Fusing wind-tunnel measurements and CFD data using constrained gappy proper orthogonal decomposition

Abstract

In this article gappy proper orthogonal decomposition (POD) is used to fuse wind-tunnel measurements and computational fluid dynamics (CFD) data to provide a consistent and more comprehensive output of greater utility. The technique is used to fuse a very limited and ‘gappy’ set of wind-tunnel surface pressure measurements with computational surface pressure and friction data. By integrating the resulting fused surface data over a complete aerodynamic surface, the corresponding aerodynamic coefficients are obtained. A comparison between these integrated aerodynamic coefficients and the wind-tunnel balance measurements show a better agreement than that obtained between CFD and the wind-tunnel experiment. In addition, the original gappy POD algorithm is modified and extended to provide an accurate and consistent match between the integrated coefficients evaluated from the fused data set and the wind-tunnel balance measurements, thus producing a set of data distributed over the entire aerodynamic surface that conforms to experiment. This is achieved by considering the wind-tunnel balance measurements as equality constraints in the gappy POD least-squares problem formulation. The technique is demonstrated for steady flow around an RAE 2822 airfoil and an industrial wing-body aircraft configuration. Also, an important feature of the methodology that is essential for its use in an industrial environment, namely regularization, is discussed.