Comparison of Point Design and Range-Based Objectives for Transonic Aerofoil Optimization

The most common aerofoil optimization problem considered is lift-constrained drag minimization at a fixed design point; however, shock-free solutions can result, which can lead to poor off-design performance. As such, this paper presents a study of the construction of the aerofoil optimization problem and its effect on the performance over a range of operating conditions. Single-point and multipoint optimizations of aerofoils in transonic flow are considered, and an improved range-based optimization problem subject to a constraint on fixed nondimensional wing loading with a varying design point is formulated. This problem is more representative of the aircraft design problem, though similar in cost to single-point drag minimization. An analytical treatment using an approximation of wave drag, which demonstrates that the optimum Mach number for a fixed shape is supercritical if the required loading is above a critical threshold, is also presented. This paper presents optimizations that show that to define an effective objective function three-dimensional effects modelled via an induced drag term must be introduced. The general trend is to produce solutions with higher Mach numbers and lower lift coefficients, and shocked solutions perform better when considering the performance in a range over the operating space. Furthermore, the resulting aerofoil shapes are supercritical in nature, a particularly promising result.