Reconstruction of skin friction topology in complex separated flows

Abstract This paper describes a theoretical method for reconstruction of the skin friction topology in complex separated flows, which is developed based on the exact relation between skin friction and surface pressure through the boundary enstrophy flux (BEF). The key of this method is that a skin friction field is reconstructed from a surface pressure field as an inverse problem by applying a variational method. For applications, the approximate method is proposed, where the composite surface pressure field is given by a linear superposition of the base-flow surface pressure field and the surface pressure variation field and the base-flow BEF field is used as the first-order approximation. This approximate method is constructive in a mathematical sense since a complex skin friction field in separated flows can be reconstructed from some elemental skin friction structures (skin friction source/sink, vortex and their combinations) by a linear superposition of some simple surface pressure structures. The distinct topological features, such as critical points, separation lines and attachment lines, naturally occur as a result of such reconstruction. As examples, some elemental skin friction structures in separated flows are reconstructed in simulations, and the skin friction fields in shock-wave/boundary-layer interactions (SWBLIs) are reconstructed from pressure sensitive paint (PSP) images obtained in wind tunnel experiments.