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Temperature and skin-friction maps on a lifting hydrofoil in a propeller wake

There are at least two direct links between the friction acting on the surface of a (slightly warmer or colder) body under the influence of an incompressible flow and the temperature distribution on the surface of the body itself. The first relies on the energy equation, which connects the evolution of the temperature distribution at the wall to the action of the skin-friction field. On the other hand, the equation of passive transport of temperature perturbations at the wall unveils a direct relationship between the celerity of propagation of thermal blobs and the friction velocity. Grounding on these relationships, this paper reports about the application of different methodologies, developed to determine skin-friction fields from surface temperature maps, to the analysis of the complex flow evolution on a lifting NACA 0015 hydrofoil immersed in a non-uniform, unsteady wake induced by a marine propeller. The adopted temperature-sensitive paint technique allows obtaining the global temperature data with the appropriate, high resolution in space and time. The approach based on the energy equation leads to an unconventional, single-snapshots optical-flow-like methodology, which allows obtaining time-resolved, relative skin-friction fields. The two approaches based on the displacement of the wall temperature perturbations enable the determination of time- and phase-averaged, quantitative skin-friction fields. One approach grounds on a classical tracking of the thermal disturbances via optical flow, the other one relies on minimizing the discrepancy between the celerity of propagation of thermal fluctuations and the behavior expected according to the Taylor hypothesis. The analysis of the skin-friction fields obtained via the three uncorrelated, complementary approaches discloses the evolution and the mutual interaction of different flow structures (manifolds) over the hydrofoil surface at lifting and zero-lift conditions: the hub and tip vortices, the blade wake, the laminar separation bubble, and the separation at trailing edge.