IHS ESDU Examples of the application of constrained multivariate optimisation techniques to the design of aerofoil sections. 99021

ESDU 99021 presents an example of the application of the constrained multivariate optimisation technique CODAS to minimisation of aerofoil drag coefficient at multiple design points. ESDU 99020 illustrates the use of constrained multivariate optimisation techniques in the minimisation of drag by the use of leading- and trailing-edge flap deflections, or by variation of the camber line of a section at a single design point of Mach number and lift coefficient. ESDU 99021 demonstrates the combined use of leading- and trailing-edge flap deflections and camber line variations to optimise aerofoil section drag coefficient at two different design points. The aim in this example is to minimise a weighted average of the drag coefficient values at two design points: Mach number of 0.71 and lift coefficient of 0.75 and Mach number of 0.66 and lift coefficient of 0.87. The Reynolds number is 20 million and transition is fixed a 5 per cent of chord on both surfaces. The flow calculation method is BVGK for viscous flow, set up to calculate the drag coefficient at the required values of lift coefficient. The basic section used is the RAE 2822 (12.11 per cent thickness/chord ratio and nose radius of curvature 0.84 per cent of chord) which was designed to have a pressure distribution with a flat rooftop extending to about 50 per cent of chord at a Mach number of 0.66 and a lift coefficient of 0.56. ESDU 99021 is one of a series that illustrate the process of using such optimisation techniques, indicate their advantages and reveal the kinds of problems that can arise. An introduction to the application of constrained multivariate optimisation techniques to the design of aerofoil section shapes is given in ESDU 99019.