stall behaviour in subsonic and transonic conditions.
The fuselage is not geometrically modelled but its influence is appropriately taken into
account for the aerodynamic coefficients evaluation. The use of sectional airfoil data
obtained via solutions of the Reynolds Averaged Navier-Stokes equations with infinite
swept wing assumptions - so called 2.5D model - is shown to greatly improve the results
over traditional 2D solutions.

I. Introduction
In a preliminary design environment, where the iterative design loops are numerous, it is important to obtain quality data as soon as possible in the early phases of conception. Several methods are developed and used in industries, including that of Valarezo and Chin, used in industry at Boeing and Bombardier Aerospace (see Cebeci et al.). The method uses the panel method to obtain the surface wing pressures, and uses a semi-empirical relation to correlate maximum lift with sectional pressure differences evaluated along the span of the wing. Another method, more recent, is that of Phillips and Alley . The method uses the lifting-line theory to evaluate sectional lift properties, and correlate these with CFD-derived correlations by introducing additional coefficients in their analytical expressions. Both theses methods do not focus on post-stall behaviour but on capturing the maximum lift coefficient.

The methods presented in this article combine an inviscid algorithm derivated from the Prandtl Lifting Line theory with viscous sectional data to provide full aerodynamic characteristics. Two families of coupling methods have been developed, each of them having their characteristics and problems that will be discussed in the present paper. In any case, the entire lift-curve, encompassing the linear, pre-stall and post-stall is predicted, with more or less accuracy concerning the post stall region at high angle of attack. The maximum lift coefficient is therefore implicitly obtained.
The paper is divided as follows. A review of the two families of Non Linear Lifting Line methods are presented after a short presentations of the inviscid methods used in this kind of coupling. A description of the angle of attack correction based algorithm developed in the research team is then presented, and validated on elliptical wing, showing among other the effect of artificial viscosity. The capabilities of the algorithm, and especially the fuselage model are then presented on generic configurations.

II.conclusion
A review of coupling algorithm have been performed. Two families of methods are presented. The first family corrects the lift circulation along the span. Theses methods require several iterations to converge and present difficulties in the post stall region. A second family of methods have then been developed, which correct the angle of attack. A algorithm have been implemented, inspired by recent existing algorithms. The algorithm have been validated on an elliptical wing, allowing comparison with analytic solutions. A strongly version of the method have also been developed, and artificial viscosity have been added, inspired by the work of Chattot. The artificial viscosity improves the prediction in the deep post stall region, and smooths oscillations of the lift distribution. Two configurations are then analyzed, a isolated high lift wing, and a wing fuselage configuration. Different geometrical representations have been studied, showing that the flat plate modelisation is accurate enough for a preliminary design context for prediction the aerodynamic coefficients. The DLR-F4 configuration at transonic flow show a good prediction of pressure coefficients along the span, except close to the root and to the tip, due to respectively the symmetry effects and the tip vortex, that are not taken into account in the algorithm. The fuselage model, despit its simplicity, shows good prediction for all the aerodynamic coefficients.