The Effect of Covariance in Fluid Model Uncertainties on Robust Aerodynamic Design Optimisation

Abstract

Robust aerodynamic design optimisation aims to combat drops in performance due to variation in design conditions. Uncertainty in Mach number is commonly used to represent variation in design flight conditions and Reynolds number is fixed. However, the Mach and Reynolds numbers share dependencies on fluid continuum parameters, such as velocity.

No studies have investigated whether treating the Mach and Reynolds numbers as independent, when they are covariant, has an effect on the development of robustly optimised airfoil designs.

The difference between independent and covariant uncertainty treatments is established mathematically and differences in boundary layer both viscosity, friction, and transition from laminar to turbulent flow are identified as theoretical sources of difference.

Testing at eight different design conditions, incompressible and compressible, viscous and near-inviscid, was conducted using deterministic and robust aerodynamic optimisations. The performance of the deterministic optimum was examined under the three sources of uncertainty: independent Mach, independent Reynolds, and covariant-by-velocity. Three populations were optimised under each of the three uncertainties for each flight condition; the resulting shapes of these robust optimisations were compared using statistical methods for differences in shape and differences in performance when re-tested under the three uncertainties.

The deterministic analysis performed at each design condition shows different degrees of variation between the independent Mach, independent Reynolds and covariant velocity uncertainties across the tested flight conditions. A difference in the shapes of the three robust populations was found for the eight flight conditions. Compressible flight conditions at more viscous Reynolds numbers showed significant performance differences.

This work found that treating Mach and Reynolds numbers as independent can lead to unexpected performance variation.