Examples of the application of constrained multivariate optimisation techniques to the design of aerofoil sections. Design point: single@ upper and lower surfaces geometry and camber line variations@ initial aerofoil: NACA 0012 and RAE 2822@ CFD: BVGK.
ESDU 01025 presents examples of the application of the constrained multivariate optimisation technique CODAS to the inverse design of aerofoil sections@ that is to determine the shape of aerofoil that has a specified pressure distribution at a given flow condition (Mach number@ lift coefficient or incidence@ Reynolds number). The first example demonstrates the ability of CODAS to obtain the shape of an aerofoil section which will match a specified complete pressure distribution. The target pressure distribution is taken as that obtained from a BVGK calculation of the flow around the RAE 2822 section at a Mach number of 0.73@ incidence of 2 degree@ Reynolds number of 6.5 million with transition at 5 per cent of chord on both surfaces. The inverse design process is started from a NACA 0012 section at a value of incidence of 1.5 degree (corresponding roughly to the expected lift coefficient) and the section is modified by increments to the upper and lower surfaces defined by their second derivatives at eight chordwise positions. For the second example the target is a shock-free upper surface pressure distribution at a Mach number of 0.72@ a lift coefficient of 0.77 and a Reynolds number of 20 million. The starting aerofoil is taken as RAE 2822 and a revised camber line is sought which will give the required pressure distribution. ESDU 01025 is one of a series illustrating the process of using such optimisation techniques@ indicating their advantages and revealing the kinds of problems that can arise. To facilitate this ESDU 01025 is in narrative form. An introduction to the application of constrained multivariate optimisation techniques to the design of aerofoil section shapes is given in ESDU 99019.